{"Affiliation":[{"label":"Affiliation","value":"Science, Faculty of","attrs":{"lang":"en","ns":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","classmap":"vivo:EducationalProcess","property":"vivo:departmentOrSchool"},"iri":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","explain":"VIVO-ISF Ontology V1.6 Property; The department or school name within institution; Not intended to be an institution name."},{"label":"Affiliation","value":"Physics and Astronomy, Department of","attrs":{"lang":"en","ns":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","classmap":"vivo:EducationalProcess","property":"vivo:departmentOrSchool"},"iri":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","explain":"VIVO-ISF Ontology V1.6 Property; The department or school name within institution; Not intended to be an institution name."}],"AggregatedSourceRepository":[{"label":"AggregatedSourceRepository","value":"DSpace","attrs":{"lang":"en","ns":"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider","classmap":"ore:Aggregation","property":"edm:dataProvider"},"iri":"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider","explain":"A Europeana Data Model Property; The name or identifier of the organization who contributes data indirectly to an aggregation service (e.g. Europeana)"}],"Campus":[{"label":"Campus","value":"UBCV","attrs":{"lang":"en","ns":"https:\/\/open.library.ubc.ca\/terms#degreeCampus","classmap":"oc:ThesisDescription","property":"oc:degreeCampus"},"iri":"https:\/\/open.library.ubc.ca\/terms#degreeCampus","explain":"UBC Open Collections Metadata Components; Local Field; Identifies the name of the campus from which the graduate completed their degree."}],"Creator":[{"label":"Creator","value":"Mossman, Michele Ann","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/creator","classmap":"dpla:SourceResource","property":"dcterms:creator"},"iri":"http:\/\/purl.org\/dc\/terms\/creator","explain":"A Dublin Core Terms Property; An entity primarily responsible for making the resource.; Examples of a Contributor include a person, an organization, or a service."}],"DateAvailable":[{"label":"DateAvailable","value":"2009-09-25T21:52:45Z","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/issued","classmap":"edm:WebResource","property":"dcterms:issued"},"iri":"http:\/\/purl.org\/dc\/terms\/issued","explain":"A Dublin Core Terms Property; Date of formal issuance (e.g., publication) of the resource."}],"DateIssued":[{"label":"DateIssued","value":"2002","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/issued","classmap":"oc:SourceResource","property":"dcterms:issued"},"iri":"http:\/\/purl.org\/dc\/terms\/issued","explain":"A Dublin Core Terms Property; Date of formal issuance (e.g., publication) of the resource."}],"Degree":[{"label":"Degree","value":"Doctor of Philosophy - PhD","attrs":{"lang":"en","ns":"http:\/\/vivoweb.org\/ontology\/core#relatedDegree","classmap":"vivo:ThesisDegree","property":"vivo:relatedDegree"},"iri":"http:\/\/vivoweb.org\/ontology\/core#relatedDegree","explain":"VIVO-ISF Ontology V1.6 Property; The thesis degree; Extended Property specified by UBC, as per https:\/\/wiki.duraspace.org\/display\/VIVO\/Ontology+Editor%27s+Guide"}],"DegreeGrantor":[{"label":"DegreeGrantor","value":"University of British Columbia","attrs":{"lang":"en","ns":"https:\/\/open.library.ubc.ca\/terms#degreeGrantor","classmap":"oc:ThesisDescription","property":"oc:degreeGrantor"},"iri":"https:\/\/open.library.ubc.ca\/terms#degreeGrantor","explain":"UBC Open Collections Metadata Components; Local Field; Indicates the institution where thesis was granted."}],"Description":[{"label":"Description","value":"A new method for creating a reflective image device has been devised based on total\r\ninternal reflection (TIR). This technique has the potential to yield a brighter, highercontrast\r\nimage than those of current reflective displays by incorporating polymeric\r\nmicro-prismatic sheets that reflect by means of TIR. High surface reflectance is achieved\r\nby efficiently redirecting ambient light toward the viewer, and an image is generated by\r\ncontrollably preventing, or \"frustrating\", the reflection in selected regions through\r\nabsorption of light in the very thin evanescent wave region near the TIR interface. The\r\ntransition between the reflective and absorptive state requires a motion of less than a\r\nmicron of the absorber, and therefore it can occur quickly and efficiently.\r\nA fundamental problem in this approach - interfacial adhesion - was ameliorated through\r\nthe use of liquid phase backing material, instead of gas. However, this complicated the\r\noptical requirements by substantially reducing the refractive index ratio at the TIR\r\ninterface. To maintain TIR over an acceptable angular range, a low refractive index\r\nperfluorinated hydrocarbon was identified as an ideal liquid, and an optical configuration\r\nwas devised to enhance the effective refractive index ratio at the interface.\r\nDetailed Monte Carlo ray tracing verified that high reflectance and a high contrast ratio\r\nare achievable with these designs over a useful range of viewing directions.\r\nElectrophoresis of pigment particles in a perfluorinated hydrocarbon has been shown to\r\nbe a practical method for modulating TIR. The observed photometric performance is\r\nconsistent with a numerical model developed to describe the interaction of an incident\r\nlight ray with a density distribution of particles near the interface. Colour pigment\r\nsuspensions have yielded, for the first time, spectrally selective control of TIR, which\r\nrequires the particles to be essentially non-scattering but selectively absorptive.\r\nThe results presented here demonstrate the feasibility of this TIR-based approach in\r\npractical reflective image device applications, and are suggestive that further\r\ndevelopment work in this area is warranted.","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/description","classmap":"dpla:SourceResource","property":"dcterms:description"},"iri":"http:\/\/purl.org\/dc\/terms\/description","explain":"A Dublin Core Terms Property; An account of the resource.; Description may include but is not limited to: an abstract, a table of contents, a graphical representation, or a free-text account of the resource."}],"DigitalResourceOriginalRecord":[{"label":"DigitalResourceOriginalRecord","value":"https:\/\/circle.library.ubc.ca\/rest\/handle\/2429\/13177?expand=metadata","attrs":{"lang":"en","ns":"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO","classmap":"ore:Aggregation","property":"edm:aggregatedCHO"},"iri":"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO","explain":"A Europeana Data Model Property; The identifier of the source object, e.g. the Mona Lisa itself. This could be a full linked open date URI or an internal identifier"}],"Extent":[{"label":"Extent","value":"19926173 bytes","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/extent","classmap":"dpla:SourceResource","property":"dcterms:extent"},"iri":"http:\/\/purl.org\/dc\/terms\/extent","explain":"A Dublin Core Terms Property; The size or duration of the resource."}],"FileFormat":[{"label":"FileFormat","value":"application\/pdf","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/elements\/1.1\/format","classmap":"edm:WebResource","property":"dc:format"},"iri":"http:\/\/purl.org\/dc\/elements\/1.1\/format","explain":"A Dublin Core Elements Property; The file format, physical medium, or dimensions of the resource.; Examples of dimensions include size and duration. Recommended best practice is to use a controlled vocabulary such as the list of Internet Media Types [MIME]."}],"FullText":[{"label":"FullText","value":"SPECTRAL CONTROL OF TOTAL INTERNAL REFLECTION FOR N O V E L INFORMATION DISPLAYS by MICHELE A N N M O S S M A N B.Sc.FL, Acadia University, 1995 M.Sc , University of British Columbia, 1997 A THESIS SUBMITTED IN PARTIAL F U L F I L L M E N T OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY 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 2002 \u00a9 Michele Ann Mossman, 2002 U B C Special Collections - Thesis Authorisation Form Page 1 of 1 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the Un i v e r s i t y of B r i t i s h Columbia, I agree that the Li b r a r y s h a l l make i t f r e e l y a v a i l a b l e for reference and study. I further agree that permission for extensive copying of t h i s thesis for s c h o l a r l y purposes may be granted by the head of my department or by his or her representatives. It i s understood that copying or p u b l i c a t i o n of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of The U n i v e r s i t y of B r i t i s h Columbia Vancouver, Canada Date (1^1 1 tJDOa. http:\/\/www.library.ubc.ca\/spcoll\/thesauth.html 4\/17\/02 A B S T R A C T A new method for creating a reflective image device has been devised based on total internal reflection (TIR). This technique has the potential to yield a brighter, higher-contrast image than those of current reflective displays by incorporating polymeric micro-prismatic sheets that reflect by means of TIR. High surface reflectance is achieved by efficiently redirecting ambient light toward the viewer, and an image is generated by controllably preventing, or \"frustrating\", the reflection in selected regions through absorption of light in the very thin evanescent wave region near the TIR interface. The transition between the reflective and absorptive state requires a motion of less than a micron of the absorber, and therefore it can occur quickly and efficiently. A fundamental problem in this approach - interfacial adhesion - was ameliorated through the use of liquid phase backing material, instead of gas. However, this complicated the optical requirements by substantially reducing the refractive index ratio at the TIR interface. To maintain TIR over an acceptable angular range, a low refractive index perfluorinated hydrocarbon was identified as an ideal liquid, and an optical configuration was devised to enhance the effective refractive index ratio at the interface. Detailed Monte Carlo ray tracing verified that high reflectance and a high contrast ratio are achievable with these designs over a useful range of viewing directions. Electrophoresis of pigment particles in a perfluorinated hydrocarbon has been shown to be a practical method for modulating TIR. The observed photometric performance is consistent with a numerical model developed to describe the interaction of an incident light ray with a density distribution of particles near the interface. Colour pigment suspensions have yielded, for the first time, spectrally selective control of TIR, which requires the particles to be essentially non-scattering but selectively absorptive. The results presented here demonstrate the feasibility of this TIR-based approach in practical reflective image device applications, and are suggestive that further development work in this area is warranted. ABSTRACT A new method for creating a reflective image device has been devised based on total internal reflection (TIR). This technique has the potential to yield a brighter, higher-contrast image than those of current reflective displays by incorporating polymeric micro-prismatic sheets that reflect by means of TIR. High surface reflectance is achieved by efficiently redirecting ambient light toward the viewer, and an image is generated by controllably preventing, or \"frustrating\", the reflection in selected regions through absorption of light in the very thin evanescent wave region near the TIR interface. The transition between the reflective and absorptive state requires a motion of less than a micron of the absorber, and therefore it can occur quickly and efficiently. A fundamental problem in this approach - interfacial adhesion - was ameliorated through the use of liquid phase backing material, instead of gas. However, this complicated the optical requirements by substantially reducing the refractive index ratio at the TIR interface. To maintain TIR over an acceptable angular range, a low refractive index perfluorinated hydrocarbon was identified as an ideal liquid, and an optical configuration was devised to enhance the effective refractive index ratio at the interface. Detailed Monte Carlo ray tracing verified that high reflectance and a high contrast ratio are achievable with these designs over a useful range of viewing directions. Electrophoresis of pigment particles in a perfluorinated hydrocarbon has been shown to be a practical method for modulating TIR. The observed photometric performance is consistent with a numerical model developed to describe the interaction of an incident light ray with a density distribution of particles near the interface. Colour pigment suspensions have yielded, for the first time, spectrally selective control of TIR, which requires the particles to be essentially non-scattering but selectively absorptive. The results presented here demonstrate the feasibility of this TIR-based approach in practical reflective image device applications, and are suggestive that further development work in this area is warranted. , T A B L E OF CONTENTS ABSTRACT ...ii LIST OF TABLES vii LIST OF FIGURES viii ACKNOWLEDGEMENTS. xi 1 INTRODUCTION 1 2 BACKGROUND 5 2 .1 T O T A L I N T E R N A L R E F L E C T I O N 5 2.1 .1 Index of refraction 5 2 . 1 . 2 Conditions for TIR at an interface 7 2 .1 .3 The evanescent wave 9 2 . 1 . 4 Frustrated TIR 11 2 . 2 G E O M E T R I C A L O P T I C S 1 2 2.2 .1 Micro-replicated sheets 13 2 . 2 . 2 Enhanced refractive index ratio 1 4 2 .2 .3 Specification of reflectance in prismatic systems 1 7 2 . 3 C O L O U R 1 8 2.3 .1 Measurement of colour 18 2 . 3 . 2 CIE method of colour specification 1 8 2 .3 .3 CIE chromaticity diagram 2 1 2 . 3 . 4 Colour filtering 2 3 2 . 4 P A R T I C L E S U S P E N S I O N S 2 7 2.4 .1 High dielectric and low dielectric constant media 3 0 2 . 4 . 2 Electrophoresis 3 1 2 . 4 . 3 Particle characterization 3 2 2 . 5 C U R R E N T D I S P L A Y T E C H N O L O G I E S . 3 3 2.5 .1 Liquid crystal displays 3 4 2 . 5 . 2 Cholesteric liquid crystal displays 3 7 2 .5 .3 Electrophoretic image displays 3 9 3 DESIGN ISSUES IN A NOVEL TIR-BASED DISPLAY 41 3.1 P R I N C I P L E O F A T I R - B A S E D R E F L E C T I V E D I S P L A Y 4 1 3 . 2 I N D E X M I S M A T C H R E Q U I R E M E N T S '... 4 3 3 . 3 S U R F A C E E N E R G Y C O N S I D E R A T I O N S 4 3 3 . 4 O P T I C A L R E Q U I R E M E N T S F O R T I R A T A S O L I D - L I Q U I D I N T E R F A C E 4 5 3 . 5 P O S S I B L E A B S O R B E R S U S E D T O F R U S T R A T E T I R 4 7 3 . 6 E N H A N C I N G I N D E X R A T I O W I T H C R O S S E D P R I S M A T I C S H E E T G E O M E T R Y 4 8 3 . 7 P I G M E N T S S U S P E N S I O N S I N L O W R E F R A C T I V E I N D E X F L U I D 5 0 i i i 3 . 8 F R U S T R A T I O N O F T I R U S I N G P I G M E N T S U S P E N S I O N S 5 4 3 . 9 E L E C T R O P H O R E T I C S U S P E N S I O N S I N A T I R - B A S E D D E V I C E 5 6 3 . 1 0 G R E Y - S C A L E C O N T R O L O F R E F L E C T A N C E 5 8 3 . 1 1 P R E V E N T I O N O F P A R T I C L E C L U S T E R I N G B Y E N C A P S U L A T I O N 5 9 3 . 1 2 S U B T R A C T I V E C O L O U R F I L T E R I N G I N A F U L L - C O L O U R I M A G E D I S P L A Y 6 1 3 . 1 2 . 1 Subtractive colour filtering in an FTIR image display 6 2 3 . 1 2 . 2 Construction of a full-colour FTIR image display 6 2 3 . 1 2 . 3 Operation of device 6 4 4 S P E C T R A L L Y S E L E C T I V E R E F L E C T A N C E B Y P I G M E N T S . 68 4 . 1 E X P E R I M E N T A L M E A S U R E M E N T O F S P E C T R A L C H A R A C T E R I S T I C S 6 8 4 .1 .1 Spectral analysis instrument 6 9 4 . 1 . 2 Set-up for measuring transmittance of static filters 7 0 4 .1 .3 Test cell construction 71 4 . 1 . 4 Set-up for measuring TIR-attenuation by pigment systems 7 4 4 . 2 E X P E R I M E N T A L M E A S U R E M E N T S O F S P E C T R A L T R A N S M I T T A N C E 7 6 4 .2 .1 Spectral transmittance characteristics of photographic filters 7 6 4 . 2 . 2 Effective spectral transmittance characteristics of pigment systems 7 8 4 . 2 . 3 Combined spectral reflectance of system 81 4 . 2 . 4 Achievable colour gamut 8 2 5 R E F L E C T A N C E M O D U L A T I O N B Y P I G M E N T P A R T I C L E S 8 3 5 .1 M E A S U R I N G R E F L E C T A N C E 8 3 5 . 2 D E S I G N O F T H E R E F L E C T A N C E M O D U L A T I O N E X P E R I M E N T 8 4 5 .3 T I M E - V A R Y I N G R E F L E C T A N C E M O D U L A T I O N 8 7 5 . 4 M E A S U R E M E N T O F C U R R E N T F L O W A N D C H A R G E T R A N S F E R 9 2 5 . 5 F A C T O R S I N F L U E N C I N G R E F L E C T A N C E M O D U L A T I O N 9 4 5.5.1 Intensity of applied field 9 5 5 .5 .2 Concentration of particles 9 8 5.5 .3 Wavelength of incident light 1 0 0 5 .5 .4 Particles with different spectral absorption characteristics 1 0 2 5 .5 .6 Reflectance at different angles of incidence 1 0 3 6 M O D E L L I N G T H E P A R T I C L E D Y N A M I C S 105 6 .1 M O D E L L I N G O P T I C A L P A T H L E N G T H W I T H C O N T I N U O U S I N D E X V A R I A T I O N S . . . 1 0 6 6 . 2 U N I F O R M D E N S I T Y P A R T I C L E L A Y E R 1 0 8 6 . 3 N O N - U N I F O R M P A R T I C L E D E N S I T Y D I S T R I B U T I O N M O D E L S 1 1 1 6.3.1 Linear density gradient distribution 1 1 3 6 .3 .2 Modified linear density gradient 1 1 5 6.3 .3 Exponentially tapered distribution 1 1 7 7 N O V E L O P T I C A L C O N F I G U R A T I O N S F O R E N H A N C I N G T I R 121 7.1 L I G H T D E F L E C T I N G L A Y E R 122 7.1.1 Refractive mode : 123 7.1.2 Reflective mode 124 7.2 L I G H T R E F L E C T I N G L A Y E R 125 7.3 L A Y E R E D S H E E T C O N F I G U R A T I O N S 127 7.3.1 3=90\u00b0 micro-prism geometry 127 7.3.2 Layered 90\u00b0\/90\u00b0 micro-prism geometry 129 7.3.3 Layered 60790790\u00b0 micro-prism geometry 131 7.3.4 Interleaved 60760\u00b0 micro-prism geometry 134 7.4 M O D E L I N G T H E S Y S T E M U S I N G M O N T E C A R L O R A Y T R A C I N G 136 7.4.1 Model set-up 136 7:4.2 Model results .' 138 7.5 E X P E R I M E N T A L R E S U L T S O F M O D U L A T E D T I R I N M I C R O - P R I S M S 148 8 C O N C L U S I O N 153 R E F E R E N C E S 158 A P P E N D I X A : U S I N G D I F F E R E N T I A L S N E L L ' S L A W T O D E T E R M I N E T H E R A Y P A T H T H R O U G H A R E G I O N O F R E F R A C T I V E I N D E X G R A D I E N T 163 A P P E N D I X B : C A L C U L A T I N G R E F L E C T E D L U M I N A N C E U S I N G T H E B I -D I R E C T I O N A L R E F L E C T A N C E D I S T R I B U T I O N F U N C T I O N . . . 165 A P P E N D I X C : 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 \u2122 E L E C T R O N I C L I Q U I D 166 A P P E N D I X D : C A L C U L A T I N G C H R O M A T I C I T Y C O O R D I N A T E S A N D L U M I N O U S R E F L E C T A N C E 167 A P P E N D I X E : S P E C T R O P H O T O M E T R Y C U R V E F O R A S U R F A C E I L L U M I N A T E D B Y S T A N D A R D I L L U M I N A N T D 6 S 171 A P P E N D I X F : S P E C I F I C A T I O N S O F T A O S T S L 2 5 1 O P T I C A L S E N S O R 173 A P P E N D I X G : A N G U L A R R E S P O N S E O F C O L L I M A T E D D E T E C T O R 175 A P P E N D I X H : S P E C T R A L T R A N S M I T T A N C E O F F I L T E R S 177 A P P E N D I X I : S P E C T R A L R A D I A N C E D I S T R I B U T I O N O F I N C A N D E S C E N T S O U R C E 179 A P P E N D I X J : E V A N E S C E N T W A V E P E N E T R A T I O N D E P T H 180 A P P E N D I X K : F R E S N E L E Q U A T I O N S 181 A P P E N D I X L : 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 \u00ae . . . 1 8 3 v APPENDIX M: TYPICAL OUTPUT FROM TRACEPRO\u00ae 185 vi L I S T O F T A B L E S T A B L E 2 - 1 . A D D I T I V E C O L O U R F I L T E R I N G 2 3 T A B L E 2 - 2 . S U B T R A C T I V E C O L O U R F I L T E R I N G 2 6 T A B L E 3 - 1 . C R I T I C A L A N G L E S A T T Y P I C A L L I Q U I D \/ P O L Y C A R B O N A T E I N T E R F A C E S 4 6 T A B L E 3 - 2 . P I G M E N T S S U S P E N D E D I N P E R F L U O R I N A T E D H Y D R O C A R B O N L I Q U I D . 5 2 T A B L E 3 - 3 . P A R T I C L E C O N C E N T R A T I O N A N D M E A N D I A M E T E R 5 2 T A B L E 3 -4 . N E T C O L O U R R E S U L T I N G F R O M A C T U A T I O N O F E L E C T R O P H O R E T I C C H A N N E L S . . . 6 7 T A B L E 4 - 1 . C A L C U L A T E D C H R O M A T I C I T Y C O O R D I N A T E S A N D L U M I N O U S R E F L E C T A N C E 8 1 T A B L E 5 - 1 . E L E C T R O P H O R E T I C M O B I L I T Y E S T I M A T E S 9 0 T A B L E 5 -2 . E S T I M A T E O F S W I T C H I N G T I M E I N R E S P O N S E T O D I F F E R E N T F I E L D S 9 6 T A B L E 6 - 1 . D I E L E C T R I C C O N S T A N T S A N D R E F R A C T I V E I N D E X V A L U E S F O R M A T E R I A L S 1 0 7 T A B L E C-1: PROPERTIES OF FC-75 A T 25\u00b0C 166 T A B L E D-1: S A M P L E C A L C U L A T I O N OF C H R O M A T I C I T Y COORDINATES 167 T A B L E E-1: S T A N D A R D I L L U M I N A N T D 6 5 171 T A B L E F - l : R E C O M M E N D E D OPERATING CONDITIONS OF TSL251 OPTICAL SENSOR 173 T A B L E F-2: E L E C T R I C A L CHARACTERISTICS OF TSL 251 OPTICAL SENSOR 173 T A B L E F-3: OPERATING CHARACTERISTICS OF TSL251 OPTICAL SENSOR 173 T A B L E M-1: R A Y HISTORY T A B L E F R O M TRACEPRO\u00ae M O D E L 186 L I S T O F F I G U R E S FIGURE 2-1. REFLECTION, REFRACTION AND T I R AT AN INTERFACE 7 FIGURE 2-2. PATH OF LIGHT RAYS IN A REFRACTIVE INDEX GRADIENT 9 FIGURE 2-3. PICTORIAL REPRESENTATION OF THE EVANESCENT WAVE 10 FIGURE 2-4. EVANESCENT WAVE DEPTH FOR GLASS\/AIR INTERFACE 11 FIGURE 2-5. (A) T I R AND (B) FRUSTRATION OF T I R BY AN ABSORPTIVE MATERIAL 12 FIGURE 2-6. (A) ISOMETRIC AND (B) CROSS-SECTIONAL VIEW OF AN OPTICAL SYSTEM 14 FIGURE 2-7. APPARENT ANGLES FOR TWO-DIMENSIONAL PROJECTION OF A RAY PATH 16 FIGURE 2-8. STANDARD C I E CHROMATICITY DIAGRAM 22 FIGURE 2-9. IDEAL TRANSMITTANCE CHARACTERISTICS FOR SUBTRACTIVE COLOUR FILTERS . 25 FIGURE 2-10. COLOUR GAMUT OF A DEVICE BASED ON SUBTRACTIVE COLOURS 26 FIGURE 3 -1. PRINCIPLE OF A TIR-BASED REFLECTIVE IMAGE DEVICE 42 FIGURE 3-2. LIGHT RAYS AT AN INTERFACE WITH INDEX RATIO OF (A) 1.05 AND (B) 2.00 43 FIGURE 3-3. FRUSTRATION OF T I R BY A CONFORMABLE ABSORBER 47 FIGURE 3-4. FRUSTRATION OF T I R BY A FLEXIBLE MEMBRANE 48 FIGURE 3-5. ONE OPTICAL ARRANGEMENT FOR A LIQUID-BASED FRUSTRATED T I R DEVICE.... 49 FIGURE 3 -6. PATH FOLLOWED BY A RAY THROUGH OPTICAL ARRANGEMENT 50 FIGURE 3-7. ELECTROPHORETIC MOBILITY MEASUREMENT SET-UP 53 FIGURE 3 -8. S E M IMAGES OF (A) CARBON BLACK AND (B) MAGENTA PIGMENT PARTICLES 54 FIGURE 3 -9. SCHEMATIC REPRESENTATION OF EVANESCENT WAVE ZONE 55 FIGURE 3-10. DESIGN OF AN F T I R DEVICE ACTUATED BY ELECTROPHORESIS 56 FIGURE 3-11. SELECTIVE ABSORPTION BY ELECTROPHORETIC CHANNELS 57 FIGURE 3-12. PARTICLE CLUSTERS FORMED AFTER (A) OS, (B) 10s, (C)40SAND(D) 180S 60 FIGURE 3-13. SCHEMATIC OF A FULL-COLOUR T I R-B ASED REFLECTIVE IMAGE DEVICE 63 FIGURE 3-14. ACTUATION OF AN F T I R DEVICE, DEMONSTRATING A NET RED COLOUR 65 FIGURE 3-15. ACTUATION OF AN F T I R DEVICE YIELDING A NET YELLOW COLOUR 66 FIGURE 4-1. OPERATION OF A SPECTRORADIOMETRIC TELECOLORIMETER 69 FIGURE 4-2. SET-UP FOR MEASURING SPECTRAL TRANSMITTANCE OF FILTERS 70 FIGURE 4-3. TOP (A) AND SIDE (B) VIEWS OF ASSEMBLED ELECTROPHORETIC TEST CELLS 72 FIGURE 4-4. MODIFIED TEST CELL INCORPORATING MICRO-PRISMS 73 FIGURE 4-5. ACHIEVING T I R BY REFRACTION THROUGH A PRISM 74 FIGURE 4-6. MEASURING ATTENUATION IN (A) T I R AND (B) FRUSTRATED T I R STATES 75 FIGURE 4-7. SPECTRAL TRANSMITTANCE MEASURED FOR PHOTOGRAPHIC FILTERS 77 FIGURE 4-8. AVERAGE TRANSMITTANCE OF PHOTOGRAPHIC FILTERS 78 FIGURE 4-9. EFFECTIVE TRANSMITTANCE OF PIGMENT SYSTEMS 79 FIGURE 4-10. AVERAGE EFFECTIVE TRANSMITTANCE FOR PIGMENT SYSTEM 79 FIGURE 4-11. EFFECTIVE SPECTRAL TRANSMITTANCE OF CARBON BLACK SYSTEM 80 FIGURE 4-12. MEASURED COLOUR GAMUT 82 FIGURE 5-1. CROSS-SECTIONAL VIEW OF LIGHT COLLIMATING TUBE 84 FIGURE 5-2. EXTENT OF ANGULAR RANGE MEASUREMENTS 85 FIGURE 5 -3. SCHEMATIC DIAGRAM OF DATA ACQUISITION SYSTEM 86 FIGURE 5-4. POSITION OF FILTERS 87 FIGURE 5-5. REFLECTANCE MODULATED BY ELECTROPHORESIS OF BLACK PARTICLES 89 FIGURE 5-6. HIGHER FREQUENCY MODULATION OF T I R 91 FIGURE 5-7. PARALLEL PLATE CAPACITOR SYSTEM 92 FIGURE 5-8. COMPARISON OF REFLECTANCE AND CURRENT 94 FIGURE 5-9. REFLECTANCE VERSUS TIME FOR VARIOUS INTENSITIES OF APPLIED FIELD 95 FIGURE 5-10. REFLECTANCE IN RESPONSE TO SLOWLY VARYING APPLIED FIELD 97 FIGURE 5-11. MODULATION BY DIFFERENT CONCENTRATIONS OF PARTICLES 99 FIGURE 5 - 1 2 . REFLECTANCE AT DIFFERENT WAVELENGTHS OF INCIDENT LIGHT 101 FIGURE 5 - 1 3 . MODULATION BY PARTICLES WITH DIFFERENT SPECTRAL ABSORPTION. 1 0 2 FIGURE 5 - 1 4 . REFLECTANCE AT DIFFERENT ANGLES OF INCIDENCE : 1 0 4 FIGURE 6 - 1 . UNIFORM DENSITY LAYER OF PARTICLES 1 0 8 FIGURE 6 - 2 . INCREASING THICKNESS OF UNIFORM DENSITY PARTICLE LAYER WITH TIME 1 0 8 FIGURE 6 - 3 . INCREASE IN PATH LENGTH AS THICKNESS INCREASES 1 0 9 FIGURE 6 -4 . ANGULAR DEPENDENCE ON PATH LENGTH IN UNIFORM DENSITY LAYER 1 0 9 FIGURE 6 - 5 . PREDICTED REFLECTANCE VALUES USING UNIFORM DENSITY MODEL 1 1 0 FIGURE 6 - 6 . PREDICTED DISTRIBUTION OF PARTICLES USING UNIFORM DENSITY MODEL 1 1 1 FIGURE 6 - 7 . DENSITY GRADIENT OF PARTICLES 1 1 2 FIGURE 6 - 8 . LINEAR DENSITY GRADIENT OF PARTICLES 1 1 3 FIGURE 6 - 9 . PREDICTED REFLECTANCE VALUES USING LINEAR DENSITY GRADIENT MODEL . . 1 1 4 FIGURE 6 - 1 0 . PARTICLE DISTRIBUTION PREDICTED BY LINEAR DENSITY GRADIENT MODEL 1 1 5 FIGURE 6 - 1 1 . MODIFIED LINEAR DENSITY GRADIENT OF PARTICLES 1 1 5 FIGURE 6 - 1 2 . REFLECTANCE PREDICTED BY MODIFIED LINEAR DENSITY GRADIENT MODEL .... 1 1 6 FIGURE 6 - 1 3 . PREDICTED DISTRIBUTION USING MODIFIED LINEAR DENSITY GRADIENT MODEL 1 1 7 FIGURE 6 - 1 4 . EXPONENTIALLY TAPERED DENSITY GRADIENT OF PARTICLES : 1 1 8 FIGURE 6 - 1 5 . REFLECTANCE PREDICTED BY EXPONENTIALLY TAPERED GRADIENT MODEL 1 1 8 FIGURE 6 - 1 6 . DISTRIBUTION PREDICTED BY EXPONENTIALLY TAPERED GRADIENT MODEL 1 1 9 FIGURE 7 - 1 . SCHEMATIC DRAWING OF OPTICAL CONFIGURATION 1 2 2 FIGURE 7 - 2 . REFRACTIVE DEFLECTING LAYER IN (A) IDEAL AND (B) NON-IDEAL CASE 123 FIGURE 7 - 3 . REFLECTIVE DEFLECTING LAYER IN IDEAL CASE : 1 2 5 FIGURE 7 - 4 . R A Y PATH THROUGH y\u00a3=90\u00b0 MICRO-PRISM SHEET ; 1 2 9 FIGURE 7 - 5 . LAYERED STRUCTURE OF 9 0 \u00b0 \/ 9 0 \u00b0 MICRO-PRISM SHEETS 1 3 0 FIGURE 7 - 6 . LIGHT RAY INCIDENT ON LAYERED 9 0 7 9 0 \u00b0 MICRO-PRISM STRUCTURE 1 3 0 FIGURE 7 - 7 . ARRANGEMENT OF 6 0 \u00b0 AND 9 0 \u00b0 MICRO-PRISM SHEETS 1 3 2 FIGURE 7 - 8 . R A Y PATH THROUGH 6 0 7 9 0 7 9 0 \u00b0 STRUCTURE 1 3 3 FIGURE 7 - 9 . INTERLEAVED STRUCTURE OF 6 0 \u00b0 MICRO-PRISM SHEETS 1 3 4 FIGURE 7 - 1 0 . R A Y PATH THROUGH LAYERED STRUCTURE OF 6 0 \u00b0 MICRO-PRISM SHEETS 1 3 5 FIGURE 7 - 1 1 . DIFFERENT ANGULAR POSITIONS OF LIGHT SOURCE 1 3 7 FIGURE 7 - 1 2 . POSITION OF LIGHT SOURCE AND TARGET PLANE FOR 9 0 7 9 0 \u00b0 SYSTEM MODEL .. 1 4 0 FIGURE 7 - 1 3 . REFLECTANCE VERSUS VERTICAL SOURCE ANGLE FOR 9 0 7 9 0 \u00b0 SYSTEM... 141 FIGURE 7 - 1 4 . LIGHT SOURCE AND TARGET PLANE POSITION FOR 7 0 7 9 0 7 9 0 \u00b0 SYSTEM MODEL. 1 4 2 FIGURE 7 - 1 5 . REFLECTANCE IN VERTICAL PLANE FOR 6 0 7 9 0 7 9 0 \u00b0 SYSTEM 143 FIGURE 7 - 1 6 . REFLECTANCE IN HORIZONTAL PLANE FOR 6 0 7 9 0 7 9 0 \u00b0 SYSTEM 1 4 4 FIGURE 7 - 1 7 . LIGHT SOURCE AND TARGET PLANE POSITION IN INTERLEAVED 6 0 7 6 0 \u00b0 MODEL 145 FIGURE 7 - 1 8 . REFLECTANCE IN HORIZONTAL PLANE FOR INTERLEAVED 6 0 7 6 0 \u00b0 SYSTEM 1 4 6 FIGURE 7 - 1 9 . REFLECTANCE IN VERTICAL PLANE FOR INTERLEAVED 6 0 7 6 0 \u00b0 SYSTEM 1 4 6 FIGURE 7 - 2 0 . CONTOUR PLOT OF REFLECTANCE VALUES FOR INTERLEAVED 6 0 7 6 0 \u00b0 SYSTEM . 1 4 7 FIGURE 7 - 2 1 . COMPARISON OF MEASURED AND PREDICTED REFLECTANCE VALUES FOR 7 0 7 9 0 7 9 0 \u00b0 SYSTEM 1 5 1 F I G U R E A - l : I N D E X G R A D I E N T R E G I O N : 163 F I G U R E A - 2 : P A T H C A L C U L A T E D U S I N G D I F F E R E N T I A L S N E L L ' S L A W 164 F I G U R E B - 1 : D E T E R M I N I N G T H E R E F L E C T A N C E O F A S U R F A C E U S I N G T H E B R D F 165 F I G U R E F - l : P H O T O D I O D E S P E C T R A L R E S P O N S I V I T Y 174 F I G U R E G - 2 : A N G U L A R R E S P O N S E O F C O L L I M A T E D D E T E C T O R 176 F I G U R E H - 1 : S P E C T R A L T R A N S M I T T A N C E O F I N T E R F E R E N C E F I L T E R S 177 F I G U R E H - 2 : S P E C T R A L T R A N S M I T T A N C E O F I N F R A R E D F I L T E R 178 F I G U R E I-1: S P E C T R A L R A D I A N C E O F I N C A N D E S C E N T S O U R C E 179 F I G U R E J -1 : E V A N E S C E N T W A V E D E P T H A T P O L Y C A R B O N A T E \/ F L U O R I N E R T \u2122 I N T E R F A C E 180 ix FIGURE L-1: E X A M P L E OF OPTICAL STRUCTURE IN TRACEPRO FIGURE M-1: T Y P I C A L R A Y D I A G R A M FOR TRACEPRO\u00ae M O D E L ACKNOWLEDGEMENTS First and foremost, I would like to thank past and present SSP team members for making the lab such an enjoyable place to work. In particular, I would like to acknowledge the assistance provided by Januk Aggarwal, Karla Boucher, Kevin Cheng, Alison Clark, Robin Coope, Roger Donaldson, Vincent Kwong, Anne Liptak, Jill Miwa, Jordan Schultz, Helge Seetzen, Kim Tkaczuk and Ben Tippett. Special thanks to Kir i Nichol for all her hard work in becoming our initial raytrace pro. Sincere thanks to Andrzej Kotlicki for his assistance and advice with this research program over the past few years. I would also like to express my appreciation to the members of my supervisory committee, Boye Ahlborn, Brian Turrell and Chris Waltham for their always helpful advice during the preparation of this thesis. The collaborative nature of bur work has provided the opportunity to learn from many professionals from the 3 M Company. Thanks to David Amey, Rolf Biernath, Steve Buckingham, Kathleen Dennison, David Kowitz, Pat McGuire, Mark Pellerite, John Potts, and Rick Weiss for the time they have devoted to this research program. Special thanks to S.P. Rao for his very significant scientific contribution in the development of the pigment particle suspensions used in this research. I am grateful to NSERC, U B C , and the family of Mr. L i Tze Fong for their financial support throughout the course of this project. To my research supervisor, Lome Whitehead: you have created in the lab a unique atmosphere, which blends both academic and industrial approaches to physics. From your approach, I have learned more than I could have hoped for, and I would like to sincerely thank you. Finally, to the \"Fromthepools\", who join me for my much-needed fix each day, thanks for keeping me afloat. To Telus, thanks for the flat rate that keeps me in close touch with my wonderful friends across the continent. And to Mom and Dad, Jennifer, Scott, Gardie, Amanda and little Zoe, thanks for making the distance between us seem so much shorter. xi 1 I N T R O D U C T I O N Reflective image devices have become increasingly important in a wide range of applications, from small displays used in hand-held electronic devices to large roadside displays used to provide information to passing motorists. In such devices, the bright regions of an image are created by reflecting ambient light toward the viewer, while the dark regions are created by absorbing this ambient light. By using spectrally selective absorption, full colour images are also possible. Although the specific requirements for a reflective image device depend on the particular application, it is always preferable to produce an image that looks bright and colourful under a wide variety of lighting conditions, with a minimum of power consumption. Despite significant research efforts by numerous organizations, current reflective image display technologies leave much to be desired. The reflectance of current commercially available reflective displays is at best 35% for a black and white image, and less than 16% for a full-colour image, as a result of inherent limitations in the mechanism by which the reflection occurs. This limited brightness makes these displays difficult to read under many common lighting conditions. While some new technologies are claimed to have the potential to exceed these reflectance values, these have not yet been proven. The work presented in this thesis establishes a new technology for a reflective image device. Total internal reflection is used as the mechanism to reflect light rays striking the surface, redirecting them back toward the viewer. Total internal reflection, typically abbreviated as \"TIR\", is the well-known phenomenon that occurs when a light ray travelling through a material arrives at an interface with a second, less optically dense material. If the ray strikes that interface with a sufficiently large incident angle, it will undergo TIR, and there will be no net transfer of light across the interface. Under these conditions, the light completely reflects, providing a mechanism of reflection that is, in principle, 100% efficient. Although there is essentially no transmitted radiation with TIR, a complete solution of the electromagnetic fields at the interface shows that some electromagnetic energy, known as the evanescent wave, does penetrate a small distance into the second material, in an exponentially tapered fashion. The penetration depth, for visible light, is typically less than 1 0.25 urn, or about half of the wavelength. The conditions for TIR depend on the optical properties in this very thin evanescent wave region, so by altering those properties, (for example, by moving a scattering or absorbing material into the region), the reflectance at the interface can be reduced. This is sometimes known as \"frustration\" of TIR. In a reflective image device based on TIR, such frustration must be selectively, and controllably, applied to generate the desired dark and light portions of the image. The general idea of evanescent wave scattering is not new; it has been used to study the optical properties of scattering materials and in the field of TIR microscopy. In addition, it has been proposed as an optical switch for fibres, where a scattering material is moved into the evanescent wave region and prevents further propagation of the light along the fibre. However, to the best of our knowledge, this thesis represents the first use of controlled frustration of TIR in a reflective image display. The TIR-based approach has three unique features in comparison to other reflective displays. First, a reflectance of near-100% is practical. Readily available optically microstructured polymeric sheets can produce the required reflection. Second, only a very slight movement of the absorber can switch the frustration on and off. The absorber need only move in and out of the evanescent wave region, a distance of less than 0.5 um, and can therefore, in principle, switch the reflectance quickly. Finally, subtractive colour filtering can be employed to yield a full colour image. Unlike other colour display technologies, this approach allows the uses of an array of efficient, subtractive filters, in a single electro-optic layer, to produce a bright, full colour display. One of the challenges of positioning an absorber in the tiny evanescent wave region is that direct physical contact is problematical, due to adhesion forces. Such adhesion would greatly increase the required actuating force and power consumption. It was therefore concluded during the course of this study that such solid-solid adhesion must be substantially reduced. One way to do so is to use a liquid, rather than air, as the second interfacial material. However liquids have a much higher refractive index than air, making it more difficult to achieve TIR than at a solid-air interface. This led to identification of a low index perfluorinated hydrocarbon liquid, as well as the development of a novel geometrical 2 approach to enhance the effective refractive index ratio in order to achieve TIR over a useful angular range with a solid-liquid interface. A number of possible absorbing materials were investigated. The most promising system uses a liquid suspension of electrostatically charged pigment particles to frustrate the TIR. These pigment particles must be optically small such that they are essentially non-scattering, and sufficiently absorptive that they effectively frustrate the TIR. Under an applied electric field, the particles can be moved into and out of the evanescent wave region to modulate the surface reflectance, using the well-known mechanism of electrophoresis. Another new result of this work is the demonstration that by using sub-optical coloured pigment particles, the spectral distribution of the reflected light can be controlled. This is a requirement for the operation of a full colour device based on TIR. To best understand the work presented here, it will be helpful to review the diverse set of physical and psychophysical phenomena involved. Chapter 2 briefly reviews some useful background information in each of these areas, as appropriate to the context of this thesis. In addition, a brief description of other reflective display technologies is included, in order to provide a framework for comparison to the new TIR-based approach. In Chapter 3, factors specifically influencing the design of a TIR-based reflective image display are discussed. In particular, the rationale for the use of a solid-liquid TIR interface, in terms of the surface energy considerations, is presented, as well as the method of enhancing the effective refractive index ratio at the interface. Key features of the pigment suspensions incorporated into the device are discussed, as well as the method of subtractive colour filtering to generate a full colour image. Experimental results demonstrating spectrally selective reflectance by the electrophoresis of pigment particles are provided in Chapter 4. This new observation is one of the cornerstones of this thesis. In addition to the demonstration of such spectral control of the reflected light, the reflectance response to time-varying electric fields was analyzed. Such time-varying reflectance modulation is crucial to the use of pigment electrophoresis in a TIR-based reflective image device, in which the image must be regularly updated. Additionally, a study of this reflectance change under a number of different experimental conditions was 3 undertaken in order to develop a more complete understanding of the dynamics of the electrophoretic pigment particles. These experimental measurements are presented in Chapter 5. One of the conclusions from these measurements is that the particles have sufficient density to modify the energy distribution in the evanescent wave, making simple absorption models incomplete. In Chapter 6, a more sophisticated model of the evolving particle density distribution near the interface was developed to explain the level of absorption measured in the previous experiments. A number of possible distributions were considered and one with a maximum density limit and an exponentially tapered tail was found to best match the experimental observations. Chapter 7 describes the investigation of several possible configurations of micro-prismatic sheets comprising a TIR-based display. Computer ray trace models were designed to determine the reflectance of these structures at different viewing angles. In the last section of this chapter, a sample of one of these structures is incorporated into an electrophoretic pigment test cell and the measured reflectance is compared with the model predictions. These results establish the feasibility of using electrophoretic pigments in an image device based on frustrated TIR, and suggest a number of areas for further work. 4 2 BACKGROUND The work presented in this thesis incorporates key ideas from several disparate fields. This introductory chapter provides a relevant background discussion in each of these areas in order to show how they relate to one another in the context of the research subsequently presented. 2.1 Total Internal Reflection The primary focus of this study involves the application of total internal reflection (henceforth abbreviated \"TIR\") to a reflective image device. TIR occurs when light traveling in a material reaches an interface with a material of lower index of refraction, at a sufficiently large incident angle. In this section, this well-known phenomenon is reviewed. 2.1.1 Index of refraction Light, being an electromagnetic disturbance, causes the displacement of local charges as it propagates through a material. These moving charges, in turn, produce additional electromagnetic disturbances that combine with the original to form a wave that travels slower than light in a vacuum. The propagation speed of this wave in a particular material depends on the properties of that material, summarized as the index of refraction, n, which is the ratio of the speed of the light in vacuum, c, to its speed in the material, v: n = - (2-1) V The index of refraction of air at STP is about 1.0003, whereas more optically dense materials such as water and glass (depending on its type) have index values of approximately 1.33 and 1.51, respectively. The value of n depends on the wavelength of the light, but for the materials considered throughout the course of this study, this wavelength dependence is quite slight. The refractive index of a material is determined by the relative permittivity, er and the relative permeability, fir. 5 tl = ^Er\\lr (2-2) In nonmagnetic materials, such as those considered in this study, \/ i r =l, and (2-2) becomes: n = yl\u00a3r (2-3) It is well known that dielectric materials can exhibit energy loss in oscillating fields and that these losses can be represented mathematically by an imaginary component of the dielectric constant.1 Similarly, the index of refraction can also have both real and imaginary components, n = n+in\" (2-4) where the imaginary component represents the absorbance of the material. In a purely transparent material, n - 0, but if the intensity of the light diminishes as the wave propagates, then n'(and therefore the imaginary component of the dielectric constant, e;. ) has a nonzero value. Under these circumstances, the intensity of the wave decreases exponentially, at a rate described by the absorption coefficient, k, of the material. The intensity, I, after the wave has propagated a distance x is given by I = Ioe^ (2-5) where To is the initial intensity, k is related toe r by the following relation\": (2-6) n A The index of refraction describes the propagation of light in optically different materials and is a fundamental concept in this study, since this parameter determines the conditions for TIR, as explained in the next section. 6 2.1.2 Conditions for TIR at an interface A typical depiction of TIR is shown in Figure 2-1. An electromagnetic wave, represented by a light ray, strikes an interface between two optically different materials, the first having a refractive index value of n\\, and the second a lower value, n.2. (a) (b) Figure 2-1. Reflection, refraction and TIR at an interface As the light ray passes from the higher index medium to the lower one depicted by Figure 2-1(a), it refracts away from the surface normal at an angle 62, as governed by (2-7), known as Snell's law: d2 = arcsin((n,\/n2)sin01) (2-7) TIR, shown in Figure 2-l(b), occurs when Snell's law generates a complex solution for the refracted angle 62. This occurs for all light rays having incident angles greater than a critical angle 6C, derived from (2-7): 9C = arcsin (n2 \\nx) (2-8) From (2-8) it is clear that the conditions for TIR depend on the ratio of the refractive indices of the two materials. 7 In many texts, the optical situation is simplified to the special case of a discontinuity in refractive index across the interface3. However, in its most general form, Snell's law describes the situation when a light ray passes from one region of uniform value of refractive index into a second having a different index value, and there is no requirement that the index transition between the two regions be abrupt. In fact, it is not uncommon to find continuous index gradients in nature4, and optical engineers often construct this transition in several steps for practical reasons5. However, the discontinuous situation depicted in Figure 2-1 is most often presented because, in this special case, the Maxwell equations can be analytically solved in a straightforward manner.6 It will be helpful to consider ray propagation in the more general case in which the refractive index changes continuously. The differential form of Snell's law, used to describe the path a light ray follows as it enters a region of refractive index gradient, is given (2-9), ^-(nr) = Vn (2-9) dl where \/ is the path length along the ray path, f is the ray direction at the point \/ and n is the index at that point. At each incremental step dl along the ray path \/, f is determined by this differential equation. A differential algorithm based on (2-9) is employed in Chapter 6 in order to predict the path and the absorption of a light ray as it passes through a distribution of pigment particles in a fluid medium. Figure 2-2 shows a situation where the refractive index gradually changes from one value to another over a distance much greater than a wavelength, with the paths predicted by numerical integration of (2-9). Here, the partial reflectance is essentially zero for angles of incidence less than the critical angle, and TIR occurs for angles greater than critical. Each light ray curves as it passes through the gradient. Just as in Figure 2-1, if the angle is less than the critical angle, the ray will transmit. Otherwise, it will reflect by TIR. 8 Figure 2-2. Path of light rays in a refractive index gradient The case where TIR occurs in a region of refractive index gradient is a key feature in the discussion presented in Chapter 6, and will be discussed in further detail there. In the meantime, it is important to consider the distribution of electromagnetic energy when TIR occurs. 2.1.3 The evanescent wave As described in Section 2.1.1, when the angle of incidence exceeds the critical angle, Snell's law generates a complex angle of refraction, written as (2-10). Since there is no real component of k 2 perpendicular to the interface, this form implies that there is no net transfer of electromagnetic energy across the interface under these conditions. However, (2-11) shows that some electromagnetic field does penetrate a small distance into the second medium, as shown pictorially in Figure 2-3. This is equivalent to the fact that in 62 = a + ib (2-10) The resultant wavenumber, k2, of the transmitted wave is complex , as in (2-11). (2-11) 9 the full solution of the Maxwell equations at the interface, the Poynting vector of the evanescent wave is parallel to the surface.9 Incident Reflected wave wave n. 7 Evanescent wave Figure 2-3. Pictorial representation of the evanescent wave This so-called evanescent wave propagates along the interface, but its strength drops off exponentially with distance into the second medium, so it effectively penetrates only a very short distance into the material. This effective penetration distance, 8, depends on the angle of incidence, 6\\ (since b depends on d\\), and the wavelength, A2, and is given by 8 (2-12). Figure 2-4 plots the evanescent wave depth for light striking a glass-air interface (n\\ = 1.5, \u00ab2= 1-0) interface, at a wavelength, Xi, of 500nm, as a function of incident angle. The critical angle, 0C, in this case is about 41.8\u00b0. The angular dependence of the plot shows that very close to the critical angle, the wave penetrates a relatively long distance into the air, and the depth rapidly declines as the incident angle decreases. Except in the very narrow range just past the critical angle, for visible light, the penetration depth is about half a wavelength, or 0.25 um. 5 = (2-12) 2n sinh b 10 6 5 4 3 2 1 H 0 0c 41 42 43 44 45 Incident angle (degrees) Figure 2-4. Evanescent wave depth for glass\/air interface As will be discussed in the following section, the occurrence of TIR at an interface can be prevented by absorbing the electromagnetic energy in the evanescent wave region. For this reason, it will be helpful to more carefully consider such interactions. As described in Section 2.1.2, the occurrence of TIR is dependent upon the optical properties of the materials. It therefore follows that reflectance can be controlled by altering the optical properties at the interface. Specifically, TIR can be prevented or \"frustrated\" by scattering or absorbing the electromagnetic energy in the evanescent wave. By moving a highly absorptive material into the evanescent wave region, almost all of the light can be absorbed, and if the absorber is returned to the region just outside the zone in which the evanescent wave penetrates, complete reflection is restored. This effect is depicted schematically in 2.1.4 Frustrated T I R Figure 2-5. (a) (b) Figure 2-5. (a) TIR and (b) frustration of TIR by an absorptive material It is remarkable that such a dramatic reduction in reflectance can occur by moving the absorber such a small distance. The fact that the evanescent wave only penetrates typically less than half a micron into the second medium is responsible for this effect. The idea of using evanescent wave scattering for an optical switch is not new; it has been proposed for a particular application in optical fibres, where a scattering material is moved into the evanescent wave region and prevents further propagation of the light along the fibre.1 0 However, the work presented in this thesis is, we believe, the first demonstration of controlled frustration of TIR in a reflective image display. The development of a practical reflective image device based on this controlled TIR approach required the use of specially designed reflective sheets. These are described in the following section. 2.2 Geometrical optics To yield a reflective image device, the effect of frustrated TIR can be employed in conjunction with special reflective sheets made by micro-replication techniques. These microstructured sheets can have customized optical properties based on their specific design details. 12 2.2.1 Micro-replicated sheets There are many applications in which it is desirable to have a material whose surface contains tiny, yet very precise, structures. For example, for the abrasives industry, microscopic pyramids of an abrasive material can be created on a sheet to yield a type of sandpaper with better qualities than the traditional random assortment of particulates.11 As the structures wear down, they maintain their pyramidal shape and, as a result, greatly extend the lifetime. In a number of fluid transport applications, very small channels have been structured into an otherwise hydrophilic material to direct fluid away from certain regions. Of particular interest in regard to this thesis, microstructured prismatic surfaces are made using clear polymer resin, and these surfaces can be designed such that TIR occurs when light is directed at the sheet.12 The process used to form these optical structures, known as micro-replication, uses a carefully designed mould, typically made of a robust metal alloy. Although there are a number of micro-replication techniques, typically the uncured polymer resin is poured into the mould and cured under high heat and pressure. The resulting microstructures are essentially optically clear in the bulk, with less than 2% absorption13, and the surfaces of the structures are optically smooth. (The phrase \"optically smooth\" means that the surface inaccuracies are much smaller than a wavelength of light.) Sheets of polycarbonate micro-prisms with a pitch of 50 um and included angle of both 90\u00b0 and 70\u00b0 are currently readily available.1 4'1 5 Research and development is continuing in the field of micro-replication, to produce sheets with new surface profiles and higher refractive indices. To describe in more detail the interaction of light with these microstructures, it is helpful to consider a specific example: Figure 2-6(a) shows an isometric drawing of an optical system having translational symmetry along a direction r\u201e. (In other words, the system has the same shape in all cross sectional planes perpendicular to r\u201e, as shown in Figure 2-6(b) and therefore has linear features, as in an extrusion.) In this example, the cross-section of the surface structure is a series of prisms having an included angle of 90\u00b0. 13 A (a) (b) Figure 2-6. (a) Isometric and (b) cross-sectional view of an optical system Light rays incident on the surface will either reflect or refract, depending on their incident angle. Figure 2-6(a) shows two rays, where ray A transmits and ray B undergoes TIR, and Figure 2-6(b) shows the projection of these paths on to such a cross sectional plane. One of the special features of an optical system having translational symmetry is the fact that a light ray traveling with a component of motion along the symmetry axis behaves as though the refractive index ratio is enhanced. This effect is important for the research described in this thesis, and it will therefore be useful to expand on this in the next section. 2.2.2 Enhanced refractive index ratio As mentioned above, under certain circumstances, a light ray with a component propagating in the direction of the translational symmetry exhibits an enhanced response to index transitions.16 Consider again the light rays shown in Figure 2-6. It is simplest to describe the path of rays in terms of the wave vector, k , of the associated plane wave, whose phase,
c 2) 1 \/ 2sin0,. = ( n \/ - i c 2 ) 1 \/ 2 s i n 0 ; (2-18) where Kis defined, as previously discussed, in (2-14). This looks just like Snell's law, if one replaces the refractive index, n, of a given medium by an effective reduced index n given by n ' = V \u00ab 2 -K2 (2-19) Since this reduction is proportionately greater for lower index materials, the result can be a 1 Q substantial enhancement of the effective index ratio between two media. This in turn enables TIR to occur over a wider range of azimuthal angles than would be the case without such propagation in the direction of translational symmetry. 16 As will be described in Section 3.3, this index ratio enhancement technique can be incorporated into a reflective image device as a way of overcoming some optical limitations. In the meantime, it is important to consider how best to measure the reflectance of a surface, as a means of evaluating its behaviour. The next section discusses the surprisingly subtle problem of describing surface reflectance in general. 2.2.3 Specification of reflectance in prismatic systems An optical surface is considered to be a structure that is macroscopically planar over a region that is larger than the scale of its surface structure or optical penetration depth, so that its macroscopic surface normal is well defined. The measurement of the reflectance of an arbitrary optical surface is a complex, but well-established field. The luminance of a surface, as seen from a particular viewing angle, is determined as the solid-angle integral of the product of the bi-directional reflectance distribution function (BRDF) and the luminance distribution of the ambient environment.19 In the special case of a perfectly diffuse surface, this relationship can be summarized as a single number called reflectance. For non-diffuse surfaces, the luminance depends on the viewing angle and the ambient luminance distribution, and this dependence is often quite complex. The prismatic structures discussed in this thesis are inherently angularly dependent, so this issue must be addressed. For simplicity in this discussion, unless otherwise indicated, the reflectance of a surface is defined as the ratio of the surface luminance, at a defined viewing angle, to that of a standard sample, when the surface and the standard are in a uniformly luminous environment. This 20 sample can be either a near-100% reflective diffuse white surface , or a near-100% reflective specular surface21, depending on the desired specifications. The calculation of reflected luminance based on the BRDF is explained in further detail in Appendix B. A l l of the above discussion is based on light rays of unspecified wavelength. In modern displays, however, it is desirable to reproduce colour information, so it is now appropriate to review the methods for specifying the colours resulting form wavelength-dependent processes. 17 2.3 Colour Light can be defined as visually evaluated radiant energy, in the wavelength band extending from about 380 nm to 780 nm, and colour is the characteristic of light by which an observer may distinguish between different spectral power distributions. This section briefly discusses some of the standard methods for measuring and producing colour. 2.3.1 Measurement of colour The measurement of the spectral distribution of radiant power results in physical information, however the evaluation of colour by a human observer is psychological. It is fascinating that some aspects of colour perception are observer-independent, whereas others are purely subjective. Here, the former are considered, which arise from the existence in the human retina of specific photoreceptor molecules having fixed universal action spectra.22 In this regard, the Commission Internationale de l'Eclairage (CIE) established a number of standards for the colour interpretation of spectral data. In particular, a set of colour-matching functions was developed using standardized conditions of observation.23 As well, the CIE has recommended the spectral power distribution of several standard illuminants, designed to behave like common natural or artificial light sources, for calculating colour. The more modern and preferred of these is Standard Illuminant D65, representing a phase of daylight at a correlated colour temperature of approximately 6500 K . 2 4 2.3.2 C I E method of colour specification Light with a given spectral power distribution is perceived to have a particular colour, but most of such colours can be reproduced by a number of different spectral power distributions. The different distributions in this set are called metamers and the basic method used to define all metameric pairs is the CIE method of colour specification.25 18 Mixing specific proportions of three primary colours can generate any colour. In other words, a particular colour, D, can be described in terms of the amounts a, b and c of primary colours A, B and C, respectively. The primary additive colours of light are considered to be blue, green and red. This arises from the fact that receptors in the human eye are predominantly responsive to light stimuli in these wavelength bands. However, it is important to note that a set of primary colours can be any three colours that are mutually independent in the sense that none can be matched by mixing the other two. The amounts a, b and c of these three primary colours can be calculated by combining the spectral power distribution of a standard source and the spectral reflectance of the object being measured. The CIE method established a basic standard for the unambiguous specification of colours by defining a set of primary functions, X, Y and Z, which can be used to convert a given spectral irradiance distribution of a light source, S(X), into standard tristimulus values. These primaries do not refer to particular colours, but instead provide a convenient approach to numerically describing colour. These primary functions are given by: D=aA+bB+bC (2-20) 780nm X k _^5 (A)x(A)AA (2-21) A=380nm 780nm Y k _^5 (A)y(A)AA (2-22) A = 380nm 780nm z k _\u00a3S(A)z(A)AA (2-23) A=380nm where k is the normalization factor that ensures that: 19 780nm 780nm 780nm k 5^ 3c(A)AA = k ]T y(A)AA = k \u00a3z (A)AA = 683 lmW' 1 (2-24) A=380nm A=380nm A=380nm and x(X), y(X), and z(A) are the defined spectral tristimulus colour matching functions, (k depends on the number of wavelength bands employed in the summation and has no physical significance. It is chosen so that the value of Y gives the luminous intensity in lumens per watt, but k subsequently cancels out in most cases.) In order to separate colour information from intensity, the chromaticity values x, y, and z are used, where: . x = (2-25) X+Y + Z y = (2-26) X+Y + Z z = (2-27) X+Y + Z In addition to specifying the colour of a source having a spectral irradiance distribution 5(A), it is useful to describe the colour of a surface having a spectral reflectance p(A), illuminated by such a source. In this situation, X, Y and Z are calculated by: 780nm X=k \u00a3S(A)p(A)x(A)AA (2-28) A=380nm 780nm Y = k \u00a3s(A)p(A)y(A)AA (2-29) A = 380nm 780nm Z = k \u00a3S(A)p(A)z(A)AA (2-30) A=380nm 20 The luminous reflectance of the surface, p, under illuminant S(A) is calculated by: 780nm jjPa)s(X)ya) p = A=380nm ( 2 . 3 1 ) 780nm X^(A)y(A) A=380nm Since x+y+z=l, the coordinates can be completely described by specifying two of the three values; by the adopted convention, chromaticity is described in terms of the x and y coordinates. These coordinates are often plotted on a chromaticity diagram, as described in the following section, as a convenient method of representation. 2.3.3 CIE chromaticity diagram For simplified representation, the chromaticity coordinates can be plotted on a rectangular grid in the form of a chromaticity diagram, shown in Figure 2-8. When plotted in this format, each colour occupies a particular point on the diagram, given by its x and y coordinates. In a three-dimensional representation, the brightness of each colour, Y , is plotted on the vertical axis, extending out of the page, and all spectral distributions representing the same colour, but different brightness, lie in a vertical line. In a colour representation, where all colours are reduced to the same intensity, this plot collapses down to the two-dimensional representation shown in Figure 2-8. Monochromatic spectral distributions, when plotted on the chromaticity diagram, make up the horseshoe-shaped curve of a standard CIE chromaticity diagram. This curve is known as the spectrum locus, and the line joining the ends of the locus is called the purple boundary. A l l possible colours lie within this enclosed area. The dotted triangle shown in Figure 2-8 shows an example set of tristimulus primaries red, blue and green, and all colours that can be matched with varying amounts of these three colours lie within this triangle.26 21 X Figure 2-8. Standard CIE chromaticity diagram Any combination of primaries can be used to define a boundary on the chromaticity diagram. The area enclosed within this boundary is referred to as the colour gamut, as it defines the range of all possible colours that can be matched by adding those primaries in various combinations. Colour gamut is an important.specification for many light-emitting or light-reflecting devices, such as cathode ray tube monitors and liquid crystal displays, since the extent of the colour gamut indicates the colour quality of the image. A large gamut means that the colours reproduced by the display can be vivid, so that a wider range of naturally occurring colours can be realistically reproduced. Although additive colour mixing, as described above, is an important way to produce colour, an important alternative involves subtractive colour employing filters. This is particularly important for a reflective display. For this reason, it will be helpful to review such colour filtering issues in a bit more detail. 22 2.3.4 Colour filtering White light contains roughly equal energy contributions from three primaries of the visible spectrum, for instance, red, green and blue wavelength bands. For discussion purposes here, \"red light\" refers to a spectral distribution with significant contribution of radiation within the red wavelength band, from 580 to 700 nm, and negligible contributions from radiation outside this band. Similarly, \"green light\" refers to a spectral distribution predominantly within the wavelength band from 500 to 580 nm, and \"blue light\" within the 450 to 500 nm band. This section compares in more detail the two main methods for mixing colours, additive and subtractive colour filtering. 2.3.4.1 Additive colours As mentioned previously, there are two approaches for mixing various colours of light. In the additive approach, red, green and blue light are added in a selected ratio to generate the desired colour. The matrix presented in Table 2-1 shows the result of the addition of one part of each of these colours. Obviously, if there is a contribution of red light in the absence of green or blue, the resulting patch of light will be red, and similarly patches of green and blue can be produced in the absence of contributions from the other two sources. Combining two of the additive primaries produces the additive secondary colours, cyan, magenta and yellow. These additive secondaries are also known as subtractive primaries, as explained in Section 2.3.4.2. Contribution from light sources Resultant colour Red Green Blue 0 0 0 Black (K) 1 0 0 Red (R) 0 1 0 Green (G) 0 0 1 Blue (B) 1 1 0 Yellow (Y) 1 0 1 Magenta (M) 0 1 1 Cyan (C) 1 1 1 White (W) Table 2-1. Additive colour filtering 23 The six colours red, green, blue, yellow, magenta and cyan are considered to be standard colours for full-colour light-emitting or light-reflecting devices. Black and white, while not strictly considered to be colours, are important to denote the absence or presence of all wavelengths in the visible spectrum. As described in the discussion of chromaticity coordinates in Section 2.3.3, varying the amounts of red, green and blue light can produce any desired colour within the available gamut. The saturation level of these three individual colours determines the achievable gamut for a particular set of primaries. For reflective displays, the additive method, while an effective method for generating colours, tends to be inefficient since the red, green and blue contributions are produced by filtering the light from a broadband source, such an incandescent or tri-stimulus phosphor fluorescent bulb, with filters having the appropriate spectral transmittance characteristics. As a result, a significant fraction of the light (in each case, approximately two thirds) is absorbed by the filters, and therefore the brightness of the resultant colour is substantially limited. 2.3.4.2 Subtractive colours The other approach for mixing colour, subtractive colour filtering, has greater relevance to this thesis. Rather than using red, blue and green filters to mix light, this system uses primary subtractive colour (cyan, magenta and yellow) filters. As mentioned in Section 2.3.4.1, these subtractive primaries are also known as additive secondary colours since they can be produced by adding two of the three additive primaries, red, green and blue. A filter with a spectral transmittance characteristic consistent with cyan absorbs wavelengths in the red band and transmits in the blue and green bands. Similarly, magenta absorbs wavelengths in the green band while transmitting in the red and blue, and yellow absorbs wavelengths in the blue band while transmitting in the green and red. Ideal transmittance characteristics for such filters are shown in Figure 2-9. 24 Figure 2-9. Ideal transmittance characteristics for subtractive colour filters Subtractive filtering can produce the same colours as the additive method, by appropriately subtracting various permutations of red, green and blue. For instance, the addition of pure green and blue light (cyan light) is spectrally equivalent to the subtraction of the contributions of red light from the visible spectrum (by a cyan filter). Table 2-2 demonstrates the filter combinations required to produce the six standard colours, as well as white and black. 25 Contribution from 1 liters Resultant colour Cyan Magenta Yellow 0 0 0 White (W) 1 0 0 Cyan (C) 0 1 0 Magenta (M) 0 0 1 Yellow (Y) 1 1 0 Blue(B) 1 0 1 Green (G) 0 1 1 Red (R) 1 1 1 Black (K) Table 2-2. Subtractive colour filtering Again, the achieved gamut is determined by the spectral quality of the filters, and all colours within the gamut can be achieved by partially filtering the light appropriately. Typically, the gamut for a colour filtering system using additive colours is defined by a triangular boundary, since the colours combine linearly. However, with subtractive colour filters, the effect is multiplicative rather than additive. As a result of this non-linear behaviour, the boundary will be defined by the six standard colours, rather than just three. A typical gamut for a device using subtractive colour filtering, shown in Figure 2-10, occupies a region of the chromaticity diagram bounded by the coordinates of the six standard colours. y X Figure 2-10. Colour gamut of a device based on subtractive colours 26 By appropriately filtering white light with selected densities of cyan, magenta and yellow filters, any desired colour within the allowable range can be generated. Spectrally, this gives the same result as the additive method, however in some circumstances this method can be much more efficient. Specifically, for reflective displays, additive colour mixing requires segmenting the display, on a microscopic scale, into \"red\", \"green\" and \"blue\" pixels, each of which absorbs a minimum of two thirds of the incident light. Thus, the maximum reflectance in the white state is about 1\/3. In contrast, with subtractive filtering, the filters are placed on top of one another, so colour pixelization is not required, and the white state has a potential reflectance approaching 1. In Chapter 3, a new approach to colour mixing is presented in which a hybrid of these two concepts yields an intermediate maximum potential reflectance of 2\/3. This approach involves coloured pigments suspended in a liquid to filter reflected light. For this reason, the behaviour of particles in suspension will be discussed in the next section. 2.4 Particle suspensions Suspensions of small particles in fluids are used in a wide variety of applications. For instance, drug delivery systems use suspensions to allow the proper dosage and release of drugs in a person's body. Photocopying and printing techniques use liquid toners, in which the pigments used to print the image are suspended in a liquid. The food industry uses particle suspensions for the preparation and preservation of many food items. These wide-ranging applications have supported a great deal of research in the field. The term \"colloid\" is often used to describe suspended particles in the size range from about 0.1 to 100 um. Usually these particles become electrostatically charged when they are suspended in a liquid, and there are a number of mechanisms by which the particles can become charged. For instance, the preferential adsorption of ions in solution can result in an electrical charge on the particle surface. The dissociation of chemical groups on the surface can also result in a charge. In some cases, substitution of surface groups can be responsible for the charge. The existence of such a surface charge is crucial in many applications, including the research described in this thesis. However, the specific charging mechanism(s) are often not known in detail. Fortunately, however, the magnitude of the charge is fairly 27 easy to determine, as discussed in Section 2.4.2, and the fact that the precise origin of the charge is unknown is seldom a problem. Since the suspension must have an overall neutral charge, for each unit charge residing on the particle surface, there must be corresponding opposite unit charge in solution. Typically a colloidal particle will have a charge equivalent to many electrons, and the countercharges reside on ionic species present in the fluid. It is common to have orders of magnitude more counterions than particles present in the suspension. For the purpose of discussion in this section, the particle is considered to be positively charged, and the counterions negatively charged. These small counterions will be attracted, by electrostatic force, to the region near a particle, forming a cloud of negative charge around the positively charged core. In this region, known as the electrical double layer, the inner layer is considered to have a surface charge consisting of the charges adhering to the particle, as well as the counterions very close to the particle surface. In such close proximity, the electrostatic force is very high, therefore overcoming the thermal motion of the counterions and binding them tightly to the particle. These counterions move with the particle, and form what is known as the Stern layer. In the outer or diffuse region of the double layer, the electrostatic force is reduced and becomes comparable to the force due to the thermal motion of the counterions. These counterions tend to remain near the particle, but are not bound to it . 2 7 One common method of characterizing these particles refers to the potential, 0, at different points within the double layer, relative to the potential at a distant point in the bulk, well outside the influence of the particle and its associated counterions. Typically, for a particle of radius a, the surface potential is denoted 0O, and the potential tends to zero in the bulk, as in equation (2-32). 0 = ^ ^ - 0 ( 2 _ 3 2 ) r The Debye length, l\/\/c, is given as the distance from the particle surface at which 0 has dropped by a factor of 1\/e. This is typically considered to be the \"thickness\" of the double layer. If the Debye length is very short, then the diffuse layers of two neighbouring particles 28 are unlikely to interact, and the particle behaviour can be predicted using some relatively straightforward analysis models. In suspensions with long Debye lengths, the diffuse layers 28 may overlap substantially, complicating the particle interactions. A particular value of potential, known as the zeta potential, \u00a3, is often cited as an important characteristic of a colloidal particle. When an externally applied force acts on a particle and causes it to move, some of the surrounding counterions will move with it. The potential at the radius within which the counterions move with respect to the solvent is defined as the zeta potential. This value is close to, but not exactly, the Stern potential. While the zeta potential is not directly measurable, it is considered to be a useful parameter for determining the electrokinetic behaviour of the particle29, as described in Section 2.4.2. The initial step in formulating a stable suspension of particles in a liquid medium requires that the net buoyancy force be sufficiently low that the particles are likely to remain at an equilibrium position in the suspension, rather than sinking or floating due to gravity. This net buoyancy force acting on the particle is the difference between the weight of the particle and the buoyant force of the liquid acting on the particle. This settling force, F, can be written in terms of the densities of the particle, p,\u201e and the surrounding liquid, pi, and the volume of the particle, V. The energy associated with this settling force is then hg(pP - Pi)V, where h is the relative position of the particle within the suspension. The settling can be counteracted by provided that this settling energy is much less than the thermodynamic energy kT: This implies that small particles, with a density closely matched to that of the surrounding medium, are most likely to yield stable suspensions. To further improve the stability of a colloidal suspension, to prevent both settling and particle aggregation, either electrostatic or steric stabilization methods can be employed. Using electrostatic stabilization, particle aggregation is reduced or eliminated by electrostatic F =g(pp-pi)V (2-33) hg(pP-p,)V \u00ab kT (2-34) 29 repulsion. Steric stabilization, on the other hand, requires a molecular dispersant mechanism. Typically, this involves adding a substance consisting of molecules that, on one end, chemically favour the particle and therefore attach to it, and on the other end, have an affinity for the liquid and readily dissolve. The result is that the dispersant molecules arrange themselves around the particle, and suspend it within the fluid. Further, these solvated molecules surround the particle and provide an excluded volume to prevent the approach of another particle.31 In some suspensions, it is both possible and desirable to incorporate both stabilization methods. The choice of method usually depends on the suspension components and formulation process. The behaviour of a particle in suspension depends in part on the properties of the fluid in which it is suspended. In the next section, a comparison is made between particles suspended in high dielectric and low dielectric constant fluids. 2.4.1 High dielectric and low dielectric constant media The behaviour of particles suspended in relatively high dielectric constant (most often aqueous) liquids is fairly well understood. It stands to reason that these systems have been well studied, since biological systems based on water, as well as substances that interact with biological systems, are so important. The behaviour of particles suspended in low dielectric constant liquids, such as the perfluorinated hydrocarbon particle systems described in this thesis, are much less well understood. The Debye length of the counterion cloud depends on both the dielectric constant and the ionic strength of the surrounding fluid. In aqueous systems, where the dielectric constant is relatively high, the electrical double layer tends to be very thin. This means that in order to characterize various particle parameters, such as diameter, charge and electrophoretic mobility, the suspension can be modeled as a system of non-interacting particles. On the other hand, in low dielectric constant fluids, the electrical double layer extends a long distance into the suspension. In these suspensions, characterization of the particle parameters is far more complicated, since the interaction of many neighbouring particles must be taken into account.32 30 The understanding of particles in low dielectric constant media is becoming increasingly important in many fields, including the development of paints, inks and toners'', and the study of oil and fuel systems.34 The research described in this thesis does not attempt to further the understanding of charging mechanisms and particle characterizations in perfluorinated hydrocarbon liquids. However, these issues are important to bear in mind when dealing with these systems, as it is necessary to recognize the complex behaviour of particles in these systems and to apply the principles and analysis methods of particle characterization judiciously. As previously mentioned, the significance in this thesis of the electrostatic charge of the colloidal particles is that they can be moved by an applied electric field. This controlled motion, known as electrophoresis, is discussed in further detail in the following section. 2.4.2 Electrophoresis Electrophoresis refers to the motion of electrostatically charged particles in response to an applied electric field. Under typical moderate applied field strengths, the drift velocity, v, of a particle is linearly proportional to the electric field strength, E. The constant of proportionality is known as the electrophoretic mobility, fi: v = pE (2-35) For a given particle, the mobility value depends on its net electrostatic charge, qnet, and its effective hydrodynamic radius, anel. The exact relationship between overall charge, radius and mobility of particles in a low-dielectric medium is complicated, as a result of the interactions of the extended double layers. However, when the particle is moving at constant velocity under the influence of an applied field, the relationship can be approximated by equating the electrostatic force, Fe, Fe = qnetE (2-36) to the drag force on a spherical particle, Fs, given by Stokes' equation35, Fs = 6Tzr\\anetv (2-37) 3 1 where 77 is the viscosity of the fluid. Combining equations (2-35), (2-36) and (2-37), the mobility is given by fi=-^\u2014 (2-38) 6nr\\anet which is proportional to the ratio qneMnet, which is in turn approximately proportional to the zeta potential. Therefore, measurement of the electrophoretic mobility provides key information about the particle. In particular, since the zeta potential is approximately: g = -^\u2014 (2-39) Anecinet where eis the permittivity, combining with (2-38) yields the relationship: Ii = ^ (2-40) 377 which is felt to be valid even for the more complex case of low dielectric constant fluids. 3 6 As reported in detail in later chapters, this research program investigated electrophoresis as an appropriate control mechanism for frustrating TIR with pigment particles. Clearly, such a use of electrophoresis requires characterization of the colloidal properties. It is therefore helpful to briefly consider the various electrokinetic techniques used to characterize various particle parameters, as discussed in the next section. 2.4.3 Particle characterization There are many methods for characterizing various particle parameters, such as size and electrostatic charge. This section briefly describes two standard characterization methods that were implemented during the course of this research. Both analysis methods are typically performed using dedicated commercial instruments. One method employed in this work uses an electroacoustic method to measure electrophoretic mobility, in which a high frequency alternating electric field is applied across 32 a sample of the suspension and the particles move electrophoretically in response to the applied field. Provided a density difference exists between the particles and the suspension medium, this motion causes an alternating acoustic wave. Measurement of the electrokinetic sonic amplitude as a function of frequency, compared with a calibrating measurement of standard suspensions, yields a value of electrophoretic mobility.3 7 Under the proper conditions, reasonable values of the mobility can be achieved using this approach. However, in the absence of a properly calibrated standard, these measured values are considered to be unreliable and, for this reason, alternate methods will be used to obtain reasonable estimates of the mobility. A different method, known as dynamic light scattering, can be used to measure the particle size distribution. In this technique, two laser beams intersect and form interference fringes in a dilute sample of the suspension. As a particle moves through the fringes by diffusion, it scatters light with an intensity that fluctuates with a frequency distribution related to its diffusion rate. The scattered light is analyzed to give a frequency spectrum from which the particle mobility distribution is calculated. Since the particle mobility is related to the size of the particles, this can be translated into the particle size distribution.38 Both of these are effective methods for characterizing particles in aqueous solutions. However, as with other particle characterization methods, the interpretation for particles in a non-aqueous medium is more difficult. As a result, these measurements can only be considered rough estimates for particles in non-aqueous media. In this chapter, a number of principles relating to a new reflective image device technology have been discussed. In order to assess this technology in context, it will now be helpful to compare devices that are currently commercially available or under development. For this reason, these current technologies are described in the following section. 2.5 Current display technologies At the moment, there are a number of reflective image display technologies; some of these are commercially available while others are in the development stage. Each of these display technologies has different advantages and disadvantages, and it will probably be the case that 33 some will be better suited to some applications that others, and a diverse set of technologies will be required to fulfill all needs in this field. 2.5.1 Liquid crystal displays Liquid crystal displays (LCD's) are by far the most common reflective display. They use a thin layer of liquid crystal material to control the reflectance of a surface. Liquid crystals represent an unusual phase of matter since, unlike typical liquids with randomly oriented molecules, their molecules exhibit some degree of orientational alignment. In descriptions of the behaviour of these molecules, their preferred orientation direction is often represented by an arrow, called the director. Depending on the substance itself and the environmental conditions, a liquid crystal can take one of a number of phases, and a few of these will be briefly described here. Perhaps the most straightforward phase is the nematic liquid crystal phase, in which the molecules orient parallel to one another and the director points in a uniform direction across the sample. In a second phase, known as the chiral nematic liquid crystal phase, the director rotates through the sample, forming a helical pattern. (Substances forming this phase are often called cholesteric liquid crystals, since the most common examples of these materials are associated with cholesterol.) Smectic liquid crystals represent a third phase and these molecules are observed to have some degree of positional, as well as orientational, alignment, since they tend to arrange into distinct layers. For the purposes of this brief review, it is not necessary to provide a detailed discussion of the properties of these materials. However, it is important to note that in all of these phases, an anisotropy results from the preferred orientation of the molecules, particularly in terms of the interaction of light with these materials. In an image display device, a thin layer of liquid crystal material is typically contained in a gap between two glass plates. An electric field applied across the gap causes the permanent or induced dipoles in the liquid crystal molecules to orient with the dipole axis parallel to the field, and therefore the director will orient with respect to the field. Although the director is typically free to point in any direction in response to a field, there are a number of ways in which it can be controlled. Before the gap is filled with liquid crystal, the inner glass 34 surfaces can be prepared by a number of methods, for instance, rubbing with a cloth or applying a chemical film, to cause the director to align in a particular orientation. In this case, near the surface, the director is constrained and cannot respond to an applied electric field. Toward the center of the gap, however, the director can orient with respect to the field. This results in an induced deformation of the liquid crystal across the gap, which can substantially affect the way in which light interacts with the material, specifically in terms of the polarization of the light. For illustrative purposes, the discussion presented here will describe the interaction of polarized light with a nematic liquid crystal sample having a uniform director. Polarization is a characteristic of light that describes the direction of the electric and magnetic fields comprising the wave. For instance, linearly polarized light is a special case in which the electric field points in a single direction. The anisotropy of a nematic liquid crystal resulting from the orientational alignment causes light that is linearly polarized parallel to the director to propagate at a different velocity than light that is linearly polarized perpendicular to the director. As a result of the behaviour, it is useful to consider, for this discussion, that light is a combination of these two linear polarizations. These two polarization components travel through a slab of nematic liquid crystal material at two different velocities, and therefore emerge from the material with a phase difference that is proportional to the thickness of the material. Thus, the orientational alignment of a liquid crystal affects the change it imparts to the polarization of incident light, which is why they are so useful in image displays. Linearly polarized light can be produced by passing unpolarized light through a polarizing material that almost completely absorbs one polarization while allowing the other polarization to pass through fairly efficiently. If two such polarizing filters are layered with perpendicular polarization directions (in an arrangement known as crossed polarizers), very little light will pass through since the linearly polarized light emerging from the first polarizer will be absorbed by the second. The insertion of an isotropic material between the two polarizers will have no effect on the transmission of light since the polarization of the light is unchanged as it passes through such a material. A liquid crystal material inserted in this region, however, changes the polarization state such that some of the light will transmit 35 through the stack. The application of an electric field across the nematic crystal can deform the crystal structure to change this anisotropy. In this manner, the amount of light that passed through the stack can be controlled. In many display applications, a liquid crystal is used in which the director rotates about an axis in a helical fashion. This can be achieved, for instance, by fixing the directors on the glass surface, and therefore forcing the liquid crystal to twist along the direction perpendicular to the surfaces. The interaction of light with these twisted structures is analogous to that of the nematic crystal just described. However, in this case, it is more appropriate to characterize the light in terms of right- and left-circularly polarized components. The helical path followed by the director causes these two components to travel at different velocities through the material, and one possible result is that linearly polarized light can emerge, with a polarization axis that depends on the thickness of the sample. Again, this anisotropy can be controlled by further deforming the crystal structure by an applied electric field. Liquid crystals can be used in two primary types of image displays, namely transmissive and reflective. Transmissive displays are constructed by stacking the appropriate polarizing filters and liquid crystal material, and they glow because they incorporate a backlight to direct light through this liquid crystal panel toward the viewer. In the bright state, the molecules are oriented so that light passes through the panel. In the dark state, the light is absorbed, and the region looks dark. To generate each of these states, the anisotropy of the liquid crystal material is changed by the application of an applied electric field. The reflective configuration is similar, but includes a polarization-preserving rear reflector instead of a backlight. In this case, the bright state again allows polarized, ambient light to pass fairly efficiently through the layers, where it reflects from the rear reflector, and passes again through the panel to return to the viewer. In the dark state, the light is absorbed, creating a dark appearance. These passive displays rely on the ambient lighting conditions, rather than a backlight, for the image on the display to be visible. A full-colour image can be generated in both the reflective and transmissive display configurations, typically using the additive colour filtering approach described in Section 36 2.3.4.1. This approach uses a filter overlay, which divides each pixel into three subpixels of blue, green and red. The brightness of each subpixel is determined by the amount of light reflecting from (or passing through) the liquid crystal assembly in the region beneath each filter subpixel, so the contributions of each colour within an individual pixel is controlled, generating a complete gamut of colours. This additive technique means that with intensely coloured filters, the maximum reflectance is only one third of that of the equivalent monochrome display. In many reflective displays available in the market today, unsaturated colours are used to enhance the overall brightness at the expense of a reduced colour gamut. As mentioned above, transmissive liquid crystal displays yield bright, colourful images by illuminating the display with a high intensity backlight. This is a visually effective technique, but because of the substantial power consumption of the backlight, it is inappropriate for low power, battery-operated device applications. Reflective displays, on the other hand, can operate on low power since they reflect the ambient light, but the maximum reflectance of such displays is quite limited. In theory, a monochrome L C D display is at most 50% reflective since at least half of the ambient light must be absorbed by the polarizer. In practice, the maximum reflectance of a typical monochrome reflective display is only 34% , and this value drops to at most 16% for a full-colour reflective liquid crystal display.4 0 A powerful frontlight is sometimes used to illuminate this display surface for improved legibility, but again this drastically increases the power required to operate the device. The technique for achieving a full-colour reflective image device based on TIR, as described in this thesis, provides a number of possible advantages over current liquid crystal displays. The most important advantage is a four-fold improvement in the reflectance, which results from the elimination of the polarizer and the use of subtractive colour filtering. 2.5.2 Cholesteric liquid crystal displays A number of organizations are currently exploring the use of cholesteric liquid crystal materials to produce full-colour reflective images. 4 1 ' 4 2 ' 4 3 Displays based on this approach may have some advantages over conventional liquid crystal displays in terms of brightness, 37 viewability and power consumption. Given these potential advantages, it is worthwhile here to briefly describe their operation. As discussed briefly in the previous section, cholesteric or chiral nematic liquid crystals are capable of switching between two different alignment states. In particular, in one state they are capable of selectively reflecting incident light within a narrow wavelength band, since constructive interference occurs when the pitch of the helical structure, or the distance required for one complete rotation, is equal to the effective wavelength of the light in the material. (Constructive interference occurs when the material properties repeat themselves over a distance equal to half the wavelength of light. In this case, although the pitch is defined as the distance required for one complete rotation of the director, the helical structure repeats itself twice in each pitch cycle.) Wavelengths of light outside this band transmit through the material. As a result, panels containing a thin layer of a cholesteric liquid crystal can be used as a filter to reflect a desired colour and transmit the rest of the light in the visible band. These molecules can also be bistable, since once the desired state is achieved, it will remain fixed when the applied voltage is removed. Such bistability offers the potential of a very low power device since the voltage need not be constantly applied. Various configurations are used to generate reflective images using cholesteric liquid crystals. In perhaps the simplest example, three liquid crystal panels are stacked over a black absorbing background material. The liquid crystal material contained in each panel is chosen and tuned to reflect one of three specific wavelength bands, for instance, blue, green or red, and such reflected light is circularly polarized in one direction only. The combination of all three coloured filters, along with the black background, allows the eight standard colours to be generated, as discussed in terms of additive colour filtering in Section 2.3.4. The reflectance of the surface can be further increased by stacking an additional set of blue, green and red filters, reflecting light with the opposite circular polarization. In theory, this type of structure can yield a maximum reflectance of nearly 100% and achieve a reasonably large colour gamut. In practice, however, there are significant losses, costs, and resolution problems associated with such a stacked structure. Typically, the maximum reflectance of current prototypes is only 35%. 4 4 38 2.5.3 Electrophoretic image displays A number of previous research efforts have been aimed at developing an image display using electrophoresis of pigment particles, in a substantially different optical principle than the approach presented in this thesis. The previous approach used pigment particles suspended in an opaque liquid. In one state, the particles were moved against the viewing surface, hiding the liquid, and therefore giving the viewing surface the appearance of the colour of the particles. In the other state, the particles were moved away from the viewing surface, so that they were hidden from view so the surface would take on the appearance of the opaque l iquid . 4 5 ' 4 6 ' 4 7 ' 4 8 A number of organizations tried to commercialize displays based on this principle but were ultimately unsuccessful because of problems caused by particle migration. Such designs require the particles to move a substantial distance (typically greater than 100 um) away from the viewing surface so that they would be sufficiently hidden from view by the opaque fluid. It was observed that when such particles moved long distances in the fluid, they tended to cluster together after repeated cycling of the applied electric field, thus degrading the image quality.4 9 This particle clustering behaviour is described in further detail in Section 3.11. Recently, a technique has been established that makes the use of an electrophoretic suspension more practical in a display. 5 0 ' 5 ' ' 5 2 This method, known as micro-encapsulation, prevents particle migration by confining the suspension within a very small volume. The primary method of this new generation of electrophoretic image displays uses a suspension of particles in a coloured fluid, contained in polymeric microcapsules having a diameter of about 100 um. The basic operation is the same as that of a conventional electrophoretic image display, where the two states are generated either by moving the particles toward the front viewing surface of the capsule, or drawing them to the non-viewing side, thereby hiding them behind the opaque fluid. However, since the particles are confined within the microcapsules, they cannot drift over time to form the particle clusters. This is a fairly new technique, but current results indicate that this approach will substantially reduce and possibly eliminate particle migration problems. 39 The TIR-based approach presented in this thesis is a fundamentally different use of electrophoresis. Perhaps the most important difference is the maximum reflectance level. In the microcapsule approach, scattering of ambient light typically causes the reflection from white titanium dioxide particles that are moved toward the viewing surface. These particles scatter light approximately equally in all directions, resulting in a diffuse appearance. This is an advantage in terms of the viewing angle of the image, but it reduces the maximum reflectance of the surface. Prototype devices using this technique have demonstrated a maximum reflectance of at most 40%. 5 3 In contrast, the TIR approach has demonstrated a maximum reflectance of nearly 100%, although this is true only for a somewhat limited range of viewing angles. A second important distinction is the distance that the particles must travel in order to alter the reflectance state. Instead of moving about 100 (im, as mentioned above, in the TIR-based approach the particles need only move less than 1 itm to shift from outside to inside the evanescent wave zone. For particles having about the same electrophoretic mobility, this implies a substantially reduced transit time required for switching between the reflective and absorptive states. As will be explained in detail in Chapter 3, the encapsulation approach can also be used in a TIR-based reflective image device by taking advantage of the microstructured geometry of the reflective sheets. In comparison with some current reflective image display technologies, it is apparent that the technique based on total internal reflection has some possible advantages, particularly in terms of its potential to generate a bright, colourful image. Having briefly introduced the background information associated with this study, it is now appropriate to discuss this new optical system in more detail. 40 3 D E S I G N ISSUES IN A N O V E L TIR-BASED D I S P L A Y As described in the previous chapter, TIR can be frustrated by scattering or absorbing the electromagnetic energy in the evanescent wave. Presented in this chapter are the key conceptual issues that were identified in the initial feasibility research regarding a possible TIR-based reflective image device. 3.1 Principle of a TIR-based reflective display The principle of reflectance modulation using frustrated TIR can be demonstrated using a simple device, shown in Figure 3-1, based on the linear prismatic structure depicted in Figure 2-6. In this device, a polycarbonate microstructured sheet, with refractive index of \u00abi = 1.59, is separated by a thin air gap, with refractive index ri2=l.O, from a black absorber. In the reflective state, a light ray, shown in the left-hand portion of Figure 3-1, enters the prismatic sheet at normal incidence, undergoes TIR at each prismatic facet and exits the sheet at 180\u00b0 to the incident ray. By moving the absorptive material into optical contact with the prismatic rear surface of the sheet, as shown in the right-hand portion of Figure 3-1, the majority of the incident light is absorbed at the first prismatic facet, and any light reflecting from this surface is further absorbed at the second facet, resulting in almost complete absorption of the light and elimination of reflection. Removing the absorber from the surface to create the thin air gap completely restores the reflection, thus allowing control of reflectance. Clearly, an absorber that can conform in some manner to the microstructured surface will most effectively frustrate the TIR. 5 4 ' 5 5 This optical switching technique has three novel features, which will be discussed in detail in later sections. First, the prismatic geometry of the microstructured sheet redirects a substantial fraction of the ambient light in a typical luminous environment, resulting in a highly reflective surface. Second, since the evanescent zone is microscopically thin, only a very small movement of the absorber is required to switch between the highly reflective and highly absorptive states. Third, the prismatic geometry allows a unique approach to subtractive colour filtering to yield a full-colour image. As a result, this display has a large 41 reflectance difference and has the potential to be switched quickly with a small amount of energy per unit area. Figure 3-1. Principle of a TIR-based reflective image device There are a number of possible methods for actuating this type of reflective image device. In one approach, an array of tiny, individually controlled micro-mechanical elements could move the absorber into and out of optical contact with the TIR surface. However, such micro-mechanical approaches are currently very expensive, and are not likely to be practical for use in the near future in an image display, especially for high-resolution images. Another method uses an array of pneumatic valves to force, by means of air pressure, specific regions of an elastomeric bladder into surface contact.56 In these regions, the elastomer will conform to the microstructure to frustrate TIR. This method is also impractical because the pneumatic control requires an air compressor, and it is limited to rather low-resolution displays. A more promising actuation method would use electrostatic force, caused by an applied electric field, to controllably move the absorber into contact. Since the electric field can be applied to selected regions of the display by standard microelectronics methods, the resolution of the resulting image can be very high. There are several absorbing materials that can be moved into contact with the TIR surface under electrostatic force, and some of these methods can operate at sufficiently low voltage to make them practical for a small, battery-operated device. This will be discussed in further detail in Section 3.5, but first it will be helpful to consider in more detail certain material constraints for TIR. microprismatic sheet (n,=1.59) air gap (n2=l) absorptive material 42 3.2 Index mismatch requirements As follows from its definition in (2-8), the critical angle decreases as the ratio of njm increases. As a result, a large index mismatch between the prismatic material and the medium at the interface means that a large angular range of light rays will exceed the critical angle and undergo TIR. Therefore, to achieve reflection for the largest possible fraction of the incident flux, it is desirable to maximize the ratio of n\\lni for a reflective display. Figure 3-2 demonstrates schematically that the fraction of incident light rays that undergo TIR depends on the refractive index ratio. Figure 3-2(a) shows that for a relatively low ratio of 1.05, the critical angle is quite high so that only the rays at glancing incidence are reflected. A much larger ratio of 2.00, as shown in Figure 3-2(b), causes many of the incident rays to be reflected. A ratio equal to 1.59, as illustrated in Figure 3-1, is achieved with a polycarbonate\/air interface, and it works quite well for a reflective image device. (a) (b) Figure 3-2. Light rays at an interface with index ratio of (a) 1.05 and (b) 2.00 Clearly, a significant refractive index ratio at the interface is an important feature of a reflective image device based on TIR. As will be discussed at length in Section 3.6, this ratio can be effectively enhanced by taking advantage of a unique optical property of the linear prismatic structures used throughout this study. In the meantime, it is important to consider certain mechanical issues concerning the contact with the absorber, particularly in terms of the surface energies involved. 3.3 Surface energy considerations In the reflectance device described schematically in Figure 3-1, TIR occurs in a polycarbonate sheet having index \u00abi=1.59, and is frustrated by a conformable absorber 43 moving in air. Although this system works quite well optically, there are undesirable surface energy effects associated with the motion. This section describes this complication in terms of the energy required to initiate and eliminate optical contact in order to estimate the power per unit area required to drive the device. It is useful to consider a typical numerical example. Consider a lxlO\" 6 m thick sheet of conformable absorbing material, such as a carbon-loaded silicone elastomer, oscillating with an amplitude of lxlO\" 6 m so that it moves substantially into and out of the evanescent wave at a frequency of 30 Hz. A sample of this membrane,' with a typical density of about l x l O 3 kgm\"3, has a mass per unit area of 10\"3 kgm\"2, a maximum speed of 1.9xl0\"4 ms\"1, and therefore a maximum kinetic energy per unit area of 1.5x10\"\" Jm\"2. Since this energy must be imparted twice per cycle, this represents a mechanical power requirement of about 10\"9 Wm\" 2 Clearly, this movement can be created with a very small amount of power. Unfortunately, the energy per unit area associated with the physical contact between the membrane and the surface at which TIR occurs is typically greater than 10\"2 Jm\"2, nine orders of magnitude greater than the mechanical energy associated with the oscillation!5 7 Clearly, in a practical device based on frustrated TIR, the absorbing material should not make physical contact with the interface since it requires too much energy to remove it. For this reason, in the course of this study, the use of liquid as the second medium was investigated as a method of effectively lubricating the TIR surface to prevent direct physical contact by the absorbing material. This is best considered in terms of the surface energies at the interfaces. These are O L A , the surface energy of the interface between the liquid and the absorber, OLs, the surface energy between the liquid and the TIR surface, and <7As, the surface energy between the absorber and the TIR surface. If the surface energy of the absorber-TIR surface interface is greater than the sum of the liquid-absorber and liquid-TIR interfaces, in other words, OAS \\>\\<7u + OLS (3-1) 44 the liquid will spread in a thin layer between the two materials. This means that, in such a case, it is energetically favourable for a very thin layer of liquid to remain between the solid surfaces rather than for the liquid to entirely flow out so the two solids make direct contact. This results in the reduction or even elimination of adhesion between the absorber and the TIR surface, and greatly reduces the energy required to drive the device. It has long been recognized that a liquid lubricant can reduce or eliminate problems associated with friction or sticking between solid parts, however this research, we believe, represents the first time this solution has been applied to facilitate the controlled frustration of TIR by a solid absorbing material. In summary, surface energy considerations make a solid-liquid interface very desirable for a controlled TIR device. However, the presence of the liquid substantially changes the optical properties at the interface, and these new optical requirements must be taken into account to ensure that TIR can still happen. This issue is the subject of the following section. 3.4 Optical requirements for TIR at a solid-liquid interface TIR is more difficult to achieve at a solid-liquid interface because the index of refraction of a typical liquid is much greater than that of air, and thus the refractive index ratio is substantially lowered. To maintain the required ratio, the index of the micro-prismatic material could be increased. However, while progress is being made in the area of micro-replication of high index materials, it is not possible at the present time to obtain optically precise, high index microstructures. For good optical quality microstructures, the maximum refractive index is currently limited to that of polycarbonate, at \u00abi=1.59. As an alternate solution, a search was carried out for low-index fluids that are compatible with electronic device requirements. Most such liquids have an index of greater than 1.4 and are therefore unsuitable for use in a high reflectance TIR device. Eventually, perfluorinated hydrocarbon liquids were identified as a promising candidate because they have a very low index of refraction of 1.276, high optical transmission (the coefficient of absorption is substantially less than 1 m\"1), and very good electrical properties (the typical dielectric constant is less than 2, and dielectric strength greater than 107 Vm\"1). Table 3-1 compares the 45 critical angle for a few liquids in contact with a polycarbonate surface. Clearly, the perfluorinated hydrocarbon liquid provides a substantial reduction in index over oil and water. However, the index ratio is still limited to about 1.25. As will be addressed in the next section, the index ratio enhancement feature described in Section 2.2.2 can be employed to make this a practical system. Liquid \u00ab 2 ni\/n2 0c Hydrocarbon oil 1.5 1.06 70.6\u00b0 Water 1.33 1.19 57.2\u00b0 Perfluorinated hydrocarbons 1.276 1.25 53.4\u00b0 Table 3-1. Critical angles at typical liquid\/polycarbonate interfaces Perfluorinated hydrocarbon liquids are composed of hydrocarbon chains in which the hydrogen atoms along the chain have been replaced by fluorine atoms. Fluorine atoms are highly electronegative, light and small (although larger than hydrogen atoms) and they can normally replace any hydrogen atom in a linear or cyclical organic molecule, forming a very short, strong carbon-fluorine bond. The strength of this bond makes perfluorinated hydrocarbons very stable, inert and resistant to breakdown against a wide variety of chemicals and temperature ranges. These liquids tend to have low refractive index as a result of the strong bonds, since the electronic orbitals cannot shift as easily in response to the field, thereby lowering the polarizability of the fluid and hence the index. Of particular interest in this thesis is a family of perfluorinated hydrocarbon liquids sold under the tradename Fluorinert\u2122, a product of the 3M Company. One of these commercially available fluids, FC-75 5 8 has the molecular formula CaF^O and is particularly well suited to this application. A detailed list of the physical and electrical properties of Fluorinert\u2122 FC-75 is provided in Appendix C. The following section describes how these unique low index liquids can be used with polycarbonate microstructures in the development of a practical device. 46 3.5 Possible absorbers used to frustrate TIR A number of possible absorbers were evaluated for frustrating TIR in a liquid medium. One candidate was a porous or channeled elastomeric structure that would conform to the surface (while being lubricated by the perfluorinated hydrocarbon liquid) and would absorb the electromagnetic energy in the evanescent zone. This material would have to be porous or channeled to allow displaced fluid to escape as the absorber moved toward the TIR interface. Such a material could be made by casting a layer of carbon-loaded silicone elastomer with an array of holes in it to allow the fluid to pass through or a series of channels on the surface to conduct the fluid into a reservoir. n 1 = l . 5 9 solid n2=\\21 liquid conformable, porous absorber (a) ( b ) Figure 3-3. Frustration of TIR by a conformable absorber A related approach would use a very thin, flexible porous membrane. In this case, the material composing the membrane need not be highly conformable since the flexible membrane itself could bend in order maintain optical contact along the surface, even in the presence of possible dust particles or small surface variations. This type of membrane could be made from a very thin polymer film, such as polyester sheeting, coated with an absorbing film. Alternately, a thin layer of metal could be vapour deposited onto a substrate that is later dissolved. In either case, this may only be practical for optical configurations where TIR occurs on a flat, not prismatic, interface. 4 7 n=1.27 liquid (a) (b) flexible membrane Figure 3-4. Frustration of T I R by a flexible membrane Both of these approaches seemed prohibitively challenging and were not selected for further analysis at this stage. Currently, the most promising absorption mechanism, and a primary focus of the research reported in this thesis, uses the electrophoresis of charged pigment particles to frustrate the TIR. As will be described in more detail in Section 3.7, pigment particles were suspended in perfluorinated hydrocarbon liquid, and the suspension was contained in a chamber at the rear of the device. In such a system, an electric field applied between transparent conductors on either side of the chamber moved the pigments, by electrophoresis, toward and away from the TIR interface. Although the pigment particles themselves were not highly conformable, they were sufficiently small that a layer of them coated the surface well. Having identified this method for frustrating TIR at a solid-liquid interface, it is now necessary to discuss in more detail the approach for enhancing the effective index ratio to ensure that TIR occurs. 3.6 Enhancing index ratio with crossed prismatic sheet geometry Consideration of the three-dimensional refractive index ratio enhancement effect described in Section 2.2.2 led to the discovery that it is possible to employ TIR at a liquid interface using conventional polycarbonate microstructured materials.59 For example, Figure 3-5 shows an arrangement developed in this investigation that uses two layers of prismatic sheet, each having translational symmetry, in which the prism layers are oriented with their symmetry 48 axis mutually perpendicular. This layered prismatic geometry, and others, are described more fully in Chapter 7. It is introduced briefly here to illustrate the index enhancement effect that is key to the design of a liquid-based TIR image device. Figure 3-6 shows the ray path, in cross-sectional views, through this layered structure. As depicted in Figure 3-6(a), the top layer of micro-prisms is used to deflect incoming light rays. This deflection causes an initially normal incidence ray to propagate with a substantial component in the direction of translational symmetry of the bottom prism surface, producing an effective enhancement of the index ratio, as described in Section 2.2.2. The deflected light therefore undergoes TIR twice in the bottom prismatic layer, as in Figure 3-6(b), and returns to the top prism sheet, where the initial deflection is \"cancelled\" and the original incident angle is restored. This works for both of the deflection directions caused by the facets of the top layer, so most of the light leaves the structure traveling outward in the normal direction. There are many optical configurations using this crossed-prismatic sheet approach, each having different characteristics and advantages, and several of these are discussed in Chapter 7. Figure 3-5. One optical arrangement for a liquid-based frustrated TIR device liquid medium top prismatic sheet bottom prismatic sheet 49 incident ray reflected ray (a) (b) Figure 3-6. Path followed by a ray through optical arrangement This layered prismatic approach is a novel application of the effective index ratio enhancement and it allows conventional micro-replicated surfaces to be used with perfluorinated hydrocarbon liquid to prevent adhesion of the absorber. Based on this concept, it is helpful to consider in more detail, in the following section, how pigments suspended in perfluorinated hydrocarbon liquid can be used to frustrate TIR. 3.7 Pigments suspensions in low refractive index fluid For ideal frustration of TIR using this method of electrophoresis, the absorptive particles must be optically small so that they do not scatter much of the light, and have a sufficiently large imaginary refractive index component that most of the light encountering these particles is absorbed. For the particles to be \"optically small\", and therefore essentially non-scattering, the product of the effective diameter of the particle, D, and the difference in refractive index values between the particle and its surroundings, An, must be substantially less than the wavelength of the light.6 1 DAn \u00ab X (3-2) As an illustration, a typical particle diameter in these experiments is 0.25 (im and the refractive index difference of 0.5 yields a product DAn of 0.125 lim, which is substantially less than A for the visible range of wavelengths of 0.4 to 0.7 (im. 50 As will be discussed later in this section, the required value of the imaginary refractive index component depends on the effective path as the light interacts with a layer of particles at the interface. If the effective path length is quite short, the particles must be highly absorptive in order to adequately frustrate the TIR. For longer path lengths, less absorptive particles are equally effective in frustrating TIR since the light interacts with a greater number of particles. An additional requirement is that the particles must have a sufficiently high electrostatic surface charge, and hence electrophoretic mobility, so that they respond quickly to an electric field of magnitude that is practical in a display device. This requirement depends on the application, but for illustrative purposes it is helpful to consider the approximate value required in a typical reflective image device, in which the applied electric field magnitude is about 105 Vm\" 1 . In such a case, if the desired switching frequency is about 10 Hz, the particles must move about 1 um, into the evanescent wave region in 0.1s. This corresponds to an electrophoretic mobility of lx lO\" 1 0 m2V\"'s\"', and a net surface charge, calculated using the relations described in Section 2.4, of 6.6xl0\"1 9 C. In the course of this research, two different suspension formulations were studied. 6 2 ' 6 3 ' 6 4 In the first, the suspensions were composed of dyed latex particles, which had been formulated by combining a solution containing the monomer with the required catalyst. The resulting polymer molecules took the form of a roughly spherical particle, of average diameter about 600 nm, with the real component of the refractive index equal to about 1.6. At our request, various dyes were added and attached to the exposed receptor sites on the particle surface. A polymer dispersant material was also included which adsorbed onto the surface of the latex core to form a swollen polymer shell.. Since these polymer chains have an affinity for both the adsorbed polymer layer and the perfluorinated hydrocarbon liquid, they provided the steric stabilization required to maintain a stable suspension, as described in Section 2.4. These latex suspensions were tested using techniques described in detail in Chapter 4, and they did exhibit a small level of frustration of TIR, at most about 10%. This degree of absorption was insufficient from a practical point of view, so a second formulation, which employed a suspension of intensely coloured pigment particles and a liquid dispersant material was investigated.65 5 1 The results presented in this thesis were obtained using four of these pigment suspensions, each containing a single colour of pigment, as listed in Table 3-2. The suspension made using carbon black particles was particularly useful in analyzing various aspects of the system since the absorption spectrum for these particles is essentially uniform over the visible band. The cyan, magenta and yellow pigments were used to cause, for the first time, spectrally selective controlled frustration of TIR. Table 3-2 lists the specific pigments used in each of these suspensions. Pigment colour Product name Supplier Black Raven Black 1200 Columbian Chemicals Cyan SpectraPak Blue Sun Chemicals Magenta Cinquasia Magenta CD3A Specialty Chemicals Yellow SpectraPak Yellow Sun Chemicals Table 3-2. Pigments suspended in perfluorinated hydrocarbon liquid After formulation, the particle concentration and mean diameter were measured. The concentration was determined simply by evaporating the solvent from a known volume of prepared suspension and weighing the resulting solid content. The amount of solid content differs among the samples, but this does not affect the results of the experiments presented in this study as each sample was diluted to a known concentration prior to testing. The mean particle diameter was measured using the dynamic light scattering method discussed in Section 2.4.3, using a Coulter Model N4 Plus analyzer.66 These results are presented in Table 3-3. Pigment Concentration Mean diameter colour (g\/lOOml) (nm) Black 5.25 118 Cyan 5.46 120 Magenta 2.84 310 Yellow 5.36 440 Table 3-3. Particle concentration and mean diameter As well, the average electrophoretic mobility of the particles was estimated by observing the motion of charged pigment particles, over a reasonably long distance, under the influence of an electric field. To perform this experiment, a test cell was prepared, comprised of two 52 glass microscope slides, between which two 2 mm wide strips of thin (50 um) brass were pressed, to be used as electrodes. The strips were separated by 20 mm, forming a cavity into which the suspension sample was injected, as sketched in Figure 3-7. Figure 3-7. Electrophoretic mobility measurement set-up When an electrical potential was applied between the two electrodes, the resulting electric field caused the pigment particles to migrate toward one electrode or the other, depending on the sign of their electrostatic charge, and the speed with which they moved depended on the electrophoretic mobility. Since the particles are intensely coloured, a distinct line was visible between the particles and the fluid and the speed was readily measured, enabling calculation of the average electrophoretic mobility. This method of visual mobility measurement assumes that the electrophoretic pigment particles move at a constant velocity in response to the electric field to which they are subjected within the fluid gap. Although it will not be discussed in detail, it should be noted that the field experienced by the particles is not simply the field applied by the electrodes; rather, the local field experienced by one charged particle is altered by the presence of neighbouring charged particles and their counterions. In addition to the electrostatic forces, each particle is subjected to hydrodynamic forces from interactions with neighbouring particles and diffusion. As a result, the electrophoretic mobility calculated from this simple visual measurement is certainly not exact, but it provides a reasonable estimate of the value. The average mobility of the particles in these sample suspensions was estimated by this technique to be 1.6xl0\"10 mV 's\" 1. particle liquid 53 Figure 3-8 shows scanning electron micrograph (SEM) images of two different samples of (a) carbon black and (b) magenta pigments. Figure 3-8. S E M images of (a) carbon black and (b) magenta pigment particles Fortunately, it was found that these formulations had a much greater ability to modulate the reflectance of a surface than the latex particles. Since the product of the particle size and the refractive index difference between the particle and surrounding medium is substantially less than a wavelength, the particles do not scatter very much.6 7 As will be described in detail in Chapter 6, it seems that the key improvement in the pigment suspension over the dyed latex lies in the higher refractive index of the pigment particles, which enhances the effective path length. This effect is described briefly in the next section. 3.8 Frustration of TIR using pigment suspensions In order to minimize the reflectance in the absorptive state of the system, it is important to develop a particle suspension capable of absorbing most of the incident light. This requires an understanding of the interaction between the light rays and the particles near the TIR interface. In this regard, a simple consideration of the frustration of TIR would suggest that maximum absorption would occur using very highly absorptive particles and that the degree of absorption would be completely determined by the number of particles occupying the region defined by the evanescent wave zone. In other words, the level of absorption should be proportional to the penetration depth of the evanescent wave (since this depth would (a) (b) 5 4 determine the number of absorbing particles that could occupy the region). This idea is depicted schematically in Figure 3-9, where in (a) a single layer of particles causes some absorption, but in (b) multiple particle layers filling the evanescent wave zone causes complete absorption. evanescent wave zone particles liquid (a) (b) Figure 3-9. Schematic representation of evanescent wave zone As explained in Section 2.1.3, the evanescent wave depth decreases with the incident angle, but this effect is only observable very close to the critical angle. Even though a substantially collimated detector is used in this study, such angular variations were below its collimation capacity. So, in the measurements described here, the evanescent wave depth is essentially independent of angle, and the observed absorption should therefore also be independent of angle. As well, since the penetration depth does depend directly on the wavelength of the incident light, so should the degree of absorption. While this represented a plausible initial theory, the experimental results presented in Chapter 5 have demonstrated that it is insufficient to explain the absorption behaviour of the particles. As a result, an alternate theory, based on density gradients of small, high index, moderately absorbing particles near the interface, has been developed. Since these particles have a substantially higher index of refraction than the surrounding fluid, the particle density gradient produces a gradient of the effective refractive index of the suspension in this region. When the incident light encounters this index gradient, it follows a different ray path than it would in the absence of the particles, since the refractive index near the surface has been substantially modified. This is discussed in detail in Chapter 6, where reflectance predictions resulting from this theory are shown to be consistent with the experimental results. 55 The next section describes how the pigment suspensions are incorporated into a TIR-based reflective image display. 3.9 Electrophoretic suspensions in a TIR-based device The simplest way to incorporate the pigment suspension is shown in Figure 3-10, in which the prismatic sheet and a rear flat substrate define a chamber that houses the suspension of pigment particles. 6 8 ' 6 9 ' 7 0 The prism facets and the rear substrate were each coated with a thin, (typically 100 nm) layer of transparent conductor, usually indium tin oxide (ITO), such that it makes direct contact with the electrophoretic suspension. (The conductor on the rear surface need not be transparent, since the light does not reach this layer, but ITO was usually used on this surface to simplify the overall system chemistry.) - V ITO coated prisms n liquid medium pigment particles V l T 0 c o a t e d (a) (b) Figure 3-10. Design of an FTIR device actuated by electrophoresis Application of an electrical potential difference between the two conductive surfaces generates an electric field throughout the liquid chamber. The pigment particles, which have an effective diameter of about 0.25 urn and an electrophoretic mobility of approximately 10\"10 m V\" s\" , would then move in response to the field. Depending on the applied polarity, the particles would either move away from the prismatic surface, as shown in Figure 3-10(a). in which case the incident light would be reflected by TIR, or they would move into optical contact with the prismatic surface to frustrate TIR, as depicted in Figure 3-10(b). The rear electrode is segmented between adjacent channels so that the pigments within each channel can be independently controlled. If the electrode were further segmented along the 56 length of the channel, the absorption of light within particular regions could be controlled to form a desired image in a pixelated fashion. For the purpose of discussion in the next few sections, some terminology to describe the important regions of the device is introduced in Figure 3-11. As is clear from Figure 3-11(a), each prismatic electrophoretic channel is bordered by two neighbouring micro-prism reflective structures. Thus, when one electrophoretic channel is actuated by pulling the particles into the evanescent wave, as shown in Figure 3-11(b), it causes light to be absorbed in each of the two adjacent reflective structures. These reflective structures together form the absorption zone associated with that channel. reflective structure f\\ (a) (f -electrophoretic channel absorption zone < > )) Figure 3-11. Selective absorption by electrophoretic channels As detailed in Section 3.10, it is possible to achieve reflectance values intermediate between the completely reflective and completely absorptive states. This so-called grey scale behaviour is required for a practical device. 57 3.10 Grey-scale control of reflectance Section 2.3 discussed the ability to achieve a complete gamut of colours by varying the relative amount of three primary colours. In terms of a TIR-based reflective image device, this requires the ability to yield not only full reflectance and absorption states, but also the continuous range of reflectance values intermediate between these two extremes. This is known as grey scale control. The continuous range of reflectance values is important both for full colour and monochrome devices. There are at least two methods by which grey scale control could be achieved using frustrated TIR. Both methods rely on the fact that the amount of absorption caused by the pigment particles depends on the degree of interaction between the evanescent energy and the particles. The first method, known as time dithering, would be appropriate in a system where the particles could be moved very quickly in and out of the evanescent wave region. These very mobile particles would be subjected to a reasonably high frequency (about 100 Hz) applied field so that they were oscillated in and out of the evanescent zone. By varying the amplitude and\/or the duty cycle of the field, the fraction of one cycle that the particles would spend in the evanescent zone, thus causing absorption, could be controlled. A second approach requires a particle system where the degree to which a particle penetrates into the evanescent wave zone depends, in a continuous manner, on the strength of the applied field. A system might exhibit this behaviour if the particles or the TIR surface were, for example, coated with an optically thick layer of a polymer material with a spring-like characteristic. In this case, in an applied field of a given strength, the particle would exert a force on this spring-like layer until it reached a position where the magnitude of the spring force equaled that of the applied force and would remain there as long as that field strength was applied. If the field was increased, the particle would move further into the evanescent zone until the forces again balanced and it settled into its new position. As a result, the level of absorption could quite accurately be controlled in such a system. The particle system tested in Chapter 5 showed a similar field-dependent behaviour, but for a somewhat different reason. This will be discussed in detail in Section 5.5.1. 58 3.11 Prevention of particle clustering by encapsulation It has been observed by numerous researchers that particles in suspension under repeated cycles of applied electric field tend to congregate into loose clusters, leaving areas of high particle concentration amidst regions of almost pure solvent.71 In preliminary tests during the course of this study, the same behaviour was encountered in the perfluorinated hydrocarbon suspensions. Particle clusters are formed by the fluid motion within the cell. These clusters consist of loosely bound particles that can be readily redispersed. The tendency for clusters to form depends on the voltage and frequency of the applied waveform, and redispersion can generally be accomplished by varying the operating voltage or frequency. The size and pattern of the pigment clusters depends on the suspension composition, cell geometry, and switching operation. In sample cells constructed and tested during the course of this study, these particle clusters often formed. In these sample cells, a particle suspension was housed between two parallel glass microscopes slide, coated on the inner surface with a layer of transparent conductor such as indium tin oxide (ITO), forming electrodes on either side of the fluid chamber. A time-varying voltage was applied across the electrodes, and the suspended particles repeatedly responded by electrophoretically moving back and forth across the cell. Initially, the particles would be uniformly dispersed in the suspension, so there was no visible non-uniformity on the surface of the sample cell. When the voltage was applied, the particle clusters would begin to form, and evolve as the switching continued. A C C D camera was positioned about 0.1 m above the cell and the images of the particle clusters were captured. The images captured for one typical sample cell are shown in Figure 3-12. In this case, white latex particles suspended in perfluorinated hydrocarbon liquid were enclosed in a 60 um thick cell, and switched by a 25 V, 0.25 Hz square waveform. 59 (c) (d) Figure 3-12. Particle clusters formed after (a) Os, (b) 10s, (c) 40s and (d) 180s This is a complex problem, thought to result from fluid disturbances in the vicinity of the moving particles during their transit across the cell. Fluid turbulence, as a result of particle motion, is thought to lead to pigment clusters, the size and pattern of which are related to the amount of charge in the suspension.72'73 Although the details of this phenomenon have been intensely studied by numerous groups, they are not well understood. However, it is widely agreed that such clustering behaviour can cause serious performance degradation and should be avoided as much as possible. It has since been established that clustering problems can be substantially avoided by encapsulating small volumes of the suspension and thereby restricting the migration of the particles, as mentioned in Section 2.5.2.74 This idea can be incorporated in the TIR-based device by minimizing the separation distance between the peaks of the micro-prisms and the flat rear substrate. In Figure 3-10, for example, the prism tips are shown attached to the 60 substrate, thus completely preventing the fluid contained in one resulting prismatic channel from flowing into neighbouring channels. This achieves encapsulation in one dimension and additional encapsulation along the prism channels could also be achieved by a variety of polymer micro-replication techniques. Although actual TIR-based reflective image devices must incorporate micro-prismatic structures, a simpler system was designed for measuring the absorption characteristics of the electrophoretic particles. For this purpose, test cells were made from a simple arrangement of glass microscope slides, thus avoiding any complicated optical effects arising from interactions with the microstructured surfaces. However, throughout the course of this research, it was advantageous to avoid particle clustering to minimize non-uniformity in the reflectance of the surface and, for practical purposes, to extend the useful lifetime of each cell. This was done by enclosing the suspension within a region between one flat surface and one microstructured surface that restricts particle motion. This will be explained in greater detail in Section 4.1. This resulted in a reasonably uniform surface reflectance, even after repeated cycling of the particles. Experiments performed with these sample cells demonstrated that a hermetic seal between adjacent fluid micro-volumes is not necessary to substantially restrict the particle motion. However, as will be addressed in the following section, there are other practical reasons why a hermetic seal may be desirable. 3.12 Subtractive colour filtering in a full-colour image display A second goal of this research program was to extend the concept of a reflective image device employing frustrated TIR to the creation of full colour. This section describes a new subtractive colour filtering approach that was devised to achieve this goal. In this approach, the spectral reflectance properties of the pigments cause them to behave as spectrally selective filters. Thus, using pigments with appropriate subtractive colour absorption characteristics, the colour of the reflected light can be controlled. This section outlines the use of subtractive colour filtering in a TIR-based reflectance device, describes a configuration of a full-colour device, and explains its operation. 61 3.12.1 Subtractive colour filtering in an FTIR image display As discussed in Section 2.3.4, the available colour gamut is determined by the spectral absorption characteristics of a set of cyan, magenta and yellow filters, and any colour within this gamut can be achieved by suitably absorbing white light using these three filters. Ideally, in a full colour display based on TIR, each reflective structure would incorporate one controllable filter for each of the three subtractive colours so that all three filters could be individually controlled on each reflective structure. One potential method of accomplishing this would use reflective structures having three facets, such as the so-called \"corner-cube\" geometry in which the three reflective facets are mutually perpendicular. In this arrangement, the absorption of light could be controlled using a different subtractive colour filter on each of the three facets. Unfortunately, at present there is no practical way to fabricate such a device. Section 3.12.2 describes an alternative method for subtractively generating full-colour images using the more feasible linear geometry that was depicted in Figure 3-11. 7 5 , 7 6 3.12.2 Construction of a full-colour FTIR image display The construction geometry that was devised to generate full-colour images bears considerable similarity to that previously presented in the monochrome version discussed in Section 3.9. In the new full colour embodiment, the sealed prismatic channels are alternately (and cyclically) filled with cyan, magenta and yellow pigment suspensions, labeled in Figure 3-13 as c, m and y. A printed, striped filter layer covers the top of each reflective structure; the coloured filter stripes in Figure 3-13 are labeled by C, M and Y corresponding to their colour. The stripe colours are assigned such that the complementary colour stripe is positioned over each reflective structure. In other words, filter Y is adjacent to channels m and c, M to channels c and y, and C to channels y and m. Thus, each reflective structure has the ability to absorb each of the three primary colours red, green and blue. In each structure, one of these bands is always absorbed but the other two can be selectively absorbed in order to yield a desired net colour. 62 cyan filter magenta filter yellow filter cyan particles magenta particles yellow particles Figure 3-13. Schematic of a full-colour TIR-based reflective image device Each filter, whether permanent or controllable, can be described in terms of its spectral transmittance function. In this discussion, C ( A ) , A f ( A ) and Y(X) w i l l be used to denote the spectral transmittance functions of the permanent filter regions C , M and Y. Similarly, c ( A ) , m( A ) and y ( A ) denote the effective spectral transmittance functions of the electrophoretic particle systems contained in channels c, m and y. Ideally, the spectral characteristics of the permanent filter w i l l be similar to those of the electrophoretic pigments, so that C ( A ) = c ( A ) , M ( A ) = m ( A ) and Y(A) = y ( A ) . It is important to note that although the design of a full-colour TIR-based reflective image device has been presented here, the actual fabrication of such a structure would be a great feat of micro-fabrication that would require substantial investment. The complexity and expense involved in such an endeavour is not unreasonable in terms of current liquid crystal display manufacturing practices. (For instance, the investment required to develop and manufacture the driving circuitry alone in a typical laptop computer display is astounding, since each individual pixel is modulated by a thin film transistor printed on the active matrix backplane.) However, this level of effort and expense is undoubtedly outside the scope of this thesis. The purpose of this work was to establish the feasibility of the individual components of the system, in order to evaluate the practicality of this technique in the development of a real display. To accomplish this, currently available, but imperfect, micro-prismatic films, as well as experimental pigment suspensions were evaluated as a practical method for controlling TIR in the micro-prisms. Given the required investment, it is not possible to 63 analyze a fully assembled colour reflective image device as presented in this section. However, as will be discussed in later chapters, the results in this thesis demonstrate that this is a valid approach, and presents an opportunity for further study in a wide range of areas. 3.12.3 Operation of device Consider the situation depicted in Figure 3-14, generating the net colour red. In this case, the magenta and yellow pigments are actuated, but the cyan pigments are not. For simplification, the intensity of light in each of the three different wavelength bands, red, green and blue, is represented by the presence or absence of a single correspondingly coloured light ray. Of course, as mentioned previously, intermediate values would also be used in a real device to produce non-saturated colours. An examination of the leftmost reflective structure (beneath filter Y) shows that the blue ray is absorbed by yellow filter Y and the red and green rays pass through the filter. The green ray is then absorbed by the magenta particles in contact with the prismatic facet. However, since the absorption in the red band is negligible for the magenta pigment, the red ray undergoes TIR at this facet and travels toward the second facet, where it again reflects and exits through the yellow filter. As a result, the region defined by this reflective structure will appear red. In terms of the spectral transmittance functions, the net spectral reflectance, P Y ( A ) , of the region can be written as the product of the two spectral transmittance functions of the filters, or pY(X)=Y(X)m(X) (3-3) Similarly in the centermost reflective structure, magenta filter M passes the red and blue rays but absorbs the green. Both red and blue rays reflect at the first facet and travel toward the second facet, where the blue ray is absorbed by the actuated yellow pigment particles in electrophoretic channel y. Again, only the red ray exits this reflective structure, and the region will appear red. The net spectral reflectance of this region can be written as: pM{X) = M{X)y{X) (3-4) 64 Finally, in the rightmost reflective structure, the red ray is absorbed by cyan filter C, and the blue and green rays are absorbed by the actuated particles in electrophoretic channels y and m. Since all the light rays are absorbed in this reflective structure, this region will appear near-black, and the spectral reflectance function can be written as: p c ( A ) = C ( A ) y ( A ) n ( A ) (3-5) Recalling that the reflective units have a centre-to-centre separation of only 50 to 100 um, these individual differently coloured bands would be unresolvable by the viewer, so the colours would appear blended together as a net resultant colour. This resulting colour can be specified by calculating the average spectral reflectance function, pa Verage(A): paverage(?i) = -^(PY pM pC(A)) (3-6) The chromaticity coordinates and surface reflectance can be calculated accordingly, using the standard method outlined in Section 2.3.2. In this particular example, the net result is that essentially all of the blue and green light is absorbed and two thirds of the red light is reflected, yielding a net red reflectance which is 67% of that of a pure red reflector. red ray green ray ~ blue ray cyan filter magenta filter yellow filter cyan particles magenta particles yellow particles Figure 3-14. Actuation of an FTIR device, demonstrating a net red colour 65 Similar arguments can be used to show how a net yellow colour is displayed on the surface. In this case, only the yellow pigments in electrophoretic channel y are actuated. As depicted in Figure 3-15, in the leftmost reflective structure, blue light rays are absorbed and the red and green rays are reflected, so this portion of the sheet would appear yellow. In the centermost structure, both blue and green rays are absorbed, leaving a red coloured appearance. Finally, the rightmost reflective structure will appear green since the red and blue rays are absorbed. The combination of one third of the total area appearing yellow, one third appearing red and the remaining one third appearing green will be a net colour of yellow with a reflectance of 67% of that of a pure yellow reflector. red ray green ray \u2014 - blue ray \u2022 cyan filter _\u00a7 magenta filter __ yellow filter S\u00b0 cyan particles %\u2022 magenta particles \u00b0o\u00b0 yellow particles Figure 3-15. Actuation of an FTIR device yielding a net yellow colour A complete description, presented in terms of the net spectral reflectance functions in Table 3-4, shows that the actuation of combinations of the electrophoretic channels generates net colours in the same manner as conventional subtractive colour filtering, as discussed in Section 2.3.4. 66 Status of channels Resultant spectral reflectance, p(X) Net colour y m c PY(A) PM(A) Pc(A) 0 0 0 Y(X) M(A.) C(X) White (W) 1 0 0 Y(X) M(X)y(X) C(X)y(X) Yel low (Y) 0 1 0 Y(X)m(X) U(X) C(X)m(X) Magenta (M) 0 0 1 Y(X)c(X) M(X)c(X) C(X) Cyan (C) 0 1 1 Y(X)m(X)c(X) M(X)c(X) C(X)m(X) Blue (B) 1 0 1 Y(k)c(k) M(X)c(X)y(X) C(X)y(X) Green (G) 1 1 0 Y(X)m(X) M(X)y(X) C(X)y(X)m(X) Red (R) 1 1 1 Y(X)m(X)c(X) M(X)c(X)y(X) C(X)y(X)m(X) Black (K) Table 3-4. Net colour resulting from actuation of electrophoretic channels This chapter has discussed the critical issues faced during the novel design of a practical reflective colour image display based on TIR in microstructured reflective sheets. It was determined that undesirable surface energy effects could be overcome by using a liquid at the TIR interface to prevent direct physical contact between the absorbing material and the TIR surface. Although the optical properties of the liquid make it more difficult to achieve TIR, a unique layered prismatic geometry, taking advantage of the three-dimensional effective refractive index ratio enhancement effect, in combination with low index perfluorinated hydrocarbon liquid, makes it possible to achieve TIR in the system using readily available, polycarbonate microstructured materials. There are a number of possible absorbers which could be used to frustrate TIR in this system, the most promising of which is a suspension of absorptive pigment particles, which can move by electrophoresis in response to an applied electric field. These pigments can be chosen with specific spectral absorption characteristics, and arranged in the system to generate, when actuated, a full colour reflective image. The frustration of TIR by electrophoresis of these coloured pigment particles represents the first demonstration of spectrally selective electrically controlled attenuation of TIR. The significance of this result may extend beyond the bound of its usefulness in a reflective image device, as described in this thesis. The ability to easily and quickly move an absorbing material into and out of optical contact with the interface to selectively absorb certain wavelengths of light while reflecting others is a key result of this work. The detailed experimental analysis of this effect is presented in the following two chapters. 67 4 S P E C T R A L L Y S E L E C T I V E R E F L E C T A N C E B Y P I G M E N T S As explained in detail in Section 3.12, the absorption characteristics of the pigment particles in the electrophoretic suspension are crucial to achieving spectrally selective reflectance control. This chapter presents the experimental design for measurement of these absorption characteristics and the experimental analysis for some typical pigment suspensions. 4.1 Experimental measurement of spectral characteristics A primary goal of this research has been to demonstrate modulation of total internal reflection by absorbing light energy, in particular by means of electrophoresis of pigment particles. In many practical applications, TIR occurs as a result of interaction of light with prismatic microstructures, and the combination of interactions with these reflective structures and the pigment particles can be quite complex. To properly evaluate the performance of these particles, it is necessary to simplify the experiment by separating the effects of the microstructures from the effects of the pigments. For this reason, the experiments performed in these next two chapters make use of high quality, large glass optical structures to produce the reflections, rather than less perfect polymeric microstructured surfaces. Section 3.12 described the use of static colour filters with the controllable electrophoretic pigment channels in a full-colour reflective image device based on modulated TIR. In that arrangement, the light is appropriately filtered first as it passes through the permanent filter overlay, so the spectral transmittance of the filter is important. The light then reflects at the prismatic facets and thus encounters the pigment system. If the pigments are present at the interface, only certain wavelengths of light will be reflected, since the others will be absorbed by the pigments, so the light is again filtered as a result of this interaction. Therefore, the reflectance of the light at this facet is spectrally equivalent to the transmittance through a similarly coloured transmission filter located at the interface. As a result, although the light is undergoing reflection rather than transmission, the pigment filter will be described in terms of its effective spectral transmittance characteristics. 68 The effective spectral transmittance characteristics of the filters and the pigment systems were measured using a spectroradiometric telecolorimeter as the primary analysis instrument in an appropriate optical set-up, as described below. 4.1.1 Spectral analysis instrument The measurement of light intensity and the analysis of colour across the electromagnetic spectrum from 380 to 780 nm were performed using a fast scanning, spectroradiometric telecolorimeter. The particular instrument used throughout the course of this study was the PR\u00ae-650 Spectrascan\u00ae. 7 7 Using this device, light passes through an objective lens and encounters a 1\u00b0 aperture, followed by a shutter mechanism. Light traveling through the aperture and shutter strikes a concave holographic diffraction grating polychromator which diffracts light and focuses the resulting spectrum onto a photodiode array, in a manner such that the spectrum is permanently aligned with the elements in the detector array and, with careful calibration, the intensity of light in 4 nm increments across the spectral band is accurately known. Figure 4-1, adapted from the PR\u00ae-650 Spectrascan\u00ae manual, is a basic schematic of this arrangement. optical 380nm 780nm detector array Figure 4-1. Operation of a spectroradiometric telecolorimeter 6 9 This instrument is a useful tool in measuring the spectral transmittance characteristics of the various filters, and effective filters, in the experimental system. It has been incorporated into the experimental set-up for the measurements presented in the following sections. 4.1.2 Set-up for measuring transmittance of static filters As mentioned previously, the spectral transmittance of subtractive colour filters are important for a number of reasons, in particular for predicting the resultant spectral reflectance of the full colour reflective image device. A simple experimental set-up was used to measure the transmittance of the filters, as shown schematically in Figure 4-2. Here, a uniform, broadband, diffuse luminance source was directed at normal incidence toward the spectroradiometric telecolorimeter, separated by a distance of about 0.3 m. First, a background measurement was taken without a filter. The filter to be measured was then placed between the source and the detector, positioned about 0.05 m from the source. The readings with the filter were divided by the background readings to yield the spectral transmittance at each wavelength. < 0.3 m > 0.05 m < > spectroradiometric telecolorimeter uniform broadband luminance source Figure 4-2. Set-up for measuring spectral transmittance of filters 70 This simple procedure was repeated for each of three subtractive coloured photographic filters. The effective spectral transmittance measurements for the electrophoretic pigment systems was somewhat more complicated as it required the construction of a test cell to house the electrophoretic suspension and apply the appropriate electric field. The next section describes the method devised to construct these cells. 4.1.3 Test cell construction To measure the effective spectral transmittance of various pigment suspensions, a test cell was designed. Once optimized, this became a standard assembly throughout this study, and a large quantity was used on a regular basis. A cell consisted of two 25 mm x 75 mm glass microscope slides, each coated on one surface with a thin layer of indium tin oxide (ITO). (This coating was typically applied by sputtering, a standard thin film deposition technique, and such coated glass pieces are available from a number of commercial sources.78) This highly transparent conducting layer, approximately 50 nm thick, had a typical transmission coefficient of greater than 0.97 and a surface resistance of about 100 Q\/square. On one slide, two small holes, as shown in Figure 4-3(a), each about 1 mm in diameter, were sandblasted through the slide. These acted as fluid ports for filling the cell with the pigment suspension. The test cell was constructed by placing the two ITO surfaces facing one another, but offset by a few millimeters to expose a region where electrical contact was made to the rTO surface of each slide, and a wire lead was secured to the conductive film using a small amount of conductive epoxy. This assembly is depicted in a side view of the cell in Figure 4-3(b). The front surface had to be made from a transparent material such as glass, as it was necessary for the light to transmit through it, but the rear surface did not need to be transparent since the light did not reach it. However, the ITO coated glass slide was appropriate since the surface was known to be uniformly smooth and conductive, and it introduced no additional substances into the system. The slides were spaced a known distance apart by a spacer ring positioned near the edge. This spacer material was chosen depending on the desired gap thickness; for very thin cells, a layer of 10 um polyester film was used, whereas for thicker cells, a layer of 60 um thick 71 polyester tape was used. The size of the spacer was wide enough to provide a uniform gap, but sufficiently narrow that it did not interfere with the fluid ports. The edges of the slides were then sealed on all four sides using clear, non-conductive epoxy. This resulted in a hermetic seal around the edge of the cell, impermeable to both the fluid suspension and air. (a) conductive epoxy (b) f lu id port spacer ring wire lead pigment suspension top slide rear slide Figure 4-3. Top (a) and side (b) views of assembled electrophoretic test cells The pigment suspension to be tested was introduced into the chamber by adding droplets through one of the fluid ports using a small gauge needle or pipette. Since the cell gap was quite narrow, the fluid was drawn between the slides quite effectively by capillary action. The fluid was added through one fluid port until all of the air bubbles were evacuated through the second port. Once the cell was filled, the ports were sealed using the clear epoxy. In many measurements using these test cells, it was desirable to maintain uniformity in pigment distribution and prevent the problems associated with particle clumping described in Section 3.11. For this reason, the rear glass slide was sometimes replaced by a length of prismatic microstructured material, also coated with ITO and positioned so that the prism tips were almost in contact with the flat top surface to create prismatic channels, as shown in the cross-sectional segment in Figure 4-4. It was desirable to minimize the separation distance between the prism and the flat surface and, since the microstructured material is somewhat 72 flexible, it was necessary to include a spacer material within the active region of the test cell, as well as around the edges, to prevent the sheet from sagging in the center and making electrical contact with the flat top surface. This was accomplished by dusting the flat surface with a random distribution of approximately 50 |J,m diameter glass micro-spheres. These micro-prisms were 25 p:m high, with a tip-to-tip spacing of 50 |im, so the micro-spheres fit snugly into the valleys between the prisms. A sufficient amount of pressure was applied to slightly embed the micro-spheres into the somewhat pliable microstructured sheet, to prevent them from moving, as well as decrease the gap distance. Figure 4-4. Modified test cell incorporating micro-prisms It was determined, by constructing a number of samples, that about 20% coverage of the active area by a single layer of micro-spheres was sufficient to maintain a reasonably uniform gap separation, but did not restrict the flow of the pigment suspension into the cell when it was filled. This new assembly confined the pigment particles primarily within the prismatic channels and prevented the deterioration associated with particle clumping. In this case, the prismatic structure was required to restrict particle migration, rather than for any unique optical function; in fact, since they were located on the rear surface of the cell, they did not interact with the incident light at all. In the experimental set-ups using these test cells, as described in Sections 4.2 and 5.2, the incident light was directed through the flat top surface of the test cell, thus avoiding any complications arising from interaction with imperfect polymeric optical microstructures. This allowed an analysis of the behaviour of the pigment suspensions, independent of contributions resulting from the reflective microstructured sheets. glass slide micro-prismatic sheet 73 4 .1 .4 Set-up for measuring TIR-attenuation by pigment systems The attenuation of TIR was measured as a function of wavelength for electrophoretic pigment samples, when these pigments were electrostatically moved into contact with the TIR surface. The suspension was sealed inside a test cell and placed underneath a right angle glass prism, shown schematically in Figure 4-5(a). This prism is required to ensure that TIR occurs at the glass\/fluid interface in the cell. The critical angle, dc, for this interface is 58.3\u00b0, so light rays incident on this interface at angle 6 greater than 58.3\u00b0 can undergo TIR. Figure 4-5(b) shows why the prism in Figure 4-5(a) is needed. In this case, light rays travel through air, with index n\\=\\.Q, striking a flat slab of glass, ^ 2=1.5, which is backed by a fluid medium with index \u00ab3= 1.276. The rays are refracted as they enter the glass medium and there is no incident angle,