Patent Publication Number: US-2023148263-A1

Title: Optical system

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     This application is a divisional filing of U.S. application Ser. No. 16/476,634, filed Jul. 9, 2019, now allowed, which is a national stage filing under 35 C.F.R. 371 of PCT/IB2018/051353, filed Mar. 2, 2018, which claims the benefit of U.S. Provisional Application No. 62/468,579, filed Mar. 8, 2017, the disclosures of which are incorporated by reference in their entireties herein. 
    
    
     TECHNICAL FIELD 
     This disclosure relates generally to an optical system and to optical components and methods relevant folded optics. 
     BACKGROUND 
     Many displays, including virtual reality (VR) displays, attempt to present realistic images that replicate a real or imaginary environment. In some applications, VR displays attempt to provide immersive simulation of a three-dimensional environment. 
     BRIEF SUMMARY 
     Some embodiments involve an optical system for displaying an image to a viewer. The system includes a plurality of optical lenses comprising first, second, and third optical lenses. The second lens is disposed between the first and third lenses. Each of the first and second lenses has an optical birefringence less than about 20 nm/cm. The third lens has an optical birefringence greater than about 10 nm/cm. Each lens has opposing first and second major surfaces. The first and second major surfaces of the first lens are substantially spherical and concave toward each other. The first major surface has a radius of curvature in a range from about 10 mm to about 500 mm. The second major surface has a radius of curvature in a range from about 16 mm to about 1500 mm. The first major surface of the second lens is substantially spherical, adjacent to and concave toward the second major surface of the first lens. The first major surface of the second lens has a radius of curvature greater than about 16 mm to about 1500 m. The first major surface of the third lens is adjacent to and convex toward the second major surface of the second lens. The first major surface of the third lens has a radius of curvature in a range from about 14 mm to about 800 mm. The second major surface of the third lens is convex toward the first major surface of the third lens, and has a radius of curvature in a range from about 18 mm to about 1300 mm. The optical system also includes a partial reflector having an average optical reflectance of at least 30% in a predetermined wavelength range. A reflective polarizer substantially reflects light having a first polarization state and substantially transmits light having an orthogonal second polarization state in the predetermined wavelength range. A first retarder layer is disposed on and conforms to the substantially flat second major surface of the second lens. 
     Some embodiments involve an optical system for displaying an image to a viewer. The system includes a plurality of optical lenses comprising at least one first lens that includes a glass and at least one second lens that includes a plastic. A partial reflector is disposed on and conforms to a curved major surface of the at least one first lens and has an average optical reflectance of at least 30% in a predetermined wavelength range. A reflective polarizer is disposed on and conforms to a curved major surface of the at least one second lens. The reflective polarizer substantially reflects light having a first polarization state and substantially transmits light having an orthogonal second polarization state in the predetermined wavelength range. A first retarder layer is disposed on and conforms to a major surface of plurality of optical lenses between the reflective polarizer and the partial reflector. The system also includes an exit pupil defining an opening therein. The optical system has an optical axis. A light ray propagates along the optical axis passing through the plurality of optical lenses, the partial reflector, the reflective polarizer, and the first retarder layer without being substantially refracted. For a cone of light incident on the optical system from an object comprising a spatial frequency of about 70, or about 60, or about 50, or about 40, or about 30 line pairs per millimeter, filling the exit pupil with a chief ray of the cone of light passing through a center of the opening of the exit pupil and making an angle (θ) of about 20 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.2. 
     Some embodiments are directed to an optical system for displaying an image to a viewer. The system includes an imager emitting an image. An exit pupil defines an opening therein. The image emitted by the imager exits the optical system through the opening of the exit pupil. A plurality of optical lenses is disposed between the imager and the exit pupil and receives the emitted image from the imager. The optical lenses include first, second, and third optical lenses. The third lens has an optical birefringence greater than about 10 nm/cm. The first and second lens each have an optical birefringence less than about 7 nm/cm and bonded to each other to form a doublet. A partial reflector is disposed on and conforms to a curved major surface of the doublet and has an average optical reflectance of at least 30% in a predetermined wavelength range. A reflective polarizer is disposed on and conforms to a curved major surface of the third lens. The reflective polarizer substantially reflects light and has a first polarization state and substantially transmits light having an orthogonal second polarization state in the predetermined wavelength range. A first retarder layer is disposed on and conforms to a major surface of the doublet. For a cone of light from an image emitted by the imager, the image comprises a spatial frequency of about 70 or about 60 or about 50 or about 40 or about 30 line pairs per millimeter, fills the exit pupil. A chief ray of the cone of light passes through a center of the opening of the exit pupil and makes an angle of about 40 degrees with an optical axis of the optical system. A modulation transfer function (MTF) of the optical system is greater than about 0.15. 
     These and other aspects of the present application will be apparent from the detailed description below. In no event, however, should the above summaries be construed as limitations on the claimed subject matter, which subject matter is defined solely by the attached claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIGS.  1 A- 1 D  are diagrams illustrating folded optical systems in which a light beam is bent as it traverses the system so that the optical path of the light is longer than the length of the system in accordance with some embodiments; 
         FIG.  2 A  shows an imager in accordance with some embodiments; 
         FIG.  2 B  shows the opening of the exit pupil of an optical system of in accordance with some embodiments; 
         FIG.  3    shows a family of curves representing the modulation transfer function (Modulus of optical transfer function (OTF)) plotted along the y axis as a function of the spatial frequency in cycles per millimeter (also referred to as line pairs per millimeter) along the x-axis for an optical system in accordance with some embodiments; 
         FIG.  4    shows an optical system in which a chief ray of the cone of light from an object passes through the center of the opening of the exit pupil and makes an angle of about 20 degrees with the optical axis; 
         FIG.  5    shows an optical system in which a chief ray of the cone of light from an object passes through the center of the opening of the exit pupil and makes an angle of about 40 degrees with the optical axis; 
         FIG.  6    shows an optical system in which a chief ray of the cone of light from an object passes through the center of the opening of the exit pupil and makes an angle of about 45 degrees with the optical axis; 
         FIG.  7    shows an optical system in which a chief ray of the cone of light from an object passes through the center of the opening of the exit pupil and makes an angle of about 55 degrees with the optical axis; and 
         FIG.  8    shows an optical system in which a chief ray of the cone of light from an object passes through the center of the opening of the exit pupil and makes an angle of about zero degrees with the optical axis. 
     
    
    
     The figures are not necessarily to scale. Like numbers used in the figures refer to like components. However, it will be understood that the use of a number to refer to a component in a given figure is not intended to limit the component in another figure labeled with the same number. 
     DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS 
       FIG.  1 A  is a diagram illustrating a folded optical system  200  in which a light beam is bent as it traverses the system so that the optical path of the light is longer than the length of the system. Optical systems disclosed herein employ folded optics and are useful for headmounted displays, such as virtual reality displays, and cameras, such as cameras included in a cell phone, for example. The disclosed optical systems include a reflective polarizer, multiple lenses, and/or a retarder disposed between a stop surface (e.g., an exit pupil or an entrance pupil) and an image surface (e.g., a surface of a display panel or a surface of an image recorder). These systems can provide an optical system having a high field of view, a high contrast, a low chromatic aberration, a low distortion, and/or a high efficiency in a compact configuration that is useful in various applications. 
     It can be desirable for a compact optical system for virtual reality applications to have high resolution (small spot size), and a wide field of view (FOV). The wide field of view provides for an immersive experience for the viewer. The small spot size makes the images sharp and clear. When traversing through the optical system from the image to the exit pupil, the spot size increases due to various aberrations including spherical aberrations, comatic aberrations, astigmatism, etc. Aberrations of the lenses and the wave-like nature of light cause light originating from one point of the image  11  (see e.g.,  FIG.  1 A ) to be distributed over an area around the ideal point at the exit pupil opening  111 . Such aberrations should be reduced to provide the desirable aspects of small spot size with a large field of view. 
     The modulation optical transfer function (MTF) is a measure of image quality characterizing the ability of an optical system to transfer contrast from an image  11  to the exit pupil opening  111 . The MTF is related spot size by Fourier transformation from the spatial domain (spot size) to the frequency domain (MTF). The MTF (and spot size) of an optical system can be expressed as a function of spatial frequency. Spatial frequency quantifies the level of detail present in an image at the exit pupil opening and is often specified in units of line pairs per mm. High spatial frequency images have a larger amount of detail than images of lower spatial frequency. MTF can be determined for tangential and sagittal orientations at different wavelengths of light and at different angles of light with respect to the optical axis. 
     Some embodiments disclosed herein are directed to folded optical systems that have a specified, e.g., high, MTF at a predetermined spatial frequency. The systems disclosed herein include multiple lenses with optical qualities that, when used in conjunction with a reflective polarizer and at least one retarder layer, provide for the MTFs that enhance the viewer experience of an immersive three dimensional virtual environment. 
       FIG.  1 A  is a side view diagram of an optical system  200  in accordance with some embodiments. The optical system  200  is configured to display an image  11  to a viewer  210  through an opening  111 . The first lens  20  is configured to receive the image  11  from an imager  10 . In some configurations, the image incident on the first lens  20  is elliptically polarized. In some configurations, the image incident on the first lens  20  is circularly polarized. 
     Each lens  20 ,  30 ,  40  has opposing first  21 ,  31 ,  41  and second  22 ,  32 ,  42  major surfaces. The first  21  and second  22  major surfaces of the first lens  20  may be substantially spherical and concave toward each other. The first major surface  21  of the first lens  20  can have a radius of curvature in a range from about 10 mm to about 500 mm. The second major surface  22  of the first lens  20  can have a radius of curvature in a range from about 16 mm to about 1500 mm. The first lens  20  can have an index of refraction of about 1.52 at about 550 nm or at 587.6 nm, for example. 
     The first major surface  31  of the second lens  30  may be substantially spherical, adjacent to, and concave toward the second major surface  22  of the first lens  20 . In some configurations, the first major surface  31  of the second lens  30  is bonded to the second major surface  22  of the first lens  20 , e.g., via an optical adhesive. 
     The first major surface  31  of the second lens  30  may have a radius of curvature greater than about 16 mm to about 1500 mm. The second major surface  32  of the second lens  30  can be substantially flat in some configurations. The second major surface  32  of the second lens  30  may have a radius of curvature greater than about 100 mm or even greater than 2000 mm, for example. According to some embodiments, the radius of curvature of the first major surface  31  of the second lens  30  is substantially equal to the radius of curvature of the second major surface  22  of the first lens  20 . In some configurations, the second lens  30  may have an index of refraction of about 1.62 at about 550 nm, e.g., at 587.6 nm. 
     The first major surface  41  of the third lens  40  can be adjacent to and convex toward the second major surface  32  of the second lens  30 . The first major surface  41  of the third lens  40  may have a radius of curvature in a range from about 14 mm to about 800 mm. The second major surface  42  of the third lens  40  may be convex toward the first major surface  41  of the third lens  40 . The second major surface  42  of the third lens  40  can have a radius of curvature in a range from about 18 mm to about 1300 mm. In some embodiments, the third lens  40  has an index of refraction of about 1.49 at about 550 nm, e.g., 587.6 nm. 
     The system  200  includes a partial reflector  50  that is disposed on and conforms to the first curved major surface  21  of the first lens  20 . According to some embodiments, the partial reflector  50  may have an average optical reflectance of at least 30% in a predetermined wavelength range. 
     A reflective polarizer  60  is disposed on and conforms to the first major surface  41  of the third lens  40 . The reflective polarizer  60  substantially reflects light having a first polarization state and substantially transmits light having an orthogonal second polarization state in the predetermined wavelength range. 
     A first retarder layer  70  is disposed on and conforms to the second major surface  32  of the second lens  30 . The first retarder layer  70  can be substantially a quarter wave retarder at at least one wavelength in the predetermined wavelength range in some embodiments. Some configurations of the optical system  200  include a second retarder layer  90 , wherein the first lens  20  is disposed between the second lens  30  and the second retarder layer  90 . Optionally, the optical system  200  includes a first linear absorbing polarizer  80 . For example, the second retarder layer  90  may be disposed between the first lens  20  and the first linear absorbing polarizer  80 . Optionally, the optical system  200  includes a linear absorbing polarizer  100 , wherein the third lens  40  is disposed between the linear absorbing polarizer  100  and the reflective polarizer  60 . 
     In some embodiments, the optical system includes each of the second retarder layer  90 , the first linear absorbing polarizer  80 , and the second linear absorbing polarizer  100 . The first lens  20  is disposed between the second lens  30  and the second retarder layer  90 . The second retarder layer  90  is disposed between the first lens  20  and the first linear absorbing polarizer  80 . The third lens  40  is disposed between the second linear absorbing polarizer  100  and the reflective polarizer  60 . 
     In some configurations, the predetermined wavelength range may comprise a wavelength of about 550 nm, e.g., may comprise the wavelength 587.6 nm. The predetermined wavelength range may extend from about 400 nm to about 700 nm in some embodiments. For example, the predetermined wavelength can include a blue primary color wavelength, a green primary color wavelength and a red primary color wavelength. 
     The optical system  200  has an optical axis  220 . The optical system is configured such that a light ray propagating along the optical axis  220  passes through the plurality of optical lenses  20 ,  30 ,  40 , the partial reflector  50 , the reflective polarizer  60 , and the first retarder layer  70  without being substantially refracted. In some configurations, at least one of the plurality of optical lenses  20 ,  30 ,  40 , the partial reflector  50 , the reflective polarizer  60 , and the first retarder layer  70  is rotationally symmetric. In some configurations, at least one of the plurality of optical lenses  20 ,  30 ,  40 , the partial reflector  50 , the reflective polarizer  60 , and the first retarder layer  70  is non-rotationally symmetric. For example, at least one of the plurality of optical lenses  20 ,  30 ,  40 , the partial reflector  50 , the reflective polarizer  60 , and the first retarder layer  70  may have at least one plane of symmetry. 
     As shown in  FIG.  1 A , the optical system  200  can includes a plurality of optical lenses, e.g., at least at least first  20 , second  30  and third  40  optical lenses. The second lens  30  is disposed between the first  20  and third  40  lenses. Each of the first  20  and second  30  lenses may have an optical birefringence less than about 20 nm/cm. The third lens  40  may have an optical birefringence greater than about 10 nm/cm. 
     According to some implementations, each of the first  20  and second  30  lenses has an optical birefringence less than about 15 nm/cm, less than about 10 nm/cm, less than about 7 nm/cm, or even less than about 5 nm/cm. The third lens  40  may have an optical birefringence greater than about 15 nm/cm or greater than about 20 nm/cm. The optical birefringence values cited herein for the first and second lenses provide for reduced leakage of the non-imaging rays through the reflective polarizer. The second major surface  32  of the second lens  30  may have a radius of curvature greater than about 2000 mm, for example. 
     The one or more of the lenses  20 ,  30 ,  40 , of the optical system  200  may be made of any suitable material such as glass. For example, one or more of the lenses e.g., the first and/or second lenses may comprise one or more of a borosilicate BK7 glass, a lanthanum crown LAK34, a lanthanum flint LAF7 glass, a flint F2 glass, a dense flint SF2, a lanthanum dense flint LASF45, and a fluorophosphate FPL51 and a fluorophosphate FPL55 glass. 
     The index of refraction of the material of the first lens  20  may be about 1.44, or about 1.50 or about 1.52 at wavelengths of about 550 nm, e.g., 587.6 nm. The first lens  20  may comprise one of more of a borosilicate BK7 glass, a fluorophosphate FPL51 glass, and a fluorophosphate FPL55 glass, for example. 
     The index of refraction of the material of the second lens  30  may be about 1.65 or about 1.73, or about 1.75, or about 1.80 at wavelengths of about 550 nm, e.g., 587.6 nm. The second lens  30  may comprise one or more of a dense flint SF2 glass, a lanthanum dense flint LASF45 glass, a lanthanum crown LAK34 glass, a lanthanum crown LAK33B glass, a lanthanum crown LAK33A glass, a lanthanum crown LAF7 glass, lanthanum flint LAK34 glass, a lanthanum flint LAF7 glass, and a flint F2 glass, for example. 
     Example combination configurations for the first  20  and second  30  lenses include: 1) the first lens  20  comprises a borosilicate BK7 glass having an index of refraction of about 1.52 at about 550 nm, e.g., 587.6 nm, and the second lens  30  comprises a dense flint SF2 glass having an index of refraction of about 1.65 at about 587.6 nm; 2) the first lens  20  comprises a fluorophosphate FPL51 glass having an index of refraction of about 1.50 at about 550 nm, e.g., 587.6 nm, and the second lens  30  comprises a lanthanum dense flint LASF45 glass having an index of refraction of about 1.80 at about 550 nm, e.g., 587.6 nm; 3) the first lens  20  comprises a fluorophosphate FPL51 glass having an index of refraction of about 1.50 at about 550 nm, e.g., 587.6 nm, and the second lens  30  comprises a lanthanum crown LAK34 glass having an index of refraction of about 1.73 at about 550 nm, e.g., 587.6 nm; 4) the first lens  20  comprises a fluorophosphate FPL51 glass having an index of refraction of about 1.50 at about 550 nm, e.g., 587.6 nm, and the second lens  30  comprises a lanthanum crown LAK33B glass having an index of refraction of about 1.76 at about 550 nm, e.g., 587.6 nm; 5) the first lens  20  comprises a fluorophosphate FPL51 glass having an index of refraction of about 1.50 at about 550 nm, e.g., 587.6 nm, and the second lens  30  comprises a lanthanum crown LAK33A glass having an index of refraction of about 1.75 at about 550 nm, e.g., 587.6 nm; 6) the first lens  20  comprises a fluorophosphate FPL55 glass having an index of refraction of about 1.44 at about 550 nm, e.g., 587.6 nm, and the second lens  30  comprises a lanthanum crown LAK34 glass having an index of refraction of about 1.73 at about 550 nm, e.g., 587.6 nm; 7) the first lens  20  comprises a fluorophosphate FPL51 glass having an index of refraction of about 1.50 at about 550 nm, e.g., 587.6 nm, and the second lens  30  comprises a lanthanum crown LAF7 glass having an index of refraction of about 1.75 at about 550 nm, e.g., 587.6 nm; 8) the first lens  20  comprises a fluorophosphate FPL55 glass having an index of refraction of about 1.44 at about 550 nm, e.g., 587.6 nm, and the second lens  30  comprises a lanthanum flint LAK34 glass having an index of refraction of about 1.73 at about 550 nm, e.g., 587.6 nm; 9) first lens  20  comprises a fluorophosphate FPL55 glass having an index of refraction of about 1.44 at about 550 nm, e.g., 587.6 nm, and the second lens  30  comprises a lanthanum flint LAF7 glass having an index of refraction of about 1.75 at about 550 nm, e.g., 587.6 nm; 10) the first lens  20  comprises a borosilicate BK7 glass having an index of refraction of about 1.52 at about 550 nm, e.g., 587.6 nm, and the second lens  30  comprises a flint F2 glass having an index of refraction of about 1.62 at about 550 nm, e.g., 587.6 nm. 
     The third lens  40  may be made of plastic, such as one or more of polymethylmethacrylate (PMMA), a polystyrene, a polyvinyl alcohol, and a polycarbonate. In some embodiments, the third lens  40  has an index of refraction of about 1.49 at about 550 nm, e.g., 587.6 nm. 
     As shown in  FIG.  1 A , the imager  10  can be disposed adjacent to and facing the first lens  20 . The imager  10  emits the image  11  which is incident on the first lens  20 . An exit pupil  110  is disposed adjacent and facing the third lens  40  and defines an opening  111  therein. The image  11  incident on the first lens  20  exits the optical system  200  through the opening  111  in the exit pupil  110 . The image  11  incident on the first lens  20  may be elliptically polarized. The exiting image at the opening  111  may be substantially linearly polarized. 
       FIG.  1 B  shows an optical system  201  that is similar in many respects to the optical system  200  of  FIG.  1 A . Optical system  201  differs at least in that system  201  does not include the second linear absorbing polarizer (element  100  in  FIG.  1 A ). 
       FIG.  1 C  shows another optical system  202  that has some similarities to  FIG.  1 A . The optical system  202  includes a half mirror  51  disposed on and conforming to the first major surface  41  of the third lens  40 . The system  202  also includes a reflective polarizer  61  disposed on and conforming to the first major surface  21  of the first lens. In the system  202 , the second retarder layer  90  is disposed adjacent to the exit pupil  110 . The first linear absorbing polarizer  80  is disposed between the second retarder layer  90  and the third lens  40 . 
       FIG.  1 D  shows yet another optical system  203  in accordance with some embodiments.  FIG.  1 D  is similar in many respects to the system  202  of  FIG.  1 C . System  203  also includes a second linear absorbing polarizer  100  disposed between the imager  10  and the first lens  20 . 
     As shown in  FIG.  2 A , the imager can be substantially a polygon.  FIG.  2 B  shows the opening  111  of the exit pupil  110  which is substantially circular. As shown in  FIGS.  2 A and  2 B , a maximum lateral dimension of an active region of the imager is D (see  FIG.  2 A ) and a maximum lateral dimension of the opening of the exit pupil is d (see  FIG.  2 B ). In some embodiments the ratio D/d is between about 1 and about 20, e.g., 1≤D/d≤20. In some embodiments, the ratio of D/d is between about 2 and about 15, e.g., 2≤D/d≤15. In some embodiments the ratio of D/d is between about 5 and about 10, e.g., 5≤D/d≤10. 
     The maximum lateral dimension of the opening  111  of the exit pupil  110  can be in a range from about 2 mm to about 10 mm or in a range from about 2 mm to about 80 mm. A separation between the exit pupil  110  and the third lens  40  can be in a range from about 5 mm to about 30 mm or in a range from about 10 mm to about 20 mm, for example. 
     According to some embodiments, the optical system  200  provides a specified modulation transfer function.  FIG.  3    shows a family of curves representing the modulation transfer function (Modulus of optical transfer function (OTF)) plotted along the y axis as a function of the spatial frequency in cycles per millimeter (also referred to as line pairs per millimeter) along the x-axis. The family of curves provides the MTF vs. spatial frequency for the optical system for various angles of light at the exit pupil opening  111  with respect to the optical axis  220  of the optical system  200 . As indicated in  FIG.  3   , the MTF vs. spatial frequency curves are plotted for 0, 20, 40, 45, and 55 degree angles of light at the exit pupil opening  111  for both transverse (T) and sagittal (S) orientations. 
     Referring again to  FIG.  1 A , some embodiments involve an optical system  200  for displaying an image  11  to a viewer  210 . The system  200  includes a plurality of optical lenses including at least one first lens  20 ,  30  comprising a glass and at least one second lens  40  comprising a plastic. A partial reflector  50  is disposed on and conforms to a curved major surface  21  of the at least one first lens  20 . The partial reflector  50  may have an average optical reflectance of at least 30% in a predetermined wavelength range. The system  200  also includes a reflective polarizer  60  disposed on and conforming to a curved major surface  41  of the at least one second lens. The reflective polarizer  60  substantially reflects light having a first polarization state and substantially transmits light having an orthogonal second polarization state in the predetermined wavelength range. A first retarder layer  70  is disposed on and conforms to a major surface  32  of plurality of optical lenses  20 ,  30 ,  40  between the reflective polarizer  60  and the partial reflector  50 . An exit pupil  110  of the system  200  defines an opening  111 . 
     The optical system  200  has an optical axis  220 . A light ray propagating along the optical axis  220  passes through the plurality of optical lenses  20 ,  30 ,  40 , the partial reflector  50 , the reflective polarizer  60 , and the first retarder layer  70  without being substantially refracted. 
     As shown in  FIG.  4   , a cone of light  300  is incident on the optical system  200  from an object  310  may comprise a spatial frequency of about 70 line pairs per millimeter, the cone of light filling the opening  111  of the exit pupil  110 . A chief ray  320  of the cone of light  300  passes through a center  330  of the opening  111  of the exit pupil  110  and makes an angle (θ) of about 20 degrees with the optical axis  220 . A modulation transfer function (MTF) of the optical system  200  can be greater than about 0.2, or greater than about 0.25, or even greater than about 0.3. 
     A cone of light  300  is incident on the optical system  200  from an object  310  may comprise a spatial frequency of about 60 line pairs per millimeter, the cone of light filling the opening  111  of the exit pupil  110 . A chief ray  320  of the cone of light  300  passes through a center  330  of the opening  111  of the exit pupil  110  and makes an angle (θ) of about 20 degrees with the optical axis  220 . A modulation transfer function (MTF) of the optical system  200  can be greater than about 0.2, or greater than about 0.25, or even greater than about 0.3. 
     A cone of light  300  is incident on the optical system  200  from an object  310  may comprise a spatial frequency of about 50 line pairs per millimeter, the cone of light filling the opening  111  of the exit pupil  110 . A chief ray  320  of the cone of light  300  passes through a center  330  of the opening  111  of the exit pupil  110  and makes an angle (θ) of about 20 degrees with the optical axis  220 . A modulation transfer function (MTF) of the optical system  200  can be greater than about 0.2, or greater than about 0.25, or even greater than about 0.3. 
     A cone of light  300  is incident on the optical system  200  from an object  310  may comprise a spatial frequency of about 40 line pairs per millimeter, the cone of light filling the opening  111  of the exit pupil  110 . A chief ray  320  of the cone of light  300  passes through a center  330  of the opening  111  of the exit pupil  110  and makes an angle (θ) of about 20 degrees with the optical axis  220 . A modulation transfer function (MTF) of the optical system  200  can be greater than about 0.2, or greater than about 0.25, or even greater than about 0.3. 
     A cone of light  300  is incident on the optical system  200  from an object  310  comprising a spatial frequency of about 30 line pairs per millimeter, the cone of light filling the opening  111  of the exit pupil  110 . A chief ray  320  of the cone of light  300  passes through a center  330  of the opening  111  of the exit pupil  110  and makes an angle (θ) of about 20 degrees with the optical axis  220 . A modulation transfer function (MTF) of the optical system  200  can be greater than about 0.2, or greater than about 0.25, or even greater than about 0.3. 
     Referring now to  FIG.  5   , a cone of light  301  is incident on the optical system  200  from an object  311  and may comprise a spatial frequency of about 70 line pairs per millimeter. The cone of light  301  fills the opening  111  of the exit pupil  110 . A chief ray  321  of the cone of light  301  passes through the center  330  of the opening  110  of the exit pupil  111  and makes an angle (θ) of about 40 degrees with the optical axis  220 , according to some embodiments, the modulation transfer function (MTF) of the optical system  200  may be greater than about 0.1, or greater that about 0.15, or even greater than 0.2. 
     A cone of light  301  is incident on the optical system  200  from an object  311  and may comprise a spatial frequency of about 60 line pairs per millimeter. The cone of light  301  fills the opening  111  of the exit pupil  110 . A chief ray  321  of the cone of light  301  passes through the center  330  of the opening  110  of the exit pupil  111  and makes an angle (θ) of about 40 degrees with the optical axis  220 . According to some embodiments, the modulation transfer function (MTF) of the optical system  200  may be greater than about 0.1, or greater that about 0.15, or even greater than 0.2. 
     A cone of light  301  is incident on the optical system  200  from an object  311  and may comprise a spatial frequency of about 50 line pairs per millimeter. The cone of light  301  fills the opening  111  of the exit pupil  110 . A chief ray  321  of the cone of light  301  passes through the center  330  of the opening  110  of the exit pupil  111  and makes an angle (θ) of about 40 degrees with the optical axis  220 . According to some embodiments, the modulation transfer function (MTF) of the optical system  200  may be greater than about 0.1, or greater that about 0.15, or even greater than 0.2. 
     A cone of light  301  is incident on the optical system  200  from an object  311  and may comprise a spatial frequency of about 40 line pairs per millimeter. The cone of light  301  fills the opening  111  of the exit pupil  110 . A chief ray  321  of the cone of light  301  passes through the center  330  of the opening  110  of the exit pupil  111  and makes an angle (θ) of about 40 degrees with the optical axis  220 . According to some embodiments, the modulation transfer function (MTF) of the optical system  200  may be greater than about 0.1, or greater that about 0.15, or even greater than 0.2. 
     A cone of light  301  is incident on the optical system  200  from an object  311  and may comprise a spatial frequency of about 30 line pairs per millimeter. The cone of light  301  fills the opening  111  of the exit pupil  110 . A chief ray  321  of the cone of light  301  passes through the center  330  of the opening  110  of the exit pupil  111  and makes an angle (θ) of about 40 degrees with the optical axis  220 . According to some embodiments, the modulation transfer function (MTF) of the optical system  200  may be greater than about 0.1, or greater that about 0.15, or even greater than 0.2. 
     Referring to  FIG.  6   , a cone of light  302  is incident on the optical system  200  from an object  312  may comprise a spatial frequency of about 70 line pairs per millimeter. The cone of light  302  fills the opening  111  of the exit pupil  110 . A chief ray  322  of the cone of light  302  passes through the center  330  of the opening  110  of the exit pupil  111  and makes an angle (θ) of about 45 degrees with the optical axis  220 . according to some embodiments, the modulation transfer function (MTF) of the optical system  200  may be greater than about 0.1, or greater that about 0.15, or even greater than 0.2. 
     A cone of light  302  is incident on the optical system  200  from an object  312  may comprise a spatial frequency of about 60 line pairs per millimeter. The cone of light  302  fills the opening  111  of the exit pupil  110 . A chief ray  322  of the cone of light  302  passes through the center  330  of the opening  110  of the exit pupil  111  and makes an angle (θ) of about 45 degrees with the optical axis  220 . according to some embodiments, the modulation transfer function (MTF) of the optical system  200  may be greater than about 0.1, or greater that about 0.15, or even greater than 0.2. 
     A cone of light  302  is incident on the optical system  200  from an object  312  may comprise a spatial frequency of about 50 line pairs per millimeter. The cone of light  302  fills the opening  111  of the exit pupil  110 . A chief ray  322  of the cone of light  302  passes through the center  330  of the opening  110  of the exit pupil  111  and makes an angle (θ) of about 45 degrees with the optical axis  220 . according to some embodiments, the modulation transfer function (MTF) of the optical system  200  may be greater than about 0.1, or greater that about 0.15, or even greater than 0.2. 
     A cone of light  302  is incident on the optical system  200  from an object  312  may comprise a spatial frequency of about 40 line pairs per millimeter. The cone of light  302  fills the opening  111  of the exit pupil  110 . A chief ray  322  of the cone of light  302  passes through the center  330  of the opening  110  of the exit pupil  111  and makes an angle (θ) of about 45 degrees with the optical axis  220 . according to some embodiments, the modulation transfer function (MTF) of the optical system  200  may be greater than about 0.1, or greater that about 0.15, or even greater than 0.2. 
     A cone of light  302  is incident on the optical system  200  from an object  312  may comprise a spatial frequency of about 30 line pairs per millimeter. The cone of light  302  fills the opening  111  of the exit pupil  110 . A chief ray  322  of the cone of light  302  passes through the center  330  of the opening  110  of the exit pupil  111  and makes an angle (θ) of about 45 degrees with the optical axis  220 . according to some embodiments, the modulation transfer function (MTF) of the optical system  200  may be greater than about 0.1, or greater that about 0.15, or even greater than 0.2. 
     Referring to  FIG.  7   , a cone of light  303  is incident on the optical system  200  from an object  313  may comprise a spatial frequency of about 70 line pairs per millimeter. The cone of light  303  fills the opening  111  of the exit pupil  110 . A chief ray  323  of the cone of light  303  passes through the center  330  of the opening  110  of the exit pupil  111  and makes an angle (θ) of about 55 degrees with the optical axis  220 . According to some embodiments, the modulation transfer function (MTF) of the optical system  200  may be greater than about 0.1, or greater that about 0.15. 
     A cone of light  303  is incident on the optical system  200  from an object  313  may comprise a spatial frequency of about 60 line pairs per millimeter. The cone of light  303  fills the opening  111  of the exit pupil  110 . A chief ray  323  of the cone of light  303  passes through the center  330  of the opening  110  of the exit pupil  111  and makes an angle (θ) of about 55 degrees with the optical axis  220 . According to some embodiments, the modulation transfer function (MTF) of the optical system  200  may be greater than about 0.1, or greater that about 0.15. 
     A cone of light  303  is incident on the optical system  200  from an object  313  may comprise a spatial frequency of about 50 line pairs per millimeter. The cone of light  303  fills the opening  111  of the exit pupil  110 . A chief ray  323  of the cone of light  303  passes through the center  330  of the opening  110  of the exit pupil  111  and makes an angle (θ) of about 45 degrees with the optical axis  220 . According to some embodiments, the modulation transfer function (MTF) of the optical system  200  may be greater than about 0.1, or greater that about 0.15. 
     A cone of light  303  is incident on the optical system  200  from an object  313  may comprise a spatial frequency of about 40 line pairs per millimeter. The cone of light  303  fills the opening  111  of the exit pupil  110 . A chief ray  323  of the cone of light  303  passes through the center  330  of the opening  110  of the exit pupil  111  and makes an angle (θ) of about 55 degrees with the optical axis  220 . According to some embodiments, the modulation transfer function (MTF) of the optical system  200  may be greater than about 0.1, or greater that about 0.15. 
     A cone of light  303  is incident on the optical system  200  from an object  313  may comprise a spatial frequency of about 30 line pairs per millimeter. The cone of light  303  fills the opening  111  of the exit pupil  110 . A chief ray  323  of the cone of light  303  passes through the center  330  of the opening  110  of the exit pupil  111  and makes an angle (θ) of about 55 degrees with the optical axis  220 . According to some embodiments, the modulation transfer function (MTF) of the optical system  200  may be greater than about 0.1, or greater that about 0.15. 
     Referring to  FIG.  8   , a cone of light  304  is incident on the optical system  200  from an object  314  may comprise a spatial frequency of about 70 line pairs per millimeter. The cone of light  304  fills the opening  111  of the exit pupil  110 . A chief ray  324  of the cone of light  304  passes through the center  330  of the opening  110  of the exit pupil  111  and makes an angle (θ) of about 0 degrees with the optical axis  220 . According to some embodiments, the modulation transfer function (MTF) of the optical system  200  may be greater than about 0.5, greater that about 0.6, or even greater than about 0.68. 
     A cone of light  304  is incident on the optical system  200  from an object  314  may comprise a spatial frequency of about 60 line pairs per millimeter. The cone of light  304  fills the opening  111  of the exit pupil  110 . A chief ray  324  of the cone of light  304  passes through the center  330  of the opening  110  of the exit pupil  111  and makes an angle (θ) of about 0 degrees with the optical axis  220 . According to some embodiments, the modulation transfer function (MTF) of the optical system  200  may be greater than about 0.5, greater that about 0.6, or even greater than about 0.68. 
     A cone of light  304  is incident on the optical system  200  from an object  314  may comprise a spatial frequency of about 50 line pairs per millimeter. The cone of light  304  fills the opening  111  of the exit pupil  110 . A chief ray  324  of the cone of light  304  passes through the center  330  of the opening  110  of the exit pupil  111  and makes an angle (θ) of about 0 degrees with the optical axis  220 . According to some embodiments, the modulation transfer function (MTF) of the optical system  200  may be greater than about 0.5, greater that about 0.6, or even greater than about 0.68. 
     A cone of light  304  is incident on the optical system  200  from an object  314  may comprise a spatial frequency of about 40 line pairs per millimeter. The cone of light  304  fills the opening  111  of the exit pupil  110 . A chief ray  324  of the cone of light  304  passes through the center  330  of the opening  110  of the exit pupil  111  and makes an angle (θ) of about 0 degrees with the optical axis  220 . According to some embodiments, the modulation transfer function (MTF) of the optical system  200  may be greater than about 0.5, greater that about 0.6, or even greater than about 0.68. 
     A cone of light  304  is incident on the optical system  200  from an object  314  may comprise a spatial frequency of about 30 line pairs per millimeter. The cone of light  304  fills the opening  111  of the exit pupil  110 . A chief ray  324  of the cone of light  304  passes through the center  330  of the opening  110  of the exit pupil  111  and makes an angle (θ) of about 0 degrees with the optical axis  220 . According to some embodiments, the modulation transfer function (MTF) of the optical system  200  may be greater than about 0.5, greater that about 0.6, or even greater than about 0.68. 
     In the optical systems shown in  FIGS.  1 A- 1 D and  4 - 8   , the plurality of optical lenses can include two lenses  20 ,  30  comprising a glass and a lens  40  comprising a plastic. Each first lens  20 ,  30  can have an optical birefringence less than about 10 nm/cm, and each second lens  40  can have an optical birefringence greater than about 10 nm/cm in some implementations. 
     In some embodiments, lenses  20 ,  30  may form a doublet. According to this embodiment, a first major surface  31  of one first lens  30  may substantially conform to and be bonded to a major surface  22  of the other first lens  20 . 
     Referring again to  FIG.  1 A , some embodiments are directed to an optical system  200  for displaying an image  11  to a viewer  210 , wherein the system  200  includes an imager  10  emitting an image  11 . The system  200  includes an exit pupil  110  defining an opening  111  therein. The image  11  emitted by the imager  10  exits the optical system  200  through the opening  111  of the exit pupil  110 . A plurality of optical lenses, for example, first  20 , second  30 , and third  40  optical lenses, are disposed between the imager  10  and the exit pupil  110 . The plurality of optical lenses  20 ,  30 ,  40  receives the emitted image  11  from the imager  10 . The third lens  40  may have an optical birefringence greater than about 10 nm/cm. The first  20  and second  30  lenses may each have an optical birefringence less than about 7 nm/cm. The first  20  and second  30  lenses are bonded to each other to form a doublet. 
     The system  200  includes a partial reflector  50  disposed on and conforming to a curved major surface  21  of the doublet  20 ,  30 . The partial reflector  50  can have an average optical reflectance of at least 30% in a predetermined wavelength range. 
     The system  200  includes a reflective polarizer  60  disposed on and conforming to a curved major surface  41  of the third lens  40 . The reflective polarizer  60  substantially reflects light having a first polarization state and substantially transmits light having an orthogonal second polarization state in the predetermined wavelength range. 
     A first retarder layer  70  is disposed on and conforms to a major surface  32  of the doublet  20 ,  30 . 
     With reference to  FIG.  5   , a cone of light  301  from an image  11  that is emitted by the imager  10  may comprise a spatial frequency of about 70 line pairs per millimeter. The image fills the exit pupil  111 . A chief ray  321  of the cone  301  of light passes through a center  330  of the opening  111  of the exit pupil  110  and makes an angle of about 40 degrees with an optical axis  220  of the optical system  200 . The modulation transfer function (MTF) of the optical system  200  may be greater than about 0.15, for example. Other configurations, such as those discussed in connection with  FIGS.  4  and  6 - 8    are also possible. 
     Embodiments disclosed herein include: 
     Embodiment 1. An optical system for displaying an image to a viewer comprising: 
     a plurality of optical lenses comprising first, second, and third optical lenses, the second lens disposed between the first and third lenses, each of the first and second lenses having an optical birefringence less than about 20 nm/cm, the third lens having an optical birefringence greater than about 10 nm/cm, each lens having opposing first and second major surfaces, 
     the first and second major surfaces of the first lens substantially spherical and concave toward each other, the first major surface having a radius of curvature in a range from about 10 mm to about 500 mm, the second major surface having a radius of curvature in a range from about 16 mm to about 1500 mm, 
     the first major surface of the second lens substantially spherical, adjacent to and concave toward the second major surface of the first lens, and having a radius of curvature greater than about 16 mm to about 1500 mm, 
     the first major surface of the third lens adjacent to and convex toward the second major surface of the second lens, and having a radius of curvature in a range from about 14 mm to about 800 mm, the second major surface of the third lens convex toward the first major surface of the third lens, and having a radius of curvature in a range from about 18 mm to about 1300 mm; 
     a partial reflector having an average optical reflectance of at least 30% in a predetermined wavelength range; 
     a reflective polarizer substantially reflecting light having a first polarization state and substantially transmitting light having an orthogonal second polarization state in the predetermined wavelength range; and 
     a first retarder layer disposed on and conforming to the substantially flat second major surface of the second lens. 
     Embodiment 2. The optical system of embodiment 1, wherein: 
     the partial reflector is disposed on and conforms to the first curved major surface of the first lens; and 
     the reflective polarizer is disposed on and conforms to the first major surface of the third lens. 
     Embodiment 3. The optical system of embodiment 1, wherein the reflective polarizer is disposed on and conforms to the first major surface of the first lens.
 
Embodiment 4. The optical system of embodiment 1, wherein the partial reflector comprises a half mirror that is disposed on and conforms to the first major surface of the third lens.
 
Embodiment 5. The optical system of any of embodiments 1 through 4, wherein each of the first and second lenses has an optical birefringence less than about 15 nm/cm.
 
Embodiment 6. The optical system of any of embodiments 1 through 4, wherein each of the first and second lenses has an optical birefringence less than about 10 nm/cm.
 
Embodiment 7. The optical system of any of embodiments 1 through 4, wherein each of the first and second lenses has an optical birefringence less than about 7 nm/cm.
 
Embodiment 8. The optical system of any of embodiments 1 through 4, wherein each of the first and second lenses has an optical birefringence less than about 5 nm/cm.
 
Embodiment 9. The optical system of any of embodiments 1 through 4, wherein the third lens has an optical birefringence greater than about 15 nm/cm.
 
Embodiment 10. The optical system of any of embodiments 1 through 4, wherein the third lens has an optical birefringence greater than about 20 nm/cm.
 
Embodiment 11. The optical system of any of embodiments 1 through 10, wherein the second major surface of the second lens has a radius of curvature greater than about 2000
 
Embodiment 12. The optical system of any of embodiments 1 through 10, wherein the second major surface of the second lens is substantially flat.
 
Embodiment 13. The optical system of any of embodiments 1 through 10, wherein the second major surface of the second lens has a radius of curvature greater than about 100.
 
Embodiment 14. The optical system of any of embodiments 1 through 13, wherein the predetermined wavelength range comprises a wavelength of about 550 nm.
 
Embodiment 15. The optical system of any of embodiments 1 through 13, wherein the predetermined wavelength range comprises 587.6 nm.
 
Embodiment 16. The optical system of any of embodiments 1 through 13, wherein the predetermined wavelength range is from about 400 nm to about 700 nm.
 
Embodiment 17. The optical system of any of embodiments 1 through 13, wherein the predetermined wavelength comprises a blue primary color wavelength, a green primary color wavelength and a red primary color wavelength.
 
Embodiment 18. The optical system of any of embodiments 1 through 17, wherein the first and second lenses each comprises a glass.
 
Embodiment 19. The optical system of embodiment 18, wherein the glass comprises one or more of a borosilicate BK7 glass, a lanthanum crown LAK34, a lanthanum flint LAF7 glass, a flint F2 glass, a dense flint SF2, a lanthanum dense flint LASF45, a fluorophosphate FPL51 and a fluorophosphate FPL55 glass.
 
Embodiment 20. The optical system of any of embodiments 1 through 17, wherein the first lens has an index of refraction of about 1.52 and the second lens has an index of refraction of about 1.62 at about 550 nm.
 
Embodiment 21. The optical system of any of embodiments 1 through 17, wherein the first lens has an index of refraction of about 1.52 and the second lens has an index of refraction of about 1.62 at 587.6 nm.
 
Embodiment 22. The optical system of any of embodiments 1 through 17, wherein the first lens has an index of refraction of about 1.44 and the second lens has an index of refraction of about 1.75 at about 500 nm.
 
Embodiment 23. The optical system of any of embodiments 1 through 17, wherein the first lens has an index of refraction of about 1.44 and the second lens has an index of refraction of about 1.75 at 587.6 nm.
 
Embodiment 24. The optical system of claim  1 , wherein the first lens comprises a borosilicate BK7 glass having an index of refraction of about 1.52 at 587.6 nm, and the second lens comprises a flint F2 glass having an index of refraction of about 1.62 at 587.6 nm.
 
Embodiment 25. The optical system of any of embodiments 1 through 17, wherein the first lens comprises a borosilicate BK7 glass having an index of refraction of about 1.52 at about 587.6 nm, and the second lens comprises a dense flint SF2 glass having an index of refraction of about 1.65 at about 587.6 nm.
 
Embodiment 26. The optical system of any of embodiments 1 through 17, wherein the first lens comprises a fluorophosphate FPL51 glass having an index of refraction of about 1.50 at about 587.6 nm, and the second lens comprises a lanthanum dense flint LASF45 glass having an index of refraction of about 1.80 at about 587.6 nm.
 
Embodiment 27. The optical system of any of embodiments 1 through 17, wherein the first lens comprises a fluorophosphate FPL51 glass having an index of refraction of about 1.50 at about 587.6 nm, and the second lens comprises a lanthanum crown LAK34 glass having an index of refraction of about 1.73 at about 587.6 nm.
 
Embodiment 28. The optical system of any of embodiments 1 through 17, wherein the first lens comprises a fluorophosphate FPL51 glass having an index of refraction of about 1.50 at about 587.6 nm, and the second lens comprises a lanthanum crown LAK33B glass having an index of refraction of about 1.76 at about 587.6 nm.
 
Embodiment 29. The optical system of any of embodiments 1 through 17, wherein the first lens comprises a fluorophosphate FPL51 glass having an index of refraction of about 1.50 at about 587.6 nm, and the second lens comprises a lanthanum crown LAK33A glass having an index of refraction of about 1.75 at about 587.6 nm.
 
Embodiment 30. The optical system of any of embodiments 1 through 17, wherein the first lens comprises a fluorophosphate FPL55 glass having an index of refraction of about 1.44 at about 587.6 nm, and the second lens comprises a lanthanum crown LAK34 glass having an index of refraction of about 1.73 at about 587.6 nm.
 
Embodiment 31. The optical system of any of embodiments 1 through 17, wherein the first lens comprises a fluorophosphate FPL51 glass having an index of refraction of about 1.50 at about 587.6 nm, and the second lens comprises a lanthanum crown LAF7 glass having an index of refraction of about 1.75 at about 587.6 nm.
 
Embodiment 32. The optical system of any of embodiments 1 through 17, wherein the first lens comprises a fluorophosphate FPL55 glass having an index of refraction of about 1.44 at about 587.6 nm, and the second lens comprises a lanthanum flint LAK34 glass having an index of refraction of about 1.73 at about 587.6 nm.
 
Embodiment 33. The optical system of any of embodiments 1 through 17, wherein the first lens comprises a fluorophosphate FPL55 glass having an index of refraction of about 1.44 at about 587.6 nm, and the second lens comprises a lanthanum flint LAF7 glass having an index of refraction of about 1.75 at about 587.6 nm.
 
Embodiment 34. The optical system of any of embodiments 1 through 33, wherein the third lens comprises a plastic.
 
Embodiment 35. The optical system of embodiment 34, wherein the plastic comprises one or more of a polymethylmethacrylate (PMMA), a polystyrene, a polyvinyl alcohol, and a polycarbonate.
 
Embodiment 36. The optical system of any of embodiments 1 through 35, wherein the third lens has an index of refraction of about 1.49 at about 550 nm.
 
Embodiment 37. The optical system of any of embodiments 1 through 35, wherein the third lens has an index of refraction of about 1.49 at 587.6 nm.
 
Embodiment 38. The optical system of any of embodiments 1 through 35, wherein the third lens comprises polymethylmethacrylate (PMMA) having an index of refraction of about 1.49 at about 550 nm.
 
Embodiment 39. The optical system of any of embodiments 1 through 35, wherein the third lens comprises polymethylmethacrylate (PMMA) having an index of refraction of about 1.49 at 587.6 nm.
 
Embodiment 40. The optical system of any of embodiments 1 through 39, wherein the radius of curvature of the first major surface of the second lens is substantially equal to the radius of curvature of the second major surface of the first lens.
 
Embodiment 41. The optical system of any of embodiments 1 through 40, wherein the first major surface of the second lens is bonded to the second major surface of the first lens.
 
Embodiment 42. The optical system of any of embodiments 1 through 41, wherein the first major surface of the second lens is bonded to the second major surface of the first lens via an optical adhesive.
 
Embodiment 43. The optical system of any of embodiments 1 through 42, further comprising an optical axis, such that a light ray propagating along the optical axis passes through the plurality of optical lenses, the partial reflector, the reflective polarizer, and the first retarder layer without being substantially refracted.
 
Embodiment 44. The optical system of any of embodiments 1 through 43, wherein at least one of the plurality of optical lenses, the partial reflector, the reflective polarizer, and the first retarder layer is rotationally symmetric.
 
Embodiment 45. The optical system of any of embodiments 1 through 43, wherein at least one of the plurality of optical lenses, the partial reflector, the reflective polarizer, and the first retarder layer is non-rotationally symmetric.
 
Embodiment 46. The optical system of any of embodiments 1 through 43, wherein at least one of the plurality of optical lenses, the partial reflector, the reflective polarizer, and the first retarder layer has at least one plane of symmetry.
 
Embodiment 47. The optical system of any of embodiments 1 through 46, wherein the first retarder layer is substantially a quarter wave retarder at at least one wavelength in the predetermined wavelength range.
 
Embodiment 48. The optical system of any of embodiments 1 through 47, wherein the first lens is configured to receive an image from an imager, the image incident on the first lens being elliptically polarized.
 
Embodiment 49. The optical system of any of embodiments 1 through 47, wherein the first lens is configured to receive an image from an imager, the image incident on the first lens being circularly polarized.
 
Embodiment 50. The optical system of any of embodiments 1 through 49 further comprising a second retarder layer, the first lens disposed between the second lens and the second retarder layer.
 
Embodiment 51. The optical system of embodiment 50 further comprising a first linear absorbing polarizer, the second retarder layer disposed between the first lens and the first linear absorbing polarizer.
 
Embodiment 52. The optical system of any of embodiments 1 through 51 further comprising a linear absorbing polarizer, the third lens disposed between the linear absorbing polarizer and the reflective polarizer.
 
Embodiment 53. The optical system of any of embodiments 1 through 52 further comprising:
 
     a second retarder layer, the first lens disposed between the second lens and the second retarder layer; 
     a first linear absorbing polarizer, the second retarder layer disposed between the first lens and the first linear absorbing polarizer; and 
     a second linear absorbing polarizer, the third lens disposed between the second linear absorbing polarizer and the reflective polarizer. 
     Embodiment 54. The optical system of any of embodiments 1 through 53, further comprising: 
     an exit pupil defining an opening therein; 
     a second retarder layer disposed between the exit pupil and the third lens; 
     a first linear absorbing polarizer disposed between the second retarder layer and the third lens. 
     Embodiment 55. The optical system of embodiment 54, further comprising: 
     an imager facing the first lens, the imager emitting an image; and 
     a second linear absorbing polarizer disposed between the imager and the first lens. 
     Embodiment 56. The optical system of any of embodiments 1 through 55, further comprising an exit pupil disposed adjacent and facing the third lens and defining an opening therein, wherein there is no linear absorbing polarizer between the third lens and the exit pupil.
 
Embodiment 57. The optical system of any of embodiments 1 through 56, further comprising:
 
     an imager disposed adjacent and facing the first lens, the imager emitting an image, the image incident on the first lens being elliptically polarized; and 
     an exit pupil disposed adjacent and facing the third lens and defining an opening therein, the image incident on the first lens exiting the optical system through the opening of the exit pupil, the exiting image being substantially linearly polarized. 
     Embodiment 58. The optical system of embodiment 57, wherein the imager is substantially a polygon and the opening of the exit pupil is substantially circular.
 
Embodiment 59. The optical system of embodiment 57, wherein a maximum lateral dimension of an active region of the imager is D and a maximum lateral dimension of the opening of the exit pupil is d, 1≤D/d≤20.
 
Embodiment 60. The optical system of embodiment 59, wherein 2≤D/d≤15.
 
Embodiment 61. The optical system of embodiment 59, wherein 5≤D/d≤10.
 
Embodiment 62. The optical system of embodiment 59, wherein a maximum lateral dimension of the opening of the exit pupil is in a range from about 2 mm to about 80 mm.
 
Embodiment 63. The optical system of embodiment 57, wherein a separation between the exit pupil and the third less is in a range from about 5 mm to about 30 mm.
 
Embodiment 64. The optical system of embodiment 57, wherein a separation between the exit pupil and the third less is in a range from about 10 mm to about 20 mm.
 
Embodiment 65. An optical system for displaying an image to a viewer comprising:
 
     a plurality of optical lenses comprising at least one first lens comprising a glass and at least one second lens comprising a plastic; 
     a partial reflector disposed on and conforming to a curved major surface of the at least one first lens and having an average optical reflectance of at least 30% in a predetermined wavelength range; 
     a reflective polarizer disposed on and conforming to a curved major surface of the at least one second lens, the reflective polarizer substantially reflecting light having a first polarization state and substantially transmitting light having an orthogonal second polarization state in the predetermined wavelength range; 
     a first retarder layer disposed on and conforming to a major surface of plurality of optical lenses between the reflective polarizer and the partial reflector; and 
     an exit pupil defining an opening therein, 
     the optical system having an optical axis, a light ray propagating along the optical axis passing through the plurality of optical lenses, the partial reflector, the reflective polarizer, and the first retarder layer without being substantially refracted, such that for a cone of light incident on the optical system from an object comprising a spatial frequency of about 70 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through a center of the opening of the exit pupil and making an angle (θ) of about 20 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.2. 
     Embodiment 66. The optical system of embodiment 65, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 70 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 20 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.25.
 
Embodiment 67. The optical system of embodiment 65, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 70 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 20 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is about 0.3.
 
Embodiment 68. The optical system of embodiment 65, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 70 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 40 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.1.
 
Embodiment 69. The optical system of embodiment 65, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 70 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 40 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.15.
 
Embodiment 70. The optical system of embodiment 65, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 70 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 40 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is about 0.2.
 
Embodiment 71. The optical system of embodiment 65, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 70 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 45 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.1.
 
Embodiment 72. The optical system of embodiment 65, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 70 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through a center of the opening of the exit pupil and making an angle of about 45 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.15.
 
Embodiment 73. The optical system of embodiment 65, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 70 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 45 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is about 0.2.
 
Embodiment 74. The optical system of embodiment 65, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 70 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 55 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.1.
 
Embodiment 75. The optical system of embodiment 65, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 70 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 55 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is about 0.15.
 
Embodiment 76. The optical system of embodiment 65, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 70 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about zero degree with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.5.
 
Embodiment 77. The optical system of embodiment 65, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 70 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about zero degree with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.6.
 
Embodiment 78. The optical system of embodiment 65, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 70 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about zero degree with the optical axis, a modulation transfer function (MTF) of the optical system is about 0.68.
 
Embodiment 79. The optical system of embodiment 65, wherein the plurality of optical lenses comprises two first lenses each comprising a glass and one second lens comprising a plastic.
 
Embodiment 80. The optical system of embodiment 79, wherein the two first lenses form a doublet, a major surface of one first lens substantially conforming to and bonded to a major surface of the other first lens.
 
Embodiment 81. The optical system of embodiment 65, wherein each first lens has an optical birefringence less than about 10 nm/cm, and each second lens has an optical birefringence greater than about 10 nm/cm.
 
Embodiment 82. An optical system for displaying an image to a viewer comprising:
 
     a plurality of optical lenses comprising at least one first lens comprising a glass and at least one second lens comprising a plastic; 
     a partial reflector disposed on and conforming to a curved major surface of the at least one first lens and having an average optical reflectance of at least 30% in a predetermined wavelength range; 
     a reflective polarizer disposed on and conforming to a curved major surface of the at least one second lens, the reflective polarizer substantially reflecting light having a first polarization state and substantially transmitting light having an orthogonal second polarization state in the predetermined wavelength range; 
     a first retarder layer disposed on and conforming to a major surface of plurality of optical lenses between the reflective polarizer and the partial reflector; and 
     an exit pupil defining an opening therein, 
     the optical system having an optical axis, a light ray propagating along the optical axis passing through the plurality of optical lenses, the partial reflector, the reflective polarizer, and the first retarder layer without being substantially refracted, such that for a cone of light incident on the optical system from an object comprising a spatial frequency of about 60 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through a center of the opening of the exit pupil and making an angle (θ) of about 20 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.2. 
     Embodiment 83. The optical system of embodiment 82, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 60 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 20 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.25.
 
Embodiment 84. The optical system of embodiment 82, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 60 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 20 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is about 0.3.
 
Embodiment 85. The optical system of embodiment 82, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 60 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 40 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.1.
 
Embodiment 86. The optical system of embodiment 82, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 60 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 40 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.15.
 
Embodiment 87. The optical system of embodiment 82, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 60 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 40 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is about 0.2.
 
Embodiment 88. The optical system of embodiment 82, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 60 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 45 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.1.
 
Embodiment 89. The optical system of embodiment 82, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 60 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through a center of the opening of the exit pupil and making an angle of about 45 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.15.
 
Embodiment 90. The optical system of embodiment 82, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 60 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 45 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is about 0.2.
 
Embodiment 91. The optical system of embodiment 82, wherein for a cone of light ( 303 ) incident on the optical system from an object comprising a spatial frequency of about 60 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 55 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.1.
 
Embodiment 92. The optical system of embodiment 82, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 60 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 55 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is about 0.15.
 
Embodiment 93. The optical system of embodiment 82, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 60 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about zero degree with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.5.
 
Embodiment 94. The optical system of embodiment 82, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 60 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center Embodiment of the opening of the exit pupil and making an angle of about zero degree with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.6.
 
Embodiment 95. The optical system of embodiment 82, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 60 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about zero degree with the optical axis, a modulation transfer function (MTF) of the optical system is about 0.68.
 
Embodiment 96. The optical system of embodiment 82, wherein the plurality of optical lenses comprises two first lenses each comprising a glass and one second lens comprising a plastic.
 
Embodiment 97. The optical system of embodiment 96, wherein the two first lenses form a doublet, a major surface of one first lens substantially conforming to and bonded to a major surface of the other first lens.
 
Embodiment 98. The optical system of embodiment 82, wherein each first lens has an optical birefringence less than about 10 nm/cm, and each second lens has an optical birefringence greater than about 10 nm/cm.
 
Embodiment 99. An optical system for displaying an image to a viewer, comprising:
 
     a plurality of optical lenses comprising at least one first lens comprising a glass and at least one second lens comprising a plastic; 
     a partial reflector disposed on and conforming to a curved major surface of the at least one first lens and having an average optical reflectance of at least 30% in a predetermined wavelength range; 
     a reflective polarizer disposed on and conforming to a curved major surface of the at least one second lens, the reflective polarizer substantially reflecting light having a first polarization state and substantially transmitting light having an orthogonal second polarization state in the predetermined wavelength range; 
     a first retarder layer disposed on and conforming to a major surface of plurality of optical lenses between the reflective polarizer and the partial reflector; and 
     an exit pupil defining an opening therein, 
     the optical system having an optical axis, a light ray propagating along the optical axis passing through the plurality of optical lenses, the partial reflector, the reflective polarizer, and the first retarder layer without being substantially refracted, such that for a cone of light incident on the optical system from an object comprising a spatial frequency of about 50 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through a center of the opening of the exit pupil and making an angle (θ) of about 20 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.2. 
     Embodiment 100. The optical system of embodiment 99, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 50 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 20 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.25.
 
Embodiment 101. The optical system of embodiment 99, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 50 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 20 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is about 0.3.
 
Embodiment 102. The optical system of embodiment 99, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 50 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 40 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.1.
 
Embodiment 103. The optical system of embodiment 99, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 50 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 40 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.15.
 
Embodiment 104. The optical system of embodiment 99, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 50 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 40 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is about 0.2.
 
Embodiment 105. The optical system of embodiment 99, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 50 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 45 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.1.
 
Embodiment 106. The optical system of embodiment 99, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 50 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through a center of the opening of the exit pupil and making an angle of about 45 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.15.
 
Embodiment 107. The optical system of embodiment 99, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 50 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 45 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is about 0.2.
 
Embodiment 108. The optical system of embodiment 99, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 50 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 55 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.1.
 
Embodiment 109. The optical system of embodiment 99, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 50 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 55 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is about 0.15.
 
Embodiment 110. The optical system of embodiment 99, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 50 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about zero degree with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.5.
 
Embodiment 111. The optical system of embodiment 99, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 50 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about zero degree with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.6.
 
Embodiment 112. The optical system of embodiment 99, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 50 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about zero degree with the optical axis, a modulation transfer function (MTF) of the optical system is about 0.68.
 
Embodiment 113. The optical system of embodiment 99, wherein the plurality of optical lenses comprises two first lenses each comprising a glass and one second lens comprising a plastic.
 
Embodiment 114. The optical system of embodiment 113, wherein the two first lenses form a doublet, a major surface of one first lens substantially conforming to and bonded to a major surface of the other first lens.
 
Embodiment 115. The optical system of embodiment 99, wherein each first lens has an optical birefringence less than about 10 nm/cm, and each second lens has an optical birefringence greater than about 10 nm/cm.
 
Embodiment 116. An optical system for displaying an image to a viewer comprising:
 
     a plurality of optical lenses comprising at least one first lens comprising a glass and at least one second lens comprising a plastic; 
     a partial reflector disposed on and conforming to a curved major surface of the at least one first lens and having an average optical reflectance of at least 30% in a predetermined wavelength range; 
     a reflective polarizer disposed on and conforming to a curved major surface of the at least one second lens, the reflective polarizer substantially reflecting light having a first polarization state and substantially transmitting light having an orthogonal second polarization state in the predetermined wavelength range; 
     a first retarder layer disposed on and conforming to a major surface of plurality of optical lenses between the reflective polarizer and the partial reflector; and 
     an exit pupil defining an opening therein, 
     the optical system having an optical axis, a light ray propagating along the optical axis passing through the plurality of optical lenses, the partial reflector, the reflective polarizer, and the first retarder layer without being substantially refracted, such that for a cone of light incident on the optical system from an object comprising a spatial frequency of about 40 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through a center of the opening of the exit pupil and making an angle (θ) of about 20 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.2. 
     Embodiment 117. The optical system of embodiment 116, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 40 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 20 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.25.
 
Embodiment 118. The optical system of embodiment 116, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 40 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 20 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is about 0.3.
 
Embodiment 119. The optical system of embodiment 116, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 40 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 40 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.1.
 
Embodiment 120. The optical system of embodiment 116, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 40 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 40 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.15.
 
Embodiment 121. The optical system of embodiment 116, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 40 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 40 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is about 0.2.
 
Embodiment 122. The optical system of embodiment 116, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 40 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 45 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.1.
 
Embodiment 123. The optical system of embodiment 116, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 40 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through a center of the opening of the exit pupil and making an angle of about 45 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.15.
 
Embodiment 124. The optical system of embodiment 116, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 40 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 45 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is about 0.2.
 
Embodiment 125. The optical system of embodiment 116, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 40 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 55 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.1.
 
Embodiment 126. The optical system of embodiment 116, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 40 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 55 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is about 0.15.
 
Embodiment 127. The optical system of embodiment 116, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 40 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about zero degree with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.5.
 
Embodiment 128. The optical system of embodiment 116, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 40 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about zero degree with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.6.
 
Embodiment 129. The optical system of embodiment 116, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 40 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about zero degree with the optical axis, a modulation transfer function (MTF) of the optical system is about 0.68.
 
Embodiment 130. The optical system of embodiment 116, wherein the plurality of optical lenses comprises two first lenses ( 20 ,  30 ) each comprising a glass and one second lens comprising a plastic.
 
Embodiment 131. The optical system of embodiment 130, wherein the two first lenses form a doublet, a major surface of one first lens substantially conforming to and bonded to a major surface of the other first lens.
 
Embodiment 132. The optical system of embodiment 116, wherein each first lens has an optical birefringence less than about 10 nm/cm, and each second lens has an optical birefringence greater than about 10 nm/cm.
 
Embodiment 133. An optical system for displaying an image to a viewer comprising:
 
     a plurality of optical lenses comprising at least one first lens comprising a glass and at least one second lens comprising a plastic; 
     a partial reflector disposed on and conforming to a curved major surface of the at least one first lens and having an average optical reflectance of at least 30% in a predetermined wavelength range; 
     a reflective polarizer disposed on and conforming to a curved major surface of the at least one second lens, the reflective polarizer substantially reflecting light having a first polarization state and substantially transmitting light having an orthogonal second polarization state in the predetermined wavelength range; 
     a first retarder layer disposed on and conforming to a major surface of plurality of optical lenses between the reflective polarizer and the partial reflector; and 
     an exit pupil defining an opening therein, 
     the optical system having an optical axis, a light ray propagating along the optical axis passing through the plurality of optical lenses, the partial reflector, the reflective polarizer, and the first retarder layer without being substantially refracted, such that for a cone of light incident on the optical system from an object comprising a spatial frequency of about 30 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through a center of the opening of the exit pupil and making an angle (θ) of about 20 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.2. 
     Embodiment 134. The optical system of embodiment 133, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 30 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 20 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.25.
 
Embodiment 135. The optical system of embodiment 133, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 30 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 20 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is about 0.3.
 
Embodiment 136. The optical system of embodiment 133, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 30 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 40 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.1.
 
Embodiment 137. The optical system of embodiment 133, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 30 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 40 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.15.
 
Embodiment 138. The optical system of embodiment 133, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 30 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 40 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is about 0.2.
 
Embodiment 139. The optical system of embodiment 133, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 30 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 45 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.1.
 
Embodiment 140. The optical system of embodiment 133, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 30 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through a center of the opening of the exit pupil and making an angle of about 45 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.15.
 
Embodiment 141. The optical system of embodiment 133, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 30 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 45 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is about 0.2.
 
Embodiment 142. The optical system of embodiment 133, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 30 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 55 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.1.
 
Embodiment 143. The optical system of embodiment 133, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 30 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about 55 degrees with the optical axis, a modulation transfer function (MTF) of the optical system is about 0.15.
 
Embodiment 144. The optical system of embodiment 133, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 30 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about zero degree with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.5.
 
Embodiment 145. The optical system of embodiment 133, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 30 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about zero degree with the optical axis, a modulation transfer function (MTF) of the optical system is greater than about 0.6.
 
Embodiment 146. The optical system of embodiment 133, wherein for a cone of light incident on the optical system from an object comprising a spatial frequency of about 30 line pairs per millimeter filling the exit pupil with a chief ray of the cone of light passing through the center of the opening of the exit pupil and making an angle of about zero degree with the optical axis, a modulation transfer function (MTF) of the optical system is about 0.68.
 
Embodiment 147. The optical system of embodiment 133, wherein the plurality of optical lenses comprises two first lenses each comprising a glass and one second lens comprising a plastic.
 
Embodiment 148. The optical system of embodiment 147, wherein the two first lenses form a doublet, a major surface of one first lens substantially conforming to and bonded to a major surface of the other first lens.
 
Embodiment 149. The optical system of embodiment 133, wherein each first lens has an optical birefringence less than about 10 nm/cm, and each second lens has an optical birefringence greater than about 10 nm/cm.
 
Embodiment 150. An optical system for displaying an image to a viewer comprising:
 
     an imager emitting an image; 
     an exit pupil defining an opening therein, image emitted by the imager exiting the optical system through the opening of the exit pupil; 
     a plurality of optical lenses disposed between the imager and the exit pupil and receiving emitted image from the imager and comprising first, second, and third optical lenses, the third lens having an optical birefringence greater than about 10 nm/cm, the first and second lens each having an optical birefringence less than about 7 nm/cm and bonded to each other to form a doublet; 
     a partial reflector disposed on and conforming to a curved major surface of the doublet and having an average optical reflectance of at least 30% in a predetermined wavelength range; 
     a reflective polarizer disposed on and conforming to a curved major surface of the third lens, the reflective polarizer substantially reflecting light having a first polarization state and substantially transmitting light having an orthogonal second polarization state in the predetermined wavelength range; and 
     a first retarder layer disposed on and conforming to a major surface of the doublet; such that for a cone of light from an image emitted by the imager, the image comprising a spatial frequency of about 70 line pairs per millimeter, filling the exit pupil with a chief ray of the cone of light passing through a center of the opening of the exit pupil and making an angle of about 40 degrees with an optical axis of the optical system, a modulation transfer function (MTF) of the optical system is greater than about 0.15. 
     Unless otherwise indicated, all numbers expressing feature sizes, amounts, and physical properties used in the specification and claims are to be understood as being modified in all instances by the term “about.” Accordingly, unless indicated to the contrary, the numerical parameters set forth in the foregoing specification and attached claims are approximations that can vary depending upon the desired properties sought to be obtained by those skilled in the art utilizing the teachings disclosed herein. The use of numerical ranges by endpoints includes all numbers within that range (e.g. 1 to 5 includes 1, 1.5, 2, 2.75, 3, 3.80, 4, and 5) and any range within that range. 
     Various modifications and alterations of the embodiments will be apparent to those skilled in the art and it should be understood that this scope of this disclosure is not limited to the illustrative embodiments set forth herein. For example, the reader should assume that features of one disclosed embodiment can also be applied to all other disclosed embodiments unless otherwise indicated.