Holographic object relay for light-field displays

Abstract

Systems and methods are disclosed for redirecting light corresponding to a light field or holographic object so that an image generated by the light field or other display is perceived by a viewer without having to address the display itself.

Description

Technical Field

[0001] The present disclosure generally relates to systems configured to generate light corresponding to a 2D, 3D, or holographic image and further configured to relay the generated holographic image to a desired location. Background Art

[0002] Many technologies exist today that are unfortunately often confused with holograms, including lenticular printing, Pepper's Ghost, glasses-free stereoscopic displays, horizontal parallax displays, head-mounted VR and AR displays (HMDs), and other such illusions generally referred to as "fauxlography." These technologies may exhibit some of the desirable properties of true holographic displays, but lack the ability to stimulate human visual sensory responses in any sufficient way.

[0003] Lightfield and holographic displays are the result of multiple projections, where the energy surfaces are positioned to provide angular, color, and brightness information about the propagation within the viewing volume. Unlike stereoscopic displays, the position of the observed convergent energy propagation path in space does not change as the viewer moves around the viewing volume, and any number of viewers can simultaneously see the propagated object in real space, as if it were physically present. Summary of the Invention

[0004] An embodiment of a holographic display system includes a first display comprising a lightfield display configured to project light along a set of projection optical paths to form at least a first holographic surface having a first projected depth profile relative to a display screen plane; and a relay system positioned to receive light from the lightfield display along the set of projection optical paths and relay the received light along a set of relay optical paths such that points on the first holographic surface are relayed to relay locations, thereby forming a first relay holographic surface having a first relay depth profile relative to a virtual screen plane, the first relay depth profile being different from the first projected depth profile. The lightfield display includes a controller configured to receive instructions for interpreting the difference between the first projected depth profile and the first relay depth profile by operating the lightfield display to output projected light such that the first relay depth profile of a first relay holographic object is an intended depth profile for a viewer.

[0005] An embodiment of a holographic display system includes a first display comprising a light field display configured to project light along a set of projection optical paths to form at least a first holographic surface, the set of projection optical paths being determined according to a first four-dimensional (4D) function defined by the light field display such that each projection optical path has a set of position coordinates and angular coordinates in a first 4D coordinate system defined relative to a display screen plane. The system further includes a relay system positioned to receive light from the light field display along the set of projection optical paths and relay the received light along a set of relay optical paths such that points on the first holographic surface are relayed to relay locations, thereby forming a first relay holographic surface, the set of relay optical paths being determined according to a second 4D function defined by the relay system such that each relay optical path has a set of position coordinates and angular coordinates in a second 4D coordinate system defined relative to a virtual screen plane. The light field display includes a controller configured to receive instructions for interpreting the second 4D function by operating the light field display to output projection light according to the first 4D function, so that the position coordinates and the angular coordinates of each relay light path in the set of relay light paths in the second 4D coordinate system allow the relay holographic surface to be presented to a viewer as intended.

[0006] An embodiment of a holographic display system includes a light field display configured to project light along a set of projection optical paths to form at least a first holographic surface and a second holographic surface in a first depth order relative to a display screen plane; a relay system positioned to receive light from the light field display along the set of projection optical paths and relay the received light along a set of relay optical paths such that points on the first holographic surface and the second holographic surface are relayed to relay positions, thereby forming a first relay holographic surface and a second relay holographic surface that can be perceived in a second depth order relative to a virtual screen plane, the first depth order and the second depth order being opposite; and a corrective optical element disposed in the set of relay optical paths, wherein each relay optical path in the set of relay optical paths has a set of position coordinates and angular coordinates in a four-dimensional (4D) coordinate system, and wherein the corrective optical element is configured to invert the polarity of the angular coordinates of each relay optical path in the first set of relay optical paths such that the first relay holographic surface and the second relay holographic surface can be perceived in a corrected depth order that is substantially the same as the first depth order.

[0007] An embodiment of a holographic display system includes a light field display configured to project light along a set of projection optical paths to form at least a first holographic surface and a second holographic surface in a first depth order relative to a display screen plane; a corrective optical element disposed in the set of projection optical paths, wherein each projection optical path in the first set of projection optical paths has a set of position coordinates and angular coordinates in a four-dimensional (4D) coordinate system, and wherein the corrective optical element is configured to reverse the polarity of the angular coordinates of each projection optical path in the set of projection optical paths, the first holographic surface and the second holographic surface having an intermediate depth order opposite to the first depth order; and a relay system positioned to receive light from the corrective optical element along the set of projection optical paths and to relay the received light along a set of relay optical paths such that points on the first holographic object and the second holographic object are relayed to relay positions, thereby forming a first relay holographic surface and a second relay holographic surface that can be perceived in a second depth order relative to a virtual screen plane, the first depth order and the second depth order being the same.

[0008] An embodiment of a holographic display system includes a first display, the first display comprising a light field display, the light field display being configured to project light along a first set of projection optical paths to form at least a first holographic surface and a second holographic surface having a first depth profile and a second depth profile relative to a display screen plane, respectively; and a first relay system, the first relay system being positioned to receive light from the light field display along the first set of projection optical paths and to relay the received light along a first set of relay optical paths, so that points on the first holographic surface and the second holographic surface are relayed to relay positions, thereby forming a first relay holographic surface and a second relay holographic surface having a first relay depth profile and a second relay depth profile relative to a virtual screen plane, respectively.

[0009] An embodiment of a holographic display system includes a first display, the first display comprising a light field display, the light field display being configured to project light along a first set of projection optical paths to form at least a first holographic surface having a first depth profile relative to a display screen plane; a first relay system, the first relay system being positioned to receive light from the light field display along the first set of projection optical paths and relay the received light along a first set of relay optical paths, so that points on the first holographic surface are relayed to relay positions, thereby forming a first relay holographic surface having a first relay depth profile relative to a virtual screen plane; and a second relay system, the second relay system being positioned to receive light from the first relay system along the first set of relay optical paths and relay the received light along a second set of relay optical paths, so that points on the first relay holographic surface are further relayed to new relay positions, thereby forming second relay holographic surfaces having second relay depth profiles respectively relative to new virtual screen planes. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1A An embodiment of a system configured to use a beam splitter and an image retroreflector to relay a holographic surface projected by a lightfield display is presented;

[0011] Figure 1B An embodiment of a system configured to use a beam splitter and multiple image retroreflectors to relay a holographic surface projected by a lightfield display is presented;

[0012] Figure 2A An embodiment of a corrective optical element configured to invert the polarity of a UV angular coordinate in a four-dimensional (4D) coordinate system is presented;

[0013] Figure 2B A top view of a waveguide placed above multiple illumination source pixels in the UV plane is shown;

[0014] Figure 2C Shown Figure 2B Side view of the illustrated embodiment in the UZ plane, where the thin lens acts as a waveguide;

[0015] Figure 3A Shown with Figure 1A An embodiment of a holographic display system similar to the system shown, in which the beam splitter and image retroreflector have been replaced by a transflector;

[0016] Figure 3B An embodiment of a holographic display system having multiple relay systems is presented;

[0017] Figure 3C Another embodiment of a holographic display system having multiple relay systems is presented;

[0018] Figure 4A A composite diagram illustrating an embodiment of a dihedral corner reflector array (DCRA);

[0019] Figure 4B A side view of an embodiment of a transflector is shown imaging a point light source;

[0020] Figure 4C An embodiment of a holographic display system having a relay system including a concave mirror is presented;

[0021] Figure 4D Another embodiment of a holographic display system having a relay system including a concave mirror is presented;

[0022] Figure 4E Another embodiment of a holographic display system having a relay system comprising a beam splitter, at least one lens, and a reflector is presented;

[0023] Figure 4F Another embodiment of a holographic display system having a relay system including a lens system is presented;

[0024] Figure 5A An embodiment of an ideal relay system is presented;

[0025] Figure 5B An embodiment of a holographic display system having a relay system configured to relay a first holographic surface and a second holographic surface projected by a lightfield display using a beam splitter and an image retroreflector is presented;

[0026] Figure 5C An embodiment of a holographic display system having a relay system configured to relay a first holographic surface and a second holographic surface projected by a light field display using a beam splitter and a concave mirror is presented;

[0027] Figure 5D Demonstrated correction Figure 5C An embodiment of the optical effect of the relay system is shown;

[0028] Figure 5E An embodiment of a holographic display system having a relay system configured to relay a first holographic surface and a second holographic surface projected by a light field display using a beam splitter and a plurality of concave mirrors is presented;

[0029] Figure 6 An embodiment of a holographic display system having a relay system configured to relay a first holographic surface and a second holographic surface projected by a lightfield display using a transflector is presented;

[0030] Figure 7An embodiment of a holographic display system having a first relay system configured to relay a first holographic surface and a second holographic surface projected by a lightfield display and to relay a third surface projected by a second display is presented;

[0031] Figure 8A An embodiment of a holographic display system having a second relay system, a plurality of displays is presented;

[0032] Figure 8B Demonstrated use Figure 8A An embodiment of performing occlusion processing using a parallax barrier;

[0033] Figure 8C Shows the perception of viewers at different locations similar to Figure 8A An embodiment of a holographic display system is shown;

[0034] Figure 8D Shown Figure 8A and 8B An abstract embodiment of a display system is shown;

[0035] Figure 8E Shown Figure 8D An embodiment of a system having a transflector with a tapered surface; and

[0036] Figure 8F Shows something like Figure 8E An embodiment of a system with a pyramidal transflector surface is shown in . DETAILED DESCRIPTION

[0037] Figure 1A An embodiment of a holographic display system is shown that includes a first display 1001, the first display comprising a light field display configured to project light along a set of projection light paths 1036 to form at least a first holographic surface 1016, the first holographic surface having a first projected depth profile relative to a display screen plane 1021. In embodiments, the first holographic surface 1016 can be any surface in a holographic scene, such as a portion of an object, a face, a background scene, etc. In embodiments, the projected depth profile of the holographic surface 1016 can include a depth that is perceptible to a viewer (not shown) viewing the first display 1001 along a normal axis (not shown) of the display 1001. Figure 1AThe holographic display system further includes a relay system 102A positioned to receive light from the lightfield display 1001 along a first set of projection optical paths 1036 and relay the received light along a set of relay optical paths 1025A such that points on the first holographic surface 1016 are relayed to relay locations, thereby forming a first relay holographic surface 1018 having a first relay depth profile relative to a virtual screen plane 1022. In an embodiment, the virtual screen plane 1022 is oriented at a non-parallel angle relative to a display screen plane 1021 of the lightfield display 1001. In an embodiment, the virtual screen plane 1022 is oriented at a perpendicular angle relative to the display screen plane 1021 of the lightfield display 1001.

[0038] In an embodiment, the depth profile of the holographic surface 1016 may include the depth perceived by the viewer 1050 observing in the direction of the virtual screen plane 1022. As illustrated in FIG1 , the first relayed depth profile of the relayed holographic surface 1018 is different from the first projected depth profile of the first holographic surface 1016: the first holographic surface 1016 is projected as an off-screen holographic surface, while the first relayed holographic surface 1018 can be perceived by the viewer 105 as an on-screen holographic surface relative to the virtual screen plane 1022.

[0039] In an embodiment, a relay system 102A may use a beam splitter 101 and an image retroreflector 1006A to relay holographic objects projected by a light field display 1001. In an embodiment, the light field display 1001 includes one or more display devices 1002 having multiple light source positions (not shown), an imaging relay 1003, which may or may not be present, for relaying images from the display devices to an energy surface 1005, and an array of waveguides 1004 that project each light source position on the energy surface 1005 into a unique direction (u, v) in three-dimensional space. The energy surface 1005 may be a seamless energy surface having a combined resolution greater than that of the surfaces of any individual display device 1002. Examples of light field displays 1001 are described in commonly owned U.S. Patent Application Publication Nos. US2019 / 0064435, US2018 / 0356591, 2018 / 0372926, and U.S. Patent Application Serial No. 16 / 063675, all of which are incorporated herein by reference for all purposes. Projected light rays 1036 can converge at locations 111 on the surface of holographic object 1016 and then diverge as they approach beam splitter 101. Beam splitter 101 can be configured to include a polarizing beam splitter, a transparent aluminum coating, or at least one dichroic filter. In an embodiment, beam splitter 101 can be oriented at a 45 degree angle relative to display screen plane 1021 and retroreflector 1006A, and retroreflector 1006 is oriented orthogonal relative to display screen plane 1021. A portion of the incident light along the projection optical path 1036 is reflected from the beam splitter 101 along a set of reflection optical paths 1037 toward the image retroreflector 1006A, while most of the remaining light passes through the beam splitter 101 into the ray along a set of transmission optical paths 1039A, which may have an impact on the image retroreflector 1006A. Figure 1A 1025A is not helpful in forming the relay holographic object 1018 in the image. In an embodiment, the retroreflector 1006A may contain a fine array of individual reflectors, such as corner reflectors. The retroreflector 1006A is used to reverse each ray of the incident light in a direction opposite to the approach direction without significant spatial offset. The rays along the optical path 1037 reverse their direction when reflected from the retroreflector 1006A, causing the approach angle of the ray to be substantially folded back to the retroreflector 1006A, and a portion of the intensity of the ray passes through the beam splitter 101 along a set of relay optical paths 1025A, thereby converging at the location 112 of the holographic object 1018. In this way, the holographic object 1016 directly projected by the light field display 1001 is relayed to form the relay holographic object 1018.

[0040] Figure 1A There may be an optional optical element 1041A positioned between the beam splitter 101 and the retroreflector 1006A. The relative position of this optional optical element 1041A is similar to Figure 1B10. Optional optical element 1041A appears in FIG. This optical element may be a polarization control element used with polarizing beam splitter 101. If display 1001 produces only one polarization state, polarizing beam splitter 101 may be arranged to direct substantially all of the display's light toward retroreflector 1006A, thereby eliminating the majority of light rays 1039A that may pass vertically through the beam splitter and not contribute to imaging holographic object 1018. Using polarizing beam splitter 101, light ray 1037 is linearly polarized upon approaching optical element 1041A, which may include a quarter-wave retarder, and circularly polarized after passing through optical element 1041A. Upon reflection from retroreflector 1006A, the majority of light on ray 1025A may be circularly polarized in the opposite direction, and for this opposite circular polarization, returning through the quarter-wave retarder will cause these light rays to be converted to a linear polarization that is rotated 90 degrees relative to the light exiting beam splitter 101 on rays along reflected optical path 1037. This light has an opposite polarization to the light reflected by beam splitter 101, so it will pass directly through beam splitter 101 instead of being deflected and contribute to the imaging of holographic object 1018. In short, quarter-wave plate optical element 1041A placed between beam splitter 101 and retroreflector 1006A can help convert most of the light reflected from beam splitter 101 from one linear polarization to the opposite linear polarization, allowing beam splitter 101 to pass this light with optimal efficiency, produce the holographic image, and limit wasted light.

[0041] In the case where the display 1001 produces unpolarized light, approximately half of the incident light 1036 on the beam splitter will be directed along the set of reflected light paths 1037 toward the retroreflector 1006A to form light rays, and approximately half of the incident light will be directed in a vertical direction along a set of transmitted light paths 1039A. This results in light ray 1039A being lost. In an embodiment, as Figure 1B As shown, Figure 1A The holographic display system may include a relay system 102B including an additional retroreflector 1006B. In an embodiment, the additional retroreflector 1006B may be positioned opposite the display 1001 relative to the beam splitter 101, symmetrical in distance but orthogonal in orientation to the retroreflector 1006A. Figure 1B A system is shown for relaying a holographic surface projected by a light field display 1001 using a holographic relay system 102B comprising a beam splitter 101 and two image retroreflectors 1006A and 1006B, each of which reflects a ray of incident light in a direction opposite to its incident direction. Figure 1AIn contrast, light rays along transmission path 1039B are retroreflected from retroreflector 1006B in the same manner as rays along reflection path 1037 are retroreflected from retroreflector 1006A. Light rays along transmission path 1039B and reflection path 1037 are retroreflected and converged at beam splitter 101 and combined along a set of relay paths 1025B to form light rays that are focused at point 112, thereby contributing to first relay holographic surface 1018. In an embodiment, the additional retroreflector 1006B and the beam splitter 101 are aligned such that the projection light transmitted through the beam splitter 101 toward the additional retroreflector is reflected from the additional retroreflector 1006B and further reflected by the beam splitter 101 along another set of relay light paths 1025B toward the virtual display screen 1022, and a set of relay light rays 1025A from the first retroreflector 1006A and the further set of relay light rays 1025B from the further retroreflector 1006B substantially overlap. Figure 1A As discussed above with respect to optional optical element 1041A shown, optical element 1041B can include a quarter-wave retarder that can cause most of the light rays along transmission path 1039B to return to beam splitter 101 with opposite linear polarization, so that most of these light rays will be directed by beam splitter 101 toward the formation of holographic surface 1018, rather than being directed directly through beam splitter 101 toward display 1001. Optional optical element 1041B can contain polarization control elements, diffractive elements, refractive elements, focusing or defocusing elements, or any other optical element.

[0042] Now refer to Figure 1A and 1B In an embodiment, the vertical distance D1 between points (such as location 111 on the directly projected surface 1016) can be the same as the horizontal distance D1 between points on the relay holographic surface 1018, such as location 112 corresponding to location 111. The relay system 102A or 102B can be configured to relay multiple holographic surfaces distributed around the display screen plane 1021, including the screen-outside surface 1016 on the side 1010 of the screen plane 1021, and the screen-inside projected surface on the side 1011 of the screen plane 1021. Figure 1A and 1BIn the example shown, surfaces 1016 are projected as off-screen holographic surfaces. These holographic surfaces can be relayed from screen plane 1021 to virtual plane 1022, such that off-screen surfaces 1016 of screen plane 1021 appear behind virtual plane 1022 relative to viewer 1050, and similarly, such that surfaces within the screen of lightfield display 1001 projected onto side 1011 of screen plane 1021 appear in front of virtual screen plane 1022 relative to viewer 1050. Thus, the depth of holographic surfaces 1016 flips polarity—location 111 of off-screen holographic surface 1016 furthest from display screen plane 1021 is relayed to location 112 of relayed holographic surface 1018 furthest from viewer 1050. To account for this depth inversion, and to present the same view and depth profile of the relay holographic surface 1016 to the observer 1050 that an observer of the directly projected off-screen holographic object 1016 would see without the relay system 102B, one approach is to reverse the polarity of the UV light field coordinates, which are two angular coordinates in the 4D light field function with coordinates (X, Y, U, V), thereby transforming the projection light rays 1036 into projection light rays 1013, each of which has an opposite slope. This transforms the off-screen holographic projection surface 1016 into an on-screen holographic projection surface 1014 with an inverted depth, which is relayed to the relay holographic surface 1020. The relay holographic surface 1020 is off-screen relative to the virtual display plane 1022 and will appear to the observer 1050 to have the same depth profile relative to the virtual screen plane 1022 as the projection object 1016 has relative to the display screen plane 1021. The projected holographic surface 1014 will appear to be depth-inverted relative to the display screen plane 1021. In summary, to project the holographic surface 1020 for the observer 1050 of the virtual screen plane 1022, the expected projected holographic surface 1016 with the expected depth profile can be rendered for the display screen 1021, and then each of the UV angular light field coordinates can be flipped to produce the depth-inverted surface 1014, which appears on the opposite side of the display screen plane 1021 from the holographic object 1016, but which is relayed by the relay system 102A or 102B into the relay holographic object 1020, which has the expected relay holographic surface and the expected depth profile relative to the virtual screen plane 1022. The 4D light field coordinate system of (X, Y, U, V) is described in commonly owned U.S. patent application publication numbers US2019 / 0064435, US2018 / 0356591, US2018 / 0372926, and U.S. patent application serial number 16 / 063,675, which are incorporated herein by reference and will not be repeated here.

[0043] In an embodiment, each projection optical path in a set of projection optical paths 1036 has a set of position coordinates and angular coordinates in a four-dimensional (4D) coordinate system defined with respect to a display screen plane, and each relay optical path in a set of relay optical paths 1025A, 1025B has a set of position coordinates and angular coordinates in a four-dimensional (4D) coordinate system defined with respect to a virtual display plane. As described above, the holographic surface 1014 can be rendered so that light forming the surface of the object 1014 will be relayed to an intended distribution of the relay surface 1020, which can be directly viewed by an observer 1050. One method of rendering the holographic surface 1014 is to first render the holographic object 1016 (the intended object to be shown in the absence of the relay system 102A or 102B) and then invert the polarity of its UV angular coordinates. This inversion of the UV coordinates may cause the holographic object 1014 to be projected instead of the object 1016, which can be relayed to the intended location of the holographic object 1020. The UV polarity inversion can be accomplished using corrective optical elements, as described below with reference to Figure 2A As summarized, or using adjustments in 4D light field coordinates, as referenced below Figure 2B and 2C Summarized.

[0044] Figure 2A An embodiment of a corrective optical element for inverting the polarity of UV angular light field coordinates is shown. Two rows of substantially identical lenses 201 and 202 are placed side by side. Lens rows 201 and 202 have a focal length f and are oriented parallel to each other, with a spacing of twice the focal length f, such that their focal planes overlap at imaginary plane 203 and that lenses 213 and 214 on opposite sides of imaginary plane 203 share a common optical axis 204. An incoming parallel light ray 211 is incident on lens 213 at an angle of incidence relative to optical axis 204 of θ in the UZ plane and φ in the VZ plane. Light ray 211 is focused by lens 213 onto focal plane 203 and then diverges toward lens 214, which refracts the ray into parallel rays 212. Parallel ray 212 leaves 20 at an angle of reverse polarity of -θ relative to optical axis 204 in the UZ plane and -φ relative to optical axis 204 in the VZ plane, resulting in a reversed direction relative to the incident direction of parallel ray 211. This relay system can be used in Figure 1A and 1B The projection optical path 1036 or the relay optical paths 1025A, 1025B are placed above the screen plane 1021 to invert the polarity of the UV coordinates of the projection holographic surface or the relay holographic surface, respectively.

[0045] In an embodiment, the light field display 1001 may include: Figure 1A and1B The controller 190 shown is configured to receive instructions for interpreting the difference between the first projected depth profile and the first relayed depth profile by operating the light field display 1001 to output projected light so that the first relayed depth profile of the first relayed holographic object is the depth profile expected for the viewer 1050. Figure 2B A top view of a waveguide 221 of a lightfield display 1001 placed above a plurality of illumination source pixels 222 in the UV plane is shown, comprising a row of pixels at V=0, a column of pixels at U=0, and individual pixels 223 and 224. In an embodiment, the waveguide 221 allows light from the pixels 222 to be projected along a set of projection light paths 1036, where each projection light path 1036 has a set of position coordinates (X, Y) and angular coordinates (U, V) in a four-dimensional (4D) coordinate system. To invert the polarity of the UV coordinates, and from Figure 1A and 1B When creating a holographic object 1014 from a light field rendered for a holographic object 1016, the polarity of the U and V coordinates will be swapped as shown, so that pixel 224 with coordinates of -U and +V will swap positions with pixel 223 with coordinates of +U and -V. All other pixels will swap positions as indicated, except for U, V = 0, 0, which remains in place.

[0046] Figure 2C Shown Figure 2B The embodiment shown is a side view in the UZ plane, with a thin lens acting as a waveguide 221. For a row of pixels 222 at V = 0, the two pixels at the minimum and maximum U coordinates are swapped. As a result, the intensity and color of the projected rays from the pixels at minimum U (231) and maximum U (232) swap positions.

[0047] Figure 3A Shows something like Figure 1A An embodiment of a holographic system configured as shown in Figure 1A In addition to the relay system 102A shown including the beam splitter 101, the image retroreflector 1006A has been replaced by a relay system comprising a single transflector 301 positioned to receive light along a set of projection optical paths 1036 and to direct the received light along a set of relay optical paths 1026. In an embodiment, the transflector 301 includes a plurality of internal reflective surfaces (at Figure 4A401, 402, as described below), and outputs the light in a first direction along a set of relay optical paths 1026 toward a virtual screen plane 1022. An example of the transflector 301 may be a dihedral corner reflector array (DCRA), which is an optical imaging element composed of a plurality of dihedral corner reflectors, which may be implemented as two thin layers of closely spaced parallel mirror planes oriented so that the planes are orthogonal to each other, as shown in FIG. Figure 4A As shown. Another example is a corner reflector micromirror array. Projection light rays 1036 can converge at location 111 on the surface of holographic surface 1016 and then diverge as they approach transreflector 301. Transreflector 301 internally reflects the divergent rays 1036 so that they exit the other side of 301 as rays along relay path 1026 and converge at location 112 of relay holographic surface 1018. This can be achieved within transreflector 301 by Figure 4A In this way, the holographic surface 1016 directly projected by the light field display 101 is relayed to form a relayed holographic surface 1018 .

[0048] Figure 4A An assembly diagram of an embodiment showing the detailed structure of a DCRA 401 and the path of a light ray passing through the DCRA 41 is shown. In an embodiment, the DCRA is composed of two layers 406 and 407 of closely spaced reflective planes that are parallel but offset in a first dimension, and in a second dimension, the direction of the reflective plane 401 in layer 406 is oriented orthogonal to the direction of the reflective plane 402 in layer 407. The reflective surfaces 401 and 402 can be mirror images. When an incident light ray 404 passes through the outer surface of the transflector (at Figure 4B 430), the incident light ray reflects some of its energy into reflected light ray 414. Light ray 404 has one component of its momentum reversed on first reflective surface 401 at location 410 and then has a substantially orthogonal momentum component reversed upon a second reflection from second reflective surface 402 at point 411.

[0049] Figure 4BA side view of an embodiment of a transreflector 421, which can be a DCRA, is shown, imaging a point source 422 of light positioned at a distance D from the transreflector 421. The transreflector 421 is aligned parallel to the XY plane. The X and Y momentum components of each of the light rays 423 from the point source 422 are reversed by the transreflector 421, causing light rays 424 exiting 421 to converge at an image point 425, a distance D from the transreflector 421. A portion of the light rays 423 are reflected from the outer surface 430 of the transreflector 421, thereby generating reflected light rays 433.

[0050] Now go to Figure 3B and 3C , a holographic surface can be relayed using a configuration with more than one repeater. If the holographic surface is relayed twice, the depth inversion of the holographic object that may have occurred by the first repeater can be undone by the second repeater. This is generally true for holographic surfaces relayed by an even number of holographic repeaters. Figure 3B A light field display system is shown comprising at least a first light field display 1001A and two relay systems 130 and 140 that together relay at least a first projected holographic surface to a final relay location. Figure 3B In the embodiment shown, holographic surfaces 121A and 122A are projected around lightfield display screen plane 1021A and relayed around virtual display plane 1022B to final relay locations 121C and 122C without depth inversion. Figure 3B Also shown is an optional second light field display 1001B, which can project image surface 123A. Instead of second light field display 1001B, surface 123A can be the surface of a real object. The image of the real object will be combined with holographic surfaces 121A and 122A by beam splitter 101 and relayed to image location 123C by a pair of relay systems 130 and 140 without depth inversion. The images of the holographic surface and the real object are combined and relayed to the new relay location, allowing the holographic surface and the real object to be displayed together without a physical display plane.

[0051] exist Figure 3B In FIG. 1 , the two relay systems 130 and 140 include transflectors 301A and 301B, respectively, but either of these relays may also include a beam splitter and a retroreflector (similar to Figure 1A13A). The holographic surfaces 121A and 122A are formed by light from the light field display 1001A along a set of projection optical paths 131A and 132A, and a portion of the light along the set of projection optical paths is directly transmitted through the beam splitter 101. The beam splitter can be any beam splitter disclosed in the present disclosure. The projection light along the set of projection optical paths 131A and 132A is relayed by the first relay system 130 along a first set of relay optical paths 131B and 132B, which respectively form a depth-inverted first relay holographic surface 121B and a second relay holographic surface 122B around the first virtual screen plane 1022A. The light along the first set of relay optical paths 131B and 132B is relayed along the second set of relay optical paths 131C and 132C by the second relay system 140, which form the third and fourth associated holographic surfaces 121C and 122C that are not depth-inverted around the new virtual screen plane 1022B. The depth profiles of the relay holographic objects 121C and 122C relative to the screen plane 1022B should be the same as the depth profiles of the source projection surfaces 121A and 122A, respectively.

[0052] Image surface 123A is the surface of a real object, or a holographic surface projected by an optional second light field display 1001B with a depth profile relative to the screen plane 1021B of the light field display 1001B. A portion of the light along input path 133Y from surface 123A is reflected by beam splitter 101 into projection optical path 133A, while another portion passes through beam splitter 101 along a set of transmission paths 133Z. Transflector 301A of relay system 130 has a reflective surface 430, and some of the incident light along projection path 133A is reflected into optical path 143A (and this is also true for light along projection paths 131A and 132A, but this is not the case in the example of FIG. 1 ). Figure 3B (not shown). A portion of the light along projection path 133A from object 123A is relayed by first relay system 130 to relay optical path 133B in the first group of relay optical paths 131B, 132B, and 133B. Optical path 133B forms depth-inverted image 123B. Some of the light along relay optical path 133B is reflected from the surface of transreflector 301B of relay system 140 along reflection path 143B (this is also true for incident light along relay optical paths 131B and 132B, but these reflections from the surface of transreflector 301B are not reflected in the image). Figure 3B). Another portion of the light along the relay optical path 133B is relayed a second time by the second relay system 140 to the relay optical path 133C in the second group of relay optical paths 121C, 132C and 133C. The relay optical path 133C forms a non-depth-inverted relay surface 123C, which is an image of the real object 123A, or a relay holographic surface 123A, wherein the relay surface 123C has the same depth profile as the source projection holographic surface 123A relative to the display screen plane 1021B for the observer 1050. The virtual screen plane relayed from the display screen plane 1021B is the virtual screen plane 1022C. The first observer 1050 will see two relay holographic surfaces 121C and 122C and the holographic image 123C of the real surface 123A or three relay holographic objects 121C, 122C and 123C. In Figure 3B In the configuration shown, by using a beam splitter 101 in place with a second light field display 1001B, holographic content from both light field displays can be superimposed into the same space around a second virtual screen 1022B without depth inversion, thereby allowing the depth range for displaying holographic objects to be increased beyond the depth range of either light field display 1001A or 1001B alone. Note that each display 1001A and 1001B can generate holographic objects in holographic object volumes near the corresponding display screen planes 1021A and 1021B, respectively. These holographic object volumes are relayed to a virtual screen plane 1022B corresponding to display screen 1021A and a virtual screen plane 1022C corresponding to display screen 1021B. The amount of separation between virtual screen planes 1022B and 1022C depends on the difference between a first distance between display 1001A and transflector 301A and a second distance between display 1001B and transflector 301A. If these distances are the same, the virtual screen planes 1022B and 1022C will overlap. It should also be noted that because the proximity of the lightfield display 1001A or 1001B to the beam splitter 101 can be adjusted, the relayed holographic object volume near the virtual screen planes 1022B and 1022C can contain one larger area or two smaller but separate areas for displaying holographic objects that are adjustable for a given application. Where the relayed holographic object volumes overlap, a combined relayed holographic object volume that is larger than the holographic object volume of either of the individual displays can be achieved. Similarly, if a real surface 123A is used in place of holographic surface 123A, the relative positions of the relayed holographic objects 121C and 122C and the holographic image 123C from the real object 123A can be adjusted and customized for any application. Note that this discussion regarding the variable spacing between the screen planes 1022B and 1022C can also apply to cases where only one relay (such as 130) is used.

[0053] Figure 3C Shown Figure 3B , but light reflected from the second transflector 301B of the second relay system 140 along a set of reflection paths 141B, 142B, and 143B is shown as being received by the second observer 1051. Figure 3B The numbers in the table apply to Figure 3C The light from the depth-inverted relay holographic objects 121B and 122B along the first set of relay optical paths 131B and 132B is reflected into the reflected optical paths 141B and 142B, respectively, and in an embodiment, may pass through a corrective optical element placed at plane 137. The corrective optical element may be similar to Figure 2A The corrective optical element shown is used to reverse the polarity of angular light field coordinates u and v, so that second observer 1051 perceives relayed holographic surfaces 121C and 122C, respectively, as having the same depth profile relative to plane 137 as source projection surfaces 121A and 122A, respectively, relative to display plane 1021 of light field display 1001A. Similarly, object 123A, which can be a holographic surface or a surface of a real object projected by display 1001B, generates light rays that are relayed by relay system 130 along relay optical path 133B forming depth-reversed image 123B and reflected by surface 430 of transreflector 301B along reflection path 143B into the light. The optional corrective optical element just described at 137 can also cause depth inversion, so that second observer 1051 sees relayed image 123C having the same depth profile as that of surface 123A. In this way, observers 1050 and 1051 will see the same holographic image at the same location.

[0054] As previously described, if the first observer 1050 sees depth-correct relayed holographic images 121C, 122C, and 123C, the corresponding light along paths 141B, 142B, and 143B approaching plane 137 will be depth-inverted images 121B, 122B, and 123B on its way to the second observer 1051. Instead of placing corrective optics at plane 137, a third relay system (not shown) can be used to invert the depth of these depth-inverted images 121B, 122B, and 123B. One disadvantage of this approach is the fact that, with an additional relay (not shown), the second observer 1051, now relaying the images (positioned at a different location to receive light from the additional relay, not shown), will not see these relayed images at the same location as the holographic images 121C, 122C, and 123C perceived by the first observer 1050.

[0055] Other focusing optical elements, defocusing optical elements, mirrored surfaces, or any combination of these may be used to relay the holographic object volume around the lightfield display plane. Figure 4C An embodiment is shown that uses curved mirrors instead of retroreflectors as focusing elements to relay the holographic object volume without depth inversion. Figure 4C An orthographic view of a triangular surface imaged using a holographic relay system 460 including both a beam splitter 462 and a concave mirror 452 is shown, where the surface is on the optical axis 453. In embodiments, the concave mirror 452 may be spherical, parabolic, or some other shape. The beam splitter 462 may be any beam splitter described herein. The triangular surface 461 is placed on a vertical axis 454 that is orthogonal to the horizontal optical axis 453. The center of curvature of the mirror C at 451 is at a distance D1 from the beam splitter. On the vertical optical axis 454, point C' 441 is also at the same distance D1 from the beam splitter. A portion of the light that leaves point C' 441 along a set of projection optical paths 465 will be reflected from the beam splitter 462 into a light ray along a set of reflection optical paths 466 that are incident on the mirror 452. Concave mirror 452 and beam splitter 462 are aligned so that a portion of light 466 reflected from beam splitter 462 toward concave mirror 452 is reflected and focused from concave mirror 452 back through beam splitter 462 along a set of relay optical paths 467 extending in a substantially opposite return direction from set of reflected optical paths 466. Light along relay paths 467 may be relayed through point C 451 toward virtual screen plane 469. Surface 461 may be a real surface or a holographic surface projected by LF display 463. Similarly, light rays along projection paths 471 from surface 461 will be reflected from beam splitter 462 into reflected optical paths 472, which are reflected from concave mirror 452, and some of the return light 473 will pass through beam splitter 462 and along relay optical paths 474, which converge to help form a relayed image 457 of surface 461 viewed by observer 450. Optional optical layer 464 may contain polarization control optics, lens elements, diffractive optics, refractive optics, etc. In one embodiment, as described above for Figure 3AAs described, optical layer 464 is a quarter wave retarder that can convert linearly polarized light into circularly polarized light, and vice versa. If a polarizing beam splitter 462 is used, then in a first state, light exiting the beam splitter 462 on the reflected light path 472 is linearly polarized. Rays along the reflected light path 472 can be converted from a first state of linear polarization to circular polarization, which is converted to an opposite circular polarization upon reflection by the mirror 452, and further converted by the quarter wave retarder 464 to a second state of linear polarization that is orthogonal to the first state. As a result, rays 473 approaching the polarizing beam splitter 462 will have an opposite linear polarization compared to the rays exiting the polarizing beam splitter 462 along the reflected light path 472, and these rays will pass through the beam splitter 462, thereby contributing to the imaging of the relayed image 457 viewed by the viewer 450 without being deflected. In Figure 4C In the configuration shown, the holographic surface projected by the LF display 463 around a display screen plane 468 (which may be the same as the display surface of the LF display 463 ) is relayed around a virtual screen plane 469 , viewable by the observer 450 .

[0056] In an embodiment, the surface near point C'441 is relayed to the vicinity of point C 451. Another feature of this optical system is that an object that is closer to the beam splitter 462 than C'441 is imaged to a position farther from the beam splitter than point C 451 by magnification, and an object that is farther from the beam splitter 462 than point C'441 is imaged to a position closer to the beam splitter than point C 451 by reduction. This means that when the holographic objects generated near point C'441 are relayed to point C 451, their depth ordering should be respected. The magnification or reduction of objects near point C'441 can be reduced by increasing the radius of curvature of the mirror 452 and / or making the depth range of the projected holographic objects smaller relative to the radius of curvature of the mirror 452 with respect to point C'441. Although in Figure 4B The example shown in shows a spherical mirror, but different configurations of mirrors can be used to perform imaging, including parabolic concave mirrors, and even spherical or parabolic convex lenses for projecting the image behind the mirror on the other side of the mirror from the viewer 450 ( Figure 4C The right side of the middle mirror 452) has an image of the converging point.

[0057] In some embodiments, Figure 4C The focusing function of the mirror 452 shown in FIG can be replaced by one or more optical elements, such as lenses, mirrors, or some combination of these elements. Figure 4EIn one embodiment shown, relay system 460 can be replaced by relay system 470, which includes a beam splitter, one or more lenses including lens 444 and optionally lens 445, and a reflector 442 on the side of the one or more lenses opposite to beam splitter 462. The reflector can be orthogonal to optical axis 453. The optical axis of the one or more lenses can be substantially aligned with optical axis 453. In this case, light rays from holographic object 461 that reflect from beam splitter 462 and toward reflector 442 will each pass through one or more lenses, and the one or more lenses will provide a focusing function. In one embodiment, a planar reflector is used, and the focal plane of at least one lens 444 or lens 445 is positioned at the focus of planar reflector 442. In a different embodiment, reflector 442 is curved. In another embodiment, one or more lenses 444, 445 are replaced by an array of much smaller lenses.

[0058] In another embodiment, the entire relay system 460 may be replaced with one or more lens-formed relays. Figure 4F An embodiment is shown in which the relay system 460 is replaced by a lens relay system 480 comprising one or more lenses that relay the holographic surface 437 to the relay holographic surface 438 about the screen plane 468 of the light field display 463. The one or more lenses comprising the lens 446 and the optional lens 447 can have a common optical axis that can be substantially aligned with the normal of the display surface 468 along the optical axis 454. The one or more lenses can perform a focusing function that optically relays an area around the display screen plane 468 to a virtual screen plane 435 that is near the optical axis but on a side of the one or more lenses away from the light field display 463. The optical system with the lenses can also contain a focal point, and the magnification or reduction of the holographic object projected by the light field display 463 near the display screen plane 468 is the same as described above for Figure 4D The configuration shown is largely the same as described.

[0059] Figure 4D488 is an orthogonal view of a holographic surface 488 being relayed to a holographic surface 489 using a holographic relay system comprising a curved concave mirror 482 and a beam splitter 485, where the holographic surface is offset from the optical axis 483. Point 481 is the focus of the mirror, which can be spherical, parabolic, or other shapes. As shown, surface 488 is a holographic surface projected from a light field display 497, but the imaging described here would also work if surface 488 were a real surface. Light paths 490C and 492C are projected from light field display 497 at different angles and converge to form another vertex of surface 488. These lights along projection paths 490C and 492C reflect from beam splitter 485 (with some loss due to passing directly through the beam splitter, which is not shown) to become light rays along reflected light paths 490D and 492D, which then reflect from the surface of mirror 482 to become light rays on relay paths 490E and 492E, which pass through the beam splitter (with some loss, which is not shown) and again converge at one vertex of image 489, helping to form image 489. Light rays along paths 491C and 493C are projected from light field display 497 at different angles and converge to form one vertex of surface 488. These light rays along 491C and 493C reflect from beam splitter 485 (with some loss due to passing directly through the beam splitter, which is not shown) to become light rays along reflection paths 491D and 493D, which then reflect from the surface of mirror 482 to become light rays on relay paths 491E and 493E, which pass through the beam splitter (with some loss, not shown) and converge again at one vertex of image 489, helping to form image 489. Light rays along projection paths 492C and 493C reflect as light rays from the beam splitter along reflection paths 492D and 493D and pass through focal point 481 of curved mirror 482, becoming rays along relay paths 492E and 493E parallel to the optical axis. The light rays along the projection paths 490C and 491C are reflected from the beam splitter as light rays along reflection paths 490D and 491D, respectively, and are parallel to the optical axis before being reflected from the curved mirror 482, so that their reflected rays along the relay paths 490E and 491E, respectively, pass through the focal point 481 of the curved mirror 482. Figure 4D In the configuration shown, the holographic surface projected by the LF display 497 around a screen plane 498 (which may be the same as the display surface of the LF display 497 ) is relayed to be projected around a virtual screen plane 469 , viewable by the observer 450 .

[0060] In an embodiment, along Figure 4DThe light rays of projection paths 490C and 491C are projected at the normal to the surface of light field display 497 at a single angle, or equivalently, a single value of the light field angle coordinate, designated as u=0 (u is in the plane of the figure—the orthogonal light field coordinate v is not referenced). Figure 4D 491D, which are then reflected from the mirror into rays along relay paths 490E and 491E. These two light rays visible to the observer 450 form different angles θ1 and θ2 with the normal 496 of the line 495 parallel to the virtual screen plane 496, and therefore contribute two different values of the light field angular coordinate u to the imaging of the relay holographic surface 489. In other words, although both rays have a single value of the light field angular coordinate u=0 as projected by the light field display 497, they have different values of u at the relay holographic surface 489, and this u value (or equivalently, angle) depends in part on the position of the object relative to the focus 481 of the mirror. Furthermore, two rays along projection paths 492C and 493C projected from light field display 497 at light field angular coordinates (u1 and u2) are reflected from the beam splitter and mirror system to become light rays along relay paths 492E and 493E. These light rays are parallel to each other and to normal 496 of virtual screen plane 469, such that they have the same light field coordinate u=0 at this virtual screen plane 469, as viewed by an observer. In other words, in forming relay holographic surface 489, the angular light field coordinates of holographic surface 488 are rearranged by holographic relay system 460, including beam splitter 485 and curved mirror 482. To correct for this, the angular light field coordinates exiting screen plane 498 of light field display 497 can be rearranged in a compensating manner to achieve the desired angular light field coordinates exiting relay virtual screen plane 469. Another potentially undesirable effect is that the normal to the light field display surface 498 (typically the light field angular coordinate u=0) typically defines the axis of symmetry for projection rays from the light field display surface 498. Light rays generated from the light field display 497 at u=0 that define the axis of symmetry from the light field display surface 498 can be relayed to the virtual screen plane 469 at effective values of u (i.e., the angle θ with the normal 496 to the virtual screen plane 469 can vary), particularly when the relayed holographic image deviates significantly from the optical axis 483. This can result in a change in the field of view. Typically, to minimize the effects of Figure 4D The change in field of view of the holographic surface relayed by the optical relay system shown can center the light field display 497 so that the holographic surface such as 488 can be relayed to a position 489 that is as close to the optical axis 483 as possible. In some embodiments, Figure 4DThe focusing function of the mirror 482 shown can be replaced by one or more optical elements such as lenses, mirrors, or some combination of these elements. Figure 4C As discussed, mirror 482 may be formed by Figure 4E In another embodiment, as described above with respect to Figure 4C As discussed, the entire relay system 460 may be replaced by a relay formed by one or more lenses, such as Figure 4F The lens relay system 480 shown in FIG.

[0061] Figure 5A An orthogonal view of a lightfield display and an ideal holographic object relay system 103 is shown, which relays two holographic objects projected at a first location on either side of a lightfield display screen plane 1021 and viewed by a first observer 1048 to two relay holographic surfaces projected at a second location on either side of a virtual display screen 1022 and viewed by a second observer 1050. The lightfield display 1001 can output light along a set of projected light paths, including light rays along projected light paths 1030Z that contribute to forming a surface 1015Z in front of 1010 of the lightfield display screen plane 1021 and light rays along projected light paths 1036Z that contribute to forming an object 1016A behind 1011 of the screen plane 1021. Light path 1035 is the traced path of light ray 1036Z originating from the lightfield display surface 1021, which is juxtaposed with the display screen plane in this example. In an ideal situation, the relayed holographic objects 1017A and 1017B on either side of the virtual screen plane 1022 appear to the observer 1050 just as the directly projected holographic objects 1015Z and 1016Z without any relay system 103 appear to the observer 1048. In other words, the LF display 1001 and the relay system 103 should be configured such that the light rays along the relay paths 1032A and 1028A forming the relayed holographic surfaces 1017A and 1018A, respectively, reach the observer 1050 in the same manner as the corresponding light rays along the projection paths 1030Z and 1036Z forming the directly projected holographic surfaces 1015Z and 1016Z, respectively, reach the observer 1048 without any relay system 103. Figure 1A 、 1B 3A and the following discussion, it will be clear that in order to generate the relayed holographic objects 1032A and 1028A using a practical implementation of the relay system 103, the positioning, depth profile and magnification of the projected objects 1015Z and 1016Z may have to be determined according to their Figure 5AThe positioning shown is adjusted, and for each of these projected holographic source objects 1015Z and 1016Z, the light field angular coordinates may have to be rearranged.

[0062] Figure 5B Shows something like Figure 1A An embodiment of a holographic display system of a holographic display system. Figure 5B The holographic display system includes a first display 1001, which can be a light field display, which is configured to project light along a set of projection light paths 1030A and 1036A to form at least a first holographic surface 1015A and a second holographic surface 1016A having a first depth profile and a second depth profile relative to a display screen plane 1021, respectively. The holographic display system further includes a relay system 104, which is positioned to receive light from the light field display 1001 along the set of projection optical paths 1030A and 1036A, and relay the received light along a set of relay optical paths 1032A and 1028A, so that points on the first projection holographic surface 1015A and the second projection holographic surface 1016A are relayed to the relay positions, and the relay positions form a first relay holographic surface 1017A and a second relay holographic surface 1018A, and the first relay holographic surface and the second relay holographic surface have a first relay depth profile and a second relay depth profile relative to the virtual screen plane 1022, respectively.

[0063] Figure 5B A holographic relay system 104 is shown including a beam splitter 1005 and an image retroreflector 1006A. The light field display 1001 may be similar to that described above with respect to Figure 1A 、 1B, 3A, and 5A. The lightfield display 1001 projects an off-screen holographic surface 1016A on the viewer side 1010 of the screen plane 1021 and projects an on-screen holographic surface 1015A on the display side 1011 of the screen plane 1021. In an embodiment, the lightfield display 1001 can output light along a set of projected light paths, including light rays along projected light paths 1036A that contribute to forming the surface 1016A and light rays along projected light paths 1030A that contribute to forming the on-screen surface 1015A (path 1033 is a ray-traced line that does not represent a physical ray). Each of the set of projected light paths 1030A and 1036A has a set of position coordinates (X, Y) and angular coordinates (U, V) in a four-dimensional (4D) coordinate system defined by the lightfield display. These light rays can diverge as they approach the beam splitter 1005. A portion of this incident light is reflected by beam splitter 1005 along a set of reflected light paths, including path 1037A from incident light 1036A and path 1031A from incident light 1030A, toward image retroreflector 1006A, while the remaining light 1034 not reflected by the beam splitter passes through the beam splitter along a set of transmitted light paths 1034 and may be lost, thereby not contributing to the imaging of relay holographic surfaces 1017A and 1017B. Retroreflector 1006A may contain a sophisticated array of individual reflectors, such as corner reflectors. Retroreflector 1006A reverses each ray of incident light paths 1037A, 1031A in a direction substantially opposite to the direction of approach without significant spatial offset. Light rays along reflected optical path 1037A reverse their direction upon reflection from beam splitter 1005, causing their approach angle to be substantially folded back toward retroreflector 1006A. A portion of their intensity passes through beam splitter 1005 along relay optical path 1028A, converging at location 1018A of the holographic surface. In this manner, holographic surface 1016A, directly projected by lightfield display 1001, is relayed to form relayed holographic surface 1018A. Similarly, rays along optical path 1031A reverse their direction upon impacting beam splitter 1005, causing their approach path to be folded back toward retroreflector 1006A. A portion of their intensity passes through the beam splitter along relay optical path 1032A, converging to form holographic surface 1017A. In this manner, holographic surface 1015A, directly projected by lightfield display 1001, is relayed to form holographic surface 1017A. The relay optical paths 1028A and 1032A constitute a set of relay optical paths that originate from the set of projection optical paths from the display 1001 to the beam splitter 1005 and then pass through the set of reflection optical paths from the beam splitter 1005 to the retroreflector 1006A.In an embodiment, each of the set of relay optical paths has a set of position coordinates (X, Y) and angular coordinates (U, V) in a four-dimensional (4D) coordinate system as defined by relay system 104. An inner screen surface 1015A, projected by lightfield display 1001 at a greater depth than an outer screen surface 1016A, is relayed as surface 1017A, which is now closer to viewer 1050 than surface 1018A relayed from 1016A. In other words, the depth profiles of holographic surfaces 1015A and 1016A projected by the lightfield display are inverted by holographic relay system 104. The vertical distance D1 between holographic surface 1016A and beam splitter 1005 is substantially the same as the horizontal distance between the corresponding relay holographic surface 1018A and beam splitter 1005. Similarly, the vertical distance D2 between the holographic surface 1015A and the beam splitter 1005 is substantially the same as the horizontal distance D2 between the relay holographic surface 1017A and the beam splitter 1005. As with . Figure 1B As discussed above with respect to optional optical element 1041A, optical element 1041A is also optional. This 1041A can be a quarter-wave retarder that causes most of the light rays along paths 1031A or 1037A to return to beam splitter 1005 with a linear polarization opposite to that of the light rays exiting beam splitter 1005. Thus, most of these light rays will be directed toward viewer 1050 rather than being deflected toward display 1001 by beam splitter 1005. Furthermore, a light ray along path 1042A, which is the projection path 1036A from holographic surface 1016A, is projected from the lightfield display perpendicular to display screen plane 1021 and is typically assigned an angular lightfield coordinate value of (u=,v)=(0,0). This light ray generates a light ray along relay path 1042B, which helps form relay holographic surface 1018A. For the observer 1050, the light ray 1042B is projected perpendicular to the virtual display plane 1022 and will be perceived as a ray with light field angular coordinates (u, v) = (0, 0) to the observer 1050. To further summarize, even after being relayed, the optical relay system 103 preserves the light ray at the light field coordinates (u, v) = (0, 0) to maintain the value, although it needs to be rearranged. Figure 2B The light field angle coordinates shown are obtained by Figure 5B The retroreflector configuration shown reverses depth. Alternatively, a corrective optical element may be included in Figure 5B In an embodiment, the holographic display system can be used to invert the depth. Figure 2AThe corrective optical element 20 shown can be positioned in the set of relay optical paths 1028A and 1032A, and the corrective optical element 20 is configured to reverse the polarity of the angular coordinates (U, V) of each relay optical path in the set of relay optical paths, so that a viewer who perceives the first relay holographic surface 1017A and the second relay holographic surface 1018A through the corrective optical element 20 will perceive the same corrected depth order as the depth order of the first holographic surface 1015A and the second holographic surface 1016A. In an embodiment, the corrective optical element 20 can be positioned in the virtual display plane. In another embodiment, the corrective optical element 20 can be positioned in a set of projection optical paths 1030A, 1036A and optically located in front of the relay system 104, and the corrective optical element 20 can be configured to reverse the polarity of the angular coordinates (U, V) of each projection optical path in the set of projection optical paths 1030A, 1036A so that the first holographic surface 1015A and the second holographic surface 1016A have a pre-corrected depth order. In an embodiment, the corrective optical element 20 can be positioned in the display screen plane.

[0064] Figure 5C A light field display 1001 and a light field display similar to those described above with respect to Figure 4C and 4D The relay system 105 of the relay system 460 in question. In an embodiment, the holographic object volume relay 105 comprises a beam splitter for redirecting diverging light from the holographic surface to a concave mirror 1007A which refocuses this diverging light into the relay holographic surface. Figure 5B The retroreflector 1006A in the Figure 5C The concave reflector 1007A in the Figure 5C In the arrangement shown, in an embodiment, the mirror may be a spherical mirror having a radius of curvature approximately equal to the optical path length between the display screen plane 1021 and the mirror surface, similar to Figure 4D The center of curvature of the mirror C'441 is located at Figure 4C The same holographic surfaces 1015A and 1016A are formed by Figure 5B The light field display 1001 is shown projecting along a set of projection light paths 1030A, 1036A. The set of projection light paths 1030A and 1036A can be considered to be determined according to a first four-dimensional (4D) function defined by the light field display 1001, such that each projection light path has a set of position coordinates (X, Y) and angular coordinates (U, V) in a first 4D coordinate system defined relative to the display screen plane 1021. Light from the holographic surface 1015A is reflected from the beam splitter 1005 into a light ray along a reflection light path 1031A, rather than along a path corresponding to the first 4D coordinate system. Figure 5BThe light from the holographic surface 1016A is directed back along the same path as the retroreflector 1006A in the beam splitter, and these rays are reflected along the relay path 1032B to converge and form the holographic surface 1017B. The relay holographic surface 1017B is slightly smaller than the source holographic surface 1015A due to the reduction performed by the concave mirror corresponding to the optical path length between the holographic surface 1015A and the mirror. In an embodiment, the mirror 1007A is a spherical mirror, and the path length between the holographic surface 1015A and the mirror 1007A is slightly greater than the radius of curvature of the surface of the mirror 1007A. Similarly, the light from the holographic surface 1016A is reflected from the beam splitter 1005 into light rays along the reflection path 1037A, rather than along the same path as the source holographic surface 1015A. Figure 5B Directed backward along the same path as the retroreflector 1006A in the image sensor, these rays are reflected along the relay path 1028B to converge and form the holographic surface 1018B. Due to the magnification performed by the concave mirror, which corresponds to the optical path length between the holographic surface 1015A and the mirror, the relay holographic surface 1018B is slightly larger than the source holographic surface 1016A. In an embodiment, the mirror is a spherical mirror and the path length between the holographic surface 1016A and the mirror 1007A is slightly smaller than the radius of curvature of the surface of the mirror 1007A. In addition, the depth ordering of the holographic surfaces is preserved by the repeater: the source surface 1016A is projected in front of the screen plane 1021 and its relay surface 1018B is also projected in front of the virtual screen plane 1022. The source surface 1015A is projected behind the screen plane 1021 and its relay surface 1017B is also projected behind the virtual screen plane 1022, in each case away from the viewer. Thus, by using the mirror 1007A, the depth ordering of the holographic surfaces has been avoided. Figure 5B Finally, because the image produced by concave mirror 1007A is flipped, the relay holographic sphere 1018B is aligned with these surfaces. Figure 5B , are projected onto a position below the relay holographic box 1017B in the reverse order of their positions as they appear in the image. The set of relay optical paths 1028B and 1032B can be considered to have been determined according to the second 4D function defined by the relay system 105, so that each relay optical path has a set of position coordinates (X, Y) and angular coordinates (U, V) in the second 4D coordinate system defined relative to the virtual screen plane 1022. The enlargement, reduction, and position change of the relay surfaces 1018B and 1017B are all the effects of applying the second 4D function in the second 4D coordinate system.

[0065] To generate a Figure 5B The relay holographic surface shown can be used to Figure 5CIn an embodiment, the light field display 1001 may include a controller 190 configured to receive instructions for interpreting the second 4D function by operating the light field display 1001 according to the first 4D function to output projection light, such that the position coordinates and the angular coordinates of each of the set of relay light paths 1028C and 1017C in the second 4D coordinate system allow the relay holographic surfaces 1018C and 1017C to be presented to a viewer as intended. Figure 5D Shows how to use Figure 5D The curved mirror configuration shown in the relay system 105 is necessary to position and magnify the holographic surface generated by the light field display 1001. Figure 5C The holographic surface 1015A in will have to be projected onto Figure 5D The holographic surface 1015C is positioned in the mirror and made slightly smaller to compensate for the magnification caused by the closer distance of the surface to the mirror. Figure 5C The holographic surface 1016A in will have to be projected onto Figure 5D and magnified to compensate for the image reduction that occurs at greater distances from the mirror. Figure 5C The positions of 1015A and 1016A in the image are swapped left and right to account for the image inversion caused by the reflection from the mirror. The result is that holographic surface 1015C is relayed to 1017C, which is the same as the image in ... Figure 5B 1017A in exactly the same position, and the holographic surface 1016C is relayed to 1018C, with Figure 5B 1018A in exactly the same position.

[0066] exist Figure 5D In FIG, the light ray group along the projection light path 1036C forming the projection holographic sphere 1016C is mapped to the light ray group along the relay light path 1028C forming the relay holographic surface 1018C. In a similar manner, in Figure 5B In the example, the light rays along the projection light path 1036A from the projection holographic sphere 1016A are mapped to the light rays along the relay light path 1028A forming the relay holographic surface 1018A. Figure 5B When , it is usually associated with the light field angle coordinate (u=,v)=(0,0), perpendicular to Figure 5B The intermediate ray 1042A projected from the virtual screen plane 1021 (or display surface 1021) is mapped to the intermediate ray 1042B perpendicular to the virtual screen plane 1022 (as viewed by the viewer 1050). In other words, for Figure 5BThe retroreflector configuration shown in , preserves the light ray generated at (u=,v)=(0,0), although it must be Figure 2B The angular coordinates u and v are swapped as shown to correct for depth inversion. However, in Figure 5D In the curved mirror relay configuration shown, where no depth inversion occurs, a center light ray 1042C in a set of projected light rays 1036C projected perpendicular to the screen plane 1021 of the light field display 1001, typically associated with the light field angular coordinate (u=,v)=(0,0), is mapped to an intermediate ray 1042D that may not be perpendicular to the virtual screen plane 1022 viewed by the viewer 1050. This is consistent with Figure 4D , where light rays 490C and 491C projected perpendicular to the display surface 497 produce light rays 490E and 491E, respectively, which produce angles θ1 and θ2 relative to the normal of the virtual screen plane 469 that vary, depending in part on the positioning of the ray's intersection with the holographic surface 488. The result is that the viewer will not see the correct light field information from light ray 1043D. Figure 5D In the example of a light field display 1001 projecting light along projection path 1042C, this specular highlight will appear on the mapped ray along relay path 1042D, which is at an angle to the normal of the virtual screen plane 1022. To correct for this, the color and intensity information projected onto the (u=,v)=(0,0) ray along projection path 1042C in the absence of relay system 106 should instead be projected onto the light ray along projection path 1043C (if relay system 106 is in place), so that this information will appear on the mapped ray along relay path 1043D, which is the (u=,v)=(0,0) ray relative to the virtual screen plane 1022 and the observer 1050. In other words, some remapping of the light field coordinates can be performed on the light field display 1001 (in addition to the magnification adjustment described previously) in order to properly relay the holographic surface using the relay optical configuration with curved mirror 1007A.

[0067] In the case where the LF display 1001 generates unpolarized light and uses a non-polarizing 50% beam splitter 1005, approximately half of the light from holographic surfaces 1015C and 1016C is lost on its first pass through the beam splitter 1005, and the other half is lost on its second pass through the beam splitter 1005, resulting in no more than 25% of the light from the holographic surfaces being relayed. If a polarizing beam splitter 1005 is used, half of the unpolarized light from holographic surfaces 1015C and 1016C may be lost on its first reflection from the beam splitter 1005, but the remaining light directed toward the mirror 1007A will be in a known first state of linear polarization. By using a quarter-wave retarder in the optional optical element 1041A, the light returning from the mirror can be mostly in a known second state of linear polarization, orthogonal to the first state, and mostly transmitted through the polarizing beam splitter 1005, thereby helping to relay the holographic surfaces 1017C and 1018C. In these cases, between 25% and 50% of the light from holographic surfaces 1015C and 1016C can be relayed to holographic surfaces 1017C and 1018C. If the lightfield display 1001 produces polarized light, this efficiency can be substantially improved by using polarizing beam splitter 1005 and quarter-wave retarder 1041A.

[0068] exist Figure 5D In FIG. 1 , half of the light from optical path 1036C or 1030C from holographic surface 1016C or 1015C, respectively, may be wasted because it passes through beam splitter 1005 to become a light ray along transmission path 1034, as shown in FIG. Figure 5C Another mirror 1007B identical to the mirror 1007A may be added, placed on the other side of the beam splitter 1005 opposite the display 1001A and orthogonal to the mirror 1007A. Figure 5E is an orthogonal view of a light field display and a holographic relay system 107 comprising a beam splitter 1005 and two concave mirrors 1007A, 1007B positioned orthogonally to each other to achieve high light transmission from the projection holographic surface to the relay holographic surface. This configuration is conceptually similar to Figure 1B1005. A second retroreflector 1006B appears in the projection path 1036C. Light rays along the projection path 1036C from the holographic surface 1016C are reflected by the beam splitter into a reflected light path 1037A directed toward the mirror 1007A, or pass through the beam splitter into a transmitted light path 1042A directed toward the mirror 1007B. Light path 1037C directed toward the mirror 1007A is reflected into a light path that is again incident on the beam splitter 1005, and a portion of this light is transmitted through the relay path 1028C (while the remaining portion of this light incident on the beam splitter 1005 (not shown) is directed downward toward the light field display 1001). Light path 1042A directed toward mirror 1007B is reflected into light path 1042B incident on beam splitter 1005, and a portion of this light is reflected into path 1028C, combining with the light path reflected by mirror 1007A (while the remainder of this light (not shown) is transmitted through beam splitter 1005 and directed back into lightfield display 1001). The same is true for light from holographic surface 1015C that is relayed into holographic surface 1017C, but these light paths are Figure 5D In an embodiment, concave mirrors 1007A and 1007B are aligned with beam splitter 1005 so that light along path 1028C reflected from mirrors 1007A and 1007B substantially overlaps.

[0069] In the case where the LF display 1001 generates unpolarized light and uses a non-polarizing 50% beam splitter 1005, almost all of the light from the holographic surfaces 1015C and 1016C is directed to either mirror 1007A or 1007B. Returning, at most half of the light reflected from each mirror may be transmitted through the beam splitter 1005 toward the display and will not contribute to the imaging of the relay holographic surface 1016C or 1017C. This places an upper limit of 50% on the efficiency of light from the holographic surfaces 1015C and 1016C to be relayed to the holographic surfaces 1017C and 1018C. However, using a polarizing beam splitter and a quarter-wave retarder as optional optical elements 1041A and 1041B, as in Figure 1A as well as Figure 5D As described in the discussion of , because most of the light directed toward each mirror has a particular linear polarization (which may be rotated 90 degrees on its return journey toward the beam splitter), substantially higher efficiency can be produced, resulting in most of the light of two different reflected polarizations being recombined when it is directed to the relay holographic surfaces 1017C and 1018C.

[0070] In some embodiments, Figures 5C-5E The focusing function of the mirrors 1007A and 1007B shown in FIG can be replaced by one or more optical elements, such as lenses, mirrors, or some combination of these elements. Figure 4CAs discussed, mirrors 1007A and 1007B may each be Figure 4E The lens 444 and reflector 442 shown are replaced. In another embodiment, Figures 5C-5D The entire relay system of and 105 and 106 may be replaced by a relay formed by one or more lenses, as described above with respect to Figure 4C Discussed Figure 4F The lens relay system 480 shown in FIG.

[0071] Figure 5D The repeater 106 of the configuration shown may be used as one or more of the repeaters in a holographic relay system comprising two repeaters, such as Figure 3B As shown. Figure 3B In the embodiment, both repeaters 130 and 140 can be replaced by relay system 106, but in Figure 3C In the embodiment, only repeater 130 can be replaced by repeater 106, because repeater 140 requires light to be transmitted in two different directions. Figure 3B Two substantially identical repeaters 106 are used in the holographic relay system configuration shown, and the effects of the reduction, magnification, and rearrangement of the light field angular coordinates (u, v) of the first repeater 130 described above with reference to 5D are at least partially reversed by the second repeater 140.

[0072] Figure 6 An embodiment of a system is shown that uses a transflector 1105 to relay a holographic surface projected by a light field display 1001. An example of element 1105 is a dihedral corner reflector array (DCRA), which is an optical imaging element composed of a plurality of dihedral corner reflectors that can be implemented as two thin layers of closely spaced parallel mirror planes oriented so that the planes are orthogonal to each other, as in Figure 4AAs shown. Another example is a corner reflector micromirror array. The light field display 1001 can be similar to the light field display 1001 discussed above with respect to FIG. The light field display 1001 projects an off-screen holographic surface 1016A on the viewer side 1010 of the screen plane 1021 and projects an on-screen holographic surface 1015A on the display side 1011 of the screen plane 1021. The transflector 1105 is positioned to receive light along the set of projection optical paths 1030A, 1036A and to direct the received light along the set of relay optical paths 1032A, 1028A. In an embodiment, each of the set of projection optical paths 1030A, 1036A has a set of position coordinates (X, Y) and angular coordinates (U, V) in a four-dimensional (4D) coordinate system defined with respect to the display screen plane 1021. In an embodiment, the transreflector 1105 internally reflects a portion of the received light at a plurality of internal reflective surfaces 401, 402 of the transreflector 1105 and outputs the light in a first direction along a set of relay optical paths 1032A, 1028A toward the virtual screen plane 1022. In an embodiment, each optical path in the set of relay optical paths 1032A, 1028A has a unique set of positional coordinates (X, Y) and angular coordinates (U, V) in a four-dimensional (4D) coordinate system defined with respect to the virtual screen plane 1022. Further, in an embodiment, the outer surface 430 of the transreflector 1105 reflects a second portion of the received light in a second direction opposite to the first direction along a set of reflective optical paths 1130, 1136. In an embodiment, the set of reflected optical paths 1130, 1136 and the set of relay optical paths 1032A, 1028A are substantially aligned such that the first relay holographic surface 1015A and the second relay holographic surface 1016A are perceived to have the same depth profile relative to the virtual screen plane 1022 from the first direction and the second direction.

[0073] In an embodiment, the projected light rays along the projection light path 1036A that converge on the surface of the holographic surface 1016, and the projected light rays along the projection light path 1030A that converge at the in-screen holographic surface 1015A (see ray trajectory line 1033) all diverge as they approach the transreflector 1105. A portion of the incident light rays along the projection light path 1036A are reflected from the outer surface 430 of 1105 into rays along the reflection light path 1136. Another portion of the incident light rays along the projection light path 1036A passes through the transreflector 1105, is reflected, and emerges as light rays along the relay light path 1028, which converge to form the relay holographic surface 1018A. Similarly, a portion of the incident light rays along projection optical path 1030A are reflected from outer surface 430 of transflector 1105 into light rays along reflection optical path 1130, while the remaining portion of the incident light rays along projection optical path 1030A are reflected within 1105 and emerge as convergent light rays along relay optical path 1032A, forming relay holographic surface 1017A. Note that after being relayed to relay surface 1017A, projection surface 1015A, which was farther from the viewer than projection surface 1016A, is now closer to the viewer after the holographic scene is relayed. The vertical distance between holographic surface 1016A and beam splitter D1 is substantially the same as the horizontal distance between relay holographic surface 1018A and beam splitter 1105. Similarly, the vertical distance D2 between the holographic surface 1015A and the beam splitter 1105 is substantially the same as the horizontal distance D2 between the relay holographic surface 1017A and the beam splitter 1105. Observer 1050 will see holographic surface 1017A floating in space slightly in front of holographic surface 1018A. Observer 1350 will see the reflective holographic surface 1018A perceived at the convergence point of a set of reflected light paths 1136, and will see the reflective holographic surface 1015A perceived at the convergence point of a set of reflected light paths 1130. However, if the holographic source surfaces 1015A and 1016A are rendered before being displayed in order to achieve the correct depth ordering of the relay holographic surfaces 1017A and 1018A, as observed by viewer 1050, this means that the depths of the surfaces are inverted around the screen plane 1021 and the light field angular coordinate UV is as shown in FIG. Figure 2B and 2C and refer to the above Figure 1A and 5B If the UV coordinates are reversed as discussed above, then for the surface reflected from the transflector 1105 surface and observed at 1350, the UV coordinates will be reversed. In other words, the depth of the holographic surface 1017A or 1018A may not be displayed correctly for the observer 1350 viewing the light ray 1130 or 1136, respectively. To correct for this, a plane similar to Figure 2AThe corrective optical element shown is used to perform UV coordinate inversion on the set of reflected light paths 1130, 1136. In another embodiment, using different light field renderings of the holographic surface 1015A or 1016A, without the corrective optical element at plane 1137, the observer 1350 can perceive the holographic surfaces 1017A and 1018A with the correct depth ordering, and as described above with respect to Figure 5B As discussed, it is possible to Figure 2A The corrective optical element shown in FIG is placed at the virtual display plane 1022 to allow the observer 1050 to also view the holographic surfaces 1017A and 1018A with the correct depth ordering. In other words, if Figure 2A Corrective optical elements such as those shown are used to allow both observers 1050 and 1350 to see the holographic surfaces 1017A and 1018A with the correct depth, then they can be placed at plane 1022 or 1137, depending on whether the light field rendering of the holographic surface from the light field display 1001 contains steps to invert the depth around the screen plane 1021 and reverse the polarity of the UV coordinates, as shown. Figure 2B shown.

[0074] Figure 7 Shown with Figure 5B The same holographic system as the holographic system of FIG, wherein another display 1201 is added opposite to the first display 1001 and sandwiching the relay system 108, and from Figure 5B The digital markings are applicable to Figure 7 The relay system 108 includes a beam splitter 1205 and a retroreflector 1006A. If 1201 is a light field display, the light field display 1201 can be configured as described above with respect to Figure 1AThe light field display 1001 discussed herein has one or more display surfaces 1202 containing multiple light source positions, an imaging relay 1203 that may or may not be present to relay images from the emissive display to an energy surface 1205, and an array of waveguides 1204 that project each light source position on the energy surface into a specific direction in three-dimensional space. Energy surface 1205 can be a seamless energy surface with a combined resolution greater than that of any individual emissive display device 1202, while plane 1221 is the screen plane of 1201. If 1201 is a traditional 2D display, relays 1203 and / or waveguides 1204 may not be present. Display 1201 can display a 2D image (not shown) or a holographic surface 1213. Rays exiting display 1201 along another set of projection paths 1231 reflect off the surface of beam splitter 1205, forming a diverging set of rays along another set of relay paths 1233, which can be traced back through imaginary path 1234 to reveal a convergence point at perceived holographic surface 1214. The vertical distance D3 between displayed surface 1213 and beam splitter 1205 is substantially equal to the horizontal distance between the beam splitter and perceived surface 1214. Observer 1050 will see holographic surfaces 1017A, 1018A and displayed surface 1214, which may or may not be holographic, depending on whether display 1201 is a lightfield display. Using a 2D display as 1201 allows for the creation of a uniform background imaging plane that can be placed at any reasonable distance from observer 1050, depending on the distance between display 1201 and beam splitter 1205. The parallax element 1207 can be placed in the path of the display 1201 at a distance 1210 from the screen plane 1201 so as to block some or all light from the display 1201 and can take the form of a portion of a liquid crystal display without a backlight, a transparent display, a real physical surface, etc. In the event that the holographic surface 1017A or the holographic surface 1018A obscures 1214 and it is not desired to display two images simultaneously, the parallax barrier 1207 can be used to obscure a portion of the surface 1214. If the parallax barrier 1207 is part of an LCD panel containing one or more polarizers and a liquid crystal (LC) layer, the beam splitter can be a polarizing beam splitter selected to reflect 100% of the polarized light that passes through 1207. Similarly, the parallax barrier 1208 can be placed above the light field display 1001 at a distance 1211 so as to block all or part of the light from the display 1001 and can take the form of a portion of a liquid crystal display without a backlight, a transparent display, a real physical surface, etc. It should be understood that the above description of the parallax barrier 1208 is not intended to be used in conjunction with the present invention. Figure 7 The various embodiments discussed in the foregoing may be implemented in part or in whole in other embodiments of the holographic display system of the present disclosure, including Figures 4C-4D and Figures 5C-5E For example, the second display 1201 and parallax elements 1207 and 1208 discussed above may be implemented to work with a relay system comprising at least one concave mirror, such as Figures 4C-4D and Figures 5C-5E Described in .

[0075] Figure 8A Shown with Figure 6 The holographic system 110 is the same as the holographic system 110, with the addition of another display 1201 opposite to the first display 1001 and sandwiched between the relay system 109, and from Figure 6 The numbered tags are applicable to Figure 8A If the display 1201 is a light field display, the light field display 1201 may be configured as described above with respect to Figure 7Lightfield display 1201 is discussed. Display 1201 can display a 2D image (not shown) or a holographic surface 1213. Rays exiting the display along another set of projection optical paths 1231 can partially reflect off the surface of transflector 1305, forming a diverging set of rays along another set of relay optical paths 1332. Rays 1231 can also pass through transflector 1305, be reflected, and emerge as light rays along a set of transmission optical paths 1333, which converge to form relay holographic surface 1314. The vertical distance D3 between display surfaces 1213 and 1305 can be substantially equal to the horizontal distance between surface 1305 and relay holographic surface 1314. Observer 1050 will see holographic surfaces 1017A, 1018A, and display surface 1314 (which may or may not be holographic), depending on whether 1201 is a lightfield display. Using a 2D display as 1201, a uniform background imaging plane can be created that can be placed at any reasonable distance from the observer 1050, depending on the distance between the display 1201 and the transflector 1305. A parallax element 1207 can be placed in the path of the display 1201 at a distance 1210 from the screen plane 1201 to block some or all light from the display 1201 and can take the form of a portion of a liquid crystal display without a backlight, a transparent display, a real physical surface, etc. In situations where the holographic surface 1017A or the holographic surface 1018A is occluding 1314 and it is undesirable to display two images simultaneously, the parallax element 1207 can be used to occlude a portion of the surface 1214. Similarly, the parallax element 1208 can be placed above the lightfield display 1001 at a distance 1211 to block all or part of the light from the display 1001 and can take the form of a portion of a liquid crystal display without a backlight, a transparent display, a real physical surface, etc. If 1201 is a light field display, then parallax elements 1207 and 1208 may not be necessary to avoid occlusion problems, as coordinated rendering of the two light field displays can be used to avoid occlusion. Typically, nothing will be placed on the intermediate plane 1137 or the virtual screen plane 1337. However, from Figure 2A The corrective optical element 20 or a similar configuration that reverses the polarity of the angular 4D light field coordinates U, V can be placed at plane 1137 instead of plane 1337, or plane 1337 instead of plane 1137, or both, or neither. Likewise, the corrective optical elements 20 at planes 1337 and 1137 can be moved closer to or further away from the transflector 1305. Another option is to have a Figure 2AThe corrective optics 20 or similar configuration can reverse the polarity of the U, V coordinates placed just above the screen plane 1021 of the light field display 1001. Finally, the system 130 can be constructed using a mirror instead of the transflector 1305, which can produce two independent views at the observer 1050 on the left side of 1305 and the observer (not shown) positioned on the right side of 1305, where each observer will only see the holographic surface from one display. It should be understood that in the above discussion of Figure 8A The various embodiments discussed in the foregoing may be implemented in part or in whole in other embodiments of the holographic display system of the present disclosure, including Figures 4C-4D and Figures 5C-5E For example, the further display 1201 and parallax elements 1207 and 1208 discussed above may be implemented to work with a relay system comprising at least one concave mirror, such as Figures 4C-4D and Figures 5C-5E As described in .

[0076] Figure 8B Shows the use of Figure 8A An embodiment of performing occlusion processing using a parallax barrier in FIG. Figure 8A The labels 1367 and 1368 apply to this figure. A portion 1367 of the parallax barrier 1207 can be activated to block light 1361 from one side of the projection surface 1213. Only orthogonal rays 1362 from the surface 1213 are shown and are partially reflected from the transflector 1305 into rays 1364 that reach the observer 1050. Rays 1362 are partially transmitted by 1305 and emerge into rays 1363, which form the projected holographic surface 1366. The blocked light rays 1361 from the portion of the surface 1213, corresponding to the blocked portion 1365 of the relayed holographic image 1366, are substantially invisible to the observer 1050.

[0077] Figure 8C Shows something like Figure 8A An embodiment of a system of systems is shown that has substantially all of the light rays that would reach an observer 1350 to the right of the transflector 1305 , but omits some of the light rays that would reach an observer (not shown) to the left of 1305 . Figure 8AThe labels apply to this figure. Observer 1350 will perceive holographic surface 1018A via diffuse rays 1337 reflected from 1305, and holographic surface 1017A via diffuse rays 1331 reflected from 1305. If display 1201 is a holographic display, holographic surface 1213 will be relayed to holographic surface 1314, and observer 1350 will see 1314 in the foreground and holographic surfaces 1017A and 1018A in the background. If display 1201 is a 2D display, observer 1350 will see a flat foreground image and holographic surfaces 1017A and 1018A in the background. Figure 8A As discussed, if 1201 is a light field display, occlusion processing can be performed by coordinating the two light fields 1001 and 1201 or using parallax barriers 1207 and / or 1208. If 1201 is a 2D display, parallax barriers 1207 and / or 1208 can be used for occlusion processing.

[0078] Figure 8D Shown Figure 8A and 8B Abstract embodiment of a display system is shown. Display 1001 projects holographic surface 1016A, which is relayed by a transflector to surface 1018A seen by observer 1050 in front of 1305. Display 1201 projects holographic surface 1213, which is relayed by 1305 to surface 1314 seen by observer 1050 behind transflector 1305. Embodiments including a partially or fully enclosed transflector surface 1305 can allow an observer to see the holographic surface in an extended viewing volume from all angles.

[0079] Figure 8E yes Figure 8D An embodiment of a system having a transreflector 1605 having an at least partially closed transreflector surface. In embodiments, the reflector surface can have a conical geometry configured to allow an observer to see the holographic surface in an extended viewing volume from all angles. The transreflector 1605 can be a dihedral corner reflector array (DCRA), which is an optical imaging element composed of a plurality of dihedral corner reflectors, which can be implemented as two thin layers of closely spaced parallel mirror planes oriented so that the planes are orthogonal to each other, such as Figure 4AAnother example is a corner reflector micromirror array. Holographic surface 1213 is projected by light field display 1201 and relayed to viewable location 1314 by the transmissive conical reflector. Similarly, 1016A is projected by display 1001 and relayed to viewable surface 1018A. This configuration allows the arrangement of holographic surfaces to be projected and relayed to locations outside the holographic cone as well as inside a full 360 degree radius around the display. There may be multiple observers at multiple locations around the display, such as the observer shown at 1050. In an embodiment, the conical surface of the transmissive reflector 1605 may have an apex 1610 aligned with the center of the display 1001 or 1201. Occlusion handling may be accomplished by coordinating the projections from the surfaces of displays 1201 and 1001, as described with respect to FIG. Figure 8A and 8C The transflector 1605 can be tapered (as shown, a right pyramid with four or more planar sides), custom shaped, and can be fully or partially closed.

[0080] In an embodiment, the transflector can be configured to have a vertex 1810 and a polygonal base 1815. For example, Figure 8F Shows something like Figure 8E An embodiment of a system with a pyramidal transflector surface 1805 is shown in FIG. In an embodiment, the vertex 1810 of the transflector 1805 can be aligned with the center of the display 1001 or 1201.

[0081] Although various embodiments according to the principles disclosed herein have been described above, it should be understood that they are presented by way of example only and are not intended to be limiting. Therefore, the breadth and scope of one or more of the present inventions should not be limited by any of the exemplary embodiments described above, but should be defined solely in accordance with the claims issuing from this disclosure and their equivalents. Furthermore, the above advantages and features are provided in the described embodiments, and the application of such issued claims should not be limited to processes and structures that achieve any or all of the above advantages.

[0082] It should be understood that the key features of the present disclosure can be employed in various embodiments without departing from the scope of the present disclosure. Those skilled in the art will recognize or be able to ascertain, using no more than routine experimentation, many equivalents to the specific methods described herein. Such equivalents are deemed to be within the scope of the present disclosure and are encompassed by the claims.

[0083] In addition, the section headings herein are provided for the purpose of being consistent with the recommendations under 37 CFR 1.77, or to otherwise provide organizational cues. These headings should not limit or characterize the one or more inventions set forth in any claims that may issue from this disclosure. Specifically, and by way of example, although a title refers to a "Technical Field," such claims should not be limited by the language describing the so-called technical field under that title. Furthermore, the description of a technology in the "Background" section should not be construed as an admission that the technology is prior art to any one or more of the inventions in this disclosure. Nor should the "Summary of the Invention" be construed as a characterization of one or more of the inventions set forth in the issued claims. Furthermore, any reference to "invention" in the singular in this disclosure should not be used to argue that there is only a single point of novelty in this disclosure. Multiple inventions may be set forth according to the limitations of multiple claims issuing from this disclosure, and such claims accordingly define the one or more inventions and their equivalents protected thereby. In all cases, the scope of such claims should be considered on their own merits in light of this disclosure and should not be construed as constrained by the headings set forth herein.

[0084] When used in conjunction with the term "comprising" in the claims and / or the specification, the use of the word "a / an" can mean "one / an", but it is also consistent with the meaning of "one or more / one or more", "at least one / at least one" and "one or more than one / one or more than one". The use of the term "or" in the claims is used to mean "and / or" unless expressly indicated to refer only to alternatives or when the alternatives are mutually exclusive, but the present disclosure supports definitions referring only to alternatives as well as to "and / or". Throughout this application, the term "about" is used to indicate that a value includes the inherent error variation of the device, method used to determine the value, or the variation that exists between study subjects. In general, but consistent with the foregoing discussion, values modified by approximate terms such as "about" or "substantially" herein may vary from the stated value by at least ±1, 2, 3, 4, 5, 6, 7, 10, 12 or 15%.

[0085] As used in this specification and in one or more claims, the words “comprising” (and any form of comprising, such as “comprise” and “comprises”), “having” (and any form of having, such as “have” and “has”), “including” (and any form of containing, such as “includes” and “include”), or “containing” (and any form of containing, such as “contains” and “contain”) are inclusive or open-ended and do not exclude additional unrecited elements or method steps.

[0086] Comparative, measurement, and timing terms such as "at," "equivalent to," "during," "completely," and the like should be understood to mean "substantially at," "substantially equivalent to," "substantially during," "substantially completely," and the like, where "substantially" means that such comparisons, measurements, and timings can be used to achieve the desired result, whether implicitly or explicitly stated. Terms such as "near," "close to," and "adjacent," relating to the relative position of elements, should mean sufficiently close to have a substantial effect on the interaction of the respective system elements. Other approximate terms similarly refer to certain conditions that, when so modified, are understood not to be necessarily absolute or perfect, but would be considered close enough to allow one skilled in the art to assure oneself that the specified conditions exist. The degree to which the description can be varied will depend on how much variation can be made and still allow one of ordinary skill in the art to recognize the modified feature as still having the desired properties and capabilities of the unmodified feature.

Claims

1. A holographic display system, comprising: The first image source comprises a first display, the first display comprising a light field display configured to project light along a set of projection light paths to form at least a first holographic surface having a first projected depth profile relative to a display screen plane; as well as a relay system positioned to receive light from the lightfield display along the set of projection optical paths and to relay the received light along a set of relay optical paths such that points on the first holographic surface are relayed to relay locations, thereby forming a first relay holographic surface having a first relay depth profile relative to a virtual screen plane, the first relay depth profile being different from the first projection depth profile; wherein the lightfield display includes a controller configured to receive instructions for interpreting a difference between the first projected depth profile and the first relayed depth profile by: operating the lightfield display to output projected light such that the first relayed depth profile of the first relayed holographic object is an intended depth profile for a viewer; It is characterized by: a second image source comprising a second display or a real object operable to provide light forming an image surface; a beam splitter configured to receive projection light from a first image source and a second image source and direct a portion thereof along a set of projection light paths to the relay system, wherein the relay system is configured to receive the projection light from the beam splitter along the set of projection light paths and relay the received projection light along a set of relay light paths to form a first relay holographic surface and a relay image surface; as well as A parallax element positioned in a set of projection light paths from a first image source or a second image source, and wherein the parallax element is operable to obscure at least a portion of a first holographic surface formed along the set of projection light paths of the first image source or an image surface formed by the second image source.

2. The holographic display system of claim 1 , wherein the light field display is configured to project the first holographic surface as an in-screen holographic surface.

3. The holographic display system of claim 1 , wherein the light field display is configured to project the first holographic surface as an off-screen holographic surface.

4. A holographic display system according to claim 1, wherein each projection light path in the set of projection light paths has a set of position coordinates and angular coordinates in a four-dimensional (4D) coordinate system, and the instructions received by the controller include reversing the polarity of the angular coordinates of the first holographic surface in the four-dimensional coordinate system.

5. The holographic display system of claim 1 , wherein the set of projection light paths forms a second holographic surface having a second projection depth profile relative to the display screen plane, and points on the second holographic surface are relayed by the relay system to relay positioning, which forms a second relay holographic surface having a second relay depth profile relative to the virtual screen plane.

6. The holographic display system according to claim 5, further comprising a corrective optical element disposed in the set of relay optical paths, wherein each relay optical path in the set of relay optical paths has a set of position coordinates and angular coordinates in a four-dimensional (4D) coordinate system, and the depth order of the first holographic surface and the second holographic surface and the depth order of the first relay holographic surface and the second relay holographic surface are reversed, and further, wherein the corrective optical element is configured to reverse the polarity of the angular coordinates of each relay optical path in the set of relay optical paths, so that a viewer who perceives the first relay holographic surface and the second relay holographic surface through the corrective optical element will perceive a corrected depth order that is the same as the depth order of the first holographic surface and the second holographic surface.

7. The holographic display system of claim 6, wherein the corrective optical element is positioned at a virtual display plane.

8. A holographic display system according to claim 6, wherein the corrective optical element includes parallel rows of lenses, each lens having the same focal length f, and the distance between the lens rows is twice the focal length, whereby the focal planes of the lens rows overlap at a virtual plane and the lenses opposite the focal planes share the same optical axis.

9. The holographic display system of claim 5, further comprising a correction optical element disposed in the set of projection optical paths and optically in front of the relay system; wherein each projection light path in the set of projection light paths has a set of position coordinates and angular coordinates in a four-dimensional (4D) coordinate system, and the correction optical element is configured to invert the polarity of the angular coordinates of each projection light path in the set of projection light paths such that the first holographic surface and the second holographic surface have a pre-corrected depth order; and and wherein the relay system is positioned to receive light from the corrective optical element along the set of projection light paths, and The first relay surface and the second relay surface are perceptible in a corrected depth order relative to the virtual screen plane, the corrected depth order being opposite to the pre-corrected depth order.

10. The holographic display system of claim 9, wherein the corrective optical element is positioned at the display screen plane.

11. A holographic display system according to claim 9, wherein the corrective optical element includes parallel rows of lenses, each lens having the same focal length f, and the distance between the lens rows is twice the focal length, whereby the focal planes of the lens rows overlap at a virtual plane and the lenses opposite the focal planes share the same optical axis.

12. The holographic display system of claim 1 , wherein the relay system comprises a beam splitter and a reflector, the beam splitter being positioned to receive light along the set of projection light paths and to reflect a portion of the received light toward the reflector along a set of reflection light paths.

13. The holographic display system of claim 12, wherein the beam splitter is oriented at a 45 degree angle relative to the display screen plane and the retroreflector, and the retroreflector is oriented orthogonal relative to the display screen plane.

14. The holographic display system of claim 12, wherein the beam splitter comprises a polarizing beam splitter.

15. The holographic display system of claim 14, wherein the relay system further comprises a quarter-wave retarder disposed between the polarization beam splitter and the retroreflector.

16. The holographic display system of claim 12, wherein the beam splitter comprises a transparent metal coating.

17. The holographic display system of claim 12, wherein the beam splitter comprises a dichroic filter.

18. The holographic display system of claim 12, wherein the retroreflector comprises a corner reflector micromirror array.

19. A holographic display system according to claim 12, wherein the reflector and the beam splitter are aligned so that light reflected from the beam splitter toward the reflector is reflected from the reflector along the set of relay light paths, and the set of relay light paths extends along a return direction opposite to the set of reflected light paths.

20. The holographic display system of claim 19, wherein the light reflected from the retroreflector is directed toward the virtual screen plane through the beam splitter.

21. The holographic display system of claim 20, wherein each relay optical path in the set of relay optical paths has a unique set of position coordinates and angular coordinates in a four-dimensional (4D) coordinate system, and the holographic display system further comprises a corrective optical element positioned at the virtual screen plane, wherein the corrective optical element is configured to invert the polarity of the angular coordinates of the relay optical path.

22. The holographic display system of claim 12, wherein the relay system comprises an additional reflector, and the beam splitter is configured to direct another portion of the received light along a set of transmitted light paths toward the additional reflector.

23. A holographic display system according to claim 22, wherein the additional reflector and the beam splitter are aligned so that the projection light transmitted through the beam splitter toward the additional reflector is reflected from the additional reflector and further reflected by the beam splitter along another set of relay optical paths toward the virtual display screen, and further, wherein the set of relay optical paths and the another set of relay optical paths substantially overlap.

24. The holographic display system of claim 1, wherein the virtual screen plane is oriented at a non-parallel angle relative to the display screen plane of the light field display.

25. The holographic display system of claim 1, wherein the virtual screen plane is oriented at a perpendicular angle relative to the display screen plane of the light field display.

26. The holographic display system of claim 1, wherein the relay system comprises a transflector positioned to receive light along the set of projection optical paths and to direct the received light along the set of relay optical paths.

27. A holographic display system according to claim 26, wherein the transflector internally reflects a portion of the received light among multiple internal reflection surfaces of the transflector and outputs the light in a first direction toward the virtual screen plane along the set of relay optical paths.

28. A holographic display system according to claim 26, wherein the transflector internally reflects a first portion of the received light among multiple internal reflection surfaces of the transflector and outputs the first portion of the received light in a first direction toward the virtual screen plane along the set of relay optical paths, and wherein the outer surface of the transflector reflects a second portion of the received light in a second direction opposite to the first direction along a set of reflection optical paths.

29. The holographic display system of claim 28, wherein the set of reflected light paths and the set of relay light paths are substantially aligned such that the first relay holographic surface is perceived to have the same depth profile relative to the virtual screen plane from the first direction and the second direction.

30. The holographic display system of claim 28, wherein each optical path in the set of relay optical paths has a unique set of position coordinates and angular coordinates in a four-dimensional (4D) coordinate system, and the holographic display system further comprises a corrective optical element positioned at an intersection with the set of relay optical paths or at an intersection with the set of reflected optical paths, wherein the corrective optical element is configured to reverse the polarity of the angular coordinates of the optical path passing therethrough.

31. The holographic display system of claim 28, wherein each optical path in the set of relay optical paths has a unique set of position coordinates and angular coordinates in a four-dimensional (4D) coordinate system, and the holographic display system further comprises a first corrective optical element and a second corrective optical element positioned in a first position and a second position, respectively, the first position intersecting the set of relay optical paths and the second position intersecting the set of reflected optical paths, and wherein the first corrective optical element and the second corrective optical element are each configured to reverse the polarity of the angular coordinates of the optical path passing therethrough.

32. The holographic display system of claim 26, wherein the transflector comprises a dihedral corner reflector array comprising a plurality of dihedral corner reflectors.

33. A holographic display system according to claim 32, wherein the dihedral corner reflector array comprises two layers of reflective planes, which are parallel but offset in a first dimension, and wherein in a second dimension, the direction of the reflective planes in one layer is oriented to be orthogonal to the direction of the reflective planes in the other layer.

34. The holographic display system of claim 1 , further comprising: the second display being positioned substantially orthogonally relative to the first display; and a beam splitter configured to receive light from the first display along the one set of projection light paths and from the second display along another set of projection light paths and to direct the received light toward the relay system.

35. The holographic display system of claim 34, wherein the second display comprises a light field display configured to project an additional holographic surface, points on the additional holographic surface being relayed by the relay system to relay points, thereby forming an additional relayed holographic surface having a depth profile relative to an additional virtual screen plane.

36. A holographic display system according to claim 35, wherein the virtual screen plane corresponding to the first display and the further virtual screen plane corresponding to the second display are positioned so as to produce two different holographic volumes.

37. A holographic display system according to claim 35, wherein the virtual screen plane corresponding to the first display and the additional virtual screen plane corresponding to the second display are positioned so as to produce a continuous holographic volume, which is larger than the individual holographic volumes associated with either virtual screen plane.

38. The holographic display system according to claim 1, wherein the relay system is disposed between the first display and the second display, wherein the relay system is configured to receive light from the second display along another set of projection optical paths and relay the received light along another set of relay optical paths.

39. A holographic display system according to claim 38, wherein the second display includes a light field display configured to project an additional holographic surface, and points on the additional holographic surface are relayed to relay points by the relay system, thereby forming an additional relayed holographic surface having a depth profile relative to the virtual screen plane.

40. The holographic display system of claim 39, further comprising a parallax element positioned in each of the set of projection light paths from the first display and the second display, and wherein each parallax element is operable to obscure at least a portion of the holographic surface formed along the corresponding set of projection light paths.

41. The holographic display system of claim 38, wherein the relay system comprises a transflector comprising at least a partially enclosed transflector surface.

42. The holographic display system of claim 41 , wherein the partially enclosed transflector surface comprises a vertex and a polygonal base, the vertex being substantially aligned with a center of the first display or the second display.

43. The holographic display system of claim 41 , wherein the partially enclosed transflector surface comprises a conical surface having an apex, the apex being substantially aligned with a center of the first display or the second display.

44. The holographic display system of claim 26, wherein the transflector comprises at least a partially enclosed transflector surface.

45. The holographic display system of claim 44, wherein the partially enclosed transflector surface comprises a vertex and a polygonal base, the vertex being substantially aligned with a center of the first display.

46. The holographic display system of claim 44, wherein the partially enclosed transflector surface comprises a conical surface having an apex, the apex being substantially aligned with a center of the first display.

47. A holographic display system comprising: a first image source comprising a first display, the first display comprising a light field display configured to project light along a set of projection light paths to form at least a first holographic surface having a first projected depth profile relative to a display screen plane, the set of projection light paths being determined according to a first four-dimensional (4D) function defined by the light field display such that each projection light path has a set of position coordinates and angular coordinates in a first 4D coordinate system defined relative to the display screen plane; as well as a relay system positioned to receive light from the lightfield display along the set of projection optical paths and relay the received light along a set of relay optical paths such that points on the first holographic surface are relayed to relay locations, thereby forming a first relay holographic surface having a first relay depth profile relative to a virtual screen plane, the first relay depth profile being different from the first projection depth profile, the set of relay optical paths being determined according to a second four-dimensional function defined by the relay system such that each relay optical path has a set of position coordinates and angular coordinates in a second four-dimensional coordinate system defined relative to the virtual screen plane; wherein the set of projection optical paths forms a second holographic surface having a second projection depth profile relative to the display screen plane, and points on the second holographic surface are relayed by the relay system to relay locations, the relay locations forming the second relay holographic surface having the second relay depth profile relative to the virtual screen plane; The light field display includes a controller configured to receive an instruction for interpreting the second four-dimensional function by: operating the light field display according to the first four-dimensional function to output projection light, so that the position coordinates and the angular coordinates of each relay light path in the set of relay light paths in the second four-dimensional coordinate system allow the first relay holographic surface and the second relay holographic surface to be presented to a viewer as expected; characterized in that a second image source comprising a second display or a real object operable to provide light forming an image surface; a beam splitter configured to receive projection light from a first image source and a second image source and direct a portion thereof along a set of projection light paths to the relay system, wherein the relay system is configured to receive the projection light from the beam splitter along the set of projection light paths and relay the received projection light along a set of relay light paths to form a first relay holographic surface, a second relay holographic surface, and a relay image surface; as well as A parallax element positioned in a set of projection light paths from a first image source or a second image source, and wherein the parallax element is operable to obscure at least a portion of a holographic surface formed along the set of projection light paths of the first image source or an image surface formed by the second image source.

48. The holographic display system of claim 47, wherein the light field display is configured to project the first holographic surface as an in-screen holographic surface.

49. The holographic display system of claim 47, wherein the light field display is configured to project the first holographic surface as an off-screen holographic surface.

50. The holographic display system of claim 47, wherein the relay system comprises a beam splitter and a concave mirror, the beam splitter being positioned to receive light along the set of projection light paths and to reflect a first portion of the received light toward the concave mirror along a set of reflection light paths.

51. The holographic display system of claim 50, wherein the beam splitter comprises a polarizing beam splitter.

52. The holographic display system of claim 51 , wherein the relay system further comprises a quarter-wave retarder disposed between the polarization beam splitter and the concave mirror.

53. The holographic display system of claim 50, wherein the beam splitter comprises a transparent metal coating.

54. The holographic display system of claim 50, wherein the beam splitter comprises a dichroic filter.

55. A holographic display system according to claim 50, wherein the concave mirror and the beam splitter are aligned so that light reflected from the beam splitter toward the concave mirror is reflected and focused from the concave mirror along the set of relay light paths, and the set of relay light paths extends along a return direction substantially opposite to the set of reflected light paths.

56. The holographic display system of claim 55, wherein the light reflected from the concave mirror is directed toward the virtual screen plane through the beam splitter.

57. A holographic display system according to claim 50, wherein the relay system includes an additional concave mirror and the beam splitter is configured to direct a second portion of the received light along a set of transmission light paths toward the additional concave mirror.

58. A holographic display system according to claim 57, wherein the additional concave mirror and the beam splitter are aligned so that the projection light transmitted through the beam splitter toward the additional concave mirror is reflected from the additional concave mirror and further reflected by the beam splitter along another set of relay optical paths toward the virtual display screen, and further, wherein the set of relay optical paths and the additional set of relay optical paths substantially overlap.

59. The holographic display system of claim 47, wherein the relay system comprises at least one lens positioned to receive light from the light field display along the set of projection optical paths and to relay the received light along the set of relay optical paths toward the virtual screen plane, and wherein the at least one lens is between the display screen plane and the virtual screen plane.

60. The holographic display system of claim 59, wherein the at least one lens has an optical axis substantially aligned with a normal to the light field display.

61. The holographic display system of claim 59, wherein the relay system comprises a first lens and a second lens having a common optical axis passing therethrough.

62. The holographic display system of claim 47, wherein the relay system comprises a beam splitter positioned to receive light from the light field display along the set of projection optical paths and to reflect a first portion of the received light along a set of reflection optical paths toward a reflector, wherein the relay system further comprises at least one lens between the beam splitter and the reflector, the at least one lens being configured to focus light passing therethrough.

63. The holographic display system of claim 62, wherein the at least one lens has an optical axis aligned orthogonally to the reflector.

64. The holographic display system of claim 62, wherein the at least one lens has a focal plane positioned at a surface of the reflector.

65. The holographic display system of claim 62, wherein the relay system comprises a first lens and a second lens between the beam splitter and the reflector.

66. The holographic display system of claim 65, wherein the first lens and the second lens have a common optical axis.

67. The holographic display system of claim 62, wherein the reflector is curved.

68. The holographic display system of claim 47, wherein the virtual screen plane is oriented at a non-parallel angle relative to the display screen plane of the light field display.

69. The holographic display system of claim 47, wherein the virtual screen plane is oriented at a perpendicular angle relative to the display screen plane of the light field display.

70. The holographic display system of claim 47, wherein the relay system is disposed between the first display and the second display, wherein the relay system is configured to receive light from the second display along another set of projection optical paths and to relay the received light along another set of relay optical paths.

71. A holographic display system according to claim 70, wherein the second display comprises a light field display configured to project an additional holographic surface, and points on the additional holographic surface are relayed by the relay system to relay points, thereby forming an additional relay surface having a depth profile relative to the virtual screen plane.

72. The holographic display system of claim 71 , further comprising a parallax element positioned in the set of projection light paths from the first display or the second display, and wherein the parallax element is operable to obscure at least a portion of the holographic surface formed along the set of projection light paths of the corresponding display.

73. The holographic display system of claim 71 , further comprising a parallax element positioned in each of the set of projection light paths from the first display and the second display, and wherein each parallax element is operable to obscure at least a portion of the holographic surface formed along the corresponding set of projection light paths.

74. The holographic display system of claim 47, wherein the second four-dimensional function comprises at least one of a magnification, a reduction, and a position change of the first four-dimensional function.

75. The holographic display system of claim 47, wherein the first four-dimensional function exchanges intensity and color information between optical paths having the same position coordinates in the first four-dimensional coordinate system.

76. A holographic display system comprising: a first image source comprising a first display, the first display comprising a light field display configured to project light along a set of projection light paths to form at least a first holographic surface and a second holographic surface in a first depth order relative to a display screen plane, the first holographic surface having a first depth profile relative to the display screen plane; a relay system positioned to receive light from the lightfield display along the set of projection optical paths and relay the received light along a set of relay optical paths such that points on the first holographic surface and the second holographic surface are relayed to relay locations, thereby forming a first relay holographic surface and a second relay holographic surface perceivable in a second depth order relative to a virtual screen plane, the first depth order and the second depth order being opposite, the first relay holographic surface having a first relay depth profile relative to the virtual display screen plane, the first relay depth profile being different from the first depth profile; as well as a corrective optical element disposed in the set of relay optical paths, wherein each relay optical path in the set of relay optical paths has a set of position coordinates and angular coordinates in a four-dimensional (4D) coordinate system, and wherein the corrective optical element is configured to invert the polarity of the angular coordinates of each relay optical path in the first set of relay optical paths so that the first relay holographic surface and the second relay holographic surface can be perceived in a corrected depth order that is substantially the same as the first depth order; characterized in that a second image source comprising a second display or a real object operable to provide light forming an image surface; a beam splitter configured to receive projection light from a first image source and a second image source and direct a portion thereof along a set of projection light paths to the relay system, wherein the relay system is configured to receive the projection light from the beam splitter along the set of projection light paths and relay the received projection light along a set of relay light paths to form a first relay holographic surface, a second relay holographic surface, and a relay image surface; as well as A parallax element positioned in a set of projection light paths from a first image source or a second image source, and wherein the parallax element is operable to obscure at least a portion of a holographic surface formed along the set of projection light paths of the first image source or an image surface formed by the second image source.

77. The holographic display system of claim 76, wherein the corrective optical element is positioned at a virtual display plane.

78. A holographic display system according to claim 76, wherein the corrective optical element includes parallel rows of lenses, each lens having the same focal length f, and the distance between the lens rows is twice the focal length, whereby the focal planes of the lens rows overlap at a virtual plane and the lenses opposite the focal planes share the same optical axis.

79. A holographic display system comprising: a first image source comprising a first display, the first display comprising a light field display configured to project light along a set of projection light paths to form at least a first holographic surface and a second holographic surface in a first depth order relative to a display screen plane, the first holographic surface having a first depth profile relative to the display screen plane; a corrective optical element disposed in the set of projection light paths, wherein each projection light path in a first set of projection light paths has a set of position coordinates and angular coordinates in a four-dimensional (4D) coordinate system, and wherein the corrective optical element is configured to invert a polarity of the angular coordinates for each projection light path in the set of projection light paths, the first holographic surface and the second holographic surface having an intermediate depth order that is opposite to the first depth order; as well as a relay system positioned to receive light from the corrective optical element along the set of projection optical paths and relay the received light along a set of relay optical paths, so that points on the first holographic object and the second holographic object are relayed to relay locations, thereby forming a first relay holographic surface and a second relay holographic surface that can be perceived in a second depth order relative to a virtual screen plane, the first depth order and the second depth order being the same, the first relay holographic surface having a first relay depth profile relative to the virtual display screen plane, the first relay depth profile being different from the first depth profile; characterized in that a second image source comprising a second display or a real object operable to provide light forming an image surface; a beam splitter configured to receive projection light from a first image source and a second image source and direct a portion thereof along a set of projection light paths to the relay system, wherein the relay system is configured to receive the projection light from the beam splitter along the set of projection light paths and relay the received projection light along a set of relay light paths to form a first relay holographic surface, a second relay holographic surface, and a relay image surface; as well as A parallax element positioned in a set of projection light paths from a first image source or a second image source, and wherein the parallax element is operable to obscure at least a portion of a holographic surface formed along the set of projection light paths of the first image source or an image surface formed by the second image source.

80. The holographic display system of claim 79, wherein the corrective optical element is positioned at the display screen plane.

81. The holographic display system of claim 79, wherein the corrective optical element comprises parallel rows of lenses, each lens having the same focal length f, and the rows of lenses are spaced apart by twice the focal length, whereby the focal planes of the rows of lenses overlap at a virtual plane and the lenses opposite the focal planes share the same optical axis.

82. A holographic display system comprising: The first image source comprises a first display, the first display comprising a light field display configured to project light along a first set of projection light paths to form at least first and second holographic surfaces having first and second depth profiles, respectively, relative to a display screen plane; as well as a first relay system positioned to receive light from the light field display along the first set of projection optical paths and relay the received light along a first set of relay optical paths, so that points on the first holographic surface and the second holographic surface are relayed to relay locations, thereby forming first and second relay holographic surfaces having first and second relay depth profiles relative to a virtual screen plane, respectively, the first relay depth profile being different from the first depth profile; a second image source comprising a second display or a real object operable to provide light forming an image surface; a beam splitter configured to receive projection light from a first image source and a second image source and direct a portion thereof along a set of projection light paths to the first relay system, wherein the first relay system is configured to receive the projection light from the beam splitter along the first set of projection light paths and relay the received projection light along a first set of relay light paths to form a first relay holographic surface, a second relay holographic surface, and a relay image surface; as well as A parallax element positioned in a set of projection light paths from a first image source or a second image source, and wherein the parallax element is operable to obscure at least a portion of a holographic surface formed along the first image source or an image surface formed by the second image source.

83. A holographic display system comprising: The first image source comprises a first display, the first display comprising a light field display configured to project light along a first set of projection light paths to form at least a first holographic surface having a first depth profile relative to a display screen plane; a first relay system positioned to receive light from the lightfield display along the first set of projection optical paths and to relay the received light along a first set of relay optical paths such that points on the first holographic surface are relayed to relay locations, thereby forming a first relay holographic surface having a first relay depth profile relative to a virtual screen plane, the first relay depth profile being different from the first depth profile; a second image source comprising a second display or a real object operable to provide light forming an image surface; a beam splitter configured to receive projection light from a first image source and a second image source and direct a portion thereof along a set of projection light paths to the first relay system, wherein the first relay system is configured to receive the projection light from the beam splitter along the first set of projection light paths and relay the received projection light along a first set of relay light paths to form a first relay holographic surface and a relay image surface; as well as A parallax element positioned in a set of projection light paths from a first image source or a second image source, wherein the parallax element is operable to block at least a portion of a first holographic surface formed by the first image source or an image surface formed by the second image source.

84. The holographic display system of claim 83, further comprising: a second relay system positioned to receive light from the first relay system along the first set of relay optical paths and relay the received light along a second set of relay optical paths so that points on the first relay holographic surface are further relayed to new relay locations, thereby forming second relay holographic surfaces each having a second relay depth profile relative to a new virtual screen plane; and The second relay system is configured to receive light from the first relay system along the first set of relay optical paths and relay a portion of the received light along the second set of relay optical paths, thereby forming the second relay holographic surface together with another relay image surface.

85. The holographic display system of claim 84, wherein the new virtual screen plane and the display screen plane are substantially parallel.

86. The holographic display system of claim 84, wherein the first depth profile of the first holographic surface projected by the first display is substantially the same as the second relay depth profile of the second relay holographic surface.

87. A holographic display system according to claim 84, wherein the image surface formed by the projected light from the second display is a holographic surface.

88. The holographic display system of claim 84, wherein the image surface formed by the projected light from the second display is a non-holographic surface.

89. The holographic display system of claim 84, further comprising a beam splitter configured to receive light from a surface of a real-world object and projected light from the first display and direct a portion of the projected light along a set of projection light paths toward the first relay system; wherein the first relay system is configured to receive projection light from the beam splitter along the set of projection optical paths and to relay a portion of the received light along the first set of relay optical paths, thereby forming the first relay holographic surface together with the relayed image of the surface of the real-world object; and Wherein the second relay system is configured to receive light from the first relay system along the first set of relay optical paths and to relay a portion of the received light along the second set of relay optical paths, thereby forming the second relay holographic surface together with another relay image of the surface of the real-world object.

90. A holographic display system according to claim 84 or 89, wherein the second relay system directs another portion of the light received from the first relay system along a set of reflected optical paths in a direction substantially opposite to the direction of the second set of relay optical paths.

91. The holographic display system of claim 90, further comprising a corrective optical element disposed in the set of reflected light paths such that a viewer sensing light along the set of reflected light paths will perceive the second relay depth profile of the second relay holographic surface.

92. The holographic display system of claim 83, wherein the first relay system comprises a beam splitter and a retroreflector.

93. The holographic display system of claim 83, wherein the first relay system comprises a transflector.

94. The holographic display system of claim 83, wherein the first relay system comprises a beam splitter and a curved reflector.

95. The holographic display system of claim 84 or 89, wherein the second relay system comprises a beam splitter and a retroreflector.

96. The holographic display system of claim 84 or 89, wherein the second relay system comprises a transflector.

97. A holographic display system according to claim 84 or 89, wherein the second relay system includes a beam splitter and a curved reflector.

98. A holographic display system according to claim 84 or 89, wherein the first relay system and the second relay system both include a beam splitter and a curved reflector, and wherein the curved reflectors of the first relay system and the second relay system have substantially the same curved geometry and the same distance as the beam splitter.

99. The holographic display system of claim 84 or 89, wherein changes in magnification or light field angular coordinates introduced by the first relay system are at least partially corrected by the second relay system.

100. The holographic display system of claim 84 or 89, wherein the first depth profile of the first holographic surface at the display screen plane is substantially identical to the second relay depth profile of the second relay holographic surface at the new virtual screen plane.

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