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Controlled extraction from light guides by means of ELE ctrophoretic modulation of total internal reflection Cheng, Ju-Chieh (Kevin) 2004

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C O N T R O L L E D E X T R A C T I O N F R O M LIGHT GUIDES B Y M E A N S OF ELE CTROPHORET1C M O D U L A T I O N OF T O T A L I N T E R N A L R E F L E C T I O N by JU-CHIEH (KEVIN) C H E N G B . S c , University of British Columbia, 2001 A THESIS S U B M I T T E D IN P A R T I A L F U L F I L L M E N T OF THE REQUIREMENTS FOR THE D E G R E E OF M A S T E R OF SCIENCE in THE F A C U L T Y OF G R A D U A T E STUDIES (Department of Physics and Astronomy) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH C O L U M B I A April 2004 © Ju-Chieh (Kevin) Cheng, 2004 Library Authorization In presenting this thesis in partial fulfillment of the requirements for an advanced degree at the Universi ty of British Columbia, I agree that the Library shal l make it freely avai lable for reference and study. I further agree that permiss ion for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publ icat ion of this thesis for f inancial gain shal l not be a l lowed without my written permiss ion. lj'C.L\el\ (Me.Jw\) ( - t e w ' t /c 0 - / i-x N a m e o ^ i o 7 ^ c i ^ 0 D a t e ( d d / m m / y y y y ) ™e°7hesis: - ^ ^ ^ Degree: K'UM^y ^ S< i ^ u ^ Y e a r : 'Zno<-\ Department of Tl,y$\t<, -4 A ^ . H ^ ^ y The University of Br i t ish 'Columbia / Vancouver , B C C a n a d a A B S T R A C T A prototype o f a prism light guide using a new variable extraction technique is discussed. Pr ism light guides are hol low structures that pipe light by means o f total internal reflection (TIR). H i g h efficiency and uniform illumination can be achieved using a uniform extraction technique along the prism light guides. However, the shapes o f extractors used for uniform extraction have to be designed specifically for different geometries o f conventional light guides. Another limitation o f the conventional systems is that the level o f extraction along the guides cannot be controlled once the extractors have been built into the light guides. Motivated to generalize the shape o f the extractor and to enable the control o f the extraction/illumination level along the light guide, a new variable extraction technique has been developed. This extraction technique is based on frustration o f TIR , electrophoresis, and photon scattering. A rectangular variable extractor based on the new technique has been made with highly scattering si l ica particles in a fluorinert suspension contained between two transparent conducting films. B y changing the polarity o f the electrical potential applied across the conducting films, the charged si l ica particles can be moved to prevent, or "frustrate," T IR (through interaction with light in the very thin evanescent wave region near the T I R interface inside the light guide) and cause scattering in which light gets extracted, whereas the opposite polarity w i l l not affect T IR . A s a result, by changing the strength o f the applied potential the level o f scattering or extraction can be varied for each extractor independently along the light guide. A Monte Carlo ray tracing analysis o f the light guide using the new extraction technique has been performed, and the results are promising. Based on the ray tracing model, a scale prototype o f the variable extractor light guide has been constructed. The prototype consists o f a prism light guide with a rectangular cross section and eight variable extractors. T o test it the light guide was then mounted on a model o f a series o f eight offices with two light sources at each end o f the guide, such that each extractor controls the il lumination level in each office. A simulation algorithm was developed to predict the extraction or il lumination level for different settings o f the applied potential i i in each office, and the performance o f the actual prototype was compared and agrees with the model prediction. A control algorithm was then programmed to adjust the level o f extraction in each office according to the needs o f the users, and the algorithm was successfully applied to the actual prototype. TABLE OF CONTENTS A B S T R A C T i i T A B L E O F C O N T E N T S iv L I S T O F T A B L E S .' v i i L I S T O F F I G U R E S v i i i A C K N O W L E D G E M E N T xi 1 I N T R O D U C T I O N 1 2 B A C K G R O U N D 4 2.1 Conventional Prism Light Guides 4 2.1.1 Total internal reflection 4 2.1.1.1 Index o f refraction 4 2.1.1.2 Conditions for T I R at an interface 6 2.1.1.3 The evanescent wave 7 2.1.2 Micro-replicated sheets: Optical Light ing F i l m ( O L F ) 9 2.1.3 Specification o f reflectance in prismatic systems 10 2.1.4 Enhanced refractive index ratio 11 2.1.5 The extractor for conventional light guides 12 2.1.6 Disadvantage o f conventional prism light guides 13 2.2 Frustrated T I R (FTIR) 14 2.3 Particle suspensions and electrophoresis 15 2.4 Hysteresis 16 2.5 Evanescent wave scattering 17 2.6 Luminous flux and Illuminance 18 3 D E S I G N I S S U E S I N A V A R I A B L E E X T R A C T O R A N D L I G H T G U I D E S U S I N G V A R I A B L E E X T R A C T O R S 20 3.1 Principle o f a FTIR-based extraction technique 20 3.2 Index mismatch requirements 21 3.3 Optical requirements for T I R at a solid-liquid interface 22 3.4 Angular requirement for TIR: apparent angle o f incidence and axial angle o f incidence 23 3.5 Particles used to frustrate T I R in low refractive index l iquid 24 3.6 Electrophoretic suspensions in a variable extractor 25 3.7 Grey-scale control o f reflectance 27 3.8 Design o f light guides using variable (FTIR-based) extraction technique 28 3.8.1 Light guides with a parabolic cross section 28 3.8.2 Light guides with a rectangular cross section 29 4 REFLECTANCE AND SCATTERING MODULATION BY SILICA PARTICLES 31 4.1 Test cel l construction 31 4.2 Measuring reflectance 32 4.3 Design o f the reflectance modulation experiment 33 4.4 Time-varying reflectance modulation 35 4.5 Measurement o f scattered light 37 4.6 Measurement o f current flow 38 4.7 Factors influencing reflectance/scattering modulation 38 4.7.1 Reflectance at different axial angles o f incidence 38 4.7.2 Intensity o f applied field 39 4.7.3 Concentration o f particles 41 5 MODELING AND CONTROLLING OF THE VARIABLE EXTRACTOR LIGHT GUIDE 43 5.1 M o d e l i n g the variable extractor light guide system using Monte Car lo ray tracing 43 5.1.1 M o d e l set-up 44 5.1.2 M o d e l results 47 5.2 The simulation algorithm of the variable extractor light guide system 49 5.3 The control algorithm for adjustment o f in-door il lumination level in the automatic light guide system 51 5.3.1 The Vi sua l Basic and Exce l program for the control algorithm 52 6 THE ACTUAL LIGHT GUIDE AND RESULTS 54 6.1 Construction details 54 6.1.1 Construction o f a series o f room-like regions 54 6.1.2 Construction o f the rectangular light guide (light guide with a rectangular cross section) 55 6.1.3 Construction o f the FTIR-based variable extractor 56 6.1.4 The amplifier & circuits 57 6.1.5 Light source and power supplies used for the variable extractor light guide 58 6.2 Methods o f measurements 59 6.2.1 Measurement o f illuminance in each room 59 v 6.2.2 Measurement o f input luminous flux at the ends o f the light guide 60 6.2.3 Measurement o f output luminous flux from the variable extractor 61 6.3 Experimental set-up and results 62 6.3.1 Operating range o f axial angles o f the light source 63 6.3.2 Distance between the light source and the opening o f the guide 65 6.3.3 Response o f the output luminous flux from the variable extractor to applied voltage and the hysteresis effect in the variable extractor 67 6.3.3.1 Mask ing effect and determination o f boundaries o f the applied voltages '.. 68 6.3.3.2 L o o k up matrix for the scattering coefficient 70 6.3.3.3 Look up table for the absorption coefficient 71 6.3.4 Operation o f the control algorithm 72 6.3.5 Comparison between the predicted and the measured illumination level 73 6.3.5.1 Testing o f the control algorithm with two sources 73 6.3.5.2 Testing o f the control algorithm with four sources 76 7 C O N C L U S I O N 82 R E F E R E N C E S . . . . . '. 85 A P P E N D I X A : P R O P E R T I E S O F F C - 7 5 F L U O R I N E R T ™ E L E C T R O N I C L I Q U I D 87 A P P E N D I X B : D E S I G N I N G A N O P T I C A L S T R U C T U R E I N T R A C E P R O ® 88 A P P E N D I X C : T Y P I C A L O U T P U T F R O M T R A C E P R O ® 90 A P P E N D I X D : L O O K U P T A B L E S F O R T H E S C A T T E R I N G A N D A B S O R P T I O N C O E F F I C I E N T S 92 A P P E N D I X E : O T H E R C A S E S T E S T E D I N S E C T I O N 6.3.5.1 105 A P P E N D I X F : O T H E R C A S E S T E S T E D I N S E C T I O N 6 .3 .5 .2 106 vi LIST OF TABLES Table A - 1: Properties o f FC-75 at 25°C 87 Table C - 1: Ray history table from TracePro® model 91 Table D - 1: L o o k up table for the scattering coefficient 103 Table D - 2: Look up table for the absorption coefficient 104 vii LIST OF FIGURES Figure 2- 1. Snell's L a w o f refraction 6 Figure 2- 2. Pictorial representation o f evanescent wave 7 Figure 2- 3. Penetration depth as a function o f the angle o f incidence 8 Figure 2- 4. (a) A ray path undergoes total internal reflection in the prism light guide: the side view o f the O L F in the light guide shown in (b) 9 Figure 2- 4. (b) A light guide with a circular cross section (translational symmetry)... 10 Figure 2- 5. (a) Apparent angles for two-dimensional projection o f a ray path and (b) the side view showing the axial angle o f incidence 11 Figure 2- 6. A sample ray tracing in a conventional prism light guide 12 Figure 2- 7. (a) The top view o f a typical shape o f the extractor used for uniform illumination and (b) the extractor inside the conventional prism light guide (prism size not to scale) 13 Figure 2- 8. (a) T I R and (b) frustration o f T I R by a scattering or absorptive material . 14 Figure 2- 9. A typical hysteresis loop 17 Figure 3- 1. Principle o f a FTIR-based extraction technique 20 Figure 3- 2. Apparent angles for two-dimensional projection o f a ray path in a hollow light guide with an exterior fluorinert l iquid chamber 23 Figure 3- 3. Angular requirement for T I R in a hollow light guide with an exterior fluorinert l iquid chamber (air-OLF-fluorinert) 24 Figure 3- 4. (a) The T I R state in a variable extractor (left) and the cross section view with the direction o f electric field (right) (not to scale) 26 Figure 3- 4. (b) The scattering state in a variable extractor (left) and the cross section view with the direction o f electric field (right) 26 Figure 3- 5. Construction o f the parabolic light guide (left) and a sample ray tracing in the guide (right) 28 Figure 3- 6. Area o f input at the parabolic cross section 29 Figure 3- 7. The construction o f the rectangular light guide and its area o f input allowed for the source beam 29 Figure 3- 8. A sample ray tracing in the rectangular light guide 30 Figure 4- 1. Construction o f the electrophoretic test cell (a) top view and (b) side view 32 Figure 4- 2. Set-up for measuring reflectance 33 Figure 4- 3. Schematic diagram of data acquisition system 34 Figure 4- 4. Reflectance modulated by electrophoresis o f si l ica particles 36 Figure 4- 5. Experimental set-up for measuring scattered light (size not to scale) 37 Figure 4- 6. Percent change in reflectance versus axial angle o f incidence 39 Figure 4- 7. Percent change in reflectance versus intensity o f applied field 40 Figure 4- 8. Percent change in reflectance versus concentration o f s i l ica particles 41 Figure 5- 1. (a) A highly collimated light source and (b) A light source with a beam (half) angle o f 4° 45 v i i i Figure 5- 2. (a) A x i a l angle o f the light source on the y-z plane and (b) Normal direction o f the source perpendicular to the x-axis 46 Figure 5- 3. The axial angles and source distance used in the T r a c e P r o ® 46 Figure 5- 4. A typical output from TracePro® for the entering/exiting flux measurements 48 Figure 5- 5. The paths o f the light fluxes from the light sources 49 Figure 5- 6. Components o f the light flux in a section (k) o f the variable extractor light guide 49 Figure 5- 7. The control interface for the Visual Basic program with the spread sheet running at the background simultaneously 53 Figure 6- 1. The dimensions o f one o f the rooms 55 Figure 6- 2. The dimensions and construction o f the variable extractor light guide 56 Figure 6- 3. The construction o f the variable extractor (not to scale) 56 Figure 6- 4. The dimensions o f the variable extractor (not to scale) 57 Figure 6- 5. The 4 X amplifier circuit using the L M 1 2 C L 80W operational amplifier . 58 Figure 6- 6. The complete scale prototype o f the variable extractor light guide system59 Figure 6- 7. Points where the relative illuminance measurements were taken in the room 60 Figure 6- 8. Measurement o f the input luminous flux at one end o f the light guide 61 Figure 6- 9. (a) Measurement o f the output luminous flux from the variable extractor and (b) A more efficient flux measurement scheme 62 Figure 6- 10. (a) A x i a l angle o f the A R 1 1 1 light source on the y-z plane and (b) Normal direction o f the source perpendicular to the x-axis 64 Figure 6 -11 . The graph o f contrast ratio versus axial angle o f A R 1 1 1 65 Figure 6- 12. Measurement set-up for determining source distance 66 Figure 6 -13 . The graph o f contrast ratio versus the percent input flux from the source 66 Figure 6- 14. Response o f output flux to the applied voltage in the variable extractor (asymmetric hysteresis curve) 67 Figure 6- 15. Clusters (net) o f si l ica particles at 40V after 2 hours 69 Figure 6- 16. The 10 by 10 look up matrix for the scattering coefficient 70 Figure 6- 17. Testing o f the control algorithm with two sources: case 1 74 Figure 6- 18. Testing o f the control algorithm with two sources: case 2 75 Figure 6- 19. Testing o f the control algorithm with two sources: case 3 76 Figure 6- 20. Testing o f the control algorithm with four sources: case 1 77 Figure 6- 21 (a). Testing o f the control algorithm with four sources: case 2 78 Figure 6- 21 (b). The amount o f extraction from each extractor for case 2 78 Figure 6- 22. Testing o f the control algorithm with four sources: case 3 79 Figure 6- 23. Testing o f the control algorithm with four sources: case 4 79 Figure 6- 24. Testing o f the control algorithm with four sources: case 5 80 Figure B - 1 (a): Example o f optical structure in T racePro® (cross section view) 88 Figure B - 1 (b): Example o f optical structure in T racePro® (side view) 89 Figure C - 1: Typ ica l ray diagram for TracePro® model 90 ix Figures E - 1 and E-2 : Other cases tested in section 6.3.5.1 105 Figures F - 1, F-2 , and F-3 : Other cases tested in section 6.3.5.2 107 x A C K N O W L E D G E M E N T First of all, I would like to thank Januk Aggarwal, Alison Clark, Vincent Kwong, Anne Liptak, Helge Seetzen, Kim Tkaczuk, and all the past and present co-op students in the Structured Surface Physics Lab for their very helpful suggestions and support. Big thanks to Michele Mossman for encouraging and guiding me through the project. I would also like to thank all the machine shop technicians for providing me, who they called "the trouble maker", all the equipments and technical support. Thank you to Tony Walters and Janis McKenna for their advice about graduate school at U B C . Special thanks to 3 M company for providing some of the key materials used in this research. Furthermore, sincere thanks to Andrzej Kotlicki for his continuous support and guidance throughout the course of this project. I gratefully thank my supervisor, Lome Whitehead, for generously providing me with his ideas and advice. I've also learned a lot from his "story of life". Finally, I would like to thank my family and friends for all their non-academic support. xi 1 INTRODUCTION Hol low prism light guide systems have been used for i l lumination in various settings, such as hazardous industrial areas, highway tunnels, and general office buildings. In such systems, the light from the end source is directed and confined within the light guide by total internal reflection (TIR), and while it is propagating through the guide, a portion o f it is extracted along the guide for the purpose o f il lumination. B y using extractors (typically white diffusive films) designed specifically for guides o f different geometries, uniform extraction or illumination can be achieved along the light guides. Despite the fact that most o f the fundamental problems associated with prism light guides have been resolved by significant research efforts, it is expensive to design specific shapes o f extractors for large light guides since a light extraction characteristic must vary along the length o f the guide to achieve uniform illumination (i.e. more light has to be extracted when farther away from the light source), and the required extraction function depends on the length and the desired emission profile. Moreover, although uniform illumination is applicable in most areas, it is sometimes preferable to be able to control the i l lumination level in different sections o f the light guide. It is also preferable to be able to mass-produce the same shaped extractors regardless o f the geometries o f the guides. The work presented in this thesis establishes a new variable extraction technique for the prism light guides, and the guides which employ this technique are called "variable extractor light guides". Frustration o f total internal reflection is used as the mechanism to control the extraction or illumination level along the light guide. Total internal reflection (TIR), the primary concept in the workings o f prism light guide systems, is a mechanism to fully conserve the energy o f light rays (electromagnetic waves) reflected at an interface between two different optically dense materials (it only happens for light rays which propagate from a medium toward a less optically dense medium provided that those rays have sufficiently large angle o f incidence at the interface). T I R confines the light rays in prism light guides as wel l as in fiber optic cables. However, the electromagnetic fields are not completely absent in medium 2 (the less optically dense medium); a transmitted wave known as the "evanescent wave" is 1 exponentially attenuated into medium 2. This attenuation depth or the penetration depth is usually less than half o f the visible wavelength (-25 urn). A s w i l l be discussed later, this evanescent wave region plays a very important role in the variable extractor since T I R at the interface can be switched on and off by changing the optical properties in the region (this process is so called "frustration" o f TIR) . In a variable extractor light guide system, such frustration is controllably applied by moving scattering materials into the evanescent wave region to generate the desired illumination level in different section o f the light guide. Although the idea o f evanescent wave scattering has been applied in many different fields such as T I R microscopy and optical switch for fibers, this thesis represents the first use o f controlled scattering and frustration o f T I R in prism light guide systems for illumination purposes. The advantages o f variable extractor light guide systems in comparison with conventional light guide systems are basically outlined above. The illumination level in different sections o f the guide can be varied based on frustration o f TIR, and a control algorithm can be applied to the light guide system using a computer to achieve uniform illumination as we l l as different desired illumination levels along the guide. In addition, the variable extractor presented in this thesis can be mass-produced for general use in light guides since the level o f extraction can be controlled along the guide with a general shape o f extractor. The most promising system for frustration o f T I R has been identified as a l iquid suspension o f electrostatically charged particles. 1 Dur ing the course o f this research, si l ica particles were used. Ideally, these particles should be similar in size to the wavelength o f visible light and sufficiently different in refractive index so that they can strongly scatter light thus effectively frustrating the T I R and extracting light out o f the guide. In addition, they should also possess a non-zero net charge. B y applying an electric field with different.polarities, the particles can be moved (by the phenomenon called electrophoresis) into and out o f the evanescent wave region to modulate the surface reflectance and scattering level. In order to fully understand the physical basis and the operation o f the variable extractor light guide, basic principles and background information with regard to the workings o f 2 the prism light guide w i l l be reviewed in Chapter 2. In addition, a brief description o f the conventional light guide system is included to provide a framework for comparison to the variable extractor light guide system. In Chapter 3, issues specifically influencing the design o f a variable extractor and a light guide using the variable extractors are discussed. The test cel l construction and performance for the variable extractor are provided in Chapter 4. Experimental results o f the reflectance response to time-varying electric fields are presented as we l l as the .factors influencing the reflectance modulation. Computer ray trace models were designed to determine the reflectance in the variable extractor light guide system. The results o f the Monte Carlo ray tracing are presented in Chapter 5. A l s o in Chapter 5, a simulation and control algorithm developed to predict and vary the extraction or il lumination level along the light guide is discussed. Chapter 6 describes the construction details for the actual scale prototype o f the variable extractor light guide system. Hysteresis effect in the variable extractor and the look up tables associated with it are also discussed. In the last section o f this chapter, the measured illumination levels for different settings are compared with the predictions obtained from the control algorithm. These results establish the feasibility o f using electrophoretic particles in the variable extractor light guide based on frustration o f T I R and scattering modulation, and they also suggest a number o f areas for further work. 3 2 B A C K G R O U N D In this chapter, basic principles wi th regard to the workings o f a variable extractor light guide system w i l l be discussed. A brief description o f conventional prism light guide system is included to provide a framework for comparison to the variable extractor light guide system. 2.1 Conventional Prism Light Guides Based on the idea o f piping light from a remote source to an interior space for illumination purposes, prism light guides have been invented. Based on total internal reflection, high efficiency uses o f light can be achieved by using prism light guide. In this section, the concepts o f conventional prism light guides are reviewed. In addition, disadvantages o f conventional prism light guides w i l l be discussed later in the section. 2.1.1 Total internal reflection The primary concept in the workings o f a prism light guide is based on the application o f total internal reflection (TIR). The condition for T I R is met when light rays propagating in a medium make contact with another medium with lower index o f refraction (i.e. less optically dense) at angles o f incidence greater than the critical angle. The fundamental principles with regard to T I R w i l l be reviewed in this section. 2.1.1.1 Index of refraction A s is wel l known, light is an electromagnetic wave. In a particular medium, the propagation speed o f this wave depends on the index o f refraction o f the medium, n, which is the ratio o f the speed o f the electromagnetic wave in vacuum, c, to that in the medium, v: .« = - (2-1) v A t standard temperature and pressure (STP), the index o f refraction o f air and water is about 1.0003 and 1.33, respectively. For more optically dense mediums such as acrylic 4 and polycarbonate, the index values are about 1.49 and 1.59, respectively. The value o f n depends on the wavelength o f the light, which is known as dispersion. 2 For the materials considered throughout the course o f this study, this effect is very small . In terms o f the relative permittivity, sT and the relative permeability, o f the medium, n becomes the fol lowing: n = ^ErfM- (2-2) There are magnetic substances that are transparent in the infrared and microwave regions o f the spectrum, but materials that are transparent in the visible are primarily considered in this study, and these are a l l essentially "nonmagnetic". In nonmagnetic materials /^=1, and (2-2) becomes: Yl-slSr (2-3) A s is generally known, the index o f refraction can have both real and imaginary components as shown in (2-4), which is analogous to the dielectric constant o f the medium. The imaginary component o f the dielectric constant describes the energy loss in oscillating fields in the medium, and that o f the index o f refraction represents the absorbance o f the medium. n = nR+ in, (2-4) In other words, n, = 0 in an absolutely transparent medium (i.e. non absorptive), whereas n, is not zero when the intensity o f light is attenuated along the medium. A s is wel l studied, the intensity o f light, 7, which drops off exponentially along a distance, y, in a medium with an absorption or attenuation coefficient, a, is given by I(y) = Ioe-ay (2-5) where IQ is the initial intensity, a (the rate o f attenuation) is related to the angular frequency, co, by the fol lowing relation 4: a = '- (2-6) 5 A l l in a l l , the index o f refraction describes the behaviour o f light in mediums o f different optical densities. It is one o f the primary concepts in this study since it determines the conditions for TIR, which w i l l be discussed in the fol lowing section. 2.1.1.2 Conditions for TIR at an interface From the boundary conditions for electromagnetic waves incident on dielectric boundaries, Snell 's L a w o f refraction can be written as: sin (9, sin<92 (2-7) f r \ sin (9, arcsin J where vi and v 2 are the speed o f light in the two mediums. From (2-1) and (2-7), (h can be solved in terms o f the indices o f refraction, n\ and m: (2-8) A s shown in Figure 2-1, an electromagnetic wave, represented by a light ray, makes contact at an interface between two different optically dense mediums. The first has a refractive index value o f n\\ the second has a lower value, n2, and as a result from (2-8), &i > 0\ as shown below. U x Dielectric n Boundary * 2 \ 6o (a) (b ) Figure 2-1. Snell's Law of refraction 6 The conditions for T I R are met when Snell 's law generates a complex angle for b\ (i.e. when ( « i / « 2 ) s i n 0\ > 1). In other words, T I R happens for a l l light rays having angles o f incidence greater than a critical angle, 0C j as shown in Figure 2-1(b), derived from (2-8) when 02 equals 90° : 6„ = arcsin (2-9) According to (2-9), the conditions for T I R depend on the ratio o f the refractive indices o f the two mediums. 2.1.1.3 The evanescent wave A s described previously, when light passes from an optically dense medium into a less dense one ( « i > ni), the propagation vector bends away from the normal as shown in Figure 2-1 (a) according to Snell 's law. In particular, i f the light is incident at the critical angle, then 62 - 90° , and the transmitted ray just travels along the interface as shown in Figure 2-1 (b). I f 0\ exceeds 6Z, there is no refracted ray at a l l , only a reflected one (TIR). Even so the electromagnetic fields are not zero in medium 2; the transmitted wave known as the "evanescent wave" is exponentially attenuated into medium 2, and there is no net transfer o f electromagnetic energy across the interface. 5 ' 6 Evanescent Wave Figure 2- 2. Pictorial representation of evanescent wave This so-called evanescent wave propagates along the interface effectively penetrating a very short distance into the medium as shown pictorially in Figure 2-2. The penetration depth, /, is given by 7 (2-10): 7 1 = An(n? s i n 2 9-n22)]12 (2-10) in which Xo is the wavelength o f light in vacuum, and 9 is the angle o f incidence with respect to the interface normal. Figure 2- 3 shows the penetration depth o f the evanescent wave for light making contact at a prism (polycarbonate)-acetonitrile interface (n\ = 1.59, « 2 = 1 -34), at a wavelength, Xo, o f 632.8 nm, as a function o f angle o f incidence. In this case, the critical angle, 6>c> is about 56.9°. Figure 2- 3. Penetration depth as a function of the angle of incidence A s shown above, the wave penetrates a relatively long distance into the second medium (acetonitrile) when its angle o f incidence is very close to the critical angle, and the depth rapidly drops off as the incident angle decreases. A s a result, the farther beyond the critical angle, the less the penetration depth and the faster the attenuation (in the very narrow range just past the critical angle). Beyond that narrow range, the penetration depth is about hal f a wavelength o f the visible spectrum, or 0.25 um as shown above. A s w i l l be discussed in section 2.2, by moving materials into the evanescent wave region to scatter or absorb the electromagnetic energy, T I R at the interface can be reduced or "frustrated". 8 As it is the fundamental concept of conventional prism light guides, a description of TIR has been presented above. The key material used to achieve TIR in conventional prism light guides will be discussed next. 2.1.2 Micro-replicated sheets: Optical Lighting Film (OLF) A typical hollow prism light guide uses a polymeric film, known as optical light film (OLF), which is a micro-replicated sheet made of polycarbonate micro-prisms with a pitch of 356 u.m and an isosceles prism angle of 90°, to achieve high reflectance along the guide. To prevent any energy loss in the prism light guide, it is important for the absorption of the reflective surface to be as low as possible. Using carefully fabricated moulds, very precise micro-structures can be made optically clear in the bulk (less than 2% absorption)9. This process is generally known as micro-replication. Figure 2- 4 (a) and (b) show a TIR path in the OLF for a prism light guide with a circular cross section. As shown below, OLF has translational symmetry along a direction r( (i.e. the structure shape of the micro-replicated film is the same in all cross sectional planes perpendicular to r f l). As a result, similar to an extrusion, the system has linear features. Figure 2- 4. (a) A ray path undergoes total internal reflection in the prism light guide: the side view of the O L F in the light guide shown in (b) 9 Figure 2- 5. (b) A light guide with a circular cross section (translational symmetry) In addition, the linear features make a light ray with a component propagating along the translational symmetry axis experience an enhanced refractive index ratio in the optical system. This enhancement is essential for determining the conditions for T I R in the prism light guide and w i l l be discussed further in section 2.1.4. For the moment, a good and simple way to define the surface reflectance should be addressed. 2.1.3 Specification of reflectance in prismatic systems A structure is considered to be an optical surface when its macroscopic surface normal is well defined (i.e. it is macroscopically planar over a region larger than the scale o f its surface structure or optical penetration depth). For an arbitrary optical surface, the reflectance measurement is quite complex since it depends not only on the viewing angle but also on the ambient luminance distribution. A t a particular viewing angle, the luminance o f a surface is obtained by taking the solid-angle integral o f the product o f the bi-directional reflection distribution function ( B R D F ) and the luminance distribution of the background. 1 0 T o simplify the complexity, the reflectance o f a surface discussed in this thesis is defined as the ratio o f the surface luminance at a particular viewing angle to that o f a reference sample (under a we l l defined and uniformly luminous environment). This reference sample can be a piece o f O L F , or a piece o f radiant mirror f i lm ( R M F , a near-100% reflective specular surface)", depending on the desired specifications. 10 2.1.4 Enhanced refractive index ratio A s mentioned in section 2.1.2, the indices o f refraction, experienced by the light rays with a component propagating in the direction o f the translational symmetry, are effectively enhanced in a prism light guide system. 1 2 The cross section and the side views o f the optical system with translational symmetry are shown in Figure 2-5. medium o medium i medium j (b) Figure 2- 6. (a) Apparent angles for two-dimensional projection of a ray path and (b) the side view showing the axial angle of incidence The relationship between the angles o f incidence as shown in Figure 2-5 (a) and (b) is given b y : 1 3 («,. 2 - « 0 2 cos 2 £ ) " 2 s in/?; = ( « / - n o 2 c o s 2 0 ) 1 / 2 s i n £ ; (2-11) where /? / and p'} are the apparent angles o f incidence o f a ray path from medium i to medium j , #is the axial angle o f incidence between the ray direction and the direction o f translational symmetry o f the system, and « ' s are the indices o f refraction in the corresponding mediums. 11 From the 3-D analogy o f Snell 's L a w in this optical system as shown in (2-11), the enhanced index o f refraction is given by: A s w i l l be described in later chapters, the operating range o f the light source(s) used for the variable extractor light guide was determined based on this index ratio enhancement. In the next section, the materials designed to extract light out o f conventional prism light guides are described. 2.1.5 The extractor for conventional light guides One o f the challenges o f constructing a hollow light guide system is finding appropriate devices to deflect the light out o f the guide and into the desired spaces. These light deflecting components are called extractors. The most common type o f prism light guides have been continuously light emitting pipes, with a continuously diffusive extractor f i lm inside the tube. When a given light ray makes contact with the extractor f i lm, it is diffused and deflected into directions with incident angles greater than the critical angle. Thus, those rays are no longer confined by the O L F in the guide. They penetrate the O L F and escape from the light guide to form desired illumination below the guide as shown in Figure 2- 6. Figure 2- 7. A sample ray tracing in a conventional prism light guide A typical extractor shape used to obtain uniform luminance along a conventional light guides is shown in Figure 2- 7 (a). The light source is located at the end o f the guide, (2-12) 12 and in order to achieve uniform luminance, the width of the extractor increases as a function of the distance from the light source since the intensity of light decreases as a function of the distance. As a result, this extractor film has to have a specific shape for a particular light guide length and diameter. For conventional light guides, the extractor is typically located in the interior of the OLF as shown in Figure 2- 7 (b). Figure 2- 8. (a) The top view of a typical shape of the extractor used for uniform illumination and (b) the extractor inside the conventional prism light guide (prism size not to scale) A number of undesirable features of conventional light guides is discussed in the next section. 2.1.6 Disadvantage of conventional prism light guides Despite the fact that most of the fundamental problems associated with prism light guides have been resolved by significant research efforts, it is still not economical to design specific shapes of extractors for large light guides since the light extraction characteristic must vary along the length of the guide to achieve uniform illumination, and the required extraction function depends on the length and the desired emission profile. Consequently, general shaped extractors cannot be mass-produced for conventional prism light guides. Moreover, the amount of extraction in conventional light guides cannot be controlled once the specifically designed extractor has been built into the guide. Source End (a) (b) 13 To counter such difficulties, a new variable extraction technique has been developed which overcomes the challenges of conventional light guides. This technique is based on frustrated TIR (FTIR), which is described in the following section. 2.2 Frustrated T IR (FTIR) As mentioned in section 2.1.1, by moving materials into the evanescent wave region to scatter or absorb the electromagnetic energy, TIR at the interface can be reduced or "frustrated", from a 100% reflective state to a highly scattering or absorptive state, as shown in Figure 2-8. Figure 2- 9. (a) TIR and (b) frustration of TIR by a scattering or absorptive material Since the evanescent wave region is typically less than half a wavelength of the visible spectrum, the material is only needed to move a small distance into the region to sufficiently frustrate TIR. Although the idea of evanescent wave scattering has previously been applied in various fields such as TIR microscopy and optical switch for fibers, the work presented in this thesis is, we believe, the first demonstration of controlled frustration of TIR and modulated extraction/scattering in a prism light guide. The development of a practical variable extraction technique for prism light guide based on this controlled TIR approach required the use of specially chosen particle suspension. This is described in the following section. .71 Evanescent Wave (a) (b) 14 2.3 Particle suspensions and electrophoresis A s previously mentioned, the significance of the electrostatic charge o f the colloidal particles in this thesis is that they can be moved by an applied electric field. This controlled motion, known as electrophoresis, has been identified as an appropriate control mechanism for frustrating T I R with micro-particles according to recent research. 1 4 The choice o f the suspended particles and suspending fluid is critical in obtaining a significant electrophoretic switching effect as described in section 2.5. In order that there be T I R at the OLF-suspension interface, the suspending fluid must have a refractive index that is less than that o f the O L F (polycarbonate). The particles must provide optical contrast with the suspending fluid; particles with a high refractive index are desirable. They must also show a nonzero electrophoretic mobil i ty (i.e. they must posses a net surface charge). Chemical compatibility with the suspending fluid is necessary as wel l . Moreover, the particles should be small and have a density nearly equal to that o f the suspending fluid to avoid sedimentation. However, i f the particles are too small, they w i l l not scatter light, and they w i l l undergo severe Brownian mot ion . 1 5 A s a result, they w i l l not effectively extract light, and their positions w i l l be more difficult to control. Particles having an average diameter size o f from 0.1 to 1 micron are most l ikely optimal. The electrical resistance o f the suspension liquid should be extremely high in order to minimize the power required for switching between the T I R and F T I R state as we l l as to reduce the rate o f any electrochemical processes in the particle suspension. It is also preferred that the particles do not aggregate over time; aggregation is hindered by Coulomb repulsive forces between particles and can be further prevented by the use o f suitable dispersants. Detailed specifications o f the particle suspension used in this research are described in Chapter 3. During the course o f this research, hysteretic behaviour o f the particles in the suspension with respect to the applied field/voltages has been observed. In the next section, a short introduction to hysteresis is provided. 15 2.4 Hysteresis Hysteresis is a phenomenon in which the response o f a physical system to an external stress depends both on the present magnitude o f that stress and also on the previous history o f the system. It can also be described as a retardation effect on recovery from elastic deformation when the forces acting upon a body are changed or removed. In other words, it represents the history dependence o f physical systems. 1 6 The term is most commonly applied to magnetic materials: i f a magnetic field is applied to an initially unmagnetized material and is then removed, the material retains a residual magnetization. The graph o f the magnetic induction B versus the magnetic field H is called a hysteresis loop. The area o f the loop is proportional to the energy loss in terms o f heat when the system completes a cycle. A typical hysteresis loop is shown in Figure 2-9. Hysteresis is present in several other systems as wel l . For example, thermal hysteresis occurs when the value o f a given property such as the dielectric constant o f a body depends both on the body's temperature and also on whether the temperature is rising or falling in the body. ' 7 In this thesis, hysteresis refers to the behaviour o f the particles in the electrophoretic suspension with respect to the applied voltages, and it w i l l be discussed in more detail in Chapter 6. 16 -3.0 u • 1 1 ' • 1 • 1 -1.0 -0.5 0.0 0.5 1.0 Magnetization (M) Figure 2- 10. A typical hysteresis loop18 2.5 Evanescent wave scattering A s described previously, F T I R occurs when materials are moved to scatter or absorb the electromagnetic energy in the evanescent wave region by means o f electrophoresis. A n electrophoretic switching effect (relative reflectance change between the T I R and F T I R state) can be obtained because the material (which is placed within the evanescent wave region) has a refractive index different from that o f the suspension l iquid. A s a result, it scatters and/or absorbs light thus removing energy from the otherwise totally reflected beam. For the purpose o f this thesis, this technique was used to modulate the extraction to achieve variable i l lumination levels along the prism light guide. Because we must quantify the il lumination level, the concepts o f luminous flux and illuminance are introduced in the next section. 17 2.6 Luminous flux and Illuminance A primary goal of this research has been to control the illumination level extracted from different sections of the light guide (i.e. in different rooms) using electrophoretic modulation of TIR by highly scattering silica particles. The relative illumination level can be measured as the illuminance at different points of the room or as the output luminous flux from the variable extractor. According to the International Commission on Illumination (CIE) International Lighting Vocabulary,19 luminous flux, Ov, is a quantity derived from radiant flux, d>e, by evaluating the radiation according to its action upon the CIE standard photometric observer, and its unit is the lumen (lm). Radiant flux, <De, is the power emitted, transmitted or received in the form of radiation, and its unit is the watt (W). The CIE standard photometric observer is the ideal observer having a relative spectral responsivity curve that conforms to the V(X) functions (where V(A) is the spectral luminous efficiency, a function used to represent the human visual response to optical radiation, and it is used in the summation in the definition of luminous flux (2-13)). For photopic (day/light) vision, where K m = 683 lm/W is the luminous efficacy of radiation at the wavelength of peak sensitivity, X is the wavelength, and c ^ > e ^ j s the spectral distribution of the radiant dX flux. Illuminance (at a point of a surface), Ev , is defined as the quotient of the luminous flux, dOv, incident on an element of the surface containing the point, and the area dA of that element. From (2-14), luminous flux can be written in terms of illuminance as follows: (2-13) dA (2-14) 18 Q>v = ^Ev-dh (2-15) In Chapter 6, detailed methods of measuring luminous flux and illuminance are provided. Having briefly introduced the background information associated with this study, it is now appropriate to discuss this new variable extraction technique in more detail. 19 3 DESIGN ISSUES IN A VARIABLE EXTRACTOR AND LIGHT GUIDES USING VARIABLE EXTRACTORS A s described in the previous chapter, T I R can be frustrated by scattering or absorbing the electromagnetic energy in the evanescent wave. In this chapter, the key conceptual issues regarding a possible extraction technique based on F T I R and the light guides employing this technique are presented. 3.1 Principle of a FTIR-based extraction technique Based on the motivations to generalize the shape o f the extractor and to control the il lumination along the light guide, a new extraction technique using frustrated T I R has been developed. This FTIR-based extraction technique can be demonstrated using the linear prismatic structure shown in Figure 2-5. Figure 3-1. Principle of a FTIR-based extraction technique A s shown in Figure 3-1, an optical lighting film ( O L F ) , with refractive index o f « i = l . 5 9 , is separated by a thin air gap, with refractive index n2=\.0, from scattering micro-particles. The left portion o f Figure 3-1 shows the highly reflective (TIR) state, and the right portion shows the scattering (FTIR) state. For the T I R state, a light ray enters the film at normal incidence and undergoes T I R at each prismatic facet. A s a result, complete reflection, which propagates at the opposite direction o f the incident ray, is achieved. B y moving the scattering particles into optical contact with the A OLF (^=1.59) Air Gap (n2=1) Scattering Particles Scattered Light 20 prismatic rear surface o f the sheet, as shown in the right-hand portion o f Figure 3-1, the majority o f the incident light is scattered at the first prismatic facet, and any light reflecting from this surface is further scattered at the second facet. A s a result, almost complete scattering/extraction o f the light and elimination o f reflection can be achieved. Removing the particles from the surface (outside the evanescent wave region) completely restores the reflection and allows control o f reflectance and light extraction. Since the evanescent wave zone is microscopically thin, only a very small movement o f the particles is required to switch between the highly reflective and highly scattering states. A s mentioned previously, a promising method for actuating this type o f extraction technique would use electrostatic force, caused by an applied electric field, to controllably move the particles into contact. Various requirements for achieving this optical switching effectively w i l l be discussed in detail in sections 3.2, 3.3 and 3.4. 3.2 Index mismatch requirements A s described in section 2.1.1.2, the higher the index mismatch ratio, « i / « 2 , the smaller the critical angle as defined in (2-9). Furthermore, a smaller critical angle implies that a larger angular range o f light rays can undergo T I R . Consequently, the key to achieving high reflectance at a surface given a large angular distribution o f light rays is to maximize the index mismatch ratio. For a typical prism light guide system, a ratio o f 1.59 is achieved with a polycarbonate (OLF)/a i r interface, and it works wel l for conventional prism light guides. Similar ly , a ratio o f 1.59 is achieved for the FTIR-based extraction technique described schematically in Figure 3- 1; T I R occurs in a polycarbonate sheet having index « i=1.59 and is frustrated by scattering particles moving in air (ri2=\). Al though this system works quite wel l optically, there is no mechanism which can control the motion o f the particles in air, and also there are undesirable surface energy effects associated with the motion; the particles should not make physical contact with the interface since it requires too much energy to remove them. Resulting from these surface energy considerations, a solid-l iquid interface has been identified to be very desirable for a controlled T I R system instead o f a solid-air 21 interface. Thus, the use o f l iquid as the second medium was applied to FTIR-based extraction technique. However, the use o f a liquid as the second medium makes the index ratio, n\lri2, at the interface quite low since the refractive index o f most liquids is greater than ni=\A. A s a result, T I R w i l l not occur for many light rays at the O L F -liquid interface. This issue w i l l be addressed further in the next section. 3.3 Optical requirements for T I R at a solid-liquid interface Due to the fact that the index o f refraction o f most l iquid is much higher than that o f air, high reflectance given a wide angular distribution o f light rays w i l l not l ikely be achieved at the O L F - l i q u i d interface. One way to improve the situation would be to use a higher index prismatic f i lm; however, the index o f a good optical prismatic f i lm is currently limited at 1.59 (polycarbonate). A s a result, it was necessary to search for lower refractive index liquids. Acetonitrile, which has an index o f 1.33, was used in the controlled T I R device in recent research. 2 1 However, due to its chemically hazardous nature and its density mismatch to the particles, it has been identified as another unsuitable candidate for the FTIR-based extraction technique. In the end, perfluorinated hydrocarbon liquids, which have an index o f 1.276, were identified as a suitable suspension 2 2 to use with the scattering si l ica particles. In addition to their low index o f refraction, these liquids also possess other desirable characteristics such as high optical transmission, low dielectric constant, and resistance to breakdown in wide temperature range. One o f the perfluorinated hydrocarbon liquids sold under the tradename F luor ine r t™ (a product o f the 3 M Company), in particular, F C - 7 5 2 3 (molecular formula: CgFieO) was used through out the course o f this research. A s an example to show the improvement in satisfying the condition for T I R using perfluorinated hydrocarbon liquids, the critical angle between the O L F - l i q u i d interface (n\lnj = 1.25) is substantially reduced to 53.4° as compared to the value o f 70.6° for the OLF-hydrocarbon o i l interface (n\/ri2 = 1.06). A detailed list o f the physical and electrical properties o f F luor ine r t™ FC-75 is provided in Appendix A . The fol lowing section describes the angular dependence o f light rays in hollow light guide system and how these low index liquids can be used with O L F in the development o f a variable extractor light guide. 22 3 .4 A n g u l a r r e q u i r e m e n t f o r TIR: a p p a r e n t angle o f i n c i d e n c e a n d a x i a l angle o f i n c i d e n c e As described in section 2.1.4, the indices of refraction are enhanced in a prism light guide system. For a hollow light guide system with an exterior fluorinert chamber (as described previously), the condition for TIR depends on the apparent angles of incidence as shown in Figure 3-2 and the axial angle of incidence. The critical angle is achieved when B J = 90 °, and from (2-11) one can write the apparent angle of incidence, B\, in terms of the axial angle of incidence, 0, for this condition. In the same fashion, one can write the apparent angle of incidence, a, in terms of B\, and as a result, a is related to 0 by: f / ' - \ I / 2 V a = sin" f 2 2 2 n~\ n, -n0 cos 0 yn0 -n0 cos 0 sin 45° -sin" * 2 r\ •n0 cos 0 2 2 TTi -nQ cos 6j where n0 = 1, n{ = 1.59, and « j = 1.276 as shown in Figure 3-2. \ a Air (n 0=l) I O L F (A7|=1.59) (3-1) Fluorinert (^=1.276) Figure 3- 2. Apparent angles for two-dimensional projection of a ray path in a hollow light guide with an exterior fluorinert liquid chamber A plot of a versus #is shown in Figure 3- 3. TIR occurs in the shaded region. 23 0 5 10 15 20 25 30 35 Axial ang le of inc idence in d e g r e e s Figure 3- 3. Angular requirement for TIR in a hollow light guide with an exterior fluorinert liquid chamber (air-OLF-fluorinert) A s shown above, the maximum axial angle o f incidence, 0, for T I R to occur is at about 31° where the apparent angle o f incidence, a, equals zero. When (9 is below 6° , a becomes imaginary. In other words, T I R occurs when the axial angle o f incidence is below 6° regardless o f the apparent angle o f incidence. Based on the T I R region as shown above, the operating range o f light source used in the variable extractor light guide was determined, and it w i l l be described in Chapter 4. 3.5 Particles used to frustrate T IR in low refractive index liquid A s described in section 2.3, particles used to frustrate T I R in a liquid suspension should be small and have a density nearly equal to that o f the suspending fluid to avoid sedimentation. They must also posses a substantial surface charge to exhibit a nonzero electrophoretic mobil i ty, and they should have an average size o f the wavelength o f the visible light in order to provide sufficient scattering/extraction from the light guide. Si l ica particles were used in this research. These nearly monodispersed spheres produced with a proprietary sol-gel technique were obtained from Geltech, Inc. 24 (Alachua, Fla). These particles have a nominal diameter o f 0.5 micron, a bulk density o f about 1.7 g/cm 3 , and a refractive index o f about 1.42. Currently, the most promising mechanism uses the electrophoresis o f charged si l ica particles to frustrate the TIR . A s mentioned previously, s i l ica particles were suspended in perfluorinated hydrocarbon l iquid using a nonflammable and chemically inert l iquid dispersant, Kry tox® 157 F S H Fluorinated O i l , 2 4 which chemically bounds the particles and the perfluorinated hydrocarbon l iquid (thus achieving stabilization o f particles in the liquid suspension). The suspension was mixed using a sonicator and contained in a cell chamber, which we call a "variable extractor". In such a system, an electric field applied between transparent conductors on either side o f the chamber moves the particles, by electrophoresis, toward and away from the T I R interface as w i l l be described in the next section. 3.6 Electrophoretic suspensions in a variable extractor A s shown in Figure 3-4, the simplest method to confine the particle suspension is to sandwich the suspension with a prismatic sheet and a rear flat substrate, thus forming a chamber . 2 5 ' 2 6 , 2 7 The prismatic facets and the surface o f the rear substrate occupied by the suspension chamber were coated with a thin layer o f transparent conductor, indium tin oxide (ITO). This layer is usually deposited on to the surface by sputtering, a standard thin film deposition technique. In addition, this ITO coating is 50 nm thick and about 97% transparent; its surface resistance is about 100 Q/square. Similar to a parallel plate capacitor, application o f an electrical potential difference between the two conductive surfaces generates an electric field throughout the liquid chamber. The si l ica particles, which have an effective diameter o f about 0.5 urn and are positively charged, would then move in response to the field. Based on the polarity o f the applied voltage, the particles can be moved away from the T I R interface thus resulting the complete reflection o f the incident ray as shown in Figure 3-4 (a). O n the other hand, they can also be moved into the evanescent wave zone to frustrate T I R and to cause scattering, as shown in Figure 3-4 (b). (The directions o f electric field are also shown; note that the field lines concentrate at the tip o f the prisms and are perpendicular to the ITO coated surfaces.) 25 Incident Wave Front ITO Coated OLF Reflected Wave Front l l I I I lEvanescent Fluorinert Suspension" Zone .OOOOOOnonpooooonnc l - Reflected Light - - V Ray ITO Coated " OLF Prisms ITO Coated Substrate Silica Particles Evanescent Zone! / n n n n n n n n n ^ i T * y i v Direction of Electric Field Figure 3- 4. (a) The TIR state in a variable extractor (left) and the cross section view with the direction of electric field (right) (not to scale) Scattered Light Scattered Light Scattered Light - V Fluorinert Po Suspension^ ^ Direction of Electric Field Figure 3- 5. (b) The scattering state in a variable extractor (left) and the cross section view with the direction of electric field (right) The variable extractor presented in this thesis has been made in such a way that the OLF and the substrate are horizontally parallel to each other. This was done because the silica particles do not perfectly density-match the fluorinert liquid suspension in the extractor, so if the OLF and the substrate were aligned any other orientation, sedimentation would occur. This constraint leads to the specific design of the light guides which will be described in section 3.8. As detailed in section 3.7, it is possible to achieve reflectance values/scattering levels intermediate between the completely reflective and completely scattering states. This so-called grey scale behaviour is required for a practical variable extractor. 26 3.7 Grey-scale control of reflectance In order to modulate selective extraction along the light guide the ability to yie ld not only full reflectance and scattering states, but also the continuous range o f reflectance values intermediate between these two extremes is required. This is known as grey scale control. One simple approach to achieve grey scale is to employ an array o f small individually controlled extractors to achieve a range o f extraction levels in a particular section o f the light guide. In this case, the grey scale control can be achieved by setting the number o f extractors (pixels) to T I R or scattering state according to the desired illumination level. However, this approach requires a large number o f extractors and complex wir ing and control, which is undesirable. Another approach to achieve grey scale control, which was applied to the variable extractor light guide system described in this thesis, is to make use o f the field/voltage dependence o f the scattering/extraction level observed in the variable extractor. The liquid dispersant (krytox) used to coat and stabilize the particles in the suspension is thought to have a spring-like characteristic. In addition, an excess amount o f dispersant was required to prevent the irreversible deposition o f particles on the surfaces o f the prism light guide, and it is possible that the excess dispersant molecules form micelles 28 that in turn coat the surfaces. A s a result, the particles would not be moved into the evanescent wave region deeply enough to sufficiently frustrated T I R under a weak electric field (since the thick micelle layer has occupied the T I R interface), and the equilibrium position o f the particles would be reached once the spring force o f the micelle layer balanced with the applied electric force. Wi th a stronger electric field, the particles would be forced to move deeper into the evanescent wave region, thus scattering more o f the incident light. Consequently, the level o f scattering could quite accurately be controlled in such a system. This approach was used to control the extraction/illumination level in the variable extractor, but the extraction-field dependence in the variable extractor shows a hysteretic behaviour, which w i l l be discussed in Chapter 6. 27 3.8 Design of light guides using variable (FTIR-based) extraction technique As described in section 3.4, for TIR to occur in the variable extractor light guide, the apparent angle of incidence, a, and the axial angle of incidence, 6, of the light rays that enter the guide, must be within a certain narrow range of angles. As a result, every single reflection inside the guide must preserve that angular range in order to maintain TIR throughout the guide. Moreover, given that the extractor must be flat, the geometry of the light guide must be designed in such a way that all the light rays that enter the guide, wil l have the same apparent angle of incidence throughout the guide. Two specially designed light guides are described in this section. 3.8.1 Light guides with a parabolic cross section One of the light guides which can preserve the angle of incidence of light rays is a guide with a parabolic cross section. The construction of this parabolic light guide is shown 29 in Figure 3-5 (left). It uses the Radiant Mirror Film (RMF) , which can achieve almost 100% surface reflectance, to preserve the specular reflections along the guide. As shown in Figure 3-5 (right), the 45° parabolic cross section can direct the light rays whose apparent angle of incidence is close to 0° to have the same contact angle of incidence to the extractor. Radiant Mirror Film Figure 3- 6. Construction of the parabolic light guide (left) and a sample ray tracing in the guide (right) The areas of input for the light sources at the end of the parabolic light guide are labelled in Figure 3-7. In order to achieve the high switching effect between the TIR and the scattering state in the extractor as will be described in Chapter 4, a well-28 collimated beam of light with apparent angle o f incidence equal to zero is desirable. The source beam must enter the light guide from the areas labelled below. Area of InputX Figure 3- 7. Area of input at the parabolic cross section The phase space is defined as the product o f the solid angle o f the source beam to the area o f input. Even though the light guide with a parabolic cross section works with the variable extractor, the phase space associated with its cross section is not sufficiently large. In the next section, a light guide with a cross section o f a larger phase space with respect to the same size o f the extractor is described. 3.8.2 Light guides with a rectangular cross section Another light guide cross section which can preserve the apparent angle o f incidence o f the light rays is a rectangular cross section. The construction o f the rectangular light guide is shown in Figure 3-8. It also uses R M F to maintain the specular reflection on the walls. OLF - L RMF- Area of Input RMF f t Variable Extractor Figure 3- 8. The construction of the rectangular light guide and its area of input allowed for the source beam 29 The area o f input is also shown above, and the phase space associated with this cross section is substantially larger than that o f a parabolic cross section for the same size o f the variable extractors. Moreover, the rectangular light guide may also be easier to mass-produce than the parabolic guide. A sample ray tracing in the rectangular light guide is shown in Figure 3-9. Figure 3- 9. A sample ray tracing in the rectangular light guide A Monte Carlo simulation o f this rectangular light guide w i l l be discussed in Chapter 5. Based on the encouraging results from this simulation, a scale model prototype o f the variable extractor light guide was then built based on this design. 30 4 R E F L E C T A N C E A N D S C A T T E R I N G M O D U L A T I O N B Y S I L I C A P A R T I C L E S In this chapter, the test ce l l construction and performance o f the variable extractor are described. Experimental design for measuring reflectance and results o f the reflectance response to time-varying electric fields are presented, as we l l as the factors influencing the reflectance/scattering modulation. 4.1 Test cell construction A test cell was designed to measure the effective reflectance and scattering/extraction level from the variable extractor. Once optimized, this became a standard assembly throughout this study, and then a larger scale version o f the variable extractor was constructed for the actual prototype o f the variable extractor light guide. The test cell consisted o f a 25 mm x 75 mm transparent glass microscope slide and a 25 m m x 75 mm piece o f O L F . The glass slide was coated on one surface wi th a thin layer o f indium tin oxide (ITO), and the O L F was coated with I T O on its prismatic surface. (The I T O coated glass slides are commercially available through various sources. 3 0) This 50 nm thick I T O layer is about 97% transparent, and its surface resistance is about lOOQ/square. A s shown in Figure 4-1 (a), the test cell was constructed by sandwiching the two ITO coated surfaces facing one another with a spacer ring o f selected thickness in between (near the edge). The two surfaces were offset by a few millimeters to reserve a region where electrical contact could be made to the ITO surface o f the O L F and o f the glass slide. A wire lead was connected to the ITO coated surfaces using a small amount o f conductive ink. The side view assembly is shown in Figure 4-1 (b). The spacer material was chosen depending on the desired gap thickness; in this case a mylar f i lm with a thickness o f 0.1 m m was used. The size o f the spacer was wide enough to provide a uniform gap and to prevent the O L F from sagging in the center and making electrical contact wi th the other surface. The edges o f the slides were then sealed on three sides using silicone adhesive. One side was left open as a fluid port for f i l l ing the cell wi th the particle suspension. 31 Spacer Ring (a) Conductive Ink (b) Fluid Port Clear Epoxy J21 Copper Wire x-Particle Suspension OLF Rear Slide Figure 4- 1. Construction of the electrophoretic test cell (a) top view and (b) side view The particle suspension to be tested was introduced into the chamber by adding droplets through the fluid port using a small gauge needle or pipette. Once the cell was filled, the port was sealed using the silicone adhesive. One observation which was made during the course of this study was that certain adhesive used to seal the edges of the cell can affect the surface charges on the particles. For example, epoxy adhesive neutralized the charge of some of the particles and made the rest oppositely charged (from positive charge to negative charge). This behaviour was investigated, and the silicone adhesive was then identified as a good sealant for the test cell since it does not cause this problem. 4.2 Measuring reflectance As described in section 3.4, the light rays which make contact with the variable extractor must have a specific narrow range of angles of incidence (apparent and axial) in order for TIR to occur. The maximum range of axial angle of incidence can be achieved when the apparent angle of incidence for all the light rays is close to zero (i.e. well collimated beam of light). As a result, a well-collimated red laser beam was used to simulate a light ray, and the apparent angle of incidence was set to zero degree for all the reflectance measurement. 32 A s discussed in section 2.1.3, the reflectance o f a surface is defined as the ratio o f the surface luminance, at a defined viewing angle, to that o f a reference sample, under the selected luminous environment o f interest. The reference sample used in this case was a piece o f ITO coated O L F . The relative surface luminance was measured using a small integrating structure equipped with a TSL251 light-to-voltage optical sensor (a monolithic si l icon integrated circuit containing a photodiode), an operational amplifier, and various feedback components. 3 1 T o prevent saturation o f the optical sensor, a 15% transmissive filter was placed at the opening o f the integrating structure. The non-scattered reflected beam o f light from the test cell surface for a specified axial angle o f incidence entered the integrating structure and generated a proportional output signal. The set-up is shown in Figure 4-2. Integrating Optical Filter Structure ^^-^V* Figure 4- 2. Set-up for measuring reflectance A method o f measuring the scattered light from the test cell w i l l be described in section 4.5. 4.3 Design of the reflectance modulation experiment In order to optimize the performance o f the variable extractor, the set up described above was used to study factors that could potentially influence the reflectance and scattering modulation in the test cel l . These included axial angle o f incidence, strength o f applied field/voltage, and concentration o f the si l ica particles in the suspension. A s each factor was tested, the others were kept constant. For each factor listed above, the reflectance was measured and plotted as a function o f time in response to variations o f Test Cell | ^" Axial Angle of Incidence c Operational Amplifier 33 applied voltage/electric field, using a customized computer controlled power supply and data acquisition system. As shown in Figure 4-3, this computer data acquisition system consisted of a GPIB-PCIIA board from which a controlled voltage was applied across the test cell by the user, through a Stanford Research Systems DS335 function generator. At a specified frequency (of the oscillating applied field), the reflectance was measured through an Advantech PCL-818HG A/D converter data acquisition card, using the light detection system as described in the previous section. The control and data acquisition program was coded in Visual Basic. The circuit set-up is shown in Figure 4-3. GPIB Control Function Generator Computer • • • • • • • • • • • • • • • • Operational Amplifier Source Input to A/D Converter Integrating Test Cell Cylinder Figure 4- 3. Schematic diagram of data acquisition system To start the program, the waveform shape, frequency and amplitude of the applied voltage from the function generator were first specified, and the desired sampling rate of the reflectance measurement was selected. The function generator then sent the voltage across the test cell. The applied voltage as well as the optical sensor amplifier voltage was sampled sequentially according to the specified sampling rate, and these measurements were recorded into a data file. From the data file, the reflectance was plotted as a function of time in response to the applied field. 34 4.4 Time-varying reflectance modulation Using the data acquisition program outlined above (with a square waveform o f applied voltage), a plot o f the reflectance as a function o f time was generated in response to the applied voltage so that the reflectance change (extraction o f light) between the T I R and F T I R states could be determined. This plot also demonstrated the time required for the variable extractor to switch between these two states. Figure 4-4 shows a sample plot o f this type, wi th f requency, /= 0.25 H z , and amplitude, Fp=40 V , and at an axial angle o f incidence o f 20° from the red laser. The suspension used in this system was made up o f 10% by mass si l ica particles suspended in the fluorinert and l iquid dispersant. During the course o f this study, at most a 10% loss o f overall reflectance was recorded due to bulk absorption in the O L F and contamination o f the I T O coating (though the specific amount o f absorption varies from sample to sample). In the data presented in this chapter, the reflectance lost due to bulk absorption was taken into account by normalizing the reflectance value. The normalized reflectance is the ratio o f the voltage from the beam reflected of f the test cel l obtained by the optical sensor (within the integrating structure discussed in section 4.2) to the maximum voltage measured with the same optical configuration on a reference sample. In this case the reference sample was a piece o f ITO coated O L F . 35 2 0.1 0 0 1 2 3 4 5 Time (s) Figure 4- 4. Reflectance modulated by electrophoresis of silica particles A s shown in Figure 4-4, initially, at time r<0, the voltage o f 40 V was applied, corresponding to an electric field o f 5 x l 0 5 V m " 1 , and the positively charged particles were therefore secured near the ITO coated mylar surface, we l l outside the evanescent wave region. A s a result, the maximum reflectance value o f 1.0 was observed. A t time r=0, the applied field was reversed to - 5 x l 0 5 V m " 1 causing the particles to move across the cell , enter the evanescent wave region near the T I R interface, and scatter some o f the incident light. The degree o f scattering increased as the number o f particles near the interface increased. In this case, the percent change o f reflectance between the maximum and minimum normalized reflectance was about 55%, and it took about two seconds to switch between those two extreme reflectance states. A s mentioned in section 3.5, a l iquid dispersant (krytox) was used to stabilize the particles in the suspension. A n excess amount o f dispersant was required to prevent the irreversible depositing o f particles on the surfaces o f the cel l . This may explain the slow switching speed between the extreme T I R and F T I R states since the excess dispersant forms micelles which interfere with the movement o f the particles in the suspension. In addition, the shape o f the response curve o f the reflectance modulation (shown in the plot above) was found to depend on the suspension used in the test cel l . 36 4.5 Measurement of scattered light Using the test cel l in the same set up described above, the scattering levels corresponding to the maximum and minimum reflectance levels were measured within the integrating sphere. The test cell was placed inside the sphere with the source illuminating the cell from outside o f the sphere. A black card was used to absorb the reflected beam so that the luminance due to the light scattered by the surface o f the test cell could be measured using a SpectroScan as shown in Figure 4-5. The scattered luminance corresponding to the maximum reflectance was measured to be about 4% of the total luminance from the source, and that corresponding to the minimum reflectance was about 50%. This implies that almost al l the change in reflectance as shown in Figure 4-4 transferred to scattered light in the test cel l . Figure 4- 5. Experimental set-up for measuring scattered light (size not to scale) 37 4.6 Measurement of current flow The current through the test cell was determined by measuring the voltage across a 10 kfi . resistor connected in series with the cel l . It was found to be about 0.02 m A when 30V was applied from the power supply, and the lower the voltage is applied, the less the current flows through the cel l . 4.7 Factors influencing reflectance/scattering modulation A s already discussed, the behaviour o f electrophoretic particles in a variable extractor can be influenced by a number o f factors. This section explores the effects o f varying the factors that can be externally controlled. 4.7.1 Reflectance at different axial angles of incidence The reflectance was measured as a function o f the incident angle o f light. The test cell and the set up previously described was used. The percent change in reflectance between the maximum and minimum normalized reflectance (corresponding to ±30V) was measured for different axial angles o f incidenc. Figure 4-6 shows a plot o f these measurements. 38 o 70 u c a- 0 11 14 17 20 23 26 Axial Angle of Incidence in Degrees Figure 4- 6. Percent change in reflectance versus axial angle of incidence For angles beyond 22°, the maximum change in reflectance measured was about 58%, whereas for angles less than 14°, the maximum change was less than 40%. To achieve an average change in reflectance of about 50%, an operating range of axial angles from the light source was determined to be between 14° to 22° (in this axial range the apparent angle of incidence has to be less than 8° for all the light rays to undergo TIR: see Figure 3-3 and recall from section 3.4 that TIR will only occur within a particular angular range) for this variable extraction technique. In other words, the beam angle of the light source used has to be within this range (i.e. a half angle of less than 4°). 4.7.2 Intensity of applied field To demonstrate the effect of varying yet another factor, the same test cell and set-up is used as previously described. Figure 4-7 shows the percent change in reflectance versus the intensity of the applied field, while the axial angle of incidence is held constant at 20°. It is seen that the percent change in reflectance increases as the applied field increases until the field reaches about 4x105 V/m (corresponding to an applied voltage of ±30V). Based on these results (as well as the effects of particle clustering at higher 39 voltages as will be described in Chapter 6) a suitable range for the applied voltage to be used in the variable extractor has been determined. tance 60 tance -• tance 50 u **— 40 CL c o £ O) '—' c ro t-30 20 O rcent 10 rcent Q. n « i- L I I l i 0 100000 200000 300000 400000 500000 600000 I n t e n s i t y o f A p p l i e d F i e l d (V/m) Figure 4- 7. Percent change in reflectance versus intensity of applied field As described in section 3.7, one possible reason for this field-driven grey scale control is that the excess dispersant molecules form micelles that in turn coat the surfaces.32 As a result, the particles would not be moved into the evanescent wave region deeply enough to sufficiently frustrated TIR under a weak electric field (since the thick micelle layer has occupied the TIR interface). With a stronger electric field, the particles would be forced to move deeper into the evanescent wave region, thus scattering more of the incident light. Even though this effect could be essential-in controlling the illumination level along the variable extractor light guide, the exact interaction mechanism in the particle suspension was not determined in this thesis. This field-driven approach was used to control the extraction/illumination level in the variable extractor, but the extraction-field dependence in the variable extractor shows a hysteretic behaviour, which wil l be discussed in Chapter 6. 40 4.7.3 Concentration of particles Another factor influencing the reflectance/scattering modulation is the concentration of the silica particles. Figure 4-8 shows the percent change in reflectance versus concentration of silica particles at a constant axial angle of incidence of 20° and an applied voltage of ±30V for the same set-up described previously. The percent change in reflectance increases as the concentration of silica particles increases (the more packing of particles the higher the scattering/extraction) until the concentration reaches 10% by mass. Q) 70 u c 0) 0- 0 1 1 ! : 1 5 10 15 20 C o n c e n t r a t i o n o f S i l i c a P a r t i c l e s b y M a s s (%) Figure 4- 8. Percent change in reflectance versus concentration of silica particles Based on this result, 10% by mass of silica particles in the liquid suspension was determined to be the suitable concentration to optimize the performance of the variable extractor. To summarize, based on individual studies of the various factors influencing the reflectance/scattering modulation, the optimal operating specifications for the variable extractor have been determined, such as the suitable operating range of the light source, the appropriate operating voltage range, and the concentration of particles in the liquid 41 suspension. The actual scale prototype o f the variable extractor light guide w i l l be discussed in Chapter 6. 42 5 MODELING AND CONTROLLING OF THE VARIABLE EXTRACTOR LIGHT GUIDE The previous chapters presented many o f the factors influencing the design o f a variable extractor light guide based on the frustration o f T I R by si l ica particles, and described how the optical system was evaluated based on the results obtained using one or two sample light rays. However, this is not enough to fully describe the system. In order to ensure a more complete understanding o f the system, Monte Carlo ray tracing was used (with a large number o f light rays) to simulate the T I R and the frustrated T I R (scattering) states within the rectangular light guide (the light guide with the rectangular cross section). In addition, a mathematical model and control algorithm were developed and programmed to predict or compute the illumination level according to the voltage settings for the extractors and the levels assigned by the user. 5.1 Modeling the variable extractor light guide system using Monte Carlo ray tracing For some physical processes, we have statistical models o f behavior at a microscopic level from which we attempt to derive an analytical model o f macroscopic behavior. For example, a luminaire (a light emitting object) is often thought o f as emitting a very large number o f random photons (photons that obey geometric optics) with certain probability density functions controlling the wavelength and direction o f the photons/light rays. F rom this, statistics may be used to derive an analytical model that can predict how the luminaire distributes its energy in terms o f the directional properties o f the probability density functions. However, one's objective is not to form a general model, but instead to describe the behavior o f a particular luminaire in a particular environment, then the behavior o f the luminaire can just be simulated numerically (by computer ray tracing). Computer ray tracing stores the data from all the light rays into memory and then generates a table o f ray history by computing and keeping track o f the distribution o f refractions or reflections o f the light rays at each interface. If the number o f surfaces (interfaces) is relatively small compared to the memory o f the computer, then this 43 straightforward approach is applicable. On the other hand, i f the number o f surfaces is not small, then the computational size would exceed the capacity o f the computer very quickly since the size increases exponentially. To solve this problem, a technique generally known as the Monte Carlo simulation is applied. It reduces the computation of light distribution at each surface by using probabilistic selection techniques with known statistical error. In order to optimize the design o f the variable extractor light guide system described in this thesis, the Monte Carlo simulation was applied (using a commercial software package 3 3) to trace the propagation o f a random selection o f rays from the light source through the variable extractor light guide. In Monte Car lo ray tracing, reflections and refractions o f light rays are randomly selected at each interface based on the Fresnel equations (i.e. the net results obtained from this random selection technique with a large number o f rays w i l l be equivalent to the results calculated from the Fresnel equations). Using a large set o f discrete rays, a continuous distribution o f rays from the light source can be simulated, and accurate results o f ray tracing can be obtained. This approach was applied to the model o f the rectangular light guide described in Section 3.11. 5.1.1 Model set-up In the ray tracing model, the reflectance o f the T I R and the scattering (frustrated TIR) states for the variable extractor light guide, (in particular the guide with a rectangular cross section), was simulated according to the operating range described in Chapter 4 (specifically axial angles between 14° and 22°) . Us ing the commercial software package, T racePro®, the end reflectance o f the rectangular light guide was simulated. The model o f the light guide with a rectangular cross section consists o f a sheet o f optical lighting film ( O L F ) on its ceil ing, two side walls coated with radiant mirror film ( R M F ) , a series o f variable extractors on its floor, and an exterior acrylic shell as described in section 3.11. The O L F simulated in the variable extractors and on the ceil ing o f the guide were drawn using A u t o C A D ® 3 4 , a three-dimensional computer-aided design program, and then imported into the ray tracing software, where they were assigned specific optical properties from a library in the software program, so that they accurately represented the desired materials. The size o f the O L F was made to be 10 44 times bigger than the actual O L F to reduce the number o f prism surfaces, thus saving the computational time required for the ray tracing. Consequently, the absorption in the O L F was set to be 10 times less to compensate for the size change. The R M F ' s were made by setting the surface reflectance o f the sidewalls o f the guide to match an experimentally derived value (0.992 in this case). The variable extractors were modeled by sheets o f O L F and a layer o f the FC-75 fluorinert with and without the scattering particle layer, as w i l l be described in details later. A variable extractor light guide with dimensions o f 3" by 6.75" by 80" was simulated in T r a c e P r o ® . _ 4 ° Source Source (a) (b) Figure 5- 1. (a) A highly collimated light source and (b) A light source with a beam (half) angle of 4° Initially, the simulated light source was modeled as a highly collimated (less than 1° collimation angle) beam o f rays as shown in Figure 5-1 (a). The axial angle o f the light source is defined as the angle between the normal direction o f the light source (which is perpendicular to the x-axis as shown in Figure 5-2 (b)) and the axial direction o f the light guide on the y-z plane as shown in Figure 5-2 (a) (the apparent angle o f incidence, a, described previously equals to zero for the normal direction). A x i a l angles o f 14°, 16°, 18°, 20° , and 22° o f the highly collimated light source, and a horizontal distance o f 23" between the light guide and the source, were used in the ray tracing model, as shown in Figure 5-3. Typical ly , a set o f 5000 random rays was used to generate the predicted reflectance values. 45 Axial Angle Axial Direction N Light Guide Light Guide N Variable Extractor (a) (b) -> x Source Figure 5- 2. (a) Ax ia l angle of the light source on the y-z plane and (b) Normal direction of the source perpendicular to the x-axis The simulated light source was then modeled as a beam of rays with a collimation (beam) half angle of 4° as shown in Figure 5-1 (b), and an axial angle of 18° was used to determine the end reflectance of the guide, as will be described in section 5.1.2. During the ray trace analysis, the intensity and position of each ray was calculated as it interacted with the refractive and reflective elements of the structure. The program stores the results in a data file, and the results are then presented in a number of forms depending on the needs of the particular analysis being performed. A typical TracePro® output and a ray diagram for visual analysis is included in Appendix C. 23" 20 l Axial Direction 1 6 ^ ; : : : : ; v < / 2 2 ' 14° N Light Guide , Variable Extractor Figure 5- 3. The axial angles and source distance used in the TracePro® To model the high reflectance (TIR) state of the system, the region immediately adjacent to the rear surface of the OLF (in the variable extractor) was assigned a refractive index value of 1.276, equal to that of the FC-75 fluorinert liquid. The low reflectance (scattering or frustrated TIR) state was modeled by adding an additional thin layer with a refractive index of 1.413 (the average index of the fluorinert liquid and the 46 sil ica particles) to the region corresponding to the area between the O L F and the fluorinert. A bulk scattering property was also inserted into that thin layer to frustrate the T I R and scatter the light incident on the O L F surface. A typical optical structure, imported into T racePro®, is shown in Appendix B . 5.1.2 Model results In the analyses discussed in the fol lowing section, the reflectance was calculated as the percent fraction o f the light flux exiting the end o f the guide to the total flux entering the other end o f the guide for the T I R and the scattering (frustrated T I R ) states. It should be noted that this model represents an ideal case and demonstrates the potential reflectance that can be achieved in the variable extractor light guide. For the highly collimated light source with axial angles o f 14° to 22° (as described previously), the ray tracing results show that the reflectance o f the T I R state is greater than 90%, whereas the reflectance o f the scattering state is less than 4%. A s a result, high reflectance can be achieved in the variable extractor light guide at the T I R state, and most o f the light flux can be extracted at the scattering state. For the light source with a beam angle o f 4° , the ray tracing results show that the reflectance o f the T I R state is about 85%, and that o f the scattering state is about 1%. In comparison to the model with the highly collimated light source, the reflectance drop for the T I R state is not surprising, since as discussed previously, some o f the light rays in the range o f the 4° beam angle escape at the OLF-fluorinert interface even at the TIR state. A s the beam angle increases, the reflectance o f the T I R state drops. A typical output from T r a c e P r o ® for the entering/exiting flux measurements is shown in Figure 5-4. 47 W/sr 700 Polar Iso-Candela Plot Using Incident rays on lightguide input 0 Min:6.7345e-017 W/sr, Max:650.52 W/sr, Total Fiux28.435 w Collected Flux:27.97 W, 2797 Rays Data covers +/- 90.000 degrees from Normal Figure 5- 4. A typical output from TracePro® for the entering/exiting flux measurements All in all, the Monte Carlo ray tracing produced promising results, and an actual scale prototype of the variable extractor light guide was constructed based on the model designed in TracePro®. The actual scale prototype of the variable extractor light guide system presented in this thesis consists of a series of rooms or offices (8 rooms in this case), a rectangular light guide (light guide with a rectangular cross section), 8 variable extractors, and 4 light sources. The dimensions of the guide were chosen so that for a well collimated light source with an axial angle of 18, the input light flux from one light source will make contact with every other variable extractor, and a second light source will cover the rest of the extractors as shown in Figure 5-5. The construction details of the actual scale prototype are discussed in Chapter 6, and a mathematical model and control algorithm for the variable extractor light guide system are described next. 48 Variable Extractor Light Guide 8 Cubic Card Board Rooms Figure 5- 5. The paths of the light fluxes from the light sources 5.2 The simulation algorithm of the variable extractor light guide system A mathematical model of the light guide system using the variable extractor is shown in Figure 5-6. The components of the light flux entering and leaving a single segment of the variable extractor light guide are depicted. Side A <&iA,k <X>a,k <J>oB,k Side B Figure 5- 6. Components of the light flux in a section (k) of the variable extractor light guide Here OiA,k is the flux into extractor 'k' from side A OoB,k is the flux out from extractor 'k' into side B <De,k is the flux emitted from extractor 'k' <I>a,k is the flux absorbed in extractor 'k' Equations (5-1), (5-2), and (5-3) approximate the flux transfer occuring in extractor 'k'. Oe, k = S A ( V ) * Ou\, k (5-1) Oa,k = aA(V)*0 1/\,k (5-2) 49 OoB, k = AA(V) * <J>iA, k (5-3) Where V is the applied voltage (in volts) across the extractor, 8 A ( V ) is the emission or scattering coefficient, OCACV) is the absorption coefficient, and XACV) is the transmission coefficient. A l l the coefficients are functions o f the voltage and the voltage history, due to hysteresis. In this model the scattering and absorption coefficients were measured for the whole range o f possible applied voltages in order to obtain complete look-up tables. These look-up tables are indexed by the applied voltage and the previously applied peak voltage, and w i l l be described in sections 6.3.3 and 6.3.4. The transmission coefficient XACV) is calculated as shown below: A.A(V) = 1 - E A ( V ) - ( X A ( V ) (5-4) If a number o f extractors are connected in series, the continuous boundary condition is: OiA,k= <DoB,(k-2) (5-5) The actual scale prototype shows that because o f the dimensions o f the light guide and the input angle from the light source, almost all the transmitted flux from one extractor (k-2) w i l l skip the extractor (k-1) that immediately follows and enter the next extractor (k) as shown in (5-5). A light source, or a number o f sources, with the total light flux <()s into extractor #1 from side A w i l l give the one-end boundary condition: OiA,i = <j)S (5-6) The fol lowing assumptions were used in this model: 1. A l l the extractors are identical so that they can share the same look up matrix for the scattering coefficients and absorption values. 2. The light flux that makes contact with the odd numbered extractors does not interact with the even numbered extractors. 3. The angular distribution o f the source beam was ignored in this simple model. 50 Based on the algorithm described above, the emitted flux (and the resulting illumination level) in each region (room) can be computed given both the input fluxes from the ends of the light guide and the voltage settings (i.e. the previous peak voltage and the current voltage) in each region. However in practice it is necessary to be able to reverse these calculations, in order to determine the voltages that will produce the desired illumination levels in each room. A control algorithm based on an iterative optimization calculation has been developed for computing these required voltage settings. The algorithm takes into account the previous voltage settings and the new illumination levels requested by the user, and then produces the appropriate control voltages to yield the desired output flux distribution, as will be described in the next section. 5.3 The control algorithm for adjustment of in-door illumination level in the automatic light guide system An automatic control algorithm was designed using an iterative optimization calculation to produce the appropriate control voltages to yield the desired output flux distribution according to the illumination levels assigned by the user. Initially, the illumination level in each room is computed given the default voltage settings (OV in this case) according to the predictions by the simulation algorithm. The voltage settings are then be adjusted in IV steps (higher or lower depending on whether the assigned illumination level is greater or less than the computed value). If at this point the assigned illumination level does not agree with the computed level within an assigned threshold value (the desired difference between the assigned and the computed illumination level), the procedure is repeated. This iteration procedure will stop when the assigned illumination level agrees with the computed one within the threshold value, or if the voltage settings are exceeding the extreme values (+/- 30V in this case). To reach the assigned illumination level, the current applied voltage and the previous peak voltage in each extractor are used (look-up tables), and the previous peak voltage is appropriately renewed from each current applied voltage. 51 This control algorithm has been programmed in Visual Basic, and the codes and the control interface o f the program are discussed in the next section. 5.3.1 The Visual Basic and Excel program for the control algorithm The simulation algorithm (section 5.2) and the look up tables for the scattering and the absorption coefficients (sections 6.3.2 and 6.3.3) were implemented and recorded in Excel . The control algorithm described above is a Visua l Basic program that has been coded to interact with the Exce l spreadsheet. The control interface o f the program is shown in Figure 5-7. The Exce l spread sheet containing the simulation algorithm and the look up tables runs simultaneously with the Visual Basic program. A s shown in Figure 5-7, the input arguments for the program are as follows: 1. input fluxes at the ends o f the light guide from the light sources in lumens (optional i f default values are given); button caption "Source 1" to "Source4", 2. desired il lumination level in each room in lumens; button caption " R o o m l Input" to "Room8 Input", 3. terminal conditions for the program (the threshold values) in lumens; button caption "Threshold 1" to "Threshold8", and 4. desired current voltage setting in each room in volts (optional); button caption "Change Vol tage" 52 File Edit View Insert Ferm. B O H . r. • QJ Ariel o r h d o . _ s x - * . A . » B K B L B M input flux (lumens) corresponding using 4 sources scattering coefficient 100; 0.064106 90 0.064106 80 0.064106 90 0.064106 0.064106 0.0641061 0.064106 0.064106 B N B O ... B P | B Q ~ 19 [previous peak room # current transmitted flux ratio 0.064106 0.064106' corresponding absorption coefficientivoltage (V) o iaBe2i3oe oi 1 0 188821308 p.' 2 0 188821308 0* 3 0 1 8 8 8 2 1 3 0 6 ] " 4 " 0168821308 0 5 0.183821308 j ] 6 0.168821308^  Oi 7 0168821308] 0 8 0 . 1 B 8 B 2 ' 3 r j 8 ' p i 0 1 1 3 8 6 2 1 3 0 8 b i ] " B R B T TBTJ iv" B W -voltage (V) 0747073192 0747073192 0 558118364 0 558118354 0.41695526 0 41695526 0.311496097 0.311496097 1 0747073192 0.747073192 1 voltage (V) absorption coefficient output illumination 0188035663 0189133606 0190231548 0 191329491 0.192427433 0193525376 0193290369 0193055362 3192S2C3bK 0 192350342 816171 7 907825 8 009211 7172512 7B8B081 7 051381 8 442408 7 534061 sum of above (turn 62 82165 Set Input Flux from Source 1 to 4 (Optional) : Sourcel Display Window for Input Illumination Level;: Input Illumination Level in Lumens Set Teiminal Condition in Lumens Display Window fa Computed Illumination Level in Lumens DispJayWincfowfof s Required Voltage Set Voltage in Volts (Optional) Start Outputtirrg Voltage to each Extractor Roomt Input Change Voltage Source2 SouiceJ Soulcei ii; Room2 Input Room3 Input Rpom4 Input | • Threshold? Thresholds Thjeshold4 | r 1 Channel 1 Channel 2 Channels V j V j ~ " v | ~ Change Change Change j Voltage VoltagE Voltage, j Start Channel 1 Stan Channel 2 Start Channels Room5 Input j Roorri6 Input Start "ompulinq Room? Input Room8 Input Change Voltage Change Voltage Change Voltage • Change Voltage & © | a Kevin i r Floppy (ft;) j S) chapters - Micro... | fe. Proiettl - Micros,., ||a Foi-itil |SMcrosoftExcel -... I [HA$J"<8 11:46 AM Figure 5- 7. The control interface for the Visual Basic program with the spread sheet running at the background simultaneously The windows shown in the control interface display the assigned illumination level, the computed illumination level, and the required voltage setting to achieve the assigned/computed illumination level. The control algorithm is activated by clicking the "Start Computing" button after all the required arguments are assigned, and the computations can been seen directly on the spread sheet located on the background of the control interface. The program can be terminated by either clicking the "Exit" button or simply closing the control interface window. Once the required voltage settings are computed, clicking the "Start Channel" buttons will apply those voltages to the actual extractors through the analogue output card and an amplifier circuit box. The experimental operation of the control algorithm is described in Chapter 6. 53 6 THE ACTUAL LIGHT GUIDE AND RESULTS A s described in Chapter 5, Monte Car lo ray tracing o f the variable extractor light guide system generated promising results. Consequently, a scale prototype o f the unit was built, and the construction details are described in section 6.1. Techniques for measuring illuminance and luminous fluxes are discussed in section 6.2. A t the end o f this chapter, the experimental set-up and results achieved from this variable extractor light guide system are described. These results establish the feasibility o f a variable extractor based on frustration o f T I R and scattering modulation using electrophoretic particles, and they also suggest a number o f areas for further work. 6.1 Construction details The actual scale prototype o f the variable extractor light guide system presented in this thesis consisted o f a series o f room-like regions (8 rooms in this case), a rectangular light guide (light guide with a rectangular cross section), 8 variable extractors, 4 light sources, the amplifier circuit, and power supplies (used for the light sources and the extractors). In the fol lowing sections, the construction details for various components are discussed. 6.1.1 Construction of a series of room-like regions For any prism light guide system, the most desirable structure for the building is a series o f rooms, (the rooms are typically offices), so that the light flux can easily propagate through the light guide without any additional mechanism needed to change the direction o f the light. Thus, a series o f eight white cubic cardboard room-like regions were constructed for the purpose o f this thesis. The dimensions o f each room, as shown in Figure 6-1, were 10" by 10" by 10" (a cube). In each room, the central 6.5" by 10" part o f the cei l ing was removed for the addition o f the variable extractor, and one o f the side walls from each room (perpendicular to the x-axis in the figure) was removed for the purpose o f flux measurement. The rectangular light guide was then mounted on the top o f the cubic rooms; the construction o f the guide is discussed in the next section. 54 10" Figure 6-1. The dimensions of one of the rooms 6.1.2 Construction of the rectangular light guide (light guide with a rectangular cross section) The light guide with a rectangular cross section described in section 3.11 was constructed after the promising results obtained from the Monte Carlo ray tracing discussed in the previous chapter. The actual light guide consisted of a sheet of optical lighting film (OLF) on its ceiling, two side walls coated with radiant mirror fdm (RMF), a series of variable extractors on its floor, and an exterior acrylic shell (see Figure 6-2). The outer dimensions of the light guide were 3.5" by 8.5" by 80", and the inner dimensions were 3" by 6.75" by 80". In order to maintain the optical quality of the light guide (i.e. conserve the angle of incidence of the light rays from the light source throughout the guide), all films (OLF and RMF) have to be flatly coated on the acrylic shell. Consequently, a vacuum was applied between the acrylic ceiling and the OLF by pumping air out of that gap, and a rubber roller was used to flatten the RMF (with sticky back) on the side acrylic walls. In addition, a sheet of RMF was used to cover the exterior acrylic shell to prevent light leakage. The rectangular light guide was then equipped with a series of eight variable extractors whose construction details are provided in the next section. 55 8,5' OLF(6.75") 3.5' R M F RM.F-(3" ) Variable Extractor Figure 6- 2. The dimensions and construction of the variable extractor light guide 6.1.3 Construction of the FTIR-based variable extractor The basic construction and materials used for the variable extractor are similar to those of the test cell described in section 4 . 1 . The extractor consisted of a sheet of ITO coated OLF, four strips of mylar spacers at the edges (the spacer ring as described in Chapter 4), and a sheet of ITO coated mylar substrate. However, for a bigger scale variable extractor it is more difficult to keep the ITO coated OLF and mylar uniformly flat, which is necessary to maintain good opticalquality and to prevent the conductive films from making electrical contact. Consequently, to achieve uniform flatness, each ITO coated film was attached with the edges glued to a piece of flat transparent acrylic, and a vacuum was created by pumping air out of the gap between the film and acrylic. S i l i c c > n e Acrylic (0.125" thick) R l f k J l w U ; „ •„ ^ C o n d u c t i v e O L F r Conductive Mylar Mylar spacer (0.004" thick) Acrylic (0.125" thick) Figure 6- 3. The construction of the variable extractor (not to scale) 56 The dimensions of the sheet of conductive (ITO coated) OLF are 6.7" by 10", and it was attached to a piece of 0.125" thick transparent acrylic (see Figure 6-3) with the same surface dimensions (same area). The same vacuum technique was used for the sheet of conductive (ITO coated) mylar with the dimensions of 8.5" by 9.5". The strips of the mylar spacer are 0.004" thick and 0.5" wide, and the four edges of the extractor occupied by the mylar spacers were covered with RMF (see Figure 6-4) to reduce the light loss due to scattering of the sealant (adhesive silicone in this case) on the spacers. The construction and dimensions of the variable extractor are shown in Figure 6-3 and Figure 6-4 respectively. In addition, a sheet of OLF was attached to the bottom of the variable extractor to enhance the contrast ratio which will be described in section 6.3.1. : to" — R M F —- .9,5" Figure 6- 4. The dimensions of the variable extractor (not to scale) As described in Chapter 5, the computed voltages from the control algorithm can be applied to the actual extractors through the analogue output card and an amplifier circuit box. The amplifier and the circuits are described in the next section. 6.1.4 The amplifier & circuits The amplifier circuit diagram is shown in Figure 6-5. The driving voltage for the LM12CL 80W operational amplifier has a limit of 25V, and the driving current has to be higher than 50mA. This circuit amplifies the input signal by four times, and the resultant signals are sent to the variable extractors. 57 3k 6k 3k 3k Figure 6- 5. The 4X amplifier circuit using the L M 1 2 C L 80W operational amplifier A commercially available halogen lamp AR111 was chosen as a suitable light source for the variable extractor, and it is discussed in the following section. 6.1 .5 L i g h t s o u r c e a n d p o w e r suppl ies used f o r the v a r i a b l e e x t r a c t o r l i g h t g u i d e As described in Chapter 3 and 4, the light sources used for the variable extractor have to be well collimated to meet the optical requirement at the solid-liquid interface. As a result, the AR111 low voltage halogen lamp35 from Osram Sylvania was chosen as the light source for the actual variable extractor light guide system due to its narrow beam half angle of four degrees. The power supply used to drive the AR111 source is a XANTREX X K W lkW 20-50 (0-20V 0-50A) DC Power Supply36 from Xantrex, and the power supply used to drive the amplifier circuit described previously is a pair of MINI-PS-100-240AC/24DC/1A Primary Switched-Mode Power Supply Units3 7 from Phoenix Contact. The complete scale prototype of the variable extractor light guide system, which consisted of the 58 components described above, is shown in Figure 6-6. In the next section, measurement procedures and arrangements are described. AR111 Variable Extractor Light Guide 1 2 3 4 5 6 7 8 8 Room-like Regions Figure 6- 6. The complete scale prototype of the variable extractor light guide system 6.2 Methods of measurements As described in Chapter 2, one of the primary goals of this research was to create a mechanism through which the illumination level extracted from different sections of the light guide (i.e. in different rooms) could be easily controlled by a user. The relative illumination level can either be measured as the illuminance at different points of the room, or as the output luminous flux from the variable extractor. Moreover, a measure of the luminous fluxes entering the light guide can be used to measure the inputs from the light sources. In the following sections, methods of measuring the illuminance and luminous fluxes are described. 6.2.1 Measurement of illuminance in each room As described in Chapter 4, the desirable operating range of axial angles for the light source used in the variable extractor light guide system is from 14° to 22°; this result was obtained from using a laser pointer to simulate a light ray. In order to confirm the operating range of axial angles using the AR111 light source, relative illuminance measurements corresponding to the range of axial angles were taken in one of the rooms at the maximum and minimum illumination level (extreme FTIR and TIR states of the extractor respectively). The experimental arrangements are discussed in a later section. As shown in Figure 6-7, the illuminance measurements were taken at three points: the 59 two inner corners and the centre of the floor of the room. The measurements were taken using the hand-held Minolta T-l Illuminance Meter. The average illuminance over the three points was calculated and used to determine the contrast ratio, which will be described in section 6.3.1. In the next section, the measurement of the input light flux at the end of the light guide from the AR111 source is described. 6.2.2 Measurement of input luminous flux at the ends of the light In section 2.6, an approximated relationship between the luminous flux and the illuminance is given by: Z Figure 6- 7. Points where the relative illuminance measurements were taken in the room guide (6-1) where Ev is the average illuminance enclosed by the total area./! . 60 Cross Section View Illuminance Meter Side View Figure 6- 8. Measurement of the input luminous flux at one end of the light guide By using the hand-held illuminance meter, the input luminous flux was approximately measured as shown in Figure 6-8. The average illuminance over those ten points was measured, and the input luminous flux value was obtained by multiplying the average illuminance by the total area of the opening of the guide. In the same fashion, the output luminous flux from the variable extractor was approximated; an efficient shortcut for measuring the luminous flux from the variable extractor is provided in the following section. 6.2.3 Measurement of output luminous flux from the variable extractor The experimental results of the actual scale prototype of the variable extractor light guide presented in this thesis were mostly based on the output luminous flux measurements from the variable extractor. As described in the previous section, the luminous flux was approximated by measuring the average illuminance across the total input/output area. In the case of the variable extractor, the average output illuminance was determined by measuring illuminance at 24 different points across the light emitting surface of the variable extractor, as shown in Figure 6-9 (a). A more efficient measurement scheme for the output luminous flux is shown in Figure 6-9 (b). Here, the average illuminance was determined by measuring illuminance at 9 different points across the light emitting surface of the extractor, instead of 24. Since the difference between the two sets (9-points and 24-points) of measurements is only 61 about ±2%, the 9-point-illuminance measurement was adopted to approximate the output luminous flux efficiently. Variable Extractor . Variable Extractor (a) ( b ) Figure 6- 9. (a) Measurement of the output luminous flux from the variable extractor and (b) A more efficient flux measurement scheme Based on the measurement techniques described above, a series of experimental results was obtained to evaluate and optimize the performance of the actual scale prototype of the variable extractor light guide system. The experimental set-up and results are described in the following sections. 6.3 Experimental set-up and results The experimental set-up required to optimize the performance of the variable extractor light guide system included the confirmation of the operating range of axial angles of the AR111 light source and the distance from the source to the guide. As mentioned previously, in order to confirm the operating range described in Chapter 4 using the AR111 light source, relative illuminance measurements corresponding to the range of axial angles were taken in one of the rooms at the maximum and minimum illumination levels using the measurement technique discussed above. The source distance from the guide was determined based on the contrast ratio between the maximum and minimum illumination levels and the amount of light entering the guide from the source. The 62 hysteresis effect in the variable extractor was examined, and it was handled by the use of look up tables for the scattering and absorption coefficients described in section 5.2. Details on how to generate the look up tables are discussed in sections 6.3.3.2 and 6.3.3.3. At the end of this section, the computed illumination level according to the control algorithm described in the previous chapter was compared with the measured value obtained from the actual scale prototype of the variable extractor light guide system. 6.3.1 Operating range of axial angles of the light source According to the illuminance measurement described in section 6.2.1 (average illuminance over the three points in the room), the contrast ratio between the maximum (frustrated TIR state) and minimum (TIR state) illumination levels in one of the rooms was determined and is defined as: ^ Ev max where Cr is the contrast ratio, Evmm is the illuminance for the maximum illumination level, and Evmm is the illuminance for the minimum illumination level in that room. Since the AR111 light source is neither a perfect point nor a perfectly collimated source, for the convenience of description the axial angle of the AR111 light source is defined as the angle between the normal direction of the light source, which is perpendicular to the x-axis as shown in Figure 6-10 (b), and the axial direction of the light guide on the y-z plane, as shown in Figure 6-10 (a). However, the actual range of angles corresponding to the axial angle of the AR111 is approximately the axial angle ± 4° (i.e. an axial angle of 18° for AR111 means the range of 14° to 22°). An experiment was then designed to determine the axial angle of the AR111 that will optimize the contrast ratio. 63 AR111 Axial Angle / Axial Direction y t N Light Guide Variable Extractor (a) (b) N f •v I l -> x Y Figure 6- 10. (a) Ax ia l angle of the AR111 light source on the y-z plane and (b) Normal direction of the source perpendicular to the x-axis The axial angle of the AR111 was set to 14°, 16°, 18°, 20°, 22°, and 25°; the variable extractor was set to output the maximum and minimum illumination levels. The contrast ratio was then determined for each axial angle. The source was set at a fixed distance of 33" from the opening of the guide for all measurements corresponding to all the axial angles listed above. As shown in Figure 6-11, the peak contrast ratio occurs at the axial angle of 18° (corresponding to the range from 14° to 22°). The contrast ratio drops at angles beyond 18° because the apparent angle of incidence for some of the light rays from the AR111 exceeds the tolerance and so these rays do not undergo TIR (as described in section 3.4). This result confirms the desirable operating range of the axial angles obtained in Chapter 4. Consequently, the axial angle of the AR111 was set tol8° for all other measurements. 64 0 1 1 L _ 1 , , I 14 16 18 20 22 24 26 Angle of Incidence in Degrees F i g u r e 6- 11. T h e graph o f contrast ratio versus ax ia l angle o f AR111 Another experiment was then performed to compromise between the amount of light flux entering the guide and the contrast ratio, and a suitable distance between the AR111 source and the opening of the guide was determined. The experimental set-up and results are discussed in the next section. 6.3.2 Distance between the light source and the opening of the guide According to the operating range of the axial angle of the AR111 light source obtained from the previous section, an experiment was designed to find a suitable source distance from the opening of the guide so that there would be a sufficient amount of light entering the guide and also a reasonable contrast ratio. Based on the input luminous flux measurement described in section 6.2.2, the input flux was measured at source distances of 23", 33", and 49" away from the opening of the guide (as shown in Figure 6-12), and the corresponding contrast ratio was determined for each case. A graph of contrast ratio versus percent input flux from the source was generated. 65 Axial Direction 33" 23" 49" N Light Guide Variable Extractor Figure 6- 12. Measurement set-up for determining source distance As shown in Figure 6-13, the more collimated (i.e. the farther away) the source is, the higher the contrast ratio becomes. As a result, the distance of 49", which corresponds to 25% input flux and a contrast ratio of 3, was determined to be a suitable source distance. 3.5 .2 2 +•* (/) c o o 20 25 30 35 Percentage Input (%; 40 45 Figure 6- 13. The graph of contrast ratio versus the percent input flux from the source Once the operating range of the source and the source distance has been determined, the response of output luminous flux from the variable extractor to applied voltage was investigated, and the hysteresis effect on the response is described in the next section. 66 6.3.3 R e s p o n s e o f the o u t p u t l u m i n o u s f l u x f r o m the v a r i a b l e e x t r a c t o r to a p p l i e d vol tage a n d the hysteres is effect i n the v a r i a b l e e x t r a c t o r As described in Chapters 3 and 4, grey scale control of the output luminous flux from the variable extractor can be achieved by varying the applied voltage (electric field) across the two transparent conductive films. Using the determined optimal light source settings (as discussed in the previous sections), the response of the output luminous flux to varying applied voltage was investigated. The output flux was measured using the technique described in section 6.2.3. • low to high low to high to low * low to high to low to high x 3 3 Q. o . ^ _ — 12 5-.-!*-* ——. ±r\ 1 u 8 £* e f 2 ' 9 -— - — i 1 -60 -40 -20 0 20 Applied Voltage (V) 40 60 Figure 6- 14. Response of output flux to the applied voltage in the variable extractor (asymmetric hysteresis curve) The output flux was measured as the voltage was varied from -45V to +45V (from low voltage to high), then back to -45V (low to high to low) and up again to +45V (low to high to low to high). The voltage was changed continuously in steps of IV, and the hysteretic behaviour was observed as shown in Figure 6-14. (Note that the sign convention for the applied voltage has been reversed from this point such that negative voltages corresponds to the TIR states and positive voltages corresponds to the scattering states). The non-zero width of the hysteresis curve indicates that there is 67 some effect that prevents the particles from freely moving away from the interface until a sufficiently strong reverse field is reached. Moreover, the hysteretic behaviour depends on the previous applied peak voltages in this case; thus, it is not possible to predict the output flux given only the current applied voltage. However, to the first order approximation, this behaviour was handled by a matrix consisting of output flux values (scattering coefficients) for any combination of last applied peak voltage and current applied voltage in the variable extractor (i.e. the indices of the matrix consisted of those two voltages). The output flux can be looked up in this matrix given the last applied peak voltage and the current applied voltage. The asymmetric hysteresis curve between + applied voltages also shows the "masking effect" of the particles which is discussed next. 6.3.3.1 M a s k i n g effect a n d d e t e r m i n a t i o n o f b o u n d a r i e s o f the a p p l i e d voltages As shown in Figure 6-14, when a positive applied voltage is applied, a higher voltage corresponds to a higher output; however, it is not the case when a negative voltage is applied. The two dashed curves both show the behaviour of the output flux from the high negative end to the high positive end of the applied voltage, and the solid curve shows the behaviour of output flux from the high positive end to the high negative end of the applied voltage. Al l of them show a trend of output flux increase as the applied negative voltage gets relatively higher along the negative direction. After a series of investigations on particle formation at relatively high voltages, the clusters of silica particles have been determined to be responsible for such behaviour. 68 Figure 6- 15. Clus te rs (net) of si l ica particles at 4 0 V after 2 hours As shown in Figure 6-15, silica particles form clusters that look like a net at relatively high voltages (±35V and above) quickly, and the higher the voltage applied the faster the clusters will form. For the case of 40V, it takes two hours for the silica particles to form observable clusters. Moreover, the "holes" on the net are only occupied by fluorinert liquid (FC-75). Since the AR111 source also contains light rays with undesirable angular distribution at the OLF-to-fluorinert interface, some of those rays will escape from the guide through the holes and generate undesirable output flux even at the TIR state. However, at relatively low voltages (+30V and below) the particles do not form clusters within about ten hours. For the case of TIR state (i.e. applying negative voltages) at relatively low voltages, there is no hole of pure fluorinert region for the light rays to escape freely, and those rays which are supposed to escape through the holes get "masked" by the particles. As a result, the output flux is lower at relatively low voltages in comparison to that at relatively high voltages (due to this masking effect) for the case of the TIR state. In contrast, some clusters are also formed for the case of the scattering state (i.e. applying positive voltages), but since the light rays will escape the guide either through the holes of the fluorinert region or through the scattering off of the particles, the output flux increases as the applied voltage increases. Based on the discussion above, the boundaries of the applied voltage have been determined to be ±30V, and it has been confirmed that the contrast ratio and the change in reflectance at ±30V is about the same as that at +45V and above in Chapter 4. The look up matrix for the scattering coefficient was then generated within this voltage range, and the matrix formation is discussed next. 69 6.3.3.2 Look up matrix for the scattering coefficient As described in Chapter 5, the simulation algorithm for the variable extractor light guide requires several parameters, one of which is the scattering coefficient S A ( V ) . The scattering coefficient depends not only on the current applied voltage but also varies with the previous peak voltages because of the hysteretic behaviour of the variable extractor. To the first order approximation, such behaviour was handled by experimentally measuring the ratio of output flux from the variable extractor to the total input flux into the guide for all possible settings of previous peak voltage and current applied voltage (within the ± 3 0 V range) using the light source settings obtained previously; the results formed a look up table (matrix) for the scattering coefficient. Initially, a 10 by 10 matrix was generated from the luminous flux measurements described previously at ten different previous peak and current applied voltages as shown in Figure 6-16. The index voltages in the matrix were chosen such that there is a constant slope of output flux over voltage between the index voltages. In this way, the scattering coefficients (output flux over input flux) for those intervals can be linearly interpolated given the coefficients at the index voltages. Current Voltages (V) Previous -45 -30 -20 - 1 0 -1 0 3 15 3 0 4 5 Peak Voltages ( V ) -45 0 .0622 0 .0557 0 .0543 0 .0573 0 .0618 0 0 8 4 8 0 .1128 0 .1295 0 1467 -30 0 .0594 0 .0549 0 .0519 0 .0496 0 .0556 0 .0617 0 0 8 2 7 0 .1135 0 .1292 0 1385 -20 0 .0595 0.0531 0 . 0 5 1 5 0 .0499 0.0501 0 .0597 0 0 7 7 9 0 .1144 0 .1272 0 1354 -10 0 .0583 0 .0523 0 .0505 0 ,0506 0 .0506 0 .0596 0 0741 0.1071 0 .1244 0 1312 -1 0 .0585 0 .0517 0 .0508 0.05 0 .0617 0.063 0 0842 0 .1047 0 .1165 0 1266 0 0 .0587 0 .0539 0 .0522 0 .0512 0 .0586 0.0641 0 0 8 0 5 0 .1106 0 .1234 0 1336 3 0 .0616 0 .0574 0 .0535 0 .0538 0 .0677 0 .0707 0 0 8 0 3 0 .1188 0 .1277 0 1364 15 0 .0609 0 .0573 0 .0549 0 .053 0 .0797 0 .078 0 1053 0 .1177 0 .1333 0 1409 30 0 .0614 0 .0582 0 .0556 0 .0545 0 .0829 0 .0786 0 1052 0 .1248 0 .1354 0 1459 4 5 0 .0638 0 .0585 0.0571 0 .0563 0.085 0 .1118 0 .1045 0 .1232 0.1371 F i g u r e 6- 16. T h e 10 by 10 look up mat r ix for the scattering coefficient 70 A 9 0 by 9 0 matrix was then constructed by filling the gaps between the index voltages in the 10 by 10 matrix so that the new increment for the index voltages is I V using linear interpolation, and the matrix was truncated to a 61 by 61 matrix so that the boundary voltages are ± 3 0 V . The 61 by 61 matrix is included in Appendix D. Other than the scattering coefficient, another one of the required parameters in the simulation algorithm is the absorption coefficient, which is described in the next section. 6.3.3.3 Look up table for the absorption coefficient In the previous section, the scattering coefficient 8 A ( V ) was approximated using an experimentally derived look up table. In a similar fashion, the absorption coefficient OCA(V) was estimated using experimental measurements, and then by using the simulation algorithm described in Chapter 5, a look up table for the absorption coefficient was generated. Instead of another matrix of coefficients, the absorption was assumed only depending on the current applied voltage, and a table of current applied voltages with the corresponding absorption coefficients was made. The measurements were taken using two variable extractors and the same source settings as described previously. The two variable extractors were in series so that the transmitted flux from the first extractor would be the total flux entering the second extractor. By fixing the applied voltage in the second extractor and varying the applied voltage in the first extractor, the output luminous fluxes from the second extractor corresponding to different applied voltages in the first extractor were measured. The transmission coefficient XACV) can then be computed from the output flux measurements from the second extractor based on the simulation algorithm, and the absorption coefficient OCA(V) is obtained after rearranging (5-4) , (the equation for A.A(V) described in Chapter 5), to become the following equation: O A ( V ) = 1 - S A ( V ) - X A ( V ) (6-3) Knowing both A.A(V) and 8 A ( V ) , a table of OCA(V) was generated. The actual look up table for the absorption coefficient is included in Appendix D. 71 The control algorithm was complete once the required parameters in the simulation algorithm had been experimentally derived. The operation of the control algorithm is discussed next. 6.3.4 Operation of the control algorithm As described in Chapter 5, the input arguments for the control algorithm are- the input fluxes from the light sources at the ends of the light guide; the desired illumination level in each room (i.e. desired output luminous flux from each extractor); the terminal condition(s) (so called the threshold values or the tolerance) for the program, and the desired current voltage setting in each room (optional). To operate the control algorithm, the input fluxes at the ends of the light guide first have to be determined. As described previously, four AR111 sources were used in the actual scale prototype of the variable extractor light guide, and a method of determining the input fluxes from the four sources by only measuring the total input flux at each end of the guide was used. Initially a default input argument of input fluxes from the four sources was entered into the program of the control algorithm, and those default values were obtained by measuring the flux entering the guide from each of the four sources separately. A randomly selected illumination level in each room was entered into the program along with the threshold value of 0.6 lumen, and the computed illumination levels and required applied voltages were obtained (using the same light source settings as described previously). Based on the measurement technique for the input and output luminous flux described earlier in this chapter, the total input flux at each end of the guide and the output flux from each extractor (at the computed required voltage settings) were measured. These measurements were then compared to the computed illumination level to calibrate the input argument of input fluxes according to the control algorithm, (i.e. The input argument of the input fluxes had been adjusted accordingly until the computed illumination level agreed with the measured value, and as a new default these input fluxes were then used throughout the study to predict the illumination level in each room for various inputs of desired illumination levels in the program.) 72 The predicted illumination level according to the control algorithm was compared to the measured value obtained from the actual light guide for different settings of the desired illumination level after this initialization procedure, and the results are presented in the next section. 6.3.5 Comparison between the predicted and the measured illumination level According to the operating procedures of the control algorithm described both in the previous section and in Chapter 5, the predicted illumination levels in each room were compared to the measured values for cases of different input settings of illumination level in each room with only two AR111 sources at one end of the guide, and for cases with four sources (i.e. two AR111 at each end as shown in Figure 6-6). The histograms of predicted illumination level (output flux) and measured illumination level in each room are presented in the following sections. 6.3.5.1 Testing of the control algorithm with two sources After initializing the input argument of the input fluxes as described previously, the control algorithm was first tested with two AR111 sources at one end of the light guide by comparing the predicted and measured illumination level in each room for different cases. Some of the extreme cases are described below. 73 X 3 3 a 3 o predicted output flux measured output flux Figu re 6 -17 . Tes t ing o f the control a lgor i thm w i t h two sources: case 1 The first case tested was setting the illumination level in each room such that the required applied voltages were all +30V for all the extractors, and the result is shown in Figure 6-17. The measured values were well predicted from the control algorithm (i.e. the measured values agreed with the predicted ones within a few percent error) as shown above. The second case was setting the illumination level in each room such that the required applied voltages were all -30V for all the extractors, and the measured illumination level in each room was also well predicted as shown in Figure 6-18. 74 =- 10 predicted output flux measured output flux Figure 6- 18. Testing of the control algorithm with two sources: case 2 The next case shown in Figure 6-19 was setting the illumination level in each room such that the applied voltages of the extractors in odd numbered rooms (i.e. room 1, 3, 5, and 7) were all -30V, and the applied voltages of the extractors in even numbered rooms were all +30V. Other cases were also tested, and they are included in Appendix E. Al l in all, the control algorithm predicts the output luminous fluxes and the required applied voltages reasonably well for cases with two AR111 sources. Testing of the control algorithm with four sources is discussed in the next section. 75 predicted output flux measured output flux Figure 6-19. Testing of the control algorithm with two sources: case 3 6.3.5.2 Testing of the control algorithm with four sources After testing the control algorithm with two sources based on assigned voltages for each extractor, four sources were set up to test the algorithm as shown in Figure 6-6 based on assigned illumination levels. According to the settings of source distance and angle described previously, cases such as uniform illumination over all the rooms were tested. The first case tested with four sources was setting uniform illumination over the eight rooms (output flux of 6 lumens from each extractor in this case); the histogram of the predicted output flux and the measured value from each extractor in each room is shown in Figure 6-20. Here the measured values were well predicted, and the uniformity of about 83% was achieved. The illumination uniformity in this case is defined as the following: Ui = (6-4) where Ui is the illumination uniformity, Om i„ is the minimum output flux, and O m a x is the maximum output flux over the eight extractors. 76 predicted output flux measured output flux Figu re 6- 20. Tes t ing o f the cont ro l a lgor i thm w i t h four sources: case 1 The next case shows that while maintaining the uniform illumination level, one of the rooms was set to be apparently brighter than all the other rooms. The measured illumination levels also agree reasonably with the predicted values as shown in Figure 6-21 (a). Moreover, to achieve uniformity in the variable extractor light guide, a different amount of extraction (i.e. applied voltage) has to be applied for different extractors. Since more light got extracted in the second room, the extractors in room 4, 6, and 8 must also extract more light out to compensate for the extraction in the second room (in order to maintain the uniformity according to the mathematical model described in Chapter 5). The amount of extraction in odd numbered rooms stayed low since the fluxes making contact to the extractors in even numbered rooms were independent of the extractors in odd numbered rooms, as discussed in Chapter 5. The amount of extraction (the scattering coefficient at the required voltage setting in case 2) for each extractor is shown in Figure 6-21 (b). 77 predicted output flux measured output flux Figure 6- 21 (a). Testing of the control algorithm with four sources: case 2 03 a ro u .2 c « .2 ro o X <D 111 o •s ° 3 o E < 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 13 Series 1 4 5 Room# Figure 6- 22 (b). The amount of extraction from each extractor for case 2 Several other cases have been tested and the results are shown in Figure 6-22, 6-23, 6-24, and also in Appendix F. 78 I predicted output flux measured output flux Room# Figure 6- 23. Tes t ing of the control a lgor i thm w i t h four sources: case 3 II predicted output flux • measured output flux Figu re 6- 24. Tes t ing of the control a lgor i thm w i t h four sources: case 4 • predicted output flux • measured output flux 1 2 3 4 5 6 7 8 Room# Figure 6- 25. Testing of the control algorithm with four sources: case 5 The minimum output flux from a variable extractor using the setting of four light sources as described previously has been determined to be about 6 lumens. This non-zero minimum was due to the undesirable angular distribution of the sources as discussed previously, and also to the intrinsic scattering at the OLF-fluorinert interface. The maximum output flux from a variable extractor depends on the settings of illumination levels for the other extractors, since more light can be used for illumination in one room if less light flux is extracted in the other rooms. As a result, the maximum and minimum flux values form a range of illumination level that the algorithm can control accurately. The main source of error in this experiment has been identified as the density mismatch between the fluorinert-krytox liquid and the silica particles in the suspension. Since the liquid does not density-match perfectly with the particles, most of the particles will concentrate at one corner or side of the variable extractor instead of being uniformly distributed if the extractor is not aligned perfectly flat. As a result, the extractor does not behave as predicted according to the look up tables in that case. 80 In addition, if other light sources or source distances are used for the variable extractor light guide system, new look up tables of scattering and absorption coefficients have to be regenerated for that particular light source setting. Al l in all, the control algorithm based on the simple mathematical model described in Chapter 5 also works reasonably well with four light sources. The comparisons in Figure 6-20 to 24 show reasonable agreement between the experiment and the predictions, and these results establish the feasibility of using electrophoretic particles in the variable extractor light guide based on frustration of TIR and scattering modulation. 81 7 C O N C L U S I O N A new variable extraction technique for the prism light guide systems, based on frustration of total internal reflection and evanescent wave scattering in the prismatic microstructures, has been investigated. Such an extraction technique makes use of the fact that TIR can be controlled by moving a light-scattering material toward or away from the interface in the light guide at which the reflection occurs. To achieve efficient frustration of TIR and extraction of light, the scattering material must move to within less than 0.25 u.m of the surface (the thin evanescent wave region), but it should not make physical contact with the TIR interface (it requires too much energy to remove the scattering material from the surface). Because of these surface energy considerations, a solid-liquid interface has been chosen for the controlled TIR system instead of a solid-air interface. Thus, the use of liquid as the second medium was applied to FTIR-based extraction technique. The use of the micro-structured sheets (in particular the optical lighting film or OLF, yielding a high surface reflectance with a index of refraction «i=1.59) forms the basis of these variable extractors, and these sheets are available from a number of commercial sources. If the index mismatch between the two interfacial mediums is large, TIR will occur over a wide range of light source incident angles. However, the use of a liquid as the second medium makes the index ratio, «i/»2> at the interface quite low since the refractive index of most liquids is greater than ri2=\A. As a result, TIR will not occur for many light rays at the OLF-liquid interface unless the light source is perfectly collimated. Perfluorinated hydrocarbon (fluorinert) liquid is a recently developed, low index fluid that can enhance the index mismatch between the two mediums. Its low refractive index value of «2=1.276, its dielectric strength, high density, and chemical compatibility with polycarbonate and particle suspensions combine to make it ideal for this use. The angular requirement of incident light rays for TIR to occur on the surface of the variable extractor (air-polycarbonate (OLF)-fluorinert interface) was determined. Based on this narrow angular requirement (the range of axial angle of incidence corresponding to the apparent angle of incidence for TIR to occur), prism light guides with either 82 parabolic or rectangular cross sections have been designed to preserve that angular range throughout the light guide. The light guide with the rectangular cross section has been proven to be more desirable than that with the parabolic cross section. Based on the experimental results of the reflectance modulation (of a single light ray simulated by a well collimated red laser beam) obtained from the sample test cells of the variable extractor, optimal operating ranges of external factors that influence the reflectance modulation (such as the axial angle of incidence, intensity of applied field/voltage, and the concentration of the scattering silica particle in the fluorinert liquid suspension) have been determined. To optimize the design, and to ensure a complete understanding of the system for a large number of light rays propagating along the variable extractor light guide, a Monte Carlo computer ray tracing was performed. The ray tracing simulated the TIR and the frustrated TIR (scattering) states of the rectangular light guide (light guide with the rectangular cross section), and the results were promising enough to build an actual scale prototype of the variable extractor light guide. A mathematical model and a control algorithm have been developed and programmed to predict or compute the extraction/illumination level according to both the field/voltage settings for the extractors and the illumination level assigned by the user. Based on the Monte Carlo computer ray tracing model, an actual scale prototype of the variable extractor light guide has been constructed. The hysteretic behaviour of the particles in the liquid suspension has been observed from the plot of output luminous flux versus applied voltage in the variable extractor. To take account the hysteresis in the variable extractor, look-up tables for scattering and absorption coefficients have been constructed and applied to the control algorithm. The final experiment described in this thesis showed the comparison between the measured illumination levels (output luminous flux) for various settings and the predictions obtained from the control algorithm, and the results were promising as the algorithm accurately predicted and controlled the extraction/illumination levels along the variable extractor light guide. The results of this thesis present an opportunity for further study in a wide range of areas. The particle suspensions used in this work have successfully demonstrated the capability of frustrating TIR, but it is important to emphasize that they are initial 83 formulations and could be improved in a number of ways. For instance, particles with higher scattering characteristics would improve the amount of extraction in the variable extractor. As well, determining dispersant and suspension that perfectly match the density of the particle would improve the stability of the system. From the point of view of practical construction, the inclusion of higher index prismatic films and/or lower index liquid suspension in the variable extractor will result in a substantial increase in the operating range of incidence angles from the light source and thus making any practical light source suitable for this extraction technique instead of limiting the use to a perfectly collimated beam of light. In summary, this thesis has outlined a physical basis for a new variable extraction technique for prism light guides based on frustration of total internal reflection and offered a solution to the limitations of the conventional prism light guide systems. 84 R E F E R E N C E S 1 Mossman, M . A., Spectral Control of Total Internal Reflection for Novel Information Displays, UBC, Vancouver, 2002 2 Hecht, E., Optics 3rd Edition, p.66, Addison Wesley, United States, 1998 3 Jackson, J.D., Classical Electrodynamics, p. 286, John Wiley & Sons, New York, 1975 4 ibid ii, p. 127 5 Griffiths, D.J., Introduction to Electrodynamics 3rdEdition, pp.413-414, Prentice Hall, New Jersey, 1999 6 ibid ii, pp.124-125 7 Remillard, J.T., et al., "Evanescent Wave Scattering by Electrophoretic Microparticles - A Mechanism for Optical Switching", Applied Optics, Vol. 21, 3536-3538, 1995 8 2301 Optical Lighting Film, Product Identification Number 70-0061-8656-6, manufactured by 3M Company, St. Paul, MN, 55144-1000, USA 9 Whitehead, L.A., et al., "New Efficient Light Guide for Interior Illumination", Applied Optics, Vol. 21(15), 2755-2757, 1982 1 0 Rea, M.S., ed., Lighting Handbook Reference and Application, p. 911, Illuminating Engineering Society of North America, New York, 1993 1 1 VM2000 Radiant Mirror Film, manufactured by 3M Company, St. Paul, MN, 55144-1000, USA Whitehead, L.A. et al, "Visual Applications of Total Internal Reflection in Prismatic Microstructures", Physics in Canada, Vol. 57(6), 329-335, 2001 Whitehead, L.A., "Simplified Ray Tracing in Cylindrical Systems", Applied Optics, Vol. 21(19), 3536-3538, 1982 1 4 ibid 1 1 5 ibid 7 1 6 http://www.lassp.cornell.edu/sethna/hysteresis/WhatIsHysteresis.html 1 7 http://www.bartleby.com/65/hy/hysteres.html 1 8 ibid 16 1 9 Zwinkels, J.C., Photometry, Radiometry, Colorimetry Course, pp.2-15 to 2-17, National Research Council Canada, Ottawa, 1998 2 0 ibid 1 2 1 ibid 7 2 2 Mossman, M.A. et al., "New Reflective Display Technique Based on Total Internal Reflection in Prismatic Microstructures", Society for Information Display Symposium Proceedings, 311-314, 2000 85 23 26 27 Fluorinert™ FC-75 Electronic Liquid, Product Identification Number 98-021 1-3996-3, manufactured by 3M Company, St. Paul, MN, 55144-1000, USA Krytox® 157 FSH Fluorinated Oil, manufactured by DuPont Company Mossman, M.A. et al., "New Reflective Display Technique Based on Total Internal Reflection in Prismatic Microstructures", Society for Information Display Symposium Proceedings, 311-314, 2000 Whitehead, L. A. et al., "Electrophoretic, Dual Refraction Frustration of Total Internal Reflection in High Efficiency Variable Reflectance Image Displays", US Patent 6,064,784, 2000 Whitehead, L. A. et al., "Electrophoretic, High Index and Phase Transition Control of Total Internal Reflection in High Efficiency Variable Reflectance Image Display Devices", US Patent 6,215,920, 2001 2 8 ibid 1 2 9 ibid 11 3 0 ITO coated glass, supplied by Delta Technologies, Ltd., 13960 North 47 th Street, Stillwater, MN, 55082-1234, USA 3 1 TSSL251 light-to-voltage optical sensor, manufactured by Texas Advanced Optoelectronic Solutions, Inc., 800 Jupiter Road, Suite 205, Piano, TX, 75074, USA 3 2 ibid 1 3 3 TracePro® raytracing software, a product of Lambda Research Corporation, 80 Taylor St., P.O. Box 1400, Littleton, MA, 01460-4400, USA 3 4 AutoCAD® computer-aided design software, a product of Autodesk, Inc., 111 Mclnnis Parkway, San Rafael, CA, 94903, USA AR111 Low Voltage Halogen Lamps, a product of Osram Sylvania, 2001 Drew Road, Mississauga, ON L5S 1S4, Canada Xantrex X K W lkW 20-50 DC power supply/a product of Xantrex Technology, 8999 Nelson Way, Burnaby, British Columbia, V5A 4B5, Canada MINI-PS-100-240AC/24DC/1A Primary Switched-Mode Power Supply Units, a product of Phoenix Contact, local distributor: THOS W. M A C K A Y & SON Ltd. 9205 Shaughhessy St., Vancouver, BC V6P 6R5, Canada 35 36 37 86 APPENDIX A: PROPERTIES OF FC-75 FLUORINERT™ ELECTRONIC LIQUID FC-75 Fluorinert™ Electronic Liquid is available from 3M Company (St. Paul, MN, USA), under product identification number 98-0211-3996-3. The properties of the material are shown in Table A - l . Prope r ty V a l u e U n i t Typical boiling point 375 K Pour point 185 K Average molecular weight 420 gmol"1 Surface tension 1.5xl0"2 Nm"' Critical temperature 500 K Critical pressure 1.6xl06 Nm" 2 Refractive index 1.276 Acoustic velocity 585 ms"1 Vapour pressure 4.1xl04 Nm" 2 Solubility of water 11 ppm Solubility of air @ STP 40 ml/lOOml Density 1.77xl03 kgm"3 Viscosity 1.42xl0"3 kgm"'s"' Specific heat 1.05xl03 Jkg'K" 1 Heat of vapourization at B.P. 8.8xl04 Jkg"1 Thermal conductivity 6.3xl02 Wm"3K"' Coefficient of expansion 0.0014 K"1 Volume resistivity 8.0xl01 3 Qm Dielectric strength (2.54 mm gap) 4.0x104 V(RMS) Dielectric constant (1 kHz) 1.86 Dissipation factor (1 kHz) <0.0001 tan 8 Table A - 1 : Proper t ies of F C - 7 5 at 25°C 87 APPENDIX B: DESIGNING AN OPTICAL STRUCTURE IN TRACEPRO® TracePro®, a commercially available computer ray tracing program, was used to optimize the design of the variable extractor light guide system as discussed in Chapter 5. To model the light guide system, some of the components of the structure (such as the OLF) were drawn using AutoCAD®, a three-dimensional computer design program, and imported into TracePro®. Figure B - l (a) and (b) show the TracePro® model, in a cross-sectional view and a side view, respectively, of the light guide with a rectangular cross section equipped with the variable extractor described in section 5.1. O L F R M F R M F Fluorine: O L F Figure B- 1 (a): Example of optical structure in TracePro® (cross section view) In TracePro®, each component was assigned the desired optical characteristics to simulate a particular material from a library of material properties. The light source directed on the surface was modeled as a highly collimated source (with a beam angle of 0° or 4°), and the angle of the source with respect to the optical system was adjusted accordingly. This procedure was used to predict the end reflectance of the light guide under various conditions. 88 Light Source 1 Figure B - 2 (b): Example of optical structure in TracePro® (side view) 89 A P P E N D I X C : T Y P I C A L O U T P U T F R O M T R A C E P R O ® TracePro® presents output data in a number of forms. Two of these forms were used most often during the ray tracing of the light guide. The first is a visual analysis of the ray paths from the source. An example of such a ray diagram is shown, for the variable extractor light guide at a TIR state, in Figure C - l . In this example, only 10 rays, superimposed on the structure, have been plotted. It is apparent from this example that most of the light rays propagate through the variable extractor light guide at the TIR state (without escaping). Figure C- 1: Typical ray diagram for TracePro® model The second is a ray (flux) history table. The path as well as the refraction and reflection events of each ray in the analysis was recorded (with the geometrical coordinates at which these events occur) in the ray history table. Table C- l shows a sample from the ray history table for the four of the ten rays plotted in Figure C - l . 90 Ray Start Split Incident Absorbed Number Number Number Type History Flux Flux X Pos. Y Pos. Z Pos. Wavelength = 0.5461 1 1 4 SpecTran 5 0 -50.38 -38 -865.9 2 1 16 SpecTran 4.95374 0 -65.03 -38 -406.8 3 1 19 SpecRefl TIR 4.93077 0 -66.67 -38 -399.9 4 1 28 SpecTran 4.9079 0 -64.76 -38 52.32 5 1 31 SpecRefl TIR 4.88515 0 -66.94 -38 59.23 6 1 34 SpecRefl TIR 4.86249 0 -65.2 -38 66.14 7 1 43 SpecTran 4.83995 0 -62.76 -38 518.3 8 1 55 SpecTran 4.79517 0 -48.11 -38 977.4 9 1 58 SpecRefl TIR 4.77293 0 -48.47 -38 984.3 10 2 4 SpecTran 5 0 53.934 -38 -807.7 11 2 7 SpecRefl TIR 4.97677 0 52.677 -38 -800.8 12 2 13 SpecTran 4.97677 0 37.464 -38 -339.1 13 2 16 SpecRefl TIR 4.95365 0 39.125 -38 -332.1 14 2 31 SpecTran 4.88492 0 36.254 -38 150.4 15 2 34 SpecRefl TIR 4.86222 0 35.255 -38 157.4 16 2 40 SpecTran 4.86222 0 50.468 -38 619.1 17 2 49 SpecTran 4.83963 0 50.769 -38 1088 18 3 4 SpecTran 5 0 -19.58 -38 -657.6 19 3 7 SpecRefl TIR 4.97667 0 -20.82 -38 -650.6 20 3 19 SpecTran 4.93032 0 -15.14 -38 -132.5 21 3 25 SpecTran 4.93032 0 -9.621 -38 371.5 22 3 28 SpecRefl TIR 4.90732 0 -10.62 -38 378.6 23 ^ j 34 SpecTran 4.90732 0 -16.14 -38 882.6 24 3 37 SpecRefl TIR 4.88441 0 -14.1 -38 889.6 25 4 4 SpecTran 5 0 3.4123 -38 -695.7 26 4 7 SpecRefl TIR 4.97669 0 1.814 -38 -688.7 27 4 10 SpecRefl TIR 4.95349 0 3.4397 -38 -681.7 28 4 13 SpecRefl TIR 4.9304 0 1.7866 -38 -674.7 29 4 19 SpecTran 4.9304 0 0.8241 -38 -181.4 30 4 34 SpecTran 4.86176 0 0.0196 -38 332.9 31 4 43 SpecTran 4.8391 0 -1.156 -38 833.2 Table C-1: Ray history table from TracePro® model Using this data, the position, direction and intensity of each ray were determined along the light guide, and the light loss due to leakage and absorption was computed. 91 A P P E N D I X D : L O O K U P T A B L E S F O R T H E S C A T T E R I N G A N D A B S O R P T I O N C O E F F I C I E N T S The 61 x 61 matrix for the scattering coefficient described in Chapter 6 is shown below (Table D-l): current app l ied vol tage ( V ) previous ( V ) -30 -29 -28 -27 -26 -25 -24 -23 -22 -21 -30 0.0549 0.0546 0.05431 0.05401 0.05371 0.05342 0.05312 0.05282 0.05253 0.05223 -29 0.05472 0.05444 0.05415 0.05387 0.05359 0.0533 0.05302 0.05274 0.05246 0.05217 -28 0.05454 0.05427 0.054 0.05373 0.05346 0.05319 0.05292 0.05266 0.05239 0.05212 -27 0.05436 0.05411 0.05385 0.05359 0.05334 0.05308 0.05283 0.05257 0.05232 0.05206 -26 0 .05418 0.05394 0.0537 0.05346 0.05321 0.05297 0.05273 0 .05249 0.05225 0.052 -25 0.054 0.05377 0.05355 0.05332 0.05309 0.05286 0.05263 0.0524 0.05218 0.05195 -24 0.05382 0.05361 0.05339 0.05318 0.05296 0.05275 0.05253 0.05232 0.05211 0.05189 -23 0.05364 0.05344 0.05324 0.05304 0.05284 0.05264 0.05244 0.05224 0.05204 0.05184 -22 0.05346 0.05328 0.05309 0.0529 0.05271 0.05253 0.05234 0.05215 0.05197 0.05178 -21 0.05328 0.05311 0.05294 0.05276 0.05259 0.05242 0.05224 0.05207 0.0519 0.05172 -20 0.0531 0.05294 0.05278 0.05262 0.05247 0.05231 0.05215 0.05199 0.05183 0.05167 -19 0.05303 0.05286 0.0527 0.05254 0.05238 0.05222 0.05206 0.0519 0.05173 0.05157 -18 0.05295 0.05278 0.05262 0.05246 0.05229 0.05213 0.05197 0.0518 0.05164 0.05148 -17 0.05287 0.0527 0.05254 0.05237 0.05221 0.05204 0.05188 0.05171 0.05155 0.05138 -16 0.05279 0.05262 0.05246 0.05229 0.05212 0.05196 0.05179 0.05162 0.05146 0.05129 -15 0.05271 0.05254 0.05238 0.05221 0.05204 0.05187 0.0517 0.05153 0.05136 0.0512 -14 0.05264 0.05247 0.05229 0.05212 0.05195 0.05178 0.05161 0.05144 0.05127 0.0511 -13 0.05256 0.05239 0.05221 0.05204 0.05187 0.0517 0.05152 0.05135 0.05118 0.05101 -12 0.05248 0.05231 0.05213 0.05196 0.05178 0.05161 0.05144 0.05126 0.05109 0.05091 -11 0.0524 0.05223 0.05205 0.05187 0.0517 0.05152 0.05135 0.05117 0.051 0.05082 -10 0.05232 0.05215 0.05197 0.05179 0.05161 0.05144 0.05126 0.05108 0.0509 0.05073 -9 0.05225 0.05208 0.05192 0.05175 0.05158 0.05141 0.05124 0.05108 0.05091 0.05074 -8 0.05218 0.05202 0.05186 0.05171 0.05155 0.05139 0.05123 0.05107 0.05091 0.05075 -7 0.05211 0 .05196 0.05181 0.05166 0.05151 0.05136 0.05122 0 .05107 0.05092 0.05077 -6 0.05204 0.0519 0.05176 0.05162 0.05148 0.05134 0.0512 0.05106 0.05092 0.05078 -5 0.05197 0.05184 0.05171 0.05158 0.05145 0.05132 0.05119 0.05106 0.05093 0.0508 -4 0.0519 0.05178 0.05166 0.05153 0.05141 0.05129 0.05117 0.05105 0.05093 0.05081 -3 0.05183 0.05171 0.0516 0.05149 0.05138 0.05127 0.05116 0.05105 0.05094 0.05082 -2 0.05176 0.05165 0.05155 0.05145 0.05135 0.05125 0.05114 0.05104 0.05094 0.05084 -1 0.05168 0.05159 0.0515 0.05141 0.05131 0.05122 0.05113 0.05104 0.05095 0.05085 0 0.05385 0.05369 0.05353 0.05337 0.0532 0.05304 0.05288 0.05272 0.05256 0.0524 92 current appl ied voltage ( V ) previous ( V ) -30 -29 -28 -27 -26 -25 -24 -23 -22 -21 0 0.05385 0.05369 0.05353 0.05337 0.0532 0.05304 0.05288 0.05272 0.05256 0.0524 1 0.05505 0.05481 0.05457 0.05433 0.05409 0.05385 0.05361 0.05337 0.05313 0.05289 2 0.05624 0.05592 0.0556 0.05529 0.05497 0.05465 0.05433 0.05401 0.0537 0.05338 3 0.05743 0.05704 0.05664 0.05625 0.05585 0.05545 0.05506 0.05466 0.05427 0.05387 4 0.05743 0.05704 0.05666 0.05627 0.05589 0.05551 0.05512 0.05474 0.05436 0.05397 5 0.05742 0.05705 0.05667 0.0563 0.05593 0.05556 0.05519 0.05482 0.05445 0.05407 6 0.05741 0.05705 0.05669 0.05633 0.05597 0.05561 0.05525 0.0549 0.05454 0.05418 7 0.0574 0 .05705 0.05671 0.05636 0.05601 0.05567 0.05532 0 .05497 0.05463 0.05428 8 0.05739 0.05706 0.05672 0.05639 0.05605 0.05572 0.05539 0.05505 0.05472 0.05438 9 0.05738 0.05706 0.05674 0.05642 0.05609 0.05577 0.05545 0.05513 0.05481 0.05448 10 0.05737 0.05706 0.05675 0.05644 0.05614 0.05583 0.05552 0.05521 0.0549 0.05459 11 0.05737 0.05707 0.05677 0.05647 0.05618 0.05588 0.05558 0.05528 0.05499 0.05469 12 0.05736 0.05707 0.05679 0.0565 0.05622 0.05593 0.05565 0.05536 0.05508 0.05479 13 0.05735 0.05708 0.0568 0.05653 0.05626 0.05598 0.05571 0.05544 0.05517 0.05489 14 0.05734 0.05708 0.05682 0.05656 0.0563 0.05604 0.05578 0.05552 0.05526 0.055 15 0.05733 0.05708 0.05684 0.05659 0.05634 0.05609 0.05584 0.0556 0.05535 0.0551 16 0.05739 0.05714 0.05689 0.05664 0.05639 0.05614 0.0559 0.05565 0.0554 0.05515 17 0.05745 0.0572 0.05695 0.0567 0.05645 0.0562 0.05595 0.0557 0.05545 0.0552 18 0.05751 0 .05726 0.05701 0.05676 0.0565 0.05625 0.056 0.05575 0.0555 0.05525 19 0.05757 0.05732 0.05706 0.05681 0.05656 0.05631 0.05605 0.0558 0.05555 0.0553 20 0.05763 0.05738 0.05712 0.05687 0.05661 0.05636 0.05611 0.05585 0.0556 0.05535 21 0 .05769 0.05743 0.05718 0.05692 0.05667 0.05641 0.05616 0.0559 0.05565 0.0554 22 0.05775 0.05749 0.05724 0.05698 0.05672 0.05647 0.05621 0.05596 0.0557 0.05544 23 0.05781 0.05755 0.05729 0.05704 0.05678 0.05652 0.05627 0.05601 0.05575 0.05549 24 0.05787 0.05761 0.05735 0.05709 0.05683 0.05658 0.05632 0.05606 0.0558 0.05554 25 0.05793 0.05767 0.05741 0.05715 0.05689 0.05663 0.05637 0.05611 0.05585 0.05559 26 0.05799 0.05773 0.05747 0.05721 0.05694 0.05668 0.05642 0.05616 0.0559 0.05564 27 0.05805 0.05779 0.05752 0.05726 0.057 0.05674 0.05648 0.05621 0.05595 0.05569 28 0.05811 0.05784 0.05758 0.05732 0.05706 0.05679 0.05653 0.05627 0.056 0.05574 29 0.05817 0.0579 0.05764 0.05737 0.05711 0.05685 0.05658 0.05632 0.05605 0.05579 30 0.05823 0.05796 0.0577 0.05743 0.05717 0.0569 0.05663 0.05637 0.0561 0.05584 93 current applied voltage (V) previous (V) -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -30 0.05193 0.05169 0.05146 0.05122 0.05098 0.05074 0.05051 0.05027 0.05003 0.04979 -29 0.05189 0.05166 0.05143 0.0512 0.05097 0.05074 0.05051 0.05028 0.05005 0.04982 -28 0.05185 0.05162 0.0514 0.05118 0.05096 0.05074 0.05051 0.05029 0.05007 0.04985 -27 0.0518 0.05159 0.05138 0.05116 0.05095 0.05073 0.05052 0.0503 0.05009 0.04987 -26 0.05176 0.05156 0.05135 0.05114 0.05094 0.05073 0.05052 0.05032 0.05011 0.0499 -25 0.05172 0.05152 0.05132 0.05112 0.05092 0.05073 0.05053 0.05033 0.05013 0.04993 -24 0.05168 0.05149 0.05129 0.0511 0.05091 0.05072 0.05053 0.05034 0.05015 0.04996 -23 0.05163 0.05145 0.05127 0.05108 0.0509 0.05072 0.05054 0.05035 0.05017 0.04999 -22 0.05159 0.05142 0.05124 0.05107 0.05089 0.05071 0.05054 0.05036 0.05019 0.05001 -21 0.05155 0.05138 0.05121 0.05105 0.05088 0.05071 0.05054 0.05038 0.05021 0.05004 -20 0.05151 0.05135 0.05119 0.05103 0.05087 0.05071 0.05055 0.05039 0.05023 0.05007 -19 0.05141 0.05127 0.05112 0.05098 0.05084 0.05069 0.05055 0.05041 0.05026 0.05012 -18 0.05131 0.05119 0.05106 0.05093 0.05081 0.05068 0.05055 0.05043 0.0503 0.05017 -17 0.05122 0.05111 0.051 0.05089 0.05078 0.05067 0.05055 0.05044 0.05033 0.05022 -16 0.05112 0.05103 0.05093 0.05084 0.05075 0.05065 0.05056 0.05046 0.05037 0.05027 -15 0.05103 0.05095 0.05087 0.05079 0.05072 0.05064 0.05056 0.05048 0.0504 0.05033 -14 0.05093 0.05087 0.05081 0.05075 0.05068 0.05062 0.05056 0.0505 0.05044 0.05038 -13 0.05084 0.05079 0.05074 0.0507 0.05065 0.05061 0.05056 0.05052 0.05047 0.05043 -12 0.05074 0.05071 0.05068 0.05065 0.05062 0.05059 0.05057 0.05054 0.05051 0.05048 -11 0.05064 0.05063 0.05062 0.05061 0.05059 0.05058 0.05057 0.05056 0.05054 0.05053 -10 0.05055 0.05055 0.05056 0.05056 0.05056 0.05057 0.05057 0.05057 0.05058 0.05058 -9 0.05057 0.05057 0.05056 0.05056 0.05055 0.05055 0.05054 0.05054 0.05053 0.05053 -8 0.0506 0.05058 0.05057 0.05055 0.05054 0.05053 0.05051 0.0505 0.05049 0.05047 -7 0.05062 0.0506 0.05057 0.05055 0.05053 0.05051 0.05048 0.05046 0.05044 0.05042 -6 0.05064 0.05061 0.05058 0.05055 0.05052 0.05049 0.05046 0.05043 0.05039 0.05036 -5 0.05067 0.05063 0.05059 0.05055 0.05051 0.05047 0.05043 0.05039 0.05035 0.05031 -4 0.05069 0.05064 0.05059 0.05054 0.0505 0.05045 0.0504 0.05035 0.0503 0.05025 -3 0.05071 0.05066 0.0506 0.05054 0.05048 0.05043 0.05037 0.05031 0.05026 0.0502 -2 0.05074 0.05067 0.05061 0.05054 0.05047 0.05041 0.05034 0.05028 0.05021 0.05014 -1 0.05076 0.05069 0.05061 0.05054 0.05046 0.05039 0.05031 0.05024 0.05016 0.05009 0 0.05223 0.05213 0.05202 0.05191 0.05181 0.0517 0.05159 0.05149 0.05138 0.05127 94 current applied voltage (V) previous (V) -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 0 0.05223 0.05213 0.05202 0.05191 0.05181 0.0517 0.05159 0.05149 0.05138 0.05127 1 0.05265 0.05259 0.05253 0.05246 0.0524 0.05234 0.05228 0.05222 0.05216 0.0521 2 0.05306 0.05305 0.05303 0.05302 0.053 0.05299 0.05297 0.05296 0.05294 0.05293 3 0.05347 0.05351 0.05354 0.05357 0.0536 0.05363 0.05366 0.05369 0.05372 0.05375 4 0.05359 0.0536 0.05361 0.05363 0.05364 0.05365 0.05366 0.05368 0.05369 0.0537 5 0.0537 0.0537 0.05369 0.05369 0.05368 0.05367 0.05367 0.05366 0.05366 0.05365 6 0.05382 0.05379 0.05377 0.05375 0.05372 0.0537 0.05367 0.05365 0.05363 0.0536 7 0.05393 0.05389 0.05385 0.05381 0.05376 0.05372 0.05368 0.05364 0.05359 0.05355 8 0.05405 0.05399 0.05393 0.05387 0.0538 0.05374 0.05368 0.05362 0.05356 0.0535 9 0.05416 0.05408 0.054 0.05392 0.05385 0.05377 0.05369 0.05361 0.05353 0.05345 10 0.05428 0.05418 0.05408 0.05398 0.05389 0.05379 0.05369 0.05359 0.0535 0.0534 11 0.05439 0.05428 0.05416 0.05404 0.05393 0.05381 0.0537 0.05358 0.05346 0.05335 12 0.05451 0.05437 0.05424 0.0541 0.05397 0.05384 0.0537 0.05357 0.05343 0.0533 13 0.05462 0.05447 0.05432 0.05416 0.05401 0.05386 0.05371 0.05355 0.0534 0.05325 14 0.05474 0.05457 0.05439 0.05422 0.05405 0.05388 0.05371 0.05354 0.05337 0.0532 15 0.05485 0.05466 0.05447 0.05428 0.05409 0.0539 0.05371 0.05353 0.05334 0.05315 16 0.0549 0.05472 0.05453 0.05435 0.05416 0.05398 0.05379 0.05361 0.05343 0.05324 17 0.05495 0.05477 0.05459 0.05441 0.05423 0.05405 0.05387 0.0537 0.05352 0.05334 18 0.055 0.05482 0.05465 0.05447 0.0543 0.05413 0.05395 0.05378 0.05361 0.05343 19 0.05504 0.05488 0.05471 0.05454 0.05437 0.0542 0.05403 0.05387 0.0537 0.05353 20 0.05509 0.05493 0.05477 0.0546 0.05444 0.05428 0.05411 0.05395 0.05379 0.05363 21 0.05514 0.05498 0.05482 0.05467 0.05451 0.05435 0.05419 0.05404 0.05388 0.05372 22 0.05519 0.05504 0.05488 0.05473 0.05458 0.05443 0.05427 0.05412 0.05397 0.05382 23 0.05524 0.05509 0.05494 0.0548 0.05465 0.0545 0.05435 0.05421 0.05406 0.05391 24 0.05528 0.05514 0.055 0.05486 0.05472 0.05458 0.05443 0.05429 0.05415 0.05401 25 0.05533 0.0552 0.05506 0.05492 0.05479 0.05465 0.05451 0.05438 0.05424 0.0541 26 0.05538 0.05525 0.05512 0.05499 0.05486 0.05472 0.05459 0.05446 0.05433 0.0542 27 0.05543 0.0553 0.05518 0.05505 0.05493 0.0548 0.05467 0.05455 0.05442 0.0543 28 0.05548 0.05536 0.05524 0.05512 0.05499 0.05487 0.05475 0.05463 0.05451 0.05439 29 0.05553 0.05541 0.05529 0.05518 0.05506 0.05495 0.05483 0.05472 0.0546 0.05449 30 0.05557 0.05546 0.05535 0.05524 0.05513 0.05502 0.05491 0.0548 0.05469 0.05458 95 previous (V) -10 -30 0.04955 -29 0.04959 -28 0.04963 -27 0.04966 -26 0.0497 -25 0.04973 -24 0.04977 -23 0.0498 -22 0.04984 -21 0.04987 -20 0.04991 -19 0.04998 -18 0.05004 -17 0.05011 -16 0.05018 -15 0.05025 -14 0.05031 -13 0.05038 -12 0.05045 -11 0.05052 -10 0.05059 -9 0.05052 -8 0.05046 -7 0.0504 -6 0.05033 -5 0.05027 -4 0.05021 -3 0.05014 -2 0.05008 -1 0.05002 current applied voltage (V) -9 -8 -7 -6 -5 -4 -3 -2 -1 0.05022 0.0509 0.05157 0.05224 0.05291 0.05358 0.05425 0.05492 0.05559 0.05019 0.0508 0.05141 0.05201 0.05262 0.05322 0.05383 0.05443 0.05504 0.05017 0.05071 0.05125 0.05179 0.05233 0.05287 0.05341 0.05395 0.05449 0.05014 0.05061 0.05109 0.05156 0.05204 0.05251 0.05299 0.05346 0.05394 0.05011 0.05052 0.05093 0.05134 0.05175 0.05216 0.05257 0.05298 0.05339 0.05008 0.05042 0.05077 0.05111 0.05146 0.0518 0.05215 0.05249 0.05284 0.05005 0.05033 0.05061 0.05089 0.05117 0.05145 0.05173 0.05201 0.05229 0.05002 0.05023 0.05045 0.05066 0.05088 0.05109 0.05131 0.05152 0.05174 0.04999 0.05014 0.05029 0.05044 0.05059 0.05074 0.05089 0.05104 0.05119 0.04996 0.05004 0.05013 0.05021 0.0503 0.05038 0.05047 0.05055 0.05064 0.04993 0.04995 0.04997 0.04999 0.05001 0.05003 0.05005 0.05007 0.05009 0.04999 0.05001 0.05003 0.05005 0.05007 0.05009 0.0501 0.05012 0.05014 0.05004 0.05006 0.05008 0.05009 0.05011 0.05013 0.05014 0.05016 0.05018 0.05019 0.05013 0.05014 0.05016 0.05017 0.05019 0.0502 0.05022 0.05023 0.05025 0.05019 0.05021 0.05022 0.05023 0.05025 0.05026 0.05027 0.05029 0.0503 0.05025 0.05026 0.05027 0.05028 0.05029 0.05031 0.05032 0.05033 0.05034 0.05035 0.05032 0.05034 0.05035 0.05036 0.05037 0.05038 0.05039 0.0504 0.05041 0.05039 0.0504 0.05041 0.05042 0.05043 0.05043 0.05044 0.05045 0.05046 0.05046 0.05046 0.05047 0.05048 0.05048 0.05049 0.0505 0.05051 0.05051 0.05052 0.05053 0.05053 0.05054 0.05054 0.05055 0.05056 0.05056 0.05057 0.05059 0.05059 0.0506 0.0506 0.0506 0.05061 0.05061 0.05062 0.05062 0.05067 0.05082 0.05097 0.05111 0.05126 0.05141 0.05156 0.0517 0.05185 0.05075 0.05104 0.05133 0.05163 0.05192 0.05221 0.0525 0.05279 0.05308 0.05083 0.05127 0.0517 0.05214 0.05257 0.05301 0.05345 0.05388 0.05432 0.05091 0.05149 0.05207 0.05265 0.05323 0.05381 0.05439 0.05497 0.05555 0.05099 0.05172 0.05244 0.05316 0.05389 0.05461 0.05533 0.05606 0.05678 0.05107 0.05194 0.05281 0.05368 0.05454 0.05541 0.05628 0.05715 0.05802 0.05115 0.05217 0.05318 0.05419 0.0552 0.05621 0.05722 0.05824 0.05925 0.05123 0.05239 0.05355 0.0547 0.05586 0.05701 0.05817 0.05932 0.06048 0.05131 0.05261 0.05391 0.05521 0.05651 0.05781 0.05911 0.06041 0.06171 96 current applied voltage (V) previous -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 0.05117 0.052 0.05283 0.05366 0.05449 0.05532 0.05615 0.05698 0.05781 0.05864 1 0.05204 0.05311 0.05417 0.05524 0.05631 0.05738 0.05844 0.05951 0.06058 0.06165 2 0.05291 0.05422 0.05552 0.05683 0.05813 0.05944 0.06074 0.06204 0.06335 0.06465 3 0.05378 0.05533 0.05687 0.05841 0.05995 0.06149 0.06304 0.06458 0.06612 0.06766 4 0.05372 0.05538 0.05704 0.0587 0.06036 0.06202 0.06368 0.06535 0.06701 0.06867 5 0.05365 0.05543 0.05721 0.05899 0.06077 0.06255 0.06433 0.06611 0.0679 0.06968 6 0.05358 0.05548 0.05738 0.05928 0.06118 0.06308 0.06498 0.06688 0.06878 0.07068 7 0.05351 0.05553 0.05755 0.05957 0.06159 0.06361 0.06563 0.06765 0.06967 0.07169 8 0.05344 0.05558 0.05772 0.05986 0.062 0.06414 0.06628 0.06842 0.07056 0.0727 9 0.05337 0.05563 0.05789 0.06015 0.06241 0.06467 0.06693 0.06919 0.07145 0.07371 10 0.0533 0.05568 0.05806 0.06044 0.06282 0.0652 0.06758 0.06995 0.07233 0.07471 11 0.05323 0.05573 0.05823 0.06073 0.06323 0.06573 0.06822 0.07072 0.07322 0.07572 12 0.05316 0.05578 0.0584 0.06102 0.06364 0.06625 0.06887 0.07149 0.07411 0.07673 13 0.05309 0.05583 0.05857 0.06131 0.06405 0.06678 0.06952 0.07226 0.075 0.07773 14 0.05303 0.05588 0.05874 0.0616 0.06446 0.06731 0.07017 0.07303 0.07588 0.07874 15 0.05296 0.05593 0.05891 0.06189 0.06486 0.06784 0.07082 0.0738 0.07677 0.07975 16 0.05306 0.05605 0.05904 0.06202 0.06501 0.068 0.07099 0.07398 0.07697 0.07996 17 0.05316 0.05616 0.05916 0.06216 0.06516 0.06816 0.07116 0.07417 0.07717 0.08017 18 0.05326 0.05627 0.05929 0.0623 0.06531 0.06832 0.07134 0.07435 0.07736 0.08038 19 0.05336 0.05639 0.05941 0.06244 0.06546 0.06849 0.07151 0.07454 0.07756 0.08058 20 0.05346 0.0565 0.05954 0.06257 0.06561 0.06865 0.07168 0.07472 0.07776 0.08079 21 0.05356 0.05661 0.05966 0.06271 0.06576 0.06881 0.07186 0.0749 0.07795 0.081 22 0.05366 0.05672 0.05979 0.06285 0.06591 0.06897 0.07203 0.07509 0.07815 0.08121 23 0.05377 0.05684 0.05991 0.06298 0.06606 0.06913 0.0722 0.07527 0.07835 0.08142 24 0.05387 0.05695 0.06004 0.06312 0.06621 0.06929 0.07237 0.07546 0.07854 0.08163 25 0.05397 0.05706 0.06016 0.06326 0.06635 0.06945 0.07255 0.07564 0.07874 0.08184 26 0.05407 0.05718 0.06029 0.06339 0.0665 0.06961 0.07272 0.07583 0.07894 0.08205 27 0.05417 0.05729 0.06041 0.06353 0.06665 0.06977 0.07289 0.07601 0.07914 0.08226 28 0.05427 0.0574 0.06054 0.06367 0.0668 0.06993 0.07307 0.0762 0.07933 0.08247 29 0.05437 0.05752 0.06066 0.06381 0.06695 0.07009 0.07324 0.07638 0.07953 0.08267 30 0.05447 0.05763 0.06079 0.06394 0.0671 0.07026 0.07341 0.07657 0.07973 0.08288 97 current app l ied vol tage ( V ) previous ( V ) c 1 2 3 4 5 6 1 8 9 -30 0 06174 0.06873 0 07572 0.08271 0 08528 0 08784 0 09041 0 09297 0 09554 0 0981 -29 0 06153 0.06843 0 07533 0.08223 0 08484 0 08745 0 09007 0 09268 0 09529 0 0979 -28 0 06133 0.06813 0 07494 0.08174 0 0844 0 08706 0 08972 0 09238 0 09504 0 09771 -27 0 06112 0.06783 0 07454 0.08125 0 08396 0 08667 0 08938 0 09209 0 0948 0 09751 -26 0 06091 0.06753 0 07415 0.08077 0 08352 0 08628 0 08904 0 09179 0 09455 0 09731 -25 0 06071 0.06723 0 07376 0.08028 0 08309 0 08589 0 08869 0 0915 0 0943 0 09711 -24 0 0605 0.06693 0 07336 0.0798 0 08265 0 0855 0 08835 0 0912 0 09405 0 09691 -23 0 06029 0.06663 0 07297 0.07931 0 08221 0 08511 0 08801 0 09091 0 09381 0 09671 -22 0 06009 0.06633 0 07258 0.07883 0 08177 0 08472 0 08767 0 09061 0 09356 0 09651 -21 0 05988 0.06603 0 07219 0.07834 0 08133 0 08433 0 08732 0 09032 0 09331 0 09631 -20 0 05967 0.06573 0 07179 0.07786 0 0809 0 08394 0 08698 0 09002 0 09307 0 09611 -19 0 05966 0.0656 0 07154 0.07748 0 08049 0 08351 0 08652 0 08953 0 09254 0 09556 -18 0 05965 0.06547 0 07129 0.0771 0 08009 0 08307 0 08606 0 08904 0 09202 0 09501 -17 0 05964 0.06534 0 07103 0.07673 0 07968 0 08264 0 08559 0 08855 0 0915 0 09446 -16 0 05963 0.06521 0 07078 0.07635 0 07928 0 08221 0 08513 0 08806 0 09098 0 09391 -15 0 05962 0.06507 0 07053 0.07598 0 07888 0 08177 0 08467 0 08757 0 09046 0 09336 -14 0 05961 0.06494 0 07027 0.0756 0 07847 0 08134 0 08421 0 08708 0 08994 0 09281 -13 0 0596 0.06481 0 07002 0.07523 0 07807 0 08091 0 08375 0 08658 0 08942 0 09226 -12 0 05959 0.06468 0 06976 0.07485 0 07766 0 08047 0 08328 0 08609 0 0889 0 09171 -11 0 05958 0.06455 0 06951 0.07448 0 07726 0 08004 0 08282 0 0856 0 08838 0 09116 -10 0 05957 0.06441 0 06926 0.0741 0 07685 0 07961 0 08236 0 08511 0 08786 0 09061 -9 0 05995 0.06504 0 07013 0.07522 0 07786 0 08049 0 08313 0 08576 0 0884 0 09104 -8 0 06033 0.06567 0 071 0.07634 0 07886 0 08138 0 0839 0 08642 0 08894 0 09146 -7 0 06072 0.0663 0 07187 0.07745 0 07986 0 08226 0 08467 0 08707 0 08948 0 09188 -6 0 0611 0.06692 0 07275 0.07857 0 08086 0 08315 0 08544 0 08773 0 09002 0 09231 -5 0 06148 0.06755 0 07362 0.07969 0 08186 0 08403 0 08621 0 08838 0 09056 0 09273 -4 0 06187 0.06818 0 07449 0.08081 0 08286 0 08492 0 08698 0 08904 0 09109 0 09315 -3 0 06225 0.06881 0 07536 0.08192 0 08386 0 08581 0 08775 0 08969 0 09163 0 09357 -2 0 06263 0.06943 0 07624 0.08304 0 08487 0 08669 0 08852 0 09034 0 09217 0 094 -1 0 06301 0.07006 0 07711 0.08416 0.08587 0 08758 0 08929 0 091 0 09271 0 09442 98 current app l ied vol tage ( V ) previous 0 1 2 3 4 5 6 7 8 9 0 0.06411 0.06957 0.07504 0.08051 0.08301 0.08552 0.08802 0.09053 0.09304 0.09554 1 0.0663 0.07101 0.07572 0.08044 0.08318 0.08592 0.08866 0.0914 0.09414 0.09688 2 0.06849 0.07245 0.07641 0.08037 0.08335 0.08632 0.0893 0.09227 0.09525 0.09822 3 0.07068 0.07389 0.0771 0.08031 0.08351 0.08672 0.08993 0.09314 0.09635 0.09956 4 0.07128 0.07498 0.07868 0.08238 0.08541 0.08844 0.09147 0.0945 0.09753 0.10056 5 0.07189 0.07608 0.08027 0.08446 0.08731 0.09016 0.09301 0.09586 0.0987 0.10155 6 0.0725 0.07718 0.08186 0.08654 0.08921 0.09188 0.09454 0.09721 0.09988 0.10255 7 0.0731 0.07828 0.08345 0.08862 0.09111 0.0936 0.09608 0.09857 0.10105 0.10354 8 0.07371 0.07937 0.08504 0.0907 0.09301 0.09531 0.09762 0.09992 0.10223 0.10454 9 0.07432 0.08047 0.08663 0.09278 0.09491 0.09703 0.09916 0.10128 0.10341 0.10553 10 0.07492 0.08157 0.08821 0.09486 0.0968 0.09875 0.10069 0.10264 0.10458 0.10652 11 0.07553 0.08267 0.0898 0.09694 0.0987 0.10047 0.10223 0 .10399 0.10576 0.10752 12 0.07614 0.08376 0.09139 0.09902 0.1006 0.10218 0.10377 0.10535 0.10693 0.10851 13 0.07674 0.08486 0.09298 0.1011 0.1025 0.1039 0.1053 0.10671 0.10811 0.10951 14 0.07735 0.08596 0.09457 0.10318 0.1044 0.10562 0.10684 0.10806 0.10928 0.1105 15 0.07796 0.08706 0.09616 0.10526 0.1063 0.10734 0.10838 0.10942 0.11046 0.1115 16 0.078 0.08708 0.09617 0.10525 0.10633 0.10741 0.10849 0.10957 0.11065 0.11173 17 0.07804 0.08711 0.09618 0.10525 0.10637 0.10749 0.10861 0.10972 0.11084 0.11196 18 0.07808 0.08713 0.09619 0.10524 0.1064 0.10756 0.10872 0.10988 0.11104 0.1122 19 0.07812 0.08716 0.0962 0.10524 0.10644 0.10763 0.10883 0.11003 0.11123 0.11243 20 0.07816 0.08718 0.09621 0.10523 0.10647 0.10771 0.10895 0.11018 0.11 142 0.11266 21 0.0782 0.08721 0.09622 0.10523 0.10651 0.10778 0.10906 0.11034 0.11162 0.11289 22 0.07824 0.08723 0.09623 0.10522 0.10654 0.10786 0.10917 0.11049 0.11181 0.11313 23 0.07828 0.08726 0.09624 0.10522 0.10658 0.10793 0.10929 0.11064 0.112 0.11336 24 0.07832 0.08728 0.09625 0.10521 0.10661 0.10801 0.1094 0.1108 0.11219 0.11359 25 0.07836 0.08731 0.09626 0.10521 0.10665 0.10808 0.10952 0.11095 0.11239 0.11382 26 0.0784 0.08733 0.09627 0.1052 0.10668 0.10815 0.10963 0.11111 0.11258 0.11406 27 0.07844 0.08736 0.09628 0.1052 0.10671 0.10823 0.10974 0.11126 0.11277 0.11429 28 0.07848 0.08738 0.09629 0.1052 0.10675 0.1083 0.10986 0.11141 0.11297 0.11452 29 0.07852 0.08741 0.0963 0.10519 0.10678 0.10838 0.10997 0.11157 0.11316 0.11475 30 0.07856 0.08743 0.09631 0.10519 0.10682 0.10845 0.11009 0.11172 0.11335 0.11499 99 current app l ied voltage ( V ) previous ( V ) 10 11 12 13 14 15 16 17 18 19 20 0.1145 0.1156 0.1166 0.1177 0.1187 0.1146 0.1156 0.1167 0.1177 0.1187 0.1147 0.1157 0.1167 0.1177 0.1187 0.1147 0.1157 0.1167 0.1177 0.1187 0.1148 0.1158 0.1 168 0.1177 0.1187 0.1149 0.1158 0.1168 0.1177 0.1187 0.1149 0.1159 0.1168 0.1177 0.1187 0.115 0.1159 0.1168 0.1178 0.1187 0.1151 0.116 0.1169 0.1178 0.1187 0.1151 0.116 0.1169 0.1178 0.1186 0.1152 0.1161 0.1169 0.1178 0.1 186 0.1145 0.1154 0.1163 0.1172 0.1181 0.1138 0.1147 0.1157 0.1166 0.1175 0.1131 0.1141 0.115 0.116 0.1169 0.1124 0.1134 0.1144 0.1154 0.1163 0.1117 0.1128 0.1138 0.1148 0.1158 0.1111 0.1121 0.1131 0.1142 0.1152 0.1 104 0.1114 0.1125 0.1136 0.1146 0.1097 0.1108 0.1119 0.113 0.114 0.109 0.1101 0.1112 0.1124 0.1135 0.1083 0.1094 0.1106 0.1117 0.1129 0.108 0.1091 0.1102 0.1113 0.1124 0.1077 0.1087 0.1098 0.1109 0.1119 0.1073 0.1084 0.1094 0.1104 0.1115 0.107 0.108 0.109 0.11 0.111 0.1067 0.1077 0.1086 0.1096 0.1105 0.1064 0.1073 0.1082 0.1091 0.11 0.1061 0.107 0.1078 0.1087 0.1096 0.1058 0.1066 0.1074 0.1083 0.1091 0.1055 0.1063 0.107 0.1.078 0.1086 -30 0.1007 0.1032 0.1058 0.1084 0.1109 0.1135 -29 0.1005 0.1031 0.1057 0.1084 0.111 0.1136 -28 0.1004 0.103 0.1057 0.1083 0.111 0.1137 -27 0.1002 0.1029 0.1056 0.1083 0.111 0.1138 -26 0.1001 0.1028 0.1056 0.1083 0.1111 0.1138 -25 0.0999 0.1027 0.1055 0.1083 0.1111 0.1139 -24 0.0998 0.1026 0.1055 0.1083 0.1112 0.114 -23 0.0996 0.1025 0.1054 0.1083 0.1112 0.1141 -22 0.0995 0.1024 0.1053 0.1083 0.1112 0.1142 -21 0.0993 0.1023 0.1053 0.1083 0.1113 0.1143 -20 0.0991 0.1022 0.1052 0.1083 0.1113 0.1144 -19 0.0986 0.1016 0.1046 0.1076 0.1106 0.1136 -18 0.098 0.101 0.104 0.1069 0.1099 0.1129 -17 0.0974 0.1004 0.1033 0.1063 0.1092 0.1122 -16 0.0968 0.0998 0.1027 0.1056 0.1085 0.1115 -15 0.0963 0.0992 0.1021 0.1049 0.1078 0.1107 -14 0.0957 0.0985 0.1014 0.1043 0.1072 0.11 -13 0.0951 0.0979 0.1008 0.1036 0.1065 0.1093 -12 0.0945 0.0973 0.1001 0.103 0.1058 0.1086 -11 0.0939 0.0967 0.0995 0.1023 0.1051 0.1079 -10 0.0934 0.0961 0.0989 0.1016 0.1044 0.1071 -9 0.0937 0.0963 0.0989 0.1016 0.1042 0.1069 -8 0.094 0.0965 0.099 0.1015 0.1041 0.1066 -7 0.0943 0.0967 0.0991 0.1015 0.1039 0.1063 -6 0.0946 0.0969 0.0992 0.1015 0.1038 0.106 -5 0.0949 0.0971 0.0992 0.1014 0.1036 0.1058 -4 0.0952 0.0973 0.0993 0.1014 0.1034 0.1055 -3 0.0955 0.0975 0.0994 0.1013 0.1033 0.1052 -2 0.0958 0.0976 0.0995 0.1013 0.1031 0.105 -1 0.0961 0.0978 0.0996 0.1013 0.103 0.1047 100 current app l ied vol tage ( V ) previous 10 11 12 13 14 15 16 17 18 19 20 0 0.098 0.1006 0.1031 0.1056 0.1081 0.1106 0.1114 0.1123 0.1132 0.114 0.1149 1 0.0996 0.1024 0.1051 0.1078 0.1106 0.1133 0.1141 0.1149 0.1156 0.1164 0.1172 2 0.1012 0.1042 0.1071 0.1101 0.1131 0.1161 0.1168 0.1174 0.1181 0.1188 0.1195 3 0.1028 0.106 0.1092 0.1124 0.1156 0.1188 0.1194 0.12 0.1206 0.1212 0.1218 4 0.1036 0.1066 0.1096 0.1127 0.1157 0.1187 0.1194 0.12 0.1206 0.1212 0.1219 5 0.1044 0.1072 0.1101 0.1129 0.1158 0.1186 0.1193 0.12 0.1206 0.1213 0.122 6 0.1052 0.1079 0.1105 0.1132 0.1159 0.1185 0.1193 0.12 0.1207 0.1214 0.1221 7 0.106 0.1085 0.111 0.1135 0.116 0.1185 0.1192 0.1199 0.1207 0.1214 0.1222 8 0.1068 0.1091 0.1115 0.1138 0.1161 0.1184 0.1191 0.1199 0.1207 0.1215 0.1223 9 0.1077 0.1098 0.1119 0.114 0.1162 0.1183 0.1191 0.1199 0.1207 0.1215 0.1224 10 0.1085 0.1104 0.1124 0.1143 0.1162 0.1182 0.119 0.1199 0.1207 0.1216 0.1225 11 0.1093 0.111 0.1128 0.1146 0.1163 0.1181 0.119 0.1199 0.1208 0.1217 0.1226 12 0.1101 0.1117 0.1133 0.1148 0.1164 0.118 0.1189 0.1199 0.1208 0.1217 0.1226 13 0.1 109 0.1123 0.1137 0.1151 0.1165 0.1179 0.1189 0.1198 0.1208 0.1218 0.1227 14 0.1117 0.1129 0.1142 0.1154 0.1166 0.1178 0.1188 0.1198 0.1208 0.1218 0.1228 15 0.1125 0.1136 0.1146 0.1157 0.1167 0.1177 0.1188 0.1198 0.1209 0.1219 0.1229 16 0.1128 0.1139 0.115 0.116 0.1171 0.1182 0.1192 0.1202 0.1213 0.1223 0.1233 17 0.1131 0.1142 0.1153 0.1164 0.1176 0.1187 0.1197 0.1207 0.1217 0.1227 0.1237 18 0.1134 0.1145 0.1157 0.1168 0.118 0.1191 0.1201 0.1211 0.1221 0.123 0.124 19 0.1136 0.1148 0.116 0.1172 0.1184 0.1196 0.1206 0.1215 0.1225 0.1234 0.1244 20 0.1139 0.1151 0.1164 0.1176 0.1188 0.1201 0.121 0.1219 0 .1229 0.1238 0.1247 21 0.1142 0.1154 0.1167 0.118 0.1193 0.1206 0.1215 0.1224 0.1233 0.1242 0.1251 22 0.1144 0.1158 0.1171 0.1184 0.1197 0.121 0.1219 0.1228 0.1237 0.1246 0.1254 23 0.1147 0.1161 0.1174 0.1188 0.1201 0.1215 0.1224 0.1232 0.1241 0.1249 0.1258 24 0.115 0.1164 0.1178 0.1192 0.1206 0.122 0.1228 0.1236 0.1245 0.1253 0.1262 25 0.1153 0.1167 0.1181 0.1196 0.121 0.1224 0.1233 0.1241 0.1249 0.1257 0.1265 26 0.1155 0.117 0.1185 0.12 0.1214 0.1229 0.1237 0.1245 0.1253 0.1261 0.1269 27 0.1158 0.1173 0.1188 0.1203 0.1219 0.1234 0.1241 0.1249 0.1257 0.1265 0.1272 28 0.1161 0.1176 0.1192 0.1207 0.1223 0.1238 0.1246 0.1253 0.1261 0.1268 0.1276 29 0.1163 0.1179 0.1195 0.1211 0.1227 0.1243 0.125 0.1258 0.1265 0.1272 0.128 30 0.1166 0.1183 0.1199 0.1215 0.1232 0.1248 0.1255 0.1262 0.1269 0.1276 0.1283 101 current applied voltage (V) previous (V) 21 22 23 24 25 26 27 28 2S 30 -30 0 11978 0 12083 0 12187 0 12292 0 12397 0.12501 0.12606 0 12711 0 12816 0.1292 -29 0 11975 0 12078 0 12181 0 12283 0 12386 0.12489 0.12592 0 12695 0 12797 0.129 -28 0 11972 0 12073 0 12174 0 12275 0 12376 0.12477 0.12578 0 12678 0 12779 0.1288 -27 0 11969 0 12068 0 12167 0 12266 0 12365 0.12464 0.12563 0 12662 0 12761 0.1286 -26 0 11967 0 12064 0 12161 0 12258 0 12355 0.12452 0.12549 0 12646 0 12743 0.1284 -25 0 11964 0 12059 0 12154 0 12249 0 12344 0.1244 0.12535 0 1263 0 12725 0.1282 -24 0 11961 0 12054 0 12148 0 12241 0 12334 0.12427 0.12521 0 12614 0 12707 0.128 -23 0 11958 0 1205 0 12141 0 12232 0 12324 0.12415 0.12506 0 12598 0 12689 0.1278 -22 0 11955 0 12045 0 12134 0 12224 0 12313 0.12403 0.12492 0 12581 0 12671 0.1276 -21 0 11953 0 1204 0 12128 0 12215 0 12303 0.1239 0.12478 0 12565 0 12653 0.1274 -20 0 1195 0 12035 0 12121 0 12207 0 12292 0.12378 0.12464 0 12549 0 12635 0.1272 -19 0 11895 0 11984 0 12073 0 12161 0 1225 0.12338 0.12427 0 12516 0 12604 0.12693 -18 0 11841 0 11932 0 12024 0 12116 0 12207 0.12299 0.1239 0 12482 0 12574 0.12665 -17 0 11786 0 11881 0 11976 0 1207 0 12165 0.12259 0.12354 0 12449 0 12543 0.12638 -16 0 11732 0 1183 0 11927 0 12025 0 12122 0.1222 0.12317 0 12415 0 12513 0.1261 -15 0 11678 0 11778 0 11879 0 11979 0 1208 0.1218 0.12281 0 12382 0 12482 0.12583 -14 0 11623 0 11727 0 1183 0 11934 0 12037 0.12141 0.12244 0 12348 0 12452 0.12555 -13 0 11569 0 11675 0 11782 0 11888 0 11995 0.12101 0.12208 0 12314 0 12421 0.12528 -12 0 11514 0 11624 0 11733 0 11843 0 11952 0.12062 0.12171 0 12281 0 1239 0.125 -11 0 1146 0 11572 0 11685 0 11797 0 1191 0.12022 0.12135 0 12247 0 1236 0.12472 -10 0 11406 0 11521 0 11637 0 11752 0 11868 0.11983 0.12098 0 12214 0 12329 0.12445 -9 0 11354 0 11465 0 11577 0 11688 0 118 0.11911 0.12022 0 12134 0 12245 0.12357 -8 0 11302 0 1141 0 11517 0 11624 0 11732 0.11839 0.11946 0 12053 0 12161 0.12268 -7 0 11251 0 11354 0 11457 0 1156 0 11664 0.11767 0.1187 0 11973 0 12076 0.1218 -6 0 11199 0 11298 0 11397 0 11496 0 11596 0.11695 0.11794 0 11893 0 11992 0.12091 -5 0 11147 0 11242 0 11337 0 11433 0.11528 0.11623 0.11718 0 11813 0 11908 0.12003 -4 0 11096 0 11187 0 11278 0 11369 0.1146 0.11551 0.11642 0.11733 0 11824 0.11915 -3 0 11044 0 11131 0 11218 0 11305 0.11392 0.11479 0.11565 0.11652 0 11739 0.11826 -2 0.10992 0 11075 0 11158 0 11241 0.11324 0.11406 0.11489 0.11572 0 11655 0.11738 -1 0.10941 0 11019 0 11098 0 11177 0.11256 0.11334 0.11413 0.11492 0 11571 0.11649 102 previous current app l ied vol tage ( V ) 21 22 23 0.11744 0.11947 0.12151 0.12355 0.12376 0.12397 0.12418 0.12439 0.1246 0.12481 0.12501 0.12522 0.12543 0.12564 0.12585 0.12606 0.12635 0.12664 0.12693 0.12722 0.12751 0.12781 0.1281 0.12839 0.12868 0.12897 0.12926 0.12955 0.12984 0.13014 0.13043 24 25 26 27 28 0 0.11572 0.11658 1 0.11794 0.11871 2 0.12015 0.12083 3 0.12237 0.12296 4 0.1225 0.12313 5 0.12264 0.1233 6 0.12277 0.12348 7 0.12291 0.12365 8 0.12304 0.12382 9 0.12317 0.12399 10 0.12331 0.12416 11 0.12344 0.12433 12 0.12358 0.1245 13 0.12371 0.12468 14 0.12384 0.12485 15 0.12398 0.12502 16 0.12431 0.12533 17 0.12465 0.12565 18 0.12499 0.12596 19 0.12532 0.12627 20 0.12566 0.12659 21 0.12599 0.1269 22 0.12633 0.12721 23 0.12667 0.12753 24 0.127 0.12784 25 0.12734 0.12815 26 0.12767 0.12847 27 0.12801 0.12878 28 0.12834 0.12909 29 0.12868 0.12941 30 0.12902 0.12972 0 11829 0 11915 0 12024 0 12101 0 12219 0 12287 0 12414 0 12474 0 12439 0 12502 0 12464 0 1253 0 12488 0 12559 0 12513 0 12587 0 12538 0 12615 0 12562 0 12644 0 12587 0 12672 0 12611 0 12701 0 12636 0 12729 0 12661 0 12757 0 12685 0 12786 0 1271 0 12814 0 12737 0 12839 0 12764 0 12863 0 12791 0 12888 0.12817 0 12913 0.12844 0.12937 0.12871 0.12962 0.12898 0.12986 0.12925 0.13011 0.12952 0.13036 0.12979 0.1306 0.13006 0.13085 0.13033 0.1311 0.13059 0.13134 0.13086 0.13159 0.13113 0.13184 0.12001 0.12178 0.12355 0.12533 0.12565 0.12597 0.12629 0.12661 0.12693 0.12725 0.12757 0.1279 0.12822 0.12854 0.12886 0.12918 0.1294 0.12963 0.12985 0.13008 0.1303 0.13052 0.13075 0.13097 0.1312 0.13142 0.13165 0.13187 0.13209 0.13232 0.13254 0.12086 0.12255 0.12423 0.12592 0.12628 0.12664 0.12699 0.12735 0.12771 0.12807 0.12843 0.12879 0.12914 0.1295 0.12986 0.13022 0.13042 0.13062 0.13083 0.13103 0.13123 0.13143 0.13163 0.13183 0.13204 0.13224 0.13244 0.13264 0.13284 0.13305 0.13325 0.12172 0.12332 0.12491 0.12651 0.12691 0.1273 0.1277 0.12809 0.12849 0.12889 0.12928 0.12968 0.13007 0.13047 0.13086 0.13126 0.13144 0.13162 0.1318 0.13198 0.13216 0.13234 0.13252 0.1327 0.13288 0.13306 0.13323 0.13341 0.13359 0.13377 0.13395 29 12258 0. 12409 0. 12559 0. 1271 0. 12754 0. 12797 0. 1284 0. 12884 0. 12927 0. 1297 0. 13013 0. 13057 0. 131 0. 13143 0. 13187 0. 1323 0. 13246 0. 13261 0. 13277 0. 13293 0. 13309 0. 13324 0. 1334 0. 13356 0. 13371 0. 13387 0. 13403 0. 13419 0 13434 0. 1345 0. 13466 0. 30 12343 12485 12627 1277 12817 12864 12911 12958 13005 13052 13099 13146 13193 1324 13287 13334 13347 13361 13374 13388 13401 13415 13428 13442 13455 13469 13482 13496 13509 13523 13536 Table D-1: Look up table for the scattering coefficient 103 The look up table for the absorption coefficient is shown in Table D-2. current voltage (V) absorption coefficient current voltage (V) absorption coefficient -30 0.188035663 1 0.236971287 -29 0.189133606 2 0.252942625 -28 0.190231548 3 0.25542575 r27 0.191329491 4 0.258048589 -26 0.192427433 5 0.264698381 -25 0.193525376 6 0.265391132 -24 0.193290369 7 0.266083883 -23 0.193055362 8 0.266776634 -22 0.192820356 9 0.267469385 -21 0.192585349 10 0.268162136 -20 0.192350342 11 0.266786075 -19 0.192800985 12 0.265410014 -18 0.193251627 13 0.264033953 -17 0.19370227 14 0.262657892 -16 0.194152912 15 0.261281831 -15 0.194603555 16 0.261361193 -14 0.195817841 17 0.261440555 -13 0.197032126 18 0.261519917 -12 0.198246412 19 0.261599279 -11 0.199460697 20 0.261678641 -10 0.200674983 21 0.261574268 -9 0.200417646 22 0.261469894 -8 0.200160309 23 0.261365521 -7 0.199902972 24 0.261261147 -6 0.199645635 25 0.261156774 -5 0.199388298 26 0.259823441 -4 0.19962422 27 0.258490107 -3 0.195660327 28 0.257156774 -2 0.203770221 29 0.25582344 -1 0.202269898 30 0.254490107 0 0.188821308 Table D- 2: Look up table for the absorption coefficient APPENDIX E: OTHER CASES TESTED IN SECTION 6.3.5.1 Other than the three cases described in section 6.3.5.1, more cases were tested on the control algorithm for the variable extractor light guide system with two light sources at one end. Plots of the measured illumination level (output flux) and predicted one are shown below (Figures E-l and E-2): 1 2 3 4 5 6 7 8 Room # 16 r -14 Room# Figures E - 1 and E-2: Other cases tested in section 6.3.5.1 105 APPENDIX F: OTHER CASES TESTED IN SECTION 6.3.5.2 Other than the cases described in section 6.3.5.2, more cases were tested on the control algorithm for the variable extractor light guide system with four light sources (two sources at each end). Plots of the measured illumination level (output flux) and predicted one are shown below (Figures F - l , F-2, and F-3): I predicted output flux I measured output flux ~B—h 111111 I I I I I I predicted output flux I measured output flux 4 5 R o o m # 106 16 U predicted output flux • measured output flux 1 2 3 4 5 6 7 8 Room # Figures F - 1 , F - 2 , and F - 3 : O the r cases tested in section 6.3.5.2 

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