RELATED APPLICATIONS 
       [0001]    This application claims benefit of U.S. Provisional Application 61/805,391 filed on Mar. 26, 2013. 
     
    
     TECHNICAL FIELD 
       [0002]    This disclosure pertains to attainment of high brightness in wide viewing angle 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; 6,891,658; 7,164,536; 7,286,280 and 8,040,591; all of which are incorporated herein by reference. 
       BACKGROUND 
       [0003]      FIG. 1A  depicts a portion of a prior art reflective (i.e. front-lit) electrophoretically frustrated total internal reflection (TIR) modulated display  10  of the type described in U.S. Pat. Nos. 6,885,496; 6,891,658; 7,164,536 and 8,040,591. 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 1 &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 1 ˜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  and  48  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  and  48  as illustrated to the left of dashed line  28 , suspended particles  26  are electrophoretically moved adjacent the surface of the monolayer of beads  18  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 or modulating 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  and  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  and  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  and  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 η 1 . A light ray  62  perpendicularly incident (through material  16 ) on hemi-bead  60  at a radial distance a from hemi-bead  60 &#39;s center 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 center 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 center 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, 3B and 3C  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 &lt;a≦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 a 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  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]    The reflective, white annular region  80  surrounding the non-reflective, dark circular region  82  presents a problem commonly referred to as the “dark pupil” problem which reduces the reflectance of the display. The display&#39;s performance is further reduced by transparent electrode  46 , which may be formed by provision of a transparent conductive coating on hemi-beads  14 . Such coatings typically absorb about 5% to 10% of the incident light. Since a light ray typically reflects several times, this can make it difficult to achieve efficient reflection. A further related problem is that it can be expensive and challenging to apply such a coating to a contoured hemispherical surface. 
         [0016]    The dark pupil problem can be addressed by reflecting back toward hemi-beads  14  (i.e. “recycling”) light rays which pass through the non-reflective, dark circular region  82  of any of hemi-beads  14 . An approach to solving this problem and enhancing the brightness of the display is to equip the display with a reflective component to reflect the light back through the pupil and towards the viewer.  FIG. 5  depicts a prior art reflective (i.e. front-lit) frustrated total internal reflection (TIR) modulated display  100  of the type described in PCT Application No. WO 2006/108285 A1 and South Korean patent No. 10-2007-7026347. Display  100  includes a transparent outer sheet  102  formed by partially embedding a large plurality of high refractive index transparent spherical or approximately spherical beads  104  in the inward surface of a high refractive index polymeric material  102  having a flat outward viewing surface  106  by which a viewer views the display image. On the surface of the plurality of spherical beads  104  is a substantially transparent electrode  107 . 
         [0017]    An electrophoresis medium  108  is contained within the reservoir or cavity formed between the portions of beads  104  which protrude inwardly from material  102  and the lower or rear sheet  110 . On the inward surface of the rear sheet  110  is an electrode layer  111 . The medium  108  is an inert, low refractive index, low viscosity liquid such as a fluorinated hydrocarbon. Other liquids may also be used as electrophoresis medium  108 . A bead:liquid TIR interface is thus formed. Medium  108  further contains a finely dispersed suspension of light absorbing, electrophoretically mobile particles  112 . 
         [0018]      FIG. 5  further depicts a prior art reflective, continuous, porous, membrane  118  disposed between the inward surfaces of hemisphere beads  116  and rear sheet  110  to enhance the brightness of the TIR display. The average diameter of the pores in the continuous membrane  118  is substantially greater (e.g. about 10 times greater) than the average diameter of absorptive particles  112 . The pores in membrane  118  constitute a sufficiently large fraction (e.g. at least 20%) of the total surface area of membrane  118  to substantially permit unimpeded passage of absorptive particles  112  through membrane  118 . Membrane  118 &#39;s outward surface  120  is highly reflective, and may be either diffusely or specularly reflective. 
         [0019]    In the absence of electrophoretic activity, as is illustrated to the left of dashed line  114  in  FIG. 5  prior art, the smaller absorptive particles  112  tend to settle through membrane  140 &#39;s pores, toward the rear electrode layer  111  on rear sheet  110  or if the electrophoretic particles are driven to the rear electrode  111  under the influence of an applied electric field. Reflectance is thus increased and enhanced, since incident light rays (e.g. ray  122 ) which would otherwise have passed through the “dark pupil” region of the hemisphere beads  116  and would have been absorbed by, such as, the absorptive particles  112  located at the lower sheet  110 , are instead reflected (e.g. ray  124 ) by membrane  118 &#39;s reflective outward surface  120 . Light rays (e.g. ray  126 ) which are incident upon reflective annular regions of the hemisphere beads are totally internally reflected (e.g. ray  128 ). 
         [0020]    When a voltage is applied across medium  108 , as is illustrated to the right of dashed line  114  in the prior art depicted in  FIG. 5 , absorptive particles  112  are electrophoretically moved through membrane  118 &#39;s pores and attracted to electrode layer  107  on the inward surfaces of hemisphere beads  116 . When so moved into this absorptive state, particles  112  absorb light rays (e.g. ray  130 ) which are incident upon the annular regions of the hemisphere beads by frustrating or modulating TIR, and also absorb light rays (e.g. rays  132 ) which do not undergo TIR and which would otherwise pass through beads  104 . Membrane  118 &#39;s pores allow absorptive particles  112  to move outwardly into contact with the surface of hemisphere beads  116  in the absorptive state; and to move inwardly away from hemisphere beads  116  in the reflective state, thus obscuring absorptive particles  112  from direct view in the reflective state. 
         [0021]    As described in the preceding paragraphs, the porous reflective membrane&#39;s purpose is to reflect the light that passes through the dark pupil of the hemi-beads  116  back through the pupil region of the hemi-beads  116  and towards the viewer to enhance the brightness of the display as depicted in  FIG. 5 . An alternative porous reflective membrane structure is disclosed herein. This disclosure pertains to a TIR-based display comprising of a frustratable (i.e. the degree to which the incident light undergoes total internal reflection can be controllably modified by altering the optical properties, and specifically the refractive index values, at or near the interface at which the light undergoes TIR), optically transparent, hemispherically-contoured front sheet and a multi-functional porous continuous reflective membrane. A hemispherically-contoured front sheet is a substantially flat sheet that has a plurality of protruding surface features, said surface features having a substantially hemispherical shape. Herein, a porous continuous membrane is further comprised of a top electrically conductive metal layer that faces the hemispherical contoured surface of the optically transparent front sheet. The top metal layer is porous and continuous and acts as both a light reflector to enhance the brightness of the display and as the top electrode layer. This new structure disclosed herein simplifies manufacturing of TIR-based displays described herein and greatly lowers manufacturing costs. Additionally, by removing the mostly transparent electrode layer from the surface of the hemispherical beads as shown in the prior art display in  FIG. 5 , less light will be lost due to absorption by the electrode layer thus further increasing the brightness of the display. ITO can degrade over time under various conditions such as exposure to high voltages, temperatures and contact with the electrophoretic medium. As ITO degrades it becomes less transparent and further absorbs light leading to a further decrease in brightness of the display. Furthermore, removing the ITO layer and replacing with a metal layer as the top electrode reduces the resistance leading to increased switching uniformity. 
         [0022]    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 
         [0023]    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. 
           [0024]      FIG. 1A  is a greatly enlarged, not to scale, fragmented cross-sectional side elevation view, of a portion of an electrophoretically frustrated or modulated prior art reflective image display. 
           [0025]      FIG. 1B  schematically illustrates the wide angle viewing range a of the  FIG. 1A  display, and the angular range β of the illumination source. 
           [0026]      FIG. 2  is a greatly enlarged, cross-sectional side elevation view of a hemispherical (“hemi-bead”) portion of one of the spherical beads of the  FIG. 1A  apparatus. 
           [0027]      FIGS. 3A, 3B and 3C  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. 
           [0028]      FIGS. 4A, 4B, 4C, 4D, 4E, 4F and 4G  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. 
           [0029]      FIG. 5  is a greatly enlarged, not to scale, fragmented cross-sectional side elevation view, of a portion of an electrophoretically frustrated or modulated prior art reflective image display equipped with a reflective porous continuous membrane and a transparent front electrode layer on the hemispherical surface. 
           [0030]      FIGS. 6A and 6B  are greatly enlarged, not to scale, fragmented cross-sectional side elevation views of a single pixel portion of an electrophoretically frustrated (i.e. modulated) reflective image display comprising of an insulating porous continuous membrane with a top porous reflective electrically conductive continuous metal layer acting as the front electrode layer located between the front hemispherical surface and the rear electrode.  FIGS. 6A and 6B  respectively depict the display pixel&#39;s light reflecting and light absorbing (i.e. non-reflective) states. 
           [0031]      FIG. 7  is a greatly enlarged, not to scale, overhead view of a portion of a porous continuous membrane with a top reflective continuous and electrically conductive metal layer. 
           [0032]      FIG. 8  illustrates the illumination of a display with a hemispherically-contoured surface in a semi-retro-reflective manner by a diffuse light source subtending an angle α. 
       
    
    
     DESCRIPTION 
       [0033]    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. 
         [0034]      FIGS. 6A and 6B  depict a display  200  comprising of a hemispherically-contoured surface  202  formed integrally with display  200 &#39;s transparent outward sheet  204 . In contrast, display  10 &#39;s hemi-spherical surface is formed by a closely packed layer of discrete beads  14  partially embedded in sheet  12  as shown in  FIG. 1A . Either hemispherical or related surface structure depicted in displays  10  and  200  can be used in combination with the inventions described herein. It should be noted that the hemispherically-contoured front sheet which comprises of a plurality of hemispherical shaped protrusions may be fabricated by various methods such, but not limited to, embossing, etching, molding, self-assembly, printing, lithography or micro-replication. Display  200  is further comprised of a rear backplane support  206  and rear backplane electrode layer  208 . The rear electrode  208  may be comprised of a patterned or segmented array or a conventional thin film transistor (TFT) array or a combination thereof. Within the cavity or reservoir  210  defined by the hemispherically-contoured surface  202  and the rear electrode layer  208  is a liquid medium  212  comprising of suspended electrophoretically mobile and light absorbing particles  214 . The particles  214  may be comprised of an organic material or an inorganic material or a combination of organic and inorganic materials. Electrophoretic particles  214  may be moved through the liquid medium  212  by application of an electric field. The liquid medium  212  may be, for example, an inert, low refractive index (i.e. less than about 1.35), low viscosity, electrically insulating liquid such as Fluorinert™ perfluorinated hydrocarbon liquid (η 1 ˜1.27) available from 3M, St. Paul, Minn. is a suitable electrophoresis medium. Other liquids, such as hydrocarbons or water can also be used as electrophoresis medium  212 . 
         [0035]    Display  200  depicted in  FIGS. 6A and 6B  further comprises of a porous continuous membrane  216  situated between hemispherical surface  202  and backplane electrode  208 . Dotted lines  218  represent the continuous nature of the porous membrane  216 . Membrane  216  may be formed of a variety of materials such as, but not limited to, glass or a polymeric material such Teflon®, Mylar®, polyethylene terephthalate, polyimide or polycarbonate. Membrane  216  has a thickness of at least about 5 to about 40 microns. More preferably, membrane  216  has a thickness of about 10 to about 20 microns. 
         [0036]    As depicted in  FIGS. 6A and 6B , membrane  216  further comprises a top porous continuous reflective metal layer  220  on the outward side of membrane  216  (facing hemi-spherically-contoured surface  202 ). Dotted lines  222  represent the continuous nature of the porous metal layer  220 . The metal layer may be comprised of, but not limited to, aluminum, gold, silver or combinations thereof. Metal layer  220  may be formed on membrane  216  by coating membrane  216 &#39;s outward surface with a reflective conductive material such as, but not limited to, electron beam evaporated, vacuum deposited or sputter coated thin metal film that serves as the common (ground) electrode of display  200 . This metal layer  220  has a thickness of at least about 0.040 microns to about 0.20 microns. More preferably it has a thickness of about 0.10 microns to about 0.20 microns. The combined membrane:metal layer structure is porous and continuous and has a thickness of at least about 5 to about 40 microns, more preferably a thickness of at least about 10 to about 21 microns. Metal layer  220  acts both as an electrode and a light reflector. This is in contrast to display  100  in  FIG. 5  where the membrane is inert and acts only as a light reflector while the front electrode  107  is instead located on the surface of hemispherical beads  116 . By preferentially having a porous metal layer  220  on the porous membrane  216  instead of on the hemispherically-contoured surface  202  greatly simplifies the manufacturing process and reduces manufacturing costs of the display. It is more difficult and costly to deposit a uniform conductive layer on the contoured hemispherical surface  202 . Additionally, having the conductive layer (i.e. front electrode) on contoured hemispherical surface  202  further requires the layer to be transparent to allow for light to pass through contoured hemispherical surface  202  to be absorbed by the electrophoretically mobile particles  214  to frustrate TIR and create a dark state. For example, ITO is a common transparent conductive material and the most likely candidate for the transparent conducting layer but is typically more expensive than, for example, aluminum. Additionally, ITO is not completely transparent as some light is absorbed (estimated to be about 5% to about 10%) thus lowering the overall reflectance and brightness of the display. Another advantage of using aluminum as the conductive layer is that it has a wider process window. If the thickness of the ITO layer is increased the resulting reflectance decreases, but if the thickness of the ITO layer is decreased enough then there is a possible risk of a loss of electrical contact between the hemispheres. The coating of ITO is directional such that when ITO is deposited on the horizontal surface of the hemispherical beads it tends to be thicker than when ITO is deposited on the vertical surfaces of the beads leading to discontinuity in the coating just above the hemisphere equator where the ITO is very thin or even non-existent. A loss of or greatly diminished electrical contact between the hemispheres reduces the capacitance of the electrode leading to detrimental effects like slower switching times. An electrode made out of aluminum, for example, has a wider process window as the thickness can vary by a factor of two without much impact on the performance. 
         [0037]    As mentioned in the preceding paragraphs, the metal:membrane structure is porous, enabling light absorbing electrophoretically mobile particles  214  to readily move through apertures  224  that penetrate both the membrane  216  and metal layer  220 , as display  200 &#39;s pixels are selectively switched between the light reflecting state ( FIG. 6A ) and the light absorbing or dark state ( FIG. 6B ). An electrophoresis medium  212  comprising of electrophoretically mobile particles  214  is maintained adjacent hemi-spherical surface  202  by containment of medium  212  within reservoir  210  defined by hemi-spherical surface  202  and backplane electrode layer  208 . The apertures  224  in the metal:membrane structure have diameters of at least about 5 microns. The apertures  224  have diameters in the range of at least about 5 microns to about 20 microns. More preferably, the apertures  224  have diameters in the range of about 10 microns to about 15 microns. The apertures  224  in the metal:membrane structure may be ordered in substantially regular arrays or aligned in a substantially random or irregular array or any combination thereof. The micron centers (i.e. the center point of each aperture) of the apertures  224  are spaced at least about 10 microns apart. More preferably apertures  224  are spaced about 25 microns to about 35 microns apart. 
         [0038]      FIG. 7  further illustrates the various aspects that must be considered in the design of the membrane:metal layer structure.  FIG. 7  is an overhead view of a portion of the apertured continuous membrane:metal layer structure. In this view looking down on the top of the reflective metal layer  220  (the membrane layer is hidden behind the metal layer), a series of apertures  224  are arranged in a substantially regular array for illustration only. As mentioned earlier, the array of apertures  224  may also be arranged in a substantially irregular or random array or any combination thereof. The diameter of each aperture, d a , may be substantially uniform as depicted in  FIG. 7  or may vary in size within the membrane:metal layer. The spacing distance of the micron centers of the apertures  224  with its neighboring apertures represented by d mc , may be substantially uniform in distance as depicted in  FIG. 7  or may vary in distance within the membrane:metal layer. 
         [0039]    In the light reflecting state shown in  FIG. 6A , particles  214  are attracted inwardly under an applied electric field towards the rear backplane electrode  208  where they accumulate. In the light absorbing state shown in  FIG. 6B , particles  214  are attracted outwardly to and accumulate atop metal layer  220  and adjacent hemi-spherical surface  202 , preventing layer  220  from reflecting light rays outwardly through the pupil region towards the viewer of the hemi-beads which form hemispherical surface  202 . More particularly, in the light reflecting state, a substantial fraction of the light rays passing through transparent outward sheet  204  undergo TIR at the inward side of hemi-spherical surface  202 . For example, representative incident light ray  226  is refracted through surface  204  and hemispherical surface  202 . Ray  226  undergoes TIR two or more times at the bead:liquid TIR interface, as indicated at points  228  and  230 . The totally internally reflected rays are then refracted back through hemispherically-contoured surface  202  and sheet  204  and emerges as ray  232 , achieving a “white” appearance in each reflection region or pixel of the display  200 . 
         [0040]    Some incident light rays, such as representative light ray  234 , are refracted through surface  204  and hemispherically-contoured surface  202  but do not undergo TIR at the bead:liquid TIR interface. Instead, ray  234  passes through hemispherically-contoured surface  202  and is reflected outwardly by metal layer  220  toward surface  202  and the viewer. The reflected ray is then refracted back through the pupil region of hemispherically-contoured surface  202  and sheet  204  and emerges as ray  236 , again achieving a “white” appearance and improving the brightness of display  200 . 
         [0041]    Some other incident light rays, such as representative ray  238 , are “lost” in the sense that they do not emerge outwardly from display  200 . For example, ray  238  is refracted through surface  204  and hemispherically-contoured surface  202 , but does not undergo TIR at the bead:liquid TIR interface and is not reflected by metal layer  220 . Instead, ray  238  passes through one of membrane  204 &#39;s apertures  224  and is absorbed, for example, at an inner wall portion of the aperture, as shown in  FIG. 6A . 
         [0042]    A switchable voltage (i.e. electric field) can be applied across electrophoresis medium  212  via electrodes  208  and  220  as indicated in  FIGS. 6A and 6B , respectively. When a pixel of display  200  is switched to the light absorbing state shown in  FIG. 6B , particles  214  are electrophoretically moved outwardly through membrane  216 &#39;s apertures  224  toward electrode  220 . The moved particles  214  form a relatively thick layer atop electrode  220 , such that the electrophoretically mobile particles  214  make optical contact with the inward side of hemispherically-contoured surface  202 , thus frustrating TIR (i.e. particles  214  are within about 0.25 micron of hemispherically-contoured surface  202 , or closer). When electrophoretically moved as aforesaid, particles  214  scatter or absorb light, by modifying the imaginary and possibly the real component of the effective refractive index at the hemi-bead:liquid TIR interface. This is illustrated by light rays  240 ,  242 ,  244  and  246  which are scattered and/or absorbed as they strike particles  214  inside the evanescent wave region at the bead:liquid TIR interface, as indicated at points  248 ,  250 ,  252  and  254 , respectively, thus achieving a “dark” appearance in each non-reflective absorption region or pixel of the display. The net optical characteristics of display  200  can be controlled by controlling the voltage applied across medium  212  via electrodes  208  and  220 . The electrodes can be segmented to control the electrophoretic activation of medium  212  across separate regions or pixels of hemispherically-contoured surface  202 , thus forming an image. 
         [0043]    Another factor to consider is the appropriate relative spacing and alignment of transparent outward sheet  204 , membrane:metal layer and rear electrode layer  208  can be achieved by providing loose or attached spacer beads and/or spacers (not shown) or a combination thereof on sheet  204 , on rear electrode layer  208  or on the membrane:metal layer or combinations thereof. The spacing between the hemispherically-contoured surface  202  and metal layer  220  atop membrane  216  is at least about 2 microns. More preferably the spacing between the hemispherically-contoured surface  202  and metal layer  220  atop membrane  216  is about 4 microns to about 6 microns. The spacing between the rear backplane electrode  208  and the bottom of membrane  216  facing the backplane electrode  208  is at least about 10 microns. More preferably the spacing between the rear backplane electrode  208  and the bottom of membrane  216  facing the backplane electrode  208  is about 30 microns to about 50 microns. The spacing between the hemispherically-contoured surface  202  and backplane electrode surface  208  that forms the reservoir cavity  210  is overall at least about 25 microns and more preferably about 30 microns to about 80 microns. In addition to the diameter of the apertures, d a , and the spacing between the micron centers, d mc , display  200 &#39;s switching speed is further dependent on the time required for particles  214  to move throughout the display as it is switched between the non-reflective and reflective states. Thus, the spacing distance between the various layers of the display is critical. 
         [0044]    The reflectance of the surface is defined as the ratio of the luminance of the display to the luminance of a diffuse white reflectance standard (typically having a perfectly diffuse, or Lambertian, reflectance of 98%) measured using the same technique and under the same illumination conditions. The reflectance of a surface that exhibits semi-retro-reflective characteristics depends on the nature of the illumination conditions. If the surface is viewed in a perfectly diffuse illumination environment, there will be no apparent increase in reflectance caused by the semi-retro-reflective characteristics. In contrast, if the surface is viewed in an illumination environment that is not perfectly diffuse, a surface that exhibits semi-retro-reflective characteristics may have an apparent increase in reflectance. Such a lighting environment as shown in  FIG. 8  on the outer surface of display  200  can be caused by illumination by a diffuse light source  260  subtending a half-angle of α, where to the extent that α is less than 90°, the apparent reflectance will increase as viewed by a viewer  262 . In one embodiment where, for example, high brightness is preferred, each hemisphere in hemispherically-contoured surface  202  may have a diameter of about 20 microns. The porous membrane:metal structure is a substantially flat sheet about 12.15 microns thick with the membrane being a thickness of about 12 microns while the metal layer a thickness of about 0.15 microns. The membrane:metal layer is perforated with about 12 micron diameter apertures  224  spaced on roughly 30 micron centers, such that the area fraction of apertures  224  on the membrane:metal layer structure is about 12%. The spacing between the hemispherically contoured surface  202  and the metal layer  220  on the membrane:metal layer is about 5 microns while the spacing between the bottom of the membrane layer  216  and top surface of the rear electrode layer  208  is about 50 microns making the total distance from the hemispherically-contoured surface  202  and rear electrode surface about 65 micron. In this embodiment, approximately 88% of the light rays incident on metal layer  220  do not encounter one of apertures  224  and are reflected by metal layer  220 . If the metal has a reflectance of approximately 80% as a result of approximately 20% absorption (such as is the case for a reflective layer of aluminum), then the membrane:metal layer will have an overall reflectance of approximately 70% (i.e. 80% reflection of 88% of the light rays incident on the membrane:metal layer). 
         [0045]    In another embodiment where a higher switching speed, for example, is preferred, each hemisphere in hemispherically-contoured surface  202  may have a diameter of about 5 microns. Membrane:metal layer structure is substantially a flat sheet about 10 microns thick with the membrane being a thickness of about 10 microns while the metal layer a thickness of about 0.10 microns. The membrane:metal layer is perforated with about 12 micron diameter apertures  224  spaced on roughly 20 micron centers, such that the area fraction of apertures  224  on the membrane:metal layer structure is about 16%. The spacing between the hemispherically-contoured surface  202  and the metal layer  220  on the membrane:metal layer is about 10 microns while the spacing between the bottom of the membrane layer  216  and top surface of the rear electrode layer  208  is about 30 microns making the total distance from the hemispherically-contoured surface  202  and rear electrode surface about 50 microns. In this embodiment, approximately 84% of the light rays incident on metal layer  220  do not encounter one of apertures  224  and are reflected by metal layer  220 . If the metal has a reflectance of approximately 80% as a result of approximately 20% absorption (such as is the case for a reflective layer of aluminum), then the membrane:metal layer will have an overall reflectance of approximately 67% (i.e. 80% reflection of 84% of the light rays incident on the membrane:metal layer. It should be noted that not only speed and brightness should be considered when factoring in the diameter, d a , of the apertures  224  and the spacing of the apertures, d mc , but also the structural rigidity and stability of the resulting porous membrane:metal layer. The more porous a structure is the weaker it may become unless a thicker membrane is used or alternative and potentially more costly materials are to be used. 
         [0046]    In the reflective state, shown in  FIG. 6A , typically about half of the light rays incident on sheet  204  are reflected by TIR. The remaining light rays reach membrane:metal layer structure and 70% of those rays are reflected by metal layer  220 . In a perfectly diffuse illumination environment where there is no gain in reflectance as a result of semi-retro-reflection, such an embodiment is about 87% reflective, where 36% of the reflectance is a result of total internal reflection of light incident on the hemispheres and 51% of the reflectance (i.e. 80% of the remaining 64% of the incident light that travel through the so-called “dark pupil” region of the hemispheres) is a result of light rays that do not encounter one of apertures  224  and are reflected by metal layer  220 . Furthermore, if the membrane:metal layer is positioned approximately at the focal plane of hemispherically-contoured surface  202 , metal layer  220  will semi-retro-reflect light rays, achieving an optical gain enhancement for all of the reflected light rays. In a lighting environment described by  FIG. 8 , where a diffuse light source  260  subtending a half-angle of α directs light onto the outward surface of outward sheet  204  from overhead (i.e. from above the display viewer&#39;s head) or somewhat from behind, rather than the primary source of illumination being positioned in front of the viewer  262 , this embodiment will have a reflectance of about 157%, approximately 1.8 times greater than the reflectance in a perfectly diffuse illumination environment. 
         [0047]    In the display embodiments described herein, they may be used in applications such as in, but not limited to, electronic book readers, portable computers, tablet computers, wearables, cellular telephones, smart cards, signs, watches, shelf labels, flash drives and outdoor billboards or outdoor signs. 
         [0048]    Embodiments described above illustrate but do not limit this disclosure. 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. Accordingly, the scope of this disclosure is defined only by the following claims.
A brightness enhancing structure for a reflective display incorporates a transparent sheet having an inward hemispherical surface, a backplane electrode, an apertured membrane between the hemispherical surface and the backplane electrode, and a light reflecting electrode on an outward side of the membrane. A voltage source connected between the electrodes is switchable to apply a first voltage to move the particles inwardly through the apertured membrane toward the backplane electrode, and a second voltage to move the particles outwardly through the apertured membrane toward the light reflecting electrode. Movement of the particles toward the light reflecting electrode frustrates total internal reflection of light rays at the hemispherical surface. Movement of the particles toward the backplane electrode permits total internal reflection of light rays at the hemispherical surface, and outward reflection from the light reflecting electrode toward the hemispherical surface of light rays which pass inwardly through the hemispherical surface.