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Modulation and enhancement of partial internal reflection at an opitical interface Liptak, Anne Helene 2004

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r  M O D U L A T I O N A N D E N H A N C E M E N T OF PARTIAL INTERNAL R E F L E C T I O N A T A N OPTICAL INTERFACE by A N N E H E L E N E LIPTAK B.Sc, University of Guelph, 2001 A THESIS SUBMITTED IN PARTIAL F U L F I L L M E N T OF T H E REQUIREMENTS FOR T H E D E G R E E OF  M A S T E R OF SCIENCE in T H E F A C U L T Y OF G R A D U A T E STUDIES (Department of Physics and Astronomy) We accept tfiis thesis as conforming to the required standard  T H E UNIVERSITY OF BRITISH C O L U M B I A OCTOBER, 2004  © Anne Helene Liptak, 2004  ABSTRACT This thesis investigates the mechanisms involved in a reflective display based on the control of partial internal reflection hereafter abbreviated PIR. This work was motivated by the development of a reflective display based on the frustration of total internal reflection. Total internal reflection can be prevented by placing an absorbing medium in 1  the evanescent wave region. The reflection is restored when the absorber is pulled out of this region. Heavily coloured pigments suspended in a perfluorinated hydrocarbon serve as absorbers; their motion in and out of the evanescent zone is accomplished using electrophoresis. When light does not undergo total internal reflection, it is not obvious that this method of changing the reflectivity would be effective. Surprisingly, a similar change in reflectance can be observed as the absorbing pigments are brought into and out of the region a few nanometres from the interface. The thesis studies of such changes in partial reflection.  The reflectance changes at a single optical interface caused by the motion of pigments were studied for light undergoing total and partial reflections. The mechanism controlling reflectance for partially reflected light is optical interference. The interference system was modeled to emulate experimental conditions with results agreeing well with experiment.  The reflectance from a system with multiple reflections was controlled using the pigment suspension. Light undergoes partial reflection on several surfaces, and the compound losses due to transmission significantly reduce the overall reflectance. To increase the overall reflectance, a layer of aluminium was deposited on selected interfaces.  To demonstrate the potential use of the modulation of PIR, flashing retroreflective panels were constructed, with the possible application of highway signs in mind. Reasonably encouraging reflectance values and contrast ratios were observed. It is suggested that  further development of this technology is warranted, with the goal of creating electronically addressed variable message signs.  i  iii  TABLE OF CONTENTS ABSTRACT  ii  T A B L E OF CONTENTS  iv  LIST OF TABLES  vii  LIST O F FIGURES  viii  ACKNOWLEDGMENTS  xii  1  INTRODUCTION  1  2  BACKGROUND  5  2.1  PROPAGATION OF LIGHT  5  2.1.1  Light in materials: index of refraction and absorption coefficient  6  2.1.2  Waves at an interface: phase effects and Snell's law  7  2.1.3  Waves at an interface: amplitude effects and the Fresnel equations  8  2.1.4  Reflectance and transmittance  9  2.1.5  Retroreflection  10  2.1.6  Total internal reflection  11  2.1.7  The evanescent wave  13  2.1.8  Frustrated total internal reflection  15  2.2  INTERFERENCE  16  2.2.1  Conditions for interference  17  2.2.2  Thin film interference  18  2.3  PARTICLE SUSPENSIONS  20  2.3.1  Double layer model  20  2.3.2  Stability of colloidal suspensions  22  2.3.3  Electrophoresis  23  2.4  3  MICRO-REPLICATED SHEETS  R E F L E C T I V E I M A G E DISPLAY BASED ON C O N T R O L L E D TIR 3.1  PRINCIPLE OF A TIR-BASED DISPLAY  23  26 26  iv  3.2  PIGMENT SUSPENSIONS A S ABSORBERS T O F R U S T R A T E TIR  27  3.3  U S E OF C O R N E R - C U B E B A S E D R E T R O R E F L E C T I V E SHEETING IN TIR DISPLAY  4  31  REFLECTANCE MODULATION AT A SINGLE INTERFACE 4.1  34  E X P E R I M E N T A L M E A S U R E M E N T OF M O D U L A T I O N A T A SINGLE INTERFACE  34  4.1.1  S ingle interface test cell construction  35  4.1.2  Measuring reflectance  36  4.1.3  Design of reflectance modulation experiment  37  4.1.4  Time-varying reflectance modulation  41  4.1.5  Factors influencing reflectance modulation  45  4.1.5.1 Particle clustering  45  4.1.5.2 Colour filters  47  4.1.5.3 Applied Field  :  :  4.1.5.4 Other effects 4.1.6 4.2  5  49 50  Establishing interference in reflectance curves M O D E L I N G M O D U L A T I O N A T A SINGLE I N T E R F A C E  51 55  4.2.1  Mathematical model  55  4.2.2  Modeling particle clustering  4.2.3  Model Results  64  4.2.4  Current understanding of modulation at a single interface  68  REFLECTANCE MODULATION AT MULTIPLE INTERFACES 5.1  ...62  72  E X P E R I M E N T A L M E A S U R E M E N T OF R E F L E C T A N C E M O D U L A T I O N A T M U L T I P L E INTERFACES  73  5.1.1  Micro-replicated film test cell construction  73  5.1.2  Design of retroreflection measurement experiment  75  5.1.3  Static reflectance measurements  80  MODELING RETROREFLECTION  83  5.2 5.2.1  Model set-up  84  5.2.2  Model results  88 V  V  6  E N H A N C E M E N T OF R E F L E C T A N C E M O D U L A T I O N A T M U L T I P L E INTERFACES  7  6.1  ENHANCEMENT BY ALIJMrNIUM DEPOSITION  95  6.2  MODELING REFLECTANCE ENHANCEMENT  99  6.3  MODELING ALUMINIUM DEPOSITION  102  6.4  EXPERIMENTAL MEASUREMENT OF REFLECTION ENHANCEMENT  105  6.4.1  Static reflectance measurements  106  6.4.2  Reflectance modulation measurements  110  APPLICATION OF PARTIAL REFELCTION MODULATION: H I G H W A Y SIGN P R O T O T Y P E S  8  9  95  :  113  7.1  TILE ASSEMBLY AND ELECTRICAL CONNECTIONS  114  7.2  FACEPLATE AND MASK FOR CHEVRON  116  FUTURE W O R K  119  8.1  INK DEVELOPMENT.  119  8.2  ENHANCEMENT THROUGH ALUMINIUM DEPOSITION  120  8.3  HIGHWAY SIGN ASSEMBLY  120  CONCLUSIONS  122  REFERENCES  126  A P P E N D I X A : Angular response of collimated detector  130  A P P E N D I X B : Calculating incident angle at the interface  132  A P P E N D I X C : Spectral transmittance of fdters...  134  A P P E N D I X D : M A T L A B code for the final model of reflectance at a single interface  136  vi  LIST OF TABLES Table 3.1 Pigments suspended in perfluorinated hydrocarbon liquid  31  Table 4.1 - Refractive indices of layers used in single interface modulation model for the center wavelength of each colour  filter...,  57  Table 5.1 - Coefficients of retroreflection for typical commercial sheeting given an observation angle of 0.2° at different entrance angles Table 6.1- Transmission of light through slides with thin layer of aluminium  76 96  Table 6.2 -Incident angles of light used in reflection measurements and the corresponding description used in Figure 6-1  97  Vll  LIST OF FIGURES Figure 2-1: Reflection and refraction at an interface with ns<n  t  ;  8  Figure 2-2: Light ray undergoing retroreflection i n a corner-cube geometry  10  Figure 2-3: Light ray o f increasing incident angle at a boundary with ni>n  12  2  Figure 2-4: Reflectance vs. incident angle for light at a boundary between glass (n=1.514) and air (n=l)  •  13  Figure 2-5: Schematic o f the evanescent wave for a light wave undergoing T I R  14  Figure 2-6: Frustrating T I R with a medium when nj=n ..  15  Figure 2-7: Frustrating T I R with a highly absorbing medium  16  f  Figure 2-8: Light path i n a thin  film  18  Figure 2-9: Schematic o f the double layer model i n colloids  21  Figure 2-10: Structures o f D i a m o n d G r a d e ™ retroreflective sheeting  24  Figure 2-11: Primary groove and facet labels for D i a m o n d G r a d e ™  film  '.  24  Figure 3-1: Frustrating T I R in prismatic film  27  Figure 3-2: TIR-based display w i t h a pigment suspension as absorber  29  Figure 3-3: Particle clustering from electrophoresis  29  Figure 3-4: Pigment suspension compression under an applied field  30  Figure 3-5: Light undergoing T I R on two o f the three corner-cube facets  32  Figure 4-1: Test cell for single interface reflectance measurements (not to scale)  35  Figure 4-2: U s e o f prism to attain incident angles beyond the critical angle  36  Figure 4-3: Angular range used for single interface reflectance measurements  37  Figure 4-4: Measurement o f test cell reflectance modulation  37  Figure 4-5: System used to limit angular range o f detected light  38  Figure 4-6: Filter, sample, and light placement i n the measurement system  39  Figure 4-7: Supports for the prism on the x-y stage  40  Figure 4-8: Schematic o f the single interface reflectance measurement system  40  Figure 4-9: Reflectance vs. time for light passing through the red filter  42  Figure 4-10: Reflectance vs. time for light passing through the green filter  43  Figure 4-11: Reflectance vs. time for light passing through the blue  filter  44  Figure 4-12: Effect o f clustering o n reflectance data  46  Figure 4-13: Effects o f dispersion and pigment colour on reflectance data  48  Figure 4-14: Effects o f varying field strengths on reflectance data  49  viii  Figure 4-15: Example of unexpected differences in reflectance modulation  50  Figure 4-16: Reflectance vs. time for carbon black ink test cell  53  Figure 4-17: Reflectance vs. time with red filter, and the average of green filter data  54  Figure 4-18: Schematic of light interaction in the three-layered mathematical model  55  Figure 4-19: Example of results from the first model compared to experimental data  58  Figure 4-20: Example of modified model results compared to experimental data  59  Figure 4-21: Schematic of light interaction in a more complex three layer system  60  Figure 4-22: Example of results from the final model compared to experimental data  61  Figure 4-23: Effect of mean velocity on model results  63  Figure 4-24: Effect of standard deviation (sd) on model results  64  Figure 4-25: Final model results compared to experimental data for red light  65  Figure 4-26: Final model results compared to experimental data for green light  66  Figure 4-27: Final model results compared to experimental data for blue light  67  Figure 4-28: Motion of the pigments in suspension during the modulation process  70  Figure 5-1: Micro-replicated film test cell (not to scale)  74  Figure 5-2: Schematic of set-up to measure coefficient of retroreflection  75  Figure 5-3: Schematic of set-up to measure true retroreflection  77  Figure 5-4: Entrance angle definition depending on rotation direction  78  Figure 5-5: (a) Integrating sphere to measure light intensity, (b) cross-sectional view  79  Figure 5-6: Acceptance angle for light detection in retroreflection measurement set-up  79  Figure 5-7: Measured reflectance vs. entrance angle for Diamond Grade™ cell filled with air and FC-75  81  Figure 5-8: Measured reflectance vs. entrance angle for M F C A cell filled with air and FC-75....81 Figure 5-9: Measured reflectance vs. entrance angle for ITO coated Diamond Grade™ cell filled with FC-75  :  83  Figure 5-10: Typical model set-up in Tracepro®  85  Figure 5-11: Typical light beam size relative to structures in the Tracepro® model  86  Figure 5-12: Modeling of FC-75 behind structured surface (see text)  87  Figure 5-13: Predicted pattern of detected flux for entrance angle of 0°  88  Figure 5-14: Modeled and experimental reflectance of M F C A cell filled with air when the axis of rotation is parallel and perpendicular to the primary groove  89  Figure 5-15: Modeled and experimental reflectance of Diamond Grade™ cell filled with air when axis of rotation parallel to primary groove  90  ix  Figure 5-16: Modeled and experimental reflectance of Diamond Grade™ cell filled with air when the axis of rotation is perpendicular to primary groove  91  Figure 5-17: Modeled and experimental reflectance of Diamond Grade™ cell filled with FC-75 when the axis of rotation is parallel and perpendicular to primary groove  92  Figure 5-18: Modeled and experimental reflectance of M F C A cell filled with FC-75 when the axis of rotation is perpendicular to primary groove  93  Figure 5-19: Modeled and experimental reflectance for M F C A cell filled with FC-75 when the axis of rotation is parallel to primary groove  94  Figure 6-1: Comparison of reflectance values for cells with a partial aluminium layer to cell without aluminium at various detection angles  97  Figure 6-2: Modeled reflectance of Diamond Grade™ with aluminium on half the primary facets and half the secondary facets  100  Figure 6-3: Modeled reflectance of Diamond Grade™ with aluminium on all primary facets... 101 Figure 6-4: Modeled reflectance of M F C A with aluminium on half the primary facets, and half the secondary facets  102  Figure 6-5: Predicted deposition of aluminium on selected facets of Diamond Grade™ sheeting 103 Figure 6-6: Orientation of sheeting in evaporation chamber  104  Figure 6-7: Predicted aluminium deposition on primary facets of Diamond Grade™  104  Figure 6-8: Actual deposition of aluminium on primary facets of Diamond Grade™  105  Figure 6-9: Experimental reflectance of M F C A cell, without aluminium (No Al) and with aluminium (Al) on half primary facets and half secondary facets, filled with FC-75 .... 106 Figure 6-10: Experimental reflectance of Diamond Grade™ cell, without aluminium (No Al) and with aluminium on half primary facets and half secondary facets (Al), filled with FC-75 107 Figure 6-11: Experimental reflectance of Diamond Grade™ cell, without aluminium (No Al) and with aluminium on primary facets (Al), filled with FC-75  108  Figure 6-12: Modeled and experimental reflectance for enhanced M F C A cell filled with air.... 109 Figure 6-13: Modeled and experimental reflectance for enhanced Diamond Grade™ cell filled with air  110  Figure 6-14: Experimental reflectance of aluminized M F C A cell filled with pigment suspension 112 Figure 7-1: Schematic of machined aluminium electrode for prototype tiles  114  Figure 7-2: Method of assembling prototype tiles  115  x  Figure 7-3: Assembled tile for prototype sign (a) top view, (b) cross-section  115  Figure 7-4: Holder with tiles from the prototype flashing panel  116  Figure 7-5: Hexagonal layout of fluorescent dots on panel faceplate for daytime visibility  117  Figure 7-6: Faceplate for prototype chevron  117  Figure A - l : Schematic of set-up to measure angular response of detection system  130  Figure A-2: Measured angular response of detector, for horizontal and vertical angles  .131  Figure A-3: Schematic of set-up to determine the vertical offset angle due to misalignment of optical sensor  131  Figure B-l: Geometry of light incident on prism  132  Figure C-l: Spectral transmittance of colour filters  134  Figure C-2: Spectral transmittance of infrared filter  135  ACKNOWLEDGMENTS I would like to begin by thanking the members of the SSP lab who made my experience in the lab an enjoyable one. The conversations, both scientific and entertaining, were valuable to me and I have learned so much from all of you.  I would like to give a special thank you to Michele Mossman, whose dedication is inspirational. Without her guidance, help, and motivation, I would not have made it through the work presented here. Not only does she make good company for tea, she also demonstrates a long-term vision and determination that only a few possess.  To my research supervisor Lome Whitehead, I thank you not only for your guidance throughout the project, but for the skills you have taught me. I value your knowledge, ideas, and management skills. The academic and industrial atmosphere you have provided in the lab was exactly what I had hoped for.  I am also grateful to Andrzej Kotlicki for his guidance throughout the project, as well as for providing an excellent environment for teaching assistants, which allowed me to enjoy my work as a T A .  I give thanks to NSERC for providing me with financial support throughout my degree.  To Lara Thompson, my housemate throughout much of this work, thank you for your friendship and for your help in editing this thesis.  Thank you to my parents, who have always supported me even when it meant I had to move across the country. And last, but certainly not least, a great big thank you to Scott. Without his loving support, I would have never made it through the courses, or the rest of this adventure in Vancouver.  1  INTRODUCTION  The ability to reliably control the light emitted or reflected from a surface is a key requirement for display technologies. Reflective displays, in which light from an external source is used to illuminate the display, alter the reflective characteristics of the illuminated surface to control the light reflection selectively, thereby creating dark and bright regions. Such modification from a reflective state to an absorptive state, referred to in this thesis as reflectance modulation, can be achieved in several ways. For example, in reflective liquid crystal displays, found on calculators and watches, light is transmitted to the back of the display where it strikes a reflective surface such as mirror and subsequently exits the display towards the viewer. This is accomplished using a coating of liquid crystal between two polarizing films, with a relative 90° phase shift between the two. Light entering through the first polarizer can only reach the reflective back surface behind the second polarizer if the liquid crystals are twisted in such a way as to rotate the polarization of the light allowing it to pass through the second polarizer. A n applied field untwists the liquid crystal layers preventing light from being transmitted through the second polarizer, creating dark regions.  A novel reflective display based onfrustratedtotal internal reflection, henceforth abbreviated TIR, with significantly higher brightness than liquid crystal displays has recently been developed in the Structured Surface Physics Laboratory at the University of British Columbia.  In such a display, reflectance is modulated by an absorbing material  that is brought into the evanescent wave region thereby frustrating the TIR causing the absorptive state and is removed to restore the reflection of the reflective state. The absorbing material may consist of pigments suspended in a clear liquid and the motion can be caused by an electric field if the particles have a net charge. Obviously, in such a display, it is essential for TIR to occur and this imposes restrictions in the optical geometry. Examples of suitable arrangements include certain prismatic or corner-cube microstructures.  1  It was believed that if the light does not undergo TIR, but instead only a partial internal reflection (PIR), the lack of evanescent wave, and hence lack of frustrated TIR, makes this reflectance modulation method ineffective. However, the lack of evanescent wave in PIR does not preclude the possibility of a reflective display similar to the one described above. The work presented in this thesis centers on reflectance modulation of PIR for use in a reflective display. While the underlying physical effect differs from the TIR-based modulation, the visual appearance is very similar, and can even yield reasonable brightness and contrast. In the case of partially reflected light, it is readily apparent that some light at the interface is reflected and some is transmitted and absorbed. Less obvious is the fact that optical interference takes place and is responsible for the "frustration" of PIR making controlled modulation possible. This mechanism is studied and modeled at a single interface, and these results are applied to more complex, multiple reflection systems.  In applications such as traffic control signage intended to increase visibility of objects, a high level of reflected light is desirable. In a system with multiple reflections, unwanted transmission can occur on several interfaces, causing undesirably low overall reflectances. The work in this thesis demonstrates the possible potential to increase the total reflection in a multiple reflection system, while maintaining the high contrast ratio needed in display technologies. For the application of traffic control signage, the reflectance modulation described here has the potential to provide a low power, high contrast alternative to current modulating light emitting diode or flip-disk systems. Low power not only lowers cost, but enables the use of a solar panel, allowing its use even in rural areas where power is not readily available.  To better understand the work presented in this thesis, Chapter 2 presents a background in light propagation and interactions at interfaces, as well as pigment suspensions that can be used to absorb light. The micro-machined structures used in static traffic control signage are also described in Chapter 2.  2  The study of the reflectance modulation described in this thesis began because of work previously performed during the development of a reflective image display based on the control of TIR. Chapter 3 details of the principles of such a display and motivates the study of partial reflection modulation.  The work performed for this thesis begins by studying the modulation of partial reflection in the simple case of reflections from a single interface. Measurements of reflectance as a response to the motion of pigments when a time-varying field was applied were performed for light within a range of incident angles and the results are given in Chapter 4. In addition, this chapter details the mathematical model of the interference responsible for the characteristics of the reflectance response.  Chapter 5 discusses the reflectance of a system with multiple reflections. The structures of interest for the purpose of traffic control signs are retroreflecting corner-cube arrays. The measurements of retroreflection of these arrays with the structures in air and immersed in the solvent used for the pigment suspension are presented in this chapter. The latter configuration represents the so-called reflective state of a display without the added complication of pigment motion. A raytracing model used to predict reflectance in such systems by tracking the light's motion through the structures is also described in Chapter 5. As expected, the overall reflectance is very dependent on the light lost at each interface due to transmission. The results in this chapter suggest that the reflectance must be improved for these retroreflective structures to be used in an effective display.  Possible enhancements of reflection in multiple reflection systems are therefore discussed in Chapter 6. Deposition of aluminium on a surface causes a high reflectance regardless of incident angle. As a result, it is not possible tofrustratethe reflection on such a surface. If aluminium is deposited on one surface in a multiple reflection system, the increase in reflection from that surface will cause the overall reflectance to be increased. When an absorber is placed at the surfaces, the light is not absorbed at the aluminized interface, but is at the non-coated ones, maintaining a dark absorptive state. The raytracing model developed to study light interactions within the structures was used to  3  predict reflectance from the various aluminium configurations modeled. Retroreflective characteristics of samples aluminized in two different configurations were measured and results are presented in Chapter 6.  The retroreflective sheeting intended for use in static traffic control signs was enhanced using the most effective aluminium deposition configuration. This aluminized film was used in the construction of a prototype flashing chevron sign to demonstrate the potential of modulating PIR in traffic control applications. The prototype exhibited encouraging contrast ratio and reflectance. Details of the prototype can be found in Chapter 7.  Chapter 8 describes the future work necessary to further understand the details of modulation of PIR and to improve its use in the possible highway sign application.  4  2  BACKGROUND  The main work presented in this thesis is related to the manipulation of reflected light at an optical interface. The ability to alter reflections depends on the properties and propagation of light as well as its interactions at interfaces. The work also involves how light interacts with pigment suspensions and microstructured surfaces. This chapter therefore briefly provides some background in each of these areas.  2.1  P r o p a g a t i o n of light  It is well known that light is an electromagnetic disturbance. A disturbance generated in an electromagnetic field propagates as a transverse wave moving independently of its source, with time-varying perpendicular electric and magnetic fields generating each other. The direction of propagation k is perpendicular to both the electric and magnetic components. Mathematically, linearly polarized light is treated as a plane wave, where both electric and magnetic fields are uniform over every plane perpendicular to the direction of propagation: E{r,t)  = E e  i C k ? T M )  0  B{7,t) = B e  iCk7T<0,)  0  (2-1)  (") 2  2  where E and B are the field amplitudes, and cois the angular frequency. The speed of 0  0  light c in vacuum is given by:  where £o is the permittivity of free space and jun is the permeability of free space.  For the work in this thesis, it is the propagation of light within a dielectric material including interactions at material boundaries that is of interest, discussed next.  5  2.1.1 Light in materials: index of refraction and absorption coefficient A homogeneous, isotropic, dielectric material contains charges that create responsive electromagnetic disturbances when interacting with light. The net result is for the phase speed of the light wave to slow down in such a medium. The speed of light in the material is given by: v=  1  (2-4)  lm  The permittivity of the material is e = K e E  where KE is the dielectric constant of the  0  material. Similarly, the permeability of the material is ju = K fl , M  0  with KM being the  dimensionless relative permeability.  A material is thus characterized by its index of refraction n, that is, the ratio of the speed of light in vacuum to that in the material: c ea „ =- = - £ -  V  (2-5)  A| £ p 0  Q  The index of refraction of air at STP is about 1.003 and in a more optically dense material such as glass, the value is approximately 1.51. Liquids generally have a refractive index larger than gases, but less than solids. For example, water has a refractive index of 1.33.  For frequencies of electromagnetic radiation within the optical range, non-conducting media considered in this thesis have relative permeabilities that do not deviate significantly from 1 so that the index of refraction can be expressed as n - ^JKE . It is known that KE, and therefore n, are frequency dependent; an effect known as dispersion. 3 In transparent materials dealt with here, the change of index over the visible spectrum is slight, but can be an important effect in the models that will be discussed in Chapter 4.  6  Light propagating through a dielectric material can experience energy losses via absorption which can be expressed mathematically as an imaginary component in the index of refraction: n = n +in  c  (2-6)  The value n represents the absorption of the material. As the wave propagates through the medium, its intensity decreases exponentially with distance x, at a rate a known as the absorption coefficient. This expression is given by:  4  I = I e-  m  0  (2-7)  a is related to n by the following relation:  47tn  a = —— A  (2-8)  The index of refraction describes the propagation of light in dielectrics, and as such, is an important characteristic of materials. It determines the reflection and transmission of light at the interface between two materials as well as the refraction angle, discussed in the following section.  2.1.2  Waves at an interface: phase effects and Snell's law  When an electromagnetic wave strikes an interface between two dielectric media, it is partially reflected and transmitted. The laws of electromagnetic theory impose restrictions known as boundary conditions on the electric and magnetic fields. For example, the components of the fields tangential to the interface must be continuous across it. The law of reflection and Snell's law are derivable from these boundary conditions.  The law of reflection states that the angle of reflected light with respect to the surface normal is equal to the angle of incident light, as depicted in Figure 2-1.  7  Figure 2-1: Reflection and refraction at an interface with ni<n  t  SnelPs law, given by equation (2-9), relates the incident direction of the light to the direction of the transmitted light, again with respect to the interface normal. The direction of transmitted light is changed if there is a difference in refractive index. If the second medium has a higher refractive index, the propagation direction is bent towards the normal, as pictured in Figure 2-1, and is bent away from the normal should the index be lower. sin 6 = n sin 6 i  2.1.3 Waves at an interface:  t  (2-9)  t  amplitude  effects and the  Fresnel  equations  In addition to the relations described in the previous section, the relationship between the amplitude of electric field vectors of the incident, reflected, and transmitted waves can be derived from boundary conditions. These are known as the Fresnel relations. Reflection and transmission coefficients are defined as the ratio of the reflected or transmitted amplitude to the incident amplitude. Since light is polarized, separate coefficients are needed when the polarization is transverse magnetic (//) or transverse electric (_L) to the dielectric interface.  The Fresnel relations for non-magnetic, insulators are:  8  ( T7  •E  oi  _ n cos Oj - n cos  \  j  9  t  t  ri; cosf?, +n, cosO,  A  /  n cos 0 - rij cos d t  t  i  n, cosr9. + n. cosd,  E., \  2n cosd t  L  E  \ oi E  i  t  t  ^  2n, cosd.  JH  n cos 6 + n cos 6, i  t  (2-10b)  (2-10c)  rij cos 0 + n cos d  j r  t  (2-10a)  (2-10d)  {  These relations are necessary in determining the fraction of light reflected or transmitted at the boundary between two media.  2.1.4 Reflectance and transmittance Reflectance R is defined as the fraction of incident power or flux that is reflected. Since energy is proportional to the absolute square of the field amplitude, the reflectance is simply:  *// =  E„  = \r,  (2-11 a)  = \r„  (2-1 lb)  Similarly, transmittance Tis the ratio of transmitted flux to incident flux:  n cos 6 t  71 = V  t  M,COS0,.  (2-12a) y  », cos 0, v  «,.cos<9,.  (2-12b) y  9  When no absorption is present in the system, energy conservation requires that  Rn +T„ = \andR  ±  +T =1.  5  ±  When the incident angle is normal to the boundary surface, the distinction between parallel and perpendicular components disappears, as R = R = R . ±  For example, 4% of  the light incident normally on an air/glass interface will be reflected since R = R = R =0.04. ±  Unpolarized or natural light has equal parallel and perpendicular components, making the reflectance the average of these components: (2-13)  2.1.5 Retroreflection Retroreflection occurs when light undergoes multiple reflections in a material and the resulting propagation direction is the exact opposite as the initial direction. This can be accomplished by several geometric configurations. A n example of such a geometry is a corner-cube, depicted in Figure 2-2. Light entering this structure undergoes an internal reflection on each of the three facets and returns towards the source.  n=1.0C  Facet 3  Facet I  n=1.0C  Figure 2-2: Light ray undergoing retroreflection in a corner-cube geometry 10  Retroreflecting structures are important in conspicuity applications where high visibility of objects is required for safety purposes. For example, retroreflective sheeting is used on road signs, where light emitted from a car's headlights is reflected back toward the nearby driver to improve night visibility. Retroreflective structures are also found on bicycle reflectors, road markers, and even clothing to increase visibility at night.  For retroreflection to be useful in these applications, it is important for the reflectance at each interface to be high to ensure good visibility. The ideal case is to have a reflectance of 1 at each interface, which is possible if the light undergoes total internal reflection, as discussed in the next section.  2.1.6 Total internal reflection When light strikes an interface between two optically different media, the first with a higher refractive index «/ than the second ri2, it refracts away from the normal at an angle specified by Snell's law as discussed in section 2.1.2. As ^increases, as depicted in Figure 2-3, the angle of the transmitted ray continues to increase until the ray is parallel to the boundary [Figure 2-3 (c)]. The value of  at this crucial state is known as the  critical angle 0 . For any incident light beyond this critical angle, all incoming energy is C  reflected back into the incident medium in a process known as total internal reflection (TIR). The incident and reflected waves have the same amplitude, and thus no light is lost to transmission in the process of TIR.  11  \ v  e n.  (a)  (b)  Figure 2-3: Light ray of increasing incident angle at a boundary with nf>n2. The critical angle is shown in (c), after which light undergoes TIR (d).  The reflectance values are not discontinuous as the incident angle increase, but can increase dramatically with a small change in angle. For example, Figure 2-4 shows a plot of reflection as a function of incident angle for the glass/air boundary.  12  Angle (degrees)  Figure 2-4: Reflectance vs. incident angle for light at a boundary between glass (n=L514) and air (n=l)  A 70% difference is predicted between light incident one degree before critical and light incident beyond critical in the situation plotted in Figure 2-4. This case represents reflectance values of circularly polarized light, which accurately represents unpolarized light encountered in most applications.  2.1.7 The evanescent wave In the case of total internal reflection, all the incident energy is reflected, yet the boundary conditions imposed by Maxwell's equations cannot be satisfied unless there is a transmitted wave. This transmitted wave however, cannot carry net energy across the boundary.  Assuming light is a plane wave, the solution for the transmitted wave at a boundary such as the one in Figure 2-3 is: ik(xsm9 +zcosf? ) t  (  (2-14)  13  When light is incident beyond critical, the angle of transmitted light 0 is complex, with a t  purely imaginary cosine. Using Snell's law (2-9), equation (2-14) becomes: / r,  :  ~  —kz\7(sin0 /sin6>J -l 2  \  ;  V  Je  ik[sm0 /smd i  c  The second term of equation (2-15) indicates that the transmitted ray propagates only in the x-direction parallel to the interface. The first term shows that the wave amplitude decays exponentially as it travels into the second medium. For this reason, the transmitted wave in the case of TIR is known as the evanescent wave.  Figure 2-5 below  is a schematic representation of the evanescent wave.  Reflected wave  Incident wave  Evanescent wave  Figure 2-5: Schematic of the evanescent wave for a light wave undergoing TIR  From (2-15), the penetration depth of the evanescent wave is:  8 =  1  A  k-yj(smdjsmd )  2  c  -1  2^(sin0,/sin0 ) C  2  -1  (2-16)  where X is the wavelength of light in the second medium. For visible light, the penetration depth is on the order of half a wavelength, except very near the critical angle, where the wave penetrates more deeply.  14  2.1.8 Frustrated total internal reflection If the evanescent wave travels with a large enough amplitude across a gap of lower index material into a region of higher refractive index, energy can flow through the gap in a process known as frustrated total internal reflection (FTIR). In this case, the evanescent wave is strong enough to drive electrons in the frustrating medium, allowing the light to propagate in this medium despite lack of contact with the incident material. This is 6  depicted schematically in Figure 2-6.  Incident wave  •  \# *  Reflected wave  «  i  >  : Gap of lower index material  Transmitted wave '  Figure 2-6: Frustrating TIR with a medium when ni=n/. The material is in the evanescent zone, but not in contact with the surface.  Consider the case where the material placed in the evanescent wave region has a higher refractive index n/than the incident medium  The resulting reflectance decreases as  most of the light is transmitted into the frustrating region, where it can be absorbed if the material has a large absorption coefficient [equation (2-8)], as shown in Figure 2-7(b). When the absorber is moved out of the evanescent zone, TIR is completely restored.  15  (a)  -(b)  Figure 2- 7: Frustrating TIR with a highly absorbing medium Since the frustration of TIR is reversible, it serves as a method to modulate reflectance at an interface, which is useful for applications such as the reflective display presented in Chapter 3.  This section considered the interaction of light with interfaces, while the following section discusses what occurs when light interacts with itself in a process known as interference.  2.2  Interference  Given that light obeys the principle of linear superposition, the resulting electric field intensity at a point in space where two or more light waves overlap is the vector sum of the individual fields. The average energy per unit area per unit time, known as irradiance /, at this point in space can differ from the direct sum of the individual component  *7 irradiances, and when it does, optical interference is observed.  In such a case, the  resulting irradiance is given by (2-17)  which can be greater than, less than, or equal to the sum of component irradiances I\+h depending on the interference term 2^LJ  2  cos 8. The phase difference 5 arises from a  combination of the light's path length difference as well as incident phase difference. If two waves begin with the same phase but travel different distances before interfering, this path length difference results in a phase difference. If the waves begin with different 16  phases, this must also be considered. It is the total relative phase difference that is responsible for observed interference.  The maximum resulting irradiance is known as total constructive interference, and occurs when the individual waves are completely in phase (5 is zero or a multiple of 2K). Total destructive interference occurs when the resulting irradiance is a minimum, occurring when the individual waves are completely out of phase (5 is an odd multiple of n). The next section describes the role of phase differences in the detection of interference in greater detail.  2.2.1 Conditions for interference In order for interference of light waves to be observed, their frequencies cannot be vastly different. If this were the case, the rapidly varying phase difference would cause the interference term in equation (2-17) to average to zero during detection. If frequencies differ only slightly, the interference remains clear and detectable.  In other words, in order to observe interference, the light waves must possess some degree of coherence. The coherence length is defined as the distance in space over which the phase can be predicted reliably. Light waves with a constant phase difference are perfectly coherent. Ideal monochromatic light is perfectly sinusoidal and has an infinite coherence length whereas real light sources, which have a spectral bandwidth rather than a single frequency, have shorter coherence lengths. For example, diffuse white light with a mean wavelength of 550nm and a bandwidth of 300nm has a coherence length of about 1 pm. Contrast this with a stabilized He-Ne laser, whose coherence length is on the order of 300m.  8  For optical interference to occur, the optical path length difference of the  interfering rays must be less than, or on the order of, the coherence length. The work in this thesis is concerned with interference involving relatively small optical path length differences, as in the case of light entering a thin film, which is discussed in the next section.  17  2.2.2 Thin film interference Consider a thin dielectric film between two semi-infinite transparent media. This film is conventionally considered to be thin as long as its thickness is on the order of the wavelength of light. However, interference is observed until the thickness is such that the reflected light waves are no longer coherent. If the film does not cause any loss of coherence, "thin film" means on the order of the coherence length of the light.  In the case of light entering a thin film as illustrated in Figure 2-8, light reflecting from the first interface, labelled ray 1, interferes with the light reflected from the second interface, labelled ray 2. Depending on the wavelength of light and the index and thickness of the film, the overall phase difference can cause total constructive interference, total destructive interference, or some intermediate case. In the case of total destructive interference, no reflection is observed and all the light is transmitted through the thin film into the second medium. Conversely, in the case of total constructive interference, no light is transmitted. An intermediate case results in partial reflection and transmission, with proportions changing as a function of the overall phase difference.  Ray 1  r thin film n  Figure 2-8: Light path in a thin film  18  This type of interference can be represented mathematically for linearly polarized light as follows. The electric field amplitude E, and magnetic field amplitudes H at the two adjacent interfaces can be related to each other using initial and boundary conditions via a characteristic matrix M:  ~E,~  H,  ~E ~  =M  n  (2-18)  This matrix can be used to calculate the reflectance and transmittance of the system given the incident angle du, the thickness of film d, and the refractive indices of each layer. the amplitude coefficients of reflection and transmission,  Given thatM =  m  2X  m  22  whose derivation are beyond the scope of this thesis, can be expressed as follows:  Y m 0  +Y Y m  H  0  Y w,, + Y Y m 0  0  2  ' 2\ m  2  1 2  _  Y m 2  2 2  +m +Y m 2l  ] 2  2  2Y  n  t=Y m 0  +Y Y m  n  0  2  1 2  (2-20)  +m + Y m 2l  2  (2-19)  22  22  where n cos 0 0  Y  2  = J — » 2  if  c  o  s  ^ / / '  (2-21)  (2-22)  when the electric field is perpendicular to the plane-of-incidence.  For film thicknesses large enough that the light waves are no longer coherent after passing through the film, interference is no longer observed. Since the boundaries are no longer correlated, the reflection coefficients from each surface can be calculated  19  separately and added to approximate the overall reflectance of the system. There are in fact higher order reflections where the light rays undergo multiple passes within the film. The exact value of reflectance measured from such a system is therefore an infinite sum of these subsequent reflections. However, since these additional reflectances are generally low, the overall reflectance is very well approximated by the sum of the first two reflections. In the case of thin film interference expressed in equations (2-19) and (2-20), this multiple summation has been performed.  2.3  Particle suspensions  A suspension of solid particles in a fluid medium is of great interest in many different fields. For example, printing toners often use coloured pigments suspended in a liquid. For particle sizes ranging from one to hundreds of nanometres, these suspensions are commonly known as colloids. While the work in this thesis makes use of colloidal suspensions to control the reflectance at an optical interface, the characteristics and behaviour of the suspension are not well understood. The work does not attempt to advance knowledge in the field; rather, the information provided here is purely intended as background information.  2.3.1 Double layer model While there is no overall charge in a colloidal suspension, particle surfaces can acquire charge when placed in a polar medium, such as water. The charge can be acquired by several mechanisms such as ion adsorption, ionisation, and ion dissolution. Counter-ions are attracted to the charged particle surface, creating an electric double layer based on the thermal motion of the ions and particles.  10  The double layer model, as its name states,  consists of two layers: an inner layer and a diffuse layer. This model ignores edge effects from the surface of the colloidal particle and, for the purpose of this discussion, also assumes that the surface is uniformly positively charged. Figure 2-9 depicts the two layers schematically. The inner region consists mostly of counter-ions, and as the distance away from the charged surface increases, the presence of co-ions increases. In  20  the inner layer, often referred to as the Stern layer, there is a large electrostatic force that is stronger than the random thermal motion, causing the counter-ions to move in the liquid along with the particle. In the diffuse layer, the electrostatic force is much weaker, and while the counter-ions tend to remain near the surface, they do not always move with the particle.  11  This model is a very good approximation of colloidal systems with low  concentrations of suspended particles.  Stern layer Particle surface  0 0 © h) 0 ©00Ok° ^  IS ©! 0® 0  '  0  T  !  Diffuse layer  Figure 2-9: Schematic of the double layer model in colloids 12  In the double layer model, an approximation of the potential at a point r from the particle with diameter a and a surface potential y/ is: 0  r  (2-23)  In this case, the reference bulk potential is assumed to be zero. The thickness of the double layer is often characterized by the Debye length \ / K , the distance at which y/ has dropped by 1/e. If the Debye length is short, the layers of neighbouring particles are unlikely to interact, simplifying the model of particle behaviour. If the Debye length is long, the diffuse layers may overlap and neighbouring particles must be included in the analysis of particle motion and behaviour.  21  The Debye length depends on the dielectric constant and ionic strength of the suspension fluid. In media with high dielectric constants such as aqueous systems, the Debye length is very short, making it possible to model the behaviour of the particles without considering interactions of nearest particles. In media with low dielectric constants such as perfluorinated hydrocarbons used in this study, the double layer is much larger and can even overlap with the nearest neighbouring double layers, increasing the complexity in modeling particle behaviour.  Additionally, the colloidal suspensions used in this study have high concentrations of particles, further complicating particle behaviour as the double layers can overlap significantly. However, the high density of particles can allow for a greater stability during electrophoresis, as discussed in the following sections.  2.3.2 Stability of colloidal suspensions Particles in suspension can settle by sinking or floating in the liquid. They can also agglomerate if it is energetically favourable to do so. The main cause of aggregation is the attractive forces between the particles; a repulsive force is thus needed to stabilize the colloid.  13  Stabilizing particles in suspension can be accomplished by electrostatic or steric methods.  14  The former involves electrostatic repulsion to keep the particles in  suspension. Steric stability on the other hand, holds the particles in solution by adding a - molecular dispersant. The dispersant is a molecule that favours the particle on one end while favouring the liquid at its other end. One end of the molecules attaches to the particle and surrounds it, and the exposed ends of dispersant allow the particle to remain suspended. The stabilization mechanism of a stabilizing agent is usually complex and involved many factors beyond the scope of this discussion.  15  22  2.3.3 Electrophoresis Electrophoresis is the motion of electrostatically charged particles with respect to a stationary liquid as a response to an applied field. Under typical moderate field strengths, the drift velocity v of a particle is linearly proportional to the electric field strength E, with a constant of proportionality known as electrophoretic mobility ji: V = /JE  (2-24)  This mobility is heavily dependant on the particle's environment. Electrokinetic behaviour depends on the potential at the surface of shear between the charged surface and the surrounding liquid. This potential is known as the zeta potential, and the position of this surface of shear varies depending on the viscosity of the solution around the particle and whether the particle has absorbed a non-ionic surfactant.  16  In addition, the  overlapping or interacting extended double layers found in low-dielectric media further complicate the relationship between particle charge and mobility. It is not surprising that mobilities are lower when a high volume fraction of particles are placed in a lowdielectric medium, as the double layers heavily overlap.  As mentioned previously, the work in the thesis uses a particle suspension to cause reflectance modulation but it is not intended to contribute to the field of colloidal suspensions. This section is meant only to introduce the reader to the complexities of the particle suspensions used for absorbing light.  2.4  M i c r o - r e p l i c a t e d sheets  Several applications can benefit from microscopically precise structures. The polishing industry uses micro-replicated structures made from abrasive material such as diamond 17  particles to increase the lifetime and efficiency of polishing films. It is also common to find micro-replicated sheets in optical applications, such as prismatic film used to redirect I C"  light to increase the brightness in typical emissive liquid crystal displays.  23  Micro-replicated sheetings of interest in this thesis are intended for optical applications. The first is known as Diamond Grade™ reflective sheeting , a prismatic film made of 19  polycarbonate used in traffic control applications. It consists of an array of pyramid-like structures, or corner-cubes, shown in Figure 2-10 below, allowing light to undergo TIR on multiple surfaces and be retroreflected, as shown earlier in Figure 2-2.  Figure 2-10: Structures of Diamond Grade™ retroreflective sheeting (a) isometric view of single corner-cube, and (b) top view of array  Diamond Grade™ reflective sheeting has a definite orientation. To orient the film, horizontal lines in Figure 2-10(b) are commonly termed the primary grooves. Facets of the corner-cube structure along this groove are referred to as primary facets, and the others as secondary facets for the purpose of this thesis and are labelled in Figure 2-11. Primary facets  Figure 2-11: Primary groove and facet labels for Diamond Grade™ film  Another micro-replicated film used during the course of the work presented is an experimental sheeting not yet commercially available, but also intended for traffic control applications. The film is currently referred to as micro-full-cube-array, or M F C A film. It is based on a similar corner-cube structure, with modifications to the geometry to  24  improve the retroreflective characteristics. M F C A film, similar to Diamond Grade™, has a distinctive axis henceforth referred to as the primary groove.  Since these reflective films were designed to take advantage of the phenomenon of TIR to provide high retroreflectance, they are ideal for use in a display which modulates light by controlling TIR.  20  This thesis extends the design of such an information display, the  important details of which are described in the following chapter.  25  3  REFLECTIVE IMAGE DISPLAY BASED ON CONTROLLED TIR  Reflective displays depend on light from an external source reflecting from its surface to the viewer. A novel reflective display based on thefrustrationof total internal reflection has previously been studied and developed by L . A . Whitehead and M . A . Mossman. The important details of this display and how it relates to the work of this thesis are discussed in this chapter.  3.1  Principle of a TIR-based display  As described in section 2.1.8, TIR can befrustratedby placing an absorber in the evanescent wave region. This absorption of light results in a dark, or absorptive, state. When the absorber is moved away from the evanescent wave region, the TIR is restored and the surface appears bright. The thin effective evanescent wave zone makes this method of reflectance modulation ideal for an efficient reflective display since it requires very little motion of the absorbing material. The modulation can therefore be done quickly with a small amount of energy per unit area resulting in a low power display, while providing very high reflectance and contrast due to the efficiency of TIR.  Figure 3-1 demonstrates the principle of frustrating TIR in a display with a two dimensional prismatic structure in which light undergoes TIR at two surfaces. If an absorbing material is brought into optical contact with the back of the structure as shown in Figure 3-1 (b), most of the incident light is absorbed at the first interface by frustration of TIR, and any reflected light is absorbed at the second facet, resulting in an almost complete absorption of the light. When the absorber is pulled away from the evanescent region, the reflection is totally restored. This yields a high contrast between the reflective state and the absorptive state.  26  microprismatic sheet ( n. =1.59) air gap absorptive material  (a)  (b)  Figure 3-1: Frustrating TIR in prismatic film (a) light undergoing TIR, resulting in high reflectance (b) TIR is frustrated using an absorber, resulting in negligible reflection  It is possible to design an absorber system with independent sections to control which parts are positioned in the evanescent wave zone of the prismatic film and which are pulled back. The result is a pixelated black and white information display. It is also 22  possible to implement subtracted colour filtering to allow for a full-colour display.  In the next section, the pigment suspension used as the absorber in both this earlier information display and the display developed in this thesis is described.  3.2  Pigment suspensions as absorbers to frustrate TIR  One might expect that the ideal absorber to frustrate TIR would be a solid highly absorbing material moved into and away from the TIR surface. However, due to the cohesive forces at the surface, too much energy is required to move such an absorber away from the surface. A n absorbing material suspended in a liquid is therefore currently most desirable for modulating TIR because of the low energy required to move the absorber through the liquid.  23  A suspension of coloured pigment particles in a clear  liquid was used as the absorber for the TIR-based reflective display. This colloidal system can be controlled using electrophoresis as a means to move the pigment particles in and out of the evanescent zone.  27  Since the refractive index of the liquid now present at the interface of the polymeric microstructure is higher than that of air, the critical angle is altered. As the index of the solvent increases, the critical angle increases. Thus, light incident between the critical angle of the surface with air and the new critical angle no longer undergoes TIR, resulting in a decreased reflectance. A low index liquid is therefore necessary in order to maximize the degree of TIR in the display system described earlier. The solvent used in the suspensions is a perfluorinated hydrocarbon sold under the trade name Fluorinert™, from the 3M Company. A perfluorinated hydrocarbon is a liquid in which the hydrogen in the hydrocarbon chain is replaced by fluorine atoms. The carbon-fluorine bond is strong, making the configuration very stable and inert. The electronic orbitals do not shift easily in the presence of an electromagnetic field, resulting in a lower index of refraction than most liquids. One product in the Fluorinert™ family of products, FC-75, has a refractive index of 1.276, lower than both water and hydrocarbon oils, making it the best choice as the solvent in the pigment suspensions.  Figure 3-2 depicts the working of a TIR display with a pigment suspension as the absorber. Since an electric field is applied across the pigment suspension to cause the particles to move, two electrodes must be present. The structured film is therefore coated with a thin continuous layer of optically clear conductive material, such as indium tin oxide (ITO). The rear substrate is also made of a conductive electrode, segmented to allow pixel control, and the gap between electrodes is filled with the pigment suspension. When a field is applied between electrodes, the particles migrate to one electrode, and, under the influence of a field with opposite polarity, migrate to the other electrode. When the pigments are in the evanescent wave region, TIR is frustrated and light is absorbed, causing the film to appear dark, as shown in Figure 3-2(b). When the field polarity is reversed, the pigments migrate out of the evanescent region, TIR is restored, and the pixel appears bright [Figure 3-1(a)].  28  ITO coated prisms  +v  liquid medium pigment particles r - o I (a)  TTO coated substrate (b)  Figure 3-2: TIR-based display with a pigment suspension as absorber (a) voltage is applied such that pigments are out of the evanescent zone allowing TIR (b) voltage polarity is reversed, and pigments frustrate TIR  24  It should be noted that the pigments do not need to be as highly absorbing as one would generally believe to frustrate TIR. The index gradient created by the concentration gradient of pigments against the interface extends the path length of the light entering the absorbing material.  25  The extended path allows for greater absorption, requiring less  absorption in the individual particles to ensure almost total absorption of the light.  While the use of an electrophoretic absorption system in a TIR display is ideal due to surface energy constraints, it is known that electrophoretic particle systems degrade over time. Suspended particles can cluster when under the influence of an applied field, leaving regions almost entirely void of particles, as illustrated in Figure 3 - 3 . This agglomeration is believed to be caused by fluid disturbances in the area of the moving particles and associated ions in its double layer. Although this tendency to aggregate has been heavily studied by many groups, the details are not yet fully understood, especially in non-aqueous systems such as that used here.  26,27  29  It has been proposed that this agglomeration can be reduced and perhaps eliminated byusing a high volume fraction of pigment particles, making the suspension a thick paste instead of a liquid.  28  The densely packed pigments can remain in suspension, and it is  probable that it is energetically unfavourable for the particles to agglomerate further. With such a high volume fraction, the particle motion is not free within the liquid, but rather depends largely on the surrounding pigment group. It is likely that this collective pigment group compresses as a response to an applied field, causing a reduction of particle density at one electrode, leaving a thin layer of solvent at the surface, much like a compressed sponge releases water. It is this thin solvent layer that allows TIR to occur at the interface. Modulation of the reflection is possible by reversing the polarity of the applied field, as shown in Figure 3-4.  Clear liquid layer Compressed pigment particles /y Compressed pigment particles Clear liquid layer  Figure 3-4: Pigment suspension compression under an applied field and the resulting thin solvent layer at one electrode  It is believed that individual particle mobility is reduced in this collective pigment group due to highly overlapping double layers. The particle volume fraction should therefore be great enough to successfully reduce clustering without causing an impractical slowing of the pigment group's response to the applied field.  During the course of research presented in this thesis, two pigment suspensions were used: a black and a dark purple suspension. In both cases, intensely coloured pigment particles are suspended in the perfluorinated liquid with a liquid dispersant to stabilize the  30  colloidal suspension as discussed in section 2.3.2. The pigments used are listed in Table 3.1 below. The black suspension was useful when studying spectrum independent effects since the absorption wavelength is uniform over the visible range.  However, due to  technical difficulties with the stability of the carbon black suspension, a dark purple suspension, comprising of a combination of blue and magenta pigments, was used for most reflection measurements described in the following chapter. Table 3.1 Pigments suspended in perfluorinated hydrocarbon liquid Pigment Colour  Product name  Supplier  Black  Raven Black 1200  Columbian Chemicals  Magenta  NRT-796-D Monastral Red-B  CIBA Specialty Chemicals  Blue  Cromophtal Blue A3R  CIBA Specialty Chemicals  3.3  Use of corner-cube based retroreflective sheeting in TIR display  As mentioned in this chapter, reflective displays based on the control of TIR demonstrate high contrast and reflectance while operating at potentially very low power. Any structure which possesses retroreflective characteristics is a suitable geometry for this type of display. For example, related work on handheld displays uses hemispherical structures.  30  As mentioned previously, retroreflective sheeting is used in traffic control applications such as road markers and highway signs. Highly retroreflective films consisting of corner-cube structures such as 3M Diamond Grade™ reflective sheeting are currently in widespread use in traffic signs, but for reasons of cost and reliability, the vast majority of these signs are simply printed with permanent messages, rather than using electronicallyaddressable variable message signs.  31  There is substantial interest in the signage industry to have relatively inexpensive, reliable variable message signs. The TIR-based reflective display holds great promise for use in this field. However, as previously mentioned, the critical angle at which TIR occurs depends on the refractive index values at the corner-cube interface. The retroreflection is reduced when the structures are immersed in the liquid suspension described above rather than air. In this case, light does not undergo TIR on one or two of the corner-cube facets, resulting in a transmitted ray out of the corner-cube structure into the pigment suspension where it is absorbed, as illustrated in Figure 3-5.  ! !  4 n=1.00  Figure 3-5: Light undergoing TIR on two of the three corner-cube facets  This reduction can be avoided by using a high refractive index microstructure, but unfortunately, there is currently no practical way to make retroreflective sheets using materials with a refractive index sufficiently high that TIR occurs at all facets when the material is in contact with the liquid suspension medium. Since the level of reflected light cannot be reduced by TIR frustration if it does not undergo TIR, it might seem reasonable to conclude that a system made with ordinary materials would not only lack high reflectance, but would also lack the high contrast achievable due to frustrated TIR. Surprisingly, in preliminary testing, it was observed that the degree of reflection can be successfully modulated by moving an absorber close to or away from the surface, even when conditions for TIR are not met. During the course of studying this type of modulation, it was found that the reflectance and contrast can be surprisingly high, which will be discussed in the next chapter.  32  The work presented in this thesis centers on the investigation of the modulation of reflection when the conditions for TIR are not met. It explores methods of enhancing this type of reflection, and studies its possible use in active messaging applications of highway signs. The study of modulation of reflection begins with a single interface, and builds to the more complicated corner-cube geometry.  33  4  REFLECTANCE MODULATION AT A SINGLE INTERFACE  It is reasonable to assume that if light does not undergo TIR at a surface, that the lack evanescent wave, and thus inability to frustrated TIR would make high contrast reflection modulation ineffective. When the conditions for TIR are not met, the reflectance at the surface is lower since some light is transmitted into the second medium. Surprisingly, despite this, the reflection can still be modulated, and under the right conditions, still provides high reflectance and high contrast. Since there is nofrustrationof an evanescent wave in the absence of TIR, it is interesting to observe the same visual reflectance modulation.  It is believed that optical interference is responsible for the high contrast modulation in the case of light undergoing partial internal reflection (PIR). A study of the reflectance modulation in the simplest case of a single interface is presented here. The experimental results of reflectance modulation through the use of pigment suspension as the absorber was modeled in an attempt to gain further understanding of the system.  4.1  Experimental measurement of modulation at a single interface  The change in reflectance at a single interface can be caused by the movement of particles into and away from the surface upon which light is reflected. This change was measured experimentally. The design and set-up of the experiments used to compare the reflectance modulation for light undergoing TIR and PIR at the interface is discussed in this section. The results of reflectance changes are discussed, as well as the model created to emulate the experimental results.  34  4.1.1 Single interface test cell construction This study begins with the most straightforward geometry, namely, a single flat interface, to isolate the change of reflectance due to pigment motion. The surface studied was the interface between glass and pigment suspension. Test cells were constructed by sandwiching a pigment suspension between a two clear non-structured electrodes, illustrated in Figure 4-1. The electrodes were glass slides 25 x 50x 1.1mm, commercially coated on one side with a thin conductive layer of indium tin oxide (ITO),  with a  conductance of about lOOn/square. A spacer made of two 30pm layers of polyester tape was used to ensure that the electrodes did not come into contact with one another 32  causing a short circuit under an applied field. Enough pigment suspension to fill the 60pm gap was spread evenly on one slide and the second slide was lowered onto the ink from one edge of the slide to the other to minimize air trapped in the cell. The outer edges of the test cell were sealed using epoxy  to prevent the solvent from evaporating  and to hold the slides in place. Electrical contact to the electrodes was made by offsetting the slides from one another and attaching a wire lead to the ITO surface of each slide using a silver-based conductive epoxy.  34  spacer tape  (a) conductive epoxy wire lead top slide  (b)  pigment suspension  rear slide  Figure 4-1: Test cell for single interface reflectance measurements (not to scale) 35  (a) top view, and (b) side view  35  4.1.2 Measuring  reflectance  The interface of interest in the test cell described above is the boundary between the glass slide and the particle suspension. In response to an electric field applied across the two electrodes, the pigment mass compresses to one electrode, leaving a thin clear solvent layer at the other as discussed in section 3.2. In this situation, the interface of interest becomes the boundary between the glass and the clear solvent layer with refractive index of approximately 1.29. The critical angle at such an interface is 58.3°. Since light must enter the glass from the surrounding air before striking this boundary, the air/glass interface must also be considered when designing a method for measuring reflectance. Light entering the glass at even extremely glancing incident angles cannot refract in such a way that it will be beyond the critical angle of 58.3°. In order to measure the reflectance of light undergoing TIR, a right angle glass prism was placed on the top face 36  of the test cell with index-matching microscope oil  to ensure optical contact. The  refraction at the prism facet allows the angle of light at the glass/suspension interface to exceed the critical angle, as pictured in Figure 4-2.  n,=l.C n =1.5 2  n  (a)  :  y  1 29^/ (b)  Figure 4-2: Use of prism to attain incident angles beyond the critical angle (a) refraction in the prism allows 0 to be beyond the critical angle (b) without prism, even glancing angles of (j) result in 0 below  critical  38  During these experiments, the change in reflectance was measured for light incident in both the TIR and PIR cases. Reflectance measurements were made by detecting light exiting the prism at particular angles in the range of 63.4° to 67.8°, corresponding to a range of 56.9° to 59.8° at the glass/liquid interface, as shown in Figure 4-3. This 3° range  36  covers light incident 1.5° beyond the critical angle of the system in its reflective state (approximately 58.3°), and light incident 1.5° shallower than the critical angle.  (a)  (b)  Figure 4-3: Angular range used for single interface reflectance measurements  The change in reflectance caused by particle motion as a response to reversing field polarity was measured in real time, as pictured in Figure 4-4, using the set-up described in the next section.  Figure 4-4: Measurement of test cell reflectance modulation. The applied field polarity 39  is reversed during measurement to obtain modulating reflectance data  4.1.3 Design of reflectance modulation experiment The system used to measure the change in reflectance was comprised of a light source, the test cell with prism, and a detection system. Each of these components had particular design issues that needed to be addressed, discussed in this section. This set-up was modified from a previous experiment designed to measure modulation of T I R .  40  37  Since the reflectivity from a surface is highly dependent on incident angle, it is important for the detection system to measure reflected light controllably within a narrow angular range. The detection system consisted of a monolithic silicon integrated circuit T S L 250 light-to-voltage optical sensor containing a photodiode, operational amplifier, and 41  various feedback components. This optical sensor was placed in a hollow tube 200mm long and 7.5mm in diameter. To limit the angular distribution of detected light, the other end of the tube was masked with two black caps each with a 1mm hole drilled in the middle and lined up concentrically with the tube. In addition, the inside of the tube was threaded and painted black to absorb any light that might have entered at a glancing angle outside the desired measuring range. This setup is illustrated in Figure 4-5.  roughened surface 42  Figure 4-5: System used to limit angular range of detected light' t  The angular response full-width-half-maximum of this collimated detection system was approximately 0.7° and the alignment offset in of the optical sensor to the holes in the caps was approximately 0.3°. Appendix A details of the methods used to measure these characteristics.  To investigate the spectral response of reflectance modulation, a red, green, or blue colour filter was placed infrontof the detector caps, as shown in Figure 4-6. In 43  addition, as only visible wavelengths are of interest, an infrared filter was placed on the 44  black caps of the detection system to ensure that any infrared light passing through the colour filter was not detected.  38  detector  infrared filter coloured filter  diffuser  halogen source  test sample  Figure 4-6: Filter, sample, and light placement in the measurement system  The light source used was a 50W halogen light bulb with a 4mm filament.  To avoid  any large non-uniformities in the source intensity, a diffuser was placed between the 46  light bulb and the sample.  The test cell and prism were placed on an x-y stage with the prism facet facing the diffuser as shown in Figure 4-6. It should be noted that since the prism base is larger than the width of the test cell, the overhanging edges were in contact with air. If these prism edges were not masked, light undergoing TIR at those glass/air interfaces would be detected thereby increasing the apparent overall reflectance of the test cell. A reference cell could be used to cancel spurious reflections, however, any movement of the prism or differences in cell width due to the epoxy sealant could easily cause differences in reflectance values which would not cancel. Thus, masking the overhanging prism base was the most reliable option for reproducibility. Black vinyl was used to mask the edges and optical contact with the prism was made using a commercial optical adhesive.  47  The prism arrangement was held in place by two supports as depicted in Figure 4-7, allowing reproducible replacement of the cell and prism once removed. The test cell and prism were positioned into the detector's line of sight by moving the x-y stage. Both test cell placement and light source height were adjusted and aligned for each detection angle to maximize the signal to the detection system.  39  support for prism  .prism  test cell  V  support for prism  x-y stage  Figure 4-7: Supports for the prism on the x-y stage  The detection system tube was mounted above the x-y stage and was controllable by coarse and fine angular adjustments. Fine adjustments allowed a change in detector tube angle as little as 0.3°. Appendix B details how the detection angle was measured and how the incident angle as the glass/pigment interface was calculated. While the detection system measured a distribution of angles, only the center angle is quoted in the following result sections. The uncertainty in the determination of this center angle is 0.3°.  A data acquisition program written in Visual Basic was used to acquire reflectance 48  measurements using the detection system. Figure 4-8 shows a schematic of the entire setup. The voltage signal outputted from the detection system was sent through a gain amplifier with a low pass filter (1Hz) to reduce noise, then into the computer system where it was converted to a digital data and saved to a file. For these experiments, the samplingfrequencywas 50 Hz. Since the detector had a narrow angular range, and the colour filters have narrow bandwidths, the signal needed to be amplified 50-200 times to be suitable input for the computer data acquisition system. Input voltage data  function generator  diffuser  Figure 4-8: Schematic of the single interface reflectance measurement system  40  The test cell was connected to a function generator outputting a 0.08Hz square wave pulse with amplitude corresponding to a field of ±5.8 x 10 V/m, to cause the pigment 5  absorber motion, in turn causing a change in reflectance at the interface. Collecting data throughout the cycle reveals the time evolution of the reflectance modulation and results are presented in the next section.  4.1.4 Time-varying reflectance modulation Reflectance measurements of test cells filled with the particle suspension were taken for several angles ranging from 1.5° beyond the critical angle to 1.5° below critical to cover the ranges of TIR and PIR. This was repeated for the three colourfilters(characterized in Appendix C) to gain spectral information. The reference cell was constructed in the same fashion as the test cell but filled with air instead of the pigment suspension. Since TIR occurs at the glass/air interface for all angles in this study, an air-filled cell makes an ideal reference of 100% reflectance. Voltage output recorded by the computer system at each detection angle was normalized by the reference voltage value of the air cell at that same angle. The resulting time-varying reflectances for the three different colour filters are shown in Figure 4-9, Figure 4-10, and Figure 4-11. In thesefigures,the curves are labelled by the center of the detected angle range of light incident at the glass/pigment interface. The dashed lines represent the times at which the polarity of the applied field was reversed.  When the test cell was rotated 180° about the axis normal to the glass surface, the measured reflectance shifted by as much as 5%. It is reasonable to assume that this is because some test cells are not entirely flat, causing the incident angles to be altered from the tilt. When such differences were measured, the average of both rotations was taken to represent the center detection angle. In addition, the reproducibility of measurements without rotation causes variations on the order of 1-3%. Errors in measurement are thus about 3%.  41  0  10  20  30  40  50  60  70  80  T i m e (seconds) Figure 4-9: Reflectance vs. time for light passing through the red filter. The angles labelled represent the incident angle of light at the glass/pigment interface (center of angular range). Dotted lines represent the times at which the field polarity was reversed.  42  0  10  20  30  40  50  60  70  80  Time (seconds)  Figure 4-10: Reflectance vs. time for light passing through the green filter.  The angles  labelled represent the incident angle of light at the glass/pigment interface (center of angular range). Dotted lines represent the times at which the field polarity was reversed.  43  10  20  30  40  50  60  70  80  Time (seconds) Figure 4-11: Reflectance vs. time for light passing through the blue filter.  The angles  labelled represent the incident angle of light at the glass/pigment interface (center of angular range). Dotted lines represent the times at which the field polarity was reversed.  The plots of reflectance versus time for the test cells containing the pigment suspension exhibit a few interesting characteristics. First, the modulation clearly continues to occur even when light does not undergo TIR. While the contrast ratio diminishes as the viewing angle is dropped beneath the critical angle, at 1.5° beneath critical it is still 14:1 and is 72:1 for light at 1° below critical for light at 515nm. The reflectance in the absorptive state is virtually identical for light incident beyond or beneath the critical angle. It is thus the change in peak reflectance that affects the contrast ratio.  Another interesting feature in the reflectance curves is the presence of an oscillation at times near the switching transition for measurements made in the PIR regime (curves for incident light at 57.6° and 56.9°). In general, one might expect such oscillations to arise from interference phenomena; this will be carefully considered in section 4.1.6. This  44  oscillation is not observed at the transition from reflective state to absorptive state, however. This will be discussed further in section 4.2.4.  The oscillating behaviour becomes less defined with time until a steady state value is reached. The peak reflectance is greater than the steady state reflectance. This could prove useful in an application where the reflectance is modulated from a reflective state to an absorptive state with a constant higher frequency. If the polarity of the applied field is reversed immediately following the reflectance peak, the reflection is thus modulated to a dark state without the decrease to the steady state reflectance. The reflective state observed in such a system is therefore only the peak reflectance, creating a higher effective contrast ratio.  It should also be noted that although the critical angle is approximately 58.3°, the maximum reflectance at this detection angle is not the same as the maximum of the curve at an angle well beyond critical. This is due to the angular spread of the detection system and the alignment offset of the detector, which allows more detection of light beneath the detection angle. The overall reflection is hence lower than light incident at the critical angle alone.  4.1.5 Factors influencing reflectance modulation There are several factors that are proposed here to explain the observed time dependence of the reflectivity. These are described separately in the following sections.  4.1.5.1  Particle clustering  Repeated trials showed that the number of observed oscillations in the PIR curves change over time even if all other conditions are held constant. A plausible explanation may be that these changes are due to ink clustering over time. In order to verify this, a new test cell was made, placed in the experimental set-up, and left switching for 100 minutes. At 20 minute intervals, reflectance measurement data was acquired. This data, presented in  45  Figure 4-12, clearly indicate a change in interference behaviour with time. The curves are numbered 1 to 4 in the order they were taken from 20 minutes to 80 minutes.  As the cell is left to switch, the reflectance minimum seen at 11 seconds and the maximum at 14 seconds in Figure 4-12 become less pronounced with time. As will be discussed in the model in section 4.2.2, this is consistent with particles agglomerating to form larger slower particles with lower mean velocities. A n interesting feature observed in Figure 4-12 is that the reflectance maximum does not appear to be affected by particle clustering. The reflectance response of this particular study suggests that agglomeration is not present immediately after the switching transition, perhaps indicating an underlying complicated surface behaviour.  After 120 minutes under the time-varying field, clumping behaviour was observed with the naked eye as the particles pull away from the surface.  •••• — •-  0.00 I 0  —  i  1  1  1  2  4  6  8  1  i  1  1  1  10  12  14  16  18  20 min 40 min 60 min 80 min  1 20  22  Times (seconds) Figure 4-12: Effect of clustering on reflectance data. Each data set was taken from the same test cell switching constantly for the amount of time labelled.  46  While clumping is hard to avoid, it can be accounted for when modeling the system. If the order of data collection is known, the model of the system can be adjusted to accommodate clustering behaviour with time. For example, in Figure 4-9, the curve labelled 59.1° has a much slower response than that of the curve labelled 59.8°, so much so that it appears the curve did not reach its maximum reflectance in the data collection time. This data was taken after the field was applied for over 10 minutes following data collection for the detection angle of 59.8°. The particles seem to have agglomerated during that time causing a slower response. The applied field was removed from the cell which was left to recover for two hours before further measurements were performed. The next data collection (at 58.3°) does not demonstrate the same slow behaviour. It has been observed that the clustering is mostly reversible if the system is allowed to recover in the absence of an applied field; however, clustering then occurs more quickly upon reintroduction of the field.  While clustering is not immediately apparent upon visual inspection, clustering does occur shortly after the application of an electric field across the pigment suspension as suggested by the slowing of the measured reflectance response. As discussed in section 3.2, a high volume fraction of pigment particles can prevent or hinder particle agglomeration since it has become energetically unfavourable to do so. While the clustering was impeded in the suspensions used in this study compared to those with lower volume fractions, agglomeration effects were nevertheless measured within minutes.  4.1.5.2  Colour filters  The reflectance at a particular angle of incidence is wavelength dependent due to dispersion. The curves of reflectance versus time measured with each colour filter have different peak reflectance values, as seen in Figure 4-13. The refractive index differences for light of different wavelengths cause the critical angle at the interface to differ by much as 0.4° in this study. While the detection angle is the same for all colour filter data,  47  that angle with respect to critical for red light is different than that of green and blue because of dispersion.  0  10  20  30  40  50  60  70  Time (seconds) Figure 4-13: Effects of dispersion and pigment colour on reflectance data. Reflectance measurements were taken using the same cell at a constant detection angle with different colour filters  Another important factor affecting the measured reflectance of a particular wavelength is the pigment suspension colour. The suspension is a combination of dark magenta and blue pigment particles so that the optical interactions with these particles are wavelength dependent. Red light and blue light will behave differently when interacting with each type of pigment. For example, the transition from reflective state to absorbing state occurs more rapidly for red light, and as blue particles appear black through a red fdter, this seems to suggest that the blue particles have a greater electrophoretic mobility. Moreover, the absorptive state in Figure 4-13 is 0.5% for red light and 4% for blue light. It is reasonable to conclude that the blue particles are more efficient at frustrating the partial reflection (for reasons unknown). However, the maximum reflectance measured 48  through the red filter (see Figure 4-9) for an incidence angle beyond the critical angle is 95 ± 3%, and not at the expected 100%. This may be due to extremely small blue particles in the solvent layer causing some absorption and/or scattering of red light. This is not yet very well understood, and is discussed in more detail in the future work section.  Applied Field  4.1.5.3  As described in equation (2-21), the velocity of the particles, and hence the change of reflectance over time, is a function of the strength of the applied field. To verify that the field does not cause additional unanticipated effects on the reflection modulation, data was collected for different field strengths, with all other parameters fixed. Figure 4-14 shows the reflectance response for applied fields of 5.8 x 10 V/m, 2.8 x 10 V/m, and 5  5  1.8 x 10 V/m. For decreasing field strengths, the increasing time to reach the peak 5  reflectance and broadening of the peak are results consistent with the decrease in particle speed. No unexpected results were observed. 0.60  0.50  3 0.40  5.8 x 10° V/m 2.8 x 10 V/m 5  0.30  1.8 x 10 V/m 5  0.20  0.10  L  0.00  10  20  30  40  50  60  70  NO  90  Time (seconds)  Figure 4-14: Effects of varying field strengths on reflectance data. Reflectance measurements were taken using the same cell under differing field strengths.  49  It should be noted that particle clustering also occurs during data collection. While the higher field strengths cause the particles to cluster more quickly, the particle velocity, and thus reflectance response, is also faster. When modulating from the reflective state to the absorptive state, it is important to maximize the contrast ratio by allowing the reflectance curve to reach its maximum, which is more likely with higher fields. Therefore, a balance must be found between clustering rate and contrast ratio.  4.1.5.4  Other effects  Despite the understanding of the factors affecting the reflectance mentioned above, some aspects of particle motion are not fully understood. For example, the particle behaviour in response to both the applied field and surrounding particles appears to vary occasionally in an unexpected way. Figure 4-15 below shows an example of two data sets taken 20 minutes apart.  ' First data set • Second data set  0  10  20  30  40  50  60  70  Time (seconds) Figure 4-15: Example of unexpected differences in reflectance  modulation.  Measurements were made 20 minutes apart with the test cell under identical  conditions. 50  The second set of reflectance data (shown as the darker curve) exhibits the broadening characteristic of slower particle motion, however, the reflectance dip following the peak is opposite of what is expected. A n 8% depression in the dip is seen between measurements, but generally, a shallower dip is seen after clustering, as shown in Figure 4-12. The intricacies of particle motion such as this are not yet fully understood.  4.1.6 Establishing interference in reflectance curves Plots of reflectance versus time, such as Figure 4-10, demonstrate an oscillatory behaviour as the pigment particles pull away from the surface. One would expect such behaviour to be due to interference phenomena; however, the complexity of the system requires verification of this claim. In the case of thin film interference, the thickness d of the clear solvent layer at which there is the first constructive peak for the red wavelength is: K  d= r  (4-1)  4n cos0, yf/(B  and for the green wavelength equation (4-1) has the same form, replacing the appropriate wavelength and refractive index. Taking the ratio of these equations gives: d  r  _  fllmgK  n  (4-2)  The ratio of film thickness at which the reflectance peaks occurs is thus equal to the ratio of wavelengths (with a factor of the film index for each wavelength). Under the assumption that the pigment particle velocity is constant, which corresponds to the solvent layer thickness increasing linearly with time, the ratio of times at which the peak reflectance occurs would also equal the ratio of wavelengths. This assumption is only valid at times near the switching transition, since at later times, as the compression of particles, and hence growth of the solvent layer, slows to a steady state. It is therefore justified to use the ratio of times at which reflectance maxima occur (soon after the transition) in the data with the red filter and the green filter to approximate the ratio of  51  wavelengths of the filters. If this ratio were equal to the ratio of wavelengths experimentally, the presence of interference would be strongly supported.  However, as mentioned previously, the pigment suspension used in the test cells consists of both magenta and blue pigment particles, making it difficult to establish interference as described above. Since green light and red light interact differently with the magenta and blue pigments, differences in the time at which the peak reflectances occur could therefore be due in part to the difference in pigment mobilities. A wavelength independent absorption is therefore necessary to confirm that the oscillatory behaviour is indeed due to interference.  A black suspension made from the carbon black pigment listed in Table 3.1 demonstrates wavelength independent absorption and was therefore used to compare reflectance 49  values obtained through the red and green filters. This black pigment suspension does not have a high volumefractionof particles like the other pigment suspension and therefore clusters very quickly under an applied field. Since simultaneous measurement with both colour filters is non-trivial in the set-up described in section 4.1.3, the experiment was performed as follows. A test cell constructed as described in section 4.1.1 filled with the black pigment suspension was placed in the experimental set-up and data of reflectance versus time was collected alternating between a green and red filter.  50  The resulting reflectance versus time is plotted in Figure 4-16 below.  52  0.7  0  0  5  10  15  20  25  Time (seconds)  Figure 4-16: Reflectance vs. time for carbon black ink test cell.  Measurements  alternated between green and red filters.  The reflectance peaks are noticeably broader when measured the second time with the same colour filter, consistent with the expected particle clustering. To best represent the reflectance curve from the green filter that would have been measured simultaneously with the first red filter measurement, the two data sets taken with the green filter immediately before and after the red filter data were averaged. This provides an excellent approximation to the clustered state during measurement with the red filter and is shown in Figure 4-17.  53  0.7  average green filter •red filter  10  15  20  25  Time (seconds) Figure 4-17: Reflectance vs. time with redfilter,and the average of greenfilterdata to represent the same clustered state as the measurement with the red filter  The data in Figure 4-17 yields a time ratio t/t  g  of 1.19 and the ratio of wavelengths is  1.27, a modest 6% difference. The error could be due to a combination of effects. First, the refractive indices of the film needed in equation (4.2) are not known for the black pigment suspension. The index difference between the glass and the solvent responsible for the level of reflection from that surface is wavelength dependent due to dispersion, as discussed in section 4.1.5.2. The peak reflectance amplitude is therefore not the identical for both colours. Since the indices of the solvent film are unknown, the index dependence of equation (4-2) was removed by simulating the case where n/ equals n/ . r  g  This was accomplished by attempting to collect data from the same angle with respect to the critical angle of each case, which would result in identical peak reflectance values for both red and green light. The detection angle for data collected with the red filter was therefore decreased by 0.3° from the angle used for the green filter. The peak reflectance for green and red were nevertheless not quite identical, but it is believed the error caused by this is on the order of 0.01; not enough to account for the calculated discrepancy. It is 54  more reasonable to conclude that the assumption of constant particle velocity is inadequate. Despite the discrepancy, it can be stated with confidence that observed oscillations in the plots of reflectance versus time are indeed due to interference effects.  4.2  M o d e l i n g m o d u l a t i o n at a single interface  The analysis of plots of reflectance versus time in this study has provided insight into the nature of the ink system. A mathematical model of the associated interference phenomenon added to this understanding, as described below.  4.2.1 Mathematical model Based on knowledge of the particle suspension used in the study and the assumed time evolution of the system under the influence of an applied field, a simple mathematical model was proposed in an attempt to emulate experimental results.  The physical layout of the model, illustrated in Figure 4-18, consists of three layers: the glass layer from which the incident ray originates, a solvent layer of thickness d, and an infinitely thick ink layer.  glas:  solvent  Figure 4-18: Schematic of light interaction in the three-layered mathematical model of the single interface system  55  The solvent layer represents the clear solvent that is in contact with the interface during the reflective state. Its exact index of refraction is unknown and is therefore estimated by comparison with other materials. This is accomplished by making test cells filled with materials of known refractive index. These cells are placed in the experimental set-up described in section 4.1.3 and the expected critical angle is verified by ensuring 100% reflectance beyond the corresponding critical angle. The reflectance of the test cell filled with the pigment suspension in the reflective state was also measured for increasing angles from below the critical angle until the maximum reflectance was reached. The critical angles were compared to deduce the refractive index of the solvent layer. This method indicates that the composition of the clear "solvent" compressed out of the solution has an index of approximately 1.29, higher than the Fluorinert™ FC-75 solvent with an index of 1.276. The solvent layer is therefore doped with a material of higher index, perhaps the dispersant used in the suspension, which has an index of approximately 1.3.  The ink layer in the model represents the compressed pigment mass. The compression of this layer changes with time in the applied field, which effectively changes the refractive index as the concentration of solvent decreases. The simplified model presented here however, assumes a compressed pigment group layer (labelled "ink layer") and a growing solvent layer each with constant refractive index. The refractive index of the ink layer is calculated using: n  ink  = fn  pjgment  + (1 — f)n  ,  solvem  where/is the estimated volume  fraction of pigments in the final compressed suspension, estimated at 0.35 based on the assumption that the compressed layer contains only pigment and dispersant.  51  For  simplicity, the absorption of the ink layer is ignored. Since the ink layer is infinite, any light transmitted into this layer no longer interacts with the boundaries and is lost, simulating absorption without actually assigning an absorption coefficient in the model. Table 4.1 below lists the layers in the model and the corresponding refractive indices used for the each wavelength modeled.  56  Table 4.1 - Refractive indices of layers used in single interface modulation model for the center wavelength of each colour filter  Model layer  n  blue (A,=475 nm)  n  green (A,= 515 nm)  n  red (k=  Glass  1.522  1.521  1.512  Solvent  1.294  1.296  1.290  Ink (f= 0.35)  1.6  1.6  1.6  660 nm)  To approximate the time evolution of the system under the influence of an applied field, the model increases the thickness of the solvent layer with time. Reflectance values can be calculated through the mathematical treatment of thin film interference, discussed in section 2.2.2, given the refractive indices of the three layers, the wavelength of incident light, and the thickness d of the solvent layer. To represent the reflectance change from absorptive state to reflective state, the model begins with d=0 and increases d in small increments to represent the growing solvent layer. While a single wavelength is used, the colour filters used in fact allow a bandwidth of wavelengths to pass and interfere with each other. The model accounts for this interference by applying a weighted sum to the reflectances obtained by repeating the calculation for discrete wavelengths accepted by the filter. Discrete steps are 0.05nm, small enough to ensure the result approaches the continuous case.  It should be noted that the mathematical treatment of the thin film interference includes the case of incident light beyond the critical angle undergoing TIR. In this case, the ink layer is ignored and no interference effects occur.  As discussed in section 4.1.5.3, the effect of lower field strengths is to slow the movement of the pigments in suspension. This model therefore does not need to account for field strength in any other manner than to adjust the velocity of the pigment particles represented by the rate of growth of the solvent layer. This model, again for simplicity, assumes constant velocity.  57  This preliminary model was coded using M A T L A B .  5 2  When the initial model results  were compared to experimental data, it was clear that other important factors needed to be considered. The resulting reflectance does not converge to a steady state reflectance value as quickly as in experiment, clearly shown in Figure 4-19. The model therefore needed to be revised to include other factors that might suppress interference effects.  Experiment Model with bandwidth only  20  40  60  80  Time (seconds) Figure 4-19: Example of results from thefirstmodel compared to experimental data. Thisfirstmodel only accounted for bandwidth of thefilters(see text).  In the real system, the boundary between solvent layer and compressed pigment group is not necessarily uniform as assumed in the mathematical model. It is reasonable to assume that as the pigments compress, the boundary between the solvent layer and the edge of the pigment group is not uniform and flat. There is a distribution in size of particles which in turn means there is a distribution of particle velocities. Following the switching transition, all particles begin to pull away from the surface resulting in a somewhat uniform solvent layer. As time progresses, smaller particles with greater mobility can diffuse more easily leaving more solvent behind in certain areas. Furthermore, interactions between particles likely increase the non-uniformity of the 58  boundary between the solvent layer and the pigment group. This non-uniformity can be modeled simply by repeating the bandwidth calculations for various particle speeds, corresponding to various rates of growth of the solvent layer. A Gaussian distribution of these different velocities was considered, and the reflectance values from each representative pigment compression speed were weighted accordingly. The mean particle speed and the standard deviation of the distribution were parameters of the model fit to the experimental data. The best fit values of mean velocity were approximately 0.1 microns per second, with standard deviations of 0.08. This speed was varied slightly depending on the coloured pigments measured, as discussed in section 4.1.5.2. A typical time evolution of reflectance given by this model is shown in Figure 4-20 below.  0.7 ~~\  Time (seconds)  Figure 4-20: Example of modified model results compared to experimental data. A Gaussian distribution of particle velocities was assumed in this model (see text).  The reflectance values are approximately 15% higher than the experimental data in the case depicted in Figure 4-20. This is probably due to the fact that the model does not account for any interaction of light within the various layers growing at different speeds. 59  The model only considers reflections from multiple smooth layers, making it an inaccurate representation of the system. While this combination of multiple smooth layers representing the pigment velocity distribution compensates for interference from the non-uniformity of the back boundary, it does not consider the scatter and absorption of light that occurs as the back surface becomes more non-uniform with time, as depicted in Figure 4-21. In reality, light that would have reflected from the back surface to be subsequently detected could instead be reflected in another direction when incident upon non-uniform sections of the boundary. Moreover, the angular extent of the source in the experiment is not large enough to counter this effect by providing light elsewhere in the system that can be scattered and detected in its place.  Figure 4-2 F Schematic of light interaction in a more complex three layer system. Light interacting with the non-uniform back layer can be scattered and absorbed, making overall reflection from that surface negligible if the angular extent of the light does not compensate.  The simplest modification of the model to increase its accuracy is to employ a factor which increasingly affects the reflection from the solvent/ink boundary with time. However, since the model uses the characteristic matrix of the three layered system, reflections from the front and back surfaces are not easily separated mathematically. To simulate the increasing non-uniformity of the surface and the resulting absorption mathematically, the index difference between the solvent layer and ink layer was altered in time. If the index of the solvent layer and the ink layer are the same, all light is transmitted (and thus absorbed, as assumed by the model). Therefore, if the difference in  60  index between these two layers decreases as the solvent layer grows, the reflected light from the back boundary decreases, accounting for the observed decrease in detected reflectance. The time evolution of the index difference is calculated using:  d(tr  (4-3)  l  \ + j3d  where n is the initial index difference between the layers, d is the solvent layer 0  thickness, and B is a parameter fitted to the experimental data. For this modeled system, the best fit is/? = 1 0 . The time dependence emerges from the solvent layer thickness d, which increases with time. Figure 4-22 shows how this modification greatly increased model accuracy.  • Final Model ' Experiment  20  40  60  80  Time (seconds) Figure 4-22: Example of results from the final model compared to experimental data. This model compensates for absorption and scatter from the back surface (see text).  61  One last effect considered in the model is the range of detection angles based on the response of the detection system as discussed in Appendix A . Again, a Gaussian distribution is assumed with the mean angle equal to the center detection angle and individual time evolutions of reflectance are summed with appropriate weighting factors. This small effect is only on the order of a few percent. The final model code, including all details discussed in this section, can be found in Appendix D.  4.2.2 Modeling particle clustering As mentioned in section 4.1.5.1, a key factor influencing the time dependence of the reflectance observed from test cells filled with pigment suspension is particle agglomeration caused by the applied field. This clustering can easily be incorporated into the model since a Gaussian velocity distribution is already implemented. There are therefore two factors to represent clustering: the mean velocity of the particles and the standard deviation. As particles cluster to form larger particles, one can assume that the mean velocity decreases. Figure 4-23 below shows the effect of decreasing mean velocity while maintaining the same standard deviation. The darker curve represents a mean velocity of 0.07pm/s compared to the light curve corresponding to a mean velocity of O.lpm/s. As expected, the slower particle motion results in a more drawn out peak, a lower peak reflectance value, and a shallower ensuing dip.  62  0.7  Figure 4-23: Effect of mean velocity on model results  Figure 4-24 on the other hand, shows the effect of changing the standard deviation while maintaining the same mean velocity of 0.1|im/s. As the standard deviation is increased, a wider range of velocities are averaged over, and the oscillations observed from interference are less pronounced.  63  Figure 4-24: Effect of standard deviation (sd) on model results  In the real system, both mean velocity and standard deviation change as the pigment particles cluster. These parameters were adjusted as necessary when fitting the model to the experimental results. Reflectance data gathered first would demonstrate less clustering effects than those taken subsequently that same day. Furthermore, clustering is partially reversible is the cell if left free from an applied field for many hours. In such a case, the mean velocity and standard deviation tend towards the original values of a newly made cell. The final model was used to simulate each experimental condition and values were compared to experiment. This comparison can be found in the following section.  4.2.3 Model Results Figure 4-25, Figure 4-26, and Figure 4-27 below demonstrate the success with which the model, with the simplified assumptions mentioned above, reproduces the experimental results.  64  Model Experiment  Time (seconds) Figure 4-25: Final model results compared to experimental data for red light. The angles labelled represent the incident angle of light at the glass/pigment interface (center of angular range).  65  Model Experiment  0  10  20  30  40  50  60  70  Time (seconds) Figure 4-26: Final model results compared to experimental data for green light. The angles labelled represent the incident angle of light at the glass/pigment interface (center of angular range).  66  Model Experiment  0  10  20  30  40  50  60  70  Time (seconds) Figure 4-27: Final model results compared to experimental data for blue light. The angles labelled represent the incident angle of light at the glass/pigment interface (center of angular range).  The differences in reflectance values between the model and experiment are due to various factors. The first discrepancy stems from the assumption that particle velocities are constant. The experimental time-dependent reflectance shows that particles slow with time as the pigment suspension approaches full compression.  Furthermore, the peak reflectance predicted by the model is consistently higher than that measured experimentally. This indicates that the factor used to account for the time evolution of back surface non-uniformity, found in equation (4-3), is not fully representative of the true experimental conditions. Also, as the detection angle approaches the critical angle, the model overestimates the reflectance. Even beyond the critical angle, the maximum reflectance of test cells does not reach the predicted 100% reflectance. As mentioned earlier, this may be due to some small particles acting as absorbers. The behaviour close to critical is not very well understood and, for all colour  67  filters, the experimental reflectance is lower than the model predicts. It is presently unclear if the underlying cause for the discrepancy in the TIR case is also responsible for the higher model reflectances at angles beneath critical. This should be studied in more detail, as discussed in section 8.1.  Despite these differences, the model is a reasonable approximation of the system and has helped develop the current understanding of particle motion.  4.2.4 Current understanding of modulation at a single interface As described earlier, if the pigment suspension is a highly concentrated paste, an applied field compresses the paste with the emergence of a thin layer of solvent at one of the electrodes. Pigment motion in response to an applied field is the same regardless of incident light, and as such, the explanation of the optical effects observed in both PIR and TIR regimes should be consistent with this motion. While the fine details of particle motion are not entirely understood, the agreement of the interference model with the observed behaviour strongly supports the view that the reflectance in the PIR regime is due to thin film interference. The current understanding of the system stemming from the model is as follows.  Figure 4-28 below depicts the motion of the pigments in suspension when light is at an incident angle beneath critical such that PIR occurs. The cycle begins in Figure 4-28(a) with the system in the so-called absorptive state. A field is applied across the electrodes and the pigments compress to leave a solvent layer along the bottom electrode. Incoming light strikes the glass/pigment suspension interface, where the reflectivity is very low. The reflectance and transmittance from that surface can be calculated using the Fresnel relations, where any transmitted light is quickly absorbed by the pigments. As the effective index of the compressed ink is high relative to the glass, most of the light is transmitted and the cell appears dark.  68  When the field polarity is first reversed as depicted in Figure 4-28(b), the motion of the pigment particles closest to the lower electrode is unimpeded since there is only a solvent layer between the particles and the boundary. The pigments can thus move to the boundary quickly while the rest of the pigment collective above undergoes a slower diffusive migration toward that boundary, with forces of attraction to the electrode and repulsive forces between like charges in competition. As the pigment group drifts to the bottom electrode, represented in Figure 4-28(c), the concentration of pigments at the top electrode drops, creating a thin layer of virtually pure solvent. It is during this apparent growth of solvent layer that thin film interference occurs, and an interference pattern is observed. The boundary between the solvent and the pigment group becomes increasingly non-uniform with time as particles compress with different velocities. Light is scattered and absorbed at this surface, and interference is no longer observed. At this point, pictured in Figure 4-2 8(d), the overall reflectance can be accurately approximated using the Fresnel relations at the glass/solvent interface, since the reflection from the back interface is negligible. Reflectance from the top boundary varies greatly depending on incident angle, but can be very high if the light is incident close to the critical angle. When the field polarity is reversed to the initial configuration, the pigments nearest the solvent/glass boundary can again quickly migrate [Figure 4-2 8(e)], causing the absorptive state to actuate more quickly than the reflective state, as observed in the experimental reflectance time evolution. It seems reasonable to assume that as the solvent region quickly fills with pigment particles of varying sizes, there is never a uniform thin layer to allow thin film interference to occur. The interference is thus only seen at the transition between absorptive and reflective states.  69  (e)L_  _  :  :  Figure 4-28: Motion of the pigments in suspension during the modulation process (a) cell appears dark as pigments are against the top surface, (b) polarity of the field is reversed and pigments close to the electrode easily migrate down, (c) pigment collective begins to pull away from the surface; thin film interference occurs and the cell begins to look bright, (d) interference is no longer observed due to non-uniformity on the back surface, reflection from top boundary observed, (e) polarity of the field is again reversed, pigments close to the top electrode easily migrate towards it and absorb light making the cell appear dark.  70  If the incident light is beyond the critical angle for the glass/solvent interface, the process involved is frustrated TIR and no interference is observed. In this case, Figure 4-28(a) represents the FTIR case where pigments in the evanescent zone absorb incident light. When the field polarity is reversed as in Figure 4-2 8(c) interference does not occur; rather, TIR is fully restored once the pigments migrate out of the evanescent zone. While the underlying physical effect is different depending on whether light undergoes TIR or PIR the overall visual effect is similar.  This chapter has dealt with the reflection modulation of partial internal reflection at a single interface with a pigment suspension as the absorber. Structures such as the cornercubes of interest in this thesis are composed of three interfaces similar to the one studied here. However, due to more complex geometry, the intensity of light and its incident angle on one corner-cube interface is often dependent on its previous interaction at another interface. It is therefore important to explore the reflectance modulation within an array of single interfaces in the appropriate configuration. The next chapter will describe the study of reflectance modulation in multiple reflection systems, and the methods used to model and understand this modulation.  71  5  REFLECTANCE MODULATION AT MULTIPLE INTERFACES  In many conspicuity applications, such as the retroreflective reflectors used on bicycles, light interacts with several interfaces before returning to the viewer. In a system where light undergoes TIR at all interfaces, the light intensity returning to the viewer is the same as the incident light. However, if the conditions for TIR are not met on every interface, light will transmit as well as reflect, resulting in an overall loss of reflected light.  As mentioned previously, the structures used in the work presented here are based on corner-cube geometry, where light undergoes reflections on three interfaces before returning along the incident direction. When this structure is surrounded by air, light entering this sheeting at most incident angles will strike the first interface beyond the critical angle and undergo TIR, strike two more facets where the conditions for TIR are also usually met, creating an overall high retroreflectance. In a reflectance modulating system with pigment suspension, the reflective state occurs when the polymeric sheeting is backed by a fluorocarbon fluid. In such a case, the conditions for TIR are not always met as the refractive index ratio is lower, and light is partially reflected and transmitted on at least one of the three interfaces. The result is a system where both total and partial reflections occur.  The previous chapter described the experimental study and the mathematical model of reflectance modulation at a single interface. This chapter describes the measurement of reflectance of two types of retroreflective sheeting. The experimental measurement technique is presented, as well as the resulting reflectance values. As with the single interface case, the system is modeled to gain further understanding and emulate experimental results.  72  5.1  E x p e r i m e n t a l m e a s u r e m e n t o f r e f l e c t a n c e m o d u l a t i o n at multiple interfaces  To test the feasibility of modulating the reflectance in a multi-interface system where both TIR and PIR occur, the retroreflectance of the two different corner-cube films described in section 2.4 was measured. Test cells described in the next section were filled with air and Fluorinert™ FC-75, and were placed in the measuring apparatus described in this chapter.  To cause reflectance modulation in a multiple interface system, a pigment suspension absorber material such as that used in the single interface test cells is required. For both experimental set-up and model however, it is simpler to first consider the case of the reflective state only to investigate light losses due to transmission at the PIR interfaces. The test cells were filled thus with the Fluorinert™ FC-75 solvent to mimic the reflective state, eliminating the added complications of particle motion. The reflectance of cells containing air was measured first. Cells were subsequently filled with the solvent and remeasured to quantify reflectance losses. The model of the systems was developed to understand the interaction of light at the surfaces before particle motion was considered. This model is discussed in section 5.2.  5.1.1 Micro-replicated  film test cell construction  Test cells made with the micro-replicated sheets were used to measure the retroreflective properties of the two films described in section 2.4. Cells were constructed to enable the structured side of the film to be immersed in media such as Fluorinert™ FC-75 or the pigment suspension. Since the films are flexible, they were laminated on clear glass to prevent sagging. Not only would sagging onto the back electrode result in a short circuit, but the angle of the light entering the film is not easily determined if the front surface is curved. The non-prismatic side of the film was laminated to a glass slide measuring 50 x 50 x 1.5mm using optically clear adhesive , as depicted in Figure 5-l(b) below. The rear 53  slide of the cell was modified depending on the medium inside the cell. If the cell was  73  filled with the pigment suspension, the rear slide had to be coated with conductive ITO to act as an electrode, and leads were attached using conductive epoxy as in the construction of test cells for single interface tests, shown in Figure 5-1 (b). (a)  • wire lead  - spacer tape conductive epoxy  (b) optical adhesive top slide  pigment suspension  Vear slide reflective film  (c)  air or FC-75 matte black paint  Figure 5-1: Micro-replicated film test cell (not to scale) (a) top view, (b) side view when filled with pigment suspension, (c) side view when filled with air or FC-75  If the cell was filled with Fluorinert™ FC-75 or air, where reflectance could not be modified, electrodes were not needed and the rear slide was not coated with ITO. In this case however, the inside of the rear slide was coated with matte black spray paint to absorb any light transmitting through the film, shown in Figure 5-1 (c). Without this absorbing layer, any transmitted light would reflect on the bottom glass interface and reenter the film causing an increase in detected reflection not representative of typical use. The paint more accurately represents the case when the cell is filled with a compressed pigment group since any transmitted light is mostly absorbed by the pigments, as established from the model of modulation at a single interface in the previous chapter.  74  The spacer used in these cells is the same material as used in the single interface test cells, two layers of 30pm polyester tape.  54  Light entering the film can interact with many structures before re-emerging to the detection system. Since some light rays exit from a different structure in the film as much as half a centimetre away from the structure they entered, the size of the test cell was made larger that the single interface cells to ensure this light was detected and to avoid edge effects. The reflection of light off the cells from varying incident angle was measured using the retroreflection measurement set-up described in the next section.  5.1.2 Design of retroreflection measurement experiment Since retroreflected light returns back to the source, measuring the reflection off a retroreflective structure is non-trivial. The placement of the measuring device cannot be in front of the light source, so a suitable measuring method must be devised.  The industry standard for characterising retroreflective sheeting is to place the sheeting in a set-up similar to the schematic shown in Figure 5-2.  55  The sheeting is placed such that  its normal vector is in the plane of the light beam axis. The observation angle ris the angle between the axis of the incident beam and the observation axis, which is the line connecting the sheeting and the detector. The entrance angle y is the angle between the illumination (light beam) axis and the axis normal to the retroreflective film.  Photoreceptor  Source  Retroreflective sheeting  Figure 5-2: Schematic of set-up to measure coefficient of retroreflection for retroreflective sheeting  56  75  Retroreflection is characterized by calculating a coefficient of retroreflection, R , in units A  of candelas per lux per square meter, for specified observation and entrance angles. Table 5.1 below provides examples of coefficients of retroreflection for commercial sheetings with an observation angle of 0.2°. Table 5.1 - Coefficients of retroreflection for typical commercial sheeting given an observation angle of 0.2" at different entrance angles RA for *=0.2°, y= -4°  R for ^ 0 . 2 ° , p= +30°  (Candela/lux/square meter)  (Candela/lux/square meter)  White Engineering Grade  98.0  67.6  White High Intensity Grade  305.4  270.3  White Microprism  308.3  97.9  Type of sheeting  A  While this coefficient of retroreflection is useful for material comparison, it does not have the feature of being an intuitive number in itself. It does not in fact represent the actual retroreflectance since the detection system is not along the same axis as the light source. Furthermore, the size of the available sources and detectors during the course of this study would have required an impractically long distance from the light source to the sample to obtain an observation angle of 0.2°.  A method of measuring true retroreflectance in percentage of incident light returning to the source is used in the context of this thesis. The set-up made use of a partially silvered mirror tilted at 45°, as depicted in Figure 5-3. The light source was placed above the mirror and the sample was positioned on the opposite side. A photodetector was placed as shown in Figure 5-3. Light exiting the source partially transmits through the mirror as well as partially reflects, but this reflected light is absorbed, as shown in Figure 5-3(a). Light strikes the sample, undergoes retroreflection, and returns to the mirror where it again partially transmits back to the source, and reflects towards the detector where it is measured, illustrated in Figure 5-3(b).  76  . absorbei  partially silvered mirror  photodetectoi  sample  rotating stage  (a) absorber  source  partially silvered mirror  photodetectoi  (b)  rotating stage  Figure 5-3: Schematic of set-up to measure true retroreflection (a) light strikes a partially silvered mirror and is partly transmitted to the sample (b) light reflecting off the sample is partially reflected to the detector  A mirror of known reflectance was used to calibrate the measurements, allowing relative retroreflection percentages to be easily calculated.  Since retroreflection depends on the entrance angle of the incident light, a range of angles was investigated. The sample was placed on a rotating stage, allowing a change of the entrance angle. A n entrance angle of 0° corresponds to light entering normal to the sample, positive angles occur when the sample is rotated in one direction, and negative angle when it is rotated in the opposite direction, as shown in Figure 5-4.  77  negative angles  positive angles  Figure 5-4: Entrance angle definition depending on rotation  direction  The light source used in the experiment is a commercially available red diode laser with a 57  center wavelength of 653nm and oval shaped beam size with major axis o f l . 6 m m .  j;  A  laser was chosen because its high degree of collimation allows for more precise knowledge of entrance angle. However, the laser light is mostly linearly polarized as opposed to typical unpolarized lighting conditions. In order to accurately represent unpolarized light, reflectance values from linear polarizations perpendicular to each other are averaged, as in equation (2-13). Experimentally, a linear polarizing filter was placed in the beam path to ensure that only one polarization was present when measurements were performed. The laser and polarizer were then rotated 90° and the measurements were repeated. The average of values of both orientations gives an excellent estimate of the reflectance of unpolarized incident light. The detection signal was measured using the same T S L 250 integrated circuit described in section 4.1.3, placed in an integrating sphere. The integrating sphere had a cylindrical 58  shape and was lined with three layers of diffusely reflective sheeting,  as depicted in  Figure 5-5. Light entering the cylinder undergoes several diffuse reflections such that the intensity of light becomes quite uniform within the cylinder. The detector provides a voltage proportional to the light intensity entering the cylinder. Since the reflectance was calculated by dividing the measurement signal by a reference signal using the same light source, the efficiency of the detection system does not need to be considered.  78  (a)  TSL 250 detector (b)  Figure 5-5: (a) Integrating sphere to measure light intensity, (b) cross-sectional view  This detection system was placed 30.5cm from the incident beam line. Since the cylinder opening has a diameter of 1.90cm, the detector accepts light with a half angle of 1.8° from the center of the light beam, as depicted in Figure 5-6.  <  30.5cm  >  Figure 5-6: Acceptance angle for light detection in retroreflection measurement set-up  The experimental set-up described in this section was used to measure the retroreflection of various samples, discussed in the following section.  79  5.1.3 Static reflectance measurements Using the set-up described above, the retroreflectance of test cells made with both cornercube films was measured and compared to a reference mirror for normalization. Figure 59  5-7 below depicts the normalized reflectance as a function of entrance angle for a Diamond Grade™ cell filled with air (squares and diamonds) and the same cell filled with Fluorinert™ FC-75 (triangles and circles). As mentioned in section 2.4, both film types possess one distinct axis known as the primary groove. The orientation of the sheeting was considered when the samples were rotated to measure the reflectance from different entrance angles. The two different data curves for each medium in Figure 5-7 represent the reflectance when the axis of rotation (in the plane of the film) is parallel and perpendicular to the primary groove. The curve labelled "air, parallel", for example, represents the reflectance of the test cell filled with air measured with the axis of rotation parallel to the primary groove of the sheeting. The orientation of the structures affects the resulting reflectance at angles other than normal incidence. It should be noted that the rotation stage used during measurement rotated in only one direction corresponding to negative entrance angles. To measure the retroreflectance for the positive angles, the sample was rotated 180° about its normal axis for each entrance angle, since both geometries are equivalent.  The reflectance results of Diamond Grade™ are shown in Figure 5-7 while those of the M F C A experimental film are shown in Figure 5-8. As expected, the reflectance of both cells filled with air is greater than the reflectance when filled with Fluorinert™ FC-75. As mentioned earlier, the higher index of the FC-75 changes the critical angle at the interface resulting in a system with light undergoing both PIR and TIR. Any light transmitted during PIR is absorbed by the black backing of the test cell and hence is not detected.  80  1 0.9 0.8 0.7 0.6  B air, parallel  0.5  • air, perpendicular A. FC-75, parallel  0.4  -5P—:«—ft-  ft  0.3  • FC-75, perpendicular  •  fi  0.2  1  0.1 0 -14 -12 -10 -8  -6 -4 -2  0  2  4  6  8  10 12 14  Entrance Angle (degrees)  Figure 5-7: Measured reflectance vs. entrance angle for Diamond Grade™ cell filled with air and FC-75. Data was taken with axis of rotation parallel and perpendicular to the primary groove. 1 0.9 0.8  9  a  a 0.7  -+•*  u <u «S  0.6  W  Pi 0.5  T  ft  *  ft ft ft ft  ft ft ft ft ft  fi  B air, parallel • air, perpendicular A FC-75, parallel  V N  "3 0.4 S u  o Z  • •  0.3 0.2 0.1 0  1A 1  • A 1  14 -12 -10  A 1 -8  • FC-75, perpendicular  • • A A 1 -6  •  A  -4  •  1 -2  i  0  •  A  2  4  A 1 6  A 8  A  A  I  i  10  12  A 14  Entrance Angle (degrees)  Figure 5-8: Measured reflectance vs. entrance angle for MFCA cell filled with air and FC-75. Data was taken with axis of rotation parallel and perpendicular to the primary groove.  81  Figure 5-7 and Figure 5-8 provide important information about the retroreflectance of these samples. When the cells are filled with air, the retroreflectance of the M F C A film is greater than that of Diamond Grade™ (demonstrating it is a superior retroreflector). However, both types of sheeting experience significant decreases in retroreflection when the cells are filled with Fluorinert™ FC-75.  In the case of Diamond Grade™ structures immersed in FC-75, the reflectance is about 2% for entrance angles between 2° and 10°. When the sheeting is placed such that the axis of rotation and the primary groove are parallel, reflectances begin to increase for entrance angles greater than 8°. It could be that for these entrance angles, light is refracted into the film such that it is beyond the critical angle for more facets than it would at smaller entrance angles.  When the M F C A structures are immersed in FC-75, the two rotation directions show different reflectance characteristics. When the axis of rotation is parallel to the primary groove, the retroreflection is about 4% for most entrance angles. When the axis of rotation is perpendicular to the primary groove, a higher reflectance of 20-32% is observed for entrance angles of 8° to 12°. This is most likely due to the same effect as described above for Diamond Grade™: TIR can occur more often (and hence PIR less often) at these entrance angles. Near normal incidence (2° entrance angle), the average reflectance of M F C A in FC-75 is 9%.  While the M F C A film retroreflection is much greater than that of Diamond Grade™ when cells are filled with FC-75, it are nevertheless too low for an effective retroreflector, and enhancement is needed for use in a conspicuity application such as traffic control signs. Possible enhancement of reflectance is discussed in the following chapter.  The cells used above lacked the conductive ITO coating required in a modulating system. By visual inspection of the films, it was noted that the ITO coated film had a higher reflectance than non-coated samples when the structures are immersed in FC-75. A test  82  cell of ITO coated Diamond Grade™ was therefore constructed and its reflectance was measured using the same set-up.  Figure 5-9 shows the improved reflectance of ITO coated films for cells filled with F C 75. It was assumed that the light did not interact with the clear thin ITO layer, however, reflectance values more than doubled. It is conceivable that constructive interference is responsible. 0.4 0.35  • ITO, parallel • ITO, perpendicular A no ITO, parallel  0.3  • no ITO, perpendicular  e SJ CU  0.25  cu T3  0.2  -A.  A  •  CU  N  0.15 O  0.1  •  0.05  • •  JL  JL  A  •  9 • A  •  A  0 -14 -12  -10  -8  -6  -4  -2  0  2  4  6  10  12  14  Entrance Angle (degrees)  Figure 5-9: Measured reflectance vs. entrance angle for ITO coated Diamond cell filled with FC-75.  Grade™  Data was taken with axis of rotation parallel and perpendicular  to  the primary groove.  5.2  Modeling retroreflection  In a system with complex geometry such as the retroreflecting sheeting, the most efficient way of modeling the reflectance is to use a computer raytracing program. Computer raytracing calculates the change in flux of rays as they strike surfaces and split into component reflected and transmitted rays, which in turn can strike other surfaces.  83  Because of the exponentially increasing number of rays to track, the computational size soon becomes unmanageable. Thresholds can be implemented but, despite this, the time and computational power required to calculate resulting flux can be unrealistically large. This problem is addressed by restructuring the model into a Monte Carlo simulation, a well known statistical implementation. In the case of raytracing, surface properties such as reflectance, transmittance and absorption are attributed statistical weights. A light ray striking a surface will not be split, but undergo only one path determined using the statistical probabilities of various outcomes. Tracing a large number of rays therefore decreases statistical variation in the resulting light distribution.  To model the corner-cube based retroreflective sheeting used in the test cells, the three dimensional structures where drawn using A u t o C A D ® ,  60  a computer aided design  program. The structures were subsequently imported into a commercial raytracing software TracePro®.  61  This raytracing software has the capacity to execute both ray  splitting and Monte Carlo ray traces. The Monte Carlo approach was used in this work.  5.2.1 Model set-up As discussed above, the design of the experimental retroreflection measurement set-up cannot place the detector and source in the same position. In computer software such as Tracepro®, it becomes possible to place a "detector" surface in front of the source since flux can be monitored at any point in space of the model. However, in order to properly account for stray light rays that might interact with the mirror such that they are detected in the experimental set-up, it was decided to model the layout as accurately as possible. This also allowed for modifications in the experimental set-up to be easily adapted in the model. Figure 5-10 below shows the typical model set-up.  84  . :  source  ^  partially silvered mirror  to detector  Figure 5-10: Typical model set-up in Tracepro®  A collimated beam of light with a wavelength of 653nm was used to simulate the experimental laser. The beam spot area was approximately 6mm . Since the microstructure surface area ranges from approximately 0.03-0.1mm depending on the type sheeting, the incident light strikes from 60 to 200 individual structures. Reflections within the material can easily spread to involve structures much further away in the sheeting. Due to the large computational power needed to model such three dimensional structures, modeling more than 300 individual corner-cubes becomes impractical. If the beam spot size were to be modeled to scale, over 1000 corner-cubes would need to be modeled to ensure internal reflections were properly accounted for, which is computationally too demanding. However, relative scaling of the beam size to the microstructure is unimportant so long as there are no edge effects and the spot shines onto more than just a few structures. This was confirmed in the model by varying the size of the light source,relative to the structures and comparing resulting reflectance values. For the implemented raytracing, the incident light beam covered approximately 30 corner-cubes, while the sheeting in total consisted of roughly 200 structures. Model results repeated with a light source 80% to 120% of this size yielded identical results, as expected.  Figure 5-11 below is an example of the light beam size compared to the  sheeting used in the model.  85  Shape of light source  Figure 5-11: Typical light beam size relative to structures in the Tracepro® model  While the number of structures in the incident beam area need not be to scale, the incident beam size relative to detector size and distance from the sample must be to scale. Since light is reflected from the sample with an angular distribution, the placement and size of the detector determines how much light is collected in both model and experiment.  Experimental data was taken for test cells filled with air and Fluorinert™ FC-75, and a model of each of these cases was created. Modeling the air cell was done simply by modeling the sheeting alone since any empty space in the model is assumed to be air. In the experimental set-up, rays transmitting through the sheeting could be reflected from the bottom surface if the cell backing had not been painted black. In the model on the other hand, transmitting light never strikes another surface, hence no absorbing backing was required. To create a three dimensional model of the cell filled with Fluorinert™ FC-75, the structured surface was subtracted out of a solid block in AutoCAD®. The resulting structure was assigned the optical properties of Fluorinert™ FC-75 in TracePro®, and was placed in contact with the structured surface, leaving no air gap, as shown in Figure 5-12.  86  < '• • .  \,  / v  y  v: v ' \ / \ " ~v v  ^  7  V - \ /  v-  \,• *  sheeting solvent layer  Figure 5-12: Modeling ofFC-75 behind structured surface (see text)  The Monte Carlo simulation with 150,000 rays was run for samples rotated from 0° to 14° in 2° increments as in experiment. As mentioned previously, the sheeting has one distinctive axis, and the reflectances differ if the axis of rotation is parallel or perpendicular to the primary grooves. Modeling was preformed for both orientations and results are given in the next section.  Absolute retroreflectance was calculated in the model by dividing the flux value at the detector surface by the maximum possible flux detectable in the model.  87  5.2.2 Model results The retroreflective films consist of an array of corner-cube structures. Light rays enter the film and reflect from multiple structures before re-emerging from the sheeting. Since the model keeps track of ray paths, it provides not only the detected flux, but also information about each ray's interaction history within the structure. Many light rays follow a path consisting of multiple reflections within the film and yet do not emerge in the expected retroreflected direction. In this case, the rays undergo a path similar to specular reflection and thus are only detected when light enters at normal incidence. For this entrance angle, the light detected is greater than expected from the front surface reflection alone. Figure 5-13 below is a sketch representing the shape of detected light predicted in the model for 0° entrance angle. This pattern was also observed experimentally. The multiple bright spots are indicative of complicated ray paths with light re-emerging from different sections of the film. These specularly reflected rays are responsible for the reflection peaks in both experimental and model results.  *  *  K. Figure 5-13: Predicted pattern of detected flux for entrance angle of 0°  Figure 5-14 shows the model results compared to experimental data when the test cells are filled with air. For all entrance angles, the experimental results are lower than the model by about 15%. The angular spread of light observed experimentally at the detector surface was greater predicted, suggesting a scattering effect. Slight imperfections in the films could cause scattering. If a surface is manufactured such that its normal vector differs from the design by even afractionof a degree, the consequential shift in angle of reflected light over many such interfaces could result in light no longer undergoing TIR at a particular surface. Moreover, the resulting direction of the exiting ray can be shifted causing the light to escape detection. Surface dirt and scratches could also cause  88  scattering within the films. Furthermore, the model assumes no bulk absorption. Any light experiencing long path lengths within the material could experience absorption in reality. The modest discrepancies between experimental data and model results are presumably due to the interaction of light rays with a great many structures such that minute surface defects cause scatter and thus create observable differences.  When the cells are filled with Fluorinert™ FC-75 (discussed below), surface scattering no longer contributes significantly. This is most likely due to the fact that the light ray does not frequently undergo TIR, and in the case of PIR further from the critical angle, a small change in incident angle does not change the reflectance as significantly as near the critical angle. Moreover, any surface impurities adhered to the surface in the air cell can be removed by the presence of a liquid, causing less surface scattering.  l 0.9 0.8  m -»-  A  0.7 0.6 0.5 O M o d e l , parallel  0.4  • M o d e l , perpendicular A Experiment, parallel  0.3  • Experiment, perpendicular  0.2 0.1  0  "i  -14 -12 -10 -8  -6  -4  1  i  i  -2  0  2  4  6  8  10  12 14  Entrance Angle (degrees)  Figure 5-14: Modeled and experimental reflectance ofMFCA cell filled with air when the axis of rotation is parallel and perpendicular to the primary groove  89  1 0.9 0.8 4>  u  e  CS +^ ii  53  0.7  H Model PG shifted  0.6  • Model PG exact  a  O  & 0.5  *  U  1  9  «  • Experiment  E3  •a a  E o  0.4  •  •  •  •  •  •  •  •  •.  0.3  S  0.2 0.1 0  — i  1  14 -12 -10  1  1  1  1  1  1  1  1  1  1  1  -8  -6  -4  -2  0  2  4  6  8  10  12  1  14  Entrance Angle (degrees)  Figure 5-15: Modeled and experimental reflectance of Diamond Grade™ cell filled with air when axis of rotation parallel to primary groove. Model was run with the sheeting misaligned by 2.5° (Model PG shifted). Predicted values for perfect alignment between primary groove and axis of rotation are labelled "PG exact".  90  1 0.9  43-  0.8  0>  c u 0»  0.7 0.6 0.5  0  0.4  "° -  E so 0.3  X  5 —  • •  —  a •  —  • •  •"  •  •  •  •  •  •  *  4  6  •  • Model • Experiment  0.2 0.1 0 .14  .12  -10  -8  -6  -4  -2  0  2  10  12  14  Entrance Angle (degrees) Figure 5-16: Modeled and experimental reflectance of Diamond Grade™ cell filled with air when the axis of rotation is perpendicular to primary groove  While the reflectance values measured experimentally are lower than predicted, the reflectance trend versus entrance angles is identical except for a few data points in Figure 5-15. These small discrepancies can be explained by a misalignment of the test cell. In experiments, the primary groove was aligned to the axis of rotation by eye, easily allowing for an unintentional shift of a few degrees. To verify this claim, the model orientation was shifted such that the primary groove and rotation axis were 2.5° apart. The results, which are also shown in Figure 5-15 labelled "model PG shifted", clearly show a decrease in reflectance due to misalignment now matching the experimental trends.  Figure 5-17, Figure 5-18, and Figure 5-19 below show the model results compared to experimental data for cells filled with FC-75. There is excellent agreement between the two except for a few data points in the M F C A sheeting results. As when immersed in air, these discrepancies can be explained by a misalignment of the experimental test cell. 91  0.5 0.45 • Model, parallel  0.4  • Model, perpendicular  4>  • Experiment, parallel  c8  • Experiment, perpendicular  u 0.35 S +J  u  01  Pi 13  0.3 0.25  • A  ik  o> N  0.2 i-  ©  0.15 0.1 0.05 0  A  ali  •• •  • • 1  14 -12 -10  1 • •  1  -8  f  -6  -4  -2  0  1  1  1  1  1  2  4  6  8  10  • 12  14  Entrance Angle (degrees)  Figure 5-17: Modeled and experimental reflectance of Diamond Grade™ cell filled with FC-75 when the axis of rotation is parallel and perpendicular to primary groove  92  0.5 0.45 0.4 cu w  C  at +* u CU  ES  0.35  •  •  •  •  0.3  • Model PG shifted  CU  • Model PG exact  0.25  • Experiment  cu  .a  0.2  !- 0.15 o  _4L  0.1 0.05 0 -14  -12  -10  -8  -6  -4  -2  0  2  4  6  10  12  14  Entrance Angle (degrees)  Figure 5-18: Modeled and experimental reflectance of MFCA the axis of rotation is perpendicular  cell filled with FC-75 when  to primary groove. Model was run with the sheeting  misaligned by 2.5° (Model PG shifted). Predicted values for perfect alignment between primary groove and axis of rotation are labelled "PG exact".  93  0.5 0.45 0.4 a  c -t^ u  ii  0.35 0.3  53  (LP £ 0.25  Q Model • Experiment  •  CU  N • PN 0.2  "CS  s  0.15  z  0.1  o  0.05  1  ?  $1  $  if  ft  -m-  0  ~i  -14 -12 -10  -6  -4  -2  0  ii -1  r  2  4  6  ? 1  $  $  QJ  1  1  1  10  12  14  Entrance Angle (degrees)  Figure 5-19: Modeled and experimental reflectance for MFCA cell filled with FC-75 when the axis of rotation is parallel to primary groove The model and experiment agree very well, implying that any scattering effects observed for cells in air are not significant when cells are filled with Fluorinert™ FC-75.  From this data, it is clear that partial reflections off multiple interfaces cause much lower overall reflectance in retroreflecting geometries than from a single interface. A method of increasing the reflectance, required for practical applications, was developed and is presented in the following chapter.  94  6  ENHANCEMENT OF REFLECTANCE MODULATION AT MULTIPLE INTERFACES  While the modulation of partial internal reflection at a single interface can potentially yield high contrast for incident angles approaching critical, in a more complicated structure with multiple reflections, the overall light loss due to light transmission into the absorbing ink becomes too significant. A method of enhancing the overall reflectance without significantly impacting the contrast ratio has been developed and is described in this chapter.  6.1  Enhancement by aluminium deposition  If a surface is coated with an aluminium layer with a thickness greater than 200nm, its reflectance in the visible light range is approximately 90%, with the remaining 10% being absorbed.  62  While this is not as efficient as TIR, in which virtually 100% of the light is  reflected, the 90% reflectance could represent a significant gain if the light would have otherwise undergone only a partial reflection at that interface. However, the reflectance of a surface with such an aluminium layer is constant regardless of material placed behind the aluminium. An aluminized surface therefore can not be modulated to an absorptive state. Thus, if all surfaces of the retroreflective corner-cube sheeting were coated in aluminium, the system could never be modulated.  Possible enhancements in a multi-surface system must be optimized such that the absorptive state is not brightened too much from the aluminium, while increasing the overall reflectance. Two solutions that have the potential to accomplish this are as follows.  The first consists of depositing a thin layer of aluminium onto all facets; a layer thin enough to allow transmission and therefore allow modulation to occur, but thick enough to enhance reflectivity. This was first attempted on the structured surfaces without much success. When an enhancement in reflective state was observed, the absorptive state was 95  severely compromised. This type of aluminization was therefore investigated more closely on a single interface test cell without the complicated geometry.  Two glass slides were coated with a thin layer of aluminium using evaporative deposition from a heated tungsten filament in a vacuum chamber with a pressure of approximately 8 x 10" Torr. The transmission at normal incidence was measured by comparing light 4  intensity differences as the slide was placed between a diffuse source and the detector. Resulting values are listed in Table 6.1.  Table 6.1 - Transmission of light through slides with thin layer of aluminium Transmission at normal incidence  Cell type Glass cell, no aluminium  93 ± 2%  Slide 1  89 ± 2%  Slide 2  80 ± 2%  These aluminized slides were then used to make a test cell, with the bottom slide spray painted black for the same reasons discussed in section 5.1.1. The aluminium was inside the cell as it would be in the case of an aluminized structured surface. An air gap was left between the slides and the reflectance was measured using the single interface reflectance measurement set-up described in section 4.1.2 at angles listed in Table 6.2. Measurements for the cells filled with air were recorded. Next, the gap was filled with Fluorinert™ FC-75 solvent to simulate the reflective state of a modulating system. The reflectance values for each cell at the different angles are shown in Figure 6-1 below. The three bar types in the chart represent the three cells: one without aluminium, cell 1 made with slide 1 and cell 2 made with slide 2. Each set of three bars represents the data for a given detection angle and filling material.  96  Table 6.2 -Incident angles of light used in reflection measurements and the corresponding description used in Figure 6-1 Description of angle TIR angle  Approximate angle 1.6° greater than the critical angle for glass/FC-75 interface  PIR angle 1  0.2° smaller than the critical angle for glass/FC-75 interface  PIR angle 2  0.7° smaller than the critical angle for glass/FC-75 interface  linium  TIR angle, backed by air  TIR angle, PIR angle 1, PIR angle 2, PIR angle 1, PIR angle 2, backed by backed by air backed by air backed by backed by FC-75 FC-75 FC-75 Detection angle, gap material  Figure 6-1: Comparison of reflectance values for cells with a partial aluminium layer to cell without aluminium at various detection angles. Cells were filled with air and FC-75.  Unfortunately, such a thin layer of deposited aluminium does not enhance the reflective state, but instead acts as an absorber to diminish the reflectance. Figure 6-1 clearly shows that the aluminized samples (striped bars) do not demonstrate a higher reflectance than the cell without aluminium (solid bar). A plausible cause is the deposition technique  97  used to make the cells. During evaporative deposition, aluminium adheres to the substrate best at high deposition rates of 2.5nm per second or greater. However, when evaporating a 5nm layer, a deposition rate one tenth this ideal rate is required, potentially affecting the layer properties. Furthermore, the formation of an oxide layer could also contribute to the lack of enhancement since light comes into contact with this layer.  The quality of aluminium deposition was subsequently tested by depositing 250nm of aluminium on a glass slide and measuring the reflectance at normal incidence using the retroreflection set-up described in section 5.1.2. The measured value was compared to a reference mirror of known reflectance to calculate the absolute reflectance. The reflectance of the aluminized side of the slide was the expected 92%; however, only 83% of light passing through the glass and striking the aluminium layer was reflected. A surprising result, since the front surface reflection from the glass should contribute to an overall increase in reflectance. These results indicate that the reflectance from the aluminium through the slide is about 10% lower than expected. Possible causes are poor adhesion of aluminium to the surface or possible contamination of the surface from impurities in the deposition chamber, as discussed further in the future work chapter.  Should future work provide insight into eliminating the extra absorption in the aluminium layer, this type of enhancement should be revisited. In the meantime, a second enhancement method is proposed. This method consists of depositing a 200nm thick layer of aluminium directionally only on selected facets of the structures. Light entering the film interacts with both aluminized and non-aluminized surfaces. The reflection from aluminized facets generally improves reflectance over PIR, and interactions at nonaluminized facets allow for modulation to the absorptive state as before. As long as the overall increase in retroreflectance does not significantly brighten the absorptive state, the contrast ratio is not adversely affected.  There are many possible choices of which facets to coat with aluminium. It is possible to model the reflectance of these aluminium configurations on the films using the raytracing  98  technique described in section 5.2.1. Such modeling was preformed to establish the most effective enhancement scheme, described in the next section.  6.2  Modeling reflectance enhancement  Enhancement of PIR was optimized using the Monte Carlo raytracing described in section 5.2 to model the reflection of retroreflective sheeting aluminized in various configurations. With the model validated by the results of non-enhanced test cells filled with Fluorinert™ FC-75, it was surmised that the model results for aluminized samples could be trusted to optimize the positioning of aluminium.  In order to simulate aluminization, facets intended to be coated with a thick layer of aluminium were assigned the surface reflectance of aluminium (90%). Raytraces were preformed for various entrance angles. Figure 6-2 and Figure 6-3 show the results for two possible aluminization configurations for Diamond Grade™ sheeting. In the first configuration aluminium is deposited on the primary facet of half the structures, and the secondary facets on the other half are coated (Figure 6-2). The second configuration, in which the only the facets along the primary groove are coated, offers a greater enhancement according to the model (Figure 6-3).  99  cu cu  C 0.7  5  cu cu  5=  0.6  CU  TJ  • perpendicular  0.5  | A parallel  cu  i 13 £  0.4  o 0.3  z  Jl  0.2  j * *  •_  i  i  "  A  0.1 0  I14  i  -12  1—  -10  —i  -6  -4  -2  0  2  4  6  10  1  12  1  14  Entrance Angle (degrees)  Figure 6-2: Modeled reflectance of Diamond Grade™  with aluminium on half the  primary facets and half the secondary facets. Predicted reflectances are given when the rotation axis is parallel and perpendicular  to the primary  groove.  100  1 0.9 0.8 <u u  B  0.7  C5>  CJ CJ  C  CJ T3  .a la o  0.6 A  0.5  •  0.4  • perpendicular  A  •  •  •  A parallel  * A • • •  A  0.3  •  •  0.2 0.1 0 0  • 1  1  -14 -12 -10  1  1  1  1  1  1  1  1  1  1  1  1  -8  -6  -4  -2  0  2  4  6  8  10  12  14  Entrance Angle (degrees) Figure 6-3: Modeled reflectance of Diamond Grade™ with aluminium on all primary facets. Predicted reflectances are given when the rotation axis is parallel and perpendicular to the primary groove.  As with the results presented in section 5.1.3, the curves labelled "parallel" represent the reflectance values for entrance angles with the axis of rotation parallel to the primary groove of the structure. Similarly, the curves labelled "perpendicular" are the results when the axis of rotation is perpendicular to the primary groove.  The geometry of the M F C A film also easily allows for half of the corner-cubes to have the primary facet aluminized while the other half to have the two secondary facets coated. For this case, the model predicts as much as 18% higher reflectance than Diamond Grade™ aluminized in the same manner. Figure 6-4 below shows the reflectance as a function of entrance angle predicted by a raytracing simulation of such a coating configuration. The labelling convention is the same as before.  101  1 0.9 0.8 0.7 u  4)  0.6  OS 0,5  -D-  0.4 E  o 0.3 0 Z  •  • perpendicular  -Q"GI  •  •  A parallel  •  •  0,2 0.1 0  A 1  1  -14 -12 -10  1  1  1  1  1  1  1  -8  -6  -4  -2  0  2  4  r~  6  — i  10  A 1  1  12  14  Entrance Angle (degrees) Figure 6-4: Modeled reflectance of MFCA  with aluminium on half the primary facets,  and half the secondary facets. Predicted reflectances are given when the rotation axis is parallel and perpendicular  to the primary groove.  In Figure 6-4, there is no significant predicted reflectance increase for positive entrance angles when the rotation axis is parallel to the primary groove. This result is not surprising since the aluminium deposition is not symmetric about the primary groove.  It is of course important to ensure that any aluminium deposition configuration modeled is physically realizable. This is discussed further in the next section, where a description modeling aluminium deposition is presented.  6.3  Modeling aluminium deposition  Modeling the reflectance of virtually any configuration of aluminium coatings is possible, however, only a few combinations of selective deposition are physically possible without masking. All surfaces in direct line of sight with the evaporative source will be coated. 102  For example, coating only the primary facets of the Diamond Grade™ sheeting is impossible without masking. The physical deposition onto a sample in a particular orientation in the deposition chamber was modeled using the raytracing program. Aluminium evaporates from a point source in a Lambertian distribution. Raytracing software can model deposition by using a Lambertian light source to simulate an evaporative source. The corresponding light distribution incident on each surface represents the resulting deposition on that surface. Figure 6-5 below is an example of the "deposition" pattern predicted by this model when Diamond Grade™ sheeting is oriented to aluminize half the primary facets. The dark regions represent the areas with deposition on the facets, with darker greys corresponding to greater deposition.  Figure 6-5: Predicted deposition of aluminium on selected facets of Diamond sheeting. Darker regions represent areas of greater  Grade  T  deposition.  As mentioned earlier, depositing aluminium on only primary facets is not possible without masking since secondary facets are always also in direct line of sight with the source. The sample was thus oriented as depicted in Figure 6-6 to minimize unwanted aluminium on the secondary facets. The dark features in Figure 6-7 represent the modeled deposition distribution for this orientation, while Figure 6-8 shows the experimental results, in which unwanted aluminium on secondary facets is also visible.  103  aluminium source  Figure 6-6: Orientation of sheeting in evaporation chamber to aluminize mostly the primary facets  104  Aluminized primary facets  Figure 6-8: Actual deposition of aluminium on primary facets of Diamond  Grade™.  Some unwanted aluminium can be seen on secondary facets, as in Figure 6-7.  The aluminium on secondary facets compromises the absorptive state, and hence contrast ratio. This aluminization geometry is therefore unfavourable for practical reflection enhancement. In addition, due to the steep deposition angle, the effective deposition rate is not very high. As mentioned earlier, aluminium deposition adheres to the substrate more effectively at deposition rates exceeding 2.5nm/sec. The low effective deposition rate causes problems in the adhesion of aluminium to the surface.  Of possible configurations, the one pictured in Figure 6-5 can be applied to both films. Of the two, M F C A film is predicted to provide a greater reflectance enhancement (see Figure 6-3), and is therefore considered more promising. For completeness, the retroreflection was experimentally measured for all enhancement geometries mentioned in this section.  6.4  Experimental measurement of reflection enhancement  The aluminium deposition enhancement was applied to several samples of Diamond Grade™ and M F C A . Diamond Grade™ samples were aluminized in the two patterns pictured in Figure 6-5 and Figure 6-7. The M F C A film was aluminized analogously to the Diamond Grade™ deposition configuration illustrated in Figure 6-5. The retroreflectance of the samples was measured to establish the degree of enhancement.  105  6.4.1 Static reflectance measurements Test cells were made as described in section 5.1.1 and filled with Fluorinert™ FC-75 to mimic the reflective state of a modulating cell. The reflectance was measured using the set-up described in section 5.1.2, and reflectance data was collected with the axis of rotation parallel and perpendicular to the primary groove as done in the non-enhanced test cell measurements.  Reflectance values for various entrance angles are compared to the non-enhanced test cells also filled with Fluorinert™ FC-75 in Figure 6-9 for M F C A sheeting and in Figure 6-10 and Figure 6-11 for Diamond Grade™. In the case of M F C A (Figure 6-9), it can be seen that there is no enhancement for positive entrance angles when the axis of rotation is parallel to the primary groove as predicted by the raytracing model (Figure 6-3). 0.4 0.35  S  e +•» u  CU  jg S  •  A  o A  z  •  0  0  A  0.25  0  0.2  A  A  o  0  ®  © <>  0.15 0.1  0  •  <•  0.05  O  •  •  U  • 1  1 14  -12  • No A l , parallel • No A l , perpendicular  A B  u ©  •  0.3  53  <u -O  •  -10  -8  -6  i  -4  w  A •  •  •  1 -2  1 0  a A l , perpendicular  *  •  A A l , parallel  •  A  LJ  ID  B  O A  1  1  i  I  1  2  4  6  8  10  • A 12  • A 14  Entrance Angle (degrees)  Figure 6-9: Experimental reflectance of MFCA cell, without aluminium (No Al) and with aluminium (Al) on halfprimary facets and half secondary facets, filled with FC-75. Measurements taken with axis of rotation parallel and perpendicular to the primary groove.  106  0.4 0.35 cu u  0.3  a  M •w u  JB  0.25  CU  C cu  Pri T3 cu  a  o  z  II No Al, parallel • No Al, perpendicular  0.2 i  A Al, parallel O Al, perpendicular  0.15 *  0.1  A  £  A  H  0.05  9  0  *  i  -14 -12 -10 -8  -6 -4  $  * —  2  i  0  —  i  2  A  A-  TH  $ 3 —  i  —  4  i  —  6  a  • i  —  8  i  —  • i  —  i  10 12 14  Entrance Angle (degrees)  Figure 6-10: Experimental reflectance of Diamond Grade™ cell, without aluminium (No Al) and with aluminium on halfprimary facets and half secondary facets (Al), filled with FC- 75. Measurements taken with axis of rotation parallel and perpendicular  to the  primary groove.  107  0.4 0.35  S  0.3  e a  1  5  1S  • No A l , parallel 0.25  A A l , parallel 0.2  cu N  0.15  La  I  • No A l , perpendicular I Q Al, perpendicular  ii  A  e  a  <•  •  .14  .12  0 •  0.1 0.05 0  •  o  •  a  0  ™  • .1  i  I  I  -10  -8  -6  A  9 -4  A  I  '  1  i  -2  0  fl  A A  9 1  1  2  4  i 6  • • i  • 10  • • 12  14  Entrance Angle (degrees)  Figure 6-IF Experimental reflectance of Diamond Grade™ cell, without aluminium (No Al) and with aluminium on primary facets (Al), filled with FC-75. Measurements taken with axis of rotation parallel and perpendicular  to the primary groove.  While the overall trend of each reflectance curve is virtually identical to the model results shown in Figure 6-4, the reflectance values are lower by almost a factor of 2. This is because the aluminium is much more absorbing than expected, as discussed in section 6.1. When the test cell is filled with air, the experimental results are again much lower than predicted, as shown in Figure 6-12 for M F C A and Figure 6-13 for Diamond Grade™. In fact, there is little difference experimentally when the cell is filled with air or Fluorinert™ FC-75. This suggests that the enhancement is successful in so far as there are no longer large differences in reflectance between cells filled with air versus FC-75. Moreover, the measured reflectance of enhanced M F C A is 22% on average, an encouraging 18% greater than non-enhanced film.  Another difference between model and experiment is the exact deposition distribution. A one degree error in aligning the sheeting in the chamber results in part of the facet to be  108  unintentionally shadowed resulting in a partially coated surface. Moreover, the source used is not a point source, but rather an extended filament, causing unwanted deposition on some facets.  1 0.9  *  0.8  cu u  csj •*-»  u cu  * *  ¥  e 0.7  * *  v  0.6  53 0.5 cu cu N  ©  • Model, parallel • Model, perpendicular  0.4 0.3 0.2  A Experiment, parallel • Experiement, perpendicular  A  /  1  &  S  '*  *  '*'  •  *  *  A  A  ^  A -A  0.1 0  i i i ; i i i > i i i i i i -14 -12 -10  -8  -6  -4  -2  0  2  4  6  8  10  12 14  E n t r a n c e A n g l e (degrees)  Figure 6-12: Modeled and experimental reflectance for enhanced MFCA air,  when the axis of rotation is parallel and perpendicular  cell fdled with  to the primary groove  109  1  0.9 D Model, parallel  0.8  • Model, perpendicular  u  A Experiment, parallel  e 0.7 u  • Experiment, perpendicular  0.6 0.5  N L.  O  -cr  •  0.4  • •  0.3 0.2 0.1  s—s—2r  .4 •••  A  • •6*1  •  *sa  •  o.  •  ^  A  0  ~i  -14 -12 -10  -6  -4 - 2  0  1  1  2  4  r  6  10  12 14  Entrance Angle (degrees) Figure 6-13: Modeled and experimental reflectance for enhanced Diamond Grade™ cell filled with air, when the axis of rotation is parallel and perpendicular to the primary groove  It should be noted that if the source is a diffuse white light instead of a red laser, the detected reflectance of enhanced M F C A is approximately 0.45 near normal incidence. This suggests that less collimation representative of typical sources results in higher detected reflectances. The visual appearance of the reflectance modulation of enhanced sheeting is extremely encouraging. In addition, should further work establish the cause of the extra aluminium absorption and thereby eliminate it, the maximum reflectance would be much improved. Even as is, the reflectance sufficiently demonstrates the potential of modulated PIR for the application presented in the next chapter.  6.4.2 Reflectance modulation measurements As discussed earlier, the aluminization configuration should provide overall increases in the reflectance while still allowing modulation to a dark absorptive state. Too much  110  aluminium increases the reflectance of the absorptive state, drastically reducing the contrast ratio.  To ensure that the contrast ratio remains reasonable in enhanced test cells filled with pigment suspensions, a commercially available retroviewer was used to visually inspect retroreflected white light.  To quantify the contrast ratio and compare reflectances to  previous results, an enhanced M F C A test cell was filled with the pigment suspension and measured using the set-up described in section 5.1.2.  Afield of 3.5 x 10 V/m was applied across the cell putting it into the reflective state, and 6  the maximum reflectance was recorded. The field polarity was reversed causing the absorptive state and the minimum reflectance was recorded. Results are plotted in Figure 6-14. Contrast ratios for red collimated light are about 6:1. While the contrast ratio of non-enhanced film is not much different, the enhancement improved reflectance by a factor of 6.  Qualitative inspection of test cells with white light also show encouraging reflectance and contrast for the intended application described next.  111  0.6  0.5  5 u  0.4  41  «s CU  ti  B reflective state, perpendicular • reflective state, parallel  0.3  TJ  k "3 0.2 hi cu  •  o  S ©  z  A absorptive state, perpendicular • absorptive state, parallel  • •  0.1  0  •  A  f  1  i  10  - iI  A  A •  -6  - 4 - 2  * 0  A •  2  •  H  •  A •  4  6  A •  8  10  Entrance Angle (degrees)  Figure 6-14: Experimental reflectance of aluminized MFCA cell filled with pigment suspension. Maximum reflectance values achieved with the applied field are labelled as reflective state; lowest values with reversefieldpolarity are labelled as absorptive state.  112  7  APPLICATION OF PARTIAL REFELCTION MODULATION: HIGHWAY SIGN PROTOTYPES  There is substantial interest in the traffic control industry to modulate the reflections of traffic control signs. Low power flashing signs are greatly needed in conspicuity applications (such as a chevron sign warning of a sharp curve in the road), particularly in rural or remote areas where electric power is not readily available. Current modulated roadside signs are emissive displays that flash using incandescent bulbs, or light emitting diodes. Retroreflective signs could be modulated based on the control of TIR and PIR, as investigated in this thesis, with inherently lower power consumption as a reflective display than the current emissive technologies. Such a sign has the potential to require only a tenth of a watt , such low power that it could easily operate in rural areas using a 64  5 Watt solar panel and a small rechargeable battery.  It was decided to demonstrate the use of modulating PIR for such an application. Since the reflective state for ITO coated Diamond Grade™ sheeting without enhancement, as measured in section 5.1.3, is better than without the conductive coating, a simple flashing panel intended to resemble a chevron sign was constructed from this material to demonstrate the display's potential and to discover possible problems in assembly. The next prototype was improved by using the enhanced M F C A sheeting to increase brightness. Both prototypes showed extremely promising contrast ratios and power consumption.  The first prototypes are 20.32 x 30.48cm (8" x 12") in size, representing one ninth the area of a large static chevron sign currently in use. Since the facilities available for evaporative deposition of aluminium only allow the aluminization of sheeting of 15.24 x 15.24cm (6" x 6"), it was decided to split the panel into eight different tiles, each 10.16 x 7.62cm (4" x 3"). Factors needing consideration during prototype design are discussed in this chapter.  113  7.1  Tile assembly and electrical connections  A total of eight tiles, each 10.16 x 7.62cm (4" x 3"), were used to construct the prototype. i  Tiles consist of the retroreflective sheeting with a conductive ITO coating, a 10.16 x 7.62 x 0.32cm (4" x 3" x % ") aluminium piece serving as the back electrode, and the pigment suspension between the electrodes to control the reflection. Each cell was assembled as follows. To prevent the film from sagging and making electrical contact with the back electrode, it was laminated onto a 10.80 x 7.62 x 0.32cm (4'/4"  x 3" x X " ) piece of clear acrylic using optical adhesive.  65  The aluminium  backplane and acrylic piece were machined with a lip, as shown in Figure 7-1, to allow space for epoxy to seal the ink in the cell. A tape spacer, like that used in single interface test cells, was placed around the edges of the aluminium with a 2mm square piece in the center of the cell to prevent electrode contact.  (a) tapped holes for electrical connection  tape spacer (b)  (c)  tape spacer lip for sealing  Figure 7-1: Schematic of machined aluminium electrode for prototype tiles  Cells were constructed by placing 1.5mL of ink on the aluminium piece and another 1.5mL on the structured surface and joining the two pieces starting from one edge to the other as demonstrated in Figure 7-2. Held in place by toggle clamps, the cell was not 66  114  sealed until excess ink had flowed out allowing any trapped air to escape. The edges were then cleaned and sealed with epoxy,  67  aluminium  pigment suspension structured surface tape spacer —  acrylic  Figure 7-2: Method of assembling prototype tiles  One side of the acrylic/film piece was longer than the underlying aluminium piece to allow a wire lead to be connected to the structured surface electrode with conductive epoxy. Figure 7-3 below illustrates the completed tile in both top and cross sectional view. wire  tape spacer  lead  (a) ( X X K i fx j f t V K ' X X X * x x X *  -conductive  < x'x'x'X'x'x'it'xVK x V x > X x"Sfx> fi < -f >fx"x" •< X'IQCMXXIIsf wsfxVfX.- ft  epoxy  acrylic. tape spacer  -optical  (b) epoxy  adhesive  -structured  seal-  particle  v  surface  aluminium  suspension  Figure 7-3: Assembled tile for prototype sign (a) top view, (b) cross-section  On each tile, the underside of the aluminium has four tapped holes, as illustrated in Figure 7-1 above, allowing it to be screwed onto an aluminium backplate 0.16cm ( / ") X  X6  thick. All cells where thus attached to this backplate which acted as a common rear  115  electrode before being placed into a holder. To make all tiles in the panel modulate simultaneously, the top electrodes of each cell were electrically connected by screwing the wire leads into a small aluminium strip isolated from the backplate contact. The holder was a machined anodized aluminium box pictured in Figure 7-4.  Each electrical  contact was connected to a coaxial connector in the holder. The time-varying field applied across the electrodes of the panel was thus provided through the coaxial cable.  electrode connection  c  o  a  x  i  a  l  c  a  b  l  e  connection  Figure 7-4: Holder with tiles from the prototype flashing panel  7.2  Faceplate and mask for chevron  The tile construction and electrical connections only allow for simultaneous modulation of all tiles. In order to have the usual chevron symbol on the sign permanently, a black vinyl mask was affixed to the faceplate partially covering the tiles.  In addition, the faceplate must provide daytime viewing of the chevron pattern.  Since  the basic structure is retroreflective, the prototype sign is highly visible at night with the use of headlights. However, under ambient daylight conditions, retroreflection offers no benefit and the sign appears dark. A modification is therefore needed for daytime visibility. The approach chosen for these prototypes was a fluorescent dotted pattern 116  printed on the faceplate with sufficient spacing to allow substantial retroreflection for night viewing. This was accomplished by screen printing fluorescent orange dots onto 1mm thick Lexan. These dots are 0.32cm (%") in diameter covering half the area of the sign in a hexagonal layout shown in Figure 7-5.  oooooooo o oo ooo o oooooooo o oo ooo o Figure 7-5: Hexagonal layout offluorescent dots on panel faceplate for daytime visibility  From a distance, the sign appears bright orange because the eye blends the dots together. At night, from a distance, the flashing part of the sign is visible through the space between dots again appearing to blend together. Visual tests of various configurations, such as different dot size and area coverage were conducted in order to find an optimum configuration. To further increase daytime visibility, an orange border was printed around the chevron. The vinyl chevron was adhered to the printed Lexan sheet, as pictured in Figure 7-6.  Figure 7-6: Faceplate for prototype chevron consisting of a lexan sheet with screen printed fluorescent orange dots, an orange border, and a black vinyl chevron  117  Without any additional filters, the modulating sign appears white from the reflected light of car headlights. Since most chevron signs currently used on the road are yellow, it was decided that a yellow filter  68  should be added under the chevron stencil to make the sign  a familiar yellow at night.  The prototypes constructed showed reasonably encouraging reflectance values and contrast ratios. Improvements for future prototypes will require more work in ink development, enhancement techniques, and assembly procedures. These are discussed in the following chapter.  118  8  FUTURE WORK  The work presented in this thesis is intended as an investigation of the modulation of partial reflection. This section provides an overview of work required to further understand the modulation with pigment suspension and to continue the development of the highway sign application described in the previous chapter.  8.1  Ink development  The particle suspension used in these studies was successful in modulating both total and partial internal reflections. However, as discussed in section 4.2.3, the agglomeration of particles under the influence of an applied field causes the contrast ratio and response time to degrade over time. While a high volume fraction of particles partially prevents aggregation, the suspension used in this study is susceptible to significant clustering after switching times of just a few hours. Potential increases in volume fraction and changes in dispersant and solvent concentrations should be studied more closely to improve the long term stability of the particle suspension.  Furthermore, the structured sheeting cells undergo an additional failure mode with the pigment suspension that is currently not well understood. Not only does the reflectance response slow with time causing decreased contrast, but patches of non-modulating sections appear with time. This effect might be caused by an unknown interaction between the ITO and pigment suspension, or might be due to field variations inherent to structured surfaces since the gap between electrodes is not constant. Another possible catalyst to degradation is the trapping of air pockets.  The suspensions used in this study are composed of both blue and magenta pigments making a dark purple ink. The different pigments behave differently and are potentially interacting in an undesirable way. The interaction could be investigated by varying the relative concentrations of the pigments and measuring the resulting spectral reflectance response. 119  Future studies of the particle suspension should include an investigation of the maximum achievable reflectance. For detection angles greater than critical, reflectance of the bright state does not reach the expected 100%. As the cause is not yet understood, the reflectance in the case of partially reflected light could experience a similar decrease unaccounted for in the model or in the current understanding of PIR modulation.  8.2  Enhancement through aluminium deposition  Future work of aluminium deposition should concentrate on the properties of the deposited aluminium. As mentioned in Chapter 6, the reflectance of the aluminium deposited on a glass surface is 10% lower than expected. A possible cause is contamination when deposition begins on the surface, potentially from the aluminium source itself. This can be investigated by keeping a shutter between the substrate and the source at the beginning of evaporation. If the cause can be understood and eliminated, the reflectance of M F C A film could increase by as much as a factor of two.  Furthermore, it was found during the course of enhancement studies that when the aluminium is deposited after the film has been ITO coated, the reflectance gain is much less pronounced than when it is deposited first. The possible cause for this is unclear. It may be that the aluminium does not adhere well to the ITO surface, or perhaps more complicated effects are responsible. To avoid the problem, it is possible to ITO coat once the aluminium has been deposited, however, investigating this problem could provide greater insight into the interface properties and hence more information regarding the reflectance modulation itself.  8.3  Highway sign assembly  Currently, reflectance modulation of the prototype chevron signs cannot be seen under daytime lighting conditions as the retroreflector geometry provides no advantage in ambient lighting. Other microstructures such as hemispheres can preferentially reflect  120  ambient light. Daytime visibility of modulating reflective signs could therefore be achieved using a configuration of alternating retroreflecting structures with hemispherical structures. Hemispherical microstructures would provide daytime modulation with ambient light, while the retroreflective sheeting would provide night time modulation visibility. As with the dots on the faceplate, the sections would need to be small enough so that from an average viewing distance, they blend together to appear homogeneous.  While many issues need to be considered for future prototypes, it is believed that none pose fundamental problems that would prevent the success of PIR modulation in this application. The ultimate goal of this technology is to use a backplane with pixel control. This would allow not only for flashing messages, but also electronically addressable variable message signs, for example, speed limit signs that could change depending on weather, or signs to display information about road conditions ahead.  121  9  CONCLUSIONS  Frustrated total internal reflection is a well known phenomenon in which the reflection at an interface can be modulated by moving an absorbing medium in and out of the evanescent wave region. Coloured pigments suspended in a clear solvent can serve as the absorbing material. Under the influence of an applied field, the pigments migrate into the evanescent wave region to frustrated TIR and, with reversed field polarity, migrate out of the zone completely restoring TIR.  The high reflectance and contrast of such a display stems from TIR and its possible frustration. One could then easily assume that such reflectance modulation is not effective for light undergoing only partial reflection at an interface. Surprisingly, modulation of partial internal reflection can also yield sufficiently high reflectance and contrast. The work presented in this thesis investigates of the optical effects responsible for modulation in the absence of an evanescent wave.  Experiments demonstrate that optical interference is responsible for the modulation of partially reflected light. Using a pigment suspension as the absorbing material between two glass slides, the reflectance as a function of applied field was measured. The measurement was repeated over a range of incident angles, in which light undergoes TIR and PIR. When light undergoes PIR, plots of reflectance versus time demonstrate an additional oscillating shape under a constant applied field consistent with interference. This oscillation is damped in time, converging to a lower, constant reflectance value. Despite this, the contrast ratio remains very promising at 75:1 for incident angles 1° below critical.  A mathematical model representing the system was developed to gain further understanding by emulating the experimental conditions. A simple three layer model consisting of a growing solvent layer between a glass layer and a pigment particle layer effectively reproduce the modulation from absorptive state to reflective state. Several factors were considered. First, the experimental system detects a range of wavelengths 122  that can interfere with one another. In addition, the system is not actually three welldefined layers with flat boundaries. As the pigments compress the thickness of the solvent layer varies along the interface, increasing non-uniformity. This was represented by using the model independently for uniform layers with different pigment velocities and applying a weighted average to obtain the overall reflectance value. However, this approach considers only independent layers and does not consider that light reflecting from one layer can be scattered or absorbed by another layer. A correction factor to account for this decrease in reflectance from the back surface adjusts the refractive index difference between the solvent layer and the pigment layer. While the final model results accurately represent the experimental data, some assumptions were found to be incorrect. The pigment velocity is not constant as assumed, and the rate at which the pigment layer becomes non-uniform is not entirely well represented by the model. This model nevertheless simulates experimental results rather well and has provided insight into the important factors in the modulation process.  Reflectance modulation on multiple interfaces in retroreflectors was also investigated. Light entering a corner-cube type retroreflector will reflect from at least three interfaces before returning to the source. Such structures are used in conspicuity applications, such as highway information signs. Modulating this reflection using a pigment suspension could prove extremely useful in making retroreflectors flash thereby increasing visibility and safety. Using raytracing software, light retroreflecting from two retroreflective sheetings were modeled. The values were also measured experimentally and the two agree well when the structures are immersed in the pigment suspension solvent Fluorinert™ FC-75. The retroreflection, however, is on average only 2-4%. This is because the pigment suspension used consists of a solvent with a higher refractive index than air, so that light undergoes PIR with low reflectance on many of the facets. While the loss of light due to transmission can be acceptable for reflectance applications with a single optical interface, the compound loss due to multiple reflections is much too high for practical applications with the retroreflectors. A n enhancement to the system was therefore developed and tested.  123  It was discovered that the most efficient way of enhancing the retroreflective films is to selectively deposit a layer of aluminium on some of the corner-cube facets. The coated facets have much improved reflectivity, but can no longer be modulated since light striking that interface will always be reflected. Samples were aluminized and measured yielding a reflectance of about 22%, representing an 18% improvement. The raytracing model developed predicted reflectances of about 45%. The difference is due to an unexpected absorption in the aluminium deposited, and should be investigated further. Nevertheless, this enhancement demonstrates great promise in a modulating multiinterface system.  As mentioned earlier, retroreflective sheeting is of particular interest in this study. The sheeting is currently used on static roadside traffic control signs and the modulation (with enhancement) of PIR makes it possible to control the reflectance of these signs to make them appear to flash, or even display variable messages. Current display technologies for this purpose are emissive, and as such, require much more power. A display based on modulating PIR is a reflective display, making it low powered, yet high contrast, and high reflectance when enhanced. To demonstrate the potential of such a technology, two retroreflective panels were assembled to simulate chevron signs. The first demonstrated the possibility of modulation of PIR for such an application, and the second, assembled with enhanced sheeting, confirmed the potential for high reflectivity. Both prototypes were successful and performed as expected. While the pigment suspension and assembly procedures require further devolvement, the modulation and enhancement of PIR together show great promise for traffic control signs.  In summary, the reflectance modulation of light previously thought effective only through the process of frustrating total internal reflection can be achieved with high contrast when the light undergoes only partial reflection. While the visual appearance is similar, the underlying cause is optical interference rather than the frustration of TIR. In a multiple reflection system, where reflectance loss is compounded at each interface, an enhancement of reflections is possible by depositing a layer of aluminium on some of the facets. Depending on the deposition geometry, this increases the overall reflection  124  without compromising the contrast ratio significantly. This technique has shown potential to increase road safety, especially in rural areas, by providing a low powered, high contrast, conspicuous flashing sign to warn of potential dangers. This use of modulated PIR is also viable for pixelated variable message signs, potentially offering better reflectance with lower power consumption than those currently in use.  125  REFERENCES  1  Mossman, M.A, et al. 'New Reflective Display Based on Total Internal Reflection In Prismatic Microstructures', SID IDRC 2000 Conference Proceedings, pp. 311-314, 2000  2  ibid 1  3  Hect, E., Optics, 3 ed., U.S.A.: Addison Wesley Longman, Inc., 1998, p.66  4  Fowles, G.R., Introduction to Modern Optics, 2 Inc., 1989, p. 157  5  Mossman, M.A., Spectral Control of Total Internal Reflection for Novel Information  rd  nd  ed., New York: Dover Publications  Displays, University of British Columbia: PhD Thesis, April 2002, p. 119 6  ibid 3, p. 125  7  ibid 5, pp. 377-382  8  ibid 5, p.311  9  Detailed derivation can be found in Hect (ibid 3) pp. 419-420  1 0  Shaw, D.J., Colloid & Surface Chemistry, 4 ed., Britain: Butterworh-Heinemann, th  1992, p. 174 11  ibid, p. 177  1 2  Based on Figure 7.1 in Shaw (ibid 10) p. 178  1 3  ibid 10 p. 190  1 4  Ross, S., Morrison, I., Colloidal Systems and Interfaces, New York: John Wiley & Sons, 1988, p. 252  1 5  ibid 10 p.235  1 6  ibid 10 p. 185  1 7  Trizact™ abrasive, manufactured by 3M Company, St. Paul, M N , 55144-1000, U S A Vikuiti™ Dual Brightness Enhancement Film, manufactured by 3M Company, St. Paul, M N , 55144-1000, U S A  126  1 9  Diamond Grade™ Reflective Sheeting, manufactured by 3M Company, St. Paul, M N , 55144-1000, U S A  2 0  ibid 5  2 1  ibid 1  2 2  Mossman, M.A., et al. 'New Reflective Color Display Technique Based on Total Internal Reflection and Subtractive Color Filtering', SID IDRC 2001 Conference Proceedings, pp. 1054-1057  2 3  ibid 5, pp.43-46  2 4  Figure created by M . A . Mossman, reproduced with permission  2 5  Mossman, M.A., Whitehead, L.A., 'Controlled Frustration of Total Internal Reflection by Electrophoresis of Pigment Particles' Applied Optics, submitted April 2004  2 6  Miirau, P., Singer, B., 'The understanding and elimination of some suspension instabilities in an electrophoretic display', Journal of Applied Physics, pp.4820-4829, 1978  2 7  Kim, J.K., et al., 'Effects of Zeta Potential and Electrolyte on Particle Interaction on an Electrode under ac Polarization', Langmuir, Vol. 8, pp. 5387-5391, 2002  2 8  Mossman M.A., et al., 'New Method of Maintaining Long-Term Image Quality in a TIR-based Electrophoretic Display' Eurodisplay 2002, pp. 851 -854, 2002  2 9  ibid 5, p. 80  3 0  Mossman, M.A., et al., ' A High Reflectance, Wide Viewing Angle Reflective Display Using Total Internal Reflection in Micro-Hemispheres', SID IDRC 2003 Conference Proceedings, pp. 233-236  3 1  ITO coated glass, product number CG-90IN-1115, supplied by Delta Technologies, Limited, 13960 North 47th Street Stillwater, M N 55082-1234 U S A  3 2  Scotch® Magic™ tape, manufactured by 3M Company, St. Paul, M N , 55144-1000, USA  3 3  Scotch-Weld Epoxy Adhesive DP-100 clear, manufactured by 3M Company, St. Paul, M N , 55144-1000, U S A  3 4  Circuitworks Conductive Epoxy, product number CW2400, manufactured by Chemtronics 8125 Bobb Centre Dr., Kennesaw, Georgia, 30152-4386, U S A  35  Figure created by M . A . Mossman, reproduced with permission  127  3 6  90° glass prism, part "prism R A 25mm TS", catalogue number 32336, manufactured by Edmund Scientific Industrial Optics Division, 101 East Gloucester Pike, Barrington, NJ 08007-1380 U S A  3 7  Type A Microscope Immersion Oil, catalogue number 16482, manufactured by Cargille Laboratories Inc., Cedar Grove NJ 07009 U S A  3 8  Figure created by M . A. Mossman, reproduced with permission  3 9  Figure created by M . A. Mossman, reproduced with permission  4 0  Mossman, M.A., Spectral Control of Total Internal Reflection for Novel Information Displays, University of British Columbia: PhD Thesis, April 2002, p. 83-87  4 1  TSL250 light-to-voltage optical sensor, manufactured by Texas Advanced Optoelectronic Solutions, Inc., 800 Jupiter Road, Suite 205, Piano, T X , 75074, U S A specifications found at: http://www.csi3.com/HOMEVIS/light_sensor.pdf  4 2  Figure created by M . A . Mossman, reproduced with permission  4 3  Colour filters: 03 FIB 006 (500nm), 03 FIB 014 (650nm), 03 FIB 004 (450nm), manufactured by Melles Griot, 55 Science Parkway, Rochester NY, 14620, U S A  4 4  Infrared Filter F C G 563, manufactured by Melles Griot, 55 Science Parkway, Rochester N Y , 14620, U S A  4 5  Halostar starlite low-voltage low-pressure pin-base lamp, product number 64440 U V S 50W 12V GY6,35, manufactured by Osram, Hellabrunner Strasse 181543 Munchen Germany  4 6  The diffuser was an 8.00 x 8.00 x 1.0 cm glass piece sandblasted on both sides  47  Optically Clear Adhesive 8161, manufactured by 3M Company, St. Paul, M N , 551441000, U S A  4 8  Visual Basic data acquisition program written by Michele A . Mossman  4 9  ibid 5 p. 80  5 0  Applied field used for this experiment is ±3.9 x 10 V/m  5 1  ibid 5, p.l 10  5 2  M A T L A B ® technical computing language, a product of The Mathworks, Inc., 3 Apple Hill Drive Natick, M A 01760-2098, U S A  5 3  ibid 46  5  128  Scotch® Magic™ tape, manufactured by 3M Company, St. Paul, M N , 55144-1000, USA A S T M International Standard E810-93b, Standard Test Method for Coefficient of  Retroreflection for Retroreflective Sheeting Figure based on Figure 3 in A S T M International Standard E810-93b, Standard Test Method for Coefficient of Retroreflection for Retroreflective Sheeting 77-009-IntelliPoint™ Plus Level, manufactured by Stanley Works, 1000 Stanley Drive New Britain, C T 06053, U S A Tyvek®, manufactured by Dupont Corporation, 1007 Market St. Wilmington D E , 19898, U S A Round flat mirror, 25mm diameter, product number 02MFG015, manufactured by Melles Griot, 55 Science Parkway, Rochester NY, 14620, U S A A u t o C A D ® computer-aided design software, a product of Autodesk, Inc., 111 Mclnnis Parkway, San Rafael, C A , 94903, U S A Tracepro® raytracing software, a product of Lambda Research Corporation, 80 Taylor St., P.O. Box 1400, Littleton, M A , 01460-4400 U S A th  CRC Handbook of Chemistry and Physics, 11 and semiconductors' (p.12-126)  ed., s.v. 'Optical properties of metals  Confirm™ Security Laminate Verifier, part number 75-0299-7344-5, manufactured by 3M Company, St. Paul, M N , 55144-1000, U S A Prototypes used 66mW, theoretical calculations for full sign predicted on the order of lOOmW. ibid 46 Horizontal hold down toggle clamp, series 227, manufactured by D E - S T A - C O U S A ibid 33 Light Amber filter, product number 102 of Chromatic Edition, manufactured by L E E Filters, 2237 North Hollywood Way, Burbank, C A 91505  129  APPENDIX A: Angular response of collimated detector In Chapter 4, the modulation of reflectance at a single interface was measured. It was important for the detection system to have a narrow detection angle to gain information about reflectance from light of specific incident angles.  To determine the angular response of the detector and thus the range of incident angles detected, a test source (the same source used for the experiment) was placed on an x-y stage and placed 2.21m (87") away from the detector positioned as depicted in Figure A - l . The test source was initially placed such that the detection system output a maximum reading and was then scanned horizontally (angles (j)) and vertically (angles 0) from that peak position. The output of the detection system was measured at angles from 0° to 1.2°. The angles 6 and (p of 0° correspond to the point of maximum response.  light source  Figure A-L- Schematic of set-up to measure angular response of detection system  The normalized response, calculated as the fraction of maximum reading for both horizontal and vertical directions can be seen in Figure A-2. The full-width-half-max, representing the degree of collimation of the detector, is about 0.7° in both directions.  130  • •  • Vertical • Horizontal  • • • II  • • *  I  fl  1.2  -1  I •i  i  1  1  -0.8 -0.6 -0.4 -0.2  1  0  •—i——~i—•—•—i  0.2  0.4  0.6  1  0.8  9 , 9 —r  1  1.2  Angle (degrees) Figure A-2: Measured angular response of detector, for horizontal and vertical angles  To establish alignment error of the detector caps and the optical sensor, collimated laser light was sent through the tube and cap towards the test source location, as illustrated in Figure A-3. The difference in the location of this laser spot and the position of maximum reading represents the offset of the detection system. The vertical offset is -0.3°, or 0.3° lower.  laser  laser spot offset angle  31 point of maximum response  Figure A-3: Schematic of set-up to determine the vertical offset angle due to misalignment of optical sensor  131  APPENDIX B: Calculating incident angle at the interface The measurement system used in Chapter 4 is used to measure the modulation of reflection for light at a given incident angle. In order to establish the angle of incidence at the test cell interface, the detector angle must be measured. The interface of interest is the boundary between the glass slide and pigment suspension. Since the glass slide is index matched to the prism, the incident angle at the bottom surface of the prism corresponds to the incident angle at the studied interface. The light must travel through air before reaching the detector, requiring some geometry to calculate the angle at the interface. Figure B - l below depicts this geometry.  Figure B-l: Geometry of light incident on prism  The desired angle at the studied interface is 0 , and the measured angle of the detector is g  Od. Using Snell's law at the prism/air interface, and using the geometry shown, the desired angle (B-4) is calculated as follows:  e =A5'+e  (B-l)  0 = arcsin •^-sinfl,  (B-2)  2  g  2  V n.  01=45"\-e 6„ = 4 5 ° + arcsin  (B-3)  d  -sin(45°-<9 ) RF  (B-4)  132  The angle of the detector &d must therefore be measured. Two methods are used to ensure agreement and accuracy. The first is to measure using an angle meter along the tube that holds the optical sensor. This measures to the nearest half degree.  The second method involves removing the optical sensor from the tube and inserting a laser in its place. The distance to the spot on the table and the height of the detector tube are measured. The angle can then be calculated using simple trigonometry. Errors in measurement are reduced by using both methods. Uncertainties are about 0.3°.  133  APPENDIX C: Spectral transmittance of filters In order to gain spectral information about the modulation of reflectance measured in Chapter 4, colour filters were placed in the detection system. The reflectance data was taken using three different interference filters obtained from Melles Griot. The filters are coated with multiple layers causing incident light to undergo multiple reflections in the filter. The optical path difference determines which wavelengths will have no phase difference allowing for maximum transmission. In such a manner, wavelengths above and below the intended wavelength do not transmit.  Red, green, and blue filters were used, and the spectral transmittance of filters was measured using a spectroradiometric telecolorimeter, and the results are shown in Figure C-I.  j  1.0 -  400  500  600  700  800  Wavelength (nm)  Figure C-F. Spectral transmittance of colour filters  1  Reference [5], Appendix H  134  As shown in Figure C - l , the redfilterhas a peak transmittance at 660nm and a fullwidth-half-maximum (bandwidth) of about 80nm. The green filter has a peak transmittance at 515nm with a bandwidth of 90nm, and the blue filter has a peak transmittance of 475nm with a bandwidth of 70nm.  To ensure the system was detecting only visible radiation, an infrared filter was used. This filter, also obtained from Melles Griot is made of KG1 Schott heat-absorbing glass that transmits in the visible range. The transmittance of this filter was measured similarly to the colour filters and the transmittance curve is show in Figure C-2."  1.0 H  400  500  600  700  800  Wavelength (nm) Figure C-2: Spectral transmittance of infrared filter  " ibid i  135  APPENDIX D: MATLAB code for the final model of reflectance at a single interface A model of reflectance modulation at a single interface was created using M A T L A B . The first step was to write a function entitled "thinfilm.m" that calculated reflectance from a three layer thin film system using the characteristic matrix discussed in section 2.2.2. The next step was to model the factors discussed in section 4.2.1. Desired model parameters are entered into the code, and the file is executed to obtain model results. Both files necessary are included below:  Thin film function: %function t o measure r e f l e c t i o n from i n t e r f e r e n c e i n %the c a s e o f t h i n f i l m ( c h a r a c t e r i s t i c m a t r i x ) %input i s a s f o l l o w s : %nl - i n d e x o f u p p e r l a y e r %n2 - i n d e x o f t h i n f i l m %n3 - i n d e x o f b o t t o m l a y e r %d - thickness of film %lambda - w a v e l e n g t h %thetai - incident angle a t nl/n2  interface  %function r e t u r n s t h e r e f l e c t a n c e o f t h ef i l m %input parameters  given  function[Rtot]=thinfilm(nl,n2,n3,d,lambda,thetai) epsilon=8.8542e-12; mu=4e-7*pi; k=2*pi/lambda; %calculate angles a t other interfaces thetal=thetai*pi/180; theta2=asin(nl/n2*sin(thetai)); theta3=asin(n2/n3*sin(theta2)); % c a l c u l a t e d needed elements f o r c h a r a c t e r i s t i c m a t r i x %both p a r a l l e l a n d p e r p e n d i c u l a r e l e m e n t s a r e n e e d e d h=nl*d*cos(theta2); kh=k*h; Y2perp=sqrt(epsilon/mu)*n2*cos(theta2) ; Y2par=sqrt(epsilon/mu)*n2/cos(theta2) ; Ylperp=sqrt(epsilon/mu)*nl*cos(thetai);  136  Ylpar=sqrt(epsilon/mu)*nl/cos(thetai); Y3perp=sqrt(epsilon/mu)*n3*cos(theta3); Y3par=sqrt(epsilon/mu)*n3/cos(theta3); % c h a r a c t e r i s t i c m a t r i x of t h e system: Mperp=[cos(kh) i * s i n ( k h ) / Y 2 p e r p ; Y 2 p e r p * i * s i n ( k h ) c o s ( k h ) ] ; Mpar=[cos(kh) i * s i n ( k h ) / Y 2 p a r ; Y 2 p a r * i * s i n ( k h ) c o s ( k h ) ] ; % r e l f e c t i o n c o e f f i c i e n t s from t h e c h a r a c t e r i s t i c m a t r i x (numerator and denomenator) rperpnum=Ylperp*Mperp(1,1)+Ylperp*Y3perp*Mperp(1,2)-Mperp(2,1)Y3perp*Mperp(2,2); rperpden=Ylperp*Mperp(1,1)+Ylperp*Y3perp*Mperp(1,2)+Mperp(2,1)+Y3perp*M perp(2,2); rperp=rperpnum/rperpden; rparnum=Ylpar*Mpar(1,1)+Ylpar*Y3par*Mpar(1,2)-Mpar(2,1)Y3par*Mpar(2,2); rparden=Ylpar*Mpar(1,1)+Ylpar*Y3par*Mpar(1,2)+Mpar(2,1)+Y3par*Mpar(2,2) rpar=rparnum/rparden; %resulting reflectance Rperp=rperp*conj(rperp); Rpar=rpar*conj(rpar) ; %Average f o r u n p o l a r i z e d l i g h t Rtot=(Rperp+Rpar)12;  137  Final model of modulation at a single interface:  %Model %Final  of reflectance at a single interface model v e r s i o n September 2004, Anne Liptak  %last variables r andt a r ematrices %and c o r r e s p o n d i n g time %keep t r a c k o f c o m p u t i n g timing=cputime;  containing  reflectance  time  %input parameters t o change lambda=0.515; %center wavelength nl=1.521; %refractive index of glass n2=1.296; %refractive index of solvent layer n3=1.6; % r e f r a c t i v e index o f compressed solvent thetai=56.9; %incident angle i n glass thetadetector=26.4; %angle o f d e t e c t o r band=0.04; %filter bandwidth f=10; %factor t o account f o r non-uniform back %Start  by accounting  %interval variables thetaint=0.12; lambdaint=0.05; mu=lambda; sigma=band;  f o r bandwidth since  interference  discrete  %mean wavelength %standard d e v i a t i o n  % g e tweight w f o r t h edifferent z=l; for j=.3:lambdaint:.8 x(z)=j ; z=z+l; end  numbers  (assuming  wavelengths  Gaussian)  intervals  Pl=zeros(1,length(x)); for i=l:length(x) PI(i)=exp(-(x(i)-mu)"2/(2*sigma 2))/(sigma*sqrt(2*pi)); end . A  P=P1./sum(x.*P1); W = x . * P;  %Now a c c o u n t z2 = l ; mu2=0.1; sigma2=0.03; vmin=0; vint=0.015; vmax=0.3;  f o r distribution  of velocities  %mean v e l o c i t y parameter %standard d e v i a t i o n parameter % v e l o c i t y range i n t h e gaussian t o consider % andinterval since d i s c r e t e values  layer  surface  % l o o p t o a s s i g n w e i g h t s t o each i n t e r v a l f o r q=vmin:vint:vmax x2(z2)=q; z2=z2+l; end .  (assume g a u s s i a n )  P2 = z e r o s ( 1 , l e n g t h ( x 2 ) ) ; for i=l:length(x2) P2(i)=exp{-(x2(i)-mu2)~2/(2*sigma2~2))/(sigma2*sqrt(2*pi)); end Pvel=P2./sum(x2.*P2); wvel=x2.*Pvel; % A l s o account f o r t h e d i f f e r e n t a n g l e s seen by d e t e c t o r z3 = l ; mu3=thetai; sigma3=0.35*cos(thetadetector*pi/180); % f i n d weights f o r t h i s d i s t r i b u t i o n of angles th=thetai-l:thetaint:thetai+1; x3(z3)=th; z3=z3+l; end . P3=zeros(1,length(x3)); for i=l:length(x3) P3 ( i ) =exp (- (x3 ( i ) -mu3 ) ~2/ (2*sigma3~2) ) / ( s i g m a 3 * s q r t ( 2 * p i ) ) ; end i for  Pangle=P3./sum(x3.*P3); wangle=x3.*Pangle; % T o t a l model: % r u n l o o p f o r a l l wavelengths i = 1; j = 1; k= 1; m= 1 ; for  and, v e l o c i t i e s o v e r time  t=0:0.4:60  % l o o p t o sum over a l l a n g l e s for k=l:length(x3) % t o speed up c a l c u l a t i o n s , any z e r o w e i g h t e d a n g l e s n o t c o n s i d e r e d i f abs(wangle(k))<le-5 rangle(k)=0; else H o o p t o sum o v e r a l l v e l o c i t i e s f o r v=vmin:vint:vmax % c o n s t a n t v, t h i s l i n e changes i f a c c e l e r a t i o n c o n s i d e r e d d=v*t; i f abs(wvel(j))<le-5 rvel(j)=0; j=j+l; else % l o o p t o sum over a l l wavelengths for i=l:length(x) i f abs(w(i))<le-5 rlambda(i)=0; 139  else  if  d<0 rlambda(i)=0; else %take n o n - u n i f o r m i t y into account by entering %index d i f f e r e n c e ndiff=0.4/(1+f*d); n3diff=ndiff+n2; %put i n t o f u n c t i o n t h a t c a l c u l a t e s r e f l e c t a n c e  rlambda(i)=thinfilm(nl,n2,n3diff,d,x(i),x3(k)); end end end %assign weights rvel(j)=rlambda*w. ; j=j+l; 1  end end  j=l; %assign weights rangle(k)=rvel*wvel.';  end end %assign weights rtime(m)=rangle*wangle.'; time(m)=t; m=m+l  end r=rtime.'; t=time.';  %final reflectance %time m a t r i x  matrix  %time t o c a l c u l a t e finaltime=cputime-timing  140  

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