Patent Publication Number: US-11640065-B2

Title: Compact head-mounted display system

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This is a divisional of U.S. application Ser. No. 17/154,405, filed Jan. 21, 2021 for “COMPACT HEAD-MOUNT DISPLAY SYSTEM”, which is a continuation of U.S. Pat. No. 10,983,353 granted Apr. 20, 2021 for “COMPACT HEAD-MOUNT DISPLAY SYSTEM”, which is a continuation of U.S. Pat. No. 10,564,430 granted Feb. 18, 2020 for “COMPACT HEAD-MOUNTED DISPLAY SYSTEM”, which are all hereby incorporated by reference herein. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to substrate light waves guided optical devices, and particularly to devices which include a reflecting surface carried by a light-transmissive 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 head-mounted applications, wherein the system should be as light and compact as possible. 
     The strive 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. 
     DISCLOSURE OF THE INVENTION 
     The present invention facilitates the provision of compact substrates for, amongst other applications, EIMDs. 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 offered by 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 the present invention enables 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, including at least first and second light-transmitting substrates each having at least two external surfaces, and further comprising an input aperture and an output aperture, wherein an external surface of the first light-transmitting substrate is optically cemented to an external surface of the second light-transmitting substrate by means of an optical adhesive defining an interface plane, the substrates and the optical adhesive u) having a refractive index, the refractive index of the optical adhesive is substantially lower than the refractive index of the first substrate defining a critical angle of the interface plane, part of the light waves entering the device through the input aperture and exiting the device through the output aperture, impinge on the interface plane of the first substrate having incidence angles smaller than the critical angle, another part of the light waves impinging on the interface plane, having incidence angles higher than the critical angle, and the interface plane is substantially transparent for the light waves impinging on the interface plane having incidence angles smaller than the critical angle. 
    
    
     
       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 purposes 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: 
         FIG.  1    is a side view of an exemplary prior art light-guide optical element; 
         FIGS.  2 A and  2 B  are diagrams illustrating detailed sectional views of an exemplary prior art array of selectively reflective surfaces; 
         FIG.  3    is a schematic sectional-view of a prior art reflective surface with two different impinging rays; 
         FIGS.  4 A and  4 B  illustrate sectional views of a transparent substrate having coupling-in and coupling-out surfaces, according to the present invention; 
         FIGS.  5 A,  5 B,  5 C and  5 D  are schematic sectional-views of folding reflecting surfaces which re-direct the coupled-out light waves into the viewer&#39;s eye, according to the present invention; 
         FIG.  6    is a graph illustrating the reflection of incident light waves on an interface plane as a function of the incident angle, according to the present invention; 
         FIG.  7    is a graph illustrating the reflection of incident light waves on the coupling-out reflecting surface as a function of the incident angle, according to the present invention; 
         FIGS.  8 A,  8 B and  8 C  illustrate sectional views of optical modules in which correcting lenses are attached to the main transparent substrate, according to the present invention; 
         FIGS.  9 A,  9 B,  9 C and  9 D  illustrate sectional views of non-active parts of the coupling-out surfaces and methods to block it ( 9 A- 9 C), or alternately, to utilize it ( 9 D), according to the present invention; 
         FIGS.  10 A and  10 B  illustrate sectional views of transparent substrates, where two light rays coupled into the substrate remotely separated from each other are, coupled-out adjacent to each other, according to the present invention; 
         FIGS.  11 A,  11 B,  11 C and  11 D  are schematic sectional-views of optical devices in which two different transparent substrates are optically attached together, according to the present invention; 
         FIGS.  12 A,  12 B,  12 C and  12 D  are schematic sectional-views of optical devices in which an angular sensitive reflecting surface is embedded inside the transparent substrate, according to the present invention; 
         FIG.  13    is a graph illustrating the reflection of the incident light waves on an angular sensitive reflecting surface as a function of the incident angle, according to the present invention; 
         FIG.  14    is another graph illustrating the reflection of the incident light waves on an angular sensitive reflecting surface as a function of the incident angle, according to the present invention; 
         FIGS.  15 A and  15 B  schematically illustrate various ways to couple light waves into the transparent substrate using a transparent prism attached to one of the external surfaces of the substrate, according to the present invention; 
         FIGS.  16 A,  16 B and  16 C  schematically illustrate various ways to mix the coupled light waves inside the substrate by optically cementing a thin transparent plate to one of the major surfaces of the substrate, according to the present invention; 
         FIG.  17    is a graph illustrating the reflection of incident light waves on an interface plane between a thin transparent plate and a major surface of the substrate as a function of the incident angle, according to the present invention; 
         FIGS.  18 A,  18 B and  18 C  are schematic sectional-views of optical devices in which two different transparent substrates are optically attached together and one of the coupling-in elements is an angular sensitive reflecting surface, according to the present invention; 
         FIG.  19    schematically illustrates the active parts of the coupling-out surface according to the viewing angle and the eye-motion-box of the system; 
         FIGS.  20 A,  20 B, and  20 C  are schematic sectional-views of optical devices in which four different transparent substrates are optically attached and two of the coupling-in elements are angular sensitive reflecting surfaces, according to the present invention; 
         FIGS.  21 A and  21 B  are graphs illustrating the reflection of incident light waves on two different angular sensitive coupling-in surfaces as a function of the incident angle according to the present invention; 
         FIG.  22    schematically illustrates active parts of a coupling-out surface according to the viewing angle and the eye-motion-box of the system, wherein at least part of the coupling-in elements are angular sensitive reflecting surfaces; 
         FIGS.  23 A,  23 B and  23 C  are schematic sectional-views of optical devices in which a reflecting surface is embedded inside the transparent substrate and the output aperture of the system is expanded, according to the present invention; 
         FIG.  24    is a graph illustrating the reflection of incident light waves on a partially reflecting surface as a function of an incident angle, according to the present invention; 
         FIGS.  25 A,  25 B and  25 C  are other schematic sectional-views of folding reflecting surfaces which re-direct the coupled-out light waves into the viewer&#39;s eye, according to the present invention; 
         FIG.  26    is a diagram illustrating exploiting more than two propagation orders of the coupled light waves inside the substrate, according to the present invention; 
         FIG.  27    is a diagram illustrating a method for fabricating the required transparent substrate according to the present invention, and 
         FIGS.  28 A,  28 B,  28 C,  28 D and  28 E  are diagrams illustrating a method for fabricating a transparent substrate, according to the present invention. 
     
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
       FIG.  1    illustrates a sectional view of a prior art light-guide optical element. The first reflecting surface  16  is illuminated by a plane light wave  18  emanating from a display source  4  and collimated by a lens  6 , located behind the device. The reflecting surface  16  reflects the incident light from the source, such that the light is trapped inside a planar substrate  20  by total internal reflection. After several reflections off the major surfaces  26 ,  27  of the substrate, the trapped light waves reach an array of partially reflecting surfaces  22 , which couple the light out of the substrate into an eye  24 , having a pupil  25 , of a viewer. 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  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: 
     
       
         
           
             
               
                 
                   
                     α 
                     
                       s 
                       ⁢ 
                       u 
                       ⁢ 
                       r 
                       ⁢ 
                       2 
                     
                   
                   = 
                   
                     
                       
                         α 
                         in 
                       
                       2 
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     As can be seen in  FIG.  1   , 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: 
     
       
         
           
             
               
                 
                   
                     β 
                     ref 
                   
                   = 
                   
                     
                       
                         α 
                         in 
                       
                       - 
                       
                         α 
                         
                           s 
                           ⁢ 
                           u 
                           ⁢ 
                           r 
                           ⁢ 
                           2 
                         
                       
                     
                     = 
                     
                       
                         
                           α 
                           in 
                         
                         2 
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     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 α′ in =−α in  and the incident angle between the trapped ray and the normal to the reflecting surface is: 
                       β   ref   ′     =         α   in   ′     -     α     s   ⁢   u   ⁢   r   ⁢   2         =         -     α   in       -     α     sur   ⁢   2             =     -       3   ⁢     α   in       2             ,           (   3   )               
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.  1   , 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 be negligible for the rays that impinge on the surface having the second direction  28 .
 
     An important issue to be considered is the actual active area of each reflecting surface. A potential non-uniformity in the resulting image might occur due to the different reflection sequences of different rays that reach each selectively reflecting surface: some rays arrive without previous interaction with a selectively reflecting surface and other rays arrive after one or more partial reflections. This effect is illustrated in  FIG.  2 A . Assuming that for example α in =50°, the ray  31  intersects the first partially reflecting surface  22  at the point  32 . The incident angle of the ray is 25° and a portion of the ray&#39;s energy is coupled out of the substrate. The ray then intersects the same partially reflecting surface at point  34  at an incident angle of 75°, without a noticeable reflection, and then intersects again at point  36  with an incident angle of 25°, where another portion of the energy of the ray is coupled out of the substrate. In contrast, the ray  38  shown in  FIG.  2 B  undergoes only one reflection  40  from the same surface. Further multiple reflections occur at other partially reflecting surfaces. 
       FIG.  3    illustrates this non-uniformity phenomenon with a detailed sectional view of the partially reflective surface  22 , which couples light trapped inside the substrate out and into the eye  24  of a viewer. As can be seen, the ray  31  is reflected off the upper surface  27 , next to the line  50 , which is the intersection of the reflecting surface  22  with the upper surface  27 . Since this ray does not impinge on the reflecting surface  22 , its brightness remains the same and its first incidence at surface  22  is at the point  52 , after double reflection from both external surfaces. At this point, the light wave is partially reflected and the ray  54  is coupled out of the substrate. For other rays, such as ray  38 , which is located just below ray  31 , the first incidence at surface  22  is at point  56 , before it meets the upper surface  27 , wherein the light wave is partially reflected and the ray  58  is coupled out of the substrate. Hence, when it impinges on surface  22  at point  60 , following double reflection from the external surfaces  26 ,  27 , the brightness of the coupled-out ray is lower than the adjacent ray  54 . As a result, all the coupled-out light rays with the same coupled-in angle as  31  that arrive at surface  22  left of the point  52 , have a lower brightness. Consequently, the reflectance from surface  22  is actually “darker” left of the point  52  for this particular couple-in angle. 
     It is difficult to fully compensate for such differences in multiple-intersection effects. Nevertheless, in practice, the human eye tolerates significant variations in brightness, which remains unnoticed. For near-to-eye displays, the eye integrates the light which emerges 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, even for moderate levels of illumination uniformity within the display, the human eye experiences a high-quality image. The required moderate uniformity can readily be achieved with the element illustrated in  FIG.  1   . For systems having large FOVs, and where a large EMB is required, a comparatively large number of partially reflecting surfaces is needed to achieve the desired output aperture. As a result, the non-uniformity due to the multiple intersections with the large number of partially reflecting surfaces becomes more dominant, especially for displays located at a distance from the eye, such as HUDs, and the non-uniformity cannot be tolerated. For these cases, a more systematic method for overcoming the non-uniformity is required. 
     Since the “darker” portions of the partially reflecting surfaces  22  contribute less to the coupling of the trapped light waves out of the substrate, their impact on the optical performance of the substrate can be only negative, namely, there will be darker portions in the output aperture of the system and dark stripes will exist in the image. The transparency of each one of the reflecting surfaces is, however, uniform with respect to the light waves from the external scene. Therefore, if overlapping is set between the partially reflective surfaces to compensate for the darker portions in the output aperture, then rays from the output scene that cross these overlapped areas will suffer from double attenuations and darker stripes will be created in the external scene. This phenomenon significantly reduces the performance not only of displays which are located at a distance from the eye, such as head-up displays, but also that of near-eye displays, and hence, it cannot be utilized. 
       FIGS.  4 A and  4 B  illustrate embodiments for overcoming the above-described problem, according to the present invention. Instead of partially overcoming the undesired secondary reflections from the partially reflecting surfaces, these reflections are utilized to expand the output aperture of the optical system. As illustrated in  FIG.  4 A , two rays  63  from a plane light waves 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 , at an incident angle of α in   (0)  in respect to axis  61 , which is normal 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 α in   (1)  or surfaces. The off-axis angle α in   (1)  between the trapped ray and the normal to the major surfaces  70 ,  72  is
 
α in   (1) =α in   (0) +2·α sur1 .  (4)
 
     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
 
α out =α in   (1) −2·α sur2 =α in   (1) −2·α sur1 =α in   (0) .  (5)
 
     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 similar to the light waves illustrated in the prior art of  FIG.  1   .  FIG.  4 B , however, illustrates, a different behavior wherein two light rays  68 , having the same incident angle of α in   (0)  as rays  63 , impinge on points  69  which are located at the right side of the reflecting surface  65 . After a first reflection from surfaces  65 , when the coupled light rays are trapped inside the) substrate at an off-axis angle of α in   (1) , the light rays are reflected from the upper major surface  70 , and impinge again on points  71  at surface  65 . The light rays are reflected again from surface  65  and the off-axis angle of the trapped rays inside the substrate is now
 
α in   (2) =α in   (1) +2·α sur1 =α in   (0) +4·α sur1 .  (6)
 
     After several reflections off the surfaces of the substrate, the trapped light rays reach the second reflecting surface  67 . The light rays  68  first impinge on points  74  which are located at the right side (which is practically an active side) of the reflecting surface  67 . After a first reflection from surfaces  67 , when the coupled light rays are still trapped inside the substrate at an off-axis angle of α in   (1) , the light rays are reflected from the lower major surface  72  and impinge again on points  76  located at the right side of the reflecting surface  67 . The light rays are then reflected again, and the off-axis angle of the light rays is now:
 
α out =α in   (2) −4·α sur1 =α in   (1) −2·α sur1 ==α in   (0) .  (7)
 
     That is to say, the light rays  68 , which are reflected twice from the coupling-in reflecting surface  65 , as well as from the active side of the coupling-out surface  67 , 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 surfaced  65  and  67 , which is also the same incident input angle of these four rays on the substrate major planes. 
     As illustrated in  FIGS.  4 A and  4 B , the optical element  64  of the present invention is differentiated from the prior art element  20  illustrated in  FIGS.  1 - 3    by some prominent characteristics: first of all, different rays emanating from the same input light waves (such as rays  63  and  68  in  FIGS.  4 A and  4 B ) propagate inside the substrate having different off-) axis angles (α in   (1)  and α in   (2) , respectively). In addition, some of the trapped light rays impinge on the same side of the coupling-out reflecting surface with two different incident angles and have to be reflected at least twice from this surface in order to be coupled out from the substrate. As a result, proper notation rules must be defined in order to correctly note the various parameters of the trapped light rays inside the substrate. For simplicity, from here on in, the refraction of the coupling-in or coupling-out light rays due to second Snell Law while entering or exiting the substrate is neglected, and it is assumed that the materials of the optical elements which are located next to the substrate&#39;s surfaces, are similar to that of the substrate. The element should be separated by an air gap or by an adhesive having lower refractive index, in order to enable the total internal reflection of the trapped rays inside the substrate. In any case, only the directions of the rays inside the substrate are considered. 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) where
 
α in   (i+1) =α in   (i) +2·α sur1 .  (8)
 
Similarly, after each reflection from the coupling-out reflecting surface the order of the trapped ray is decreased by one from (i) to (i−1) where
 
α in   (i−1) =α in   (1) −2·α sur2 .  (9)
 
The angular spectrum of light waves which are located in a given order are confined by the two extreme angles of these order, that is:
 
α in   (i) (min)&lt;α in   (i) &lt;α in   (i) (max),  (10)
 
where, α in   (i) (min) and α in   (i) (max) are the minimal and the maximal angles of the order (i), respectively. The direction of the central light wave of the image is:
 
                         α     i   ⁢   n       (   i   )       (   cen   )     =           α     i   ⁢   n       (   i   )       (   max   )     +       α     i   ⁢   n       (   i   )       (   min   )       2       ,           (   11   )               
The FOV of the image inside the substrate is:
 
FOV=α in   (i) (max)−α in   (i) (min),  (12)
 
The FOV inside the substrate does not depend on the order (i). The entire angular spectrum of the light waves which are located in a given order (i) are denoted by
 
 F   (i) ≡{α in   (i) (min),α in   (i) (max)},  (13)
 
where
 
 F   (i+1)   =F   (i) +2·α sur1 .  (14)
 
The incident angles of the light rays on the coupling-in and coupling-out reflecting surfaces are also can be denotes as α si   (i)  and α so   (i) , respectively, where
 
α si   (i) =α in   (i) +α sur1   (15)
 
and
 
α so   (i) =α in   (i) −α sur2 .  (16)
 
     It is apparent from Eqs. (5) and (7) that in order for the output direction of different rays which undergo different number of reflections from the reflecting surfaces to be the to same, the two reflecting surfaces should be strictly parallel to each other. In addition, any deviation between the incident angles of the trapped light rays on the two major surfaces will cause, at each reflecting cycle, a drift in the off-axis angle α in   (i) . Since the trapped light rays from the higher order undergo a much smaller number of reflections from the major surfaces of the substrate than those from the lower order, the drift of the low order will be much more noticeable than that of the high order. As a result, it is required that the parallelism between the major surfaces of the substrate will be achieved to a high degree. 
     In order that the light waves will be coupled into the substrate  64  by total internal reflection, it is necessary that for the entire FOV of the image the off-axis angle inside the substrate will fulfill the equation
 
α in   (1) &gt;α cr ,  (17)
 
where, α cr  is the critical angle for total internal reflection inside the substrate. On the other hand, in order for the light waves to be coupled out from the substrate, it is necessary that the entire FOV of the image the off-axis angle of the output light waves will fulfill the equation:
 
α in   (0) &lt;α cr .  (18)
 
Combining Eqs. (9), (11), (12) and (17) yields
 
                       α     i   ⁢   n       (   0   )       (     c   ⁢   e   ⁢   n     )     =           α     i   ⁢   n       (   1   )       (   min   )     +     FOV   2     -     2   ·     α     s   ⁢   u   ⁢   r   ⁢   2           &gt;       α     c   ⁢   r       +     FOV   2     -     2   ·       α     s   ⁢   u   ⁢   r   ⁢   2       .                   (   19   )               
In order for the entire first two orders to be coupled inside the substrate the condition
 
α in   (2) (max)&lt;90°−α sur2   (20)
 
must be fulfilled. In addition, even for material having an extremely high refractive index, and even where the external media which is adjacent to major surfaces of the substrate is air, the critical angle is limited by
 
α cr &gt;32°.  (21)
 
Combining Eqs. (9), (12), (18), (20) and (21) yields
 
3α sur2 &lt;90°−FOV−α cr ,  (22)
 
which yields, even for moderate FOV of 10° inside the substrate, the limitation of:
 
α sur2 &lt;16°  (23)
 
Combining Eqs. (19), (21) and (23) yields, the limitation of:
 
α in   (0) (cen)&gt;5°⇒α out   (0) (cen)&gt;9°,  (24)
 
wherein, α out   (0) (cen) is the inclined output angle in the air, namely, the coupled-out image is substantially inclined in relation to the normal to the substrate plane. For wider FOVs and smaller α sur2 , the inclination angle will be increased. Usually however, it is required that the coupled-out image, which is projected to the viewer&#39;s eye, will be oriented substantially normal to the substrate plane.
 
     As illustrated in  FIG.  5 A , the inclination of the image can be adjusted by adding a partially reflecting surface  79  which is inclined at an angle of 
                 α     i   ⁢   n       (   0   )       (     c   ⁢   e   ⁢   n     )     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. As illustrated in  FIG.  5 B , in order to minimize distortion and chromatic aberrations, it is preferred to embed surface  79  in a 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.  5 C , to replace the single reflecting surface  80  with as 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 interface plane  83  ( FIG.  5 D ) between the substrate  64  and the prism  80 . On the one hand, the first order image F (1)  should be reflected from that plane, while the zero order image F (0)  should substantially pass through it, after being reflected from surface  67 , with no significant reflections. In addition, as illustrated in  FIGS.  5 A- 5 C , after being reflected from surface  79 , the optical wave passes again through the interface plane  83  and here also it is required that the undesired reflections will be minimized. A possible way to achieve it this, as illustrated in  FIG.  5 D , is to use an air gap in the interface plane  83 . It is preferred, however, in order to achieve a rigid system, to apply an optical adhesive in the interface plane  83 , in order to cement the prism  80  with the substrate  64 . This approach is illustrated hereby with an optical system having the following parameters:
 
α sur1 =α sur2 =10°; F   (0) ={30°,40°}; F   (1) ={50°,60°}
 
 F   (2) ={70°,80°}.  (25)
 
The light waves are s-polarized. The optical material of the substrate  64  and the prisms  80  and  82  is Schott N-SF57 having a refractive index of n d =1.8467, and the optical adhesive is NOA 1315, having a refractive index of n 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 therefore, they are totally reflected from the interface plane  83 . 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.
 
       FIG.  6    illustrates the graph of the reflection from the interface plane coated with an appropriate AR coating as a function of the incident angle for three different wavelengths: 450 nm, 550 nm and 650 nm, which practically cover the relevant photopic region. As shown, the reflection is 100% for the angular spectrum above 45°, while it is below 3% for the incident angles {30°, 40°} of the zero order, as well as for the light waves which pass again substantially normal to the plane  83  after being reflected from surface  79 . 
     Another requirement is that surface  67  will be reflective for the incident angles of the higher orders α so   (1)  and α so   (2) , as well as transparent for the coupled-out light waves which pass through this plane after being coupled out from the substrate, reflected by surface  79 , and pass again through the interface plane  83 . That is, for the exemplified system given above, the surface should be reflective for incident angles above 40° and substantially transparent for incident angles below 15°. Here also an air gap between surface  67  and prism  82  is a possible solution, but here again it is preferred to cement the element together with an optical adhesive. The requirements from the dielectric coating that should be applied to the surface  67  is therefore to be reflective for the incident angles of 40°&lt;α so   (1) &lt;45° (above 45° the light rays are totally reflected from the surface), and substantially transparent for the incident angles below 15°. 
       FIG.  7    illustrates the graph of the reflection from the interface plane coated with an appropriate angular sensitive coating as a function of the incident angle for three different wavelengths: 450 nm, 550 nm and 650 nm. As shown, the reflection is higher than 93% for the angular spectrum between 40° and 45°, while it is below 2% for the incident angles below 15° as required. 
     Concerning the reflectance of surface  79 , this parameter depends on the nature of the optical system. In non-see-through systems, such as virtual-reality displays, the substrate can be opaque, and the transmittance of the system has no importance. In that case, it is possible to apply a simple highly reflecting coating, either metallic or dielectric, on the surface. In that case, since on the one hand the reflection of surfaces  65  and  79  is very high for the impinging light waves and on the other hand the reflection of surfaces  67  and  83  is very high for the light waves that should be reflected from them and very low for light waves that should be transmitted through them, the total efficiency of the optical system can be high. In see-through systems, such as EIMDs for military or professional applications, or for augmented reality systems, wherein the viewer should see the external scene through the substrate, surface  79  should be at least partially transparent. As a result, in such a case a partially reflecting coating should be applied to surface  79 . The exact ratio between the transmission and the reflection of the coating should be determined according to the various requirements of the optical system. In the event that an array of partially reflecting surfaces  79   a ,  79   b  . . . is used to reflect the light waves to a viewer&#39;s eye, the reflectance of the coating should be the same for all the partially reflecting surfaces in order to project a uniform image to the viewer&#39;s eye as well as to transmit a uniform external seen. 
     In all of the embodiments of the invention described hereinabove, the image transmitted by the substrate is focused to infinity. However, there are applications or uses where the transmitted image should be focused to a closer distance, for example, for people who suffer from myopia and cannot properly see images located at long distances.  FIG.  8 A  illustrates an embodiment for implementing a lens, based on the present invention. A collimated image  84  is coupled into the substrate  64  by the reflecting surface  65 , reflected (once or twice, depending on the order of the coupled rays) by the angular selective reflecting surface  67 , passes through the interface plane  83 , is partially reflected by the array of partially reflecting surfaces  79   a ,  79   b , and passes again through surface  83  into the eye  24  of a viewer. The ophthalmic plano-concave lens  86 , which is attached to the upper surface  70  of the substrate, focuses the images to a convenient distance, and optionally corrects other aberrations of the viewer&#39;s eye, including astigmatism. Since the lens  86  is attached to prism  82 , which is not active in the mechanism for trapping of the optical waves inside the substrate  64  by total internal reflection, a simple cementing procedure can be used to optically attach the lens  86  to prism  82 . There are applications, however, such as illustrated in  FIG.  8 B , where the lens  86  should have an extended aperture, and hence, it should also be attached to the upper surface  70  of the substrate. Here, since this surface is active in trapping the light waves inside the substrate, an isolation layer should be provided in the interface plane  85  between the lens and the substrate, to ensure the trapping of the image rays inside the substrate by a total internal reflection. A possible way to achieve this is to use an air gap in the interface plane  85 . It is preferred, however, as explained above, to apply an optical adhesive in the interface plane, in order to cement the prism  82  with the lens  86 . As illustrated above in relation to  FIG.  6   , an appropriate AR coating can be applied to the interface plane  85 , in order to minimize the Fresnel reflections from this plane. 
     In all of the embodiments of the invention described above, it is assumed that the external scene is located at infinity. There are however applications, such as for professional or medical staff, where the external scene is located at closer distances.  FIG.  8 C  illustrates a system for implementing a dual lens configuration, based on the present invention. A collimated image  84  is coupled into the substrate  64  by the reflecting surface  65 , reflected by the angular selective reflecting surface  67 , passes through the interface plane  83 , is partially reflected by the array of partially reflecting surfaces  79   a ,  79   b  . . . and passes again through surface  83  into the eye  24  of a viewer. Another scene image  90  from a close distance is collimated to infinity by a lens  89 , and then passed through the substrate  64  into the eye. The lens  86  focuses the images  84  and  90  to a convenient distance, usually the original distance of the external scene  90 , and corrects other aberrations of the viewer&#39;s eye, if required. Since the lower surface  81  of prism  80  is not active with regard to the optical waves that are coupled inside the substrate  64  by total internal reflection and directed by the reflecting surface  79  into the viewer&#39;s eye, it is possible to optically attach a prism  80  with a lens  89  using a conventional cementing procedure. 
     The lenses  86  and  89  plotted in  FIGS.  8 A- 8 C  are simple plano-concave and plano-convex lenses, respectively. To keep the planar shape of the substrate, it is possible, however, to instead utilize Fresnel lenses, which can be made of thin molded plastic plates with fine steps. Moreover, an alternative way for realizing the lenses  86  or  89 , instead of as fixed lenses as described above, is to use electronically controlled dynamic lenses. There are applications where it is required that the user will be able not only to see a non-collimated image, but also to dynamically control the focus of the image. Recently, it has been shown that a high resolution, spatial light modulator (SLM) can be used to form a dynamic focusing element. Presently, the most popular sources for that purpose are LCD devices, but other dynamic SLM devices can be used as well. High resolution, dynamic lenses having several hundred lines/mm are known. This kind of electro-optically controlled lenses can be used as the desired dynamic elements in the present invention, instead of the fixed lenses described above in conjunction with  FIGS.  8 A- 8 C . Therefore, the operator can determine and set, in real time, the exact focal planes of both the virtual image projected by the substrate  64  as well as the real image of the external view. 
     The embodiment of the present invention illustrated in  FIGS.  4 - 8    has several significant advantages as compared to the embodiment of the prior art illustrated in  FIGS.  1 - 3   . The main reason for this is that because of the small angle of α sur2 , the active area of the output aperture of the substrate having a single reflecting surface  67 , is much larger than that of a substrate having a single coupling-out partially reflecting surface which is based on the prior art technology. For example, a substrate with a single reflecting surface  67  having an inclination angle of α sur2 =10° has an output aperture that will require at least 3-4 facets for a substrate of the prior art technology with a same thickness having an inclination angle of α sur2 ˜30°. As a result, the fabrication process of the substrate will be much simpler than that of the prior art. In addition, since for many applications only a single facet is needed to achieve the required output aperture, the projected image can be much smoother and with higher optical quality than that of the multi-facet element of the prior art. There are, however, some considerations that should be taken into an account concerning the output and the input apertures of the optical device of the present invention. 
     Regarding the output aperture as illustrated in  FIG.  9 A , a ghost image problem might be accrued at the edge of the reflecting surface  67 . As shown, a ray  91  having an off-axis angle α in   (0)  is traced from the output aperture backward to the input aperture of the substrate  64 . The ray  91  impinges on the reflecting surface at point  93   a  and is reflected not only twice, but rather three times from the reflecting surface  67 . As a result, the ray is trapped inside the substrate  64  having an off-axis angle α in   (3) , which is located in the third order of the coupled-in light waves. As illustrated in  FIG.  9 A , this angle fulfils the relation α in   (3) &gt;90°−α sur2 , and as a result, it is not a “legal” angle. As seen, the ray  91  is reflected from the third point  93   c  not toward the lower major surface  72  but toward the upper surface  70 . Therefore, ray  91  will impinge on surface  72  at the angle
 
α in   (3) (act)=180°−α in   (3) =180°−2·α sur2 −α in   (2) .  (26)
 
As a result, after an odd number of reflections from the major surfaces the ray will be reflected from the input surface  65  at the angle
 
α in   (2) (act)=α in   (3) (act)−2·α sur2 =180°−4·α sur2 −α in   (2) .  (27)
 
Consequently
 
α in   (0) (act)=α in   (2) (act)−4·α sur2 =180°−12·α sur2 −α in   (0) .  (28)
 
     Evidently, this angle in not necessarily the required angle α in   (0) . Using, for example, the parameters of the example given above in relation to Eq. (23), and assuming that α in   (0) =31°, the actual ray that is coupled into the substrate  64 , in order to be coupled-out as ray  91 , has the direction of α in   (0) (act)=29°. That is to say, not only is the “right” ray that should be coupled out as ray  91  missing from the image, and consequently, a gap will be formed in the image, but instead there is another ray originated from a “wrong” direction, which creates a ghost image. 
     A possible way to overcome this problem is illustrated in  FIG.  9 B . As shown, a flat transparent plate  95  is cemented to the lower surface  72  of the substrate  64  defining an interface plane  96 . The ray  91  is reflected now only twice from surface  67  before being coupled into the substrate  64 . Therefore, the coupled ray  97  propagates inside the substrate having an off-axis angle α in   (2)  which is a “legal” direction, and no ghost image is created in the image. In a case where it is required to minimize the Fresnel reflections of the coupled ray  97  at points  98  from the interface plane  96 , it will be preferred to use optical cement having a refractive index similar to that of the substrate  64  and plate  95 . 
     An alternative manner of overcoming the ghost image problem is illustrated in  FIG.  9 C . Here, the reflecting surface  79  is shifted inside the prism  80  such that it does not cover the entire aperture of the reflecting surface  67 . That is to say, the rays that are reflected at the far edge by segment  99  of the reflecting surface  67  are not reflected back to the viewer&#39;s eye by surface  79 . As a result, part of surface  67  is practically blocked from being active and the segment  99  becomes non-active. Therefore, the ray  91  having the “wrong” direction does not illuminates the viewer&#39;s eye and the ghost image is avoided. The exact parameters of the solution to the ghost image problem (if same exists at all), such as which embodiment to use, or whether to use a combination thereof, the thickness of plate  95  or the shift of surface  79  can be determined according to the various parameters of the optical system such as the required measure of the output aperture, the FOV of the system and the desired overall thickness of the substrate. 
     Another alternative for overcoming the ghost image problem is illustrated in  FIG.  9 D . As illustrated here, the coupled ray  91  impinges on the lower major surface  72  before impinging on the reflecting surface  65  having an off-axis angle α in   (3) , namely, the same off-axis angle it has while reflected from surface  67  at the third point  93   c . As a result, the coupled ray  91  is reflected three times from surface  65  at points  93   d ,  93   e  and  93   f  before being coupled out from the substrate having the off-axis angle α in   (1) , which is the “proper” angle. In order for the triple reflection from surface  67  to be compensated by a triple reflection from surface  65 , it is necessary for the ray to be reflected the same number of reflections from the upper surface  70 , as well as from the lower surface  72 , namely, if the ray is reflected from surface  67  upward toward surface  70 , then it also should be reflected from surface  72  upward toward surface  65 . Usually, it is not possible to design the optical system such that all the optical rays which are reflected three times from surface  67  will also be reflected three times from surface  65 . Only a small part of the rays which illuminate the segment  99  ( FIG.  9   c   ) of surface  67 , and consequently, are reflected three times from surface  67 , reach the EMB of the optical system. Usually, with a proper selection of the various parameters of the optical system, such as the inclination angle of the reflecting surfaces  65  and  67  and the thickness, the length and the refractive index of the substrate, it is possible to design the system such that for most of the relevant optical rays the triple reflection from surface  67  will be compensated by a triple reflection from surface  65  so that the ghost images and the gaps in the image will be avoided. 
     Another issue that should be considered is the required measurement of the input aperture. In order to avoid gaps and stripes in the image it is desired that all the orders of the coupled-in light waves will fill the substrate such that the reflecting surface  67  will be entirely illuminated by the coupled-in light waves. As illustrated in  FIG.  10 A , to ensure this, the points on the boundary line  100  between the edge of the reflective surface  65  and the lower surface  72  of the substrate  64 , should be illuminated for a single light wave by two different rays that enter the substrate in two different locations: a ray  101  (dotted line) that illuminates directly surface  65  at the boundary line  100 , and another ray  102  (dashed line) which is first reflected by the reflecting surface  65  at point  103  and then by the upper surface  70  of the substrate  64  before illuminating the lower surface  72  just left to the boundary line. As illustrated, the two rays  101  and  102  from the same point in the display source, which are propagated at the first order inside the substrate, are coupled into the substrate  64  remotely located from each other:  101  at the left edge and  102  approximately at the center of surface  65 , respectively. The rays are, however, coupled out by the coupling-out element  67  located adjacent to each other at the right part of surface  67 . Therefore, the entire area of surface  65  between points  103  and  100  should be illuminated by the light wave were the rays  101  and  102  originated from. Consequently, this area should be entirely illuminated by all the light waves that are coupled into the substrate. 
     Similarly, as illustrated in  FIG.  10 B , the points on the boundary line  100  between the edge of the reflective surface  65  and the lower surface  72  should be illuminated for the same single light wave that illustrated above in  FIG.  10 A , by two other different rays that enter the substrate in two different locations: a ray  105  (dashed-dotted line) that illuminates surface  65  at the boundary line  100  after one reflection from surface  65  at a point located just right to  103  and one reflection from surface  70 , and another ray  106  (solid line) which is reflected twice by the reflecting surface  65  and twice by the upper surface  70  of the substrate  64  before illuminating the lower surface  72  just left to the boundary line. As illustrated, the two rays  105  and  106  from the same point in the display source, which are propagating at the second order inside the substrate, are coupled into the substrate  64  remotely located from each other:  105  approximately at the center and  106  close to the right edge of surface  65 , respectively. They are, however, coupled out by the coupling-out element  67  located adjacent to each other at the left part of surface  67 . Therefore, the entire area of surface  65  between points  103  and the right edge  104  of surface  65  should be illuminated by the light wave, where the rays  105  and  106  originated from. Consequently, this area should be entirely illuminated by all the light waves that are coupled into the substrate. There are two conclusions from  FIGS.  10 A and  10 B : 
     a. the entire area of surface  65  should be illuminated by light waves that are coupled into the substrate, and; 
     b. the first order of the coupled light waves illuminates the left part of surface  65  and is coupled out at the right part of surface  67 , while the second order of the coupled light waves illuminates the right part of surface  65  and is coupled out at the left part of surface  67 . 
     As illustrated in  FIGS.  10 A- 10 B , the aperture of the coupling-in surface  65  is similar to that of the coupling-out surface  67 . There are, however, systems having wide FOVs and large EMBs, and therefore, a large output aperture is required. In addition, it is desired that the entire optical system will be as compact as possible. Consequently, it is necessary to minimize the input aperture of the substrate. As a result, there is a contradiction between the opposing requirements of simultaneously achieving a large output aperture along with a small input aperture. Therefore, an appropriate method should be found to reduce the input aperture for a given output aperture, or alternatively, to increase the output aperture for a given input aperture. 
     An embodiment for increasing the output aperture for a given input aperture is illustrated in  FIGS.  11 A- 11 D . As shown in  FIG.  11 A , an optical ray  107  having an input direction of α in   (0)  impinges on an optical element  109  composed of two substrates  110   a  and  110   b , wherein the lower surface  111   a  of substrate  110   a  is attached to the upper surface  112   b  of substrate  110   b  defining an interface plane  117 . Unlike the substrates which are illustrated in  FIGS.  4 - 10   , the coupling-in element  114   a  of the upper substrate  110   a  is not a simple reflecting surface as surface  65  in substrate  64 , but a partially reflecting surface, meaning that the input ray  107  is split into two rays (preferably having the same brightness)  107   a  and  107   b  which are reflected from surfaces  114   a  and  114   b  and coupled inside substrates  110   a  and  110   b , respectively by total internal reflection. Unlike surface  114   a , surface  114   b  can be a simple reflecting surface. As shown, rays  107   a  and  107   b  are reflected once from the left parts of surfaces  114   a  and  114   b , respectively, and propagated inside the substrates in the first order having an angle of α in   (1) . Consequently, they are coupled out from the substrate by a single reflection from the right parts of the coupling-out surfaces  116   a  and  116   b  having an output angle of α in   (0) .  FIG.  11 B  illustrates the same embodiment where now the input ray  107  impinges on the right side of surfaces  114   a  and  114   b . As a result, rays  107   a  and  107   b  are reflected twice from surfaces  114   a  and  114   b , respectively, and propagated inside the substrates in the second order having an angle of α in   (2) . Consequently, they are coupled out from the substrate by a double reflection from the left parts of the coupling-out surfaces  116   a  and  116   b  having an output angle of α in   (0) . As seen, surface  114   a  which is practically the input aperture of the optical device  109 , has approximately half the size of the output aperture, which is practically the combination of the coupling-out surfaces  116   a  and  116   b  together. 
     There are two contradicting requirements from the interface plane  117  between the substrates  110   a  and  110   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  110   a  should substantially pass through it, after being reflected from surface  116   a , with no significant reflections. Similarly, surface  117  should be transparent to ray  107   b  that passes through surface  114   a  having the input angle of α in   (0) . In addition, for see-through systems, the transparency of optical device  109  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  117 . An alternative manner for achieving this while maintaining the rigidness of the device, is to cement substrates  110   a  and  110   b  together using the same cementing method which utilizes low-index adhesive, as illustrated hereinabove in relation to the interface plane  83  in  FIG.  5 D . 
     In the embodiment illustrated in  FIGS.  11 A- 11 B  the two substrates  110   a  and  110   b  are similar to each other, i.e., the inclination angles α sur1  of the coupling-in devices  114   a  and  114   b , as well as the inclination angles α sur2  of the coupling-out devices  116   a  and  116   b , are the same. In addition, the two substrates have the same thickness. It is possible, however, to attach two substrates having two different characteristics. As illustrated in  FIG.  11 C , the upper substrate  110   a  has the same parameters as the system illustrated above in relation to Eq. (23). The lower substrate however has the following parameters:
 
α sur1 =α sur2 =11°; F   (0) ={24°,35°}; F   (1) ={46°,57°}
 
 F   (2) ={68°,79°}.  (29)
 
The light waves are s-polarized. The optical material of the substrates  110   a  and  110   b  is as before, Schott N-SF57, having a refractive index of n d =1.8467 and the optical adhesive is NOA 1315, having a refractive index of n d =1.315. The critical angle is therefore α cr &gt;45.4°. The FOV of the image that is coupled into, and then from, the device  109 , is increased from F (0) ={30°, 40°} in the single substrate  64  to F (0) ={24°, 40°} in the double substrate element  109 . All the light waves propagating in the first order and having the combined FOV of F (1) ={46°, 60°} have off-axis angles higher than the critical angle, and therefore, they are totally reflected from the interface plane  117  between the substrates. Since the practical output aperture of each substrate directly depends on tan α sur2 , the thickness of the lower substrate  110   b  should be slightly increased, in order to equalize the output apertures of the two substrates. The output aperture of element  109  is doubled as compared to that of the single substrate  64  in  FIG.  5 A  and the FOV is increased by 6°. The penalty is that the thickness of the device is doubled and the brightness of the coupled out image is reduced by 50%. In the event that the left edge of surface  116   a  is not active, as illustrated above in relation to  FIGS.  9 A- 9 C , it is possible to block this part by slightly shifting the lower substrate  110   b . As illustrated in  FIG.  11 D , the reflecting surfaces  116   a  and  116   b  are no longer co-linear. The left edge  118  of surface  110   a  does not coincide with the right edge  120  of substrate  110   b , which is slightly shifted rightward, and hence, the inactive part  122  of surface  110   a  is practically blocked.
 
     Still an alternative embodiment to practically decrease the input aperture of the optical device is illustrated in  FIGS.  12 A- 12 B . Here, the fact that, as illustrated in  FIGS.  10 A and  10 B , the light waves which impinge on the left part of the coupling-in surface  65  are reflected only once from surface  65 , and hence, propagate inside the substrate  64  having the first order off-axis angle of α in   (1) , while the light waves which impinge on the right part of the coupling-in surface  65  are reflected twice from surface  65 , and hence, propagate inside the substrate  64  having the second order off-axis angle of α in   (2) , is exploited. As illustrated in  FIG.  12 A , an angular sensitive partially reflecting surface  124  is embedded inside the substrate  64 . Surface  124  is parallel to the coupling-in surface  65  and the coupling-out surface  67 , namely, the inclination angle of surface  124  in relation to the major surfaces of the substrate  64  is:
 
α spr =α sur1 =α sur2 .  (30)
 
For the entire FOV of the image, which is propagating inside the substrate  64 , surface  124  is substantially transparent for light waves having an incident angle of
 
α sp   (0) =α in   (0) +α spr =α in   (1) −α spr   (31)
 
and is substantially, evenly partially, reflective for light waves having an incident angle of
 
α sp   (1) =α in   (1) +α spr =α in   (2) −α spr .  (32)
 
     In addition, it is assumed that only the left part  125  of the coupling-in surface  65  is illuminated by the image&#39;s light waves. As illustrated in  FIG.  12 A , a ray  127  impinges on the left part  125  of surface  65 , is coupled into the substrate  64  after one reflection from surface  65 , and hence, propagates inside the substrate  64  having the first order off-axis angle of α in   (1) . After a few reflections from the major surfaces of the substrate  64 , the ray  127  impinges on surface  124  at point  128   a . Since the ray impinges on the surface from the left side, it behaves similarly to the rays that impinge on surface  67 , and hence, Eq. (16) should be used to calculate to incident angle of ray  127  at point  128   a . Hence,
 
α sp   (128a) =α in   (1) −α spr .  (33)
 
     As a result, the condition of Eq. (31) is fulfilled and ray  127  passes through surface  124  without any significant reflectance. After one reflection from the upper major surface  70 , ray  127  impinges again on surface  124  at point  128   b . Now, the ray impinges on the surface from the right side and it behaves similarly to the rays that impinge on surface  65 , and hence, Eq. (15) should be used to calculate to incident angle of ray  127  at point  128   b . Thus,
 
α sp   (128b) =α in   (1) +α spr .  (34)
 
     As a result, the condition of Eq. (32) is fulfilled and ray  127  substantially evenly split by surface  124 , namely, approximately half of the intensity of the light ray passes through surface  124  as ray  129  and continues to propagate inside the substrate  124  having the same off-axis angle of α in   (1) , while the other half of the intensity of the light ray is reflected from surface  124  as ray  130 , and continues to propagate inside the substrate  124  having the off-axis angle of
 
α in   (1) +2·α spr =+α in   (1) +2·α sur1 =α in   (2) .  (35)
 
     Specifically, ray  130  propagates inside the substrate  64  having the second order off-axis angle of α in   (2) . After one reflection from the lower major surface  72  of the substrate  64 , the ray  129  impinges on surface  124  at the point  128   c . Since the ray again impinges on the surface from the left side, it behaves similarly to the rays that impinge on surface  67 , and hence, Eq. (16) should again be used to calculate to incident angle of ray  129  at point  128   c  and, again
 
α sp   (128c) =α in   (1) −α spr ,  (36)
 
The condition of Eq. (31) is fulfilled, ray  129  passes through surface  124  without any significant reflectance and continues to propagate inside the substrate having the first order off-axis angle. Consequently, if the entire left part  125  of surface  65  is illuminated by all the light waves coupled into the substrate, the substrate  64 , as explained above in relation to  FIG.  10 A , will be filled by the first order of the coupled light waves. After being split by surface  124 , part of the light will continue to fill the substrate by the first order, while the part of the light which is reflected by surface  124  will now fill the second order of the coupled light waves. As a result, substantially the entire aperture of the coupling-out surface  67  will be illuminated by the first and the second orders of the coupled waves and the output light waves will be coupled-out from substantially the entire active aperture of surface  67 . As a result, while the output aperture remains the entire active aperture of surface  67 , the input aperture of the substrate is practically reduced by a half. The penalty is that the brightness of the coupled-out light waves is also reduced by a half.
 
     A similar embodiment for reducing the input aperture by a half is illustrated in  FIG.  12 B . Here, only the right part of the coupling-in surface  65  is illuminated by the input light waves. As shown, a ray  132  impinges on the right part  134  of surface  65 , is coupled into the substrate  64  after two reflections from surface  65 , and hence, propagates inside the substrate  64  having the second order off-axis angle of α in   (2) . After a few reflections from the major surfaces of the substrate  64  the ray  132  impinges on surface  124  at the point  135   a . Since the ray impinges on the surface from the left side it behaves similarly to the rays that impinges on surface  67 , and hence, Eq. (16) should be used to calculate to incident angle of ray  132  at point  135   a . Hence,
 
α sp   (135b) =α in   (2) −α spr =α in   (1) +α spr .  (37)
 
     As a result, the condition of Eq. (32) is fulfilled, and ray  132  is substantially evenly split by surface  124 ; approximately half of the light ray passes through surface  124  as ray  136  and continues to propagate inside the substrate  124  having the same off-axis angle of α in   (2) , while the other half of the light ray is reflected from surface  124  as ray  137  and continues to propagate inside the substrate  124  having the off-axis angle of
 
α in   (2) −2·α spr =α in   (2) −2·α sur1 =α in   (1) .  (38)
 
     Specifically, ray  137  propagates inside the substrate  64  having the first order off-axis angle of α in   (1) . After one reflection from the lower major surface  72  of the substrate  64 , the ray  137  impinges on surface  124  at the point  135   b . Since the ray impinges on the surface from the left side, it behaves similarly to the rays that impinge on surface  67 , and hence, Eq. (16) should be used to calculate to incident angle of ray  127  at point  128   c . Thus,
 
α sp   (135b) =α in   (1) −α spr ,  (39)
 
the condition of Eq. (29) is fulfilled, ray  137  passes through surface  124  without any significant reflectance, and it continues to propagate inside the substrate having the first order off-axis angle.
 
     The practical function of the embodiment illustrated in  FIG.  12 B  is similar to that illustrated in  FIG.  12 A . Only half of the input aperture  65  is illuminated by the input light waves, while the output light waves are coupled out from the entire aperture of the coupling-out surface  67 . The difference is that while in  FIG.  12 A  only the left part  125  of surface  65  is illuminated by the input light waves, in  FIG.  12 B  the right part  134  of surface  65  is used, but the outcome is similar, and the entire output surface is exploited. Usually, the decision as to which part of surface  65  to actually use, depends on the various parameters of the optical system. 
     The embodiment illustrated in  FIGS.  12 A- 12 B , wherein as angular selective reflecting surfaces is embedded inside the substrate  64 , can be exploited for other usages, not necessarily for reducing the input aperture. An issue that should be considered is the uniformity of the input light waves that illuminate the input aperture  65 . Assuming, for instance, that the brightness of ray  101  in  FIG.  10 A  is lower than that of ray  102 , as a result of a non-perfect imaging system, this non similarity will hardly be seen by a direct viewing of the input plane wave, because of the remoteness between the rays. After being coupled into the substrate  64 , however, this condition changes and the two rays  101  and  102  propagate inside the substrate  64  adjacent to each other. Consequently, the two rays that are reflected from surface  67  and are coupled out from the substrate, have different brightness. Unlike the input light wave, however, the two rays are now adjacent to each other and this dissimilarity will be easily seen as a dark line in the coupled-out image. The same problem occurs if the brightness of ray  106  in  FIG.  10 B  is lower than that of ray  105 , or vice versa. 
       FIG.  12 C  illustrates an embodiment which overcomes this non-uniformity problem. Here, the same angular sensitive partially reflecting surface  124  is embedded inside the substrate  64 , but now the entire input aperture  65  is illuminated by the input light waves. As shown, two different rays,  127  which illuminates the left part  125  close to the center of surface  65 , and  132  which illuminates the far edge of the right part  134  (and consequently, have lower brightness than ray  127 ), are propagated inside the substrate  64  having the first and the second order off-axis angles, respectively. The two rays coincide at point  138  on surface  124  and as explained above in relation to  FIGS.  12 A and  12 B , both of them will be partially reflected by the surface  124  and partially pass through it. As a result, ray  139 , which propagates inside the substrate having a first order off-axis angle, will be a mixture of the part of ray  127  which passes through surface  124 , and the part of ray  132  which is reflected by the surface. In addition, ray  140 , which propagates inside the substrate having a second order off-axis angle, will be a mixture of the part of ray  132  which passes through surface  124  and the part of ray  127  which is reflected by the surface. Rays  139  and  140  are thus mixtures of the original rays  127  and  132 , but unlike the original rays, the two rays  139  and  140  which are originated from surface  124  now have a similar brightness. As a result, assuming that the entire aperture of surface  65  is illuminated by the input light waves, the uniformity of the light waves that will originate from surface  124  will have much better uniform distribution over the output aperture than previously, and the non-uniformity issue will be considerably improved. 
     Another issue that should be considered is the parallelism between the major surfaces of the substrate. As explained above in relation to  FIGS.  4 A- 4 B , the two major surfaces of the substrate  64  should be strictly parallel to each other, since any deviation between the incident angles of the trapped light rays on the two major surfaces will cause, at each reflecting cycle, a drift in the off-axis angle α in   (i) , and since the trapped light rays from the higher order undergo a much smaller number of reflections from the major surfaces of the substrate than those from the lower order, the drift of the low order will be much more noticeable than that of the high order. There are, however, applications wherein a very high resolution is required. In addition, the ratio between the length and the thickness of the substrate can be high, and hence, the number of reflections from the major surfaces of the lower order can be very, and therefore the required parallelism cannot be achieved by conventional fabrication methods. 
     A possible approach for overcoming the above problem is illustrated in  FIG.  12 D . An angular sensitive reflecting surface  141 , which is parallel to surfaces  65  and  67 , is embedded inside the substrate  64 , but here the reflecting characteristics of this surface are different than that of surface  124  in  FIGS.  12 A- 12 C . For the entire FOV of the image which propagates inside the substrate  64 , surface  141  is substantially transparent, as previously, for light waves having an incident angle of
 
α sp   (0) =α in   (0) +α spr =α in   (1) α spr .  (40)
 
For light waves, however, having an incident angle of
 
α sp   (1) α in   (1) +α spr =α in   (2) −α spr ,  (41)
 
surface  141  is now substantially reflective. As before, surface  141  will be substantially transparent for the coupled light rays  127  and  132  impinging thereon at points  142  and  144 , respectively, having a first order off-axis angle and impinge on the right side of the surfaces. For point  146  however, where rays  127  and  132  coincide together having a first order off-axis angle impinging on the left side of surface  141  and a second order off-axis angle impinging on the right side of surface  141 , respectively, surface  141  will be substantially reflective. As a result, rays  127  and  132  will be reflected from surface  141  having a second and a first order off-axis angle, respectively, namely, rays  127  and  132  exchange their off-axis angles at the coinciding point  146 . Therefore, assuming that surface  141  is located at the center of substrate  64 , evenly positioned between surfaces  65  and  67 , rays  127  and  132  undergo a similar number of reflections from the major surfaces of the substrate  64 . Assuming that the entire aperture of surface  65  is illuminated by the input light waves, for each input light wave all the coupled rays will have substantially the same number of reflections from the major surfaces of the substrate  64 , and the parallelism issue will thus be considerably improved.
 
     The realization of the angular sensitive reflecting surface  124  which is utilized in the embodiments of  FIGS.  12 A- 12 C  is illustrated hereby with an optical system having the following parameters:
 
α sur1 =α sur2 =12°; F   (0) ={21°,31°}; F   (1) ={45°,55°}
 
 F   (2) ={69°,79°};α sp   (0) ={33°,43°};α sp   (1) ={57°,67°}.  (42)
 
The light waves are s-polarized. The optical material of the substrate  64  is Schott N-SF6 having a refractive index of n d =1.8052, and the optical adhesive which is adjacent to surface  124  is NTT 6205, having a refractive index of n d =1.71.
 
       FIG.  13    illustrates the graph of the reflection from the reflective surface  124  coated with an appropriate angular sensitive 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 approximately 50% for the angular spectrum between 57° and 67°, while it is very low for the incident angles {33°, 43°} of the zero order. 
     The realization of the angular sensitive reflecting surface  141  utilized in the embodiment of  FIG.  12 D , is illustrated hereby with an optical system having same the parameters as those presented above in Eq. 42, where the optical adhesive which is adjacent to surface  141  is NOA 165, having a refractive index of n d =1.52. 
       FIG.  14    illustrates the graph of the reflection from the reflective surface  141  coated with an appropriate angular sensitive 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% for the angular spectrum above 57°, while it is practically zero for the incident angles {33°, 43°} of the zero order. 
     In all the embodiments illustrated in  FIGS.  4 - 11   , the coupling-in element is a slanted reflecting surface. The reason for this is the necessity to couple the first, as well as the second, order of the light waves inside the substrate. For the embodiments illustrated in  FIGS.  12 A- 12 B , however, where only the first or the second order is, respectively, coupled into the substrate by the coupling-in element, other optical means can be utilized. As illustrated in  FIG.  15 A , a prism  148  is optically attached to the upper major surface  70  of the substrate  64 . Two light rays  149  and  150  from the same input light wave, impinge on the two edges of the input aperture  152  of the prism  148 , where the inclination angle of the light rays inside the prism is α in   (1) . While the left ray  149  illuminates the upper major surface  70  just right to edge  153  of the prism, the right ray  150  passes through surface  70 , is totally reflected from the lower surface  72 , and then impinges on the upper surface  72  just left to the edge  153 . As a result, the two rays  149  and  150  are coupled inside the substrate  64 , having the first order off-axis angle of α in   (1) , while propagating inside the substrate  64  adjacent to each other. After being partially reflected at points  154  and  156  from surface  124 , the reflected rays  158  and  160  propagate inside the substrate  20  adjacent to each other having the second order off-axis angle of α in   (2) . Consequently, all the rays of the same input light waves covering the input aperture  152 , will fill the substrate by the first order light waves, and after being partially reflected from surface  124 , will also fill the substrate by the second order light waves. As a result, the output light waves are coupled out from the substrate by the entire active aperture of surface  67 . A slightly different embodiment is illustrated in  FIG.  15 B  where the coupling-in element is a prism  162  which is optically attached to a slanted edge  163  of the substrate. As illustrated, in the embodiments of  FIGS.  15 A and  15 B , the input aperture is significantly smaller than that of the embodiments illustrated in  FIGS.  4 - 11   . Naturally, realizing modified embodiments wherein light waves having the second order off-axis angles are directly coupled into the substrate utilizing coupling-in prisms similar to those illustrated in  FIGS.  15 A and  15 B , is also possible. In that case light waves having the first order off-axis angles will be created inside the substrate in a method similar to that illustrated in  FIG.  12 B . 
     Another issue that should be considered is the uniformity of the light waves that are split by surface  124  in the embodiments of  FIGS.  12 A- 12 C . As illustrated, the trapped rays having the first order off-axis angle of α in   (1)  are partially reflected only once from the left side of surface  124 . As illustrated in  FIG.  16 A , there are rays, however, which are partially reflected twice from surface  124 . As shown, ray  164  is first partially reflected from surface  124  at point  165 , located in proximity to the intersection between surface  124  and the upper major surface  70 . The part of ray  164  which passes through surface  124  at point  165  is reflected from the lower major surface  72 , passes through surface  124 , is reflected from the upper surface  70  and then is partially reflected again from surface  124  at point  166 . Since the brightness of this part of the ray has been already reduced by a half, while splitting at point  165 , the brightness of the split rays from point  166  will be approximately 25% of that of the original ray  164 , namely, ray  164  has been split into three different rays: ray  164   a  which is reflected from surface  124  at point  165  and has about a half of the brightness of the original ray  164 , and rays  164   b  and  164   c , which pass through surface  164  at point  165  and then pass again, or are reflected, respectively, by surface  164  at point  166 , which rays have about a quarter of the brightness of the original ray  164 . As a result, there are rays in the image waves which are less bright than the others, and these variations might be seen as dark stripes in the coupled-out image. This phenomenon is negligible for the light waves having the higher off-axis angles in the FOV, but it is, however, more significant for the light waves having the lower off-axis angles. 
     In order to solve the unevenness problem of the image which is coupled out from the substrate, it is important to understand the difference between this problem and an unevenness problem of a conventional display source which emits a real image from the display plane. Generally, the unevenness of an image, which is projected from a conventional display source, is caused by the non-uniformity of the display itself, e.g., different pixels of the display emit light waves having different intensities. As a result, the only way to solve the unevenness problem is to directly manage the pixels of the display. The cause for the unevenness of the image illustrated hereinabove in relation to  FIG.  16 A , however, is completely different. Here, the unevenness is caused by a non-uniformity of the different rays of a single light wave, which is associated with a single pixel in the image, meaning that different rays belonging to the same plane light wave, and consequently having the same direction, have different intensities. Therefore, the unevenness of this plane wave can be solved if the various rays of this uneven wave will be mixed together. Hence, a proper mixing arrangement should be advantageously be added to the substrate  64 , in order to improve the uniformity of the plane waves, which are trapped inside the substrate by total internal reflection. 
     As illustrated in  FIG.  16 B , this unevenness problem may be solved by attaching a flat transparent plate  167  to one of the major surfaces  72  of the substrate  64 , wherein a beam-splitting arrangement is applied to the interface plane  168  between the substrate  64  and the transparent plate  167 . As illustrated, two light rays,  164  and  169 , having different intensities intersect each other at point  170  located at the interface plane  168 . Ray  164 , which is illustrated above in  FIG.  16 A , has already been partially reflected by surface  124 , and hence, has a lower brightness then the original ray. The other ray  169 , which passes through the interface plane at point  171  and is reflected by the lower surface  172  of the plate  167 , did not yet pass through surface  124 , and hence, it has a higher intensity. As a result of the beam-splitting arrangement which is applied there, each one of the two intersecting rays is partially reflected and partially passes through the interface plane. Consequently, the two rays interchange energies between themselves, and the emerging ray  164   d  from the intersection point  170  has an intensity which is closer to the average intensity of the two incident rays  164  and  169 . As a result, the intensity of ray  164   d , which is partially reflected by surface  124  at point  166 , is higher than previously and the non-uniformity problem is relaxed. (There are more intersections and splitting of rays  164  and  169  in  FIG.  16 B  but to simplify the figure, only the intersection at point  170  and the emerging of ray  164   d  from there is plotted). In addition to the mixing of rays  164  and  169  at point  170 , rays  164   b  and  164   c  which emerged from point  166  are mixed again with other rays (not shown) at points  174  and  175 , respectively, on the interface plane  168 , and their intensities become even closer to the average intensity of the coupled-out image wave. 
     The most efficient beam-splitting arrangement is to apply a partially reflecting coating to the interface plane, wherein half of the incoming light wave is transmitted and half is reflected from the surface. In that case, the intensities of the emerging ray  164   d  are to substantially the average intensity of the two incident rays  164  and  169 , and the mixing between the rays is optimal. The main drawback of the coating method, however, is that in order to avoid aberrations and smearing of the image, the direction of the trapped rays inside the substrate should be strictly retained. Therefore, a high degree of parallelism should be maintained for the three reflecting surfaces: the upper surface  70  of the substrate  64 , the lower surface  172  of the plate  167  and the interface plane  168 . As a result, the external surfaces of the substrate  64  and the plate  167  should have high parallelism and very good optical quality before attaching them together. Applying an optical coating to one of these external surfaces, however, will require a coating process which usually deforms the surfaces of the coated plate, especially if this plate is particularly thin. Another problem is that the light rays which are reflected from surface  67  intersect with the interface plane  168  before being coupled out from the substrate  64 . As a result, a simple reflecting coating cannot easily be applied to the interface plane  168 , since this plane should also be transparent to the light-waves that exit the substrate  64 , as well as transparent to the light wave from the external scene for see-through applications. Thus, the light-waves should pass through plane  168  without substantial reflections at small incident angles and should be partially reflected at higher incident angles. This requirement complicates the coating procedure and increases the probability that the coated plate will be deformed during the coating process. Consequently, since even a minor deformation will deteriorate the performance of the imaging system, an alternative mixing arrangement should be applied. 
     An alternative embodiment is illustrated in  FIG.  16 C . Here, the substrate  64  and the plate  167  are optically cemented using an optical adhesive  176  having a refractive index, which is substantially different than the refractive index of the light transmitting substrate  64  and the flat plate  167 . As a result of the differences between the refractive indices and the oblique incident angles of the trapped rays, as compared to the interface plane  168 , the Fresnel reflections from plane  168  will be significant and the light waves which are coupled inside the substrate, will be partially reflected from the interface plane. Practically, the incident rays are reflected twice from the interface plane  168 , once from the interface plane between the substrate  64  and the adhesive  176 , and the second time from the interface plane between the optical adhesive  176  and the transparent plate  167 . As illustrated, three different rays  164 ,  169  and  178  are trapped inside the substrate. The two rays  169  and  178  intersect each other at point  171  which is located at the interface plane  168 . As a result of the Fresnel reflections, each one of the two intersecting rays is partially reflected and partially passes through the interface plane. Consequently, the two rays interchange energies between themselves and the emerging rays  179  and  180  from the intersection point  171  have intensities which are closer to the average intensity of the two incident rays  169  and  178 . Similarly, the two rays  164  and  179  intersect each other at point  170 , interchange energies between themselves and the emerging rays  181  and  182  from the intersection point  170  have intensities which are closer to the average intensity of the two incident rays  164  and  179 . Therefore, the three rays  164 ,  179  and  178 , interchange energies during this process and their intensities are now closer to the average intensity. Rays  164  and  178  do not interchange energies directly, but indirectly through the two separate interactions with ray  179 , at points  170  and  171 . 
     The optimal mixing will be achieved if the Fresnel reflections from the interface plane  168  are close to 50%. Since, however, Fresnel reflections are very sensitive to the incident angle, it is impossible to find an optical adhesive having a refractive index that yields Fresnel reflection of 50% for the entire FOV of the coupled image, and since the trapped rays intersect not only once, but rather a few times with the interface plane, it is possible to find a mixing arrangement that will be acceptable even for Fresnel reflections which are very different than the optimal value of 50%. The realization of the ray mixing interface plane  167  which is utilized in the embodiments of  FIGS.  16 B- 16 C  is illustrated herein with an optical system having same parameters as given above in Eq. 42, where the optical adhesive which is used to cement the substrate  64  with the flat plate  167 , is NTT-E3341 having a refractive index of n d =1.43. 
       FIG.  17    illustrates a graph of the reflection from the interface plane  167  as a function of the incident angle for the wavelength 550 nm (the other wavelengths in the photopic region have similar curves) for the entire first order FOV F (1) ={45°, 55°}. As shown, the reflection is 100% for the angular spectrum above 53° as a result of total internal reflection, and hence, no mixing effect is achieved for these angles. For the entire second order FOV F (2) ={69°, 79°}, all the light waves are totally internally reflected from the interface plane  168  and no mixing effect is achieved for the entire order. As has been explained above, however, the non-uniformity problem is substantially negligible for the rays having these angles. For the other spectral range of α in   (1) &lt;52°, the reflection is between 20% and 80%, and a good mixing effect can be achieved. In addition, the device illustrated here is not limited to utilization of a single flat plate. Two or more flat plates, having various thicknesses and refractive indices, can be optically attached to one or both of the major surfaces using various optical adhesives. In any case, the exact parameters of the transparent plates and the adhesives can be used according to the various requirements of the systems. 
     In the embodiment  109  illustrated in  FIGS.  11 A- 11 D , it was assumed that the beamsplitter  114   a  evenly splits each input ray into two rays, which have substantially the same brightness and are coupled inside substrates  110   a  and  110   b , by total internal reflection. As a result, the beamsplitter  114   a  is not sensitive to the incidence angle of the input light wave, and in addition, the output brightness is reduced by about 50%.  FIGS.  18 A- 18 C  illustrate a modified version of device  109 , wherein the input beamsplitter  183  is sensitive to the incident angle of the input light waves and, 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 which are coupled out from the substrate do not have to illuminate the entire active area of the coupling-out surface, as was done in the embodiments of  FIGS.  11 A- 11 D , was utilized. 
     As illustrated in  FIG.  19   , showing the rays that should impinge on surface  79  in order to illuminate the EMB  197 , the two marginal and the central light waves of the image are coupled out from the substrate and re-directed 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  67 R,  67 M and  67 L of the coupling-out reflecting surface  67 , respectively, and are reflected by surface  79  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  67 , and the original brightness will be preserved. To achieve this, the angular range of the light waves F sur1   (0) ≡{α min , α max }, which impinge on the input surface  183  ( FIG.  18 A ), is divided into three substantially equal segments: F low ≡{α min , α max }, F mid   (0) ≡{α m1 , α m2 } and F max   (0) ≡{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   (0) ={α m2 , α max } will be coupled out from the upper substrate  110   a  by the both parts of the coupling-out element  190   a  and  190   b ; the light waves having the lower incident angles in the FOV of F min   (0) ≡{α min , α m1 } will be coupled out from the lower substrate  110   b  by the both parts of the coupling-out element  190   c  and  190   d , and the light waves in the FOV of F mid   (0) ≡{α m1 , α m1 } will be coupled out from the upper substrate  110   a  by the lower coupling-out element  190   b  and from the lower substrate  110   b  by the upper coupling-out element  190   c.    
     In order to achieve this, surface  183  should substantially reflect all the light waves in F max   (0)  such that they will be coupled into the upper substrate  110   a  and substantially transmit all the light waves in F min   (0) , such that they will be coupled by the reflecting surface  114  into the lower substrate  110   b . In addition, part of the light waves in F mid   (0)  should be reflected by surface  183  in such a way that they will be trapped inside the upper substrate  110   a , but will be coupled out only by the lower part of the coupling-out element  190   b  and part of the light waves in F mid   (0)  should be pass through surface  183  in such a way that they will be trapped inside the lower substrate  110   b  but will be coupled out only by the upper part of the coupling-out element  190   c . As illustrated in  FIGS.  4 A and  4 B , the light waves which propagate inside the substrate having the first order off-axis angles are coupled out from the substrate by the upper part of the coupling-out element  67 , while the light waves propagating inside the substrate having the second order off-axis angles are coupled out from the substrate by the lower part of the coupling-out element  67 . Therefore, in order to achieve the coupling-in requirements of the light waves in F mid   (0) , it is necessary for the light waves in this FOV to be coupled inside the upper substrate  110   a  having the second order off-axis angles, and hence, will be coupled out by the lower part  190   b , and in addition, will be coupled inside the lower substrate  110   b  having the first order off-axis angles, and hence, will be coupled out by the upper part  190   c.    
     Consequently, the angular sensitive reflecting surface  183  should fulfill the following three characteristics for the entire photopic range:
         a. substantially total reflective for the angular range of {α m2 , α max };   b. substantially transparent for the angular range of {α min , α m1 }; and   c. substantially total reflective for the angular range of {α m1 , α m2 } at the upper part  183   a  ( FIG.  18 C ) of surface  183  and substantially transparent for the angular range of {α m1 , α m2 } at the lower part  183   b  ( FIG.  18 C ) of surface  183 .       

     It is possible to achieve these requirements by applying angular sensitive dielectric coatings on surfaces  183   a  and  183 , but the realization process of these coatings can be fairly complicated. A simpler method is to cement surfaces  183   a  and  183   b  to the inert part  177  of device  109  using optical adhesives having proper refractive indices that yield critical angles of α m1  and, α m2  at surfaces  183   a  and  183   b , respectively. The high transparency for angles lower than the respective critical angles can be achieved using proper AR coatings 
       FIG.  18 A  illustrates two rays  184   a  and  184   b  from the same plane input wave having incident angles of α si   (0) &lt;α m1  which impinge on the lower and the upper parts of surface  183 , respectively. As a result of condition (b) described hereinabove, the rays pass through surface  183  and are coupled into the lower substrate  110   b  by the reflective surface  114  having the first and the second order off-axis angles, respectively. Consequently, the rays are coupled-out from the substrate by the reflective surfaces  190   c  and  190   d , respectively.  FIG.  18 B  illustrates two rays  185   a  and  185   b  from the same plane input wave having incident angles of α si   (0) &gt;α m2  which impinge on the lower and the upper parts of surface  183 , respectively. As a result of condition (a) described hereinabove, the rays are reflected from surface  183  and are coupled into the upper substrate  110   a  having the first and the second order off-axis angles, respectively. Consequently, the rays are coupled-out from the substrate by the reflective surfaces  190   a  and  190   b  respectively.  FIG.  18 C  illustrates two rays  186   a  and  186   b  from the same plane input wave having incident angles of α m1 &lt;α si   (0) &lt;α m2 , which impinge on the surfaces  183   b  and  183   a , respectively. As a result of condition (c) described hereinabove, ray  186   b  is reflected from surface  183   a  and is coupled into the upper substrate  110   a  having the second order off-axis angle. Consequently, the ray is coupled-out from the substrate by the lower reflective surface  190   b . In addition, ray  186   a  passes through surface  183   b  and is coupled into the lower substrate  110   b  by the reflective surface  114  having the first order off-axis angle. Consequently, the ray is coupled-out from the substrate by the upper reflective surfaces  190   c , as required. 
     Usually, it will be difficult to cement surface  183  to the inert part  177  such that the two parts  183   a  and  183   b  will be cemented to part  177  by two different adhesives, without any cross-talk between the parts. As illustrated in  FIG.  18 C , a possible way for overcoming this problem is by fabricating substrate  110   a  of two parallel slices  110   aa  and  110   ab , attached together at the interface plane  189 . Three critical issues should be considered during the fabrication process of the upper substrate  110   a  as a combination of  110   aa  and  110   ab . Firstly, in order to avoid the trapping of the second order light waves in the upper slice  110   aa  by total internal reflection from the interface plane  189 , it is essential that the optical adhesive used to optically attach the slices  110   aa  and  110   ab  will have a refractive index close to that of the slices. In addition, in order to prevent distortion of the coupled-out image, the coupling in surfaces  183   a  and  183   b  and the coupling-out surfaces  190   a  and  190   b  should be strictly co-linear, respectively. Furthermore, since it will be difficult to completely prevent residual Fresnel reflections of the trapped light waves, especially those having the second order off-axis angles, the interface plane  189  should be parallel to the major surfaces  111   a  and  112   a  of substrate  110   a.    
     An alternative embodiment to realize the required angular-sensitive beamsplitter is illustrated in  FIGS.  20 A- 20 C . As shown, the overall optical device  199  is constructed of four different substrates  191   a ,  191   b ,  191   c  and  191   d , which are optically cemented together defining three interface planes,  193   a ,  193   b  and  193   c , respectively. Another difference from the embodiment of  FIGS.  18 A- 18 C  is that here the beamsplitters  183   a  and  183   b  are interchanged, e.g., surfaces  183   a  and  183   b  are cemented to the inert part  177  of element  199  using optical adhesives having proper refractive indices that now yield critical angles of α m1  and, α m2  at surfaces  183   b  and  183   a , respectively. 
       FIG.  20 A  illustrates two rays  184   a  and  184   b  from the same plane input wave having incident angles of α si   (0) &lt;α m1 , which impinge on surface  183   b  and  183   a , respectively. As previously, the rays pass through the surfaces and are coupled into the substrates  191   d  and  191   c  by the reflective surfaces  195   b  and  195   a , respectively. Although the rays plotted in the figure have only the first order off-axis angles, it is clear that the input light waves illuminate the entire areas of surfaces  195   a  and  195   b , and hence, they fill the entire first and second off-axis angles and as a result illuminate the entire active areas of surfaces  190   c  and  190   d  which couple them out of the substrates. 
       FIG.  20 B  illustrates two rays  185   a  and  185   b  from the same plane input wave having incident angles of α si   (0) &gt;α m2 , which impinge on surface  183   b  and  183   a , respectively. As previously, the rays are reflected from the surfaces and are coupled into the substrates  191   b  and  191   a , respectively. As described above, the input light waves illuminate the entire areas of surfaces  183   a  and  183   b , and hence, they fill the entire first and second off-axis angles and as a result illuminate the entire active areas of surfaces  190   a  and  190   b , which couple them out of the substrates. 
       FIG.  20 C  illustrates two rays  186   a  and  186   b  from the same plane input wave having incident angles of α m1 &lt;α si   (0) &lt;α m2 , which impinge on the surfaces  183   b  and  183   a , respectively. Since the beam-splitting mechanism was interchanged between surfaces  183   a  and  183   b , ray  186   a  is now reflected from surface  183   b , and is coupled into substrate  191   b  and coupled out by the reflective surface  190   b . In addition, ray  186   b  now passes through surface  183   a  and is coupled into substrate  191   c  by the reflective surface  195   a , and consequently, is coupled-out from the substrate by the reflective surface  190   c  as required. 
     Since each one of the four substrates  191   i  (i=a, b, c, d) functions independently, there are no longer any constraints on the co-linearity of each adjacent coupling-in and coupling-out surfaces as there were according to the embodiments of  FIGS.  18 A- 18 C . The only constraint is that for each separate substrate  191   i , 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. 
     The implementation of the angular sensitive reflecting surfaces  183   s  and  183   b  utilized in the embodiments of  FIGS.  18 A- 18 C and  20 A- 20 C  is illustrated herein with an optical system having the following parameters for substrate  110   a  of  FIGS.  18 A- 18 C  and substrates  191   a  and  191   b  of  FIGS.  20 A- 20 C :
 
α sur1 =α sur2 =9°; F   (0) ={36°,46°}; F   (1) ={54°,64°}
 
 F   (2) ={72°;82°};α sp   (0) ={45°,55°};α sp   (1) ={63°,73°},  (43)
 
     and the following parameters for substrate  110   b  of  FIGS.  18 A- 18 C  and substrates  191   c  and  191   d  of  FIGS.  20 A- 20 C :
 
α sur1 =α sur2 =10°; F   (0) ={30°,40°}; F   (1) ={50°,60°}
 
 F   (2) ={70°,80°};α sp   (0) ={40°,50°};α sp   (1) ={60°,70°}.  (44)
 
The light waves are s-polarized. The optical material of the substrate  64  is Schott N-SF57 having a refractive index of n d =1.846, and the optical adhesives which are adjacent to surfaces  183   a  and  183   b  in  FIGS.  18 A- 18 C  (or surfaces  183   b  and  183   a  in  FIGS.  20 A- 20 C ) are NTT-E3337 and NOA 1315, having refractive indices of n d =1.315 and n d =1.42, respectively. The overall FOV of the coupled-in image is F (0) ={30°, 46°} (which is practically a FOV of 30° in the air) and the angular range of F sur1   (0) ≡{39°, 55°} is divided into three substantially equal segments: F low   (0) ≡{39°, 45°}, F mid   (0) ≡{45°, 50°} and F max   (0) ≡{50°, 55°}.
 
       FIG.  21 A  illustrates the graph of the reflection from the reflective surface  183   a  in  FIG.  18 C  (or surface  183   b  in  FIG.  20 C ) 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 45.6°, while it is very low for the incident angles of {39°, 44.5°}.  FIG.  21 B  illustrates the graph of the reflection from the reflective surface  183   b  in  FIG.  18 C  (or surface  183   a  in  FIG.  20 C ) 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 50.7°, while it is very low for the incident angles of {39°, 50°}. 
       FIG.  22    illustrates the two marginal and the central light waves of the image which are coupled out from the substrate and re-directed into the viewer&#39;s eye  24 . As shown, the light waves  185 ,  186 , and  184 , having the zero order off-axis angles of α in   (0) (max), α in   (0) (mid) and α in   (0) (min), are illuminating each only the reflection surfaces  190   a - 190   b ,  190   b - 190   c  and  190   c - 190   d , respectively, and are reflected by surface  79  into to EMB  197 . The extent of the EMB  197  is set by the two marginal rays  185 R and  184 L, which are reflected form the two edges of the overall coupling-out aperture of element  199 , and is not influenced at all by the rays  185 R and  184 L which “moved” to the center of the coupling-out aperture as a result of the new arrangement. Consequently, the EMB  197  of the embodiment which is illustrated in  FIGS.  18 A- 18 C and  20 A- 20 C  has the same large aperture as the EMB of the embodiment which is illustrated in  FIGS.  11 A- 11 C , while the output brightness is doubled. 
       FIGS.  20 A,  20 B and  20 C  illustrate outlines of embodiments comprising two pairs of 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 increases the required input 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 required to increase the aperture of the image by a factor of n, n pairs of transparent substrates should be attached together, wherein for each pair the coupling-in, as well as the coupling-out, surfaces should be adjacently located in the same manner as, for example, surfaces  183   a  and  183   b , and  190   a  and  190   b  ( FIG.  20 A ), respectively. In addition, all the coupling-out surfaces should be adjacently located as surfaces  190   i  in embodiment  199 . The angular range of the light waves which impinge on the input surface of the upper pair 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 substrates are denoted as S j , where j is the running index from bottom (j=1) to top (j=2n), then the coupling-in elements of substrates S 1  and S 2  from the lower pair are regular reflecting surfaces. All the other 2n−2 coupling-in elements are angular sensitive partially reflecting surfaces fulfilling, for each substrate S j  (j&gt;2), the following conditions for the entire photopic range: 
     a. substantially totally reflective for the angular range of α si   (0) &gt;α j−2 , and 
     b. substantially transparent for the angular range of α si   (0) &lt;α j−2 . 
     That is to say, the coupling-in element of substrate S j  should reflect all the impinging light waves having incident angles higher than the limit angle of α j−2 , to couple these light waves inside substrate S j , and to substantially transmit all the other light waves toward the input aperture of substrate S j−2 . As explained above, the simplest way to achieve these requirements is to cement each respective coupling-in surface to the adjacent inert part of the embodiment, using optical adhesives having proper refractive indices that yield critical angles of α j−2 . 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 pairs of transparent substrates, will have the following characteristics:
         a. aside from the bottom and the top substrates, the light waves which are coupled inside each substrate S j  (j=2 . . . 2n−1) are those in the angular range of {α j−2 , α j } (α min  and α max  are denoted here as α 0  and α 2n−1  respectively). The light waves coupled inside substrates S 1  and S 2n  are those in the angular ranges of {α 0 , α 1 } and {α 2n−2 , α 2n−1 }, respectively.   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), is coupled inside two adjacent substrates—S j  and S j+1  and is consequently coupled out from the embodiment by the respective coupling-out element  190   j  and  190   j+1 . 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 a proper design, however, substantially all the coupled light waves will cover the designated EMB of the system.       

     In all the embodiments illustrated in  FIGS.  11 - 20   , one of the outcomes of expanding the output aperture is that the thickness of the optical module is also expanded, accordingly. There are applications however, where it is required to have a large output aperture while still keeping the substrate as thin as possible.  FIG.  23 A  illustrates an embodiment wherein the output aperture is expanded without increasing the substrate&#39;s thickness. As shown, an angular sensitive partially reflecting surface  198  is embedded inside the substrate  200 . Surface  198  is parallel to the coupling-in surface  65  and the coupling-out surface  67 . The inclination angle of surface  198  in relation to the major surfaces of the substrate  200  is:
 
α prs =α sur1 =α sur2 .  (45)
 
For the entire FOV of the image propagating inside the substrate  200 , surface  198  is substantially evenly partially reflective, that is, it evenly reflects and transmits the coupled-in light waves having an incident angle of
 
α sp   (0) =α in   (0) +α spr =α in   (1) −α spr   (46)
 
and is totally reflective for light waves having an incident angle of
 
α sp   (1) =α in   (1) +α spr =α in   (2) −α spr .  (47)
 
     In addition, the surface is substantially transparent for the light waves which are coupled-out from the substrate and re-directed into the viewer&#39;s eye, as well as for the light waves from the external scene. 
     As illustrated in  FIG.  23 A , a ray  202  is coupled into the substrate  200  after one reflection from surface  65 , and hence, propagated inside the substrate  200  having the first order off-axis angle of α in   (1) . After a few reflections from the major surfaces of the substrate  200 , the ray  202  impinges on surface  198  at the point  206   a . Since the ray impinges on the surface from the left side, it behaves similarly to the rays that impinge on surface  67 , and hence, Eq. (16) should be exploited to calculate to incident angle of ray  202  at point  206   a , namely,
 
α sp   (206a) =α in   (1) −α spr .  (48)
 
     As a result, the condition of Eq. (46) is fulfilled, and ray  202  is substantially evenly split by surface  198 , namely, approximately half of the intensity of the light ray  202  is reflected from surface  198  as ray  202   a  having the off-axis angle of α in   (0) , and hence, is coupled out from the substrate  200  through the lower surface  72 . The other half of the intensity of the light ray  202  passes through surface  198  as ray  202   b  and continue to propagate inside the substrate  200  having the same off-axis angle of α in   (1) . After one reflection from the upper major surface  70 , ray  202   b  impinges again on surface  198  at point  206   b . Now, the ray impinges on the surface from the right side, and it behaves similarly to the ray that impinges on surface  65 , and hence, Eq. (15) should be used to calculate to incident angle of ray  202   b  at point  206   b , so that
 
α sp   (206b) =α in   (1) +α spr .  (49)
 
As a result, the condition of Eq. (47) is fulfilled and ray  202   b  is totally reflected form surface  198 , and continues to propagate inside the substrate  200  having the off-axis angle of
 
α in   (1) +2·α spr =+2·α sur1 =α in   (2) .  (50)
 
     Specifically, ray  202   b  propagates inside the substrate  200  having the second order off-axis angle of α in   (2) . After two reflections from the coupling-out surface  67 , ray  202   b  is coupled out from substrate  200  having the same off-axis angle α in   (0)  as ray  202   a.    
     As also illustrated in  FIG.  23 A , another ray  204  is coupled into the substrate  200  after two reflections from surface  65 , and hence, propagates inside the substrate having the second order off-axis angle of α in   (2) . After a few reflections from the major surfaces of the substrate  64 , the ray  204  impinges on surface  198  at point  207   a . Since the ray impinges on the surface from the left side and behaves similarly to the rays that impinge on surface  67 , Eq. (16) should hence be used to calculate the incident angle of ray  204  at point  207   a . Hence,
 
α sp   (207a) =α in   (2) −α spr =α in   (1) +α spr .  (51)
 
As a result, the condition of Eq. (47) is fulfilled and ray  204  is totally reflected from surface  198  and continues to propagate inside the substrate  200  having the off-axis angle of
 
α in   (2) −2·α spr =α in   (2) −2·α sur1 =α in   (1) .  (52)
 
     Specifically, ray  204  propagates inside the substrate  200  having the first order off-axis angle of α in   (1) . After one reflection from the lower major surface  72  of the substrate  200 , the ray  204  impinges again on surface  198  at the point  207   b . Similarly to the behavior of ray  202  at point  206   a , ray  204  is substantially evenly split by surface  198 . Approximately half of the intensity of the light ray  204  is reflected from surface  198  as ray  204   a  having the off-axis angle of α in   (0) , and hence, is coupled out from the substrate  200  through the lower surface  70 . The other half of the intensity of the light ray  204  passes through surface  198  as ray  204   b  and continues to propagate inside the substrate  200  having the same off-axis angle of α in   (1) . After one reflection from the coupling-out surface  67 , ray  204   b  is coupled out from substrate  200  having the same off-axis angle α in   (0)  as rays  202   a ,  202   b  and  204   a . As a result, the output aperture of substrate  200  is the combination of surfaces  198  and  67 . Consequently, the practical active area of the output aperture of substrate  200  has been doubled as compared to that of substrate  64 , which is illustrated in  FIG.  4   , while the thickness of the substrate remains the same. On the other hand, the brightness of light waves coupled out from substrate  200  has been reduced by 50% as compared to that of substrate  64 . 
     The expanding embodiment illustrated in  FIG.  23 A  is not limited to one substrate or only one partially reflecting surface. Optical systems which are composed of a few different substrates, or a few different partially reflecting surfaces which are embedded inside a single substrate, are also feasible.  FIG.  23 B  illustrates an optical system  208  wherein two different substrates  210   a  and  210   b  are attached together. Two partially reflecting surfaces  212   a  and  212   b , having the same optical characteristics as surface  198  in  FIG.  23 A , are embedded inside substrates  210   a  and  210   b , respectively. An input ray  214  is split by the beam-splitting surface  216  into two parts: a ray  214   a  which is coupled by surface  216  into substrate  210   a , and ray  214   b  which passes through surfaces  216  and is coupled by surface  218  into substrate  210   b . The coupled rays  214   a  and  214   b  are split by surfaces  212   a  and  212   b  respectively. The rays  214   aa  and  214   ba  are reflected by these surfaces and coupled out from the substrate, while rays  214   ab  and  214   bb  pass through theses surfaces and are coupled out from the substrate by the reflecting surfaces  220   a  and  220   b , respectively. As a result, the output aperture of the system  208  is composed of four surfaces:  212   a ,  212   b ,  220   a  and  220   b , and the active area of this aperture is expanded accordingly. As shown, in embodiment  208 , the coupling-out surfaces  212   b  and  220   b  of the lower substrate  210   b  partially can block, if required, the non-active parts of surfaces  212   a  and  220   a , respectively. 
     In the embodiments illustrated in  FIGS.  23 A and  23 B , it was assumed that the partially reflecting surfaces which are embedded in the substrates evenly split the intensities of the impinging light waves, namely, the reflectance (and hence, the transmittance) of the surface is 50% for the entire angular spectrum of the coupled image. It should be noted however, that due to the same arguments which were considered in relation to  FIGS.  19  and  22   , that the light waves having off-axis angles in the upper part of the angular spectrum of the image, are mostly coupled out into the EMB by the partially reflective surface  198 , while the light waves having off-axis angles in the lower part of the angular spectrum of the image, are mostly coupled out into the EMB by the reflective surface  67 . As a result, it will be advantageous to provide a partially reflective coating on the partially reflecting surface that will have a reflectance higher and lower than 50% for the upper and lower regions of the angular spectrum, respectively. In that case, since the brightness of the light waves in the upper and lower regions depends on the reflectance and transmittance of the partially reflecting surface  198 , respectively, it will be higher than 50% for these regions. On the other hand, for the light waves in the central region of the angular spectrum, which are evenly coupled out into the EMB by the partially reflecting surface  198  and the reflecting surface  67 , the reflectance and accordingly, the brightness, will be around 50%, which is slightly lower than the brightness at the edges of the image. For most of the back and front illuminated displays, such as LCD and LCOS, however, the illumination, and hence, the brightness of the display sources, are usually stronger at the center of the display. As a result, the non-uniform reflectance curve of the partially reflecting surface can compensate for the non-uniform illumination and in addition the overall brightness of the coupled-out image is improved. 
     An alternative embodiment  255 , wherein the output aperture is expanded without increasing the substrate&#39;s thickness and without the necessity to resort to a special partially reflecting coating as required for surface  198 , is illustrated in  FIG.  23 C . 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  65  and the coupling-out  67  surfaces. The inclination angle of surface  256  in relation to the major surfaces of the substrate  258  is:
 
α sur3 =α sur1 =α sur2 .  (53)
 
     As shown in  FIG.  23 C , a ray  260  is coupled into the substrate  258  after one reflection from surface  65 , and hence, propagates inside the substrate  258  having the first order off-axis angle of α in   (1) . After a few reflections from the major surfaces of the substrate  258  the ray  260  impinges on surface  256 . Since the ray impinges on the surface from the right side, it behaves similarly to the rays that impinges on surface  67 , and hence, it is coupled out from the substrate  258  having an off-axis angle α in   (0)  and is then reflected (or partially reflected in see-through applications) into the viewer&#39;s eye similarly to what is illustrated in  FIGS.  5 A- 5 C . The reflected ray is, however, not propagated here undisturbed into the viewer&#39;s eye, as in the embodiments illustrated in  FIGS.  5 A- 5 C . Instead, the reflected ray impinges on a partially reflecting surface  264   a , which is parallel to surface  79   a , and is coupled inside a flat prism  267 , which is attached to the upper surface  70  of the substrate  268  in a similar way that prism  80  is attached to the lower surface  72  of the substrate. Thus, one way to achieve the above is to use an air gap in the interface plane  268  between the prism  267  and the substrate  258 , while another way for achieving a rigid system, is to apply an optical adhesive having a proper refractive index in the interface plane  268 , in order to cement the prism  268  with the substrate  258 . 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   (0)  and impinges again on surface  256 . The ray impinges on the surface from the left side and behaves similarly to the ray that impinges on surface  65 , and hence, after two reflections from surface  256 , it propagates inside the substrate  258  having the second order off-axis angle of α in   (2) . After two 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   (0)  and is 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.  23 C , another ray  262  is coupled into the substrate  258  after two reflections from surface  65  and propagates inside the substrate having the second order off-axis angle of α in   (2) . After a few reflections from the major surfaces of the substrate  258 , the ray  262  impinges on surface  256 . The ray impinges on the surface from the right side and behaves similarly to the rays that impinge on surface  67 , and hence, is coupled out from the substrate  258  having an off-axis angle α in   (0)  and is then reflected by surface  79   b  (or partially reflected in see-through applications), 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 surface  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  260  is reflected from surface  264   b  as ray  262   b  having an off-axis angle of α in   (0) , and impinges again on surface  256 . The ray impinges on the surface from the left side and behaves similarly to the ray that impinges on surface  65 , and hence, after one reflection from surface  256  it propagates inside the substrate  258  having the first order off-axis angle of a α in   (1) . 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   (0)  and is 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 of the four rays— 260   a ,  260   b ,  260   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 practical active area of the output aperture of substrate  258  has been doubled as compared to that of substrate  64 , which is illustrated in  FIG.  4   , 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 as compared to that of substrate  64 . There are ways, however, to improve to brightness of the coupled-out light waves. 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 to s-polarization) and substantially transparent to the orthogonal polarization (preferably to p-polarization). In such a case the transmittance of the external scene for see-through applications can be achieved, since the entire element  255  is now substantially transparent to the one 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  254   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.  23 C , 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. 
     The embodiment for expanding the output aperture by embedding a reflecting surface  256  into the substrate  258 , as illustrated in  FIG.  23 C , is not limited to a single reflecting surface. 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. 
     The realization of the partially reflecting surface  198 , embedded inside the substrate  200  shown in  FIG.  23 A , is illustrated herein with an optical system having the following parameters:
 
α sur1 =α sur2 =10°; F   (0) ={30°,40°}; F   (1) ={50°,60°}
 
 F   (2) ={70°,80°};α sp   (0) ={40°,50°};α sp   (1) ={60°,70°}.  (53)
 
     The light waves are s-polarized. The optical material of the substrate  200  is Schott N-SF57 having a refractive index of n d =1.846, and the optical adhesive which is adjacent to surfaces  198  is NTT-AT9390, having refractive index of n d =1.49, and hence, the critical angle is α cr =53.5°. The reflectance of surface  198  is designed to be monotonic increasing from 44% at α sp   (0) =40° to 55% at α sp   (0) =50°. 
       FIG.  24    illustrates the graph of the reflection from the partially reflecting surface  198  coated with an appropriate 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 an angular spectrum of {60°, 70°}. In addition, the reflectance curve increases from 44% at 40° to 55% at 50°, while it is very low for the incident angles below 15°, as required. 
       FIGS.  5 A- 5 D  illustrate embodiments for directing the coupled-out light waves into the viewer&#39;s eye  24  where the light waves are reflected back by a reflecting surface  79  and pass again through the substrate  64  toward the viewer&#39;s eye. An alternative way, in which the viewer&#39;s eye is positioned at the other side of the substrate, is illustrated in  FIGS.  25 A- 25 C . As shown in  FIG.  25 A , four rays,  222   a ,  222   b ,  222   c  and  222   d  from the same light wave, are coupled into the substrate  64  by the reflecting surface  65 , and then coupled out by the surface  67  having the off-axis angle α in   (0) . The coupled-out light rays are reflected by the reflecting surface  224 , which is inclined at an angle of 
               α   ref     =       90   ⁢   °     -         α   in     (   0   )       (   cen   )     2             
to the lower major surface  72  of the substrate, towards the viewer&#39;s eye. The main drawback of this embodiment is that the longitudinal dimension (along the y-axis) of the reflecting surface  224  is big, resulting in a large and cumbersome optical system.
 
       FIG.  25 B  illustrates an alternative version of this embodiment in which an array of parallel reflecting (or alternatively partially reflecting) surfaces having the same inclination angle as surface  224 , is positioned next to the exit aperture of the substrate  64 . The array  225  can be embedded inside a transparent prism  226  having preferably refractive index similar to that of the substrate  64 . The optical system can now be much more compact than that illustrated in  FIG.  25 A , depending on the number of the reflecting surfaces in the array  225  and the thickness of prism  226 . As shown, the reflecting surfaces illustrated in  FIG.  25 B  are adjacent to each other, i.e., the right side of each surface is adjacent to the left side of the projection of the adjacent surface. There are still a few issues with the proposed embodiment. As shown, ray  222   b  (dashed line) is reflected by the upper part of surface  225   a , which (at least partially) prevents the continuation of the ray  222   b ′ (gray arrow) from reaching the reflecting surface  225   b  at point  227 . As a result, the part of surface  225   b  below point  227  is blocked by surface  225   a  and is actually non-active (at least partially, depending on the reflectivity of surface  225   a ). In addition, the presented arrangement is suitable for the central coupled-out light waves, but not for the light waves having lower off-axis angles. As shown, the coupled-out ray  228  (the part of the ray which is still coupled inside the substrate is not shown here) having the off-axis angle 
               -     FOV   2       ,         
is blocked by the lower part of surface  225   c.  
 
       FIG.  25 C  illustrates a modified version of this embodiment in which the lower parts of the reflecting surfaces  225  which comprise the non-active parts, are trimmed and the thickness of prism  226  is reduced, accordingly. The main outcome of this version is that the reflecting surfaces  225  are no longer adjacent to each other. As illustrated, the intersection  230  of the coupled-out light waves with lower surface  232  of prism  226  has the form of alternated dark and bright stripes. This significantly reduces the performance of displays which are located at a distance from the eye, such as HUDs, wherein the stripes will be noticeably seen by the viewer&#39;s eyes, and hence, this method cannot be utilized for these applications. 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. Moreover, the active area of the reflecting surfaces  225  can be further trimmed to yield a lower fill-factor of the illuminated areas on surface  232 . While the projection  230  of the reflecting surfaces  225  on surface  232  are the areas in which the coupled-out light waves of the projected image pass through towards the viewer&#39;s eye, the other non-illuminated areas  234  are the “slits” where the light waves from the external scene can pass through toward the eye, for see-through applications. Consequently, the ratio between the brightness of the projected image and that of the external scene can be controlled by setting the proper fill-factor of the projected areas  230 , accordingly. In addition, the reflectance of the reflecting surfaces  225  can be materialized by applying to the surfaces an optical adhesive having refractive index which is lower than that of the prism  226 , such that the oblique angles of incident of the coupled-out light waves on the reflecting surfaces  225  will be higher than the critical angle to yield total internal reflection of the light waves from the surfaces. The “trimmed array” embodiment illustrated in  FIG.  25 C , deflecting the coupled-out light into the viewer&#39;s eye, can also be applied to the embodiments illustrated in  FIG.  5 C . This means that the reflecting surfaces  79   i  (i=a, b . . . ) will no longer be located adjacent to each other, and the ratio between the brightness of the projected image and that of the external scene will be determined by setting the proper fill-factor of the reflecting surfaces  79   i  in the prism  80 , as well as by setting the reflectance of surfaces  79   i . In addition, the “trimmed array” embodiment can also be applied to the multi-reflecting surfaces embodiment illustrated in  FIG.  23 C . That is to say, the reflecting surfaces  264   i  (i=a, b . . . ) will no longer be adjacent to each other, and the ratio between the brightness of the light waves passing though the reflecting surfaces  264   i  to reach the viewer&#39;s eye and the light waves which are reflected by these surfaces to be coupled again into the substrate, will be determined by setting the proper fill-factor of the reflecting surfaces  264   i  in the prism  267 , as well as by setting the reflectance of surfaces  264   i.    
     The re-directing embodiment illustrated in  FIGS.  25 B and  25 C  is mainly appropriate for embodiments where the coupling-out surfaces are totally reflecting. For embodiments such as those illustrated in  FIGS.  23 A and  23 B , where part of the coupling-out elements are partially reflecting surfaces, care must be taken that light waves from the external scene will not penetrate the partially reflecting surface  200 , be reflected by surfaces  225  into the viewer&#39;s eye, and hence, create a ghost image. 
     In all the embodiments illustrated hereinabove, it was assumed that light waves having only the first and the second orders of axis-axis angles, propagate inside the substrate. There are systems, however, having comparatively small FOVs, where even the third order can be utilized. Referring to  FIG.  5 C  and assuming, for example, an optical system having the following parameters:
 
α sur1 =α sur2 =9°; F ″)={18°,27°}; F   (1) ={36°,45°}
 
 F   (2) ={54°,63°}; F   (3) ={72°,81°}  (54)
 
where the light waves are s-polarized, the optical material of the substrate is Schott N-SF57 having a refractive index of n d =1.846, and the optical adhesive which is used to cement the substrate  64  to the prism  80  is NTT-E3337 having refractive index of n d =1.42, wherein the interface plane  83  ( FIG.  5 D ) between substrate  64  and prism  80  covers the entire lower major surface  72 . The critical angle of the lower surface is therefore α cr   l =50.3. The interface between the substrate and the collimating element of the input light waves is an air gap and the critical angle of the upper surface is therefore α cr   u =32.8. All of the optical rays in the higher orders of F (2)  and F (3)  have off-axis angles higher than the critical angles and they are therefore totally reflected from the interface plane  83 , as well as from the upper surface  70 . In addition, the light waves in the first order are totally reflected from the upper surface  70 , and hence, they can be used to create the second and the third orders during the coupling-in process. On the other hand, all the optical rays in the first order impinge on the interface plane  83  at an incident angle lower than the critical angle there, and hence, they cannot propagate inside the substrate by total internal reflection. In addition, during the coupling-out process the light waves which are transferred to the first order by the reflections of the higher orders from surface  67  pass through the interface plane  83  and are coupled out from the substrate  64  as the output light waves by the coupling-out element  67 . The input light waves are in the zero order of F (0) , the output light waves are in the first order of F (1)  while the light waves that propagate inside the substrate are in the higher orders of F (2)  and F (3) . Consequently, since the width of the input light waves required to create the higher orders is much narrower than that of the coupled-out first order, the actual input aperture of the system will be substantially smaller that the output aperture.
 
     As illustrated in  FIG.  26   , an input ray  250  impinges on substrate  64  having an off-axis angle α in   (0) . After three reflections from surface  65  at points  252   a ,  252   b  and  252   c , this ray is coupled inside the substrate and propagates inside it having the third order off-axis angle of α in   (3) . After a few reflections from the major surfaces of the substrate  64 , the ray  250  impinges on surface  67 . After two reflections from the surface at points  254   a  and  254   b  it is coupled out from the substrate  64  having an off-axis angle α in   (1) . The light ray  250  is then reflected by surface  79   a , substantially normal to the substrate&#39;s major surface into the viewer&#39;s eye  24 . 
       FIGS.  27   a  and  27   b    illustrate a method for fabricating the required transparent substrates. First, a group of prisms  236  is manufactured, having the required dimensions. These prisms can be fabricated from silicate-based materials, such as Schott SF-57 with the conventional techniques of grinding and polishing, or alternatively, they can be made of polymer or sol-gel materials using injection-molding or casting techniques. The appropriate surfaces of these prisms are then coated with the required optical coatings  237 . Finally, the prisms are glued together to form the desired substrate  238 . In applications in which the quality of the optical surfaces is critical, the final step of polishing the outer surfaces, or at least part of them, can be added to the process. 
       FIGS.  28   a - 28   e    illustrate another method for fabricating the transparent substrates. A plurality of transparent flat plates  239  coated with the appropriate optical coatings  240  step (a) (if required) are cemented together using the appropriate optical adhesives so as to create a stacked form  242  step (b). A number of segments  244  step (c) are then sliced off the stacked form by cutting, grinding and polishing, to create the desired substrates  246  step (d). Several elements  248  can be cut-off from each slice  246 , as shown by a top view of step (e).  FIGS.  27  and  28    illustrate methods for fabricating substrates having only two reflecting surfaces. For other embodiments, such as those illustrated in  FIG.  12  or  23   , where other reflecting surfaces are embedded inside the substrates, a larger number of prisms ( FIG.  27   ) or flat plates ( FIG.  28   ) should be added to the fabrication process accordingly. 
       FIGS.  5 - 26    illustrate various features which can be added to the basic configuration illustrated in  FIGS.  4 A- 4 B , including: various types of folding reflecting surfaces ( FIGS.  5  and  25   ); external correcting lenses ( FIGS.  8 A- 8 C ); blocking of the non-active part of the coupling-out elements ( FIGS.  9 A- 9 C ); a special compensation design ( FIG.  9 D ); combining of a few substrate together ( FIGS.  11 ,  18 ,  20  and  23 B ); embedding an angular sensitive reflecting surface in the substrate for reducing the input aperture ( FIGS.  12 A- 12 B ) or for mixing the coupled-in light waves ( FIGS.  12 C- 12 D ); adding different coupling-in elements ( FIGS.  15 A- 15 B ); cementing a thin transparent plate to one (or more) of the major surfaces of the substrate to mix the coupled-in light waves ( FIGS.  16 B- 16 C ); utilizing angular sensitive coupling-in surfaces for increasing the brightness of the optical system ( FIGS.  18  and  20   ); embedding partially reflecting surfaces inside the substrate or next to the major surfaces of the substrate to increase the output aperture of a single substrate ( FIGS.  23 A- 23 C ) and using more than two propagation orders of the coupled light waves inside the substrate ( FIG.  26   ). Eventually, any combination of any number of these features can be added together to the basic embodiment which is illustrated in  FIGS.  4 A- 4 B , according to the specific requirements of the optical system. 
     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.