Abstract:
A reflective display having a plurality of transparent hemi-beads ( 120 ), each having a reflective region ( 80 ) surrounding a non-reflective region ( 82 ). Each hemi-bead has an associated light absorptive fluid droplet ( 122 ) having a normally relaxed shape contacting the non-reflective region, thereby frustrating total internal reflection of light rays at the droplet/hemi-bead interface. An electrical potential is selectably applied across selected droplets. Application of the electrical potential across a droplet deforms the droplet away from the hemi-bead associated with the droplet, such that light rays ( 158 ) incident on the non-reflective region are refracted toward substrate ( 124 ) and reflected back through hemi-bead ( 120 ) in an approximately opposite direction ( 166 ); and such that light rays ( 162 ) incident on the reflective region are semi-retro-reflected ( 168 ). Removal of the electrical potential allows the droplet to resume the relaxed shape.

Description:
REFERENCE TO RELATED APPLICATION 
       [0001]    This application claims the benefit of United States provisional patent application Ser. No. 60/759,772 filed 17 Jan. 2006. 
     
    
     TECHNICAL FIELD 
       [0002]    This application pertains to brightness enhancement of reflective image displays of the type described in U.S. Pat. Nos. 5,999,307; 6,064,784; 6,215,920; 6,865,011; 6,885,496 and 6,891,658; in United States Patent Application Publication No. 2006-0209418-A1; and in International Patent Publication No. WO 2006/108285 all of which are incorporated herein by reference. 
       BACKGROUND 
       [0003]      FIG. 1A  depicts a portion of a prior art reflective (i.e. front-lit) image display  10  in which total internal reflection (TIR) is electrophoretically modulated as described in U.S. Pat. Nos. 6,885,496 and 6,891,658. Display  10  includes a transparent outward sheet  12  formed by partially embedding a large plurality of high refractive index (e.g. η 1 &gt;˜1.90) transparent spherical or approximately spherical beads  14  in the inward surface of a high refractive index (e.g. η 2 &gt;˜1.75) polymeric material  16  having a flat outward viewing surface  17  which viewer V observes through an angular range of viewing directions Y. The “inward” and “outward” directions are indicated by double-headed arrow Z. Beads  14  are packed closely together to form an inwardly projecting monolayer  18  having a thickness approximately equal to the diameter of one of beads  14 . Ideally, each one of beads  14  touches all of the beads immediately adjacent to that one bead. Minimal interstitial gaps (ideally, no gaps) remain between adjacent beads. 
         [0004]    An electrophoresis medium  20  is maintained adjacent the portions of beads  14  which protrude inwardly from material  16  by containment of medium  20  within a reservoir  22  defined by lower sheet  24 . An inert, low refractive index (i.e. less than about 1.35), low viscosity, electrically insulating liquid such as Fluorinert™ perfluorinated hydrocarbon liquid (η 3 ˜1.27) available from 3M, St. Paul, Minn. is a suitable electrophoresis medium. Other liquids, or water can also be used as electrophoresis medium  20 . A bead:liquid TIR interface is thus formed. Medium  20  contains a finely dispersed suspension of light scattering and/or absorptive particles  26  such as pigments, dyed or otherwise scattering/absorptive silica or latex particles, etc. Sheet  24 &#39;s optical characteristics are relatively unimportant: sheet  24  need only form a reservoir for containment of electrophoresis medium  20  and particles  26 , and serve as a support for backplane electrode  48 . 
         [0005]    As is well known, the TIR interface between two media having different refractive indices is characterized by a critical angle θ c . Light rays incident upon the interface at angles less than θ c  are transmitted through the interface. Light rays incident upon the interface at angles greater than θ c  undergo TIR at the interface. A small critical angle is preferred at the TIR interface since this affords a large range of angles over which TIR may occur. 
         [0006]    In the absence of electrophoretic activity, as is illustrated to the right of dashed line  28  in  FIG. 1A , a substantial fraction of the light rays passing through sheet  12  and beads  14  undergoes TIR at the inward side of beads  14 . For example, incident light rays  30 ,  32  are refracted through material  16  and beads  14 . The rays undergo TIR two or more times at the bead:liquid TIR interface, as indicated at points  34 ,  36  in the case of ray  30 ; and indicated at points  38 ,  40  in the case of ray  32 . The totally internally reflected rays are then refracted back through beads  14  and material  16  and emerge as rays  42 ,  44  respectively, achieving a “white” appearance in each reflection region or pixel. 
         [0007]    A voltage can be applied across medium  20  via electrodes  46 ,  48  (shown as dashed lines) which can for example be applied by vapour-deposition to the inwardly protruding surface portion of beads  14  and to the outward surface of sheet  24 . Electrode  46  is transparent and substantially thin to minimize its interference with light rays at the bead:liquid TIR interface. Backplane electrode  48  need not be transparent. If electrophoresis medium  20  is activated by actuating voltage source  50  to apply a voltage between electrodes  46 ,  48  as illustrated to the left of dashed line  28 , suspended particles  26  are electrophoretically moved into the region where the evanescent wave is relatively intense (i.e. within 0.25 micron of the inward surfaces of inwardly protruding beads  14 , or closer). When electrophoretically moved as aforesaid, particles  26  scatter or absorb light, thus frustrating TIR by modifying the imaginary and possibly the real component of the effective refractive index at the bead:liquid TIR interface. This is illustrated by light rays  52 ,  54  which are scattered and/or absorbed as they strike particles  26  inside the thin (˜0.5 μm) evanescent wave region at the bead:liquid TIR interface, as indicated at  56 ,  58  respectively, thus achieving a “dark” appearance in each TIR-frustrated non-reflective absorption region or pixel. Particles  26  need only be moved outside the thin evanescent wave region, by suitably actuating voltage source  50 , in order to restore the TIR capability of the bead:liquid TIR interface and convert each “dark” non-reflective absorption region or pixel to a “white” reflection region or pixel. 
         [0008]    As described above, the net optical characteristics of outward sheet  12  can be controlled by controlling the voltage applied across medium  20  via electrodes  46 ,  48 . The electrodes can be segmented to control the electrophoretic activation of medium  20  across separate regions or pixels of sheet  12 , thus forming an image. 
         [0009]      FIG. 2  depicts, in enlarged cross-section, an inward hemispherical or “hemi-bead” portion  60  of one of spherical beads  14 . Hemi-bead  60  has a normalized radius r=1 and a refractive index m. A light ray  62  perpendicularly incident (through material  16 ) on hemi-bead  60  at a radial distance a from hemi-bead  60 &#39;s centre C encounters the inward surface of hemi-bead  60  at an angle θ 1  relative to radial axis  66 . For purposes of this theoretically ideal discussion, it is assumed that material  16  has the same refractive index as hemi-bead  60  (i.e. η 1 =η 2 ), so ray  62  passes from material  16  into hemi-bead  60  without refraction. Ray  62  is refracted at the inward surface of hemi-bead  60  and passes into electrophoretic medium  20  as ray  64  at an angle θ 2  relative to radial axis  66 . 
         [0010]    Now consider incident light ray  68  which is perpendicularly incident (through material  16 ) on hemi-bead  60  at a distance 
         [0000]    
       
         
           
             
               a 
               c 
             
             = 
             
               
                 η 
                 3 
               
               
                 η 
                 1 
               
             
           
         
       
     
         [0000]    from hemi-bead  60 &#39;s centre C. Ray  68  encounters the inward surface of hemi-bead  60  at the critical angle θ c  (relative to radial axis  70 ), the minimum required angle for TIR to occur. Ray  68  is accordingly totally internally reflected, as ray  72 , which again encounters the inward surface of hemi-bead  60  at the critical angle θ c . Ray  72  is accordingly totally internally reflected, as ray  74 , which also encounters the inward surface of hemi-bead  60  at the critical angle θ c . Ray  74  is accordingly totally internally reflected, as ray  76 , which passes perpendicularly through hemi-bead  60  into the embedded portion of bead  14  and into material  16 . Ray  68  is thus reflected back as ray  76  in a direction approximately opposite that of incident ray  68 . 
         [0011]    All light rays which are incident on hemi-bead  60  at distances a≦a c  from hemi-bead  60 &#39;s centre C are reflected back (but not exactly retro-reflected) toward the light source; which means that the reflection is enhanced when the light source is overhead and slightly behind the viewer, and that the reflected light has a diffuse characteristic giving it a white appearance, which is desirable in reflective display applications.  FIGS. 3A ,  3 B and  3 C depict three of hemi-bead  60 &#39;s reflection modes. These and other modes coexist, but it is useful to discuss each mode separately. 
         [0012]    In  FIG. 3A , light rays incident within a range of distances a c ≦a 1  undergo TIR twice (the 2-TIR mode) and the reflected rays diverge within a comparatively wide arc φ 1  centered on a direction opposite to the direction of the incident light rays. In  FIG. 3B , light rays incident within a range of distances a 1 &lt;a≧a 2  undergo TIR three times (the 3-TIR mode) and the reflected rays diverge within a narrower arc φ 2 &lt;φ 1  which is again centered on a direction opposite to the direction of the incident light rays. In  FIG. 3C , light rays incident within a range of distances a 2 &lt;a≦a 3  undergo TIR four times (the 4-TIR mode) and the reflected rays diverge within a still narrower arc φ 3 &lt;φ 2  also centered on a direction opposite to the direction of the incident light rays. Hemi-bead  60  thus has a “semi-retro-reflective,” partially diffuse reflection characteristic, causing display  10  to have a diffuse appearance akin to that of paper. 
         [0013]    Display  10  has relatively high apparent brightness, comparable to that of paper, when the dominant source of illumination is behind the viewer, within a small angular range. This is illustrated in  FIG. 1B  which depicts the wide angular range α over which viewer V is able to view display  10 , and the angle β which is the angular deviation of illumination source S relative to the location of viewer V. Display&#39;s  10 &#39;s high apparent brightness is maintained as long as β is not too large. At normal incidence, the reflectance R of hemi-bead  60  (i.e. the fraction of light rays incident on hemi-bead  60  that reflect by TIR) is given by equation (1): 
         [0000]    
       
         
           
             
               
                 
                   R 
                   = 
                   
                     1 
                     - 
                     
                       
                         ( 
                         
                           
                             η 
                             3 
                           
                           
                             η 
                             1 
                           
                         
                         ) 
                       
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where η 1  is the refractive index of hemi-bead  60  and η 3  is the refractive index of the medium adjacent the surface of hemi-bead  60  at which TIR occurs. Thus, if hemi-bead  60  is formed of a lower refractive index material such as polycarbonate (η 1 ˜1.59) and if the adjacent medium is Fluorinert (η 3 ˜1.27), a reflectance R of about 36% is attained, whereas if hemi-bead  60  is formed of a high refractive index nano-composite material (η 1 ˜1.92) a reflectance R of about 56% is attained. When illumination source S ( FIG. 1B ) is positioned behind viewer V&#39;s head, the apparent brightness of display  10  is further enhanced by the aforementioned semi-retro-reflective characteristic. 
         [0014]    As shown in  FIGS. 4A-4G , hemi-bead  60 &#39;s reflectance is maintained over a broad range of incidence angles, thus enhancing display  10 &#39;s wide angular viewing characteristic and its apparent brightness. For example,  FIG. 4A  shows hemi-bead  60  as seen from perpendicular incidence—that is, from an incidence angle offset 0° from the perpendicular. In this case, the portion  80  of hemi-bead  60  for which a≧a c  appears as an annulus. The annulus is depicted as white, corresponding to the fact that this is the region of hemi-bead  60  which reflects incident light rays by TIR, as aforesaid. The annulus surrounds a circular region  82  which is depicted as dark, corresponding to the fact that this is the non-reflective region of hemi-bead  60  within which incident rays are absorbed and do not undergo TIR.  FIGS. 4B-4G  show hemi-bead  60  as seen from incident angles which are respectively offset 15°, 30°, 45°, 60°, 75° and 90° from the perpendicular. Comparison of  FIGS. 4B-4G  with  FIG. 4A  reveals that the observed area of reflective portion  80  of hemi-bead  60  for which a≧a c  decreases only gradually as the incidence angle increases. Even at near glancing incidence angles (e.g.  FIG. 4F ) an observer will still see a substantial part of reflective portion  80 , thus giving display  10  a wide angular viewing range over which high apparent brightness is maintained. 
         [0015]    An estimate of the reflectance of an array of hemispheres corresponding to the inward “hemi-bead” portions of each one of spherical beads  14  depicted in  FIG. 1A  can be obtained by multiplying the reflectance of an individual hemi-bead by the hemi-beads&#39; packing efficiency coefficient f. Calculation of the packing efficiency coefficient/of a closely packed structure involves application of straightforward geometry techniques which are well known to persons skilled in the art. The hexagonal closest packed (HCP) structure depicted in  FIG. 5  yields a packing efficiency f∝π/(6·tan 30°) ˜90.7% assuming beads  14  are of uniform size. 
         [0016]    Although the HCP structure yields the highest packing density for hemispheres, it is not necessary to pack the hemi-beads in a regular arrangement, nor is it necessary that the hemi-beads be of uniform size. A random distribution of non-uniform size hemi-beads having diameters within a range of about 1-50 μm has a packing density of approximately 80%, and has an optical appearance substantially similar to that of an HCP arrangement of uniform size hemi-beads. For some reflective display applications, such a randomly distributed arrangement may be more practical to manufacture, and for this reason, somewhat reduced reflectance due to less dense packing may be acceptable. However, for simplicity, the following description focuses on the  FIG. 5  HCP arrangement of uniform size hemi-beads, and assumes the use of materials which yield a refractive index ratio η 1 /η 3 =1.5. These factors are not to be considered as limiting the scope of this disclosure. 
         [0017]    As previously explained in relation to  FIG. 2 , a substantial portion of light rays which are perpendicularly incident on the flat outward face of hemi-bead  60  at distances a&lt;a c  from hemi-bead  60 &#39;s centre C do not undergo TIR and are therefore not reflected by hemi-bead  60 . Instead, a substantial portion of such light rays are scattered and/or absorbed by prior art display  10 , yielding a dark non-reflective circular region  82  ( FIGS. 4A-4G ) on hemi-bead  60 .  FIG. 5  depicts a plurality of these dark non-reflective regions  82 , each of which is surrounded by a reflective annular region  80 , as previously explained. 
         [0018]    Hemi-bead  60 &#39;s average surface reflectance, R, is determined by the ratio of the area of reflective annulus  80  to the total area comprising reflective annulus  80  and dark circular region  82 . That ratio is in turn determined by the ratio of the refractive index, η 1 , of hemi-bead  60  to the refractive index, η 3 , of the medium adjacent the surface of hemi-bead  60  at which TIR occurs, in accordance with Equation (1). It is thus apparent that the average surface reflectance, R, increases with the ratio of the refractive index η 1 , of hemi-bead  60  to that of the adjacent medium η 3 . For example, the average surface reflectance, R, of a hemispherical water drop (η 1 ˜1.33) in air (η 3 ˜1.0) is about 43%; the average surface reflectance, R, of a glass hemisphere (η 1 ˜1.5) in air is about 55%; and the average surface reflectance, R, of a diamond hemi-sphere (η 1 ˜2.4) in air exceeds 82%. 
         [0019]    Although it may be convenient to fabricate display  10  using spherically (or hemispherically) shaped beads as aforesaid, even if spherical (or hemispherical) beads  14  are packed together as closely as possible within monolayer  18  ( FIG. 1A ), interstitial gaps  84  ( FIG. 5 ) unavoidably remain between adjacent beads. Light rays incident upon any of gaps  84  are “lost” in the sense that they pass directly into electrophoretic medium  20 , producing undesirable dark spots on viewing surface  17 . While these spots are invisibly small, and therefore do not detract from display  10 &#39;s appearance, they do detract from viewing surface  17 &#39;s net average surface reflectance, R. 
         [0020]    The above-described “semi-retro-reflective” characteristic is important in a reflective display because, under typical viewing conditions where light source S is located above and behind viewer V, a substantial fraction of the reflected light is returned toward viewer V. This results in an apparent reflectance which exceeds the value 
         [0000]    
       
         
           
             R 
             = 
             
               1 
               - 
               
                 
                   ( 
                   
                     
                       η 
                       3 
                     
                     
                       η 
                       1 
                     
                   
                   ) 
                 
                 2 
               
             
           
         
       
     
         [0000]    by a “semi-retro-reflective enhancement factor” of about 1.5 (see “A High Reflectance, Wide Viewing Angle Reflective Display Using Total Internal Reflection in Micro-Hemispheres,” Mossman, M. A. et al., Society for Information Display, 23rd International Display Research Conference, pages 233-236, Sep. 15-18, 2003, Phoenix, Ariz.). For example, in a system where the refractive index ratio η 1 /η 3 =1.5, the average surface reflectance, R, of 55% determined in accordance with Equation (1) is enhanced to approximately 85% under the semi-retro-reflective viewing conditions described above. 
         [0021]    Individual hemi-beads  60  can be invisibly small, within the range of 2-50 μm in diameter, and as shown in  FIG. 5  they can be packed into an array to create a display surface that appears highly reflective due to the large plurality of tiny, adjacent, reflective annular regions  80 . In these regions  80 , where TIR can occur, particles  26  ( FIG. 1A ) do not impede the reflection of incident light when they are not in contact with the inward, hemispherical portions of beads  14 . However, in regions  82  and  84 , where TIR does not occur, particles  26  may absorb incident light rays—even if particles  26  are moved outside the evanescent wave region so that they are not in optical contact with the inward, hemispherical portions of beads  14 . The refractive index ratio η 1 /η 3  can be increased in order to increase the size of each reflective annular region  80  and thus reduce such absorption losses. Non-reflective regions  82 ,  84  cumulatively reduce display  10 &#39;s overall surface reflectance, R. Since display  10  is a reflective display, it is clearly desirable to minimize such reduction. 
         [0022]    Disregarding the aforementioned semi-retro-reflective enhancement factor, a system having a refractive index ratio η 1 /η 3 =1.5 has an average surface reflectance, R, of 55%, as previously explained. Given the HCP arrangement&#39;s aforementioned packing efficiency of about 91%, the system&#39;s overall average surface reflectance is 91% of 55% or about 50%, implying a loss of about 50%. 41% of this loss is due to light absorption in circular non-reflective regions  82 ; the remaining 9% of this loss is due to light absorption in interstitial non-reflective gaps  84 . Display  10 &#39;s reflectance can be increased by decreasing such absorptive losses through the use of materials having specific selected refractive index values, optical microstructures or patterned surfaces placed on the outward or inward side(s) of monolayer  18  ( FIG. 1A ). 
         [0023]    For example, since display  10 &#39;s maximum surface reflectance is determined by the ratio of the refractive index values of hemi-bead  60  and electrophoretic medium  20 , the reflectance can be increased by substituting air (refractive index=1.0) as electrophoretic medium  20  instead of a low refractive index liquid (refractive index less than 1.35). 
         [0024]    Display  10 &#39;s surface reflectance can be increased, as described below, without using particles suspended in an electrophoretic medium. 
         [0025]    The foregoing examples of the related art and limitations related thereto are intended to be illustrative and not exclusive. Other limitations of the related art will become apparent to those of skill in the art upon a reading of the specification and a study of the drawings. 
     
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         [0026]    Exemplary embodiments are illustrated in referenced figures of the drawings. It is intended that the embodiments and figures disclosed herein are to be considered illustrative rather than restrictive. 
           [0027]      FIG. 1A  is a greatly enlarged, not to scale, fragmented cross-sectional side elevation view of a portion of a prior art reflective image display in which TIR is electrophoretically modulated. 
           [0028]      FIG. 1B  schematically illustrates the wide angle viewing range a of the  FIG. 1A  display, and the angular range fi of the illumination source. 
           [0029]      FIG. 2  is a cross-sectional side elevation view, on a greatly enlarged scale, of a hemispherical (“hemi-bead”) portion of one of the spherical beads of the  FIG. 1A  apparatus. 
           [0030]      FIGS. 3A ,  3 B and  3 C depict semi-retro-reflection of light rays perpendicularly incident on the  FIG. 2  hemi-bead at increasing off-axis distances at which the incident rays undergo TIR two, three and four times respectively. 
           [0031]      FIGS. 4A ,  4 B,  4 C,  4 D,  4 E,  4 F and  4 G depict the  FIG. 2  hemi-bead, as seen from viewing angles which are offset 0°, 15°, 30°, 45°, 60°, 75° and 90° respectively from the perpendicular. 
           [0032]      FIG. 5  is a top plan (i.e. as seen from a viewing angle offset 0° from the perpendicular) cross-sectional view of a portion of the  FIG. 1  display, showing the spherical beads arranged in a hexagonal closest packed (HCP) structure. 
           [0033]      FIGS. 6A and 6B  are schematic, cross-sectional side elevation and top plan views respectively, on a greatly enlarged scale, depicting a prior art fluid (water) droplet submerged in a fluid (air) background medium and electro-wetting a solid surface. 
           [0034]      FIGS. 7A and 7B  are cross-sectional side elevation views, on a greatly enlarged scale, of a reflective display hemi-bead in which TIR is modulated by electro-deformation of a fluid interface, with  FIG. 7A  depicting the relaxed, TIR-frustrated (non-reflective) state and  FIG. 7B  depicting the electro-deformed, TIR-enabled (reflective) state. 
           [0035]      FIGS. 8A and 8B  are oblique schematic pictorial illustrations of the fluid droplet of  FIGS. 7A and 7B  respectively, with  FIG. 8A  depicting the relaxed, TIR-frustrated (non-reflective) state and  FIG. 8B  depicting the electro-deformed, TIR-enabled (reflective) state. 
           [0036]      FIGS. 9A and 9B  are schematic, cross-sectional side elevation and top plan views, on a greatly enlarged scale, of the fluid droplet of  FIGS. 8A and 8B , with an associated electrode and voltage source. 
           [0037]      FIGS. 10A and 10B  are similar to  FIGS. 7A and 7B  respectively, but show coplanar hydrophobic and hydrophilic regions atop a substrate. 
           [0038]      FIGS. 11A ,  11 B and  11 C schematically illustrate droplet deformation. 
           [0039]      FIGS. 12A and 12B  are cross-sectional side elevation views, on a greatly enlarged scale, of a reflective display hemi-bead in which TIR is modulated by electro-deformation of a fluid interface relative to an absorptive substrate, with  FIG. 12A  depicting the relaxed, TIR-frustrated (non-reflective) state and  FIG. 12B  depicting the electrodeformed, TIR-enabled (reflective) state. 
       
    
    
     DESCRIPTION 
       [0040]    Throughout the following description specific details are set forth in order to provide a more thorough understanding to persons skilled in the art. However, well known elements may not have been shown or described in detail to avoid unnecessarily obscuring the disclosure. Accordingly, the description and drawings are to be regarded in an illustrative, rather than a restrictive, sense. 
         [0041]    It is useful to review some aspects of the electro-wetting phenomenon.  FIGS. 6A and 6B  depict a first fluid (e.g. water) droplet  130  on a uniform, homogeneous, solid surface  132 . Droplet  130  and surface  132  are submerged in a second fluid (e.g. air) background medium  134 . In the absence of external forces, such as friction, droplet  130  (shown in solid outline in  FIGS. 6A and 6B ) assumes a smooth, semi-spherical shape on surface  132 . 
         [0042]    Droplet  130 , surface  132  and medium  134  intersect at three interfaces: (1) the interface between droplet  130  and surface  132 ; (2) the interface between droplet  130  and background medium  134 ; and (3) the interface between surface  132  and background medium  134 . Each interface is characterized by a well-defined surface tension or surface energy, as described by Young&#39;s equation: 
         [0000]      γ SD γ DB  cos θ 1 −γ SB =0 
         [0000]    where, γ SD  is the surface tension or surface energy at the interface between droplet  130  and surface  132 ; γ DB  is the surface tension or surface energy at the interface between droplet  130  and background medium  134 ; γ SB  is the surface tension or surface energy at the interface between surface  132  and background medium  134 ; and θ 1  is the contact angle between droplet  130  and surface  132  as shown in  FIG. 6A . Young&#39;s equation yields a single, unique solution at which the sum of these three surface energies is minimized. This minimum energy state defines the shape of droplet  130 . For example, a water droplet submerged in an air background medium will “bead up” when placed on a surface formed of Teflon® material, as the droplet adapts to minimize the total surface energy of the droplet-background medium-surface system. The “contact line” is the line at which the three aforementioned interfaces intersect, shown at  138  in  FIGS. 6A and 6B . Since droplet  130  is a semi-sphere, contact line  138  is a circle at the base of droplet  130  where it contacts surface  132 . 
         [0043]    It is well known that the surface energy relationships at contact line  138  can be changed via “electro-wetting” by applying an electric field between droplet  130  and an electrically insulated electrode  140  located beneath surface  132 . Specifically, consider the case of a conductive (e.g. water) droplet  130  on surface  132 . An electrical potential source  142  can be electrically connected to apply an electrical potential between electrode  140  and droplet  130 . This subjects droplet  130  to an electric field, increasing the surface area of droplet  130  as it adapts to minimize the total surface energy of the droplet-background medium-surface system by assuming a somewhat flattened shape  130 A (shown in dotted outline in  FIGS. 6A and 6B ). The surface area increase causes a corresponding contact angle reduction (indicated at θ 2  in  FIG. 6A ) and a corresponding expansion of the circular contact line (indicated at  138 A in  FIGS. 6A and 6B ) as the droplet spreads out on surface  132 . 
         [0044]    In theory, electro-wetting can be used to efficiently and reproducibly change the shape of droplet  130  on surface  132 . However, in practice, surface  132  is insufficiently smooth, or insufficiently chemically homogeneous, or both. Porosity of surface  132 , or the presence of chemical impurities or dust particles on surface  132  unpredictably affects the contact angle θ, causing friction as the contact line moves across surface  132 . Such friction results in “contact angle hysteresis,” disrupting accurately reversible movement of droplet  130  from an initial position to an intermediate position and back to the same initial position. Efficient, accurately reversible movement of droplet  130  between different positions is a desirable attribute in a number of applications, but attainment of that attribute is often limited by contact angle hysteresis. 
         [0045]      FIGS. 7A and 7B  depict a reflective display hemi-bead  120  which does not require particles  26  or electrophoresis medium  20  to electrophoretically modulate TIR. Instead, TIR is modulated in hemi-bead  120  by electrostatically deforming the interface of a light absorptive non-aqueous medium such as oil droplet  122  on substrate  124 . Such electro-deformation would ordinarily be inhibited by contact line hysteresis, which would tend to limit efficient, controllable movement of the contact line between droplet  122  and substrate  124 , thus impeding accurately reversible movement of droplet  122  between the TIR-frustrating (i.e. non-reflective) position shown in  FIGS. 7A and 8A  in which droplet  122  has a normally relaxed shape and causes optical interference with light rays that would otherwise be reflected by TIR or transmitted through hemi-bead  120 , and the TIR-enabling (i.e. reflective) position shown in  FIGS. 7B and 8B  in which droplet  122  is deformed into a generally hemi-toroidal shape away from and not contacting hemi-bead  120 &#39;s central, circular non-reflective region. If droplet  122  is sufficiently absorptive and contacts a sufficiently large portion of hemi-bead  120 , then light rays will be adequately absorbed, regardless of whether droplet  122  contacts hemi-bead  120 &#39;s annular reflective region; or contacts hemi-bead  120 &#39;s non-reflective, central circular region; or contacts both regions. This is because light rays which strike hemi-bead  120 &#39;s annular reflective region undergo TIR and are reflected onto hemi-bead  120 &#39;s non-reflective, central circular region—as previously described in relation to  FIGS. 3A ,  3 B and  3 C—whereupon such reflected rays are absorbed. Consequently, it does not matter whether droplet  122  contacts hemi-bead  120 &#39;s annular reflective region or not. 
         [0046]    The aforementioned contact angle hysteresis limitation can be overcome by applying a hydrophilic coating  128  to substrate  124 , then patterning substrate  124  to form a plurality of reflective, circular hydrophobic regions  126  atop hydrophilic coating  128 , with one region  126  vertically aligned beneath each hemi-bead  120 . The diameter of each region  126  is selected, taking into account the spacing between hemi-bead  120  and substrate  124 , such that droplet  122  naturally makes optical contact with hemi-bead  120 &#39;s central, circular non-reflective region. 
         [0047]    “Hydrophobic” substances, such as oils, waxes and fats, repel or tend not to combine with water. “Hydrophilic” substances, such as the hydroxyl, carbonyl, carboxyl, amino, sulfhydryl and phosphate functional groups have an affinity for water or are readily absorbed or dissolved in water. Oil droplet  122  may be a droplet of a fluid such as Dow Corning® OS-30 fluid (a volatile methylsiloxane, referred to herein as “oil,” available from Dow Corning Corporation, Midland, Mich. 48686). 
         [0048]    Circular hydrophobic region  126  may be formed by printing a wax-based (i.e. hydrophobic) ink (e.g. ColorStix® 8200 Ink—Black, Xerox Part Number 016-2044-00, available from Xerox Corporation—Office Group, Wilsonville, Oreg. 97070-1000) directly onto a hydrophilic-coated film (e.g. 132 Medium Blue Colour Effects Lighting Filters, available from Lee Filters, Andover, Hampshire, SP10 5AN, England) using a consumer grade ink printer (e.g. a Phaser® 8200DP Solid Ink Printer, Xerox Part Number 8200DP, available from Xerox Corporation, Wilsonville, Oreg. 97070-1000). 
         [0049]    Oil droplet  122  ( FIGS. 7A ,  7 B) is surrounded by an aqueous liquid background medium  150  such as water. Oil droplet  122  has a first refractive index (e.g. about 1.5). Hemi-bead  120  is formed of a hydrophilic substance, or its inward surface (i.e. the surface closest to substrate  124 ) is coated with a hydrophilic substance. Hemi-bead  120  has a second refractive index (e.g. about 1.5). The first refractive index should not be substantially less than the second refractive index. Oil droplet  122  is absorptive, so it will normally have a higher effective refractive index than hemi-bead  120 , since light absorption is caused by the imaginary component of the refractive index. Such higher effective refractive index is desirable. By contrast, a transparent (i.e. non-absorptive) oil having a higher refractive index than hemi-bead  120  is undesirable in the embodiment of  FIGS. 7A and 7B . However, regardless of whether oil droplet  122  is absorptive or non-absorptive (as it may be in some cases), it should have a real component of refractive index that is not substantially less than the real component of refractive index of hemi-bead  120 . Oil droplet  122  naturally assumes a shape such that about 25% of hemi-bead  120 &#39;s central, inward surface area (i.e. the area corresponding to hemi-bead  120 &#39;s central, circular non-reflective region) is in optical contact with oil droplet  122 . 
         [0050]    Oil droplet  122  may contain a light absorptive dye or dye mixture. Accordingly, light ray  158  incident on hemi-bead  120 &#39;s non-reflective, central circular region—which would otherwise be refracted through hemi-bead  120  toward substrate  124  as previously described in relation to ray  62  depicted in FIG.  2 —is absorbed at the interface between hemi-bead  120  and oil droplet  122 , as shown at  160  in  FIG. 7A  which depicts the TIR-frustrated or non-reflective state. Light ray  162  incident on hemi-bead  120 &#39;s reflective, annular region—which would otherwise undergo TIR and be reflected back in a direction approximately opposite that of the incident ray as previously described in relation to rays  68 ,  72 ,  74 ,  76  depicted in FIG.  2 —is also absorbed at the interface between hemi-bead  120  and oil droplet  122 , as shown at  166  in  FIG. 7A . More particularly, since oil droplet  122  does not (and need not) contact a significant portion of hemi-bead  120 &#39;s annular region, light ray  162  initially undergoes TIR at hemi-bead  120 &#39;s annular region as shown at  164 , and is reflected onto hemi-bead  120 &#39;s non-reflective, central circular region—as previously described in relation to  FIGS. 3A ,  3 B and  3 C—whereupon the reflected ray is absorbed as shown at  166  since further TIR of the ray is frustrated by the optical contact of oil droplet  122  with hemi-bead  120 &#39;s central, circular region. 
         [0051]    Oil droplet  122  must be sufficiently close to be in optical contact with hemi-bead  120 , that is, within less than 250 nm of hemi-bead  120 &#39;s inward surface. However, since hemi-bead  120 &#39;s inward surface is hydrophilic, its surface energy characteristics are such that a microscopically thin layer of water  150  remains between hemi-bead  120 &#39;s inward surface and oil droplet  122 . Accordingly, oil droplet  122  does not adhere to hemi-bead  120 &#39;s inward surface, and can be easily and reproducibly electro-deformed to move oil droplet  122  away from or toward hemi-bead  120  to modulate TIR as explained below. 
         [0052]    Oil droplet  122  wets circular hydrophobic region  126  by leaving a microscopically thin film of oil thereon. More particularly, oil droplet  122  wets the entirety of circular hydrophobic region  126 , namely the region within contact line  154  which coincides with the circumference of circular hydrophobic region  126 . Contact line  154  does not move—thereby avoiding the aforementioned problems associated with contact line hysteresis—notwithstanding localized changes in the shape of oil droplet  122  which occur as portions of oil droplet  122  bulge, flatten, etc. to minimize the total surface energy of the oil droplet-background medium-surface system in response to different electric fields applied between electrode  156  and background medium (i.e. water)  150 . 
         [0053]    One such electrode  156  is vertically aligned beneath each hemi-bead  120 , on the inward side of substrate  124 . Each electrode  156  is generally circular is shape, but includes a thin longitudinal portion  157  ( FIG. 9B ) which extends to the edge of droplet  122  as shown in  FIGS. 9A and 9B . The circular portion of electrode  156  has approximately the same diameter as hemi-bead  120 &#39;s non-reflective, central circular region (i.e. the region analogous to hemi-bead  60 &#39;s non-reflective region  82  shown in  FIGS. 4A-4G  and  9 A). As shown in  FIGS. 9A and 9B , electrical potential source  142  is electrically connected to controllably apply an electrical potential between each electrode  156 ,  157  and background medium (water)  150 . Longitudinal electrode portion  157  facilitates electrical connection between circular electrode portion  156  and electrical potential source  142 . Longitudinal electrode portion  157  also facilitates deformation of droplet  122  by application of a relatively small electrical potential (i.e. less than several hundred volts and ideally considerably less than several hundred volts—assuming that longitudinal electrode portion  157  has a very thin insulating coating). 
         [0054]    Although not wishing to be bound by any theory, the inventor believes that since droplet  122  is thickest at its center, the electrostatic pressure required to deform droplet  122  to remove substantially all oil from the droplet&#39;s central region would require an extremely large electric field and hence require application of a very high electrical potential. This is schematically shown in  FIG. 11A  in which the dashed lines represent progressive stages of deformation of droplet  122  toward substrate  124  as indicated by dashed arrow  125 . However, if longitudinal electrode portion  157  extends to the edge of droplet  122 , then application of a relatively small electrical potential initiates deformation of droplet  122 —not from the droplet&#39;s center as shown in FIG.  11 A—but from the droplet&#39;s outer edge (i.e. the edge coinciding with contact line  154 ) where droplet  122  is thin and where the electric field concentration is high due to the electrode&#39;s shape. This is shown in  FIGS. 11B and 11C . Specifically, the closely-spaced arrows in  FIG. 11B  represent relatively high concentration of electric field lines near the edge of droplet  122  (i.e. the edge coinciding with contact line  154 ), and the widely-spaced arrows represent relatively low concentration of electric field lines away from the edge of droplet  122 . The dashed lines in  FIG. 11C  schematically illustrate progressive stages of inward deformation of droplet  122  in the direction of dashed arrow  129 , when droplet  122  is subjected to an electric field as shown in  FIG. 11B . The gap in the electro-deformed droplet  122  shown in  FIG. 8B  represents a depression in the droplet&#39;s otherwise generally hemi-toroidal shape, such depression coinciding with longitudinal electrode portion  157 , it being understood that a thin fluid (i.e. oil) film nevertheless remains on hydrophobic region  126  in this depressed region of droplet  122 . 
         [0055]    Background medium  150  (e.g. water) is attracted toward substrate  124  by the electric field around electrode  156 . Since the water does not completely displace the oil (i.e. a microscopically thin film of oil remains on circular hydrophobic region  126 ) contact line  154  does not move. More particularly, as oil droplet  122 &#39;s shape changes to minimize the total surface energy of the oil-water system, contact line  154  remains in the same position—coinciding with the circumference of circular hydrophobic region  126 —throughout a wide range of droplet shape changes. Since oil droplet  122  is stable for a wide range of shapes, contact line  154  does not move, even if droplet  122  undergoes substantial deformation. Oil droplet  122  is thus confined atop circular hydrophobic region  126 , within circular contact line  154 . 
         [0056]    The shape of oil droplet  122  on circular hydrophobic region  126  can be rapidly altered by applying an electric field across droplet  122 , between electrode  156  and background medium (water)  150 . When the field is applied, the high dielectric constant water tends to move into the high electric field region, so as to minimize the total surface energy of the system, consequently deforming the low dielectric constant oil droplet  122  by squeezing (i.e. electro-deforming) it away from the high electric field region into a generally hemi-toroidal shape such that the droplet is away from and does not contact the central, non-reflective region of hemi-bead  120 , as seen in  FIG. 7B . Oil droplet  122  can be rapidly, reversibly moved on circular hydrophobic region  126  between the relaxed, non-reflective shape and the electro-deformed, reflective shape shown in  FIGS. 7A and 7B  respectively by suitably varying the electric field applied across droplet  122 . The volume of oil in relaxed droplet  122  ( FIGS. 7A and 8A ) remains the same as the volume of oil in electro-deformed droplet  122  ( FIGS. 7B and 8B ). 
         [0057]    In the electro-deformed, TIR-enabled (i.e. reflective) state shown in  FIG. 7B , oil droplet  122  is squeezed (i.e. deformed) away from and does not contact any portion of hemi-bead  120 . A thin layer of oil nevertheless remains on and coats the entirety of circular hydrophobic region  126 , within contact line  154 , including the central portion of circular hydrophobic region  126  directly beneath hemi-bead  120 &#39;s non-reflective, central circular region. In this electro-deformed, reflective state, light ray  158  incident on hemi-bead  120 &#39;s non-reflective, central circular region is refracted through hemi-bead  120  toward substrate  124  which reflects the ray back through hemi-bead  120  in a direction approximately opposite that of incident ray  158  as shown at  166  in  FIG. 7B . Light ray  162  incident on hemi-bead  120 &#39;s reflective, annular region undergoes TIR within hemi-bead  120  and is reflected back in a direction approximately opposite that of incident ray  162 , as shown at  168  in  FIG. 7B . 
         [0058]    The transition between the  FIG. 7A  TIR-frustrated (i.e. non-reflective) state and the  FIG. 7B  TIR-enabled (i.e. reflective) state is completely defined by the energetics of the system. Consequently, the transition can occur extremely quickly and reproducibly, facilitating construction of a display capable of displaying full motion video images. Moreover, since the embodiment of  FIGS. 7A and 7B  does not require particles  26 , potential problems associated with particle agglomeration are avoided. 
         [0059]    The optical properties of substrate  124 , hydrophobic regions  126  and hydrophilic coating  128  are not critical. It is only desirable that central area  127  above and corresponding to electrode  156  (i.e. the area within oil droplet  122 &#39;s electro-deformed generally hemi-toroidal shape shown in  FIGS. 7B and 8B ) be either specularly or diffusely reflective. For example, substrate  124 , hydrophobic regions  126  and hydrophilic coating  128  may each be either specularly or diffusely reflective; or hydrophobic regions  126  may be transparent, with hydrophilic coating  128  and substrate  124  both being either specularly or diffusely reflective; or hydrophobic regions  126  and hydrophilic coating  128  may both be transparent, with substrate  124  being either specularly or diffusely reflective. 
         [0060]      FIGS. 12A and 12B  depict an embodiment in which the uppermost portion of substrate  124 , namely hydrophobic region  126 , is absorptive, instead of being reflective as previously described in relation to  FIGS. 7A ,  7 B,  10 A and  10 B. Also, in the embodiment of  FIGS. 12A and 12B , droplet  122  is non-absorptive (i.e. transparent) instead of being absorptive as in the case of droplet  122  previously described in relation to  FIGS. 7A ,  7 B,  10 A and  10 B. Droplet  122  thus has a higher refractive index than hemi-bead  120  in the embodiment of  FIGS. 12A and 12B .  FIG. 12A  depicts the TIR-frustrated or non-reflective state in which droplet  122  has a normally relaxed shape and causes optical interference with light rays that would otherwise be reflected by TIR or transmitted through hemi-bead  120 .  FIG. 12B  depicts the TIR-enabling (i.e. reflective) state in which droplet  122  is deformed into a generally hemi-toroidal shape away from and not contacting hemi-bead  120 &#39;s central, circular non-reflective region. 
         [0061]    In the TIR-frustrated or non-reflective state ( FIG. 12A ) light ray  178  incident on hemi-bead  120 &#39;s non-reflective, central circular region is refracted through hemi-bead  120  and droplet  122  toward substrate  124  as previously described in relation to ray  62  depicted in  FIG. 2 , and is absorbed by absorptive hydrophobic region  126  as shown at  180 . Light ray  182  incident on hemi-bead  120 &#39;s reflective, annular region initially undergoes TIR as indicated at  184 , but the reflected ray is then refracted through hemi-bead  120  and droplet  122  toward substrate  124  and is also absorbed by absorptive hydrophobic region  126  as shown at  186  in  FIG. 12A . 
         [0062]    In the electro-deformed, TIR-enabled (i.e. reflective) state shown in  FIG. 12B , oil droplet  122  is squeezed (i.e. deformed) away from and does not contact any portion of hemi-bead  120 . A thin layer of oil nevertheless remains on and coats the entirety of circular hydrophobic region  126 , within contact line  154 , including the central portion of circular hydrophobic region  126  directly beneath hemi-bead  120 &#39;s non-reflective, central circular region. In this electro-deformed, reflective state, light ray  188  incident on hemi-bead  120 &#39;s non-reflective, central circular region is refracted through hemi-bead  120  toward substrate  124  and is absorbed by absorptive hydrophobic region  126  as shown at  190  in  FIG. 12B . Light ray  192  incident on hemi-bead  120 &#39;s reflective, annular region undergoes TIR within hemi-bead  120  and is reflected back in a direction approximately opposite that of incident ray  192 , as shown at  194  in  FIG. 12B . It can thus be seen that a substantial fraction of light rays incident on hemi-bead  120 &#39;s non-reflective, central circular region are transmitted through hemi-bead  120  to substrate  124  when droplet  122  is in the electro-deformed, reflective state shown in  FIG. 12B . 
         [0063]    Although some light rays are absorbed in the electro-deformed, TIR-enabled (i.e. reflective) state shown in  FIG. 12B , the embodiment of  FIGS. 12A and 12B  nevertheless has practical application. For example, it may be more feasible in some cases to provide an absorptive substrate than to provide a sufficiently absorptive fluid medium (e.g. oil containing a light absorptive dye) to yield adequate light absorption in the previously described embodiments of  FIGS. 7A &amp; 7B  and  10 A &amp;  10 B. 
         [0064]    While a number of exemplary aspects and embodiments have been discussed above, those of skill in the art will recognize certain modifications, permutations, additions and sub-combinations thereof. For example, hydrophobic regions  126  need not be patterned atop hydrophilic coating  128  as shown in  FIGS. 7A and 7B . Instead, hydrophobic regions  126  may be formed in the same plane as hydrophilic coating  128 , as shown in  FIGS. 10A and 10B . In this example, hydrophobic regions  126  may be transparent, with substrate  124  and hydrophilic coating  128  each being either specularly or diffusely reflective. It is therefore intended that the following appended claims and claims hereafter introduced are interpreted to include all such modifications, permutations, additions and sub-combinations as are within their true spirit and scope.