WO2022245713A1 - Reflective display device with dead-space reducing optical elements - Google Patents

Abstract

A display device can include reflective pixels that include an output surface having an active surface and an inactive surface, where the reflective pixel can controllably reflect a color of light from the active surface. The device also includes a dead-space reducing optical element positioned over the reflective pixels, including a pixel facing surface including an pixel interface aperture positioned to interface with the active surface and to receive light reflected through the active surface, and a viewing surface, opposite the pixel facing surface, including an output aperture positioned to direct the light received at the pixel interface aperture outwardly from the viewing surface, where the output aperture has an area that is larger than an area of the pixel interface aperture and less than or equal to a pixel area.

Description

REFLECTIVE DISPLAY DEVICE WITH DEAD-SPACE REDUCING OPTICAL ELEMENTS

CROSS REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to U S. Provisional Application No. 63/189,588, filed May 17, 2021 , entitled “Reflective Display Device with Dead-Space Reducing Optical Elements,” which is incorporated herein by reference in its entirety.

TECHNICAL FELD

[0002] The present disclosure generally relates to reflective display devices, and in particular to optical elements incorporated in ref lective display devices.

BACKGROUND

[0003] Reflective display pixels can have a pixel area that can include an active surface and an inactive surface. At the active surface, (AACT) incoming ambient illumination is controliabiy reflected outwards towards a viewer or viewers. The inactive surface (A:MACT) generally frames the active area. The inactive area can absorb the incoming light or reflects it (or scatters it) as unmodulated am blent background noise. The portion of ambient illumination striking this inactive pixel area is undesirable, as it reduces the pixel^’s actively modulated net viewing brightness, and in some instances, it also reduces the pixel’s effective contrast ratio by elevating the level of spurious background light.

SUMMARY

[0004] In some aspects, the techniques described herein relate to a reflective display device, including (1) a reflective pixel including: an output surface including an active surface and an inactive surface, a fluid chamber positioned over a reflective surface within the active surface, and an electrically controlled actuator configured to controliabiy cause reflection of a color of light outwardly from the active surface by altering pressure within the fluid chamber to cause corresponding changes in a quantity of fluid within the fluid chamber; and (2) a dead-space reducing optical element positioned over the output surface of the reflective pixel, the dead-space reducing optical element Including: a pixel facing surface including a pixel interface aperture positioned to interface with the active surface of the reflective pixel and to receive the light reflected through the active surface of the reflective pixel, a viewing surface opposite the pixel facing surface, the viewing surface including an output aperture positioned to direct the light received at the pixel interface aperture outwardly from the viewing surface, wherein the output aperture has an area that is larger than an area of the pixel interface aperture and less than or equal to a pixel area including an area of the active surface and an area of the inactive surface, and at least one sidewall that extends between the pixel facing surface and the viewing surface.

[0005] In some aspects, the techniques described herein relate to a reflective display device, including: (1) a reflective pixel including an output surface including an active surface and an inactive surface, the ref lective pixel configured to controliably reflect a color of light outwardly from the active surface; and (2) a dead-space reducing optica! element positioned over the output surface of the reflective pixel, the dead-space reducing optica! element including: a pixel facing surface including a pixel interface aperture positioned to interface with the active surface of the reflective pixel and to receive the light reflected through the active surface of the reflective pixel, a viewing surface opposite the pixel facing surface, the viewing surface Including an output aperture positioned to direct the light received at the pixel interface aperture outwardly from the viewing surface, wherein the output aperture has an area that is larger than an area of the pixel interface aperture and less than or equal to a pixel area including an area of the active surface and an area of the inactive surface, and at least one sidewall that extends between the pixel facing surface and the viewing surface.

[0008] In some aspects, the techniques described herein relate to a reflective display device, including: a reflective pixel including an output surface including an active surface and an inactive surface, the reflective pixel configured to controliably reflect a color of light outwardly from the active surface; and a transparent dead-space reducing optical element positioned over the output surface of the reflective pixel, including: a pixel facing surface positioned to interface with the active surface of the reflective pixel and to receive light reflected through the active surface of the reflective pixel, a curved viewing surface opposite the pixel facing surface, the curved viewing surface positioned to direct ambient incident light to the active area, and to direct light received at the pixel facing surface outwardly from the curved viewing surface to form a virtual image of the active surface having an area that is greater than an area of the active surface and equal to or less than an area of the reflective pixel, wherein the curved viewing surface has a convex shape, and at least one sidewall that extends between the pixel facing surface and the curved viewing surface. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] Further aspects of the present disclosure will be readily appreciated upon review of the detailed description of its various embodiments, described below, when taken in conjunction with the accompanying drawings.

[0008] FIG. 1A-1 F show various views of a portion of a ref lective display device incorporating a first dead-space reducing optical element.

[0009] FIGS. 1G-1 H show various views of a portion of a reflective display device incorporating a second dead-space reducing optical element.

[0010] FIGS. 2A-2F show various views of a portion of a reflective display device Incorporating a third exam pie dead-space reducing optical element.

[0011] FIGS. 2G-2I show perspective views of Fresnel lens equivalents of the example dead- space reducing optical elements.

[0012] FIGS. 2J-2L illustrate operating principles of example dead-space reducing optical elements.

[0013] FIGS. 3A-3F show detailed cross-sectional views of a portion of display devices with various optical elements.

DETAILED DESCRIPTION

[0014] Before the present disclosure is described in greater detail, it is to be understood that this disclosure is not limited to particular aspects described, and as such may, of course, vary, it is also to be understood that the terminology used herein is forthe purpose of describing particular aspects only, and is not intended to be limiting. The skilled artisan will recognize many variants and adaptations of the aspects described herein. These variants and adaptations are intended to be included in the teachings of this disclosure.

[001 S] Ail publications and patents cited in this specification are cited to disclose and describe the methods and/or materials in connection with which the publications are cited. Ali such publications and patents are herein incorporated by references as if each individual publication or patent were specifically and individually indicated to be incorporated by reference. Such incorporation by reference is expressly limited to the methods and/or materials described in the cited publications and patents and does not extend to any lexicographical definitions from the cited publications and patents. Any lexicographical definition in the publications and patents cited that is not also expressly repeated in the instant specification should not be treated as such and should not be read as defining any terms appearing in the accompanying claims. The citation of any publication is for its disclosure prior to the filing date and should not be construed as an admission that the present disclosure is not entitled to antedate such publication by virtue of prior disclosure. Further, the dates of publication provided could be differentf rom the actual publication dates that may need to be independently confirmed.

[0016] Although any methods and materials similar or equivalent to those described herein can also be used in the practice or testing of the present disclosure, the preferred methods and materials are now described. Functions or constructions well-known in the art may not be described in detail for brevity and/or clarity. Embodiments of the present disclosure will employ, unless otherwise indicated, techniques of nanotechnology, organic chemistry, material science and engineering and the like, which are within the skill of the art. Such techniques are explained fully in the literature.

[0017] It should be noted that ratios, concentrations, amounts, and other numerical data can be expressed herein in a range format. It is to be understood that such a range format is used for convenience and brevity, and thus, should be interpreted in a flexible manner to include not only the numerical values explicitly recited as the limits of the range, but also to include all the individual numerical values or sub-ranges encompassed within that range as if each numerical value and sub-range is explicitly recited. To illustrate, a numerical range of “about 0.1% to about 5%” should be interpreted to include not only the explicitly recited values of about 0.1% to about 5%, but also include individual values (e.g., 1%, 2%, 3%, and 4%) and the sub-ranges (e.g., 0.5%, 1.1%, 2.2%, 3,3%, and 4.4%) within the indicated range. Where the stated range includes one or both of the limits, ranges excluding either or both of those included limits are also included in the disclosure, e.g. the phrase “x to y” includes the range from ‘x’ to y as well as the range greater than ‘x’ and less than ‘y’_· The range can also be expressed as an upper limit, e.g. ‘about x, y, z, or less’ and should be Interpreted to include the specific ranges of ^‘about x’, ‘about y’, and ‘about z’ as well as the ranges of less than x^', less than y^!, and less than z^'. Likewise, the phrase ‘about x, y, z, or greater’ should be interpreted to include the specif ic ranges of ‘about x’, ‘about y’, and ‘about z’ as well as the ranges of ‘greater than x’, greater than y’, and ‘greater than z^!. In some embodiments, the term “about” can include traditional rounding according to significant figures of the numerical value. In addition, the phrase “about ‘x’ to y”, where ‘x’ and y are numerical values, includes “about ‘x^’ to about ‘y”\ [0018] In some instances, units may be used herein that are non-metric or non-SI units. Such units may be, forinstance, in U.S. Customary Measures, e.g., as set forth by the National Institute of Standards and Technology, Department of Commerce, United States of America in publications such as NIST HB 44, NIST HB 133, NISTSP 811, NIST SP 1038, NBS Miscellaneous Publication 214, and the like. The units in U.S. Customary Measures are understood to include equivalent dimensions in metric and other units (e.g., a dimension disclosed as Ί inch” is intended to mean an equivalent dimension of “2.5 cm”; a unit disclosed as “1 pcf is intended to mean an equivalent dimension of 0.157 kN/m³; ora unit disclosed 100°F is intended to mean an equivalent dimension of 37.8°C; and the like) as understood by a person of ordinary skill in the art.

[0019] Unless defined otherwise, ail technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the specification and relevant art and should not be interpreted in an idealized or overly formal sense unless expressly defined herein.

[0020] The articles “a” and “an,” as used herein, mean one or more when applied to any feature in embodiments described in the specification and claims. The use of “a” and “an” does not limit the meaning to a single feature unless such a limit is specifically stated. The article “the” preceding singular or plural nouns or noun phrases denotes a particular specified feature or particular specified features and may have a singular or plural connotation depending upon the context in which it is used.

[0021] Electrically modulatabie reflective display pixels can include an opticaily-activearea (AACT) or an active surface, where incoming ambient illumination is reflected outwards towards a viewer or viewers, and an inactive area (AINACT) or an inactive surface that is not modulated. If these two areas were equal, a pixel fill factor (AACT/(AACT+ AINACT)) would be equal to 1 , where the pixel fill factor can be described as a ratio of an area of the active surface to a sum of the area of the active surface and an area of the inactive surface. The sum of the areas of the active and the inactive surfaces can also be referred to as a pixel area. The inactive area can absorb the incident light or reflect (or scatter) the incident light as unmodulated ambient background noise. The portion of ambient illumination striking this inactive pixel area can be undesirable, as it reduces the pixel’s actively modulated net viewing brightness, and in some cases it also reduces the pixel’s effective contrast ratio (CREFF = Bright State Brightness/Dark State Brightness) by elevating the level of spurious background light (adversely brightening the pixel’s Dark State, alternately called the electrically modulatable pixel’s black state or off state).

[0022] As discussed below, optical elements can be used in conjunction with the reflective pixels to reduce the effect of the inactive area on the image seen by the viewer, in particular, the optical elements can reduce the contribution of the light reflected or scattered from the inactive surface of the pixel in the image seen by the viewer.

[0023] The electrically-modulated reflective pixels can be assembled into the large-scale close- packed 2D arrays of actively controlled color configurable displays for use in electronic displays, including on-premise digital signage, fuel pricers, dynamic architectural facades, automotive roadway billboards, or any other display applications. Afield of viewforthe pixel can be described as an angular range about the pixel’s optica! axis normal to its output surface and in the horizontal viewing plane. While it is preferable in some use cases that the angular range be as wide as possible, full +/-90 hemispherical viewing may not be needed. In some instances, maintaining near peak brightness over at least +/-45-degrees may be desired with at least a reasonable brightness over+/-60 to +/-80-degrees depending on the particular use.

[0024] In some instances, the field of view can refer to an angular range over which the electrically-controlled color of the ambientiy-ii!uminated reflective pixels can be distinguished visually by an observer. In one example, the field of view can be measured goniometricaliy by mechanically rotating a calibrated brightness measuring instrument through a range of angular directions from the pixel axis (which is the axis normal to the pixel surface) to angles as large as 80-degrees from this axis. This brightness measuring instrument can be focused on one circular measurement area upon the colored surface of the ambiently-iiluminated array of pixels. The instrument can be positioned at a sufficient distance from the array of pixels to assure a brightness measuring spot (circular measurement area) whose diameter covers more than one pixel of the same electrically-controlled color, in some instances, the brightness measuring instrument can be a spectroradiometer (such as, for example, a Photo Research PR-650 or equivalent) or a spectrometer. In some such instances, the brightness measuring instrument can also measure the pixel array’s average color (or chromaticity, x and y) within the measurement area at each angular direction. The field of view can be determined quantitatively as the angle from the pixel axis where the ambient contrast ratio of a chosen color or colors (e.g,, red, green, blue, and white) fails below a typical industry visibility-standard such as 2:1. Ambient contrast ratio, in turn, can refer to a ratio of the brightness of the colored pixels to the brightness of the same pixels when electrically-switched to their black or off-state. [0026] Fixe! Brightness (in Cd/m²) can refer to a net or average brightness of more than a single pixel area, as opposed to the brightness measured at a small spot in the center of a single pixel’s active area. This distinction is relevant as the electrically-modulated pixels have active areas that are considerably smaller than the pixel’s overall size, creating a dark dead-space area framing each active electricaily-modulated pixel area, to the optical elements discussed herein substantially hide this dead-space framing (or border region) from the incoming ambient illumination and/or from external viewers, by expanding (or appearing magnify) the size of the pixel^'s light-reflecting active areas to match (or nearly match) the outermost size of the individual pixels themselves, doing so in a way that makes the pixel’s light-reflecting active areas seem as if they were packed beside each other edge-to-edge with minimal (greatly reduced) boarder width. One approach to measuring the brightness improvement associated with this board-width reduction includes measuring the brightness over a diameter greater than the overall size of more than one full pixel of the small color.

[0026] FIG. 1A-1 F show a schematic of a portion of a display device incorporating a first optical element. The display device 100 includes a 2D array of pixels 114 whose topmost output surface 102 presents an electrically-controlled reflective color 116 over its WA x WA active surface 120. The 2D array of pixels 114 are coupled with a 2D array of dead-space reducing optical elements 110 positioned over the output surface of the pixels 114. The pixel 114 includes an output surface comprising an active surface 120 and an inactive surface 130 that surrounds the active surface 120. In some instances, the inactive surface 130 can be a bezel or a frame behind which control mechanism for the active surface 120 can be positioned. The pixel 114 can include a controlling mechanism that enables electrically controlling reflection of a color of light outwardly from the active surface 120. The inactive surface 130 may absorb, reflect, or scatter Incident light. However, unlike the active surface 120, the reflection of light through the inactive surface 130 is not controlled.

[0027] The optical elements 110 can include a pixel facing surface 180 comprising a pixel interface aperture 124. The pixel interface aperture can have an area that is less than an area of the pixel facing surface. In the optica! elements 110, the pixel interface aperture 124 can include a portion of the pixel facing surface 180 that Is directly over the active area 120 of the pixel 114. The pixel interface aperture 124 may also be a portion of the pixel facing surface 180 that has the same dimensions as the active surface 120 of the pixel 114. The pixel interface apertures 124 also can have a width and length (Wi x W!) that is equal to the width and length of the active surface 120. in some instances, the optical element 110 can be positioned over the active area 120 such that the pixel facing surface 180 is parallel to the active surface 120. In some instances, the optical element 110 can be positioned over the active surface 120 such that when viewed in a direction normal to the active surface 120, the perimeter of the active surface 120 lies within the perimeter of the pixel facing surface 180. in some such instances, the perimeter of the active surface 120 projected normally on the pixel facing surface 180 can represent the perimeter of the pixel interface aperture 124. In some such instances, where the complete perimeter of the active surface 120 projected normally on the pixel facing surface 180 does not lie outside the perimeter of the pixel facing surface 180, the optical element 110 can be considered to be fully aligned with the active surface 120 or with the pixel 114. The optical element 110 can be considered to be partially aligned with the active surface 120 or with the pixel 114 when at least a portion of the perimeter of the active surface 120, when projected normally onto the pixel facing surface 180 lies outside the perimeter of the pixel facing surface 180.

[0028] The optical elements 110 also can include a viewing surface 182, opposite the pixel facing surface 180. The viewing surface 182 can have an output aperture 184, which outwardly directs light received at the pixel interface aperture 124. The output aperture 184 can have dimensions that are iarger than the corresponding dimensions of the pixel interface aperture 124. Further, the viewing surface 182 can have dimensions that are larger than the corresponding dimensions of the pixel facing surface 180. Furthermore, the viewing surface 182 can have dimensions that are less than or equal to the corresponding dimensions of the pixel 114. An output aperture 128 can represent a portion of the viewing surface 182 that displays an image of the active surface 120. The perimeter of the output aperture 126 can extend up to the perimeter of the viewing surface 182. In some Instances, the size WO x WO of the output apertures 126 can be equal to or less than the size WP x WP of the pixeis 114. Because the output apertures 126 of optical elements 110 are arranged to overhang their smaller pixel interface apertures 124, they effectively hide exterior visibility to the surrounding inactive surface 130 shown just for clarity as a checkerboard pattern, but generally as the black regions surrounding each pixel’s active surface 120

[0029] The display device 100, and its included optical elements 110 shown in FIG. 1A, receive ambient light spread over each pixel’s active surfaces 120, and the received light is then rereflected back outwards from the pixels 114, through the optical elements 110 and to viewers of display device 100 through each optical element’s output aperture 126. As a favorable consequence of light reflections within pixels 114 and within optical elements 110, the light output from each optical element is spread substantially over the majority of the area of the output aperture 126. As a consequence of this arrangement, viewers perceive the actively-colored pixel areas 138 (also referred to as the output aperture) as packed together more tightly than they would seem to be when the pixels are viewed without dead-space hiding optical elements 110, and with no perceived loss in brightness. As a result, an effective fill-factor is increased significantly, with the fill becoming nearly 100% (meaning that the viewable output aperture area 126 closely approaches the pixel^'s 114 area). The optically magnified output image and its color 116, in that case, nearly fills each pixel’s physical area (WP x WP).

[0030] The display device 100 can be configured geometrically and optically to enable high fill- factor (defined as the actively-modulated aperture area 120 divided by the sum of the actively- modulated aperture area and the surrounding unmodulated dead-space area 102). The display device 100 shown in FIG. 1A further allows the widest possible useful range of moduiated-color viewing angles for what appears to viewers as magnified output image colors 138, these magnified colors viewed brightly and clearly over a full range of oblique viewing directions extending smoothly from the pixel’s optical axis (orthogonal to the pixel surface) to the widest angular directions of view consistent with intended use and with a satisfactory contrast ratio (the fully-modulated color brightness divided by the corresponding black state brightness), in some instances, a maximum viewing angle refer to a largest viewing angle at which one or more of the contrast, brightness, and or color shifts, or the display device 100 are within acceptable ranges. As an example, the acceptable range for contrast, brightness or color shifts can be within 100% to about 50%, or within 100% to about 40%, or within 100% to about 30% of the respective contrast, brightness or color shift when viewed in a direction normal to the viewing surface 182. in some instances, the maximum viewing angle can be about +/-60 degrees to about +/-20 degrees with respect to an optica! axis that is normal to the viewing surface 182. The optica! element 110 can include solid or liquid optically transparent materials such as, for exam pie, gels, glass, etc.

[0031] FIG. 1 B illustrates a cross-sectional view of the display device 100 shown in FIG. 1A. The widths of the element’s pixel interface apertures 302 and output apertures 301 (Wl and WO) are matched as closely as feasible to the dimensions of the reflective pixel’s active width WA, 314 and the pixel’s complete edge-to-edge width WP 303, respectively. When WI=WA and WO=WP, the angular range of geometric output viewing 324 is restricted to +/-Q3 by geometrical relations of aperture sizes and sidewall shape. But a more realistic description of the range of output viewing (which may be smaller than the geometrically imposed angular width) may defer to the angular range where the pixel’s color contrast ratio remains greater than what may be considered as minimum color visibility in the given image display application of use (typically greater than 2:1).

[0032] The optical elements 310 (110 in FIG. 1A) that are coupled with pixels 114 can be configured as Etendue-preserving from their pixel interfacing aperture 302 to output aperture 301. Output apertures 301 (126 in FIG. 1A) can be made wider than their corresponding pixel interface apertures 302, with WO=WP WI=WA. The output apertures 301 are packed together as tightly as manufacturing methods allow so that visibility of the pixel dead-space 321 (102 FIG. 1A) underneath is nearly fully blocked as shown in the perspective view of FIG. 1A and the cross- sectional view of FIG, 1 B, The dimensional relations of these reflective Etendue-preserving optical elements 310 can be summarized by Equations 1 , 2 and 3 (1 and 2 according to the Sine Law, 3 as Snell’s Law of Refraction). The associated tiited-paraboiic sidewall shapes 311 for such Etendue-preserving reflectors can be constrained by boundary conditions of these equations and verified using computers running commercial ray tracing software, such as for example ZEMAX OpticStudio (produced by ZEMAX, LLC) or ASAP (produced by Breau!t Research Organization).

[0033] Transparent optically-reflecting elements designed to be ideally Etendue-preserving by Equations 1 and 2, from their incoming aperture to their out-going aperture (and visa-versa) means that the optical Invariant (aperture size times the effective angle or solid angle of the light passing through each aperture) is constrained by the optical element’s sidewall shape and the Second Law of Thermodynamics to remain constant. Designs of this type preserve brightness and flux efficiencies from aperture to aperture, a performance that cannot be further improved upon (and stand as a thermodynamic limit). Many optical elements, especially ref ractlve ones including plano-convex and Fresnel lenses, that are not strictly ideal in their preservation of Etendue can still be effectively utilized as dead-space hiding optical elements. While non-ideally performing optical elements used in substitution for ideally Etendue-preserving ones may reduce overall system efficiency or some other system performance metric, their relative performance losses may still be justified (and offset) by their reduced thickness, by their lower material volumes, by their ease of manufacturing, or their lower manufacturing cost, to mention a few. When system constraints are applied, such as reduced thickness as one example, the so- constrained optica! element may still be considered as being Etendue-preserving within the bounds of the applied constraint. That is to say the so-constrained optical element has been designed as dose to preserving of Etendue as the imposed constraints ai!ow. Non-idea!!y designed reflective optical elements In some Instances may cause a fraction of the Incoming light to be reflected internally within the reflective optical element without that light ever having touched the active surface of the electrically-controlled pixels. Because of this, the internally reflected light is unmodulated and escapes as glare that may degrade the viewing quality of the display device.

[0034] During operation, the output apertures 301 of optical elements 310 are bathed generally with incoming ambient ilium ination 350 in FIG, 1 B that may originate as the diffuse illumination of the daytime sky, as direct radiation from the sun, as the light imparted by external lighting elements (or luminaires) whose flooding illumination has been directed towards output apertures 301 or any other source of ambient lighting failing upon them. While this illumination 350 may have net directional characteristics, it can be assumed that the output apertures 301 receive ambient light in any angular direction over the -90-degrees to + 90-degrees hemisphere above them (+7-03, 324), and that this incoming light then ref racts according to Snell’s law (Equation 3) into the solid optical elements 310 of this embodiment with cone angle 355, +/-Q2322. When the incoming light 355 reaches the reflective sidewalls 311 of optical elements 310, it is reflected downwards within the optic whether by total internal reflection at the dieiectrical!y-reflective boundary between RI2 and air, or by an external metallic surface-coating placed on sidewalls 311 , to the optical element’s pixel interface apertures 302, whereupon the light as received is further ref racted downwards at the input-aperture boundary 302 into a coupling medium 308 and the pixel Interface apertures 304 of the reflectively-colored pixels 114. in-coming ambient light 355, on entering the electrically-controlled medium of the reflectively-colored pixels 114, is modulated in color by the pixel’s medium and back-reflected by the pixels internal back-reflector 307 upwards back into optical elements 310 as back-reflected light cone 380, and then as the result of further reflections at sidewalls 311 , directed outwards through the output aperture 301 into airwithin +/-Q3 optical cone 324 set by the optical elements geometric relations. While general mathematical sidewall shape expressions have been derived adhering to the boundary conditions of Equations 1-3, and straightforward spreadsheet models also can be constructed. Ray trace modeling software also can be used to design and test the display device 100. In some instances, a portion or complete surface of the sidewall 311 can be coated with a reflective coating. The coating can be a metal coating, such as silver, aluminum, etc. coating, in some Instances, the sidewalls 311 may not Include a coating, however the sidewalls 311 can still reflect incident light due to total internal reflection. In some other instances, the sidewalls 311 may be partially reflective or not reflective. For example, the sidewalls 311 can scatter or diffuse light. [0036] FIG. 1C is a perspective view of a single electrically-controlled pixel 400 (pixel 114 in FIG. 1A). Dimensions of the pixel’s e!ectrica!!y-active light-reflecting active surface are VVA x WA centered in an area of the pixel WP x WP. Only the centered WA x WA aperture 418 (also referred to as “active surface 418”) reflects am blent light with a brightly-visib!e electrically-controlled color 116, the reflection coming from an internal reflective surface covering a substantial portion of the WAx WA active surface 416. This internal reflective layer not shown can be designed for specific use with different reflectors at the bottom of the optical stack of active surface 416, each having different characteristics beneficial for different applications. Reflector characteristics include, but are not limited to: Lambertian, specular (mirrored), retroreflective (facets or lenses), and electronically controlled reflectivity properties such as polymer dispersed liquid crystal (PDLC).

[0038] Ambient light striking the inactive framing region 410 (inactive surface 130, FIG. 1A) surrounding the active surface 418 is lost to absorption and scattering. Such wasted light reduces the pixel’s effective brightness to an observer by the ratio (WA²/WP²), which is especially undesirable in 2D arrays of such pixels 400. Dead-space width within pixel 314 is WD/2, 412, and absorbs (and or scatters) the ambient light falling upon it to no useful effect. FIGS. 1A and 1 B provide the means to mitigate such optical loss, by combining pixel 400 with optical elements 110/310 that together, not only hide the ineffective dead-spaces 410 in between the pixel’s active surface 418, but they also effectively increase the pixel’s viewable brightness by piping ambient light over the pixel’s full output aperture area WP x WP 418.

[0037] FIG. 1 D shows in perspective view an example array of three WP x WP pixels 400 in what may be referred to as a 3 x 1 array that corresponds with the three side-by-side pixels 114 shown illustratively in the cross-section of FIG. 1 B. FIG. 1 A shows a 3x3 array of pixels 114. Pixels 400 may be switched electrically between reflective colors, from black 510, to white 520, to any particular color 530 enabled by mixtures of its internal fluids (e.g., red, yellow, blue, green, cyan, magenta).

[0038] In some applications (such as, e.g., roadside billboards, indoor signage and outdoor signage), very large-scale tightly-packed N x M arrays of pixels 400 with their coupled dead-space hiding optical elements can be formed. Commercial roadside billboards, as one example, are typically 14 feet high and 48 feet wide (3.4:1). When the reflective pixels are made, for example, 18.6 mm x 18.6 mm (0.653 in x 0.653 in) edge-to-edge, the complete billboard size array would be 257 pixels by 882 pixels (-227,000 total pixels). Of course, the number of pixels in the display can vary based on the size of the display device as well as on the pixel size. The sizes of the display and the pixel sizes mentioned above are only examples, and other display sizes and pixel sizes can be used.

[0039] FIG. 1 E shows a perspective view of an example configuration of the pixel 400 shown in FIG. 1 D in combination with a corresponding dead-space-hiding Etendue-preserving optical element as illustrated in FIGS. 1A as 110 and 1 B as 310. In the example shown in Figure 1 E, WP=16.6 mm and WA=11.6 mm. Of course, these values are only example values, and that various implementations can have their respective values. This corresponds to an effective dead- space 102, WD of (16.6-11.6)/2 or 2.5 mm and a Fill-Factor of (11.6)² / (18.6)² or 49%. The electrically controlled color 116, as also shown schematically in FIG. 1 A fills the pixel’s WAx WA active area with color 116. The pixel 400 can include a transparent colored layer or layers above a reflective means that back-ref lects either specularly, specularly with some diffusive scattering, or retro-ref lectively as from a ref !ective-microstructure whose back reflection is not specular, but rather back in the general direction or directions of the light incident upon it. All ambient input light that is received by these colored layers 116 or 316 is reflected back out through them and then through the optical elements 110 (FIG. 1A) and 310 (FIG. 1 B) included above them as shown.

[0040] The pixel 400 can include a relatively smaller active surface 416 (WA x WA) than its outermost package area 418 (WP x WP). The consequence of this area size difference (WP²- WA²) is that when assembled into a close-packed array of pixels 400, the overall array brightness appears dimmer (or duller) to a viewer than the effective brightness of each pixel’s active surface 416. The reason for this brightness reduction is that the ambient light in lumens received by the overall array of pixels 400 is only reflected back partially towards the viewer (as by each active surface 416), and the effective brightness of the array of pixels 400 is thereby diluted by the inactive pixel-frames (or dead-spaces) surrounding each active surface. The optical elements discussed herein overcome this loss in viewable brightness by the coupling the Etendue- preserving optica! element with the pixel, such as those elements 110/310 shown in FIGS. 1A, 1 B and 1 E whose output apertures are made substantially the same size as the pixel’s outer edges, and as such receive substantially all the ambient light applied to it, while simultaneously hiding the dead-space. Because of this, the pixel’s full brightness is achieved. In some example implementations, a gain of about 2 times the net brightness of the pixel array itself can be achieved by including the optical elements.

[0041] The dielectric Etendue-preserving optical elements 310 of FIG. 1 E according to equations 1-3 can represent combinations of design opportunities through the many possible combinations of their pixel interface aperture dimensions, output aperture dimensions, distance between input and output apertures and the chosen refractive index, plus the desired angular range at the output aperture (also the ambient-light-receiving aperture) and the desired angular range presented at the elements pixel interface aperture coupling to the electrically-controlled pixels 400).

[0042] In some examples, as discussed above (1) WI=WA and (2) WO=WP can be maintained for the optical elements. In addition, the dielectric material chosen for the Etendue-preserving optical elements can include, for example, an optically-ciearand readily castable/m oidable optical polymer e.g., silicone, whose RM .42, for example, can be coupled easily at the element’s pixel Interface aperture 418 with a near index-matching opticaliy-clear liquid (gel, adhesive or epoxy) at, or as immersed in, a part of the eiectricaily-controiled pixel’s outermost surface. The refractive index of 1.42 mentioned above, and other values discussed herein are only examples. Based on the implementation, the value of the refractive indices can vary, and can range between about RM to about Ri=2.42 (i.e., Rl of diamond), in some examples, the angular range at the output (or light receiving) aperture 418 in FIG. 1 E can be +/-90-degrees in air. In some non-limiting examples, W!= 11.8 mm and W016.8 mm, H is set for the optical element by Equations 2 and 3 and the +/-90-degrees acceptance angle for ambient illumination in air (+/-Q2 = ASSN[1/1.42] ~= 44.76-degrees, the Critical Angle of light in RM .42). Under these example constraints, H=(0.5^*(WO+Wi))/TAN [ ASIN [1/1.42]] ~= 0.5^*(WO+WI) = 14.1 mm, with TAN [ ASIN [1/1.42]] ~= 1. Equation 1 above then determines the angular range at the element’s pixel interface aperture 416 as being +/-Q1 = ASIN [ (WO/Wi) ^* SIN [62]] ~= ASIN [1] = +/-90-degrees. This wide +/-90-degree angular range at pixel interface aperture 416 of optical element 310 (or 110) can be achieved by metalizing the otherwise opticaiiy dear molded or cast sidewall surfaces of element 310 in order to eliminate failures of total internal reflection inside the element for very high-angle rays striking the element’s sidewall in its lower region (pixel interface aperture 416 to HM ~Q.25^*H). This metaiized region can be denoted by the sidewall regions below dotted lines 810. in some examples, metal coatings can be vapor-deposited or sputter-deposited silver with outer surface protection for oxidation, or vapor-deposited aluminum also with outer surface protection for oxidation, in yet another example, optical elements of the same size and shape can be made of metai or plastic initially as hollow four-sided bins whose internal sidewalls are then metaiized with either highly-refiective silver or aluminum, before filling the hollow cavities with opticaliy-clear material, such as, for example, silicone (RM .42) (or any other opticaiiy clear material such as glass, plastic, etc.). [0043] In one example, the profile shape 620 of the sidewalls 311 can include a parabola tilted at angle 02 about its focal point 630 which lies at the opposing edge of pixel interface aperture 416. in some instances, once tilted or rotated, the mathematical expression for sidewall profile 620 can be calculated parametrically, and fit to a multi-order optical polynomial, which for the specific design parameters used in FIGS. 1A, 1 B and 1E is as one exam pie the fourth order polynomial Z = AX⁴+BX³+CX²+DX+E, where in one example, A=1.236, B=-33.4, C=338, D=-1514.9 and E=2534, with a precision of fit coefficient R²=G.9973. Whenever the aperture dimensions Wl and WO are changed to satisfy changes in pixel geometry that might be imposed in manufacturing or in meeting the image display needs of various applications, so does the element height, H (as discussed above), and so do the polynomial coefficients for curve fitting the calculated Etendue- preserving sidewall shape. In some examples, the sidewalls can have a flat profile, or a profile that is a combination of linear and/or non-linear segments.

[0044] FIG. 1 F, also shown in perspective view, illustrates a tightly-packed 3 x 3 array 600 of the pixels 400 and the corresponding optical elements shown in FIG. 1 E. This figure also shows how various color modulations may be applied electrically to the Individual pixels 400, changing their color and then transferring that color through optical reflections to the output apertures 602 (418 in FIG. 1 E) of the included optical elements 605 (also 110 and 310 in previous figures). As one example, consider the pixel whose pixel interface aperture is white 510A. The Etendue- preserving optical element 606 attached to this particular pixel, outputs substantially the same white light color 510B over substantially its whole output aperture area 602. The x, y color coordinates of the pixel color 510A may shift slightly as a result of the various reflections taken inside optical element 606 and because of any dispersion in its refractive index, in practice, this color shift may be small to negligible, and the part-to~part color-shifting differences between any of the optical elements 605/606 in the array system 600 may also be small to negligible. With reference to the example of FiG. 1 F, the particular white output aperture colors 645B, 650B, 630B, 510B and 640B, while shown having the same white-state chromaticity, may indeed be each held to the same white-state chromaticity’s, as in a white background area, or they may each be made slightly different in chromaticity and brightness as the prevailing arrays image content requires.

[0045] As another color-changing example, consider the central pixel of the 3 x 3 array of FIG. 1 F. This center pixel is switched to its most absorbing black state color 520A (not visible) and is output as the reflected color 520B. The color contrast ratio of each pixel is referenced to the brightness of such an illustrious black color (referred to with equal meaning as the system’s dark state, black state or off state). The white-to-black contrast ratio is the brightness of color 510B divided by the brightness of color 520B. As another example, consider the lower left corner pixel with output aperture color 530B, which for illustration purposes may be red. The red contrast ratio is then the brightness of output aperture color 530B divided by the dark state brightness of color 520B.

[0046] The arrangement of the system 600 shown in FIG. 1 F was fabricated (electrically- controlled pixels 400 and corresponding Etendue-preserving optical elements 310), assembled into array system 600 and its optica! performance was measured in an optics laboratory. For validation purposes, the 3 x 3 array of Etendue-preserving optical elements shown in FIG. 1 F was formed of silicone. Individual optical elements 310 were fabricated first individually as shown in FIG. 1 E and then their output apertures 602 were bonded to a clear optical film, using clear optical adhesive, edge-to-edge in the 3 x 3 pattern shown in FIG. 1 F. Optical coupling liquid (Ri - 1.41) was applied to each element’s smaller pixel interface aperture and the optical element array placed pixel interface apertures down on top of a corresponding 3-pixel by 3-pixel region of a larger pixel array, with each optical element’s pixel interface apertures pressed into optical contact with each corresponding pixel’s outer surface, as illustrated in FIG. 1 F. A general level of ambient illumination was provided to illuminate all the receiving apertures 602 equally, and viewing brightness was measured axially using a PHOTO RESEARCH PR-650 SpectraScan Colorimeter. The instrument’s +/-1 -degree measuring-spot diameter varies from 5.2 mm at a focal distance of 14” to a much larger measuring diameter covering one entire output aperture or many output apertures depending on the distance between instrument and array 600. When the focal distance was set so the instrument’s measurement diameter covered one 16.6 mm x 16.6 mm output aperture, the measured brightness was found to be 1.85 times greater than the same measurement made on the same pixel without attachment of the optical array. Without total internal reflection (TIR) failures in the lower portion of the unmetai!ized Etendue-preserving optical elements, the ideal brightness gain expected is approximately that of the reciprocal of the geometrical fill-factor 1 / (11 ,6²/18.47²) = 1/0.496, which is forthis example, 2.02. Given that the fabricated optica! element fill-factor was slightly less than 1 and allowance for the expected light losses from TIR failures, the measured brightness improvement was 1.85. In addition, measurements of brightness as a function of angle confirmed substantial brightness gains to about 45-degrees from normal. Depletions in pixel viewing beyond 45-degrees were attributed to the lack of metallization on the lower portion of each bare optical element.

[0047] FIGS. 1G-1 H illustrate a perspective view and a designated cross-section of a second optical element 700 used in conjunction with a reflective pixel. In particular, the second optical element 700 can be used in place of or in addition to the first optical element discussed above in relation to FIGS. 1A-1 F. FIG. 1G shows a perspective view of the optical elements 700 as a hollow reflective sidewall version of the dead-space-hiding Etendue-preserving examples erf FIGS. 1A_: 1 B, 1 E and 1 F. That is, the hollow cavity portions 710 of the array of optical elements 700 are formed by the forming (molding or casting) of a solid material (plastic or metal) 720 whose smooth sidewalls 725 are then made highly-reflecting by, for exam pie, adding a vapor or sputter- deposited silver or aluminum surface coating, and then protected from oxidation with sapphire or glass top-coat. Each optical element can include a pixel facing surface 782 that defines a pixel interface aperture 780 that is positioned to interface with the active surface of the pixel 114 and receives light that is reflected through the active surface. The optica! element 700 also includes a viewing surface 784 that positioned opposite the pixel facing surface 782 and defines an output aperture 786 that Is positioned to direct the light received at the pixel interface aperture 780 outwardly from the viewing surface 784. Similar to the first optical element 100, an area of the output aperture 786 is larger than an area of the pixel interface aperture 780 and less than or equal to the area of the pixel 114.

[0048] In this hollow optical element 700, the volume of cavities 710 may be filled with either air (RM) or within an optically-clear polymer, 715. When the sidewalls 725 of hollow cavities 710 are metallized and filled with silicone, the optica! element 700 of FIG. 1G behaves in a manner discussed above in relation to FIGS. 1A-1 F, but without the light losses to TIR failures that can occuron the lower (most highly curved) portions of the bare uncoated optical elements 310. When hollow reflecting cavities 710 are filled with air, only the ambient illumination falling within the predesigned angular cone +/-Q2 (Q2 ~ ASIN [1/1.42] = 44.76-degrees, when RM .42) is able to reach the pixel’s pixel interface aperture. Only that angular cone is color-modulated and back-reflected as colored output light. Ambient illumination with higher angles of incidence is actually back- reflected by making multiple reflections with sidewalls 725 themselves, and has no practical value. But viewers looking at the reflective display along directions contained within that angular cone perceive the ~ 2X brightness increase. Changing the design of optica! cavities 710 to widen the +/-44, 78-degree viewing range is possible, but with a progressively greater loss of brightness advantage. Widening the angular range also can be achieved by reducing the dimensions of the cavities output aperture. As a trade-off, reducing the output aperture width may reduce the degree to which the dead-space is hidden in the image seen by the viewer.

[0049] FIG. 1 H represents cross-section 730 of the illustrious 3 x 3 hollow optica!-reflecting-cavily array of the second optical elements 700 as shown in FIG. 1G. The second optica! elements 700 include a cross-sectional structure 740 and symmetrically-shared sidewalls 725A and 725B which dispose in mirror symmetry about sidewail centerline 750 that intersects at the interface of adjacent pixels 114. The second optical elements 700 also include the symbolic metallic coating 760 (drawn thicker than other lines for illustration purposes only) of all the equivalently curved sidewalls 725, 725A and 725B. The determination of the height H of the second optical element 700 can be determined in a manner similar to that discussed above in relation to the first opticai element 110 shown in FIGS. 1A-1 F.

[0050] FIGS 2A~-2L illustrate an example display device 800 incorporating a third exam pie dead- space hiding optical element 810. In particular, where instead of an optically-coupled Etendue- preserving optical element attached to each to hide dead spaces and increase the effective fill- factor and visible brightness, an air-coupled opticai lens cut to cover the complete pixel area is disposed above the pixel’s active surface by the distance achieving an image magnification enabling nearly 100% fill-factor via a virtual image of the pixels active surface magnified as closely- matched to the pixel’s area as possible.

[0051] FIG. 2A shows In perspective view the display device 800, but one based on the equivalent dead-space hiding power of an equally-sized array of truncated pillow (Imaging) lenses used in place of the Etendue-preserving (non-imaging) opticai elements described above, in this view, the second example optical elements 810 are combined with the electrically-controlled pixels 400 (FIGS, 1C and 1 D) is illustrated as for this example as a 3 x 3 array of individual plano-convex !ens!ets, truncated to exactly fill the overall aperture 830 created by the WP x WP electrically- controlled reflective pixels 400. in this example, a folded and magnified virtual image 840 of the pixel’s WA x WA active surface 832 is created, with the lens height 841 , HT above the active area and internal back-ref lector of pixel 400, height HT adjusted fora net magnification of WP/WA. As an example, with WP=18.6 mm and WA = 11.6, a magnification of 16.6/11.6=1.43 can be achieved. The third example dead-space hiding optical element 810 can include a pixel facing surface 804 that is positioned to interface with the active surface of the pixel. The pixel facing surface 804 can receive light reflected through the active surface of the pixel. The optical element 810 also can include a curved viewing surface 811 opposite the pixel facing surface 804. The curved viewing surface 804 Is positioned to direct ambient incident light to the active area, and to direct reflected light received from the active area at the pixel facing surface 804 outwardly from the curved viewing surface 811 to form the magnified virtual image 840.

[0052] FIG. 2B shows hemispherical lens 850 of radius R, 855, which is over-sized to support the electrically-controlled pixel’s WP x WP outer dimensions. [0053] FIG. 2C shows the center cross-section of hemispherical lens 850, illustrating how the useful portion of oversized hemispherical lens 850 is actually spherical lens-section 852 whose diameter 853 (also chord 854 of hemispherical lens 850) has been matched to the width 853, WP, of pixel 400. Hemispherical lens 850 (or equally it’s minor segment 851 with minor arc 798) can include a cylindrical extension 858 of thickness H11 , 860A or880B. Hemispherical lens 850 and its minor segment 851 are but two of many useful imaging-lens formats compatible with this embodiment. For example, shallower spherical lenses, conical lenses, and aspheric lenses, and including their thinner Fresnel lens equivalents, may be applied in a similar manner within the present dead-space hiding optical elements. The curved viewing surface 811 can include the hemispheric (or other shapes mentioned above) portion of the lens 850 that has been truncated to match the width 853 or the dimension WP of the pixel 400. The pixel facing surface can be the bottom surface of the cylindrical extension 858.

[0054] FIG. 2D shows a cross-sectional view of a representative conical or aspheric lens 870 with cross-sectional width 875 equal to the width of pixel 400, WP. Lens 870 has a radius of curvature R, 877 (also called the vertex radius), a sag (or sagitta) 874 calculated by the well-established equation for an optical polynomial, including a conic constant (0 for spherical, -1 for parabola, +1 for hyperbolic curvatures as well established) and optional aspherica! coefficients). Lens designs regardless of their form (hemispherical, spherical, conical or aspheric) that produce a reasonably well-focused virtual image of the active area WA x WA of pixel 400 whose image size extends edge-to-edge across the pixel area (WP x WP), thereby hiding the pixel’s dead-space and achieving nearly a 100% fill-factor as discussed above can be used in conjunction with the pixel 400. Lenses may also have a cylindrical extension 872 of thickness HT1 , 860C. Although not illustrated in the cross-section of FIG. 2D, the lenses 870 can be cut square so that their edge boundaries match those of pixel 400, Such a square-cutting process is illustrated in FIGS. 2E and 2F for hemispherical, spherical, conical, and aspheric lenses. Shaded lens surface 880 illustrates the result of cutting or forming lens 882 (850, 851 and 810 in FIGS 2A - 2D). Such surfaces 880 are flat, planar, and to be optically coupled to other lenses 882 when lenses 882 are packed tightly together in an N x M array, as was illustrated in the perspective view of FIG. 2A. FIG. 2E shows the illustrative hemispherical lens cut to match the outer WPx WP dimensions erf pixel 400, enabling tight packing in an N x M array of lens elements. FIG. 2F shows a thinner version of the lens element of FIG. 2E, where functionally unnecessary thickness has been removed by truncation, creating a best mode version of illustrative hemispherical lens as it was shown in the array system 800 of FIG. 2A. This truncation retains ail the imaging lens’s fundamental optical power and Image formation qualities. [0055] FIGS. 2G - 21 are perspective views of Fresnel tens equivalents 890 of tenses 810, 850, 851 and 870 discussed above. Aside from being divided into N radial zones 892, FIG. 2G, each having a surface curvature 894 as in FIG. 2H matching the corresponding curvature at the equivalent radius of the bulk lens design being Fresnelized, the optical performance is essentially the same. That is to say that when properly elevated above the object to be imaged (e.g., the WA x WA active area of pixel 400), its virtual image is magnified to WP x WP, thereby equally hiding the pixel’s dead-space and increasing the fill-factor to nearly 100% of a pixel array such as the illustrative 3 x 3 array, 895, as shown in the perspective view of FIG. 2! which covers a (3xWP) by (3xWP) spatial area.

[0058] The cross-sectional views of FIGS. 2J - 2L are provided to show how lenses 810, 850, 851 , 883 and 890 are deployed to hide pixel dead-spaces, thereby increasing the viewing brightness of pixel array’s by about 2X and increasing the viewable fill-factor to nearly 100%.

[0057] FIG. 2J shows a computerized trace of a few collimated paraxial rays 970 directed at the spherically-curved lens surface 972 (also referred to as a curved viewing surface) of the third optical element 810. Lens surface 972 has been drawn spherically for illustrative purpose only, and may be equally illustrated as a conic surface or an aspherlcal surface or as any Fresnelized counterpart. Probe rays 970 come of a reasonable focus at a back-focus length, BFL 974, which shows that when the refractive Index of the lens is equal to, for exam pie, 1.4917 (acry!ic/PMMA) the rays converge to blur circle 980 about 18,4 mm from the lens’s plane surface 976, on back focal plane 978, The BFL of course can vary based on the shape of the curved lens surface and the thickness HT, 930, of any cylindrical extension 977 from the planar lens bottom 976. This cylindrical lens extension 977 can be filled with air as a lens-spacing region or polymer of a given Rl. The refractive index, Rl of this cylindrical region also effects the BFL.

[0058] One way to calculate this focal distance exactly is to follow extreme rays 981-983 invoking Snell’s Law (Equation 3) at each interface (which is precisely what the above computerized ray trace does for every ray created, whether specifically chosen rays or stochastically generated ones). As an example, if the illustrative ray 981 is 5 mm from optical axis on the horizontal X axis, the length of chord 985 is 10 mm. With example lens radius being 12.7 mm, ray 981 is at an angular location tilted from the optical axis 968 by the angle b, 890, b= ASIN [5/12.7] = 23.18 degrees. This makes intersection height Z = 5/ TAN [23.18] = 11.67 mm. Refracted distance D = Z^*TAN [b-a] = 1.62 mm, b=23.18-degrees as above and angle a, 973 being equal to ASIN [SIN [b] / (1.4917)] = 15.3-degrees from Snell’s Law. And because of this, ray 982 intersects plane 8/6 1.62 mm closer to the optical axis than it started, 3.4 mm from the axis rather than 5 mm. Accordingly, BFL 874 is (3.38)/TAN [11.77] = 16.4 mm, which agrees with the ray trace result.

[0059] FIG. 2K shows the result of tracing the same rayset 968 from FIG, 2J, but with a reflective surface 901 (e.g., of a reflective pixel 114 within the active surface of the pixel 114) just below the lens’s piano-surface 976, Back-reflector 901 acts as a mirror-plane and folds the incoming rays back through the body of the lens, creating a double-pass through the lens medium. Not only does back-reflector 901 , fold the ray-trajectories upwards, but in doing so it reflects the rays back towards their incident source, flipping the lens^'s focus 980 from beneath the lens as in FIG. 2J, to a focus 908 located above the lens in FIG. 2K. It also creates virtual image 910 of reflector 901. illustrative rays 915, 916, 917, 918, 919 and 920 trace the folded optical path of incident ray 915, as does the symmetrical set of rays 921 , 922, 923, 924, 925 and 926. The two ray paths cross at front side focal point 908 the defines the location of the lenses effectively-folded back focal length, FBFL 904. in this situation, back-reflector 901 serves as the object to be imaged by the lens. In this configuration, virtual image 910 is created and magnified (or de-magnified) depending on height (HI) 930 of the lens’s plane surface 976 with respect to back-reflector 901 and the refractive index of the lens, and whether this cylindrical region 949 of thickness HT in FIG. 2K (and 977 in FIG. 2J) is filled with air or a specific dielectric material of refractive index, Rl.

[0080] A non-sequential optical ray tracing software (e.g., ASAP NextGen 2020 produced by BRO (Breault Research Organization)) was used to trace the probe ray-sets 970, but it was also used to simulate the image that was formed as perceived by viewer 932 as a function of the illustrative hemispherical lens’s height (HT) 930 above the object. Weli-coiiimated axial light was provided for the incoming illumination in this particular evaluation. As an example, dimensions 11.6 mm x 11.6 mm were assumed for the back-reflector 901. In the simulation, the height of the virtual image was determined at best focus relative to the back-reflector’s location set at Z-axis or vertical height, Z=Q. Reasonably well-focused magnified (or de-magnified) images of back- reflector 901 were obtained when the distance between the lens’s plane surface 976 and back- reflector 901 were held between 0 and about 3 mm, with the refractive index in this lens separation region being air, RM . Outside this range the image formations were distorted. Well- focused 16.6 mm x 16.6 mm images were found to occur when this illustrative single circular lens’s height 930 above back-reflector 901 in air was set between a subset of this range, 0 mm to about 1 mm. These simulated results were confirmed by viewing the image of an actual 11.6 mm x 11.6 mm active area of pixel 400 using a commercially supplied G diameter acrylic hemispherical lens (also called a half-bail lens). By this experiment, a clearly-focused and slightly magnified virtual image of the real co!ored-plxe! 400 was observed even when the piano surface of this lens was resting directly on top of the outer surface of the pixel’s 11.6 mm x 11.6 mm actively colored aperture. As the hemispherical lens was raised above this pixel surface, the image of the pixel’s active area appeared to magnify progressively, gradually filling and then overfilling the 1” lens diameter, distorting gradually in shape and uniformity, finally distorting severely and transforming to a reduced circular shape. Similar behaviorwas observed in the more idealized computerized simulations.

[0081] The image magnification exam pie of FIG. 2K demonstrates the effectiveness of using an imaging-lens such as the illustrative hemisphere 972 in a manner that effectively hides a dead- space 932 which lies a distance DS, 932, beyond the edge boundaries of the object to be imaged. The object, in this case, is the 11.6 mm x 11.6 mm back-reflector901. The dead-space is created by the frame created by the WP x WP dimensions of element 936, in this example, 16.6 mm x 16.6 mm. The virtual image 910 of element 901 can be magnified -2.1 times to obscure view of the opaque frame regions of element 936. When the lens’s offset distance HT, 930, is 0.0 to about 0.35 mm, the resulting image magnification of the pixel aperture’s 11.6 mm x 11.6 mm back-reflector is in fact -2.1. 16.6²/11 ,6² = 2.05.

[0082] FIG. 2L illustrates a schematic cross-section showing the main functional relationships between the elements of this dead-space-hiding (and brightness increasing) example optical element in conjunction with an eiectricaliy-controlled ref iective pixels 400. The hemispherical lens 868 of radius R, 940, is disposed a particular height (HT) 930 above the topmost output surface (e.g., the active surface) of electrically-controlled reflective pixel 400, and as such, illumination from an ambient source (sun, daytime sky, flood lighting etc.) 942 transmits into and through lens 972 as incoming light rays 944. The incoming illumination passes into pixel 400 and reflects from its internal back-reflector 901 while becoming outgoing light of the electrically-selected color 946 because of its interaction with the pixel’s active coloring fluids 950. The ambient illumination erf the WA x WA active region pixel 948 of pixel 400 is imaged by lens 972 and its virtual image 910 is so formed visible to viewer 952 according the discussion above associated with FIG. 2K. Ambient light 944 flows into and out of pixel 400 by means of the pixel’s integral back-reflector, and when the magnification provided by the lens 972 is WP²/WA² the effective fill-factor approaches 100%.

[0063] While the embodiment of FIG. 2L achieves its brightness increase and dead-space hiding benefits via an imaging element, the effect is similar to the equivalent benefits shown in FIGS. 1 A, 1 B, and 1 E-1 H using a non-imaging element, preferably a four-sided reflective Etendue- preserving optica! element.

[0064] FIGS. 3A - 3F show schematic cross-sectional views of a display device with optical elements. In particular, the cross-sectional views shown in FIGS. 3A-3F can be similar to the schematic cross-section of FIG 1 B, but showing detailed view of the interna! construction of the eiectronicaily-controilabie pixels 400 placed side-by-side and in conjunction with the imaging and non-imaging optical elements deployed to hide pixel dead-spaces, increase the pixel array’s fill- factor and increase the pixel arrays effective viewing brightness. Each figure shows a source of ambient illumination 1114 directed towards the illustrative pixel array as directed light 1113, That incoming light 1113 flowthrough the various internal layers of the pixel cross-sections and is back- reflected as outgoing light 1115 to be received by a viewer or viewers 1116 a distance from the pixel array, it should be noted that the schematics are not drawn to scale, and certain dimensions are magnified forsake of added detail.

[0065] FIG. 3A shows the cross-sectional view of reflective pixel array system 1100 for a 3-pixel array including the four-sided Etendue-preserving optical elements 1111 as shown in FIGS. 1A, 1 B, 1 E, 1 F, 1G and 1 H and the electricaliy-controilable reflective-colored pixels 400 of FIGS. 1 and 2. Pixel layers comprising thickness 1119, G1 , are drawn with exaggerated thicknesses for illustration purposes only. In some example implementations, layers 11Q7A, 11Q8A, 1107B, 1108B, 1107C, 11Q8C and 1105 combine to a total thickness G1 , ranging from 10 pm to 10000 pm depending on intended use. Pixel back-ref lectors 1103, each about VVA mm x WA mm on their edges, are mounted (and centered) on the WP mm x WP mm pixel body structure 1101 , which can be either flexible or rigid. In some examples, the back-reflector 1103, which receives the incoming light 1113 and back-ref lects it outwards as 1115, may be made of a white Lambertian reflecting material, a metallically-coated specularly-reflecting material, a metallically-coated specularly-reflecting material containing a surface micro-structure that may be made to be retro or semi-retro reflecting. Back-reflector 1103 may also be made of com binations of such reflective materials along with optical active materials, such as for example, polymer-dispersed liquid crystals (PDLC). Region 1102, as one example, is an air-gap (or air-pocket) between back- reflector 1103 and Its associated sealing surface 1103B, but may also be a dielectric material. Layer elements 1105, 1107C, 1107B and 1107A shown shaded with black-dots, indicate patterned adhesive applied layer by layer to ensure adequate sealing between pixel structure 1101 and the non-air optical surfaces (11G8C, 11G8B, and 1108A) that back-reflected light encounters in sequence after leaving the surface of reflector 1103. These non-air optical layers 1108C, 1108B, and 11G8A are formed as flexible, optica!ly-transparent coupons, comprising individually controllable regions of optically-actlve fluids 1112. Optically-active fluids 1112 are contained within optically-clear membrane materials and placed in vertical stack 1120 one above the other within each of the three individual pixels illustrated. Three-layer stack 1119 of thickness G1 generally contains at least one layer, with its sequentially stacked regions 1112 (one per layer) containing a colored ink or optically absorptive liquid (having a particularly chosen absorption spectrum and resulting color) that is pumped into them through thin fluid vias (not shown) from backside fluid reservoirs (also not shown). Electric signals are applied to actuators for each pump (and its associated fluid reservoir, one reservoir for each fluid color), so as to modulate or eiectrically-control the amount of liquid pumped into each of the associated visible fluidic regions 1112 (from substantially no liquid to an upper liquid-volume-limit constrained by the mechanical design and membrane construction of regions 1112). In a subtractive color system such as this one, the more liquid pumped into each of regions 1112, the more spectral energy is absorbed (and thereby subtracted) from the transmitting light increasing color saturation. When the total liquid volume in vertically-stacked regions 1112 is maximized, the absorption is so strong that the pixel’s active area appears black, creating the system’s black (or off) state.

[0086] FIG 3A describes a three-color example display device 1100 (e.g. fluid regions of cyan, yellow, and magenta, or CMY, each color stacked above the other in a sequential (or subtractive) manner. In such subtractive CMY color systems, light absorption from each layer (or layers) imparts color to the transmitting light by subtracting from the incident light color 1113 (typically white). The same cross-sectional structure can be applied with fewer active layers. When used with only one of the three layers shown, a single optically active fluid region 1112 per pixel may perform monochromaticaliy (e.g., switching between black and white, red and white, green and white, etc.), in the case of a black-and-white (B&W) monochrome image display applications, stack 1120 would comprise one optically-active fluid region 1112 containing a wide-band absorbing (black) fluid connected to only one electrically-controlled pump and fluid reservoir located below pixel body 1101. FIG. 3B shows an exploded cross-sectional view of the full optical stack 1120 of FIG. 3A.

[0067] FIG. 3C shows the cross-sectional view of an example display device 1200 with four-sided dielectric Etendue-preserving opticai elements 1211. The smaller apertures of optical elements 1211 In this embodiment may be coupled to the display device’s outer-most flexible and optica!ly- transparent coupon (membrane) materials 1208C (in this three-layer, three color example) with an optical coupling medium 1209 that may be either liquid, gei, an optically clear and compliant adhesive or air. FIG. 3D shows an exploded cross-sectional view of the full optical stack 1220 of FIG. 3C.

[0068] FIG. 3E shows the cross-sectionai view of an example display device 1300, otherwise identical to the electrically-controlled pixel embodiment of FIG. 3A except that in this example, the four-sided non-imaging (Etendue-preserving) dead-space-hiding optical elements 1111 are replaced with corresponding array of four-sided imaging optical elements 1311 as they were described by FIGS. 2A -2F.

[0069] FIG. 3F shows the cross-sectional view of a display device 1400, otherwise identical to the electrically-controlled pixel embodiment of FIG. 3A except that in this form, the four-sided nonimaging (Etendue-preserving) dead-space-hiding optical elements 1111 are replaced with corresponding array of four-sided Fresnel-type imaging optical elements 1411 as described above in relation to FIGS.2G -2I.

[0070] In the example display devices discussed above, the reflective pixel can be implemented in various technologies. In one example, the reflective pixel can be implemented using fluidic actuators that control a quantity of fluid within a chamber positioned between a reflective element of the reflective pixel and the active surface, causing the reflective pixel to controiiabiy reflect a color of light outwardly from the active surface. As an example, the reflective pixel can include one or more examples described in US Patent Application No. 17/048,904, entitled “Display Techniques Incorporating Fluidic Actuators and Related Systemsand Methods,” filed October 12, 2020, which is incorporated by reference herein in its entirety. The reflective pixels can include a fluid chamber positioned over the reflective element within the active surface, and an actuator configured to controiiabiy cause reflection of a color of light outwardly from the active surface by altering a quantity of fluid within the fluid chamber. The actuator can be electrically actuated, and can result in the actuator altering pressure in the fluid chamber or adjacent chamber to cause corresponding changes in the quantity of fluid within the fluid chamber.

[0071] In some examples, the reflective pixel can employ electrostatic shutters, such as those discussed in U.S. Patent Application No. 15/710,063, entitled “Highly Reflective Electrostatic Shutter Display,” filed September 20, 2017, which is incorporated by reference herein in its entirety.

[0072] In some examples, the reflective pixel can include an electrowetting reflective pixel. Electrowetting is an effect that, upon applying some electricity, alters a material’s apparent contact angle and wettability. Wettability can be described as a measure of how readily liquids can rest on the surface of a materia!. By reducing the wettability, the materia! repels the liquid resting on it. The end result is that you can alter the shape of the liquid. Depending on the materials chosen, in the unenergized state the droplet can form a com pact droplet on the surface — but by applying some electric field over the droplet and substrate, the droplet will increase its apparent contact angle and contact area with the substrate, spreading out to cover the substrate surface as a response. This change in the physical properties scan be utilized modulate the amount of light reflected by an underlying reflector. Some examples of electrowetting reflective pixels are discussed in US Patent 9,274,331 , which is incorporated by reference herein in its entirety, in some examples, the ref lective pixels can include an electrophoretic pixel, such as those employed in E-!nk technology. In electrophoretic pixels, charged particles move in response to an applied electric field with a velocity relative to the surrounding fluid. This mechanism is used to position colored charged particles between an underlying reflector and an output surface. At least one example of the electrophoretic pixels is discussed in U.S. Patent No. 10,908,472, which is incorporated by reference herein in its entirety.

[0073] The discussion herein describes several aspects of the display device that can be implemented separately or in combination with other aspects of the disclosure without departing from the disclosure. The following lists a non-limiting set of aspects of the display device should not be confused with the claims.

[0074] Aspect 1 : This aspect includes a reflective display device, including a reflective pixel including an output surface comprising an active surface and an inactive surface, a fluid chamber positioned over a reflective surface within the active surface, and an electrically controlled actuator configured to controiiabiy cause reflection of a color of light outwardly from the active surface by altering pressure within the fiuid chamber to cause corresponding changes in a quantity of fiuid within the fiuid chamber. The display device also Includes a dead-space reducing optical element positioned over the output surface of the reflective pixel, the dead-space reducing optical element including: a pixel facing surface comprising a pixel interface aperture positioned to interface with the active surface of the reflective pixel and to receive the light reflected through the active surface of the reflective pixel, a viewing surface opposite the pixel facing surface, the viewing surface com prising an output aperture positioned to direct the light received at the pixel interface aperture outwardly from the viewing surface, wherein the output aperture has an area that is larger than an area of the pixel interface aperture and less than or equal to a pixel area comprising an area of the active surface and an area of the inactive surface, and at least one sidewall that extends between the pixel facing surface and the viewing surface. [0076] Aspect 2: The reflective display device according to any one of Aspects 1-15, wherein the dead-space reducing optical element is Etendue preserving from the pixel interface aperture to the output aperture.

[0078] Aspect 3: The reflective display device according to any one of the Aspects 1-15, wherein the at least one sidewall comprises a total Internal reflection surface.

[0077] Aspect 4: The reflective display device according to any one of the Aspects 1-15, wherein an effective fill factor defined as a ratio of the area of the output aperture to the pixel area is greater than a pixel fill factor defined as a ratio of an area of the active surface and the pixel area.

[0078] Aspect 5: The reflective display device according to any one of the Aspects 1-15, wherein the effective fill factor is greater than about 0.85, greater than about 0.9, or greater than about 0.95 and up to about 0.98 or up to about 1.

[0079] Aspect 6: The reflective display device according to any one of the Aspects 1-15, wherein at least one dimension of the pixel interface aperture is equal to or less than a corresponding dimension of the active surface, and wherein the at least one dimension of the output aperture is equal to or less than a corresponding dimension of the pixel area.

[0080] Aspect 7: The reflective display device according to any one of Aspects 1-15, wherein the reflective display device has a perceived brightness that is higher than a perceived brightness of the otherwise same display device except without the dead-space reducing optical element when measured under the otherwise same conditions.

[0081] Aspect 8: The reflective display device according to any one of the Aspects 1-15, wherein the reflective display device has an effective contrast ratio that is higher than an effective contrast ratio of the otherwise same display device except without the dead-space reducing optical element when measured under the otherwise same conditions.

[0082] Aspect 9: The reflective display device according to any one of the Aspects 1-15, wherein the reflective display device has a maximum viewing angle of at least +/-60 degrees to at least +/-80 degrees.

[0083] Aspect 10: The reflective display device according to any one of the Aspects 1-15, wherein the dead-space reducing optical element comprises a solid or a liquid and optically transparent material between the pixel interface aperture and the output aperture. [0084] Aspect 11 : The reflective display device according to any one of the Aspects 1-15, wherein the dead-space reducing optical element comprises air between the pixel interface aperture and the output aperture.

[0085] Aspect 12: The reflective display device according to any one of the Aspects 1-15, wherein the at least one sidewall comprises a metal surface or a metalized surface.

[0086] Aspect 13: The reflective display device according to any one of the Aspects 1-15, wherein the display device includes adjacent reflective pixels with adjacent respective optical elements, and wherein a shape of the sidewalls of the adjacent respective optical elements is symmetrical about a centerline that intersects at a point of interface of the adjacent reflective pixels.

[0087] Aspect 14: The reflective display device according to any one of the Aspects 1-15, wherein a height H of the optical element, measured as a distance between the pixel facing surface and the viewing surface can be determined based on (Q.5^*(WQ+V¥i))/TAN [ASIN [1/Rij], wherein WO represents a dimension of the output aperture, W! represents a corresponding dimension of the pixel interface aperture, and Rl represents a refractive index of the optical element.

[0088] Aspect 15: The reflective display device according to any one the Aspects 1-15, wherein the at least one sidewall can have a parabolic curvature.

[0089] Aspect 16: A reflective display device, including a reflective pixel comprising an output surface comprising an active surface and an inactive surface, the reflective pixel configured to controllabiy reflect a color of light outwardly from the active surface. The reflective device also includes a dead-space reducing optical element positioned over the output surface of the reflective pixel, the dead-space reducing optical element including: a pixel facing surface comprising a pixel interface aperture positioned to interface with the active surface of the reflective pixel and to receive the light reflected through the active surface of the reflective pixel, a viewing surface opposite the pixel facing surface, the viewing surface comprising an output aperture positioned to direct the light received at the pixel interface aperture outwardly from the viewing surface, wherein the output aperture has an area that is larger than an area of the pixel interface aperture and less than or equal to a pixel area comprising an area of the active surface and an area of the inactive surface, and at least one sidewall that extends between the pixel facing surface and the viewing surface.

[0096] Aspect 17: The reflective display device of Aspect 16, wherein the reflective pixel is an electrowetting reflective pixel. [0091] Aspect 18: The reflective display device according to any one of the Aspects 16-30, wherein the reflective pixel is an electrophoretic pixel.

[0092] Aspect 19: The reflective display device according to any one of the Aspects 16-30, wherein the reflective pixel is an electrostatic shutter pixel.

[0093] Aspect 20: The reflective display device according to any one of the Aspects 16-30, wherein the dead-space reducing optical element is Etendue preserving from the pixel interface aperture to the output aperture.

[0094] Aspect 21 : The reflective display device according to any one of the Aspects 16-30, wherein the at least one sidewall comprises a total internal reflection surface.

[0095] Aspect 22: The reflective display device according to any one of the Aspects 16-30, wherein an effective fill factor defined as a ratio of the area of the output aperture to the pixel area is greater than a pixel fill factor defined as a ratio of an area of the active surface and the pixel area.

[0098] Aspect 23: The reflective display device according to any one of the Aspects 16-30, wherein the effective fill factor is greater than about 0.85, greater than about 0.9, or greater than about 0.95 and up to about 0.98 or up to about 1.

[0097] Aspect 24: The reflective display device according to any one of the Aspects 16-30, wherein at least one dimension of the pixel interface aperture is equal to or less than a corresponding dimension of the active surface, and wherein the at least one dimension of the output aperture is equal to or less than a corresponding dimension of the pixel area.

[0098] Aspect 25: The reflective display device according to any one of the Aspects 16-30, wherein the reflective display device has a perceived brightness that is higher than a perceived brightness of the otherwise same display device except without the dead-space reducing optica! element when measured under the otherwise same conditions.

[0099] Aspect 26: The reflective display device according to any one of the Aspects 16-30, wherein the reflective display device has an effective contrast ratio that is higher than an effective contrast ratio of the otherwise same display device except without the dead-space reducing optical element when measured under the otherwise same conditions.

[0100] Aspect 27: The reflective display device according to any one of the Aspects 16-30, wherein the reflective display device has a maximum viewing angle of at least +/-60 degrees to at least +/-80 degrees. [0101] Aspect 28: The reflective display device according to any one of the Aspects 16-30, wherein the dead-space reducing optical element comprises a solid and optically transparent material between the pixel interface aperture and the output aperture.

[0102] Aspect 29: The reflective display device according to any one of the Aspects 16-30, wherein the dead-space reducing optica! element comprises air between the pixel interface aperture and the output aperture.

[0103] Aspect 30. The reflective display device according to any one of the Aspects 16-30, wherein the at least one sidewall comprises a metal surface or a metalized surface.

[0104] Aspect 31 : A reflective display device, including a reflective pixel comprising an output surface comprising an active surface and an inactive surface, the reflective pixel configured to controllabiy reflect a color of light outwardly from the active surface, and a transparent dead-space reducing optical element positioned over the output surface of the reflective pixel, including a pixel facing surface positioned to interface with the active surface of the reflective pixel and to receive light reflected through the active surface of the reflective pixel, a curved viewing surface opposite the pixel facing surface, the curved viewing surface positioned to direct ambient incident light to the active area, and to direct light received at the pixel facing surface outwardly from the viewing curved viewing surface to form a virtual image of the active surface having an area that is greater than an area of the active surface and equal to or less than an area of the reflective pixel, wherein the curved viewing surface has a convex shape, and at least one sidewall that extends between the pixel facing surface and the curved viewing surface.

[01 OS] Aspect 32: The reflective display device according to any one of the Aspects 31-40, wherein at least one of the at least one sidewall forms a sidewall of another transparent dead- space reducing optical element associated with an adjacent reflective pixel.

[0108] Aspect 33: The reflective display device according to any one of the Aspects 31-40, wherein the dead-space reducing optical element has a width and a length, and wherein the width and the length are equal to or less than the corresponding dimensions of the reflective pixel,

[0107] Aspect 34: The reflective display device according to any one of the Aspects 31-40, wherein the ref iective pixel further includes a fluid chamber positioned over a reflective surface within the active surface and an electrically controlled actuator configured to controllabiy reflect the color of light outwardly from the active surface by altering pressure within the fluid chamber to cause corresponding changes in a quantity of fluid within the fluid chamber. [0108] Aspect 35: The reflective display device according to any one of the Aspects 31-40, wherein the pixel facing surface is separated from the active surface by an air gap.

[0109] Aspect 36: The reflective display device according to any one of the Aspects 31-40, wherein the pixel facing surface is separated from the active surface by an intermediate optically transparent material.

[0110] Aspect 37: The reflective display device according to any one of the Aspects 31-40, wherein the convex shape includes a truncated hemispheric shape.

[0111] Aspect 38: The reflective display device according to any one of the Aspects 31-40, wherein the convex shape includes an aspheric shape.

[0112] Aspect 39: The reflective display device according to any one of the Aspects 31-40, wherein the curved viewing surface can be a Fresnel equivalent of any one of a hemispheric shape and an aspheric shape.

[0113] Aspect 40: The reflective display device according to any one of the Aspects 31-40, wherein the area of the virtual image of the active surface is a function of at least one of a distance of the pixel facing surface from the active surface, dimensions of the curved viewing surface, and a refractive index of the optical element.

[0114] It should be emphasized that the above-described aspects of the present disclosure are merely possible examples of implementations and are set forth only fora clear understanding of the principles of the disclosure. Many variations and modifications may be made to the above- described embodiments of the disclosure without departing substantially from the spirit and principles of the disclosure. All such modifications and variations are intended to be included herein within the scope of this disclosure.

Claims

CLAIMS What we claim is:

1. A reflective display device, comprising:

(1 ) a ref lective pixel comprising: an output surface comprising an active surface and an inactive surface, a fluid cham ber positioned over a reflective surface within the active surface, and an electrically controlled actuator configured to controilabiy cause reflection of a color of light outwardly from the active surface by altering pressure within the fluid cham ber to cause corresponding changes in a quantity of fluid within the fluid chamber; and

(2) a dead-space reducing optical element positioned over the output surface of the reflective pixel, the dead-space reducing optical element including: a pixel facing surface comprising a pixel interface aperture positioned to interface with the active surface of the reflective pixel and to receive the light reflected through the active surface of the reflective pixel, a viewing surface opposite the pixel facing surface, the viewing surface com prising an output aperture positioned to direct the light received at the pixel interface aperture outwardly from the viewing surface, wherein the output aperture has an area that is larger than an area erf the pixel interface aperture and less than or equal to a pixel area comprising an area of the active surface and an area of the inactive surface, and at least one sidewall that extends between the pixel facing surface and the viewing surface.

2. The reflective display device according to claim 1 , wherein the dead-space reducing optical element is Etendue preserving from the pixel interface aperture to the output aperture.

3. The reflective display device according to claim 1 or claim 2, wherein the at least one sidewall comprises a total internal reflection surface.

4. The reflective display device according to any one of claims 1-3, wherein an effective fill factor defined as a ratio of the area of the output aperture to the pixel area is greater than a pixel fill factor defined as a ratio of an area of the active surface and the pixel area.

5. The reflective display device according to claim 4, wherein the effective fill factor is greater than about 0.85, greater than about 0.9, or greater than about 0.95 and up to about 0.98 or up to about 1.

8. The reflective display device according to any one of claims 1-3, wherein at least one dimension of the pixel interface aperture is equal to or less than a corresponding dimension of the active surface, and wherein the at least one dimension of the output aperture is equal to or less than a corresponding dimension of the pixel area.

7. The reflective display device according to any one of claims 1-8, wherein the reflective display device has a perceived brightness that is higher than a perceived brightness of the otherwise same display device except without the dead-space reducing optical element when measured under the otherwise same conditions.

8. The reflective display device according to any one of claims 1-7, wherein the reflective display device has an effective contrast ratio that is higher than an effective contrast ratio of the otherwise same display device except without the dead-space reducing optical element when measured under the otherwise same conditions.

9. The reflective display device according to any one of claims 1-8, wherein the reflective display device has a maximum viewing angle of at least +/-60 degrees to at least +/-80 degrees.

10. The reflective display device according to any one of claims 1-9, wherein the dead-space reducing optical element comprises a solid or a liquid and optically transparent material between the pixel interface aperture and the output aperture.

11. The reflective display device according to any one of claims 1-10, wherein the dead-space reducing optical element comprises air between the pixel interface aperture and the output aperture.

12. The reflective display device according to any one of claims 1-11 , wherein the at least one sidewall comprises a metal surface or a metalized surface.

13. The reflective display device according to claim 12, wherein the display device includes adjacent reflective pixels with adjacent respective optical elements, and wherein a shape of the sidewalls of the adjacent respective optical elements is symmetrical about a centerline that intersects at a point of interface of the adjacent reflective pixels.

14. The ref lective display device according to any one of claims 1-13, wherein a height H of the optical element, measured as a distance between the pixel facing surface and the viewing surface can be determined based on (0.5^*(WO+W!))/TAN [ASIN [1/R!]], wherein WO represents a dimension of the output aperture, Wl represents a corresponding dimension of the pixel interface aperture, and Ri represents a refractive index of the optical element.

15. The reflective display device according to any one of claims 1-14, wherein the at least one sidewall can have a parabolic curvature.

16. A reflective display device, comprising:

(1) a refiective pixel comprising an output surface comprising an active surface and an inactive surface, the ref iective pixel configured to controliabiy reflect a color of light outwardly from the active surface; and

(2) a dead-space reducing optical element positioned over the output surface of the reflective pixel, the dead-space reducing optical element including: a pixel facing surface comprising a pixel interface aperture positioned to interface with the active surface of the reflective pixel and to receive the light reflected through the active surface of the reflective pixel, a viewing surface opposite the pixel facing surface, the viewing surface com prising an output aperture positioned to direct the light received at the pixel interface aperture outwardly from the viewing surface, wherein the output aperture has an area that is larger than an area of the pixel interface aperture and less than or equal to a pixel area comprising an area of the active surface and an area of the inactive surface, and at least one sidewall that extends between the pixel facing surface and the viewing surface.

17. The reflective display device according to claim 16, wherein the reflective pixel is an eiectrowetting refiective pixel.

18. The reflective display device according to claim 16, wherein the reflective pixel is an electrophoretic pixel.

19. The reflective display device according to claim 16, wherein the reflective pixel is an electrostatic shutter pixel.

20. The reflective display device according to any one of claims 16-19, wherein the dead- space reducing optical element is Etendue preserving from the pixel interface aperture to the output aperture.

21. The reflective display device according to any one of claims 16-20, wherein the at least one sidewall comprises a total internal reflection surface.

22. The reflective display device according to any one of claims 16-21 , wherein an effective fill factor defined as a ratio of the area of the output aperture to the pixel area is greater than a pixel fill factor defined as a ratio of an area of the active surface and the pixel area.

23. The reflective display device according to claim 22, wherein the effective fill factor is greater than about 0.85, greater than about 0.9, or greater than about 0.95 and up to about 0.98 or up to about 1.

24. The ref lective display device according to any one of claims 16-23, wherein at least one dimension of the pixel interface aperture is equal to or less than a corresponding dimension of the active surface, and wherein the at least one dimension of the output aperture is equal to or less than a corresponding dimension of the pixel area.

25. The reflective display device according to any one of claims 16-24, wherein the reflective display device has a perceived brightness that is higher than a perceived brightness of the otherwise same reflective display device except without the dead-space reducing optical element when measured under the otherwise same conditions.

26. The reflective display device according to any one of claims 16-25, wherein the reflective display device has an effective contrast ratio that is higher than an effective contrast ratio of the otherwise same reflective display device except without the dead-space reducing optical element when measured under the otherwise same conditions.

27. The reflective display device according to any one of claims 16-26, wherein the reflective display device has a maximum viewing angle of at least +/-60 degrees to at least +/-80 degrees.

28. The reflective display device according to any one of claims 16-27, wherein the dead- space reducing optical element comprises a solid and optically transparent material between the pixel interface aperture and the output aperture.

29. The reflective display device according to any one of claims 16-28, wherein the dead- space reducing optical element comprises air between the pixel interface aperture and the output aperture.

30. The reflective display device according to any one of claims 16-29, wherein the at least one sidewall comprises a metal surface or a metalized surface.

31. A reflective display device, comprising: a reflective pixel comprising an output surface comprising an active surface and an inactive surface, the ref lective pixel configured to controliab!y reflect a color of light outwardly from the active surface; and a transparent dead-space reducing optical element positioned over the output surface of the reflective pixel, comprising: a pixel facing surface positioned to interface with the active surface of the reflective pixel and to receive light reflected through the active surface of the reflective pixel, a curved viewing surface opposite the pixel facing surface, the curved viewing surface positioned to direct ambient incident light to the active area, and to direct light received at the pixel facing surface outwardly from the curved viewing surface to form a virtual image of the active surface having an area that is greater than an area of the active surface and equal to or less than an area of the reflective pixel, wherein the curved viewing surface has a convex shape, and at least one sidewall that extends between the pixel facing surface and the curved viewing surface.

32. The reflective display device according to claim 31 , wherein at least one of the at least one sidewall forms a sidewall of another transparent dead-space reducing optical element associated with an adjacent reflective pixel.

33. The reflective display device according to any one of claims 31-32, wherein the dead- space reducing optical element has a width and a length, and wherein the width and the length are equal to or less than the corresponding dimensions of the reflective pixel.

34. The reflective display device according to any one of claims 31-33, wherein the reflective pixel further includes a fluid cham her positioned over a reflective surface within the active surface and an electrically controlled actuator configured to controllabiy reflect the color of light outwardly from the active surface by altering pressure within the fluid chamber to cause corresponding changes in a quantity of fiuid within the fluid chamber.

35. The reflective display device according to any one of claim s 31-34, wherein the pixel facing surface is separated from the active surface by an air gap,

36. The reflective display device according to anyone of claims 31-34, wherein the pixel facing surface is separated from the active surface by an intermediate optically transparent material.

37. The reflective display device according to any one of claims 31-36, wherein the convex shape includes a truncated hemispheric shape.

38. The reflective display device according to any one of claims 31-36, wherein the convex shape includes an aspheric shape.

39. The reflective display device according to any one of claims 31-36, wherein the curved viewing surface can be a Fresnel equivalent of any one of a hemispheric shape and an aspheric shape.

40. The reflective display device according to any one of claims 31-36, wherein the area erf the virtual image of the active surface is a function of at least one of a distance of the pixel facing surface from the active surface, dimensions of the curved viewing surface, and a refractive index of the optical element.