Optical element and display device with optical element

Abstract

Provided is a display comprising a retro-transmissive optical element (203) for generating a floating image (207) from an image source (205). The element (203) comprises two optical portions. The first portion has a planar surface configured to receive and transmit light from (205) positioned on one side of (203) and oriented at a first acute or parallel dihedral angle γ≥0 relative to the planar surface. The first portion includes a plurality of unit cells, each configured to transmit incident light in the opposite direction to the light's propagation vector projected onto the planar surface. The second portion, positioned opposite the planar surface, includes a faceted surface with multiple tilted facets, at least some of which are inclined at a second acute dihedral angle α≠0 relative to the planar surface. In use, the display forms a floating image (207) at dihedral angle β relative to the planar surface, where β>γ.

Description

[0001] Optical element and display device with optical element

[0002] FIELD OF THE INVENTION

[0003] The present invention relates generally to retro- transmissive optical elements for a floating image display device, such as a mid-air or augmented reality display device, as well as the floating image display device comprising said optical element. In particular, floating image display devices are capable of creating digital images, which appear floating in the air with no additional screen material (e.g. water mist, fog, glass, etc. ) required.

[0004] BACKGROUND

[0005] Conventional displays are typically fixed to surfaces or encased within enclosures, limiting their flexibility and visual impact. There is an increasing demand for display technologies that create the illusion of “floating” images to enhance visual appeal and user engagement.

[0006] Floating image display devices using retro-transmissive optical elements (typically in the form of array plates) are known for creating “floating” images without the need for additional projection materials like glass or fog. These systems may employ optical elements composed of micrometer-scale corner reflectors to refocus light rays from an image source via a specific number of reflections, forming a real aerial image that appears suspended in space.

[0007] Specifically, an image source positioned on one side of an array of corner reflectors and at an angle to the array produces or projects a mirrored “floating” image of the image source on the other side of the array. Said otherwise, the projected “floating” image appears at the same angle to the array as the image source, but flipped upside down.

[0008] As a result, while such floating image display devices offer advantages for interactive and contact-free applications, including medical, industrial, and commercial uses, existing designs are constrained by size and viewing angle requirements. These limitations hinder the development of compact, versatile devices, which are increasingly demanded for modern applications.

[0009] Moreover, conventional retro-transmissive optical elements may reflect rays from the image source more than the aforementioned specific number of reflections, yielding parasitic images at the user’s eye position that are typically detrimental to the floating image effect.

[0010] The present invention aims to address one or more of the aforementioned problems.

[0011] SUMMARYAs such, in a first aspect of the present invention, there is provided a retro-transmissive optical element for producing a floating image from an image source, comprising a first optical portion and a second optical portion. The first optical portion provides a substantially planar surface, the planar surface being configured to, in use, receive and transmit therethrough light from the image source which is positioned facing one side of the optical element and is angled at a first acute or parallel dihedral angle y > 0 relative to the planar surface. The first optical portion also comprises a plurality of reflective unit cells which are each configured to, in use, reflect light from the image source in the opposite direction to the propagation vector of the light projected onto the planar surface. The second optical portion provides a faceted surface opposite to the planar surface, wherein the faceted surface comprises a plurality of tilted facets, wherein at least some of the tilted facets are angled at a second acute dihedral angle a 0 relative to the planar surface such that, in use, light from the image source is transmitted through the optical element to form a projected floating image on the other side of the optical element which is angled at a floating image dihedral angle ft relative to the planar surface which is greater than the first dihedral angle 0 > y.

[0012] Accordingly, the retro-transmissive optical element receives light from the image source through its planar (e.g. bottom) surface, wherein a propagation vector of the light projected onto the planar (e.g. bottom) surface can be defined. The plurality of reflective unit cells of the first optical portion therefore act to reflect light in the opposite direction to the propagation vector of the light projected onto the planar (e.g. bottom) surface, thereby mirroring, in the direction of the propagation vector, the image received through the planar (e.g. bottom) surface. The faceted (e.g. top) surface of the second optical portion is then that through which light from the image source may be further tilted. For instance, if the faceted surface is the top surface and the planar surface is the bottom surface, the top surface of the second optical portion is then that through which the reflected light from the first optical portion light may exit the optical element.

[0013] The present inventors have thus discovered that by providing the faceted (e.g. top) surface with a plurality of tilted facets, the dihedral angle a of a tilted facet (measured from the bottom surface to said given tilted facet of the top surface) controls the angle at which light leaves the tilted facet, and thereby the angles of the plurality of tilted facets control the dihedral angle ft of the projected floating image (measured from the planar (e.g. bottom) surface to the projected floating image). The present optical element therefore enables a projected floating image on the other side of the optical element (i.e. on the side opposite to that facing the image source) to be angled at the angle ft relative to the planar (e.g. bottom) surface which ismuch greater than the dihedral angle y of the image source (measured from the image source to the planar (e.g. bottom) surface) positioned below the optical element.

[0014] This enables a vast reduction in foot print of a floating image display device incorporating the present optical element, as the image source may be positioned at a small angle, and even parallel, to the optical element whilst still retaining a projected floating image tilted sufficiently far enough away from the optical element to produce a sufficiently high quality floating image.

[0015] Moreover, the present Inventors have further discovered that by using the tilted facets, so-called parasitic images (which are typically detrimental to the floating image effect) have suppressed visibility, as the image rays contributing to the parasitic image may be directed away from a user’s eye in use via the tilted facets.

[0016] For the avoidance of doubt, the material of the first and second optical portions enables light to propagate (i.e. transmit) through the body of the optical portion, other than parts of an optical portion configured to reflect light in a certain direction or otherwise block light, as specified. For instance, by the planar (e.g. bottom) surface being configured to receive and transmit therethrough light, it is understood to mean also enable light to transmit through the planar (e.g. bottom) surface.

[0017] The planar (e.g. bottom) surface is in a substantially planar (e.g. bottom) plane, however this does not necessarily mean the planar (e.g. bottom) surface is continuous, for instance there may be gaps in the planar (e.g. bottom) surface such that it is a discretised surface. All that is required is that the planar (e.g. bottom) surface is provided in a substantially planar plane. Moreover, the planar (e.g. bottom) surface need not be the most extremal surface of the optical element on the side facing toward an image source or towards the projected floating image in use. For instance, the optical element may comprise other protrusions such that a surface of the optical element may be defined which is closer in use to the image source or the projected floating image, as appropriate, than the planar (e.g. bottom) surface of the first optical portion.

[0018] For the avoidance of doubt, the dihedral angles may be defined relative to the planar (e.g. bottom) surface (which can conceptually be the dividing line between the first and second optical portions). The projected floating image has a user-facing side and an optical elementfacing side (i.e. a non-user-facing side). The planar (e.g. bottom) surface has a source-facing side (the side facing the image source) and a projection-facing side (the side facing the optical-element-facing side of the projected floating image, i.e. the non-user-facing side of the projected floating image).

[0019] First dihedral angle y > 0 is the acute dihedral angle measured relative to the planar (e.g. bottom) surface, namely the acute dihedral angle measured between the image sourceand the source-facing side of the planar (e.g. bottom) surface, which is thus defined to always be positive.

[0020] The second dihedral angle of the tilted facets, some of which may be zero, but at least some of which are at a #= 0, is the acute dihedral angle measured from the side of the tilted facet facing the planar (e.g. bottom) surface and the planar (e.g. bottom) surface itself (c can be positive or negative, as discussed below).

[0021] The dihedral angle of the projected floating image (floating image dihedral angle) is the dihedral angle (which can range from acute through to obtuse) measured between the projection-facing side of the planar (e.g. bottom) surface and the optical-element-facing side (non-user-facing side) of the projected floating image.

[0022] The first acute dihedral angle can be up to, and even including, 90°.

[0023] The first optical portion may comprise a plurality of prism elements, each prism element providing a respective one of the reflective unit cells, wherein each prism element comprises a bottom face, and wherein the plurality of bottom faces provides the planar surface.

[0024] Preferably, the plurality of prism elements are provided in a substantially two-dimensional array.

[0025] Each prism element may comprise a pair of reflective side faces which are each substantially orthogonal to each other and to the planar surface, and wherein each prism element is configured to reflect light from the image source in the opposite direction to the propagation vector of the light projected onto the planar surface by a first reflection in one of the reflective side faces and a second, consecutive reflection in the other of the reflective side faces.

[0026] In embodiments wherein each prism element comprises a pair of reflective side faces which are each substantially orthogonal to each other and to the planar surface: (i) the each prism element may be configured such that the first and second reflections are total internal reflections; or (ii) each pair of reflective side faces may comprise a reflective coating, optionally wherein the reflective coating comprises a metallic or dielectric film.

[0027] Each of the prism elements may comprise one or more further side faces, other than the pair of reflective side faces. Said one or more further side face(s) may be positioned at a different angle to the pair of reflective side faces and / or to the planar (e.g. bottom) surface (i.e. they need not be orthogonal). Said one or more further side face(s) may each be substantially planar, or may each be curved, or some may be substantially planar and others substantially curved.

[0028] The prism elements may be arranged in a triangular, rhombic, or hexagonal grid. Of course, alternatively, the prism elements may be arranged in any other regular grid geometry, such as square or rectangular grids.However, advantageously, the present Inventors have recognised that by arranging the prism elements in a non-rectangular grid may minimise moire artefacts created by the mismatch between the typically rectangular display pixel grid period of the image source used and the grid period of the prism elements.

[0029] The prism elements may be arranged in an irregular grid.

[0030] The present Inventors have recognised that by arranging the prism elements in an irregular grid may further reduce distortions and / or further minimise moire artefacts.

[0031] The separation between adjacent prism elements may be in the range between 1 pm and 2 cm.

[0032] As will be appreciated, for regular grids, the separation between adjacent prism elements is the period of the grid.

[0033] The optical element may comprise a light-absorbing material provided in the spacings between the prism elements.

[0034] The light-absorbing material may be metal, plastic, paint, or other suitable light absorbing material.

[0035] By providing a light absorbing material, the image ray originating from the image source which contributes to the projected floating image can reach the user only by passing through the micro-prisms, thus eliminating secondary parasitic images that can be detrimental to the floating image effect.

[0036] The thickness of the light-absorbing material may be no more than 100% of the height of the prism elements.

[0037] Each prism element may have a lateral size, measured in the same plane as that of the planar surface, of between 0.1 pm and 10 mm, and preferably between 1 pm and 2 mm.

[0038] Each prism element may have a vertical size, measured in the direction orthogonal to the plane of the planar surface, of between 0.1 pm and 100 mm, and preferably between 1 pm and 10 mm.

[0039] The first optical portion may comprise: (i) a plurality of corner mirror elements arranged in an array, wherein the plurality of corner mirror elements provides the plurality of reflective unit cells; or (ii) a stacked louver mirror array arrangement comprising a pair of louver mirror arrays arranged so as to be stacked one on the other and rotated by 90° relative to each other, wherein each of the louver mirror arrays comprises a plurality of mirror plates arranged substantially parallel to each other, and wherein the plurality of mirror plates of both louver mirror arrays together provide the plurality of reflective unit cells.

[0040] In embodiments wherein the first optical portion comprises a plurality of corner mirror elements arranged in an array, or a stacked louver mirror array arrangement or, indeed, a plurality of prism elements: (i) the second optical portion may comprise an array of triangularprism-elements each having a top face which is angled relative to the planar surface and a side face angled perpendicular to the planar surface such that the plurality of top faces provides the plurality of tilted facets; or (ii) the second optical portion may comprise an array of triangular prism-elements each having a top face which is angled relative to the planar surface and a side face which is angled relative to the planar surface such that only the plurality of top faces provide the plurality of tilted facets; or (iii) the second optical portion may comprise an array of triangular prism-elements each having a top face which is angled relative to the planar surface and a side face which is angled relative to the planar surface such that the plurality of top faces and side faces together provide the plurality of tilted facets.

[0041] The side faces may not contribute to the plurality of tilted facets, and wherein said side faces may comprise a coating of light-absorbing material.

[0042] The light-absorbing material may be metal, plastic, paint, or other suitable light absorbing material.

[0043] By providing a light absorbing material, the image ray originating from the image source which contributes to the projected floating image can reach the user only by passing through the top face, thus eliminating secondary parasitic images that can be detrimental to the floating image effect.

[0044] A lateral size of the second optical portion, measured in a first direction in the plane of the planar surface, may be configured to be at least as large as a lateral size of the first optical portion measured in the first direction.

[0045] In a particularly preferred embodiment, the first and second optical portions may be provided from the same bulk of homogeneous material. Said otherwise, the first and second optical portions may be comprised by the same singular piece of material, for instance both first and second optical portions being provided by a plurality of prism elements. This is advantageous as it reduces the complexity of fabricating the optical element and may be optimal in reducing the total amount of costly optical material of the optical portions.

[0046] For instance, in embodiments wherein the first optical portion comprises a plurality of prism elements, each prism element providing a respective one of the reflective unit cells may comprise a top face which is angled relative to the planar surface such that the plurality of top faces provides the plurality of tilted facets.

[0047] As such, each prism element provides a part of both the first optical portion and the second optical portion. The present Inventors have recognised that using prism elements specifically is particularly convenience for manufacture, convenience for control during design optimisation, and uses much less costly material.

[0048] Each element may be provided on or within an optically transparent plate.

[0049] At least some of the tilted facets may be tilted at different second acute dihedral angles as others of the tilted facets.The optical element may comprise a first end and a second end which are both in the same plane as the planar surface, wherein, in use, the first end is closer to the projected floating image than the second end and the second end is further from the projected floating image than the first end, and wherein the second acute dihedral angles of the plurality of tilted facets are varied from the first end to the second end so as to reduce focal plane bending and image distortion of the projected floating image.

[0050] The optical element may comprise a central region between the first end and the second end, and wherein the plurality of tilted facets may be configured to have a varying second acute dihedral angle from: (i) a > 0 for tilted facets at the first end, to (ii) a < 0 for at least some tilted facets in the central region, to (iii) a = 0 for tilted facets at the second end.

[0051] That is, the present Inventors have recognised that by introducing a varying angle a from the first end to the second end, such as from a > 0 to a < 0 from the side of the optical element closest to the user (i.e. closest to the projected floating image) towards the central region of the optical element and then raising again to a = 0 at the far (second) end of the optical element, it is possible to correct focal plane bending and image distortion of the projected floating image.

[0052] Alternatively, in some embodiments, all of the tilted facets are angled at substantially the same second acute dihedral angle a #= 0 relative to the bottom surface.

[0053] The present invention also extends to the floating image display device that can (and does) use such optical elements according to the first aspect and any of its embodiments.

[0054] Thus, in a second aspect of the present invention, there is provided a floating image display comprising: the retro-transmissive optical element of any preceding claim; and the image source which is positioned facing the optical element on one side of the optical element and is angled at the first dihedral angle y relative to the planar surface, such that light from the image source is transmitted through the optical element to form the projected floating image.

[0055] Thus, the floating image display device is capable of creating digital image which appear floating, e.g., in the air, to a user positioned at the correct location, with no additional screen material such as water mist, fog, or glass required.

[0056] The image source may be an LCD, LED, OLED, QLED, or micro-LED display screen. Of course, any other type of display screen as known in the art may suitably be used as the image source.

[0057] The floating image display device may be a mid-air or augmented reality display device.

[0058] It will be appreciated herein that the term “mid-air” should not be interpreted narrowly to cover only explicitly devices for use in ambient “air” environments, but rather should beinterpreted broadly to encompass other non-air environments. For instance, the floating image display device may be used to generate the “mid-air” projected floating image in an underwater environment, for instance as part of underwater diving apparatus or other underwater display devices such as in deep sea oil rig environments or the like. Alternatively, the floating image display device may be used to generate the projected floating image in a vacuum environment, such as in an extra-terrestrial environment such as on exterior of a space station or craft.

[0059] The display device may include a casing, configured to hold or support at least the optical element and the image source. Optionally a touchless sensor and / or a processor coupled thereto, as described below, may also be supported to be held by the casing. The casing may be waterproof or may be vacuum-compatible, such that the floating image display device may be used in the corresponding environments.

[0060] The lateral size of the optical element may be configured to be larger than the lateral size of the projected floating image.

[0061] The image source may be positioned facing the planar surface such that the planar surface is closer to the image source than the faceted surface is from the image source and that the faceted surface is closer to the projected floating image than the planar surface is from the projected floating image.

[0062] Alternatively, the image source may be positioned facing the faceted surface such that the faceted surface is closer to the image source than the planar surface is from the image source and that the planar surface is closer to the projected floating image than the faceted surface is from the projected floating image.

[0063] The display device may comprise a lenticular lens array positioned in between the image source and the optical element, wherein the lenticular lens array is configured to, together with the image source and the optical element, create a 3D illusion effect with the projected floating image.

[0064] The display device may be an interactive display device further comprising: a touchless sensor; and a processor coupled to the touchless sensor, the processor being configured to detect, with the touchless sensor, if a user interacts with the projected floating image.

[0065] For instance, the projected floating image may be that of a “touch screen” type, comprising digital buttons or other interactive features. These digital buttons or other interactive features may typically be configured as guides for a user. A user may then “touch” a button by physically placing a user-controlled object (such as a finger or hand, or handheld object such as a pen or pointer) in the position of the projected floating image where the button is projected, which is detected by the processor by means of the touchless sensor. Thus, the action associated with pressing said button, or engaging with any other interactive feature, may be actuated by the processor.It is noted that at no point does the user physically interact (i.e. physically touch) a screen. Rather, the user needs only position the user-controlled object at the correct location of the projected floating image. Thus, the interactive display device of the present invention may advantageously be used to prevent the spread of infectious deceases and contamination transfer in manufacturing, research, medical care, etc. which otherwise may occur through the typical and unavoidable contact exchange when using a conventional touch screen. Moreover, in many scenarios, such as industrial manufacturing, research, medical care, food preparation, cold or fridge-like environments, a user may typically wear gloves, such as protective gloves, which may inhibit optimal use of a conventional touch screen. Again, this problem is alleviated by the interactive display device of the present invention, e.g., as the touchless sensor may be easily configured to detect both a gloved and gloveless finger or hand.

[0066] Thus, the interactive display device may be comprised by one of the following systems so as to provide an interactive display thereto: an airport check-in terminal; a hotel check-in terminal; a medical point-of-care terminal; a food ordering terminal; a medical device; a manufacturing equipment; a retail equipment; a display equipment of for trade or fashion shows.

[0067] BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Various embodiments of the invention will now be described, by way of example only, and with reference to the accompanying drawings in which:

[0069] Figure 1 shows an example of a conventional floating image display device as known in the art;

[0070] Figure 2 shows a floating image display device, according to an embodiment of the invention;

[0071] Figure 3 shows a retro-transmissive optical element according to an embodiment of the invention;

[0072] Figure 4 shows a single prism element of the optical element of Figure 3;

[0073] Figure 5 shows side-on views of a prism elements, according to embodiments of the invention;

[0074] Figure 6 shows the direction of parasitic image rays from a floating image display device according to an embodiment of the invention;

[0075] Figure 7 shows top-down views of different optical elements, according to embodiments of the invention;

[0076] Figure 8 shows the results of an optical element which produces a curved projected floating image, according to an embodiment of the invention;Figure 9 shows the results of an optical element which corrects for the curved projected floating image, according to an embodiment of the invention;

[0077] Figure 10 shows a corner mirror element which can be used in embodiments of the invention;

[0078] Figure 11 shows a stacked louver mirror array arrangement which can be used in embodiments of the invention; and

[0079] Figure 12 shows triangular prism array which may be used in embodiments of the invention.

[0080] DETAILED DESCRIPTION

[0081] Figure 1 shows an example of a conventional floating image display device 101 as known in the art. The left-hand panel is a solid view, the middle panel is a see-through line drawing, and the right-hand panel is a side-on view. The display device 101 can be used to project a floating image “mid-air” and thus may be a mid-air or augmented reality display device 101.

[0082] The key element of display device 101 is a retro-transmissive array plate (RTAP) 103, which is a specialised optical element 103 typically composed of a large number of micrometer-scale corner reflectors. The purpose of the RTAP 103 is to refocus image rays coming from an image source 105 (typically an LCD, LED, OLED, QLED, micro-LED or a different kind of a display screen) positioned on one side of the plate to a mirror position on the other side of the plate, creating a real projected image 107 which appears to be “floating” in the air. Unlike other “floating” display arrangements, the image 107 is projected directly onto the air, and no additional screen material (e.g. water mist, fog, glass, etc. ) is required.

[0083] In a typical implementation of Figure 1, the RTAP 103 is positioned horizontally or at a small angle to a surface of the surrounding casing 109 of the display device 101, and the image source 105 is placed below at the desired angle in respect to this horizontal plane (which may be a hole or transparent window in the casing 109) and is hidden from the user by the surrounding casing 109. The casing 109 may typically contain other components, including electronics, computers, sensors, etc. This way, the original image source 105 is not directly observable by the user, emphasising the floating image effect.

[0084] However, by their design, the conventional display device 101 of Figure 1 is only able to create a mirrored “floating” projected image 107 of the image source 105. Therefore, the projected image 107 appears at the same angle to the RTAP plate as the image source, but flipped upside down, as shown in the right-hand panel of Figure 1. Said otherwise, the image source 105 must be tilted at an acute dihedral angle y relative to the RTAP 103. The RTAP 103 reflects light rays from the image source 105 (in the opposite direction to the propagationvector of the light rays projected onto the RTAP 103), e.g. via corner reflectors or other reflective elements producing a retro-transmissive effect, resulting in the projected image 107 also being tilted at the same acute dihedral angle y relative to the RTAP 103 on the opposite side.

[0085] As a result, the size of the floating image display device 101 is defined by the required size of the projected image 107 and the required angle y relative to the RTAP 103 (or indeed relative to the hole or window in the casing 109) at which the project image 107 is to be observed by the user. In a typical arrangement, as shown in Figure 1, this limits the ability to create compact device which are highly desired for majority of the listed applications, as the display device 101 requires sufficient depth (indicated by double-arrow “di” in Figure 1) in which to host the tilted image source 105.

[0086] Figure 2 shows a floating image display device 201, according to an embodiment of the present invention. The left-hand panel is a solid perspective view, the middle panel is a see-through line drawing in the same perspective view, and the right-hand panel is a see-through line drawing in side-on view.

[0087] Crucially the display device 201 uses a novel retro-transmissive optical element 203, as described in more detail below. This optical element enables an image source 205 (which may be similar to image source 105) to be placed at an acute dihedral angle y (or even parallel y = 0) to the optical element 203 while still creating a projected floating image 207 at a dihedral angle ft relative to the optical element 203 on the opposite side which is greater than the acute dihedral angle of the image source 205, ? > y. As known, a “dihedral angle” is defined as follows: for two planes intersecting along a line, the dihedral angle is the measure of the angle between two lines, each lying on one of the planes and both perpendicular to the line of intersection at the same point.

[0088] Thus, the depth (indicated by double-arrow “d in Figure 2) in which to host the tilted image source 205 may be much smaller than conventional devices, resulting in a more compact arrangement.

[0089] The display device 201 includes a surrounding casing 209, in which at least the image source 205 as well as other components, including electronics, computers, sensors, etc. may be held.

[0090] Thus the display device 201 may be used as a mid-air or augmented reality display device. If the device 201 further includes a lenticular lens array (discussed in more detail below) on top of the image source 205 (i.e. on the side facing the optical element 203), then the display device 201 may produce a projected floating image 207 having a 3D illusion effect. Other 3D illusion creating optical elements may be used instead of a lenticular lens.The display device 201 may further include a touchless sensor and a processor coupled to the touchless sensor. The processor may then be configured to detect, with the touchless sensor, if a user interacts with the projected floating image, yielding an interactive display device 201. One or both of the touchless sensor and the processor may for instance be also included in the casing 209 of the display device 201.

[0091] As such, the present display device 201 may be used for many applications, including, but not limited to: airport check-in terminals, hotel check-in terminals, medical point-of-care terminals, food ordering terminals, displays for medical devices, displays for manufacturing equipment, as displays for trade and fashion shows with a “wow effect”, etc. When combined with said touchless sensor (such as ultrasound, optical, thermal, or other sensors, or indeed any other gesture recognition device), they create an interactive display similar to a touch screen, but with an additional benefit of preventing physical contact between the user and the device. Therefore, the present display device 201 can prevent the spread of infectious deceases and contamination transfer in manufacturing, research, medical care, etc.

[0092] Figure 3 shows a retro-transmissive optical element 203 according to an embodiment of the invention. The optical element 203 is for producing a floating image from an image source, and may for instance be used as the optical element of the floating image display device 201 of Figure 2. The upper-left panel of Figure 3 shows a see-through line drawing side-on view of optical element 203, the lower-left panel shows a top-down solid view of the optical element 203 (i.e. viewed from the side of the optical element opposite to that of the image source 205 in use), and the right-hand panel shows a solid perspective view of the optical element 203. For the avoidance of doubt, the “bottom” of the optical element 203 is that which faces the image source 205 in use, whereas the “top” of the optical element 203 is the side opposite to the bottom and which faces the projected image 207 in use.

[0093] The optical element 203 is composed of a large number of micrometer-size prism elements 311 assembled on or formed within an optically transparent plate 313 and made from an optically transparent material, such as glass, plastic, quartz, sapphire, etc. The horizontal (in-plane) size (indicated by double-arrows “wi” and “w in the lower-left panel of Figure 3) of the micro-prism is in the range between 1 pm and 2 mm, where wi and W2 need not necessarily be equal. The vertical (out-of-plane) size (indicated by double-arrows “h” in the right-hand panel of Figure 3) of the micro-prism is in the range between 1 pm and 10 mm.

[0094] Figure 4 shows a single prism element 311 of the optical element 203 of Figure 3. The lower-left panel shows a see-through line drawing face-on view of the prism element 311 from the top. The upper-left panel shows a see-through line drawing side-on view of the prism element 311. The middle panel shows a see-through line drawing perspective view of the prism element 311 according to one embodiment, and the right-hand panel shows a solidperspective view of the prism element 311 according to another embodiment comprising absorbing material (as discussed more below).

[0095] The prism element 311 has one bottom face 415 providing a substantially planar bottom surface, one top face 417, and three or more side faces. Two side faces of prism element 311 form a pair of reflective side faces 419 and are positioned at (or at an angle close to) 90° in respect to each other and configured to reverse the projection of the light propagation vector onto the plane which is orthogonal to both of these faces, namely the plane in which the bottom face 415 lies (the bottom planar surface).

[0096] This is shown via the doubled-lines in Figure 4 (or thick lines in the right-hand panel of Figure 4), which indicate the propagation of a ray of light from image source 205. In the lefthand and middle panels of Figure 4, light rays propagating through the optical element 203 are shown in double lines which are dashed, whereas those propagating outside the optical element 203 are indicated with full double lines.

[0097] In particular, as shown in the left-hand panels of Figure 4, light ray 421a initially impinges on the prism element 311. The light ray 421a will have a light propagation vector having a component in the bottom planar surface, otherwise termed the propagation vector of the light projected onto the bottom planar surface of the bottom face 415. This is shown by the dashed arrows 421b in the left-hand panels of Figure 4. The reflection of light 421a in the opposite direction to the propagation vector of the light projected onto the bottom planar surface 421b is achieved through two consecutive reflections of the image rays from the pair of reflective side faces 419 as shown in Figure 4.

[0098] Namely, the image rays 421a enter prism element 311 through the bottom face 415, then is consequently reflected off the first and then consecutively off the second of the reflective faces 419. This results in the light after the two reflections (and indeed after leaving the prism element 311 or the optical element 203) having a light propagation vector having a component in the bottom planar surface which is opposite to the component originally impinging on the bottom of the prism element 311, as indicated by the dashed arrows 421c in the left-hand panels of Figure 4 which is opposite to dashed arrows 421b.

[0099] The other side faces of the prism element 311 may be positioned at a different angle or rounded. The reflective property of the side faces is typically achieved through the total internal reflection, but can be also achieved by coating the side faces of the micro-prisms with a reflective material, such as metal, dielectric films, etc.

[0100] The top face 417 of the prism element 311 through which the image rays exit may be positioned at an angle a with respect to the bottom face 415 of the prism element 311 (counted from the bottom to the top face), through which the image rays enter. This way, the angle a may be used to control the angle <p at which the image rays leave the prism element 311 andtherefore adjust the rotation of the plane of the projected floating image 207 with respect to the plane of the optical element 203, namely beyond any tilting achieved via refraction of the light ray as it leaves the prism and propagates in the surrounding medium. The angle a may be thus greater than 0° but less than 90°. Preferably, the angle a is between 0° and 60°. Most preferably, less than or equal to 30°. Figure 5 shows side-on views of a prism element 311, wherein the prism element of the upper panel has a = 0°, whereas the prism element 311 of the lower panel has a = 4° according to an embodiment of the invention.

[0101] In the upper panel, when a is 0°, the projected floating image 107 appears at the mirror position with respect to the plane of the optical element 103, i.e. if the image source (i.e. display screen) 105 is position at an angle of -45° with respect to the plane of the optical element 103, then its projected floating image 107 is projected onto a plane positioned at +45° with respect to the plane of the optical element 103. This is reminiscent of the conventional devices of Figure 1.

[0102] In contrast, when a is 4° and the image source 205 is placed below the plane of the optical element 203 at an angle of 0° (i.e. the optical element 203 and image source 205 are parallel to each other), then projected floating image 207 is projected onto a plane positioned at +57° with respect to the plane of the optical element 203. As will be appreciated, here the plane of the optical element 203 is the plane in which the bottom faces 4 15 of each of the prism elements 311 of the optical element lies (the bottom planar surface). This way, it is possible to make a compact floating image display device 201 by positioning an image source 205 and optical element 203 parallel to each other or at a small angle, while creating a “midair” projected floating image 207 at the desired angle to the user.

[0103] In general, the material of the prism elements 311 may be glass, crystalline, plastic, polymer, or any other optical material. The prism elements 311 are created on top of or within an optically transparent plate 313 as shown in Figures 3-4, which can be made of the same or different material. The plate 313 is preferably substantially uniform with the top and the bottom surfaces parallel to each other. The prism elements 311 can be created using subtractive, additive, forming, or other methods. For example, by etching, 3D printing, hot-embossing, injection moulding, nano-imprinting, or similar methods.

[0104] In addition to light rays from the image source 205 experiencing two reflections as described above, there will be other light rays that will experience different number of reflections with the resulting light propagation vector having a component in the bottom planar surface which is not opposite to the component originally impinging on the bottom of the prism element 311 (thus, not achieving the retro-transmission effect). In this example, zero or one reflection. If these rays reach the user’s eye, they may result in parasitic images that are typically detrimental to the floating image effect. By utilising the top face 417 of the prismelements 311 that is not parallel to the bottom face 415 (e.g., oblique micro-prisms), it is possible not only to control the rotation of the projected floating image 207 as described above, but also suppress the visibility of the parasitic images by directing the image rays that form them away from the user’s eye, as shown in Figure 6 (with the parasitic rays shown with light grey and the image forming rays shown with black colour).

[0105] For instance, by tailoring the angle a, less than 6 % of the light rays reaching a user, in use, may be light rays having undergone zero or one reflection. As will be appreciated, determining the optimal a (either a single a for each prism element 311 of the optical element 203, or a distribution of different values of a for different prism elements 311 of the optical element 203) in order to reduce to less than 6 % is a matter of routine implementation and straight forward optimisation well within the ambit of the skilled person.

[0106] Referring again to Figure 3, the ratios between the lateral (in-plane, i.e. w1 and w2 in Figure 3) and the vertical (out-of-plane, i.e. h in Figure 3) sizes of the prism elements 311 affects the portion of image rays that pass through the optical element 203 with two reflections. To achieve higher brightness and quality of the floating image, this ratio needs to be optimised to allow maximum portion of the image rays to pass through the optical element 203 with two reflections while directing rays which do not contribute to the formation of the floating mid-air image away from the user’s eye.

[0107] Furthermore, referring again to Figure 4, a light-absorbing material 423, such as metal, plastic, paint, or other, may be placed in the openings between the prism elements 311 (i.e. gaps or spacings), so that light rays originating from the image source 205 can reach the user only by passing through the prism elements 311, thus further helping to eliminate secondary parasitic images that can be detrimental to the floating image effect. The thickness of this material layer may range between 0 and 100% of the height of the prism elements 311 (“h” in Figure 3).

[0108] Figure 7 shows a top-down view of different optical elements 203, according to embodiments having the prism elements 311 arranged in different grid-like configurations.

[0109] The upper left-hand panel of Figure 7 shows the prism elements 311 arranged in a square grid, the lower left-hand panel of Figure 7 shows the prism elements 311 arranged in a hexagonal grid, the upper right-hand panel of Figure 7 shows the prism elements arranged in a rhombic grid, whereas the lower right-hand panel of Figure 7 shows the prism elements 311 arranged in an irregular grid.

[0110] In particular, the present Inventors have discovered that the non-rectangular grid can be used to minimise moire artefacts created by the mismatch between the pixel grid period of the image source 205, which is typically rectangular, and the grid period of the prism elements 311 of the optical element 203. The period of the grid may be in the range between 1 pm and 2 cm. The grid period of the prism elements 311 of the optical element 203 and the horizontal(in-plane, i.e. wi and W2 in Figure 3) size of the prism elements 311 affects the resolution of the projected floating image 207 with the smaller prism element 311 horizontal (in-plane) size and smaller grid size corresponding to a higher resolution of the projected floating image 207 formed.

[0111] The angle a can be the same between all prism elements 311 or varied across the array of prism elements 311 , thus allowing additional flexibility which can be used to suppress image distortions and artefacts of the projected floating image 207, or indeed produce additional effects.

[0112] Figure 8 shows the results of an optical element 203 which produces a curved projected floating image, according to an embodiment. Here, the prism elements have a square cross-section of 300 pm by 300 pm (wi = W2 = 300 pm) and they are arranged in a square grid arrangement (similar to the upper left-hand panel of Figure 7) with a 100 pm gap between the neighbouring prism elements 311. The angle a = -5° for all prism elements 311 and the optical element 203 is parallel to the image source 205. The resulting focal plane of the projected floating image 207 is curved and the image itself is distorted as shown in the right-hand panel of Figure 8. For the avoidance of doubt, in the scenario where the projected floating image 207 is curved, it is to be noted that the “angle” of the projected floating image is defined as the tangent of the curve providing the smallest angle.

[0113] Of course, in some scenarios it may be desirable to produce a curved image, with distortions arising from the curvature being accounted for via appropriate deformation of the image at the image source 205 or via the geometrical parameters of the prism elements 311 such as lateral / vertical sizes or tilts of the top face 317 of selected ones of the prism elements 311.

[0114] Figure 9 shows the results of an optical element 203 which corrects for the curved projected floating image shown in Figure 8, according to an embodiment. Here, the parameters of the optical element 203 and image source 205 are the same as that of the embodiment of Figure 8, with the exception of the angles a of the top faces 317 of the prism elements 311. In particular, by introducing a varying angles a from +3° from the side of the optical element 203 closest to the user to -4° towards the centre of the optical element 203, and then raising the angles a again to 0° at the far end of the optical element 203, it is possible to correct focal plane bending and image distortion (of Figure 8) as shown in the right-hand panel of Figure 9.

[0115] The present Inventors have thus recognised that the aforementioned prism elements 311 are just one (preferred) embodiment for providing both the retro-transmissive effect of the optical element 203 and the tilting of the projected floating image 207. However, what is important is that the optical element 203 comprises:(i) a first optical portion providing a planar bottom surface and which has a plurality of reflective unit cells which are each configured to, in use, reflect light from the image source 205 in the opposite direction to the propagation vector of the light projected onto the bottom surface; and

[0116] (ii) a second optical portion providing a top surface opposite to the bottom surface and comprising a plurality of tilted facets which are tilted such that, in use, light from the image source 205 is transmitted through the optical element 203 to form a projected floating image 207 on the other side of the optical element 203 which is angled at p > y (with y being the angle of the image source 205 relative to the optical element 203).

[0117] That is, the plurality of reflective unit cells together converts a diverging set of light rays from image source 205 on one side of the optical element 203 into a converging set of light rays of the image source 205 on the other side of the optical element 203. Typically this may be done via two reflections to reflect the light in the opposite direction to the propagation vector of the light projected onto the bottom surface, however the skilled person would be aware of how to provide reflective unit cells which achieve this in greater than two reflections, such as in three or more reflections.

[0118] In the above-described embodiments wherein the optical element 203 comprises prism elements 311, the pair of reflective side faces 419 of each prism element 311 provides a reflective unit cell, such that there is a plurality of reflective unit cells, whereas the top faces 417 of prism elements 311 provides at least some of the tilted facets at angles a for controlling the tilt of the projected floating image 207. However, other designs may be used for one or both of the first and second optical portions.

[0119] For instance, Figure 10 shows a corner mirror element 1031 which can be used as a reflective unit cell of the first optical portion of optical element 203, according to an embodiment. The left-hand panel of Figure 10 shows a top-down solid view of the corner mirror element 1031, and the right-hand panel shows a solid side-on view of the corner mirror element 1031.

[0120] The corner mirror element 1031 shown here has a pair of reflective mirrors 1019 positioned substantially orthogonal to one another, and which are configured to reverse the projection of the light propagation vector onto the plane which is orthogonal to both of these mirrors 1019. As will be appreciated, the pair of reflective mirrors 1019 performs a similar role as described above in relation to the reflective side faces 419 in relation to Figure 4. The reflective mirrors 1019 may however be provided other than in a prism element format, e.g. via fabricating micro-structure mirror plates with optical flatness and precise angles, as known in the art.In the left-hand panel of Figure 10, light rays propagating through the optical element 203 are shown in double lines which are dashed, whereas those propagating outside the optical element 203 are indicated with full double lines. Similar to in Figure 4, light ray 421a initially impinges on the optical element 203. The light ray 421a will have a light propagation vector having a component in the plane orthogonal to both the mirrors 1019 (which may typically be the planar surface of the optical element 203 configured to receive, in use, light from the light source 205), shown by the dashed arrows 421b in the left-hand panel of Figure 10. The reflection of light 421a in the opposite direction to the propagation vector of the light projected onto said orthogonal plane is achieved through two consecutive reflections of the image rays from the pair of reflective mirrors 1019, resulting in the component of the light ray in the orthogonal plane, shown as 421c in Figure 10, being in the opposite direction to that 421b of the originally impinging light ray 421a.

[0121] Figure 11 shows a stacked louver mirror array arrangement 1127 which can provide the plurality of reflective unit cells of the first optical portion of optical element 203, according to an embodiment.

[0122] The stacked louver mirror array arrangement 1127 is formed of a pair of louver mirror arrays 1129 arranged so as to be stacked one on the other and rotated by 90° relative to each other. Each louver mirror array 1129 is formed from a plurality of mirror plates 1119 arranged substantially parallel to each other, and substantially equally spaced from one another so as to enable light rays 421a from the image source 205 to propagate through the stacked louver mirror array arrangement 1127, as shown by the double line arrows in Figure 11.

[0123] Each mirror plate 1119 has a reflective planar mirror surface (indicated by the dark grey shading in Figure 11), and preferably both sides of each mirror plate 1119 has a reflective planar mirror surface. Preferably, as shown, for each louver mirror array 1129, the mirror plates 1119 are arranged to define a plane of the louver mirror array 1129 and are orientated such that the reflective mirror surface(s) are orthogonal to the plane of the louver mirror array 1129.

[0124] Similar to the above, light ray 421a will have a light propagation vector having a component in the plane of the louver mirror array 1129 (which may typically be the planar surface of the optical element 203 configured to receive, in use, light from the light source 205). The reflection of light 421a in the opposite direction to the propagation vector of the light projected onto said louver mirror array plane may be achieved through two consecutive reflections of the light ray 421a, with the first reflection from a mirror plate 1119 in one of the louver mirror arrays 1129 and the second reflection from a mirror plate 1119 in the other of the louver mirror arrays 1129, as shown in Figure 11. Thus, it is the mirror plates 1119 of both louver mirror arrays 1129 which together provide the plurality of reflective unit cells as described above.Moreover, the embodiment of Figure 11 is an example wherein reflecting light from the image source 205 in the opposite direction to the propagation vector of the light projected onto the bottom surface need not necessarily require precisely two reflections as described above, but may instead be achieved with greater than two reflections. For instance, when both sides of each mirror plate 1119 are reflective planar mirror surfaces, the stacked louver mirror array arrangement 1127 may be configured such that desired light rays from the image source 205 (i.e. those intended to result in the projected floating image 207) are reflected more than once between pairs of mirror plates of the same louver mirror array 1129, as shown by the portion of light ray 1121a reflecting multiple times in the upper louver mirror array 1127 in Figure 11.

[0125] As will be appreciated, there is a variety of different configurations for the plurality of reflective unit cells, depending on the desired properties of the projected floating image 207. For instance, arranging the reflective unit cells in a radial configuration (e.g. along concentric circular array lines, or concentric elliptical array lines) may be used to increase the viewing angle at which the user is able to view the projected floating image 207.

[0126] Figure 12 shows triangular prism array 1227 which may be used in embodiments of the present invention. The upper-left panel of Figure 12 shows a solid side-on view of the triangular prism array 1227, the lower-left panel shows a top-down solid view of the triangular prism array 1227 (i.e. viewed from the side of the optical element 203 opposite to that of the image source 205 in use), and the upper-right panel shows as zoomed-in view of the upperleft panel, and the lower right-hand panel shows a solid perspective view of the triangular prism array 1227.

[0127] In particular, the triangular prism array 1227 may provide, or at least contribute to, the aforementioned second optical portion of the optical element 203. That is, the triangular prism array 1227 may be used with the array of corner mirror elements 1031 or stacked louver mirror array arrangement 1127, such as those respectively described in the embodiments of Figures 10 and 11. The triangular prism array 1227 may also be used with the arrays of prism elements 311, such as those described in the embodiments of Figures 3-9 but with the top faces 417 parallel to the bottom faces 415 (a = 0°, e.g. as shown in the upper panel of Figure 5), to tilt the projected floating image such that 0 > y. Indeed, it is even considered that the triangular prism 1227 may be used in conjunction with the arrays of prism elements 311 described in the embodiments of Figures 3-9 with tilted top faces 417 (a =# 0°), to provide further control over the tilt and quality of the projected floating image 207.

[0128] Thus, a plate containing an array of triangular prisms 1227 as shown in Figure 12 may be placed above or below the plurality of reflective unit cells of the first optical portion.

[0129] The array of triangular prisms 1227 is formed from a plurality of triangular prism elements 1233. Here, the triangular prism elements 1233 are shown extending linearly in the lateral in-plane direction, i.e. along W2 in Figure 12. Alternatively, the triangular prism elements1233 may extend in a curvilinear manner, for instance the plurality of reflective unit cells are arranged in a radial configuration.

[0130] The triangular prism elements 1233 each have a substantially planar bottom face 1215, such that they are all co-planar in a bottom plane. The triangular prism elements 1233 each have a substantially planar top face 1217, wherein the top face 1217 is angled with respect to the bottom face 1215 to define the triangular profile of the triangular prism element 1233, as shown in the upper-right panel of Figure 12. The triangular profile is completed by side face 1235, which may be provided at an angle between 30° to 90° with respect to the bottom face 1215. In the example shown in Figure 12, the side faces 1235 are all substantially perpendicular to the bottom faces 1215.

[0131] Of course, the angles of the tilt of the top faces 1217 may vary between different triangular prism elements 1233, and / or the angles of the tilt of the side faces 1235 may vary between different triangular prism elements 1233. In the example shown in Figure 12, all of these angles are kept substantially constant across the different triangular prism elements 1233 of the array of triangular prisms 1227.

[0132] An absorbing material, such as metal, plastic, paint, and other, may be applied to the side face 1235 to block imaging rays from exiting through this face and thus preventing formation of the secondary parasitic images.

[0133] In embodiments wherein the array of triangular prisms 1227 is used in conjunction (i.e. arranged below or above) an array of prism elements 311 such as those shown in Figure 3 (whether those prism elements 311 have tilted top faces 417 or otherwise), the size and arrangements of the triangular prism elements 1233 can be similar to those of the prism elements 311. For instance, the lateral size of triangular prism elements 1233 along wi in Figure 12 may be similar to the lateral size of prism elements 311 along wi in Figure 3.

[0134] Similarly, wherein the array of triangular prisms 1227 is used in conjunction (i.e. arranged below or above) other types of plurality of reflective unit cells such as those described above in relation to Figures 10 or 11, the size and arrangements of the triangular prism elements 1233 can be similar to the spacings associated with or between the reflective unit cells (e.g., the spacings between adjacent corner mirror elements 1031, or the spacings between adjacent mirror plates 1119 in a louver mirror array 1127)

[0135] As will be appreciated, the array of triangular prisms 1227 provides a similar effect as creating an angle between the top 417 and bottom 415 faces of the prism element 311 in the embodiments of Figures 3-9, and can be used in conjunction or without. Thus, said otherwise, in embodiments, it is the top faces 1217 of triangular prism elements 1233 which provide at least some of the tilted facets of the second optical portion at angles a for controlling the tilt of the projected floating image 207.The material of the triangular prism elements 1233 may be glass, crystalline, plastic, polymer, or any other optical material.

[0136] The triangular prism elements 1233 in Figure 12 are created on top or within a transparent optical plate 1213, which can be made of the same or different material. The plate is preferably substantially uniform with the top and the bottom surfaces parallel to each other.

[0137] Similar to the prism elements 311 described above, the triangular prism elements 1233 can be created using subtractive, additive, forming, or other methods. For example, by etching, 3D printing, hot-embossing, injection moulding, nano-imprinting, or similar methods.

[0138] The lateral (in-plane, i.e. wi and W2 in Figure 12) dimensions of the array of triangular prisms 1227 are selected according to the size of: (i) the image source 205 to be used; (ii) the plurality of reflective unit cells (e.g. the array of prism elements 311 of Figures 3-9); and (iii) the overall dimensions of the device 201. To avoid vignetting and other undesired image distortion effects the size of the array of triangular prisms 1227 should be at least as large as the desired size of the array of reflective unit cells.

[0139] Thus, in general, the lateral dimensions of the optical element 203, in any of the abovedescribed embodiments, are selected according to the size of the image source 205 to be used in conjunction therewith, as well as the overall dimensions of the display device 201. To avoid vignetting, the optical element 203 size is preferably larger than the desired size of the projected floating image 207. The optical element 203 size may be, for example, 11.5 cm by 6.0 cm or 75 cm by 45 cm, although very many different sizes can be used without departing from the scope of the present invention.

[0140] Finally, an additional plate containing lenticular lens array (lenticular lens array plate, LLAP) may be placed on top of the image source 205 to create a 3D illusion effect with the display device 201. The material of the lenticular lenses may be glass, crystalline, plastic, polymer, or any other optical material. The lenticular lenses are created on top or within a transparent optical plate, which can be made of the same or different material as that of optical element 203. The plate is preferably substantially uniform with the top and the bottom surfaces parallel to each other. Lenticular lenses can be created using subtractive, additive, forming, or other methods. For example, by etching, 3D printing, hot-embossing, injection moulding, nano-imprinting, or similar methods. The LLAP should be at least as large as the image display.

[0141] In the above exemplary embodiments, for clarity, the “bottom surface” has been used to denote the planar surface closest to image source 205 in use, whereas the “top surface” (or “top face”) has been used to denote tilted facets furthest away from image source 205 (i.e. closest to the projected floating image 207). However, it will be appreciated that this is only a preferred embodiment, and describing this way is merely a matter of convenience for descriptive purposes. For instance, in some embodiments, the surface comprising the tiltedfacets may be the “bottom” surface closest to the image source 205 in use, and the planar surface may be the “top” surface furthest from the image source 205 (and thus closest to the projected floating image 207) in use. Moreover, the tilted facets of the second optical portion could in fact be provided facing the planar surface of the first optical portion (e.g., leaving gaps therebetween which may be filled with other material to that of the reflective unit cells, etc).

Claims

CLAIMS1. A retro-transmissive optical element for producing a floating image from an image source, comprising:a first optical portion providing a substantially planar surface, the planar surface being configured to, in use, receive and transmit therethrough light from the image source which is positioned facing one side of the optical element and is angled at a first acute or parallel dihedral angle y > 0 relative to the planar surface, the first optical portion comprising a plurality of reflective unit cells which are each configured to, in use, reflect light from the image source in the opposite direction to the propagation vector of the light projected onto the planar surface; anda second optical portion providing a faceted surface opposite to the planar surface, wherein the faceted surface comprises a plurality of tilted facets, wherein at least some of the tilted facets are angled at a second acute dihedral anglea 0 relative to the planar surface such that, in use, light from the image source is transmitted through the optical element to form a projected floating image on the other side of the optical element which is angled at a floating image dihedral angle ft relative to the planar surface which is greater than the first dihedral angle 0 > y.

2. The optical element of claim 1 , wherein the first optical portion comprises a plurality of prism elements, each prism element providing a respective one of the reflective unit cells, wherein each prism element comprises a bottom face, and wherein the plurality of bottom faces provides the planar surface.

3. The optical element of claim 2, wherein each prism element comprises a pair of reflective side faces which are each substantially orthogonal to each other and to the planar surface, and wherein each prism element is configured to reflect light from the image source in the opposite direction to the propagation vector of the light projected onto the planar surface by a first reflection in one of the reflective side faces and a second, consecutive reflection in the other of the reflective side faces.

4. The optical element of claim 3, wherein:(i) the each prism element is configured such that the first and second reflections are total internal reflections; or(ii) each pair of reflective side faces comprise a reflective coating, optionally wherein the reflective coating comprises a metallic or dielectric film.

5. The optical element of any one of claims 2-4, wherein the prism elements are arranged in a triangular, rhombic, or hexagonal grid.

6. The optical element of any one of claims 2-4, wherein the prism elements are arranged in an irregular grid.

7. The optical element of claims 5 or 6, wherein the separation between adjacent prism elements is in the range between 1 pm and 2 cm.

8. The optical element of any one of claims 2-7, wherein the optical element comprises a lightabsorbing material provided in the spacings between the prism elements.

9. The optical element of claim 8, wherein the thickness of the light-absorbing material is no more than 100% of the height of the prism elements.

10. The optical element of claim 1, wherein the first optical portion comprises:(i) a plurality of corner mirror elements arranged in an array, wherein the plurality of corner mirror elements provides the plurality of reflective unit cells; or(ii) a stacked louver mirror array arrangement comprising a pair of louver mirror arrays arranged so as to be stacked one on the other and rotated by 90° relative to each other, wherein each of the louver mirror arrays comprises a plurality of mirror plates arranged substantially parallel to each other, and wherein the plurality of mirror plates of both louver mirror arrays together provide the plurality of reflective unit cells.

11. The optical element of any one of claims 2-10, wherein:(i) the second optical portion comprises an array of triangular prism-elements each having a top face which is angled relative to the planar surface and a side face angled perpendicular to the planar surface such that the plurality of top faces provides the plurality of tilted facets; or(ii) the second optical portion comprises an array of triangular prism-elements each having a top face which is angled relative to the planar surface and a side face which is angled relative to the planar surface such that only the plurality of top faces provide the plurality of tilted facets; or(iii) the second optical portion comprises an array of triangular prism-elements each having a top face which is angled relative to the planar surface and a side face which is angledrelative to the planar surface such that the plurality of top faces and side faces together provide the plurality of tilted facets.

12. The optical element of claim 11, wherein the side faces do not contribute to the plurality of tilted facets, and wherein said side faces comprise a coating of light-absorbing material.

13. The optical element of claims 11 or 12, wherein a lateral size of the second optical portion, measured in a first direction in the plane of the planar surface, is configured to be at least as large as a lateral size of the first optical portion measured in the first direction.

14. The optical element of any one of claims 2-9, wherein each prism element comprises a top face which is angled relative to the planar surface such that the plurality of top faces provides the plurality of tilted facets.

15. The optical element of any preceding claim, wherein at least some of the tilted facets are tilted at different second acute dihedral angles as others of the tilted facets.

16. The optical element of any preceding claim, wherein the optical element comprises a first end and a second end which are both in the same plane as the planar surface, wherein, in use, the first end is closer to the projected floating image than the second end and the second end is further from the projected floating image than the first end, and wherein the second acute dihedral angles of the plurality of tilted facets are varied from the first end to the second end so as to reduce focal plane bending and image distortion of the projected floating image.

17. The optical element of any preceding claim, wherein the optical element comprises a central region between the first end and the second end, and wherein the plurality of tilted facets are configured to have a varying second acute dihedral angle from: (i) a > 0 for tilted facets at the first end, to (ii) a < 0 for at least some tilted facets in the central region, to (iii) a = 0 for tilted facets at the second end.

18. The optical element of any of claims 1-14, wherein all of the tilted facets are angled at substantially the same second acute dihedral angle a0 relative to the bottom surface.

19. A floating image display device comprising:the retro-transmissive optical element of any preceding claim; andthe image source which is positioned facing the optical element on one side of the optical element and is angled at the first dihedral angle y relative to the planar surface, such that light from the image source is transmitted through the optical element to form the projected floating image.

20. The floating image display device of claim 19, wherein the floating image display device is a mid-air or augmented reality display device.

21. The display device of claims 19 or 20, wherein the lateral size of the optical element is configured to be larger than the lateral size of the projected floating image.

22. The display device of any one of claims 19-21, wherein the image source is positioned facing the planar surface such that the planar surface is closer to the image source than the faceted surface is from the image source and that the faceted surface is closer to the projected floating image than the planar surface is from the projected floating image.

23. The display device of any one of claims 19-22, comprising a lenticular lens array positioned in between the image source and the optical element, wherein the lenticular lens array is configured to, together with the image source and the optical element, create a 3D illusion effect with the projected floating image.

24. The display device of any one of claims 19-23, wherein the display device is an interactive display device further comprising:a touchless sensor; anda processor coupled to the touchless sensor, the processor being configured to detect, with the touchless sensor, if a user interacts with the projected floating image.

25. The interactive display device of claim 24, wherein the interactive display device is comprised by one of the following systems so as to provide an interactive display thereto: an airport check-in terminal; a hotel check-in terminal; a medical point-of-care terminal; a food ordering terminal; a medical device; a manufacturing equipment; a retail equipment; a display equipment of for trade or fashion shows.

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