Patent Publication Number: US-2022236575-A1

Title: Highly efficient compact head-mounted display system

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of U.S. application Ser. No. 16/753,170, filed Apr. 2, 2020 for “HIGHLY EFFICIENT COMPACT HEAD-MOUNT DISPLAY SYSTEM”, which is hereby incorporated by reference herein. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to substrate-based light waves guided optical devices, and particularly to devices which include a reflecting surface carried by a light-transmissive substrate and a dynamic partially reflecting surface which is attached the substrate. 
     The invention can be implemented to advantage in a large number of imaging applications, such as, head-mounted and head-up displays, cellular phones, compact displays, 3-D displays, compact beam expanders, as well as non-imaging applications such as flat-panel indicators, compact illuminators and scanners. 
     BACKGROUND OF THE INVENTION 
     One of the important applications for compact optical elements is in head-mounted displays (HMDs), wherein an optical module serves both as an imaging lens and a combiner, in which a two-dimensional display is imaged to infinity and reflected into the eye of an observer. The display can be obtained directly from either a spatial light modulator (SLM), such as a cathode ray tube (CRT), a liquid crystal display (LCD), an organic light emitting diode array (OLED), or a scanning source and similar devices, or indirectly, by means of a relay lens, or an optical fiber bundle. The display comprises an array of elements (pixels) imaged to infinity by a collimating lens and transmitted into the eye of the viewer by means of a reflecting or partially reflecting surface acting as a combiner for non-see-through and see-through applications, respectively. Typically, a conventional, free-space optical module is used for these purposes. As the desired field-of-view (FOV) of the system increases, such a conventional optical module becomes larger, heavier and bulkier, and therefore, even for a moderate performance device, is impractical. This is a major drawback for all kinds of displays but especially in HMDs, wherein the system should be as light and compact as possible. 
     The need for compactness has led to several different complex optical solutions, all of which, on the one hand, are still not sufficiently compact for most practical applications, and on the other hand, suffer major drawbacks in terms of manufacturability. Furthermore, the eye-motion-box (EMB) of the optical viewing angles resulting from these designs is usually very small, typically less than 8 mm. Hence, the performance of the optical system is very sensitive, even for small movements of the optical system relative to the eye of the viewer, and do not allow sufficient pupil motion for conveniently reading text from such displays. 
     The teachings included in Publication Nos. WO2017/141239, WO2017/141240, and WO2017/141242, are herein incorporated by reference. 
     SUMMARY OF THE INVENTION 
     The present invention facilitates the provision of compact substrates for, amongst other applications, HMDs. The invention allows relatively wide FOVs together with relatively large EMB values. The resulting optical system offers a large, high-quality image, which also accommodates large movements of the eye. The optical system according to the present invention is particularly advantageous because it is substantially more compact than state-of-the-art implementations, and yet it can be readily incorporated, even into optical systems having specialized configurations. 
     A further application of the present invention is to provide a compact display with a wide FOV for mobile, hand-held applications such as cellular phones. In today&#39;s wireless internet-access market, sufficient bandwidth is available for full video transmission. The limiting factor remains the quality of the display within the device of the end-user. The mobility requirement restricts the physical size of the displays, and the result is a direct-display with poor image viewing quality. The present invention enables a physically compact display with a large virtual image. This is a key feature in mobile communications, and especially for mobile internet access, solving one of the main limitations for its practical implementation, thereby enabling the viewing of digital content of a full format internet page within a small, hand-held device, such as a cellular phone. 
     A broad object of the present invention is, therefore, to alleviate the drawbacks of state-of-the-art compact optical display devices and to provide other optical components and systems having improved performance, according to specific requirements. 
     In accordance with the present invention there is therefore provided an optical device comprising an input aperture, an output aperture, a light-transmitting substrate having at least two major surfaces and edges, composed of a first optical material, a coupling-in element positioned outside of the substrate and composed of a second optical material, for coupling light waves having a field-of view into the substrate, a first flat reflecting surface located between the two major surfaces of the light-transmitting substrate for reflecting the coupled-in light waves to effect total internal reflection from the major surfaces of the substrate, a second flat reflecting surface having at least one active side located between the two major surfaces of the light-transmitting substrate for coupling light waves out of the substrate, and a redirecting optical element positioned outside of the substrate for redirecting light waves coupled-out from the substrate into a viewer&#39;s eye, wherein the refractive indices of the first and the second optical materials are substantially different and the ratio between the field of view of the light waves coupled-out from the substrate into the viewers&#39; eye and the field of view of the light waves coupled inside the substrate, is substantially bigger than the refractive index of the first optical material. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention is described in connection with certain preferred embodiments, with reference to the following illustrative figures so that it may be more fully understood. 
       With specific reference to the figures in detail, it is stressed that the particulars shown are by way of example and for the purpose of illustrative discussion of the preferred embodiments of the present invention only, and are presented to provide what is believed to be the most useful and readily understood description of the principles and conceptual aspects of the invention. In this regard, no attempt is made to show structural details of the invention in more detail than is necessary for a fundamental understanding of the invention. The description taken with the drawings are to serve as direction to those skilled in the art as to how the several forms of the invention may be embodied in practice. 
       In the drawings: 
         FIGS. 1A and 1B  are a side view of a prior art exemplary light-transmitting substrate; 
         FIGS. 2A and 2B  illustrate desired reflectance and transmittance characteristics of selectively reflecting surfaces, used in a prior art exemplary light-transmitting substrate, for two ranges of incident angles; 
         FIG. 3  illustrates a reflectance curve as a function of the incident angle for an exemplary dielectric coating; 
         FIG. 4  is a schematic sectional view of a light-transmitting substrate, wherein the coupling-in, as well as the coupling-out elements, are diffractive optical elements; 
         FIGS. 5A and 5B  illustrate sectional views of a transparent substrate having coupling-in and coupling-out surfaces, and a partially reflecting combining element; 
         FIGS. 6A and 6B  are schematic sectional views of an active folding partially reflecting element which dynamically redirects the coupled-out light waves into a viewer&#39;s eye, according to the present invention; 
         FIGS. 7A and 7B  are other embodiments of schematic sectional views of an active folding partially reflecting element which dynamically redirects the coupled-out light waves into a viewer&#39;s eye, according to the present invention; 
         FIGS. 8A, 8B, and 8C  illustrate sectional views of a dynamic partially reflecting element comprising two identical transferrable arrays of parallel mirrors, according to the present invention; 
         FIGS. 9A, 9B, and 9C  illustrate sectional views of another dynamic partially reflecting element comprising three transferrable arrays of parallel mirror, according to the present invention; 
         FIGS. 10A and 10B  illustrate some optical characteristic of a prior art optical system during a period of one frame-time; 
         FIGS. 11A and 11B  illustrate some optical characteristic of an optical system during a period of one frame-time, according to the present invention; 
         FIGS. 12A and 12B  illustrate some optical characteristic of an optical system during a period of one frame-time, wherein the display source of the system is based on a time sequential color imaging, according to the present invention; 
         FIGS. 13A, 13B, and 13C  illustrate sectional views of a transparent substrate comprising a coupling-in surface, two coupling-out surfaces, a dynamic partially reflecting element and dynamic re-coupling surfaces, according to the present invention; 
         FIGS. 14A, 14B, 14C, and 14D  illustrate sectional views of a transparent substrate comprising a coupling-in surface, three coupling-out surfaces, a dynamic partially reflecting clement, dynamic re-coupling surfaces, an eyeball tracking unit, and a dynamic control unit, according to the present invention; 
         FIGS. 15A and 15B  illustrate a dynamic partially reflecting element, comprising an electrically switchable transreflective mirror, pixelized into a two-dimensional array of pixels, according to the present invention; 
         FIGS. 16A and 16B  illustrate a dynamic partially reflecting element, comprising two identical, two-dimensional arrays of transferrable mirrors, according to the present invention; 
         FIGS. 17A, 17B, and 17C  illustrate sectional views of a transparent substrate comprising a coupling-in surface, two coupling-out surfaces, a pair of angular sensitive reflecting elements and an array of redirecting surfaces, according to the present invention; 
         FIG. 18  schematically illustrates active parts of a coupling-out surface according to the viewing angle and the eye-motion-box (EMB) of the system; 
         FIGS. 19A and 19B  are graphs illustrating the reflection of incident light waves on two different angular sensitive coupling-out surfaces as a function of the incident angle, according to the present invention; 
         FIG. 20  schematically illustrates active parts of redirecting elements according to the viewing angle and the eye-motion-box of the system, wherein at least part of the coupling-out elements are angular sensitive reflecting surfaces; 
         FIG. 21  illustrates sectional views of a transparent substrate comprising a coupling-in surface, two coupling-out surfaces, an array of angular sensitive reflecting elements and an array of redirecting surfaces, according to the present invention; 
         FIG. 22  illustrates sectional views of a transparent substrate comprising a coupling-in surface, three coupling-out surfaces, an array of angular sensitive reflecting elements and an array of redirecting surfaces, according to the present invention; 
         FIG. 23  illustrates sectional views of a transparent substrate comprising an angular sensitive coupling-in surface, two coupling-out surfaces, a pair of partially reflecting elements for coupling the light waves out of the substrate and an array of redirecting surfaces, according to the present invention; 
         FIG. 24A  illustrates a sectional view of a transparent substrate comprising an angular sensitive coupling-in surface, two coupling-out surfaces, a pair of angular sensitive reflecting elements for coupling the light waves out of the substrate and an array of redirecting surfaces, according to the present invention; 
         FIG. 24B  illustrates a sectional view of a transparent substrate comprising an angular sensitive coupling-in surface, two coupling-out surfaces, a pair of angular sensitive reflecting elements for coupling the light waves out of the substrate and an array of redirecting surfaces, wherein different parts of the substrate arc composed of different optical materials; 
         FIGS. 25A, 25B and 25C  are graphs illustrating the reflection of incident light waves on three different angular sensitive surfaces as a function of the incident angle, according to the present invention; 
         FIG. 26  is a graph illustrating the brightness efficiency of the light waves as a function of the FOV of the system; 
         FIGS. 27A and 27B  illustrate sectional views of a transparent substrate comprising a single coupling-out surface, a redirecting prism and a coupling-in prism, wherein different parts of the substrate are composed of different optical materials; 
         FIG. 28A  is a schematic sectional-view of folding reflecting surfaces which redirect the coupled-out light waves into the viewer&#39;s eye, according to the present invention; 
         FIG. 28B  is a graph illustrating the brightness of the coupled-out light waves as a function of the aperture, according to the present invention; 
         FIGS. 29A, 29B and 29C  are schematic sectional views of a HUD system comprising active folding partially reflecting element which dynamically redirects the coupled-out light waves into both of the viewer&#39;s eyes, according to the present invention; 
         FIGS. 30A and 30B  are schematic sectional top and side views of another HUD system wherein the light waves propagate inside the substrate along the vertical axis, according to the present invention; 
         FIGS. 31A, 31B and 31C  are schematic sectional views of yet another HUD system comprising at least one pair of angular sensitive coupling-out surfaces and a single flat partially reflecting element which redirects the coupled-out light waves into both viewer&#39;s eyes, according to the present invention; 
         FIGS. 32A and 32B  are graphs illustrating the reflection of incident light waves on two different angular sensitive coupling-out surfaces as a function of the incident angle, according to the present invention, and 
         FIG. 33  schematically illustrates active pails of the single flat redirecting element according to the viewing angle and the head-motion-box of the system, wherein at least part of the coupling-out elements are angular sensitive reflecting surfaces. 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
       FIG. 1A  illustrates a sectional view of a prior art light-transmitting substrate. The first reflecting surface  16  is illuminated by a collimated light wave  12  emanating from a display source  4  and collimated by a lens  6  located between the source  4  and a substrate  20  of the device. The reflecting surface  16  reflects the incident light from the source such that the light wave is trapped inside the planar substrate  20 , by total internal reflection. After several reflections off the major surfaces  26 ,  27  of the substrate  20 , the trapped light waves reach a partially reflective element  22 , which couple the light out of the substrate into the eye  24 , having a pupil  25 , of a viewer. Herein, the input surface of the substrate will be defined as the surface through which the input light waves enter the substrate, and the output surface of the substrate will be defined as the surface through which the trapped light waves exit the substrate. In the case of the substrate illustrated in  FIG. 1 , both the input and the output surfaces coincide with the lower surface  26 . Other configurations are envisioned, however, in which the input and the image light waves from the displace source  4  are located on opposite sides of the substrate, or on one of the edges of the substrate. 
     The element which couples-out the light waves from the substrate can be either a single partially reflective surface  22 , as illustrated in  FIG. 1A , or an array of partially reflecting surfaces  22   a,    22   b  etc. as illustrated in  FIG. 1B . In see-through systems, such as HMDs for augmented reality (AR) applications, wherein the viewer should see the external scene through the substrate, the partially reflecting surfaces  22  should be at least partially transparent to enable the external light rays  33  to pass through the substrate and to reach the viewer&#39;s eye  24 . The optimal value of the transmissivity of the partially reflecting surfaces, however, is not a constant and depends on the lighting conditions of the external scene. For bright scenes, in order to improve the contrast of the projected image, it is required that the reflectivity of the partially reflecting surfaces will be high to maximize the brightness of the image, while the transmissivity of the surfaces should be relatively low to prevent the external scene from dazzling the viewer. On the other hand, for dark external scenes, it is required that the transmissivity of the surfaces should be relatively high in order not to block the external view. As a result, it would be advantageous to have an optical system wherein the transmissivity (and consequently the reflectance) of the partially reflecting surfaces  22  can be dynamically controlled, either manually by the viewer, or automatically by a pre-set mechanism which measures the brightness of the external view. Unfortunately, for most of the present technologies which are used to materialize see-through augmented reality systems, the possibility to utilize active partially reflecting surfaces is impractical. 
     Referring to the optical embodiment illustrated in  FIG. 1B  and assuming that the central light wave of the source is coupled out of the substrate  20  in a direction normal to the substrate surface  26 , the partially reflecting surfaces  22   a ,  22   b  are flat, and the off-axis angle of the coupled light wave inside the substrate  20  is α in , then the angle α sur2  between the reflecting surfaces and the major surfaces of the substrate is: 
     
       
         
           
             
               
                 
                   
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     As can be seen in  FIG. 1B , the trapped rays arrive at the reflecting surfaces from two distinct directions  28 ,  30 . In this particular embodiment, the trapped rays arrive at the partially reflecting surface  22  from one of these directions  28  after an even number of reflections from the substrate major surfaces  26  and  27 , wherein the incident angle β ref  between the trapped ray and the normal to the reflecting surface is: 
     
       
         
           
             
               
                 
                   
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     The trapped rays arrive at the partially reflecting surface  22  from the second direction  30  after an odd number of reflections from the substrate surfaces  26  and  27 , where the off-axis angle is a α′ in =−α in  and the incident angle between the trapped ray and the normal to the reflecting surface is: 
     
       
         
           
             
               
                 
                   
                     
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     where, the minus sign denotes that the trapped ray impinges on the other side of the partially reflecting surface  22 . As further illustrated in  FIG. 1B , for each reflecting surface, each ray first arrives at the surface from the direction  30 , wherein some of the rays again impinge on the surface from direction  28 . In order to prevent undesired reflections and ghost images, it is important that the reflectance he negligible for the rays that impinge on the surface having the second direction  28 . 
     A solution for this requirement that exploits the angular sensitivity of thin film coatings was previously proposed in the Publications referred to above. The desired discrimination between the two incident directions can be achieved if one angle is significantly smaller than the other one. It is possible to provide a coating with very low reflectance at high incident angles, and a high reflectance for low incident angles. This property can be exploited to prevent undesired reflections and ghost images by eliminating the reflectance in one of the two directions. For example, choosing β ref ˜25°, it can be calculated that: 
     
       
         
           
             
               
                 
                   
                     
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     If a reflecting surface is determined for which β′ ref  is not reflected but β ref  is, then the desired condition is achieved. 
     Referring now specifically to  FIGS. 2A and 2B , these figures illustrate desired reflectance behavior of partially reflecting surfaces. While the ray  32  ( FIG. 2A ), having an off-axis angle of β ref ˜25°, is partially reflected and coupled out of the substrate  20 , the ray  36  ( FIG. 2B ), which arrives at an off-axis angle of β′ ref ˜75° to the reflecting surface (which is equivalent to β′ ref ˜105°), is transmitted through the reflecting surface  34 , without any notable reflection. 
       FIG. 3  illustrates the reflectance curve of a typical partially reflecting surface of this specific system, as a function of the incident angle for S-polarized light with the wavelength λ=550 nm. For a full-color display, similar reflectance curves should be achieved for all the other wavelengths in the photopic region. There are two significant regions in this graph: between 65° and 85°, where the reflectance is very low, and between 10° and 40°, where the reflectance increases monotonically with increasing incident angles. As can be seen in  FIGS. 2 and 3 , the requested reflectance behavior of the partially reflective surfaces  22  of the embodiment illustrated in  FIGS. 1A and 1B  is not conventional, and indeed, cannot be materialized as an active partially reflective surface using present technologies. Furthermore, even if such a requested active technology were to be found in the future, to keep the low reflectance at the higher angular region, the reflectance at the lower angular region cannot be higher than 20%-30% and hence, the maximum achievable efficiency is comparatively low. As a result, the idea of utilizing an active partially reflecting surface for the embodiment illustrated in  FIGS. 1A and 1B  is impractical. 
     Another approach to couple light waves into and out from a light-guided optical clement is by using diffractive elements. As illustrated in  FIG. 4 , the light rays  38  and  40  are coupled into the transparent substrate  20  by a diffractive element  48 , and after some total internal reflection from the external surfaces of the substrate, the light rays are coupled-out from the substrate by a second diffractive clement  50 . As illustrated, ray  38  is coupled-out at least twice at two different points  52  and  54  on element  54 . Consequently, to achieve uniform output light waves, the diffraction efficiency of element  50  should be increased gradually along the ξ axis. It is, however, complicated to materialize dynamic gratings using the present techniques, and it is practically impossible to achieve same for the particularly requested grating function of element  50 . As a result, it is not possible to apply the idea of utilizing a dynamic element for the diffractive embodiment illustrated in  FIG. 4 . 
       FIGS. 5A and 5B  illustrate embodiments for overcoming the above-described problem, according to the present invention. Instead of using a single element ( 22  in  FIG. 1A or 50  in  FIG. 4 ), which performs the dual function of coupling the light waves out of the substrate  20 , as well as directing the light waves into the user&#39;s eye  24 , the requested function is divided into two different elements; namely, one element which is embedded inside the substrate couples the light waves out of the substrate, while a second conventional partially reflecting element which is located out of the substrate, redirects the light waves into the viewer&#39;s eye. As illustrated in  FIG. 5A , two rays  63  (dashed lines) from a plane light wave emanating from a display source and collimated by a lens (not shown) enter a light transparent substrate  64 , having two parallel major surfaces  70  and  72 , through the input aperture  86  of the coupling-in prism  55 , at an incident angle of α in   (0)  with respect to the major surfaces  70 ,  72  of the substrate. The rays impinge on the reflecting surface  65 , which is inclined at an angle α sur1  to the major surfaces of the substrate. The reflecting surface  65  reflects the incident light rays such that the light rays are trapped inside a planar substrate  64  by total internal reflection from the major surfaces. In order to differentiate between the various “propagation orders” of the trapped light waves, a superscript (i) will denote the order i. The input light waves which impinge on the substrate in the zero order are denoted by the superscript (0). After each reflection from the coupling-in reflecting surface the order of the trapped ray is increased by one from (i) to (i+1). The off-axis angle α in   (1)  between the trapped ray and the normal to the major surfaces  70 ,  72  is 
     
       
         
           
             
               
                 
                   
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     After several reflections off the surfaces of the substrate, the trapped light rays reach a second flat reflecting surface  67 , which couples the light rays out of the substrate. Assuming that surface  67  is inclined at the same angle to the major surfaces as the first surface  65 , that is to say, surfaces  65  and  67  are parallel and α sur2 =α sur1 , then the angle α out  between the coupled-out rays and the normal to the substrate plane is 
     
       
         
           
             
               
                 
                   
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     That is to say, the coupled-out light rays are inclined to the substrate at the same angle as the incident light rays. So far, the coupled-in light waves behave similarly to the light waves illustrated in  FIG. 1A .  FIG. 5A , however, illustrates, a different behavior wherein two light rays  68  (dashed-dotted lines), having the same incident angle of α in   (0)  as rays  63 , impinge on the tight side of the reflecting surface  65 . After two reflections from surface  65 , the light waves are coupled inside the substrate  64  by a total internal reflection, and the off-axis angle of the trapped rays inside the substrate is now 
     
       
         
           
             
               
                 
                   
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     After several reflections off the major surfaces of the substrate, the trapped light rays reach the second reflecting surface  67 . The light rays  68  are reflected twice from the coupling-out surface  67  and are coupled out from the substrate at the same off-axis angle α out  as the other two rays  63  which are reflected only once from surfaces  65  and  67 , which is also the same incident input angle of these four rays on the substrate major planes. 
     As illustrated in  FIG. 5A , the inclination angle α out  of the image can be adjusted by adding a partially reflecting surface  79  which is inclined at an angle of 
     
       
         
           
             
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             2 
           
         
       
     
     to the surface  72  of the substrate. As shown, the image is reflected and rotated such that it passes again through the substrate substantially normal to the substrate major surfaces and reaches the viewer&#39;s eye  24  through the output aperture  89 . To minimize distortion and chromatic aberrations, it is preferred to embed surface  79  in a redirecting prism  80 , and to complete the shape of the substrate  64  with a second prism  82 , both of them fabricated of a material similar to that of the substrate. In order to minimize the thickness of the system, it is possible, as illustrated in  FIG. 5B , to replace the single reflecting surface  80  with an array of parallel partially reflecting surfaces  79   a ,  79   b , etc., where the number of the partially reflecting surfaces can be determined according to the requirements of the system. 
     There are two contradicting requirements from the coupling-out surface  67 . On the one hand, the first two order images F (1)  and F (2)  should be reflected from that plane, while on the second hand, the zero order image F (0)  from the substrate  64  should substantially pass through it, after being reflected from surface  79 , with no significant reflections. In addition, for see-through systems, the transparency of the optical system for substantially normal incident light ray  83  from the external scene should be as high as possible. A possible way to achieve this is to use an air gap in surface  67 . For achieving a rigid system, it is preferred, however, to apply an optical adhesive in surface  67 , in order to cement the substrate  64  with prism  82  using an optical adhesive having a refractive index, which is substantially smaller than that of the substrate. 
     An alternative approach is to exploit a moth-eye film, or any similar hyperfine structure, as the required angular sensitive reflective mechanism. That is to say, when prism  82  is attached to the external surface  67  of the substrate  64 , an air gap film is cemented to prism  82  such that the hyperfine structure faces surface  67  after the attachment. Therefore, when the coupled-in light waves inside the substrates  64  impinge on the hyperfine structure at different oblique angles, they “see” only the external part of the periodic structure. The actual refractive index, which is “seen” by the incoming optical light waves, is therefore close to the refractive index of the air, and the total internal reflection mechanism is preserved. On the other hand, the air gap film is substantially transparent to the incoming light waves from the external scene  83  or to the light waves which are coupled out from the substrate  64  and reflected back by surface  79 . In any of the proposed approaches, to minimize the Fresnel reflections of the transmitted light waves from the coupling-out surface  67 , it is preferred to apply a suitable anti-reflective (AR) coating to this surface. 
     As explained above with regard to  FIG. 1A , in see-through systems such as HMDs for augmented reality (AR) applications, wherein the viewer should see the external scene through the substrate, the partially reflecting surfaces  79  should be at least partially transparent to enable the external light rays  63  and  68  passing through the substrate and reaching the viewers eye  24 . Since surfaces  79  are only partially reflective, only part of the coupled light waves  63  and  68  is reflected by surfaces  79  and reaches the viewer&#39;s eye, while another part of the light waves  84  passes through surfaces  79 , coupled out from the prism  80  and do not reach the viewer&#39;s eye. Similarly, since surfaces  79  are only partially transmissive, only part of the external light rays  83  passes through surfaces  79  and reaches the viewer&#39;s eye, while another part of the light rays  85  is reflected from surfaces  79 , coupled out from the prism  80  and does not reach the viewer&#39;s eye, as well. Naturally, the efficiency of the projected image can be increased on account of the external scene, and vice-versa, namely, by increasing the reflectivity of the partially surfaces  79  the brightness of the coupled rays  63  and  68  is increased. Consequently, however, the transmissivity of surfaces  79  is decreased, and hence, the brightness of the external image  83  is reduced accordingly. 
     In contradiction to the embodiments illustrated in  FIGS. 1-4 , the combiner  79  that reflect the coupled-out light from the substrate to the viewer&#39;s eye and at the same time transmits the external rays, is a conventional partially reflecting mirror without any special or complicated characteristics as surfaces  22  and  50  of the embodiments illustrated in  FIGS. 1 and 4  respectively. As a result, it is possible to dynamically control the reflectivity (and consequently, the transmissivity) of the partially reflective surfaces  79  according to the external lighting conditions and the specific image which is projected to the viewer&#39;s eye. One method to control the reflectivity of surfaces  79  is by using an electrically switchable transreflective mirror, which is a solid-state thin film device made from a special liquid crystal material, and which can be rapidly switched between pure reflection, partial-reflection, and total transparent states. The required state of the switchable mirror can be set either manually by the user or automatically by using a photometer which controls the reflectivity of the mirror according to the external brightness. For the sake of simplicity, it will he assumed henceforth that the absorption of the dynamic partially reflecting device is negligible, and that the sum of the reflectivity and the transmissivity of the device is summed up to a value of approximately one. 
       FIGS. 6A and 6B  illustrate use of the switchable mirror in two extreme situations.  FIG. 6A  illustrates a condition in which the external scene should be blocked from interfering with the projected image, for example, wherein a video movie is projected, and the brightness of the external scene is relatively high. As shown, the dynamic surface  79  is switched into a total-reflection state and, as a result, the coupled out light rays  63  and  68  from the substrate are totally reflected from surface  79  to the viewer&#39;s eye, while the external rays  83  are totally reflected, as well, and hence, are prevented from reaching the viewer&#39;s eye.  FIG. 6B  illustrates a different condition wherein it is essential not to block the image from the external scene at all, and it is not necessary at that moment to project information from the coupled image into the viewer&#39;s eye. As shown, the dynamic surface  79  is switched into a total-transparent state and, as a result, the coupled out light rays  63  and  68  from the substrate pass substantially through surfaces  79   a  and  79   b , and hence, are prevented from reaching the viewer&#39;s eye, while the external rays  83  pass substantially through surfaces  79   a  and  79   b , as well, and hence, reach the viewer&#39;s eye undisturbed. 
       FIGS. 7A and 7B  illustrate use of the switchable mirror in two different intermediate situations.  FIG. 7A  illustrates a condition in which the projected image should be properly combined with the external image, but the brightness of the external scene is comparatively high, and hence, it should be mostly blocked from interfering with the projected image. On the other hand, the efficiency of the projected image should be high enough to achieve a reasonable contrast. As shown, the dynamic surface  79  is switched into a primary reflection state, namely, the reflection of the switchable mirror is much higher than its transmission. As a result, the coupled out light rays  63  and  68  from the substrate are mainly reflected from surface  79  to the viewer&#39;s eye, while only small part of the light waves passes through surface  79 . On the other hand, the external rays  83  are mostly reflected from surface  79  and only small part reaches the viewer&#39;s eye.  FIG. 7B  illustrates a different condition wherein the external scene is comparatively dark, and it is necessary to prevent the projected image from dazzling the viewer. As shown, the dynamic surface  79  is switched primarily into a transmission state, and thus, the reflection of the switchable mirror is much lower than its transmission. As a result, the coupled out light rays  63  and  68  from the substrate mainly pass through surfaces  79   a  and  79   b , and hence, only a small portion of the light rays reaches the viewer&#39;s eye, while the external rays  83  mostly pass through surfaces  79   a  and  79   b , as well, and hence reach the viewer&#39;s eye substantially undisturbed. 
     Another approach for achieving the required dynamic partially reflecting clement is illustrated in  FIGS. 8A-8C . As shown in  FIG. 8A , an array of parallel minors  791   a ,  791   b , etc. is embedded inside the transparent plate  80   a . The mirrors are inclined at an angle of 
     
       
         
           
             
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     to the major surface  72  of the substrate. The fill-factor of the mirrors inside the plate is substantially a half. Assuming that the projection of a mirror on the major surface  72  is d, then the lateral distance between two adjacent mirrors is d. Another identical plate  80   b  is located adjacent to plate  80   a . As illustrated in  FIG. 8A , the edges of the plates are located adjacent to each other, and each mirror  792   i  (i=a, b, c . . . ) in plate  80   b  is positioned exactly below the mirror  791   i  in plate  80   a . As a result, the reflectivity, and consequently, the transmissivity of the embodiment of  FIG. 8A , is substantially 50% for the coupled-out image waves, as well as for the light waves from the external scene. As illustrated in  FIG. 8B , plate  80   b  is translated by a distance of d/2 in relation to plate  80   a , resulting in the reflection-transmission ratio of the embodiment being modified to approximately the ratio of 75%/25%. In the embodiment of  FIG. 8C , plate  80   b  is translated by a distance d in relation to plate  80   a , and the embodiment is substantially reflective. Eventually, plate  80   b  can be translated by any other intermediate distance, and hence, the reflection-transmission ratio of the embodiment can be any value between 50%:50% and 100%:0%. 
     The main drawback of the embodiment illustrated in  FIGS. 8A-8C  is that the maximum achievable transmissivity is limited by the value of 50%. This fault is severe for optical systems wherein the transmissivity should be comparatively high to let the external scene reach the viewer&#39;s eye with minimal interference.  FIGS. 9A-9C  illustrate an embodiment composed of three identical transparent plates, wherein the fill-factor of the embedded mirrors is ⅓, namely, assuming that the projection of a mirror on the major surface  72  is d, then the lateral distance between two adjacent mirrors is 2d. As illustrated, the distances between the edges of two adjacent plates are 0, d, and 2d, and consequently, the reflection-transmission ratios are substantially 33%:67%, 67%:33% and 100%:0% for the embodiments of  FIGS. 9A, 9B, and 9C , respectively. Eventually, plates  80   b  and  80   c  can be translated by any other intermediate distances, and hence, the reflection-transmission ratio of the embodiment can be any value between 33%:67% and 100%:0%. As a result, the systems illustrated in  FIGS. 9A-9C  have a higher dynamic range as compared to that of  FIGS. 8A-8B  and the maximal achievable transmissivity is 67% instead of 50%. The dynamic range can be even further increased by using embodiments having larger numbers of identical plates. For example, for an embodiment having n plates wherein in each plate the fill-factor of the mirrors is 1/n, the reflection-transmission ratio of the embodiment can be any value between 
     
       
         
           
             
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     and 100%:0%. 
     Hitherto, it has been assumed that the reflectivity of the partially reflecting surface  79  can be modified, and hence, the ratio between the efficiencies of the virtual image coupled out from the substrate and the external scene can be dynamically modified to achieve optimal performance in a given scenario. In all the embodiments illustrated thus far, however, improving the efficiency of one of the two images is to the detriment of the other image, that is to say, it is not possible to achieve a system wherein the efficiencies of the projected and the external images are very high simultaneously, using the above-illustrated embodiments. For a dynamic partially reflecting element, however, having a switching time which is smaller than the frame-time of the image which is projected into the substrate, it is possible to improve the total efficiency of the system, namely it is possible to increase the brightness of the projected image as well as that of the external image, which reaches the viewer&#39;s eye without increasing the power consumption of the optical system. 
       FIGS. 10A-10B  illustrate optical characteristics of a conventional system during a period of one frame-time τ f . It is assumed that the average brightness of the coupled-in image B 0  and the external scene B s , are constants and that the reflection of the partially reflective element is substantially 50%, i.e., the potential efficiency is equally divided between the projected and the external images and particularly the brightness of the virtual image and that of the external scene which are projected into the viewer&#39;s eye (neglecting residual losses inside the substrate and Fresnel reflections from the external surfaces), are B 0 /2 and B S /2, respectively. 
       FIG. 11A  illustrates a modified system wherein during each frame-time the image is projected from the display source and coupled into the substrate only during a limited time slot having a period of τ f /n. The average brightness of the coupled-in image during that time slot is increased by a factor of n to n·B 0 . It is assumed that the brightness of the projected image depends linearly on the power consumption of the display source. Since the product of the operation period with the average brightness is identical for the two systems of  FIGS. 10A and 11A , they will have substantially the same power consumption.  FIG. 11B  illustrates the reflection curve of the partially reflecting element wherein this element is substantially reflective only during a limited time slot having a period of τ f /n, wherein this time slot is synchronized with that of the projected brightness illustrated in  FIG. 11A . During the rest of the frame-time, the partially reflective element is substantially transmissive. As a result, the average brightness of the projected image is increased by a factor of two from B 0 /2 to B 0 , while the brightness of the external scene is increased to 
     
       
         
           
             
               
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     Naturally, by reducing the actual switching time, namely, by increasing the factor n, it is possible to improve the efficiency of the external scene. 
       FIGS. 12A and 12B  illustrate a modified version of the system shown in  FIGS. 11A and 11B . The display source here is based on a time sequential color imaging, in which the color images are generated by sequentially laying down three basic colors of red, green, and blue (RGB) light in a single image frame, which typically lasts 1/f of a second, where f is the frequency of the system, usually 50 or 60 hertz. The frame-time τ f  is divided into three equal sub-periods τ f /3, wherein in each one, only one color is illuminating the display. It is also assumed that the dynamic partially reflecting element can be controlled to yield a high reflection in each one of the primary three colors while having at the same time high transmittance for the other two colors. As illustrated in  FIG. 12A , during each frame-time for each of the three primary colors, the image is projected from the display source and coupled into the substrate only during a limited time slot having a period of τ f /n. The average brightness of the coupled-in image during that time slot is 
     
       
         
           
             
               
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       FIG. 12B  illustrates the reflection curve of the partially reflecting element wherein this element is substantially reflective for each of the three primary colors only during a limited time slot having a period of τ f /n, wherein each of these three slots is synchronized with the respective slot of the projected brightness as illustrated in  FIG. 12A . The average brightness of the projected image is B 0 , while the brightness of the external scene is 
     
       
         
           
             
               
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     The exploitation of a dynamic partially reflecting element can be particularly advantageous for the multi-facet element  255  illustrated in  FIG. 13A . As shown, a reflecting surface  256  is embedded inside the substrate  258 . Surface  256  has the same reflecting characteristics as surface  67  and is parallel to the coupling-in and the coupling-out surfaces  65  and  67 . A ray  260  having an off-axis angle of α in  is coupled into the substrate  258  after one reflection from surface  65 . and after a few reflections from the major surfaces of the substrate  258  impinges on surface  256 . The ray is coupled out from the substrate  258  and is then partially reflected into the viewer&#39;s eye in a similar manner as to that which is illustrated in  FIGS. 5A-5B . The reflected ray is, however, in this case is not propagated undisturbed into the viewer&#39;s eye, as in the embodiments illustrated in  FIGS. 5A and 5B . Instead, the reflected ray impinges on a partially reflecting surface  264   a , which is parallel to surface  79   a  and coupled inside a flat prism  267 , which is attached to the upper surface  70  of the substrate  268 . Part of the intensity of the light ray  260  which impinges on surface  264   a , passes through the surface as ray  260   a  and continues to propagate toward the viewer&#39;s eye. Since surfaces  79   a  and  264   a  are parallel, the other part of the intensity of the light ray  260  is reflected from surface  264   a  as ray  260   b  having an off-axis angle of α in  and impinges again on surface  256 . After two reflections from surface  256 , it propagates inside the substrate  258 , and after two more reflections from the coupling-out surface  67 , the ray  260   b  is coupled out from substrate  258  having the same off-axis angle α in . The ray is then reflected from surface  79   d , which is parallel to surface  79   a , into the viewer&#39;s eye having the same direction as ray  260   a.    
     As also illustrated in  FIG. 13A , another ray  262  is coupled into the substrate  258  after two reflections from surface  65 , and after a few reflections from the major surfaces of the substrate  258 , the ray  262  impinges on surface  256 . The ray is coupled out from the substrate  258  having an off-axis angle α in  and is then partially reflected by surface  79   b , which is parallel to surface  79   a , into the viewer&#39;s eye in a similar manner to ray  260 . The reflected ray impinges on the partially reflecting surface  264   b  which is parallel to surfaces  79   b  and  264   a  and is coupled inside prism  267 . Part of the intensity of the light ray  262 , which impinges on surface  264   b , passes through the surface as ray  262   a  and continues to propagate toward the viewer&#39;s eye. Since surfaces  79   b  and  264   b  are parallel, the other part of the intensity of the light ray  262  is reflected from surface  264   b  as ray  262   b  having an off-axis angle of α in , and impinges again on surface  256 . After one reflection from surface  256  it propagates inside the substrate  258 , and after one reflection from the coupling-out surface  67 , the ray  262   b  is coupled out from substrate  258  having the same off-axis angle α in . The ray is then reflected from surface  79   c , which is parallel to surface  79   b , into the viewer&#39;s eye having the same direction as ray  260   a . Hence, all four of the rays,  260   a ,  260   b ,  262   a , and  262   b , which originated from the same point on the display source, reach the viewer&#39;s eye having the same propagating direction. 
     As a result, the output aperture of substrate  258  is the combination of surfaces  256  and  67 . Consequently, the active area of the output aperture of substrate  258  has been doubled as compared to that of substrate  64 , which is illustrated in  FIG. 5 , while the thickness of the substrate remains the same. On the other hand, the brightness of light waves coupled out from substrate  258  has been reduced by a factor of two as compared to that of substrate  64 . Furthermore, not only the coupled-out light waves  260  and  262  of the virtual image impinge on the partially reflecting surfaces  264 A and  264 B, but also rays  82  from the external scene. As a result, the brightness of these waves is reduced by the same factor accordingly. There are ways, however, to improve the brightness of the coupled-out light waves of both images. For embodiments wherein the light waves coupled inside the substrate are linearly polarized, such as systems where the display source is an LCD or an LCOS display, the partially reflecting surfaces  79   i , as well as  264   i  (i=a, b, . . . ), can be designed to be polarization-sensitive reflecting surfaces. These surfaces are reflective (or partially reflective) for one polarization (preferably for the s-polarization) and substantially transparent to the orthogonal polarization (preferably for the p-polarization). In such a case, the transmittance of the external scene for see-through applications can be improved, since the entire element  255  is now substantially transparent to the polarization (which is orthogonal to that of the light waves coupled inside the substrate). While the reflecting surfaces  79   i  can be totally reflective for the relevant polarization (which is the same as that of the light waves coupled inside the substrate), surfaces  264   i  should be partially reflective for this polarization, wherein the exact reflection coefficient of the surfaces can be determined according to the number of reflecting surfaces  264   i  in the system. For the embodiment illustrated in  FIG. 13A , wherein two reflective surfaces  256  and  67  are embedded inside the substrate  258 , a reflection coefficient of 0.5 can yield a total brightness efficiency of 50% for the light waves coupled inside the substrate and transmittance of 50% for the external scene. 
     An alternative embodiment for improving the efficiencies of both of the images, which can be applied to polarized as well as non-polarized image sources, is illustrated in  FIGS. 13B and 13C . Here, surfaces  79   i , in addition to surfaces  264   i , are dynamic reflecting surfaces. As illustrated in  FIGS. 11A and 11B , during each frame-time the image is projected from the display source and coupled into the substrate only during a limited time slot having a period of τ f /n wherein the average brightness of the coupled-in image is n·B 0 . In addition, as illustrated in  FIG. 13B , the elements  79   i  and  264   i  are reflective only during the same time slot, wherein surfaces  79   i  are substantially reflective and the reflectivity of surfaces  264   i  is around 50%. As illustrated in  FIG. 13C , during the rest of the frame-time, the reflective elements  79   i  and  264   i  are substantially transmissive, and the external light rays reach the viewer&#39;s eye without any interference. As a result, the average brightness of the projected image even for a non-polarized image is increased by a factor of two from B 0 /4 to B 0 /2, while the brightness of the external scene is increased to 
     
       
         
           
             
               
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     The embodiment for expanding the output aperture by embedding a reflecting surface  256  into the substrate  258 , as illustrated in  FIGS. 13A and 13B , is not limited to a single reflecting surface. For optical systems having wide FOVs together with relatively large EMB values, an array of n flat reflecting surfaces  256   i  (i=a, b . . . ), which are parallel to the output reflecting surface  67 , can be embedded internally inside the substrate to increase the output aperture of the substrate by a factor of n+1. Consequently, the number of the reflecting surfaces  264   i  (i=a, b . . . ) should be increased accordingly, to completely cover the output aperture of the embedded surfaces  256   i . The reflectance and lateral extension of each reflecting surface  264   i  should be designed to ensure the uniformity characteristics of the light waves coupled into the viewer&#39;s eye. 
     As illustrated in  FIGS. 14A to 14D , the efficiency of a system having an additional number of coupling-out facets  256   i  can be increased by adding an eyeball tracking unit  272  to the optical system. Eyeball tracking is the process of measuring either the location, the point of gaze, or the motion of an eye relative to the display, namely, an eyeball tracker is a device for measuring eye positions and eye movement. The most popular method for operating this device is by utilizing an optical method for measuring eye motion. Light from an emitter, typically infrared, is reflected from the eye and sensed by a video camera, or some other specially designed optical sensors. The information is then analyzed to extract eye rotation and translation from changes in reflections. Video-based eye trackers typically use corneal reflection and the center of the pupil as features to track over time. 
     In accordance with the present invention, it would be advantageous to physically combine the two optical units, namely, the dynamically controlled stereoscopic display and the eyeball tracking unit. The system should also contain a dynamic control unit  276 , which will be capable of setting, by identifying the position and gazing point of the viewer&#39;s eyes, the operation times and the reflectance for each of the reflecting surfaces  264   i . Seen in  FIG. 14A  is an optical system. wherein three coupling out surfaces,  256   a ,  256   b  and  67  are embedded inside the substrate  258 . To achieve coupled-out light waves having a uniform brightness over the entire output aperture, the reflectance of the partially surfaces  264   i , which are adjacent to the coupling-out surfaces  256   a  and  256   b , should be set to 67% and 50%, respectively. The maximal efficiency of the coupled-out light waves, in that case, is approximately 33%. 
     For optical systems, however, having a large EMB values, not all the light waves which are coupled out from the substrate are exploited simultaneously. As a result, the efficiency of the optical system can be improved by increasing the brightness of the light waves that reach the viewer&#39;s eye on account of the other light waves. As illustrated in  FIG. 14B , the viewer&#39;s eye is located in the right section of the EMB. Consequently, the eye is illuminated mostly by light waves which are coupled out by surface  256   a , and hence, it would be advantageous to increase the brightness of these light waves on account of those which are coupled out by surfaces  256   b  and  67 . This improvement can be achieved by decreasing the reflectance of surfaces  264   a  and  264   b , which are adjacent to surface  256   a . Therefore, most of the light waves will pass through surfaces  264   a  and  264   b  into the viewer&#39;s eye, and only a small part thereof will be reflected and coupled-in again into the substrate. 
     A different situation is illustrated in  FIG. 14C , wherein the viewer&#39;s eye is located in the central section of the EMB. Consequently, the eye is illuminated mostly by light waves which are coupled out by surface  256   b , and hence, it would be advantageous to increase the brightness of these light waves on account of those which are coupled out by surfaces  256   a  and  67 . This improvement can be achieved by increasing the reflectance of surfaces  264   a  and  264   b , which are adjacent to surface  256   a , and reducing the reflectance of surfaces  264   c  and  264   d , which are adjacent to surface  256   b . Therefore, most of the light waves will be reflected from surfaces  264   a  and  264   b , coupled-in again into substrate  258  and coupled out by surface  256   b . Now, most of the remaining light waves will pass through surfaces  264   c  and  264   d  into the viewer&#39;s eye, and only a small part thereof will be reflected and coupled-in again into the substrate. 
     A further different situation is illustrated in  FIG. 14D , wherein the viewer&#39;s eye is located in the left section of the EMB. Consequently, the eye is illuminated mostly by light waves which are coupled out by surface  67 , and hence, it would he advantageous to increase the brightness of these light waves on account of those which arc coupled out by surfaces  256   a  and  256   b . This improvement can be achieved by increasing the reflectance of surfaces  264   a  and  264   b , as well as surfaces  264   c  and  264   d , which are adjacent to surfaces  256   a  and  256   b , respectively. As a result, most of the light waves will be reflected from surfaces  264   a  and  264   b , as well as from surfaces  264   c  and  264   d , will be coupled-in again into substrate  258 , and then coupled out by surface  67  to reach the viewer&#39;s eye undisturbed. Eventually, the exact values of the reflectance of surfaces  264   i  will be set by the control unit according to the position and gazing point of the viewer&#39;s eyes, the EMB and the FOV of the optical system, and other possible relevant parameters. 
     Hereinbefore, it has been assumed that the reflectivity (and therefore the transmissivity) of the dynamic partially reflective element is constant over its entire aperture. There arc situations, however, where it would be beneficial to use a dynamic element wherein its reflectance can be modified locally. That is to say, different parts of the dynamic element will have various degrees of reflectivity. By combining this ability with the eyeball tracking unit  272  and the dynamic control unit  276 , it will be possible to adjust the local reflection of the dynamic element optimally. The exact localized reflectivity can be set according to the type of the information which is projected to the viewer&#39;s eye, the location of the symbols or the video in the FOV of the image, the brightness of the external scene, and the position and the gazing point of the viewer&#39;s eyes. 
       FIGS. 15A and 15B  illustrate possible embodiments for achieving a requested dynamic element. As shown in  FIG. 15A , the active area of reflectivity the electrically switchable transreflective mirror  280  is pixelized into a two-dimensional array of pixels  281 , wherein the reflectivity of each pixel can be separately set by the dynamic control unit  276  (not shown). As demonstrated in  FIG. 15B , a sub-area  282  of element  280  has been set to be substantially reflective; another two sub-areas  283  and  286  are partially reflective while the other active area  289  of element  280  is substantially transmissive. 
     A different approach for achieving the required dynamic partially reflective element is illustrated in  FIGS. 16A and 16B . As shown in  FIG. 16A , the dynamic element is composed of two identical arrays ( 291  and  292 ) of sub-mirrors  295 , wherein each sub-mirror can be separately translated by the dynamic control unit  276  (not shown). Since the sub-mirror can be small and light elements, it is possible to translate them using piezoelectric devices. The fill factor of each array is 50%, and each sub-mirror in array  291  is located substantially adjacent to the relative sub-mirror in array  292 . As a result, the reflectivity and the transmittance of element  290  here are around 50% over the entire area of the dynamic element  290 .  FIG. 16B  illustrates a different situation wherein in two different locations  296  and  297  some sub-mirrors in array  292  have been laterally translated to yield high reflectance in these areas. 
     In the embodiment illustrated in  FIGS. 13A to 13C and 14A to 14D , the output aperture of the optical system has been extended utilizing external partially reflecting surfaces  264 , which were attached to the upper surface  70  of the substrate  258 .  FIGS. 17A to 17C  illustrate an alternative embodiment for expanding the output aperture wherein the coupling-out surface  256  is sensitive to the incident angle of the coupled light waves. As shown in  FIG. 17A , optical rays  320   a  and  320   b  having an input direction of α in   (0)  impinge on an optical element  309 , composed of two substrates  310   a  and  310   b , wherein the lower surface  311   a  of substrate  310   a  is attached to the upper surface  312   b  of substrate  310   b  defining an interface plane  317 . 
     There are two contradicting requirements from the interface plane  317  between the substrates  310   a  and  310   b . On the one hand, the first two orders image F (1)  and F (2)  should be reflected from that plane, while the zero order image F (0)  from the upper substrate  310   a  should substantially pass through it, after being reflected from surfaces  256  and  67 , with no significant reflections. Similarly, surface  317  should be transparent to rays  320   a  and  320   b  entering the substrate through element  318  having the input angle of α in   (3) . In addition, for see-through systems the transparency of the optical system for substantially normal incident light, should be as high as possible. A possible way to achieve this is to use an air gap in the interface plane  317 , however, for achieving a rigid system, it is preferable to apply an optical adhesive in the interface plane  317 , in order to cement the substrates  310   a  and  310   b . This approach is illustrated with an optical system having the following parameters: 
     
       
         
           
             
               
                 
                   
                     
                       
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     The light waves are s-polarized. The optical material of the substrates  310   a  and  310   b  is Schott N-SF57 having a refractive index of v d =1.8467, and the optical adhesive is NOA 1315, having a refractive index of v d =1.315. The critical angle is therefore α cr &gt;45.4°. All the optical rays in the higher orders F (1)  and F (2)  have off-axis angles higher than the critical angle and are therefore totally reflected from the interface plane  317 . All the optical rays in the zero order impinge on the interface plane at an incident angle lower than the critical angle, and hence, they pass through it. To minimize the Fresnel reflections of the coupled-out light waves from the interface plane, however, it is preferred to apply a suitable anti-reflective (AR) coating to this plane. 
     In contradistinction to the substrates illustrated in  FIGS. 13A to 14D , the coupling-out elements  256   a  and  256   b  are not conventional reflecting surfaces as surface  256  in substrate  258 , but angular sensitive reflective surfaces. Each one of the surfaces is substantially total reflective for the part of the angular range of the coupled-in light waves inside the respective substrate, and substantially transparent for the other part of the angular range. Unlike surfaces  256   a  and  256   b , surfaces  67   a  and  67   b  could be conventional reflecting surface, such as surface  67  in the embodiments of  FIGS. 5A and 5B . As a result, the efficiency of the optical system is significantly improved, and the brightness of the coupled-out image is substantially retained, similar to that of the input image. To achieve this improvement, the fact that the light waves coupled out from the substrate are not required to illuminate the entire active area of the coupling-out surface is utilized. 
     As illustrated in  FIG. 18 , showing the rays that should impinge on the partially reflective surface  79  for illuminating the EMB  197 , the two marginal ( 107 R,  107 L) and the central ( 107 M) light waves of the image are coupled out from the substrate and redirected into the viewer&#39;s eye  24 . As shown, the light waves  107 R,  107 M, and  107 L, having the zero order off-axis angles α in   (0) (max), α in   (0) (mid) and α in   (0) (min), illuminate only the parts  79 R,  79 M and  79 L of the partially reflecting surface  79 , respectively, which reflect into to EMB  197 . As a result, a method can be found where the coupled-in light waves are split in such a way that they will illuminate only the required respective part of surface  79 , and the original brightness will be preserved. To achieve this, the angular range of the light waves FL sur1   (1) ≡{α min ,α max }, which impinge on the angular sensitive coupling-out surfaces  256   a  and  256   b  at the incident angles of α sur   (1) =α in   (0) +α sur1 =α in   (1) −α sur1  ( FIG. 17A ), is divided into three substantially equal segments: F low   (1) ≡{α min ,α m1 }, F mid   (1) ≡{α m1 ,α m2 } and F max   (1) ≡{α m2 ,α max }. The aim of the embodiment is that the light waves having the higher incident angles in the FOV of F max   (1) ≡{α m2 ,α max } will be coupled out from the substrates  310   a ,  310   b  by the angular sensitive coupling-out element  256   a  and  256   b ; the light waves having the lower incident angles in the FOV of F min   (1) δ{α min ,═ m1 } will be coupled out from the substrates  310   a ,  310   b  by the coupling-out element  67   a  and  67   b , and the light waves in the FOV of F mid   (1) ≡{α m1 ,α m1 } will be coupled out from the upper substrate  310   a , by the coupling-out element  67   a  and from the lower substrate  310   b , by the angular sensitive coupling-out element  256   b.    
     In order to achieve this, surfaces  256   a  and  256   b  should substantially reflect all the light waves in F max   (1)  such that they will be coupled-out from the substrates  310   a  and  310   b  and substantially transmit all the light waves in F min   (1) , such that they will continue to propagate inside the substrate and be coupled-out by the reflecting surfaces  67   a  and  67   b . In addition, the light waves in F mid   (1)  should pass-through the angular sensitive surface  256   a , continue to propagate inside the substrate  310   a  and be coupled-out by the surface  67   a , but will be coupled-out from substrate  310   b  by the angular sensitive surface  256   b . 
     Consequently, the angular sensitive reflecting surfaces  256   a  and  256   b  should fulfill the following three characteristics for the entire relevant photopic range:
         a. substantially total reflective for the angular range of {α m2 ,α max };   b. substantially transparent for the angular range of {a min ,α m1 }; and   c. while the lower surface  256   b  is substantially total reflective for the angular range of {α m1 ,α m2 } the upper surface  256   a  is substantially transparent for the same angular range of {α a1 ,α m2 }.       

     It is possible to achieve these requirements by applying angular sensitive dielectric coatings on surfaces  256   a  and  256   b , but the process for achieving these coatings can be fairly complicated. A simpler way is to cement the optical part adjacent to surfaces  256   a  and  256   b  using optical adhesives having proper refractive indices that yield critical angles of α m1  and, α m2  at surfaces  256   a  and  256   b , respectively. The high transparency for angles lower than the respective critical angles can be achieved using proper AR coatings. To simplify the fabrication process of the angular sensitive surfaces, it is usually required that the Abbe numbers of the optical adhesive and the optical material of the substrate will be similar to avoid undesired chromatic effects in the image. It is possible, however, to achieve the required reflecting curves utilizing proper thin-film coating design techniques, even for cases where the Abbe numbers of the adhesive and the optical material are substantially different. 
       FIG. 17A  illustrates two rays  320   a  and  320   b  from the same plane input wave having incident angles of α si   (1) &lt;α m1  which impinge on the angular sensitive coupling-out elements  256   a  and  256   b , respectively. As a result of condition (b) stated hereinabove, both rays pass through surfaces  256   a  and  256   b . Ray  320   a  is reflected three times from the coupling-in element  65   a , trapped inside the substrate  310   a  at an off-axis angle of α in   (3) =α in   (0) +6√α sur1 , and is reflected twice from surface  256   a  before being impinged on the left part of surface  256   a  at an incident angle of α si   (1) =α in   (1) −α sur1 . Ray  320   b  is reflected twice from the coupling-in element  65   b , trapped inside the substrate  310   b  at an off-axis angle of α in   (2) =α in   (0) +4·α sur1 , and is reflected once from surface  256   b  before being impinged on the left part of surface  256   b  at an incident angle of α si   (1) =α in   (1) −α sur1 . After passing through surface  256   a , ray  320   a  continues to propagate inside substrate  310   a  at an off-axis angle of α in   (1) , and after a single reflection from surface  67   a  is coupled-out from substrate  310   a  and redirected into the viewer&#39;s eye by the partially reflecting surface  79   b.  After passing through surface  256   b , ray  320   b  is reflected once from the left side of surface  256   b , continues to propagate inside substrate  310   b  at an off-axis angle of α in    (2) , and after a double reflection from surface  67   b  is coupled-out from substrate  310   b , and redirected into the viewer&#39;s eye by the partially reflecting surface  79   b.    
       FIG. 17B  illustrates two rays  321   a  and  321   b  from the same plane input wave having incident angles of α si   (0) &gt;α m2  which impinge on the angular sensitive coupling-out elements  256   a  and  256   b , respectively. As a result of condition (a) stated hereinabove, both rays are reflected from surfaces  256   a  and  256   b  and are coupled-out from the substrates  310   a  and  310   b  by these angular sensitive reflective surfaces respectively. Ray  321   a  is reflected once from the coupling-in element  65   a , trapped inside the substrate  310   a  at an off-axis angle of α in   (1) =α in   (0) +2·α sur1 , and impinges on the right part of surface  256   a  at an incident angle of α si   (1) =α in   (1) −α sur . Ray  320   b  is reflected twice from the coupling-in element  65   b , trapped inside the substrate  310   b  at an off-axis angle of α in   (2) =α in   (0) +4·α sur1 , and is reflected once from surface  256   b  before being impinged on the left part of surface  256   b  at an incident angle of α si   (1)=α   in   (1) −α sur1 . After being reflected and coupled-out from the substrates, rays  321   a  and  321   b  are redirected by the partially reflecting surface  79   a  into the viewer&#39;s eye. 
       FIG. 17C  illustrates two rays  322   a  and  322   b  from the same plane input wave having incident angles of α m1 &lt;α si   (0) &lt;α m2 , which impinge on the angular sensitive coupling-out elements  256   a  and  256   b , respectively. Ray  322   a  is reflected once from the coupling-in element  65   a , trapped inside the substrate  310   a  at an off-axis angle of α in   (1) =α in   (0) +2·α sur1 , and impinges on the right part of surface  256   a  at an incident angle of α si   (1) =α in   (1) −α sur1 . As a result of condition (c) stated hereinabove, ray  322   a  passes through surfaces  256   a  and after a single reflection from the left side of surface  256   a,  ray  322   a  continues to propagate inside substrate  310   a  at an off-axis angle of α in   (2) , and after a double reflection from surface  67   a  is coupled-out from substrate  310   a , and redirected into the viewer&#39;s eye by the partially reflecting surface  79   b . Ray  322   b  is reflected once from the coupling-in element  65   b , trapped inside the substrate  310   b  at an off-axis angle of α in   (1) =α in   (0) +2·α sur1 , and impinges on the right part of surface  256   b  at an incident angle of α si   (1) =α in   (1) −α sur1 . As a result of condition (c) stated hereinabove, ray  322   b  is reflected from surface  256   b,  coupled-out from the substrate  310   b,  and is redirected by the partially reflecting surface  79   a  into the viewers eye. 
     The implementation of the angular sensitive reflecting surfaces  256   a  and  256   b  utilized in the embodiments of  FIGS. 17A, 17B and 17C  is illustrated herein with an optical system having the following parameters for the optical system  309 : 
     
       
         
           
             
               
                 
                   
                     
                       
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     The light waves are s-polarized. The optical material of the substrate  64  using Schott N-SF57 having a refractive index of v d =1.846, and the optical adhesives which are adjacent to surfaces  256   a  and  256   b  in  FIGS. 17A-17C  are NOA-139 and NOA 1315, having refractive indices of v d =1.315 and v d =1.39, respectively. The overall FOV of the coupled-in image is F (0) ={32°,44°} (which is practically a FOV of 22° in the air) and the angular range of F sur1   (0) ={41°,53°} is divided into three substantially equal segments: F low   (0) ={41°,45°}, F mid   (0) ={45°,49°} and F max   (0) ={49°,53°}. 
       FIG. 19A  illustrates the graph of the reflection from the angular sensitive reflective surface  256   b  in  FIGS. 17A, 17B and 17C  coated with an appropriate AR dielectric coating as a function of the incident angle for three different wavelengths: 450 nm, 550 nm and 650 nm. As shown, the reflection is 100%, due to total internal reflection for angular spectrum above 45.4°, while it is very low for the incident angles of {41°,44.9°}.  FIG. 19B  illustrates the graph of the reflection from the angular sensitive reflective surface  256   a  in  FIGS. 17A, 17B and 17C  coated with an appropriate AR dielectric coating as a function of the incident angle for three different wavelengths: 450 nm, 550 nm and 650 nm. As shown, the reflection is 100%, due to total internal reflection, for angular spectrum above 48.8°, while it is very low for the incident angles of {41°,48.6}. 
     Since each one of the two substrates  310   a ,  310   b  functions independently, there are no longer any constraints on the co-linearity of each adjacent coupling-in and coupling-out surfaces. The only constraint is that for each separate substrate  310   a  or  310   b , the major surfaces and the coupling-in and the coupling-out surfaces should be parallel to each other, respectively. Moreover, each separate substrate can have a different thickness and a different inclination angle, according to the requirements of the optical system. 
       FIG. 20  illustrates the two marginal and the central light waves of the image which are coupled out from the substrate and redirected into the viewer&#39;s eye  24 . As shown, the light waves  320 ,  321  and  322 , having the zero order off-axis angles of α in   (0) (min), α in   (0) (max) and α in   (0) (mid), are illuminating each only the parts of the partially reflecting surfaces  79   a  and  79   b  which are required to illuminate the EMB  197 ; the rightmost light wave  321  (dashed-dotted lines) is reflected only from the right surface  79   a ; the leftmost light wave  320  (dotted lines) is reflected only from the left surface  79   b , while the central light wave  322  (dashed lines) is reflected from the left part of the right surface  79   a , and the right part of the left surface  79   b . All the light waves reach the viewer&#39;s eye over the entire extent of the EMB  197 . Consequently, the EMB  197  of the embodiment illustrated in  FIGS. 17A to 17C and 20  has the same brightness as the embodiment illustrated in  FIGS. 5A and 5B , while the output aperture is doubled. Apparently, the brightness of the coupled-out light waves can he increased furthermore by exploiting partially reflecting surfaces  79 , which can be dynamically controlled according to the methods illustrated beforehand in relation to  FIGS. 6A to 12B . As a result, the brightness of the coupled-out image waves which reaches the viewer&#39;s eye can be increased to a level very close to the brightness of the light waves coupled into the substrate, namely, the brightness efficiency of the element can be nearly 1. 
       FIGS. 17A to 17C and 20  illustrate outlines of embodiments comprising a pair of substrates, and two angular sensitive coupling-out surfaces embedded respectively inside these substrates, wherein the output aperture is increased by a factor of two without reducing the brightness of the projected image. There are systems, however, having a wide FOV and an input aperture remotely located from the EMB, which significantly increase the required output aperture of the main substrate. In these cases, increasing the aperture by a factor of two in not enough and a higher increasing factor is required. To achieve this goal, the above-illustrated increasing method can be generalized to increasing factors of n&gt;2. 
     Assuming that it is necessary to increase the aperture of the image by a factor of n, as illustrated in  FIG. 21 , n−1 pairs of angular sensitive coupling-out surfaces should be inserted respectively into the substrates. For each pair, the surfaces should be adjacently located in the same manner as surfaces  256   a  and  256   b  are located in substrates  310   a  and  310   b.  In addition, the projection of the lower angular sensitive coupling-out surface, over the major surface of the substrate, should be adjacently located to the projection of the upper angular sensitive coupling-out surface of the consecutive pair. The angular range of the light waves which impinge on the coupling-out surfaces F sur1 ≡{α min ,α max } is divided now into 2n−1 substantially equal segments, by setting 2n−2 equally separated angles α j . That is, F 1 ≡{α min ,α 1 }, F 2 ≡{α 1 ,α 2 } . . . F j ≡{α j−1 ,α j } and F 2n−1 ≡{α 2n−2 ,α max }. Assuming that the angular sensitive coupling-out surfaces are denoted as S j , where j is the running index from right (j=1) to left (j=2n−2), then each surface S j  of the 2n−2 elements should fulfill the following conditions for the entire relevant photopic range:
         a. substantially totally reflective for the angular range of α si   (0) &gt;α 2n−j−1 , and   b. substantially transparent for the angular range of α si   (0) &lt;α 2n−j−1 ,       

     wherein, the coupling-out element S j  should reflect all the impinging light waves having incident angles higher than the limit angle of α 2n−j−1 , to couple-out these light waves from the substrate, and to substantially transmit all the other light waves toward the next coupling-out element S j+2 . As explained above, the simplest way to achieve these requirements is to cement the optical parts adjacent to the respective coupling-out surface, using optical adhesives having proper refractive indices that yield critical angles of α 2n−j−1 . Also, as previously described, the high transparency for incident angles lower than the respective critical angles, can be achieved using proper AR coatings. 
     The above illustrated embodiments, comprising n−1 pairs of angular sensitive coupling-out surfaces, will have the following characteristics:
         a. The light waves which are coupled-out by each surface S j (j=1 . . . 2n−2) are those in the angular range of {α 2n−j−1 ,α 2n−j+1 } (α min  and α max  are denoted here as α 0  and α 2n−1  respectively). The light waves coupled-out by the conventional coupling-out element  67   a  and  67   b  are those in the angular ranges of {α 0 ,α 2 } and {α 0 ,α 1 }, respectively, while the light waves which are coupled-out by the first surface S 1  are those in the angular range of {α 2n−2 ,α max }.   b. each light wave (inside the angular range of the light waves which impinge on the input surface of the upper pair F sur1 ≡{α min ,α max }) having an incident angle of α j−1 &lt;α s &lt;α j  (j=1 . . . 2n−1), is coupled-out by two adjacent surfaces −S 2n−j  and S 2n−j+1  and is consequently redirected into the viewer&#39;s eye by the respective part of the k partially reflecting surfaces  79   i  (i=J . . . k). Therefore, each light wave which is coupled inside the embodiment by total internal reflection, is coupled out by 1/n part of the overall coupling-out element. By proper design, however, substantially all the coupled light waves will cover the designated EMB of the system.       

     It has been previously assumed that two adjacent substrates are exploited to increase the output aperture by a factor of n without reducing the brightness of the projected image. For systems having a relatively wide FOV, however, it will be more appropriate to utilize three, instead of two adjacent substrates. In that case, as illustrated in  FIG. 22 , n−1 triplets of angular sensitive coupling-out surfaces should be inserted respectively into the three substrates,  301   a ,  310   b , and  310   c . For each triplet the surfaces should be adjacently located, and the projection of the lower angular sensitive coupling-out surface should be adjacently located to the projection of the upper angular sensitive coupling-out surface of the consecutive triplet, in the same manner described heretofore in relation to the double substrate. The angular range of the light waves which impinge on the coupling-out surfaces F sur1 ≡{α min ,α max ) is divided now into 3n−2 substantially equal segments, by setting 3n−3 equally separated angles α j . That is, F 1 ≡α min ,α 1 }, F 2  {α 1 ,α 2 } . . . F j ≡{α j−1 ,α j } and F 3n−2 ≡{α 3n−3 ,α max }. As previously, each surface S j  of the 3n−3 elements should be substantially totally reflective for the angular range of α si   (0) &gt;α 3n−j−2 , and substantially transparent for the angular range of α si   (0) &lt;α 3n−j−2 . 
     That is to say, the coupling-out element S j  should reflect all the impinging light waves having incident angles higher than the limit angle of α 3n−1−2 , to couple-out these light waves from the substrate, and to substantially transmit all the other light waves toward the next coupling-out clement S j+3 . 
     The above illustrated embodiments, comprising n−1 triplets of angular sensitive coupling-out surfaces, will have the following characteristics:
         a. The light waves which are coupled-out by each surface S j (j=1 . . . 3n−3) are those in the angular range of {α 3n−j−2 ,α 2n−j+1 } (α min  and α max  are denoted here as α 0  and α 3n−2  respectively). The light waves coupled-out by the conventional coupling-out element  67   a ,  67   b  and  67   c  are those in the angular ranges of {α 0 ,α 3 }, { 0 ,α 2 } and {α 0 ,α 1 }, respectively, while the light waves which are coupled-out by the first surface S 1  are those in the angular range of {α 3n− ,α max }.   b. each light wave (inside the angular range of F sur1 ≡{α min ,α max }) having an incident angle of α j−1 &lt;α s &lt;α j (j=1 . . . 3n−2), is coupled-out by three adjacent substrates—S 3n−j−1 , S 3n−j  and S 3n−j+1  and is consequently redirected into the viewer&#39;s eye by the respective part of the k partially reflecting surfaces  79   i  (i=1 . . . k).       

     Clearly, the number of the adjacent substrates that can be exploited to increase to output aperture is not limited to three. Any number m of adjacent substrates and (n−1)·m of angular sensitive surfaces can be utilized according to the various parameters of the optical system. 
       FIG. 23  illustrates an alternative embodiment for expanding the output aperture wherein not only the coupling-out surfaces, but also some of the coupling-in surfaces, are sensitive to the incident angle of the input waves. As shown, an optical ray  364  impinges on an optical element  355 , composed of two substrates  360   a  and  360   b . wherein the lower surface  361   b  of substrate  360   a  is attached to the upper surface  361   c  of substrate  360   b  defining an interface plane  368 . The coupling-in element  365  of the first substrate  360   a  is an angular sensitive reflecting surface, wherein the coupling-in element  366  of the lower surface is a reflecting surface which is located beneath the surface  365 . The input ray  364 , which enters the upper substrate  360   a  through the front surface  363  of the intermediate prism  367 , can either be totally reflected by surface  365  and coupled inside the upper substrate  360   a  (dashed line), can substantially pass through surface  364  to be coupled by surface  367  inside the lower substrate  360   b  (dotted line), or may be partially reflected by surface  364  and coupled inside substrate  360   a , as well as inside substrate  360   b.    
     Ray  364   a , which is coupled inside the upper substrate  360   a , can either he totally reflected by the angular sensitive reflecting surface  362   a  to be coupled out from element  355  as ray  364   ba , or substantially pass-through surface  362   a  to be coupled again by surface  362   a  inside the upper substrate  360   a  and coupled out from the element  355  by the coupling-out element  67   a  as ray  364   ab , or may be partially reflected by surface  362   a  and coupled out from element as rays  364   aa  and  364   ab . 
     Ray  364   b , which is coupled inside the lower substrate  360   b , can either be totally reflected by the angular sensitive reflecting surface  362   b  to be coupled out from element  355  as ray  364   ba , or could substantially pass-through surface  362   b  to be coupled again by surface  362   b  inside the lower substrate  360   b  and be coupled-out from the element  355  by the coupling-out element  67   b  as ray  364   bb,  or be partially reflected by surface  362   b  and he coupled out from element as rays  364   ba  and rays  364   bb.    
     The simplest way to obtain element  355  is by designing elements  362   a ,  362   b  and  365  as conventional beamsplitters which are not sensitive to the incident angle of the input waves. As a result, each input ray will be evenly split by the partially reflecting surfaces, and hence, be coupled-out from all the reflecting surfaces as rays  364   aa ,  364   ab ,  364   ba  and  364   bb . Consequently, for each input light wave the output aperture will be the projection of surfaces  362   a ,  362   b ,  67   a  and  67   b  on the lower surface  361   d . The output aperture is expanded by a factor of 4 compared to the input aperture, which is the projection of surfaces  365  and  367  on surface  361   d . Accordingly, however, the brightness of the coupled-out light wave is attenuated by a factor of 4 as compared to that of the input light wave. 
     Another way to achieve element  355  is to divide the angular range of the light waves F sur1   (1) ≡{α min ,α max }, which impinge on the angular sensitive coupling-in surface  365  and the coupling-out surfaces  362   a  and  362   b  at the incident angles of α sur   (1) =α in   (0) +α sur1 =α in   (1) −α sur1 , into four substantially equal segments: F low   (1) {α min ,α m1 }, F mid1   (1) ≡{α m1 ,α m2 }, F mid2   (1) ≡{α m2 ,α m3 } and F max   (1) ≡{α m3 ,α max }. The aim of the embodiment is that the light waves having the higher incident angles in the FOV of F max   (1) ≡{α m2 ,α max } will be reflected by angular sensitive surface  365  and be coupled into the upper substrate  360   a,  while the light waves having the lower incident angles in the FOV of F min   (1) ≡{α min ,α 2 } will pass through the angular sensitive surface  365  and be coupled into the lower substrate  360   b.  After being coupled into the upper substrate, the light waves having the most higher incident angles in the FOV of F max   (1) ≡{α m3 ,α max } will be reflected by angular sensitive surface  362   a  and be coupled out from the substrate, while the second higher incident angles in the FOV of F mid2   (1) ≡{α m2 ,α m3 } will pass through the angular sensitive surface  362   a  and be coupled out from the substrate by the coupling-out element  67   a.  After being coupled into the lower substrate, the light waves having the third higher incident angles in the FOV of F mid1   (1) ≡{α m1 ,α m2 } will be reflected by angular sensitive surface  362   d  and coupled out from the substrate, while the most lower incident angles in the FOV of F min   (1) ≡{α min ,α m2 } will pass through the angular sensitive surface  362   b  and be coupled out from the substrate by the coupling-out element  67   b.  The main advantage of this option is the output aperture is increased by a factor of 4, but disadvantageously, the achievable EMB of the system is actually zero. 
     An alternative embodiment is to modify the reflection curves of the angular sensitive surfaces  365 ,  362   a  and  362   b,  such that the reflection curves as a function of the incident angle, will not fall sharply as did those of surfaces  256   a  and  256   b  shown in  FIGS. 19A and 19B . As seen, part of the light waves will be coupled into both the upper and the lower substrates and part of the light waves which are coupled inside a given substrate  360   i  (i=a,b) will be coupled-out by both the angular sensitive surface  362   i  and the coupling-out element  67   i.  Specifically, part of the light waves in the second highest angular segment F mid2   (1)  will pass through surface  365  and be coupled inside the lower substrate  360   b,  while part of the light wave in the angular segment F mid2   (1)  will be reflected by surface  365  and coupled inside the upper substrate  360   a.  The light waves having the incident angles in the FOV of F up   (1) ≡{α up ,α max } will be coupled inside the upper substrate  360   a  (wherein α up &lt;α m2 ), while the light waves having the incident angles in the FOV of F low   (1) ≡{α min ,α low } will be coupled inside the lower substrate  360   b  (wherein α low &gt;α m2 ) As a result, the light waves having the incident angles in the FOV of F both   (1) ≡{α up ,α low } will be coupled inside the upper substrate  360   a  as well as the lower substrate  360   b.    
     Similarly, part of the light waves in the second highest angular segment F mid2   (1)  will be reflected by surface  362   a  and coupled out the substrate  360   a,  while part of the light wave in the angular segment F max   (1)  will pass through surface  362   a  and be coupled out the substrate  360   a  by the coupling-out element  67   a.  In addition, part of the light waves in the angular segment F min   (1)  will be reflected by surface  362   b  and coupled out the substrate  360   b,  while part of the light wave in the angular segment F mid1   (1)  will pass through surface  3626   b  and be coupled out the substrate  360   b  by the coupling-out element  67   b.  By proper design, the output brightness of the coupled-out light waves will be moderately attenuated, but the requested EMB of the system will be covered by the entire angular range of the output light waves. 
     Another issue to consider is the maximum achievable FOV of the image which is projected into the viewer&#39;s eye. In most of the substrate-guided based HMD technologies, either reflective or diffractive, the light waves are coupled out from the guiding substrate substantially normal to the major surfaces of the substrate. Consequently, due to the Snell refraction from the substrate the external FOV of the image is: 
     
       
         
           
             
               
                 
                   
                     F 
                     
                       ( 
                       
                         o 
                         ⁢ 
                         u 
                         ⁢ 
                         t 
                       
                       ) 
                     
                   
                   ∼ 
                   
                     
                       F 
                       
                         ( 
                         in 
                         ) 
                       
                     
                     · 
                     
                       v 
                       s 
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     wherein the FOV inside the substrate is F (in)  and the refractive index of the substrate is v s . The orders of the light waves which are coupled inside the substrate should be strictly separated, namely, 
     
       
         
           
             
               
                 
                   
                     α 
                     min 
                     
                       ( 
                       1 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         α 
                         min 
                         
                           ( 
                           0 
                           ) 
                         
                       
                       + 
                       
                         2 
                         · 
                         
                           α 
                           
                             s 
                             ⁢ 
                             u 
                             ⁢ 
                             r 
                             ⁢ 
                             1 
                           
                         
                       
                     
                     &gt; 
                     
                       
                         α 
                         max 
                         
                           ( 
                           0 
                           ) 
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     Therefore, the internal FOV is limited by the constraint 
     
       
         
           
             
               
                 
                   
                     F 
                     
                       ( 
                       
                         i 
                         ⁢ 
                         n 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         α 
                         
                           ma 
                           ⁢ 
                           x 
                         
                         
                           ( 
                           0 
                           ) 
                         
                       
                       - 
                       
                         α 
                         
                           mi 
                           ⁢ 
                           n 
                         
                         
                           ( 
                           0 
                           ) 
                         
                       
                     
                     &lt; 
                     
                       2 
                       · 
                       
                         
                           α 
                           
                             s 
                             ⁢ 
                             u 
                             ⁢ 
                             r 
                             ⁢ 
                             1 
                           
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     wherein usually a margin of at least 2 degrees should be kept between α max   (0)  and α min   (1)  to confirm the separation between the two orders. The limitation of Eq. (12) yields for systems wherein the refraction indices of the substrate, the coupling-in and the coupling-out elements are equal. 
     Referring to  FIGS. 24A and 24B , the substrates  360   a  and  360   b,  the coupling-in prism  367 , and the redirecting prism  80  are all fabricated from the same optical material, and as a result, the two marginal rays,  371  and  372 , coupled inside the element  355 , are refracted into different directions only when passing through the input surface  363  and the output surface  361   a  of the system. As a result of the similarities between the optical materials which compose element  355 , the coupled rays do not experience any refraction when passing through the interface surfaces  369 ,  81  between the substrates and the coupling-in  367  and the redirecting  80  prisms, respectively. Since the optical rays are refracted only at angles with close proximity to the normal of the entrance  363  and the exit  361   a  surfaces, the directions of the rays are modified according to the approximated equation: 
     
       
         
           
             
               
                 
                   
                     
                       α 
                       
                         o 
                         ⁢ 
                         u 
                         ⁢ 
                         t 
                       
                     
                     ∼ 
                     
                       
                         
                           v 
                           in 
                         
                         
                           v 
                           out 
                         
                       
                       · 
                       
                         α 
                         in 
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     and subsequently, the limitation of Eq. (10) is sustained. 
     The fact that the optical rays enter the substrate at highly oblique angles can be exploited to improve the above limitation. As illustrated in  FIG. 24B , the coupling-in  367  and the redirecting  80  prisms as fabricated from the same optical material having refractive index which have the following optical characteristics 
     
       
         
           
             
               
                 
                   
                     
                       v 
                       ρ 
                     
                     &lt; 
                     
                       v 
                       s 
                     
                   
                   ; 
                   
                     
                       A 
                       p 
                     
                     ∼ 
                     
                       A 
                       s 
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     wherein v p  is the refractive index of the prisms  367  and  80 , and A p ,A s  are the Abbe numbers of the prisms and the substrates respectively. As a result of the dissimilarities between the optical material of the substrates  360   a,    360   a  and that of the coupling-in  367  and the redirecting prisms  80 , and the high obliquity that rays  371  and  372  incident at the interface surfaces  369  and  81 , the rays currently experience substantial refraction when passing through the interface surfaces  369  and  81 . Since prisms  367  and  80  have the same optical characteristics, the refractions at surfaces  369  and  81  for each passing ray will have the same magnitude and the opposite directions respectively, and therefore, they will be mutually compensated. The angular deviation between two different light rays inside the prisms as a function of the deviation inside the substrates can be calculated according to the approximated equation 
     
       
         
           
             
               
                 
                   
                     
                       Δ 
                       ⁢ 
                       
                         α 
                         p 
                       
                     
                     ∼ 
                     
                       
                         
                           v 
                           s 
                         
                         
                           v 
                           p 
                         
                       
                       · 
                       
                         
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             α 
                             s 
                           
                         
                         
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             α 
                             p 
                           
                         
                       
                       · 
                       
                         Δα 
                         s 
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     wherein α s  and α p  are the off-axis angles inside the substrate and the prisms, respectively. Similarly, the angular deviation between the rays outside of element  355  is 
     
       
         
           
             
               
                 
                   
                     Δ 
                     ⁢ 
                     
                       α 
                       out 
                     
                   
                   ∼ 
                   
                     
                       
                         v 
                         p 
                       
                       · 
                       Δ 
                     
                     ⁢ 
                     
                       
                         α 
                         p 
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     Consequently, the ratio between the angular deviation outside element  355  and inside the substrates  360   a  and  360   b  is 
     
       
         
           
             
               
                 
                   
                     
                       Δ 
                       ⁢ 
                       
                         α 
                         out 
                       
                     
                     ∼ 
                     
                       
                         v 
                         s 
                       
                       · 
                       
                         
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             α 
                             s 
                           
                         
                         
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             α 
                             p 
                           
                         
                       
                       · 
                       
                         Δα 
                         s 
                       
                     
                   
                   , 
                   or 
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
             
               
                 
                   
                     F 
                     
                       ( 
                       
                         o 
                         ⁢ 
                         u 
                         ⁢ 
                         t 
                       
                       ) 
                     
                   
                   ∼ 
                   
                     
                       F 
                       
                         ( 
                         in 
                         ) 
                       
                     
                     · 
                     
                       v 
                       s 
                     
                     · 
                     
                       
                         
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             α 
                             s 
                           
                         
                         
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             α 
                             p 
                           
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
           
         
       
     
     That is to say, by modifying the optical material of the prisms  369  and  80 , it is possible to increase the FOV of the system in the air by a factor of 
     
       
         
           
             
               
                 cos 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   α 
                   s 
                 
               
               
                 cos 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   α 
                   p 
                 
               
             
             . 
           
         
       
     
     It should be noted that in order to keep the constraint of Eq. (12), the light waves having the incident angles of α in   (1) &lt;α up  should not be coupled inside the upper substrate  360   a,  and the light waves having the incident angles of α in   (1) &gt;α low  should not be coupled inside the lower substrate  360   b.  The first requirement can be achieved by constructing the interface surface  369  as an angular sensitive reflecting surface, which will be substantially total reflective for the angular range of {α up ,α max } and substantially transparent for the angular range of {α min ,α up }, in a similar manner to the construction of surfaces  256   a  and  256   b,  as illustrated in relation to  FIGS. 19A and 19B . As a result, all the light waves in the angular range of {α min ,α up } which will be reflected by surface  365  will be coupled-out from the upper substrate through surface  369  into the prism  367  and blocked by surface  379  of prism  367 . The second requirement could be achieved by causing that all the light waves in the angular range of {α low ,α max } to be totally internally reflected by surface  365 , and hence, be coupled inside only the upper substrate  360   a.    
     It should be further noted here that for the most of the relevant display systems, the two requirements should he fulfilled over the entire photopic region. As mentioned with regard to the fabrication process of the angular sensitive surfaces  256   a  and  256   b,  it is usually required that the Abbe numbers of the optical adhesive, which is adjacent to the surface and the optical material of the substrate, will be similar to avoid undesired chromatic effects in the image. There are cases, however, wherein the Abbe numbers of the adhesive and the optical material are substantially different. The chromatic dispersion due to the variation between the Abbe numbers can be compensated by choosing an optical material for the coupling-in and the redirecting of prisms  367  and  80 , having an Abbe number which is different than that of the substrates  360   a  and  360   b.  By proper selection, the difference between the Abbe numbers can induce a chromatic dispersion having the same magnitude and opposite direction. As a result, the two induced dispersions will be mutually compensated. 
     The implementation of the angular sensitive reflecting surfaces  362   a,    362   b  and  365  to utilized in the embodiment of  FIG. 24B  illustrated herein with an optical system having the following parameters for substrate  360   a : 
     
       
         
           
             
               
                 
                   
                     
                       
                         α 
                         
                           sur 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                       
                       = 
                       
                         
                           α 
                           
                             sur 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                         = 
                         
                           8 
                           ⁢ 
                           ° 
                         
                       
                     
                     ; 
                     
                       
                         F 
                         
                           ( 
                           0 
                           ) 
                         
                       
                       = 
                       
                         { 
                         
                           
                             3 
                             ⁢ 
                             R 
                           
                           , 
                           
                               
                           
                           ⁢ 
                           
                             50 
                             ⁢ 
                             ° 
                           
                         
                         } 
                       
                     
                     ; 
                     
                       
                         F 
                         
                           ( 
                           1 
                           ) 
                         
                       
                       = 
                       
                         { 
                         
                           
                             54 
                             ⁢ 
                             ° 
                           
                           , 
                           
                               
                           
                           ⁢ 
                           
                             66 
                             ⁢ 
                             ° 
                           
                         
                         } 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                           F 
                           
                             ( 
                             2 
                             ) 
                           
                         
                         = 
                         
                           { 
                           
                             
                               70 
                               ⁢ 
                               ° 
                             
                             , 
                             
                               82 
                               ⁢ 
                               ° 
                             
                           
                           } 
                         
                       
                       ; 
                       
                         
                           α 
                           
                             s 
                             ⁢ 
                             u 
                             ⁢ 
                             r 
                           
                           
                             ( 
                             1 
                             ) 
                           
                         
                         = 
                         
                           { 
                           
                             
                               46 
                               ⁢ 
                               ° 
                             
                             , 
                             
                               58 
                               ⁢ 
                               ° 
                             
                           
                           } 
                         
                       
                       ; 
                       
                         
                           α 
                           
                             s 
                             ⁢ 
                             u 
                             ⁢ 
                             r 
                           
                           
                             ( 
                             2 
                             ) 
                           
                         
                         = 
                         
                           { 
                           
                             
                               62 
                               ⁢ 
                               ° 
                             
                             , 
                             
                               74 
                               ⁢ 
                               ° 
                             
                           
                           } 
                         
                       
                     
                     , 
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
     and the following parameters for substrate  360   b : 
     
       
         
           
             
               
                 
                   
                     
                       
                         α 
                         
                           s 
                           ⁢ 
                           u 
                           ⁢ 
                           r 
                           ⁢ 
                           1 
                         
                       
                       = 
                       
                         
                           α 
                           
                             sur 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                         = 
                         
                           10.5 
                           ⁢ 
                           ° 
                         
                       
                     
                     ; 
                     
                       
                         F 
                         
                           ( 
                           0 
                           ) 
                         
                       
                       = 
                       
                         { 
                         
                           
                             31 
                             ⁢ 
                             ° 
                           
                           , 
                           
                             43 
                             ⁢ 
                             ° 
                           
                         
                         } 
                       
                     
                     ; 
                     
                       
                         F 
                         
                           ( 
                           1 
                           ) 
                         
                       
                       = 
                       
                         { 
                         
                           
                             52 
                             ⁢ 
                             ° 
                           
                           , 
                           
                             64 
                             ⁢ 
                             ° 
                           
                         
                         } 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         F 
                         
                           ( 
                           2 
                           ) 
                         
                       
                       = 
                       
                         { 
                         
                           
                             73 
                             ⁢ 
                             ° 
                           
                           , 
                           
                             85 
                             ⁢ 
                             ° 
                           
                         
                         } 
                       
                     
                     ; 
                     
                       
                         α 
                         
                           s 
                           ⁢ 
                           u 
                           ⁢ 
                           r 
                         
                         
                           ( 
                           1 
                           ) 
                         
                       
                       = 
                       
                         { 
                         
                           
                             41.5 
                             ⁢ 
                             ° 
                           
                           , 
                           
                             53.5 
                             ⁢ 
                             ° 
                           
                         
                         } 
                       
                     
                     ; 
                     
                       
                         α 
                         
                           s 
                           ⁢ 
                           u 
                           ⁢ 
                           r 
                         
                         
                           ( 
                           2 
                           ) 
                         
                       
                       = 
                       
                         
                           { 
                           
                             
                               62.5 
                               ⁢ 
                               ° 
                             
                             , 
                             
                               74.5 
                               ⁢ 
                               ° 
                             
                           
                           } 
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
           
         
       
     
     The light waves are non-polarized. The optical material of the substrates  360   a  and  360   b  is advantageously Ohara S-LAH88 having a refractive index of v d =1.917, an Abbe number of 30.6, and the optical material of the prisms  367  and  80  is Ohara S-FTM-88 having a refractive index of v d =1.592 and an Abbe number of 35.3. The optical adhesives which are adjacent to surfaces  369 ,  365 ,  368  (and  81 ),  362   a  and  362   b  are NOA 142, NOA 76, NOA 148, Noa 170 and NOA 61, having refractive indices of n s =1.42, 1.51, 1.48, 1.70 and 1.56, respectively. The overall FOV of the coupled-in image inside the substrates  360   a  and  360   b  is F (0) ={31°,50°}. The overall FOV of the coupled-in image inside the prisms  80  and  367  is F (0) ={38°,67°}, and the overall FOV of the coupled-in image in the air is F (0) ={−23°,23°}, namely, the system has an FOV of 46° along a single axis. The thickness of each substrate is 1 mm and the active area of the output and the input apertures are 25.5 mm and 6.5 mm, respectively. 
     The FOV in the air, as seen by the viewer, is expanded by a factor of 2.4 as compared to the combined FOV inside the substrates  360   a  and  360   b,  and therefore, the limitation given in Eq. (10) is overcome. By utilizing the expansion illustrated in  FIG. 24B , wherein the refractive index of prisms  367  and  80  is substantially smaller than that of the substrates  360   a  and  360   b,  it is possible to materialize a system wherein the ratio between the external FOV in the air and the FOV inside the substrate is significantly bigger than the refractive index of the substrate. This expansion can be exploited not only for the specific configuration illustrated in  FIG. 24B , but generally for any substrate, even with a single coupling-out element, having optical material different than the coupling-in and the redirecting prisms. 
       FIGS. 25A to 25C  illustrate the reflectance curves of the angular sensitive reflecting surfaces  362   a,    362   b  and  365  as the function of the normalized FOV inside the substrates. 
       FIG. 26  illustrates the efficiency of element  355  as a function of the FOV. As shown, in most of the FOVs the efficiency is between 45% and 50%, while at the edges of the FOVs the efficiency is substantially higher. Even though the output aperture is expanded by a factor of four, the efficiency is attenuated only by a factor of two. Regarding the non-uniformity of the efficiency at the edges of the FOV, for most of the back and front illuminated displays such as LCD and LCOS, the illumination, and hence, the brightness of the display sources, are usually stronger at the center of the display as a result of the Gaussian distribution of the illuminating light source. Consequently, the non-uniform efficiency curve of the system can compensate for the non-uniform illumination, and in addition, the brightness of the coupled-out image can be improved. For display sources having a uniform brightness distribution, it is possible to attenuate the higher intensities at the edges of the image either electronically or optically by reducing the reflectance of surface  67   b  of  FIG. 24B  for light waves at the left edge of the FOV and by reducing the transmission of surface  81  for light waves at the right edge of the FOV. 
     The expansion can be exploited not only for the specific configuration illustrated in  FIG. 24B , but generally for any substrate. As illustrated in  FIG. 27A , this expansion is utilized for a system having a single substrate  64  and a single coupling-out surface  67 , wherein the two marginal rays  382  and  383  are coupled into the substrate through a coupling-in prism  367  and are redirected into the viewer&#39;s eye  24  by a redirecting prism  80 , wherein the substrate  64  has an optical material different than the coupling-in and the redirecting prisms.  FIG. 27B  illustrates an embodiment wherein the marginal rays  386  and  389  are coupled into the substrate by reflection from an external surface  363  of the coupling-in prism  367 . 
     The non-uniformity of the projected image into the viewer&#39;s eye will be referred to with reference to  FIG. 28A . Three different rays,  331 ,  332  and  333   a  are coupled-out from the substrate  64  by coupling-out element  67  and then redirected by the partially reflecting surfaces  79   a  and  79   b  into the viewer&#39;s eye. On the other hand, ray  333   b  pass through surface  79   b  before being reflected by surface  79   a.  As a result, the brightness of ray  333   b  is attenuated by surface  79   b,  as a function of the transmittivity of that surface, before reaching the viewer&#39;s eye. As illustrated in  FIG. 28B , which plots the normalized brightness of the coupled-out light waves as a function of the lateral coordinate x of the output aperture  89 , the output brightness is reduced at a central part of the output aperture. This brightness pattern has the form of a dark stripe over a bright background, or, for an array of several partially reflecting surfaces  79   a,    79   b,    79   c  . . . , a pattern of alternating dark and bright stripes, not shown. For near-to-eye displays, the eye integrates the light wave emerging from a single viewing angle and focuses it onto one point on the retina, and since the response curve of the eye is logarithmic, small variations, if any, in the brightness of the display, will not be noticeable. Therefore, if the stripes are dense enough (namely, the lateral dimension of each stripe is significantly smaller than the eye&#39;s pupil), and if the eye is positioned close enough to the substrate, the viewer can still experience a high-quality image even with the stripes. For displays which are located at a distance from the eye, however, such as head-up displays (HUDs), the stripes will be noticeably seen by the viewer&#39;s eyes, which significantly reduces image quality and the overall performance of the optical system. Therefore, a solution must be found to the stripes phenomenon to allow the exploitation of the projection elements, proposed in this application, for far-from-eyes applications. 
     There are several different alternatives for achieving the HUD configuration. As illustrated in  FIG. 29A , a collimated image  322   a,    322   b  is coupled into the substrates  310   a ,  310   b  from the side part of the viewer&#39;s head and is propagating inside the substrate along the horizontal axis. In that case, exit pupil of the optical system  255   a  is determined by both eyes of the viewer, and hence, is extended significantly compared to an EMB of a near-to eye system, wherein the image is projected into a single eye of a viewer. Consequently. the output aperture of the optical system should be increased accordingly, a single coupling-out element is not enough and at least a few different coupling-out elements should be utilized to accomplish the required aperture. 
       FIG. 29A  illustrates a possible embodiment wherein four coupling-out elements,  256   a,    256   b,    67   a  and  67   b,  are utilized according to the embodiment in relation to  FIG. 17 . The problem with the dark stripes occurs in this embodiment: while the light rays  322   ba  and  322   bb  are coupled out from the substrates  310   a  and  310   b  by the coupling-out elements  67   a  and  256   b,  respectively, and then redirected by the partially reflecting surfaces  79   d  and  79   b  into the viewer&#39;s eyes, and ray  322   ba  is attenuated by surface  79   b  before being reflected by surface  79   c  into the viewer&#39;s eyes. A possible solution for the non-uniformity to problem is to utilize a single partially reflecting surface  79  (as illustrated in  FIG. 5A ) instead of an array of surfaces. The result of utilizing this solution, however, is that the thickness of the prism  80 , and consequently the size of the entire optical system, will be increased beyond the point of a reasonable use of the system. Another possible solution is to utilize a dense array of surfaces wherein the lateral dimension of each element is in the order of 1-2 mm. As a result, the lateral dimension of the partially blocked segment in each element will be in the order of 0.1-0.2 mm and will be unnoticeable at a watching distance of 30-50 cm. 
     An alternative solution to the non-uniformity problem, exploiting dynamically controlled partially reflecting surfaces, is illustrated in  FIGS. 29B and 29C . It is assumed that the dynamic surfaces  79   i  (i=a, b, . . . ) are operated as a totally reflective p section (p&lt;1) of each frame-time to yield a system having a reflectivity of p and a transmissivity of (1−p). Instead of operating the reflectance of all the dynamic surfaces simultaneously, it is possible to operate them alternately, namely, the surfaces having an odd index and those having an even index arc activated as reflective surfaces at two exclusively separated operating times during each frame-time. Since each surface is partially blocked only by its right adjacent surface, and two adjacent surfaces are not activated simultaneously any more, the partial blocking problem is avoided. As illustrated in  FIG. 29B , only surfaces  79   a,    79   c  and  79   e  are activated, during the first period of time p, as fully reflective, while surfaces  79   b  and  79   d  are fully transparent. As a result, ray  322   ba  is no longer blocked by surface  79   b  and is redirected, after being coupled-out by surface  256   b,  into the viewer&#39;s eyes. As illustrated in  FIG. 22C , only =faces  79   b  and  79   d  are activated, during the second period of time p, as fully reflective while surfaces  79   a,    79   c  and  79   e,  are fully transparent. Now, the light rays  322   a  and  322   bb  are coupled out from the substrates  310   a  and  310   b  by the coupling-out elements  67   a  and  256   b,  respectively, and then redirected by the active reflective surfaces  79   d  and  79   b  into the viewer&#39;s eyes, while ray  322   ba  passes through the transparent surface  79   c.  With this proposed embodiment, different rays reach the viewer&#39;s eye at different time slots. All of these time slots, however, are contained in the same frame-time, for all the light rays of the image. Therefore, because of the persistence of vision, the light rays from all the pixels of the display source will be integrated into the viewer&#39;s eye, thereby creating a single image. Since the two sets of surfaces are alternately operated at two distinct time periods p during a single time frame, the value of p should satisfy the condition 
     
       
         
           
             
               
                 
                   p 
                   &lt; 
                   
                     0.5 
                     . 
                   
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
           
         
       
     
     As a result, the efficiency of the projected image into the viewer&#39;s eyes cannot exceed the value of 50%. 
     An alternate configuration for the HUD embodiment, wherein the display source and the collimating module  360  are positioned at the lower (or the upper) part of the is optical module and the coupled light waves are propagating along the vertical axis, is illustrated in  FIGS. 30A to 30B . Here, the exit pupil is extended along the normal axis to the propagation direction inside the substrate and the aperture should be extended accordingly. The non-uniformity issue can also be solved here similarly to the manner illustrated with reference to  FIGS. 29A to 29C , but an even simpler solution can be utilized here. Unlike the embodiments of near-to-eye displays, wherein the combiner should be substantially normal to the line-of-sight of the viewer, for the HUD configurations, it is possible to rotate the combiner around the horizontal axis (or another axis which is normal to the line of sight of the viewer) at a substantial angle, which is usually around 45□. 
     As illustrated in  FIG. 31A , it is possible to design the configuration of the coupling-in and the coupling-out element, such that the central light wave of the image (that is, the light wave which is located at the center of the FOV of the image), after being coupled-out by the coupling-out element, is refracted from the substrate at a direction which is oriented at a substantial off-axis angle which is nearly 45′ relative to the major surfaces of the substrate. As a result, since the substrate is rotated at an approximate angle of 45′, the partially reflecting surface  79  should not be rotated with respect to the major surface to redirect the light waves into the viewer&#39;s eyes. Element  79  can be a single flat partially reflecting element which is attached to the major surface  72  of the substrate. Consequently, the light waves which arc coupled out from the substrate are redirected into the viewer&#39;s eye by a flat uniform surface and the nonuniformity issue is totally aborted. 
       FIGS. 31A to 31C  illustrate a possible embodiment wherein four coupling-out elements,  256   a,    256   b,    67   a  and  67   b,  are utilized to expend the output aperture along the vertical axis according to the aforementioned embodiments in relation to  FIGS. 17A to 17C . Seen in  FIG. 31A  are two rays  420   a  and  420   b  from the same plane input wave having incident angles of α m1 &lt;α si   (0) &lt;α m2,  which impinge on the angular sensitive coupling-out elements  256   a  and  256   b,  respectively. Ray  420   a  is reflected once from the coupling-in element  65   a,  trapped inside the substrate  410   a  at an off-axis angle of α in   (1) =α in   (0) =+2·α sur1 , and impinges on the right part of surface  256   a  at an incident angle of α si   (1) =α in   (1) −α sur1 . As a result of condition (c) described with reference to  FIGS. 17A to 17C  hereinabove, ray  420   a  passes through surfaces  256   a  and after a single reflection from the left side of surface  256   a,  it continues to propagate inside substrate  410   a  at an off-axis angle of α in   (2) , and after a double reflection from surface  67   a  is coupled-out from substrate  410   a,  and redirected into the viewer&#39;s eye by the flat partially reflecting surface  79 . Ray  420   b  is reflected once from the coupling-in element  65   b,  trapped inside the substrate  410   b  at an off-axis angle of α in   (1) =α in   (0) +2·α sur1 , and impinges on the right part of surface  256   b  at an incident angle of α si   (1) =α in   (1) −α sur1 . As a result of condition (c) described hereinabove, ray  420   b  is reflected from surface  256   b,  coupled-out from the substrate  410   b  and is redirected by the flat partially reflecting surface  79  into the viewer&#39;s eye, wherein the parallel rays  420   a  and  420   b  propagate substantially co-linear to the viewer&#39;s line-of-sight. 
       FIG. 31B  illustrates two rays  421   a  and  421   b  from the same plane input wave having incident angles of α si   (1) &lt;α m1  which impinge on the angular sensitive coupling-out elements  256   a  and  256   b,  respectively. As a result of condition (b) described hereinabove with reference to  FIGS. 17A to 17C , both rays pass through surfaces  256   a  and  256   b.  Ray  421   a  is reflected twice from the coupling-in element  65   a,  trapped inside the substrate  410   a  at an off-axis angle of α in   (2) =α in   (0) +4·α sur1 , and reflected once from surface  256   a  before being impinged on the left part of surface  256   a  at an incident angle of α si   (1) −α sur1 . Ray  421   b  is reflected once from the coupling-in element  65   b,  trapped inside the substrate  410   b  at an off-axis angle of α in   (2) =α in   (0) +2·α sur1 , and impinges on the left part of surface  256   b  at an incident angle of α si   (1) =α in   (1) −α sur1 . After passing through surface  256   a,  ray  421   a  continues to propagate inside substrate  410   a  at an off-axis angle of α in   (1) , and after a single reflection from surface  67   a  is coupled-out from substrate  410   a  and redirected into the viewer&#39;s eye by the flat partially reflecting surface  79 . After passing through surface  256   b,  ray  421   b  is reflected once from the left side of surface  256   b,  continues to propagate inside substrate  410   b  at an off-axis angle of α in   (2) , and after a double reflection from surface  67   b  is coupled-out from substrate  410   b,  and redirected into the viewer&#39;s eye by the flat partially reflecting surface  79 . 
       FIG. 31C  illustrates two rays  422   a  and  422   b  from the same plane input wave having incident angles of α si   (0) &gt;α m2  which impinge on the angular sensitive coupling-out elements  256   a  and  256   b,  respectively. As a result of condition (a) described hereinabove with reference to  FIGS. 17A to 17C , both rays are reflected from surfaces  256   a  and  256   b  and are coupled-out from the substrates  410   a  and  410   b  by these angular sensitive reflective surfaces, respectively. Ray  422   a  is reflected once from the coupling-in element  65   a , trapped inside the substrate  410   a  at an off-axis angle of α in   (1) =α in   (0) +2·α sur1 , and impinges on the right part of surface  256   a  at an incident angle of α si   (1) =α in   (1) −α sur1 . Ray  422   b  is reflected twice from the coupling-in element  65   b,  trapped inside the substrate  410   b  at an off-axis angle of α in   (2) =α in   (0) +4·α sur1 , and is reflected once from surface  256   b  before being impinged on the left part of surface  256   b  at an incident angle of α si   (1) =α in   (1) −α sur1 . After being reflected and coupled-out from the substrates, rays  422   a  and  422   b  are redirected by the flat partially reflecting surface  79  into the viewer&#39;s eye. 
     The implementation of the rotated HUD system utilized in the embodiments of  FIGS. 31A to 31C  is illustrated herein with an optical system having the following parameters: 
     
       
         
           
             
               
                 
                   
                     
                       
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                         = 
                         
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                     ; 
                     
                       
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                             18 
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                             66 
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                         F 
                         
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                         F 
                         
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                           ⁢ 
                           r 
                           ⁢ 
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                       = 
                       
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                             54 
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                             ⁢ 
                             ° 
                           
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   ( 
                   22 
                   ) 
                 
               
             
           
         
       
     
     The light waves are s-polarized and the system has a quasi-monochromatic display source having a wavelength of λ=550 nm. The optical material of the substrate  64  is Schott N-SF57 having a refractive index of v d =1.846, and the optical adhesives which are adjacent to surfaces  256   a  and  256   b  is NOA 1315, having refractive indices of v d =1315. The overall FOV of the coupled-in image is F (0) ={18°,28°} (which is practically an FOV of F (air) ={35°,61°} in the air). The angular range of F sur1   (0) ≡{30°,40°} is divided into three substantially equal segments: F low   (0) ≡{30°,33.3°}, F mid   (0) ≡{33.3°36.7°} and F max   (0) ≡{36.7°,40°}. The optical materials which yield critical angles of 33.3° and 36.7° for a substrate having a refractive index of v d =1.846 should be 1.013 and 1.103, respectively. Optical material having the required optical indices cannot be practically found. Therefore, for optical system using quasi-monochromatic light it is possible to “shift” leftward the reflectance curve of the angular sensitive surface utilizing a proper dielectric coating. 
       FIG. 32A  illustrates a graph of the reflection from the angular sensitive reflective surface  256   a  in  FIGS. 31A to 31C , coated with an appropriate dielectric coating as a function of the incident angle for the wavelength of 550. As shown, the reflection is substantially 100%, even below the critical angle of 45□, for angular spectrum above 37°, while it is very low for the incident angles of {30°,36.4°}.  FIG. 25B  illustrates the graph of the reflection from the angular sensitive reflective surface  256   b  in  FIGS. 24A to 24C  coated with an appropriate dielectric coating as a function of the incident angle for the wavelength of 550. As shown, the reflection is 100%, even below the critical angle of 45□, for angular spectrum above 33.7°, while it is very low for the incident angles of {30°,33°}. 
       FIG. 33  illustrates two marginal and central light waves of the image which are coupled out from the substrate and redirected into the viewer&#39;s eyes  24 R and  24 L. As shown, the light waves  420 ,  421  and  422 , having the zero order off-axis angles of α in   (0) (min),α in   (0) (max) and α in   (0) (mid), are illuminating each only the parts of the flat partially reflecting surface  79  which are required to illuminate the EMB. That is to say, the rightmost light wave  422  (dashed-dotted lines) is reflected only from the right part of surface  79 , the leftmost light wave  421  (dashed lines) is reflected only from the left part of surface  79 , while the central light wave  420  (dotted lines) is reflected from the central part of surface  79 . All the light waves reach the viewer&#39;s eyes over the entire extent of the HMB  297 . Consequently, the HMB  297  of the embodiment illustrated in  FIG. 33  has been extended without decreasing the image&#39;s brightness, and when the non-uniformity issue is entirely resolved. The brightness of the coupled-out light waves can be increased even furthermore by exploiting a dynamically controlled partially reflecting surface  79 . The maximal efficiency of the dynamic surface  79  is not currently limited to 50% as in the embodiment illustrated in  FIG. 29 , and it can be practically increased to nearly 100%. That is to say, the brightness of the coupled-out image waves which reaches the viewer&#39;s eyes could be close to the brightness of the light waves coupled into the substrate. 
     It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrated embodiments and that the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. 
     In particular it should be noted that features that are described with reference to one or more embodiments are described by way of example rather than by way of limitation to those embodiments. Thus, unless stated otherwise or unless particular combinations are clearly inadmissible, optional features that are described with reference to only some embodiments are assumed to be likewise applicable to all other embodiments also.