Patent Publication Number: US-2022229306-A1

Title: Display system and light guide

Description:
BACKGROUND 
     An optical system may include a display panel and a lens system that receives light from the display panel and directs the light to a viewer&#39;s eye. 
     SUMMARY 
     In some aspects of the present description, a display system including an imager for forming an image, and a projection lens system for projecting the image formed by the imager is provided. The imager comprises a plurality of discrete spaced apart pixels. For each pixel in the plurality of pixels, the imager is configured to emit a cone of light having a central ray which has a direction that varies with location of the pixel in the imager. The variation increasing a brightness of an image projected through the projection lens system by at least 30 percent. 
     In some aspects of the present description, a display system including a projection lens system having one or more lenses centered on an optical axis, a light guide and a spatial light modulator is provided. The light guide includes a light insertion portion adapted to receive light; a light transport portion disposed to receive light from the light insertion portion; and a light extraction portion disposed to receive light from the light transport portion. The light extraction portion is configured to provide a light output central ray direction having an angle with respect to the optical axis that varies with location on an output surface of the light extraction portion. The light extraction portion is separated from the light insertion portion along the optical axis forming a space between the light extraction portion and the light insertion portion. The spatial light modulator is in optical communication with the light extraction portion and the light guide is folded such that the light extraction portion faces the light insertion portion. 
     In some aspects of the present description, a display system including a projection lens system having one or more lenses and having a largest lateral optically active dimension; an imager having a largest lateral optically active dimension; and a light guide is provided. An image formed by the imager is projected by the projection lens system. The light guide receives light from a light source and includes a light extraction portion disposed between the projection lens system and the imager. The light extraction portion includes a plurality of discrete spaced apart light extraction features for extracting and directing the received light toward the imager. The largest lateral optically active dimension of the projection lens system is no more than 80 percent of the largest lateral optically active dimension of the imager. 
     In some aspects of the present description, a light guide including a light insertion portion adapted to receive light; a light transport portion disposed to receive light from the light insertion portion through a first fold; and a light extraction portion disposed to receive light from the light transport portion through a second fold is provided. The light extraction portion is spaced apart from and faces the light insertion portion. 
     In some aspects of the present description, a light guide including a light insertion portion adapted to receive light; a light transport portion disposed to receive light from the light insertion portion; and a light extraction portion disposed to receive light from the light transport portion is provided. The light received by the light insertion portion propagates predominately along a first direction. The light transport portion has a first segment and the light received by the light transport portion propagates predominately along a second direction in the first segment. The light received by the light extraction portion propagates predominately along a third direction. A first included angle between the first and second directions is at least 140 degrees and a second included angle between the first and third directions is less than 40 degrees. 
     In some aspects of the present description, a display system including a projection lens system and a light guide is provided. The light guide includes a light insertion portion adapted to receive light, and a light extraction portion disposed to receive light from the light insertion portion. The light received by the light insertion portion propagates predominately along a first direction. The light received by the light extraction portion propagates predominately along a second direction. An included angle between the first direction and the second direction is at least 120 degrees. The light extraction portion includes a plurality of light extraction features adapted to extract light from the light extraction portion towards the projection lens system. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1A  is a cross-sectional view of an optical system; 
         FIGS. 1B-1C  are cross-sectional views of displays; 
         FIG. 2A  is a cross-sectional view of an optical system; 
         FIG. 2B  is a cross-sectional view of light output from a pixel in a reference light emitting system; 
         FIG. 2C  is a cross-sectional view of light output from a pixel in a light emitting system; 
         FIGS. 3-5  are cross-sectional views of optical systems; 
         FIGS. 6-8  are schematic cross-sectional views of light emitting systems; 
         FIG. 9  is a cross-sectional view of a light redirecting layer; 
         FIG. 10  is a cross-sectional view of a light emitting system; 
         FIGS. 11A-11B  are cross-sectional views of pixels including light redirecting elements; 
         FIGS. 12-15  are schematic cross-sectional views of light emitting systems; 
         FIG. 16A  is a cross-sectional view of an optical system; 
         FIGS. 16B-16C  are cross-sectional and perspective views, respectively, of a display system; 
         FIGS. 17-22  are cross-sectional views of light emitting systems; 
         FIG. 23  is a cross-sectional view of a lens system; 
         FIG. 24  is a cross-sectional view of a light emitting system; 
         FIG. 25  is a schematic top view of a head-mounted display; 
         FIGS. 26-28  are schematic cross-sectional views of light guides; and 
         FIG. 29  is a schematic representation of an included angle between two directions. 
     
    
    
     DETAILED DESCRIPTION 
     Display systems can include a display panel and a lens system that receives light from the display panel and transmits at least a portion of the light through an exit pupil of the display system. The lens system may include a reflective polarizer, a partial reflector adjacent to and spaced apart from the reflective polarizer, and a quarter wave retarder disposed between the reflective polarizer and the partial reflector. The partial reflector transmits at least some of the light received from the display panel through the reflective polarizer and through the exit pupil. Such display systems can provide a wide field of view in a compact system that can be used in head-mounted displays such as virtual reality displays, for example. Useful display systems are described in co-pending U.S. Provisional Patent Application No. 62/214,049 filed Sep. 3, 2015 and hereby incorporated by reference herein to the extent that it does not contradict the present description. 
     According to the present description, it has been found that the fraction of light emitted by the display panel that is transmitted through the exit pupil can be substantially increased compared to conventional display systems by altering the light output of the display panel such that one or both of a direction of the light output or a degree of collimation of the light output is suitably altered. As described further elsewhere herein, this can be achieved by including a light redirecting layer between the display panel and the partial reflector (for example, by including a light redirecting layer directly on a surface of the display panel), or by modifying a backlight used to illuminate the display panel. 
       FIG. 1  is a schematic cross-sectional view of optical system  100  including light emitting system  132 , lens system  119  and exit pupil  135 . Light emitting system  132  is adapted to provide a light output that can be efficiently utilized by lens system  119 . Light emitting system  132  may include a light redirecting layer and/or an at least partially collimating backlight. Suitable light emitting systems are described further elsewhere herein. Light emitting systems such as light emitting system  132  may be pixelated and may be referred to as a pixelated system or as a pixelated display. Optical system  100  may be a display system that can be utilized, for example, in a head-mounted display. 
     Lens system  119  includes a first optical stack  110  disposed between the light emitting system  132  and the exit pupil  135 , a second optical stack  120  is disposed between the first optical stack  110  and the exit pupil  135 . Each of the first and second optical stacks  110  and  120  may be substantially planar or may be curved about one or two axes. In some embodiments, each of the first and second optical stacks  110  and  120  are convex toward the light emitting system  132  along orthogonal first and second axes. An x-y-z coordinate system is provided in  FIG. 1 . The orthogonal first and second axes may be the x- and y-axes, respectively. 
     The first optical stack  110  includes a first optical lens  112  having opposing first and second major surfaces  114  and  116  respectively. The first optical stack  110  includes a partial reflector  117  disposed on the first major surface  114 . The partial reflector  117  has an average optical reflectance of at least 30% in a desired or pre-determined plurality of wavelengths and may have an average optical transmission of at least 30% in the desired or pre-determined plurality of wavelengths, which may be any of the wavelength ranges described elsewhere herein. In some embodiments, the partial reflector  117  has an average optical reflectance of at least 40% in a desired or pre-determined plurality of wavelengths and an average optical transmission of at least 40% in the desired or pre-determined plurality of wavelengths. 
     The second optical stack includes a second optical lens  122  having first and second major surfaces  124  and  126 . The second optical stack  120  includes a reflective polarizer  127  disposed on the second major surface  126  and includes a quarter wave retarder  125  disposed on the reflective polarizer  127 . Quarter wave retarder  125  may be a film laminated on the reflective polarizer  127  or may be a coating applied to the reflective polarizer  127 . The optical system  100  may include one or more additional retarders. For example, a second quarter wave retarder may be included in first optical stack  110  and may be disposed on the second major surface  116 . The first quarter wave retarder  125  and any additional quarter wave retarders included in optical system  100  may be quarter wave retarders at at least one wavelength in the pre-determined or desired plurality of wavelengths. The second optical stack  120  may alternatively be described as including the second lens  122  and the reflective polarizer  127  disposed on the second lens  122  and the first quarter wave retarder  125  may be regarded as a separate layer or coating that is disposed on the second optical stack  120  rather than being included in the second optical stack  120 . In this case, the first quarter wave retarder  125  may be described as being disposed between the first optical stack  110  and the second optical stack  120 . In some embodiments, the first quarter wave retarder  125  may not be attached to the second optical stack  120 , and in some embodiments, the first quarter wave retarder  125  is disposed between and spaced apart from the first and second optical stacks  110  and  120 . In still other embodiments, the first quarter wave retarder  125  may be disposed on the partial reflector  117  and may be described as being included in the first optical stack  110  or may be described as being disposed between the first and second optical stacks  110  and  120 . 
     One or both of the first and second lenses  112  and  122  may be refractive lenses. A refractive lens is an optical lens that provides a desired optical power under transmission. In some embodiments, one or both of the first and second lenses  112  and  122  may have low or substantially zero optical power under transmission and may provide optical power under reflection due to the shape of the lens(es). An optical system including a reflective polarizer and a partial reflector disposed adjacent to an spaced apart from one another may be referred to as a folded optical system since such system provided a folded light path as illustrated in  FIG. 1A . An optical system which does not provide such a folded optical path but includes refractive lenses may be described as a refractive optical system. 
     Light rays  137  and  138  are each transmitted from the light emitting system  132  through the exit pupil  135 . Light ray  138  may be a central light ray whose optical path defines a folded optical axis  140  for optical system  100 , which may be centered on the folded optical axis  140 . 
     The light emitting system  132  may include any suitable type of display panel including, for example, liquid crystal display (LCD) panels and organic light emitting diode (OLED) display panels. The display panel may be substantially flat or planar as illustrated in  FIG. 1A , or may be curved as illustrated in  FIG. 1B , or may include a plurality of flat or planar panels disposed at obtuse angles relative to one another as shown in  FIG. 1C , for example.  FIG. 1B  is a schematic cross-sectional view of light emitting system  132   b  which includes display panel  130   b  which may be curved about at least one axis and may be concave toward the lens(es) of the optical system (e.g., the display panel  130   b  may be curved toward the lenses  112  and  122 ). Display panel  130   b  may be curved in one dimension (a simple curve) or in two dimensions (a compound curve). For example, display panel  130   b  may be curved in one or both of the orthogonal x- and y-directions. A display panel curved in two dimensions may have two different radii of curvature (e.g., the curvature in the x- and y-directions may be different. Such displays may be referred to as toroidal).  FIG. 1C  is a schematic cross-sectional view of light emitting system  132   c  which includes substantially planar panels  130   c - 1 ,  130   c - 2  and  130   c - 3 . The panels  130   c - 1  and  130   c - 2  are disposed at an obtuse angle θ 1  relative to each other, and the panels  130   c - 2  and  130   c - 3  are disposed at an obtuse angle θ 2  relative to each other. The panels  130   c - 1 ,  130   c - 2  and  130   c - 3  are disposed to face the lens(es) of the optical system (e.g., the panels  130   c - 1 ,  130   c - 2  and  130   c - 3  may face toward the lenses  112  and  122 ). Either of the displays panels  130   b  and  130   c  may be used in the light emitting system  132  of  FIG. 1A  and may be used in other optical systems described elsewhere herein. 
     Referring again to  FIG. 1A , light ray  137  (and similarly for light ray  138 ) is, in sequence, emitted from light emitting system  132 , transmitted through second major surface  116  (and any coatings or layers thereon), transmitted through first optical lens  112 , transmitted through partial reflector  117 , transmitted through the quarter wave retarder  125  disposed on the reflective polarizer  127 , reflected from reflective polarizer  127 , transmitted back through quarter wave retarder  125 , reflected from partial reflector  117 , transmitted through quarter wave retarder  125 , transmitted through reflective polarizer  127 , transmitted through second lens  122 , and transmitted through exit pupil  135 . Light ray  137  may be emitted from the light emitting system  132  with a polarization state which is rotated to a first polarization state upon passing through quarter wave retarder  125 . The light emitting system  132  may include polarization conditioning elements in order to provide the desired polarization state. Light emitting systems which emit light in the desired polarization state can result in a high contrast image. The first polarization state may be a block state for the reflective polarizer  127 . After light ray  137  passes through first quarter wave retarder  125 , reflects from partial reflector  117  and passes back through quarter wave retarder  125 , its polarization state is a second polarization state substantially orthogonal to the first polarization state. Light ray  137  can therefore reflect from the reflective polarizer  127  the first time that it is incident on the reflective polarizer  127  and can be transmitted through the reflective polarizer  127  the second time that it is incident on the reflective polarizer  127 . 
     Other light rays (not illustrated) reflect from the partial reflector  117  when incident on the partial reflector  117  in the minus z-direction or are transmitted by the partial reflector  117  when incident on the partial reflector  117  in the plus z-direction. These rays may exit optical system  100 . 
     In some embodiments, substantially any chief light ray that is emitted from the light emitting system  132  and transmitted through the exit pupil  135  is incident on each of the first optical stack  110  and the second optical stack  120  with an angle of incidence less than about 30 degrees, less than about 25 degrees, or less than about 20 degrees, the first time or each time that the chief light ray is incident on the first or second optical stacks  110  or  120 . In any of the optical systems of the present description, substantially any chief light ray emitted by the light emitting system  132  and transmitted through the exit pupil  134  is incident on each of the reflective polarizer and the partial reflector with an angle of incidence less than about 30 degrees, less than about 25 degrees, or less than about 20 degrees, the first time or each time that the chief light ray is incident on the reflective polarizer or the partial reflector. If a large majority (e.g., about 90 percent or more, or about 95 percent or more, or about 98 percent or more) of all chief rays emitted by the light emitting system and transmitted through the exit pupil satisfy a condition, it may be said that substantially any chief ray satisfies that condition. 
     Various factors can cause light to be partially transmitted through the reflective polarizer  127  the first time that light emitted by the light emitting system  132  is incident on the reflective polarizer  127 . This can cause unwanted ghosting or image blurriness at the exit pupil  135 . These factors can include performance degradation of the various polarizing components during forming and unwanted birefringence in the optical system  100 . The effects of these factors can combine to degrade the contrast ratio and efficiency of the optical system  100 . The effects of these factors on the contrast ratio is described in more detail in co-pending U.S. Provisional Patent Application No. 62/214,049 filed Sep. 3, 2015 and previously incorporated herein by reference. Such factors can be minimized by using relatively thin optical lenses, which can reduce unwanted birefringence in the lenses, for example, and using thin optical films, which can reduce optical artifacts arising from thermoforming optical films, for example. In some embodiments, the first and second optical lenses  112  and  122  each have a thickness less than 7 mm, less than 5 mm, or less than 3 mm, and may have a thickness in a range of 1 mm to 5 mm, or 1 mm to 7 mm, for example. In some embodiments, the reflective polarizer  127  may have a thickness of less than 75 micrometers, less than 50 micrometers, or less than 30 micrometers. In some embodiments, the contrast ratio at the exit pupil  135  is at least 40, or at least 50, or at least 60, or at least 80, or at least 100, or at least 150, or at least 200, or at least 300 over the field of view of the optical system  100 . 
     A film can be shaped into a compound curve (curved about two orthogonal axes) by any forming process that deforms or stretches the film into the desired shape. Suitable forming processes may or may not include elevated temperatures (thermoforming). Suitable forming processes include thermoforming and/or pressurization processing (deforming or stretching the film into the desired shape via the application of pressure). It has been found that a convex reflective polarizer curved about two orthogonal axes that is made by forming a polymeric multilayer optical film that was uniaxially oriented prior to forming is particularly advantageous when used in the optical systems of the present description. For example, it has been found that the contrast ratio can be significantly higher when utilizing such film compared to using other reflective polarizers. However, other reflective polarizers, such as non-uniaxially oriented multilayer polymeric film reflective polarizers or wire grid polarizers, may also be used. In some embodiments, the uniaxially oriented multilayer reflective polarizers is APF (Advanced Polarizing Film, available from 3M Company, St. Paul, Minn.). In some embodiments, optical systems include a thermoformed APF or a pressure-formed APF and any or substantially any chief ray in the optical system that is incident on the thermoformed APF or the pressure-formed has a low angle of incidence (e.g., less than about 30 degrees, less than about 25 degrees, or less than about 20 degrees). 
     In some embodiments, a lens system may be utilized that includes a substantially flat reflective polarizer rather than a curved reflective polarizer. In some embodiments, the reflective polarizer is curved about one axis and in some embodiments, the reflective polarizer is curved about two orthogonal axes. The reflective polarizer may be a multilayer optical film that is substantially flat or that is substantially curved about an axis or about two orthogonal axes. The reflective polarizer may be a wire grid polarizer that is substantially flat or that is substantially curved about an axis or about two orthogonal axes. It has been found that by suitably choosing the shapes of the various major surfaces (e.g., second major surface  126  and first major surface  114 ) that the optical system can provide distortion sufficiently low that the image does not need to be pre-distorted. In some embodiments, the light emitting system  132  is adapted to emit an undistorted image. The partial reflector  117  and the reflective polarizer  127  may have different shapes selected such that a distortion of the emitted undistorted image transmitted through the exit pupil  135  is less than about 10%, or less than about 5%, or less than about 3%, of a field of view at the exit pupil  135 . The field of view at the exit pupil may be greater than 80 degrees, greater than 90 degrees, or greater than 100 degrees, for example. 
       FIG. 2A  is a cross-sectional view of optical system  200  including lens system  219 , a light emitting system  232  and an exit pupil  235 . Lens system  219  includes a first optical stack  210  and a second optical stack  220 . Light emitted from pixels  241 ,  242  and  243  is illustrated in  FIG. 2A . Light  247  from pixel  241  includes a chief ray which is transmitted through a center of the exit pupil  235 . First optical stack  210  includes a lens  212  and a partial reflector disposed on the major surface of lens  212  facing exit pupil  235 . Second optical stack  220  includes a lens  222  and includes a reflective polarizer disposed on the major surface of lens  222  facing the light emitting system  232 . A quarter wave retarder is included either disposed on the reflective polarizer facing the partial reflector or disposed on the partial reflector facing the reflective polarizer. Lens  212  and lens  222  are convex toward light emitting system  232  about orthogonal axes (e.g., x- and y-axes). In other embodiments, one or both of the first and second lenses may have one or more surfaces that are not convex. In some embodiments, one or both lenses are plano-convex and in some embodiments, one or both lenses are plano-concave. In some embodiments, one lens is plano-convex and the other is plano-conave. In some embodiments, the reflective polarizer is disposed on a surface that is convex towards the display and the quarter-wave retarder is disposed on a flat surface. The surface that is convex towards the display can be, for example, the curved surface of a plano-convex lens that is disposed with the curved surface of the lens facing the display or the curved surface of a plano-concave lens that is disposed with the flat surface of the lens facing the display.  FIGS. 2B-2C  schematically illustrates light emitted from pixel  241   b  of light emitting system  232   b  and light emitted by pixel  241   c  of light emitting system  232   c , both corresponding to pixel  241  of light emitting system  232  of  FIG. 2A . Light from a conventional display panel would typically be emitted in a bundle of light  239   b , which may have a Lambertian distribution having a central ray  237   b  along a normal to the display panel, for example. In some embodiments, light emitting system  232   c  includes a light redirecting layer that bends the direction of the central ray  237   b  towards the direction of the chief ray  247 . In these cases, light emitting system  232   b  may be otherwise equivalent to light emitting system  232   c  but without the light redirecting layer. As described further elsewhere herein, the light redirecting layer may include a plurality of light redirecting elements with each light redirecting element corresponding to a different group of pixels in a display panel. An angle α is illustrated between the chief ray  247  and the central ray  237   b  in  FIG. 2B . In some embodiments, for at least one pixel, the light redirecting element corresponding to the pixel reduces the angle α between the central light ray  247   c  and the chief light ray  247  emitted by the pixel. In some embodiments, light emitting system  232   c  includes an at least partially collimating backlight that may direct a light output such that the direction of the central ray  237   c  is bent towards the direction of the chief ray  247 . As described further elsewhere herein, an at least partially collimating backlight produces a light output that is substantially more collimated than a Lambertian output. In these cases, light emitting system  232   b  may be otherwise equivalent to light emitting system  232   c  but with a backlight that produces a substantially Lambertian output with the central ray directed normal to a display surface. 
     A light redirecting layer that reduces a divergence angle of light received by the light redirecting layer may be said to at least partially collimate the light. In some embodiments the angle α is reduced for the light emitting system  232   c  relative to the otherwise equivalent light emitting system  232   b  by at least 5 degrees, or at least 10 degrees, for at least one pixel. In some embodiments the angle α is reduced for the light emitting system  232   c  relative to the otherwise equivalent light emitting system  232   b  by at least 5 degrees, or at least 10 degrees, for a majority (more than half) of the pixels or for substantially all of the pixels. 
     An acceptance angle φ for lens system  219  is illustrated in  FIGS. 2B-2C . A greater proportion of light emitted from pixel  241   c  of light emitting system  232   c  is within the acceptance angle φ compared to the proportion of light emitted from pixel  241   b  of the otherwise equivalent light emitting system  232   b  that does not include a light redirecting layer or an at least partially collimating backlight. This may be due to one or both of redirecting the central light ray closer to the chief ray direction and at least partially collimating the light output. A light emitting system including a plurality of pixels may also be referred to as a pixelated system or a pixelated display and an optical system including the light emitting system and a lens system may be referred to as a display system or as an imaging system. An otherwise equivalent light emitting system not including a light redirecting component (e.g., a light redirecting layer or an at least partially collimating backlight) may be referred to as a reference pixelated system and the corresponding display system including the reference pixelated display system may be referred to as an otherwise equivalent display system or as a reference display system. In some embodiments, for each pixel in the plurality of pixels, the pixelated system is adapted to emit a cone of light having a central ray where the central ray has a direction that varies with location of the pixel in the pixelated system such that a total luminous energy emitted by the pixelated system that is within the acceptance angle of the optical lens system is at least 30 percent higher, or at least 50 percent higher, or at least 100 percent higher, or at least 200 percent higher, or at least 300 percent higher, or at least 400 percent higher than that of a reference pixelated system that is equivalent to the pixelated system except that directions of central rays of the reference pixelated system are normal to the pixels. 
     In some embodiments, a brightness of an optical system of the present description at the exit pupil of the optical system is at least 20 percent higher, or at least 30 percent higher, or at least 100 percent higher, or at least 200 percent higher, or at least 300 percent higher, or at least 400 percent higher than that of an otherwise equivalent optical system not including a light redirecting component. As described further elsewhere herein, the light redirecting component may be a light redirecting layer, a plurality of light redirecting elements (e.g., a microlens array or a plurality of prismatic elements), or an at least partially collimating backlight. 
       FIG. 3  is a schematic cross-sectional view of optical system  300  including light emitting system  332 , exit pupil  335 , integral optical stack  310  including optical lens  312  having first and second major surfaces  314  and  316 . Light emitting system  332  may be any of the light emitting systems described elsewhere herein and may include a light redirecting layer and/or a partially collimating backlight, for example. First quarter wave retarder  325  is disposed on first major surface  314  of optical lens  312  and reflective polarizer  327  is disposed on first quarter wave retarder  325  opposite optical lens  312 . Partial reflector  317  is disposed on second major surface  316  of optical lens  312  and second quarter wave retarder  315  is disposed on partial reflector  317  opposite optical lens  312 . Optical system  300  may be centered on folded optical axis  340  which may be defined by an optical path of a central light ray transmitted from the light emitting system  332  through the exit pupil  335 . In some embodiments, optical lens  312  is a monolithic component. 
     Integral optical stack  310  can be made by first forming reflective polarizer  327  with first quarter wave retarder  325  coated or laminated to reflective polarizer  327  and then thermoforming the resulting film into a desired shape. As described further in co-pending U.S. Provisional Patent Application No. 62/214,049 filed Sep. 3, 2015 and previously incorporated herein by reference, the thermoforming tool may have a shape different than the desired shape so that the film obtains the desired shape after cooling. Partial reflector  317  and second quarter wave retarder  315  may be prepared by coating a quarter wave retarder onto a partial reflector film, by coating a partial reflector coating onto a quarter wave retarder film, by laminating a partial reflector film and a quarter wave retarder film together, or by first forming lens  312  (which may be formed on a film that includes reflective polarizer  327  and first quarter wave retarder  325 ) in a film insert molding process and then coating the partial reflector  317  on the second major surface  316  and coating the quarter wave retarder  315  on the partial reflector  317 . In some embodiments, a first film including reflective polarizer  327  and first quarter wave retarder  325  is provided an a second film including partial reflector  317  and second quarter wave retarder  315  is provided and then integral optical stack  310  is formed by injection molding lens  312  between the first and second thermoformed films in a film insert molding process. The first and second films may be thermoformed prior to the injection molding step. Other optical stacks of the present description may be made similarly by thermoforming an optical film, which may be a coated film or a laminate, and using a film insert molding process to make the optical stack. A second film may be included in the film insert molding process so that the lens formed in the molding process is disposed between the films. 
     In alternate embodiments, the first quarter wave retarder  325  may be disposed on second major surface  316  rather than on first major surface  314 . The integral optical stack may be formed by thermoforming the reflective polarizer  327  into the desired shape and injection molding lens  312  onto the reflective polarizer  327 . The first quarter wave retarder  325  may then be coated (e.g., spin coated) onto the second major surface  316  and then the partial reflector  317  can be vapor coated onto the first quarter wave retarder  325 . A second quarter wave retarder can be coated onto the partial reflector, or disposed on the display panel  332  or positioned between the partial reflector  317  and the display panel  332 . 
     The partial reflector  317  has an average optical reflectance of at least 30% in a desired or pre-determined plurality of wavelengths and may have an average optical transmission of at least 30% in the desired or pre-determined plurality of wavelengths, which may be any of the wavelength ranges described elsewhere herein. The first quarter wave retarder  325  and any additional quarter wave retarders included in optical system  300  may be quarter wave retarders at at least one wavelength in the pre-determined or desired plurality of wavelengths. The multilayer reflective polarizer  327  substantially transmits light having a first polarization state (e.g., linearly polarized in a first direction) and substantially reflects light having an orthogonal second polarization state (e.g., linear polarized in a second direction orthogonal to the first direction). As described further elsewhere herein, the multilayer reflective polarizer  327  may be a polymeric multilayer reflective polarizer (e.g., APF) or may be a wire grid polarizer, for example. 
     Light ray  337  is emitted from the light emitting system  332  and transmitted through the exit pupil  335 . Light ray  337  is transmitted through second quarter wave retarder  315  and partial reflector  317  into and through lens  312 . Other light rays (not illustrated) reflect from partial reflector  317  after passing through second quarter wave retarder  315  and are lost from the optical system  300 . After making a first pass through lens  312 , the light ray passes through first quarter wave retarder  325  and reflects from reflective polarizer  327 . Light emitting system  332  may be adapted to emit light having a polarization along the pass axis for reflective polarizer  327  so that after passing through both second quarter wave retarder  315  and first quarter wave retarder  325  it is polarized along the block axis for the reflective polarizer  327  and therefore reflects from the reflective polarizer  327  when it is first incident on it. In some embodiments, a linear polarizer is included between the light emitting system  332  and the second quarter wave retarder  317  so that light incident on second quarter wave retarder  315  has the desired polarization. After light ray  337  reflects from reflective polarizer  327 , it passes back through first quarter wave retarder  325  and lens  312  and is then reflected from partial reflector  317  (other light rays not illustrated are transmitted through partial reflector  317 ) back through lens  312  and is then again incident on the reflective polarizer  327 . After passing through first quarter wave retarder  325 , reflecting from partial reflector  317  and passing back through first quarter wave retarder  325 , light ray  337  has a polarization along the pass axis for reflective polarizer  327 . Light ray  337  is therefore transmitted through reflective polarizer  327  and is then transmitted through exit pupil  335 . 
       FIG. 4  is a cross-sectional view of optical system  400  including an optical stack  410 , a light emitting system  432  and an exit pupil  435 . Light emitting system  432  may be any of the light emitting systems described elsewhere herein. Light emitted from pixels  441 ,  442  and  443  is illustrated in  FIG. 4 . Light from pixel  441  includes a chief ray  447  which is transmitted through a center of the exit pupil  435 . The light emitting system may include a plurality of light redirecting elements that steer and/or partially collimate the light output of a display panel so that a greater proportion of the light output it directed into the acceptance angle of the optical stack  410 . Optical stack  410  includes a lens  412 , a reflective polarizer  427  disposed on the major surface of lens  412  facing exit pupil  435 , and a partial reflector  417  disposed on the major surface of lens  412  facing the image surface  430 . A quarter wave retarder is included in optical stack  410  between the reflective polarizer and the lens  412  or between the partial reflector and the lens  412 . Lens  412  is convex toward image surface  430  about orthogonal axes (e.g., x- and y-axes). 
       FIG. 5  is a cross-sectional view of optical system  500  including a light emitting system  532 , a lens system  519  and an exit pupil  535 . Light emitting system  532  may be any of the light emitting systems described elsewhere herein and may include a display panel and one or more optical components (e.g., a light redirecting layer and/or a partially collimating backlight) adapted to steer and/or partially collimate a light output of the display panel so that a larger proportion of the light output is within an acceptance angle of the lens system  519 . 
     Lens system  519  includes a first lens  512 , an optical stack  520  including a second lens  522 , and an optical stack  560  including a third lens  562 . Optical stack  520  includes a partial reflector disposed on the major surface of second lens  522  facing exit pupil  535  and includes a reflective polarizer disposed on the major surface of third lens  562  facing the image surface  530 . A quarter wave retarder is included either in optical system  500  disposed on the reflective polarizer facing the partial reflector, or disposed on the partial reflector facing the reflective polarizer. The reflective polarizer and the partial reflector are each convex toward image surface  530  about orthogonal axes (e.g., x- and y-axes). Three bundles of light rays at three locations on the light emitting system  532  are illustrated. The light rays in each bundle are substantially parallel at the exit pupil  535 . 
       FIG. 6  is a schematic side view of light emitting system  632  including pixelated light source  630  and light redirecting layer  650 . Light emitting system  632  may be used for any of light emitting systems  132 ,  232 ,  332 ,  432 , and  532 , in optical system  100 ,  200 ,  300 ,  400  and  500 , respectively, for example. Light redirecting layer  650  may be separated from pixelated light source  630  or may be attached to or integrated with the pixelated light source  630 . Pixelated light source  630  includes a plurality of discrete spaced apart pixels. For example, pixelated light source  630  may comprise a high definition display panel having an array of 1080 by 1920 pixels. Light from a single pixel is illustrated in  FIG. 6 . Pixel  641  emits a cone of light  639  including central light ray  637 . Cone of light  639  is a diverging light having a cone angle of θ 1 . Each portion of light redirecting layer  650  or each light redirecting element of light redirecting layer  650  receives a cone of light emitted by a pixel corresponding to the portion or to the light redirecting element and transmits received light as a cone of light having one or both of the direction of the central ray and the cone angle of the transmitted light different from that of the received cone of light. In the illustrated embodiment, portion  656  receives cone of light  639  and transmits the received light as cone of light  649  having central ray  647 . Cone of light  649  may be a diverging light and has a cone angle of θ 2 . Central ray  647  has a different direction than central ray  637 . Is some embodiments, an angle α between the direction of central ray  647  and the direction of central ray  639  may be, for example, at least 5 degrees or at least 10 degrees, and may be less than 80 degrees, or less than 60 degrees, or less than 50 degrees. The cone angle θ 2  may be at least 2 degrees, or at least 5 degrees, or at least 10 degrees, or at least 15 degrees lower than the cone angle θ 1 . In some embodiments, one or both of the cone angles θ 1  and θ 2  may be greater than 10 degrees, or greater than 15 degrees, or greater than 20 degrees, or greater than 30 degrees. In some embodiments, the angle α between may be approximately zero and the cone angle θ 2  may be substantially less than the cone angle θ 1 . In some embodiments, the cone angles θ 1  and α 2  may be approximately equal and the angle α between may be substantially greater than zero. In some embodiments, the angle α may be substantially greater than zero and the cone angle θ 2  may be substantially less than the cone angle θ 1 . 
     As described further elsewhere herein, light redirecting layer  650  may include a plurality of light redirecting elements with each light redirecting element corresponding to a group of pixels in the pixelated light source  630 . The group of pixels includes at least one pixel and may include a single pixel or a plurality of pixels. In some cases, the different groups of pixels may share one or more common pixels. In other cases, no two different groups of pixels contain a common pixel. A light redirecting layer may be said to comprise a plurality of light redirecting elements if the elements are discrete elements or if the light redirecting layer includes abruptly varying structures such as microlenses or Fresnel lenses. In some embodiments, light redirecting layer  650  may include a plurality of portions with each different portion corresponding to a different group of pixels in the pixelated light source  630 . In some embodiments, the portions may be discrete light redirecting elements or a plurality of discrete light redirecting elements. In other embodiments, a light redirecting layer may include a plurality of substantially continuously varying portions without abruptly varying structures. 
       FIG. 7  is a schematic side view of light emitting system  732  including pixelated light source  730  and light redirecting layer  750 . Light emitting system  732  may be used for any of light emitting systems  132 ,  232 ,  332 ,  432 , and  532 , in optical system  100 ,  200 ,  300 ,  400  and  500 , respectively, for example. Pixelated light source  730  includes a plurality of pixels which includes at least first and second pixels  751  and  752 . Image  751  of pixel  741  is a virtual image located behind the pixel  741  (in the z-direction from the pixelated light source  730 ). Similarly, image  752  of pixel  742  is a virtual image located behind the pixel  742 . Images  751  and  752  are disposed on image surface  755  which may be substantially planar or substantially non-planar. Light redirecting layer  750  includes a plurality of portions, each different portion corresponding to a different group of pixels in the pixelated light source  730 . In the illustrated embodiment, each group of pixels is a single pixel. Portion  756  of light redirecting layer  750  corresponds to pixel  741  and portion  757  of light redirecting layer  750  corresponds to pixel  742 . Images  751  and  752  may be located at different distances from portions  756  and  757 . In some embodiments, light redirecting layer  750  includes a plurality of lenses (or other light redirecting elements as described elsewhere herein) and portions  756  and  757  each include a lens. Images  751  and  752  may be located at different distances from the respective lenses in portions  756  and  757 . Pixelated light source  730  includes a plurality of pixels and may emit a first image. The light redirecting layer  750  may form a virtual second image of the first image behind the plurality of pixels. In other embodiments, the light redirecting layer may produce a real image instead of a virtual image. This is illustrated in  FIG. 8 . 
       FIG. 8  is a schematic side view of light emitting system  832  including pixelated light source  830  and light redirecting layer  850 . Light emitting system  832  may be used for any of light emitting systems  132 ,  232 ,  332 ,  432 , and  532 , in optical system  100 ,  200 ,  300 ,  400  and  500 , respectively, for example. Pixelated light source  830  includes a plurality of pixels which includes at least first and second pixels  851  and  852 . Image  851  of pixel  841  is a real image located in front of pixel  841  (in the minus z-direction from the pixelated light source  830 ). Similarly, image  852  of pixel  842  is a real image located in front of pixel  842 . Images  851  and  852  are disposed on image surface  855  which may be substantially planar or substantially non-planar. Light redirecting layer  850  includes a plurality of portions, each different portion corresponding to a different group of pixels in the pixelated light source  830 . In the illustrated embodiment, each group of pixels is a single pixel. Portion  856  of light redirecting layer  850  corresponds to pixel  841  and portion  857  of light redirecting layer  850  corresponds to pixel  842 . Pixelated light source  830  includes a plurality of pixels and may emit a first image. The light redirecting layer  850  may form a real second image of the first image in front of the plurality of pixels. Images  851  and  852  may be located at different distances from portions  856  and  857 . In some embodiments, light redirecting layer  850  includes a plurality of lenses (or other light redirecting elements as described elsewhere herein) and portions  856  and  857  each include a lens. Images  851  and  852  may be located at different distances from the respective lenses in portions  856  and  857 . 
     An example of a light redirecting layer is illustrated in  FIG. 9  which is a cross-sectional view of light redirecting layer  950  including a plurality of lenses  954  on a layer  930 . Layer  930  may be a display panel or an outer layer in a display panel, for example, and the plurality of lenses  954  may be formed directly on the display panel. Alternatively, layer  930  may be a polymer substrate, for example, and light redirecting layer  950  may be attached or laminated to a display panel. The plurality of lenses  954 , which may be a plurality of microlenses, may be arranged periodically with a pitch P. The pitch P may be similar to but larger than a pitch between pixels in a display panel. The pitch P may be selected such that lenses positioned near the center of the display panel have an optical axis that is approximately aligned with a corresponding pixel, while lenses away from the center of the display panel have an optical axis that is laterally offset (e.g., offset in a plane of the display panel which may be parallel to the x-y plane of  FIG. 9 ) from the corresponding pixel. In some embodiments, the offset increases monotonically from a center of the display panel to an edge of the display panel. The monotonic increase in the offset may be a linear increase or a non-linear increase. 
     Light redirecting layers, such as those including microlens arrays, can be made by a variety of different techniques. Such techniques includes include photopolymer reflow, gray scale lithography, laser ablation, dip coating of curable monomers on patterned hydrophobic/hydrophilic substrates, ink jet printing of curable monomers, diamond turning, ion beam or wet etching, and electrodeposition. Other suitable processes include two-photon processes such as those described in U.S. Pat. No. 7,583,444 (DeVoe et al.). 
       FIG. 10  is a schematic side view of light emitting system  1032  which includes a plurality of discrete spaced apart pixels  1044  and a light redirecting layer  1050  which includes a plurality of light redirecting elements  1054 . Light redirecting elements  1054  may correspond to lenses  954 . A lens may be included for all pixels in a display panel or for only some of the pixels. For example, pixels a region near an optical axis of an optical system including the light emitting system  1032  may optionally not include light redirecting elements. Light emitting system  1032  may be used for any of light emitting systems  132 ,  232 ,  332 ,  432 , and  532 , in optical system  100 ,  200 ,  300 ,  400  and  500 , respectively, for example. Light redirecting element  1056  receives a cone of light  1039  from pixel  1041  and transmits the received light as a cone of light  1049 . As described further elsewhere herein, the cone of light  1049  may have one or both of the cone angle and central ray direction changed from that of the cone of light  1039 . The plurality of pixels  1044  are disposed along a surface  1033 , which in the illustrated embodiment is a substantially planar surface. In other embodiments, the surface  1033  may be curved. For example, a curved display panel (e.g., LCD or OLED panel) may comprise the plurality of pixels. A surface, such as surface  1033 , along which pixels are disposed may be referred to as a pixelated surface. 
     The plurality of pixels in  FIG. 10  are represented by discrete spaced apart dark lines. In other figures, pixels may be represented by open spaces between dark lines. In  FIG. 10 , the spaces between the dark lines represent gaps between adjacent pixels. Pixels  1044  have a pixel width w, which may be a width across the pixel along a repeat direction (e.g., the y-direction in  FIG. 10 ) of the pixels, and a gap g, which may be a width of the space between adjacent pixels along the repeat direction. In some embodiments, adjacent pixels are spaced apart by about 10 percent to about 100 percent of the pixel width (e.g., g/w is in a range of about 0.1 to about 1). In some embodiments, the gap between adjacent pixels includes a light absorbing material  1036 , which may be, for example, black chrome. In OLED displays, for example, a light absorbing black matrix may be included between adjacent pixels as is known in the art. Including a light absorbing material between adjacent pixels can improve contrast in an optical system including a light emitting system and a lens system having a partial reflector since light incident on the lens system that is reflected back to the light emitting system can be at least partially absorbed by the light absorbing material. In other embodiments, the gap between adjacent pixels is substantially light transmissive. This may be the case in an at least partially transparent display panel, such as an at least partially transparent OLED display panel, for example. In this case, contrast can be improved since light incident on the lens system that is reflected back to the light emitting system can be at least partially transmitted through the light emitting system without reflecting back through the lens system which could cause a reduction in contrast. In some embodiments, the spacing between adjacent pixels may be small. For example, in some embodiments, the gap between adjacent pixels is less than 10 percent of the pixel width, or less than 5 percent of the pixel width (e.g., g/w is less than 0.1, or less than 0.05). In some embodiments, the gap, g, between adjacent pixels is less than 2 micrometers, or less than 1 micrometer, or less than 0.5 micrometers. 
       FIG. 11A  illustrates a pixel  1142  including a light emitter  1141  and a lens  1154   a . The light emitter  1141  emits cone of light  1139  having central ray  1137 , and lens  1154   a  receives the cone of light  1139  and transmits the received light as cone of light  1149  having central light ray  1147 . Lens  1154   a  is centered on optical axis  1140  which is laterally offset from light emitter  1141  by a distance d. Pixel  1142  may correspond to the combination of pixel  1041  and light redirecting element  1056 , for example. A light emitting system including a plurality of the pixels  1142  may be used for any of light emitting systems  132 ,  232 ,  332 ,  432 , and  532 , in optical system  100 ,  200 ,  300 ,  400  and  500 , respectively, for example. As described further elsewhere herein, the lateral offset distance d may increase monotonically from a center of a display panel to an edge of the display panel. 
     A light redirecting element may be a lens which may include a spherical or aspherical portion rotationally symmetric about an optical axis of the lens, or may be a prismatic element which may have one or more curved surfaces.  FIG. 11B  shows a lens or light redirecting element  1154   b  which may be used in place of lens  1154   a . In some embodiments, a plurality of light redirecting element  1154   b  may be arranged periodically with a pitch selected to match a corresponding pixel pitch in a pixelated light source. The pixels in the pixelated light source may be disposed along a pixelated surface  1133  which may be a substantially planar surface or a substantially curved surface. Light redirecting element  1154   b  includes opposing first and second sides  1131   a  and  1131   b  and a curved surface  1131   c  connecting the first and second sides  1131   a  and  1131   b . Light redirecting element  1154   b  can be described as having a lens portion  1194  which includes the curved surface  1131   c  and a prismatic base portion  1196 . The base portion  1196  may have a square or rectangular cross-section, for example, in a plane parallel to surface  1133  containing the light emitter  1141   b  (a plane parallel to the x-y plane of  FIG. 11B ). First and second sides  1131   a  and  1131   b  may be planar faces, for example. The base portion  1196  may have a circular cross-section, for example, in a plane parallel to the surface  1133 . First and second sides  1131   a  and  1131   b  may then be opposite sides of a cylindrical base  1196 . In some embodiments, the first side  1131   a  extends further from the surface  1133  along a normal to the surface  1133  (normal along the minus z-direction) than the second side  1131   b . A prismatic element may be understood to include a prism component (e.g., base portion  1196 ) and a lens component (e.g., curved surface  1131   c ) where the lens component has at least one convex surface. 
     Light emitter  1141   b  emits a first cone of light having a central light ray  1137   b . The first cone of light is received by light redirecting element  1154   b  and transmitted as a second cone of light having central light ray  1147   b . Central light ray  1137   a  may be along a first cone axis and central light ray  1137   b  may be along a second cone axis. An angle α between the first and second cone axes may be at least 5 degrees or at least 10 degrees, or may be in a range of 5 degrees to 50 degrees or to 60 degrees, for example. The light redirecting element  1154   b  may be asymmetric about the first cone axis. The curved surface  1131   c  may be rotationally asymmetric about the first cone axis and substantially rotationally symmetric about axis  1193  which is not parallel to the first cone axis and may not be parallel to the second cone axis. 
     In some embodiments, an imaging system includes a plurality of light emitters  1141   b  and a plurality of light redirecting elements  1154   b . The light emitter  1141   b  together with the corresponding light redirecting element  1154   b  may be referred to as a pixel and an imaging system may include a plurality of such pixels. In some embodiments, for a first pixel in the plurality of pixels, a first angle between the first and second cone axes is greater than 5 degrees, or greater than 10 degrees, and for a different second pixel in the plurality of pixels, a second angle between the first and second cone axes is greater than 5 degrees, or greater than 10 degrees, and is different from the first angle. In some embodiments, for a majority of pixels in the plurality of pixels, the first and second cone axes are not parallel and in some embodiments, for a majority of pixels in the plurality of pixels, an angle between the first and second cone axes is at least 5 degrees, or at least 10 degrees, or in a range of 5 degrees to 50 degrees or to 60 degrees. 
       FIG. 12  is a schematic side view of light emitting system  1232  including a display panel  1230  comprising a plurality of discrete spaced apart pixels and disposed to receive light from backlight  1236  and transmit patterned light through light redirecting layer  1250 . Display panel  1230  may be any suitable spatial light modulator such as a liquid crystal display (LCD) panel, or a grating based modulator, or an interference based modulator, or an electrochromic modulator, or an electrophoretic modulator. In other embodiments, an organic light emitting display (OLED) comprises the plurality of discrete spaced apart pixels and the backlight  1236  may be omitted. Light emitting system  1232  may be used for any of light emitting systems  132 ,  232 ,  332 ,  432 , and  532 , in optical system  100 ,  200 ,  300 ,  400  and  500 , respectively, for example. 
     In some embodiments, backlight  1236  may be an at least partially collimating backlight. A backlight may be said to be an at least partially collimating backlight if the light output from the backlight is substantially more collimated than a Lambertian light output. In some embodiments, at least 50 percent of a lumen output of the at least partially collimating backlight is in a 60 degree, or a 50 degree, or a 40 degree, or a 30 degree, or a 25 degree, or a 20 degree full width cone. In some embodiments, at least 60 percent of a lumen output of the at least partially collimating backlight is in a 70 degree, or a 60 degree, or a 50 degree, or a 40 degree, or a 30 degree, or a 25 degree full width cone. 
       FIG. 13  is a schematic side view of light emitting system  1332  including pixels  1341 ,  1342 , and  1343 . Light emitting system  1332  may be used for any of light emitting systems  132 ,  232 ,  332 ,  432 , and  532 , in optical system  100 ,  200 ,  300 ,  400  and  500 , respectively, for example. Each pixel is adapted to emit a cone of light having a central ray and a cone angle. Pixel  1341  emits cone of light  1349  having central light ray  1347  which in the illustrated embodiment is parallel to optical axis  1340 , which may be an optical axis of a lens system disposed to receive light from light emitting system  1332 . Pixel  1342  emits a cone of light having a full width cone angle θ. Light emitting system  1332  may include a display panel with a light redirecting layer adapted to reduce the cone angle of light emitted by the display panel, which may be an LCD or an OLED display panel, for example. In other embodiments, an at least partially collimating backlight may be used with a display panel to produce an output with a lowered cone angle compared to that produced with a conventional backlight. For example, an at least partially collimating backlight may produce a light output such that at least 50 percent of the lumen output is in a 50 degree full width cone or in any of the ranges described elsewhere herein for a partially collimating backlight. A light redirecting layer may be included to further reduce the cone angle or the light redirecting layer may be optionally omitted. In the illustrated embodiment, the light output direction of each of the pixels  1341 ,  1342  and  1343  is substantially parallel to the optical axis  1340 . In other embodiments, the light redirecting layer and/or the at least partially collimating backlight may alter the direction of light emitted from the light emitting system. This is illustrated in  FIGS. 14-15 . 
       FIG. 14  is a schematic side view of light emitting system  1432  including pixels  1441 ,  1442 , and  1443 . Light emitting system  1432  may be used for any of light emitting systems  132 ,  232 ,  332 ,  432 , and  532 , in optical system  100 ,  200 ,  300 ,  400  and  500 , respectively, for example. Each pixel emits a cone of light having a cone angle and a central ray. Pixel  1441  emits cone of light  1449  having a central ray  1447  emitted along a direction making an angle α to the optical axis  1440  of the light emitting system  1432  or of a lens system disposed to receive light from light emitting system  1432 . Pixel  1442  emits a cone of light having a cone angle θ. Light from each of pixels  1441  and  1443  is bent toward optical axis  1440 , while light from pixel  1442  is emitted substantially along optical axis  1440 . In some embodiments, light from each of pixels  1441 ,  1442 , and  1443  are at least partially collimated. In other embodiments, light from the pixels may have a direction altered without being at least partially collimated. In some embodiments, an at least partially collimated backlight is used to produce at least partially collimated light output from light emitting system  1432 . In some embodiments, a first portion of the backlight is configured to emit light at least partially collimated in a first direction and a different second portion of the backlight is configured to emit light at least partially collimated in a second different direction. For example, light from the backlight at a location corresponding to pixel  1441  may be at least partially collimated along the direction of central ray  1447  and light from the backlight at a location corresponding to pixel  1442  may be at least partially collimated along a direction parallel to the optical axis  1440 . In some embodiments, light from the at least partially collimated backlight may be partially collimated along a direction which varies smoothly across the emitting surface of the backlight. 
       FIG. 15  is a schematic side view of light emitting system  1532  including pixels  1541 ,  1542 , and  1543 . Each pixel emits a cone of light having a cone angle and a central ray. Pixel  1541  emits cone of light  1549  having a central ray  1547  emitted along a direction making an angle α to the optical axis  1540  of the light emitting system  1532  or of a lens system disposed to receive light from light emitting system  1532 . Pixel  1542  emits a cone of light having a cone angle θ. Light from each of pixels  1541  and  1543  is bent away optical axis  1540 , while light from pixel  1542  is emitted substantially along optical axis  1540 . In some embodiments, light from each of pixels  1541 ,  1542 , and  1543  are at least partially collimated. In other embodiments, light from the pixels may have a direction altered without being at least partially collimated. In some embodiments, an at least partially collimated backlight is used to produce at least partially collimated light output from light emitting system  1532  as further described in connection to  FIG. 14 . 
       FIG. 16A  is a cross-sectional view of optical system  1600  including lens system  1619 , and light emitting system  1632  which includes liquid crystal display panel  1630  and backlight  1636  which is an at least partially collimating backlight and may be adapted to provide an output direction that varies with location. Backlight  1636  includes light guide  1663  which includes collimating optical element  1660  and light extraction element  1665  having a surface  1667  structured such that light is extracted from the light guide  1663  as an at least partially collimated light. Backlight  1636  further includes light source  1661  which is configured to inject light into collimating optical element  1660 , and back reflector  1668  disposed adjacent light extraction element  1665 . Light source  1661  may be any suitable light source such as a light emitting diode (LED) or a plurality of LEDs. Light from the light source  1661  may be at least partially collimated as it passes through collimating optical element  1660  by virtue of the tapered geometry of the collimating optical element  1660 . Light is extracted from light extraction portion  1665  towards back reflector  1668  and the light is then reflected from the back reflector  1668  and is transmitted through the light extraction portion  1665  as an at least partially collimated light along desired output directions towards lens system  1619 . 
     In some embodiments, an at least partially collimating backlight that is adapted to provide an output direction that varies with location is combined with a light redirecting layer. In such embodiments, backlight provides an output that is partially turned towards a desired direction to be utilized by the lens system and the light redirecting layer receives this partially turned light and transmits light in a direction more closely matched to the desired direction for the lens system. 
     Collimating element  1660  is a light insertion portion of the light guide  1663 . Light guide  1663  further a light transport portion  1664  disposed to receive light from the collimating optical element  1660  through first fold  1671  and to transport light to the light extraction element  1665  through second fold  1674 . Structured surface  1667  of light extraction element  1665  may include light extractors oriented to produce light output along desired output directions. The surface can be suitably structured by using a structured stamping tool, such as a structured nickel stamping tool, for example. Suitable stamping tools can be prepared by machining, such as by single point diamond machining Exemplary diamond turning systems and methods can include and utilize a fast tool servo (FTS) as described in, for example, PCT Published Application No. WO 00/48037 (Campbell et al.), and U.S. Pat. Nos. 7,350,442 (Ehnes et al.) and 7,328,638 (Gardiner et al.). An at least partially collimated backlight may include gratings adapted to produce light output along desired output directions. Such backlights are described by Fattal et al., “A multi-directional backlight for a wide-angle, grasses-free three dimensional display”, Nature, Vol. 495, pp. 348-351, Mar. 21, 2013. In some embodiments, structured surface  1667  may include a series of steps  1666  with sloped portions  1669  between the steps as described, for example, in U.S. 2013/0321913 (Harold et al.) which is hereby incorporated herein by reference to the extent that it does not contradict the present description. Steps  1666  and sloped portions  1669  in structured surface  1667  can be formed by machining, for example. The sloped portions  1669  cause light to be extracted from the light extraction element  1665 . The distribution of output directions of such backlights can be adjusted by adjusting the distribution of slopes of the sloped portions  1669  between the steps  1666 . In some embodiments, the steps have a curved shape as described further elsewhere herein (see, e.g.,  FIG. 16C ). 
     Optical system  1600  has an exit pupil  1635  and further includes optical polarizer  1670  which may be a reflective polarizer, an absorptive polarizer, a combination of an absorptive and reflective polarizer, or may optionally be omitted. 
     Lens system  1619  includes first and second optical lenses  1610  and  1620 . First lens  1610  includes a major surface  1614  upon which is disposed a partial reflector having an average optical reflectance of at least 30% in a desired plurality of wavelengths as described elsewhere herein. Second lens  1620  includes a major surface  1626  upon which is disposed a reflective polarizer, which may be a thermoformed or pressure-formed reflective polarizer and may be a polymeric multilayer reflective polarizer or a wire grid polarizer, for example. A quarter-wave retarder may be disposed on the reflective polarizer. 
     Any of optical systems  100 ,  200 ,  300 ,  400 ,  500  or  1600  for example, may be referred to as a display system or as an imaging system. Any of these optical systems may be used in a head-mounted display such as a virtual reality display. 
       FIGS. 16B and 16C  are cross-sectional and perspective views, respectively, of display system  1600   b  including an imager  1630   b  for forming an image and a projection lens system  1619   b  for projecting the image formed by the imager  1630   b . The imager  1630   b  includes a plurality of pixels. For each pixel in the plurality of pixels, the imager is configured to emit a cone of light having a central ray. The central ray has a direction that varies with location of the pixel in the imager  1630   b  by virtue of the geometry of the light extraction element  1665 . In some embodiments, the variation of the central ray direction increases a brightness of an image projected through the projection lens system by at least 30 percent, or at least 50 percent or at least 100 percent, or at least 200 percent. The image projected through the projection lens is a patterned light that may or may not be in focus throughout the image. For example, the image projected through the projection lens may have a central portion forming an in-focus image and a peripheral portion which may not be in focus. The projection lens system  1619   b  may be a refractive lens system as illustrated in  FIG. 16B  or may be a folded optical system including first and second partial reflectors adjacent to and spaced apart from each other. For example, in some embodiments, the projection lens system  1619   b  corresponds to the lens system  119  and the first partial reflector corresponds to partial reflector  117  while the second partial reflector corresponds to reflective polarizer  127 . In some embodiments, the projection lens system  1619   b  has an acceptance angle and the variation in the central ray direction increases light emitted by the imager  1630   b  that is within the acceptance angle by at least 30 percent, or at least 50 percent or at least 100 percent, or at least 200 percent. 
     In some embodiments, the projection lens system  1619   b  has a largest lateral optically active dimension D 1  that is less than about 80 percent (or less than about 60%, or less than about 50%, less than about 40%) of a largest lateral optically active dimension D 2  of the imager  1630   b . The largest lateral optically active dimension of a component refers to the largest lateral dimension, which is the largest dimension in the x-y plane of  FIG. 16B , of the portion of the component which is optically utilized in forming the output of the display system  1600   b . For example, a pixelated display panel typically has a rectangular area of pixels that is optically active with some border region around the rectangular area of pixels that is not optically active. The largest lateral optically active dimension is the diagonal of the rectangular area of pixels in this case. As another example, a lens may have a circular area that receives and transmits light and the diameter of this circular area is the largest lateral optically active dimension in this case. 
     The display system  1600   b  includes a light guide  1663  having a light insertion portion  1660   b  and a light extraction portion  1665   b  in optical communication with the light insertion portion  1660   b  and with the imager  1630   b . The light guide  1663   b  is folded such that such that the light extraction portion  1665   b  faces the faces the light insertion portion  1660   b . The light guide  1663   b  includes a light transport portion  1664   b  configured to receive light from the light insertion portion  1660   b  from first fold  1671   b  and transport the light to the light extraction portion  1665   b  through second fold  1673   b . The imager  1630   b  may be a reflective spatial light modulator (e.g., a liquid crystal on silicon (LCoS) panel) disposed between the light extraction portion  1665   b  and the light insertion portion  1660   b . Alternatively, the imager may be a transmissive spatial light modulator disposed proximate the light extraction portion opposite the light insertion portion as illustrated in  FIG. 16A . In the embodiment of  FIG. 16B , light is extracted from light extraction portion  1665   b  as an at least partially collimated light towards imager  1630   b  which reflects an imaged light back through light extraction portion  1665   b  towards lens system  1619   b.    
     Lens system  1619   b  has an optical axis  1640   b  (parallel to z-axis). The light insertion portion  1660   b  and the light extraction portion  1665   b  are spaced apart along an optical axis  1640   b  of the lens system  1619   b . The optical axis  1640   b  intersects the light insertion portion  1660   b  and the light extraction portion  1665   b.    
     In some embodiments, structured surface  1667   b  includes a series of steps  1666   b  with sloped portions  1669   b  between the steps  1666   b  as described for structured surface  1667 , steps  1666  and slope portions  1669  of  FIG. 16A . Steps  1666  or  1666   b  may be described as discrete spaced apart light extraction features. Other discrete spaced apart light extraction features suitable for extracting light from the light extraction portion can be used in place of the steps. In some embodiments, the shape of the light extraction features concentrates light toward the imager by a combination of curvature around the z-axis, which concentrates light along the x-axis, and changes in angle of the extraction features along the y-axis, which concentrates light along the y-axis. The extraction features may be uncoated material, relying on total internal reflection (TIR) to extract light, or may be coated with a metallic or dielectric reflector. Alternatively, the entire extracting surface  1667  or  1667   b  may be coated with a reflective polarizer. This can be created through a MacNeille polarizer, a wire grid polarizer, or a polymeric multilayer optical film reflective polarizer such as APF or Dual Brightness Enhancement Film (DBEF) available from 3M Company, St Paul, Minn. The reflective polarizer can be shaped to conform to the extracting elements. This can be done by, for example, applying a thin layer of an adhesive to the structured surface  1667  or  1667   b , and applying a reflective polarizer film (such as APF) to the surface with heat and/or pressure to conform the film to the structured surface. One or more surfaces of the light guide  1663  or  1663   b  may have a low index coating with the refractive index of the coating being able to maintain TIR conditions within the light guide. In some embodiments, the low index coating has a refractive index about 0.05 to 0.2 lower than the refractive index of the light guide (unless specified differently, refractive index refers to the refractive index as measured at 532 nm). The low index coating may be optically thick and may have a physical thickness of at least 0.5 micrometers or at least 1 micrometer, for example. 
     Other suitable light guides suitable for use in optical system  1600  or display system  1600   b  are illustrated in  FIGS. 26-28 . 
       FIG. 26  is a schematic cross-sectional view of light guide  2663  including a light insertion portion  2660  adapted to receive light  2638 ; a light transport portion  2664  disposed to receive light from the light insertion portion  2660 , the light transport portion  2664  having a first segment  2664 - 1  and a second segment  2664 - 2 ; and a light extraction portion  2665  disposed to receive light from the light transport portion  2664 . The light  2638  received by the light insertion portion  2660  propagates predominately along a first direction  2681 , the light received by the light transport portion  2683  propagates predominately along a second direction  2683  in the first segment  2664 - 1 , and the light received by the light extraction portion propagates predominately along a third direction  2685 . A first included angle between the first and second directions  2681  and  2683  is at least 140, or at least 150 degrees, or at least 160 degrees, or is about 180 degrees, and a second included angle between the first and third directions is less than 40 degrees, or less than 30 degrees, or less than 20 degrees. In the illustrated embodiment, the first included angle is about 180 degrees and the second included angle is about zero degrees. The first and second included angles can be changed by changing the orientation of the light insertion portion  2660  and/or the orientation of the light extraction portion  2685  such that one of both of the portions is tilted from the x-y plane. The included angle between two directions refers to the principle value of the inverse cosine (which is, by definition, in a range of zero to 180 degrees) of the dot product of the unit vectors along the two directions. For example, referring to  FIG. 29 , which is a schematic representation of an included angle between two directions, the inverse cosine of the dot product of unit vectors  2981  and  2985  gives the angle φ which is the included angle between a first direction along unit vector  2981  and a second direction along unit vector  2985 . Since an included angle must be between zero and 180 degrees, specifying an included angle as greater than 140 degrees is equivalent to specifying the included angle as between 140 degrees and 180 degrees, for example. 
     The light transport portion  2664  is disposed to receive light from the light insertion portion  2660  through a first fold  2671  and to transport the light to the light extraction portion  2665  though a second fold  2674 . The second fold  2674  includes a first sub-fold  2674 - 1  and a second sub-fold  2674 - 2 . 
       FIG. 27  is a schematic cross-sectional view of light guide  2763  which includes a light insertion portion  2760  adapted to receive light  2738 , and a light extraction portion  2765  disposed to receive light from the light insertion portion  2760 . The light extraction portion  2765  receives light from the light insertion portion  2760  through fold  2771 . The light received by the light insertion portion  2760  propagates predominately along a first direction  2781 , and the light received by the light extraction portion  2765  propagates predominately along a second direction  2765 . An included angle between the first direction  2781  and the second direction  2785  is at least 120 degrees, or at least 140 degrees, or at least 160 degrees. For example, the included angle may be in a range of 160 to 180 degrees, or may be about 180 degrees as illustrated. The light extraction portion  2765  may include a plurality of light extraction features adapted to extract light from the light extraction portion towards a projection lens system as illustrated in  FIGS. 16A-16C , for example. An angle within 5 degrees of zero degrees may be described as about zero degrees and an angle within 5 degrees of 180 degrees may be described as about 180 degrees. 
     The light guides  2663  and  2763  each include a light insertion portion adapted to receive light; a light transport portion disposed to receive light from the light insertion portion through a first fold; and a light extraction portion disposed to receive light from the light transport portion through a second fold. In each case, the light extraction portion is spaced apart from and faces the light insertion portion. In some embodiments, the light extraction portion and the light insertion portion may contact each other or may be separated by only a small gap.  FIG. 28  is a schematic cross-sectional view of light guide  2863  which includes a light insertion portion  2860  and a light extraction portion  2865  optically connected to each other through a fold  2871 . The light extraction portion  2865  may include a plurality of light extraction features adapted to extract light from the light extraction portion  2865  towards a projection lens system as illustrated in  FIGS. 16A-16C , for example. Light propagates in light insertion portion  2860  primarily along first direction  2881  and light propagates in light extraction portion  2865  primarily along second direction  2885 . The included angle between the first and second directions  2881  and  2885  may be in at least 140 degrees, for example. 
     In some embodiments, a light redirecting layer includes a concave surface that is concave toward the pixelated light source with each different portion of the concave surface corresponding to a different group of pixels in the pixelated light source. The portions of the concave surface may be in one to one correspondence with the groups of pixels. This is illustrated in  FIG. 17  which is a schematic side view of light emitting system  1732  including light redirecting layer  1750  and pixelated light source  1730 . Light emitting system  1732  may be used for any of light emitting systems  132 ,  232 ,  332 ,  432 , and  532 , in optical system  100 ,  200 ,  300 ,  400  and  500 , respectively, for example. In the illustrated embodiment, light redirecting layer  1750  includes a single optical element having a concave surface  1758  which is concave towards light redirecting layer  1730 . Pixelated light source  1730  includes a plurality of pixels  1744  which includes a plurality of groups of pixels including groups  1741   a ,  1741   b ,  1741   c , and  1741   d . Concave surface  1758  includes a plurality of portions  1756   a ,  1756   b ,  1756   c , and  1756   d . Each different portion corresponding to a different group of pixels. For example, light from group of pixels  1741   a  may pass through portion  1756   a  of concave surface  1758  and may substantially not pass through other portions of the concave surface  1758 . This can be achieved placing the pixels in close proximity to the concave surface  1758 . In embodiments where an LCD panel comprises the plurality of pixels, a thin outer glass layer may be used as described elsewhere herein in order to position the light redirecting layer  1750  closer to the plurality of pixels. In embodiments where an LCD panel comprises the plurality of pixels, the light redirecting layer  1750  may be formed from an outer glass layer of the LCD panel as described elsewhere herein in order to position the surface  1758  close to the plurality of pixels  1744 . In some embodiments, when pixelated light source  1732  is used in an optical system including a lens system, such as those including a partial reflector and a reflective polarizer as described elsewhere herein, any light from a group of pixels that passes through any portion of concave surface  1758  other than the portion corresponding to the group of pixels may be outside an acceptance angle of the lens system and therefore not utilized by the optical system. 
       FIG. 18  is a schematic cross-sectional view of light emitting system  1832  including a liquid crystal display panel  1830 , a backlight  1836 , and a light redirecting layer  1850  having a concave light redirecting surface  1858 . Although a liquid crystal display panel is illustrated in  FIG. 18 , light redirecting layer  1850  may be used with other types of pixelated displays, such as an OLED display, for example. Light emitting system  1832  may be used for any of light emitting systems  132 ,  232 ,  332 ,  432 ,  532 , in optical system  100 ,  200 ,  300 ,  400  and  500 , respectively, for example. Liquid crystal display panel  1830  includes a plurality of pixels  1844  disposed between first and second glass layers  1876  and  1878 . The plurality of pixels  1844  includes first pixel  1841  and second pixel  1842 . A first polarizer  1872  is disposed between the light redirecting layer  1850  and the liquid crystal display panel  1830  and a second polarizer  1873  is disposed between the liquid crystal display panel  1830  and the backlight  1836 . The backlight  1836  may be an at least partially collimating backlight as described elsewhere herein. Light emitting system  1832  is centered on an optical axis  1840 . Light redirecting layer  1850  is a single light redirecting element in the illustrated embodiment. Light redirecting layer  1850  includes a concave light redirecting surface  1858  which is concave toward liquid crystal panel  1830 . Concave light redirecting surface  1858  includes first portion  1856  adapted to receive light from first pixel  1841  and includes second portion  1857  adapted to receive light from second pixel  1842 . In some embodiments, concave light redirecting surface  1858  includes a plurality of different portions with each different portion being in one to one correspondence with a different pixel, or with a different group of pixels, in the plurality of pixels  1844 . 
       FIG. 19  is a schematic cross-sectional view of light emitting system  1932  including a liquid crystal display panel  1930 , a backlight  1936 , and a light redirecting layer  1950  having a concave light redirecting surface  1958 . Liquid crystal display panel  1930  includes a plurality of pixels  1944  disposed between first and second glass layers  1976  and  1978 . The light redirecting layer  1950  is formed from first glass layer  1976  by, for example, etching the outer surface of the first glass layer  1976  to form concave light redirecting surface  1958 . Suitable glass etching methods that can be used to form concave light redirecting surface  1958  are known in the art and are described, for example, in U.S. Pat. Pub. No. 2002/0079289 (Doh). Suitable glass etchants include hexafluorosilicic acid and hydrogen fluoride. 
     The plurality of pixels  1944  includes first pixel  1941  and second pixel  1942 . A first polarizer  1972  is disposed on concave light redirecting surface  1958 , and a second polarizer  1973  is disposed between the liquid crystal display panel  1930  and the backlight  1936 . The backlight  1936  may be an at least partially collimating backlight as described elsewhere herein. Light emitting system  1932  is centered on an optical axis  1940 . Concave light redirecting surface  1958  includes first portion  1956  adapted to receive light from first pixel  1941  and includes second portion  1957  adapted to receive light from second pixel  1842 . As described further elsewhere herein, in some embodiments, concave light redirecting surface  1958  includes a plurality of different portions with each different portion being in one to one correspondence with a different pixel, or with a different group of pixels, in the plurality of pixels  1944 . 
     Light emitting system  1932  may be used for any of light emitting systems  132 ,  232 ,  332 ,  432 ,  532 , in optical system  100 ,  200 ,  300 ,  400  and  500 , respectively, for example. 
     In some embodiments of light emitting system  1832  or  1932 , each different portion of the concave light redirecting surface corresponds to a different group of pixels in the plurality of pixels and receives a first diverging light emitted by a pixel in the group of pixels having a first cone angle and transmits the received light as a second diverging light having a second cone angle less than the first cone angle. In some embodiments, light from a pixel in a group of pixels is either substantially not transmitted through any portion of the light redirecting layer not corresponding to the group of pixels or is at most partially transmitted through a portion of the light redirecting layer not corresponding to the group of pixels in a direction that is not within an acceptance angle of a lens system adapted to receive light from the light emitting system. 
       FIG. 20  is a schematic cross-sectional view of light emitting system  2032  including a plurality of light redirecting elements which includes light redirecting element  2056  and  2057 , a liquid crystal display panel  2030  having a plurality of discrete spaced apart pixels  2044  provided by a liquid crystal layer between first and second glass layers  2076  and  2078 . The first glass layer  2076  may have a reduced thickness compared to conventional LCD displays or compared to the second glass layer  2078  in order to position the light redirecting elements  2056  and  2057  closer to the apertures defining the plurality of pixels  2044 . Although a liquid crystal display panel is illustrated in  FIG. 20 , light redirecting elements  2056  and  2057  may be used with other types of pixelated displays, such as an OLED display, for example. The liquid crystal display panel  2030  is disposed between first and second polarizers  2072  and  2073  and is illuminated by backlight  2036  which may be an at least partially collimating backlight as described elsewhere herein. Each light redirecting element may correspond to a group of pixels in the plurality of pixels, where the group may be a single pixel or a plurality of pixels. Light redirecting elements may be included for some, for most, or for all of the pixels. For example, light redirecting elements may be included for all pixels except for pixels located near an optical axis of the light emitting system  2032  or of an optical system including a lens system and the light emitting system  2032 . Light emitting system  2032  may be used for any of light emitting systems  132 ,  232 ,  332 ,  432 ,  532 , in optical system  100 ,  200 ,  300 ,  400  and  500 , respectively, for example. Each of the light redirecting elements may be prismatic elements and may optionally include one or more curved surfaces. In alternate embodiments, a plurality of microlenses may be used in place of some or all of the prismatic elements. In still other embodiments, a light redirecting layer comprising a Fresnel lens may be used in place of individual light redirecting elements. This is illustrated in  FIG. 21 . 
       FIG. 21  is a cross-sectional view of light emitting system  2132  including light redirecting layer  2150  and liquid crystal display panel  2130  which includes a plurality of discrete spaced apart pixels  2144 . Although a liquid crystal display panel is illustrated in  FIG. 21 , light redirecting layer  2150  may be used with other types of pixelated displays, such as an OLED display, for example. Liquid crystal panel  2130  is disposed between first and second polarizers  2172  and  2173  and illuminated by backlight  2136 , which may be an at least partially collimating backlight as described elsewhere herein. Light redirecting layer  2150  includes light redirecting elements  2156  and may be a Fresnel lens or may be a blazed diffraction grating. In some embodiments, at least some of the light redirecting element  2156  are concentric rings. Each light different redirecting element  2156  may correspond to a different group of pixels in the plurality of discrete spaced apart pixels  2144 . For example, if a light redirecting element is a concentric ring shaped element, the group of pixels corresponding the light redirecting element may be the plurality of pixels disposed under the concentric ring. In still other embodiments, light redirecting layer  2150  may be replaced by other types of light redirecting elements. For example, light redirecting layer  2150  may be a holographic optical element. 
     Light emitting system  2132  may be used for any of light emitting systems  132 ,  232 ,  332 ,  432 ,  532 , in optical system  100 ,  200 ,  300 ,  400  and  500 , respectively, for example. 
       FIG. 22  is a schematic cross-sectional view of light emitting system  2232  including liquid crystal display panel  2230  which includes a plurality of pixels  2244  and first and second glass layers  2276  and  2278 . A plurality of lenses including lenses  2256  and  2257  are formed in first glass layer  2276 . The lenses may be formed by etching the first glass layer  2276  and filling the etched out regions with a material having a refractive index different than that of the first glass layer  2276 . For example, a higher refractive index material may be used in order to reduce a divergence angle of light emitted by a corresponding pixel. Suitable high index materials include polymeric materials filled with high refractive index nanoparticles such as those described in U.S. Pat. No. 8,343,622 (Liu et al.) which is hereby incorporated herein to the extent that it does not contradict the present description. Each different lens in the plurality of lenses may correspond to a different group of pixels in the plurality of pixels. Each group of pixels may be a single pixel or may include a plurality of pixels. Light emitting system  2232  may be used for any of light emitting systems  132 ,  232 ,  332 ,  432 ,  532 , in optical system  100 ,  200 ,  300 ,  400  and  500 , respectively, for example. 
     The light redirecting layer or light redirecting elements of any of the light emitting systems  1732 ,  1832 ,  1932 ,  2032 ,  2132  and  2232 , may be adapted to bend light output from at least one pixel, or of a majority of the pixels, toward or away from an optical axis of the light redirecting layer or light redirecting elements or toward or away from an optical axis of a display system incorporating a lens system and the light redirecting layer or elements. 
     An alternative to including a light redirecting layer on a display panel is to include a light redirecting layer on a lens disposed to receive light from a display panel.  FIG. 23  is a schematic cross-sectional view of lens system  2319  including first and second optical lenses  2310  and  2320 . First optical lens  2310  includes opposing first and second major surfaces  2314  and  2316 , the first major surface  2314  being an inner major surface and the second major surface  2316  being an outer major surface. Second optical lens  2320  includes opposing first and second major surfaces  2324  and  2326 . Lens system  2319  includes a partial reflector which may be disposed on first major surface  2314  of first lens  2310 . Lens system  2319  also includes a reflective polarizer configured to substantially transmit light having a first polarization state and substantially reflect light having an orthogonal second polarization state. The reflective polarizer is disposed adjacent to and spaced apart from the partial reflector and may be disposed on the second lens  2320 . In some embodiments, the reflective polarizer is disposed on second major surface  2326 . In some embodiments, a quarter-wave retarder is disposed on the reflective polarizer. The partial reflector may have an average optical reflectance of at least 30% in a desired plurality of wavelengths as described elsewhere herein. 
     The second major surface  2316  of the first optical lens  2310  includes a plurality of light redirecting elements  2350  including light redirecting elements  2356  and  2357 . Each light redirecting element is adapted to receive a first cone of light and transmit the received light as a second cone of light towards the partial reflector. For example light redirecting element  2356  is adapted to receive first cone of light  2339  and transmit the received light as second cone of light  2349 . As described further elsewhere herein, each light redirecting element may be adapted to change one or both of a divergence angle and a central ray direction of the received cone of light. Lens system  2319  may be used in place of lens systems  119  or  219  in the optical systems  100  or  200 , respectively, for example. 
     The reflective polarizer included in lens system  2319  may be curved about one or two orthogonal axes. In some embodiments, the reflective polarizer is a multilayer polymeric film and in some embodiments the reflective polarizer is a thermoformed or pressure-formed multilayer reflective polarizer such as APF as described elsewhere herein. 
     In some embodiments, a brightness of a display system including a pixelated light emitting system and lens system  2319  disposed to receive light emitted by the pixelated system at an exit pupil of the display system is at least 30 percent higher than that of an otherwise equivalent display system not including the plurality of light redirecting elements  2350 . In some embodiments, the brightness of the display system at the exit pupil is at least 100 percent higher, or at least 200 percent higher, or at least 300 percent higher than that of the otherwise equivalent display system. 
       FIG. 24  is a schematic cross-sectional view of a portion of a display system  2400  including a light emitting system  2432  which includes a plurality of light emitting pixels  2444 . Each light emitting pixel includes an optional optically transparent first light redirecting element  2456  having an average optical transmittance of at least 50% in a desired plurality of wavelengths, an optically reflecting second light redirecting element  2457  concave toward the first light redirecting element  2456  and having an average optical reflectance of at least 50% in the desired plurality of wavelengths, and a light emitting material  2441  disposed between the first and second light redirecting elements  2456  and  2457 . The light emitting material  2441  may be included in a display panel  2430  which may be an at least partially transmissive OLED display panel, for example. The display panel  2430  is shown as a substantially planar panel in  FIG. 24 , but in other embodiments the display panel may be curved (see, e.g.,  FIG. 1B ) or may include a plurality of planar portions not all in a same plane (see, e.g.,  FIG. 1C ). In some embodiments, a center  2442  of the second light redirecting element  2457  lies within the light emitting material  2441 . For example, the second light redirecting element  2457  may have a concave reflective surface having a center of curvature or a focal point that lies within the light emitting material  2441 . In some embodiments, light emitted by the light emitting material  2441  is substantially collimated by the first and second light redirecting elements  2456  and  2457 . In some embodiments, the optional first light redirecting element  2456  is omitted and light emitted by the light emitting material  2441  is substantially collimated by the second light redirecting element  2457 . For example, light emitting material in the panel  2430  may emit a diverging first cone of light  2439  which is reflected from a concave second light redirecting element and transmitted through a first light redirecting element as substantially collimated light  2449 . 
     Display system  2400  may further include a lens system, such as lens systems  119  or  219 , for example, disposed to receive light from the light emitting system  2432  and transmit at least a portion of the received light to an exit pupil of the display system  2400 . 
     Optical transmittance or reflectance of various components (e.g., partial reflector, quarter-wave retarder, transmissive optical elements, and reflective optical elements) may be specified by an average in a desired or predetermined plurality of wavelengths. The desired or pre-determined plurality of wavelengths may, for example, be any wavelength range in which the optical system is designed to operate. The pre-determined or desired plurality of wavelengths may be a visible range, and may for example, be the range of wavelengths from 400 nm to 700 nm. In some embodiments, the desired or pre-determined plurality of wavelengths may be an infrared range or may include one or more of infrared, visible and ultraviolet wavelengths. In some embodiments, the desired or pre-determined plurality of wavelengths may be a narrow wavelength band, or a plurality of narrow wavelength bands, and the partial reflector, for example, may be a notch reflector. In some embodiments, the desired or pre-determined plurality of wavelengths include at least one continuous wavelength range that has a full width at half maximum of no more than 100 nm, or no more than 50 nm. 
     Any of the optical systems of the present description may be used in a device such as a head-mounted display (e.g., a virtual reality display).  FIG. 25  is a schematic top view of head-mounted display  2590  including a frame  2592 , first and second display portions  2594   a  and  2594   b  which may include any of the optical systems of the present description. In the illustrated embodiment, first display portion  2594   a  includes lens system  2519   a  and light emitting system  2532   a  and display portion  2594   b  includes lens system  2519   b  and light emitting system  2532   b . Each of lens systems  2519   a  and  2519   b  may include a reflective polarizer and a partial reflector as described elsewhere herein. Each of light emitting systems  2532   a  and  2532   b  may include a plurality of pixels and a light redirecting layer and/or an at least partially collimating backlight as described elsewhere herein. In some embodiments, lens systems  2519   a  and  2519   b  are centered on an optical axis (e.g., an axis parallel to the z-axis in  FIG. 25 ) and light emitting systems  2532   a  and  2532   b  are disposed at an obtuse angle relative to the corresponding optical axis. In other embodiments, the light emitting systems  2532   a  and  2532   b  are disposed at right angles to the corresponding optical axis and may be centered on the corresponding optical axis. Light redirecting layers of the light emitting systems  2532   a  and  2532   b  may redirect light output by the corresponding pixels so that it is within the acceptance angle of the corresponding lens system. In embodiments where the light emitting system is disposed at an obtuse angle to the optical axis of a lens system, the light redirecting elements of the light emitting system may include a curved surface, such as curved surface  1131   c , which is asymmetric about the optical axis. 
     EXAMPLES 
     Example 1 
     A folded optic lens system with elements described in the following table was modeled using Zemax 15 lens design software. 
     
       
         
           
               
               
               
               
               
               
               
             
               
                   
                   
               
               
                   
                   
                   
                 Thick- 
                   
                 Semi- 
                   
               
               
                   
                 Surface 
                 Radius 
                 ness 
                   
                 Diameter 
               
               
                   
                 Type 
                 (mm) 
                 (mm) 
                 Material 
                 (mm) 
                 Conic 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 OB 
                 Standard 
                 Infinity 
                 Infinity 
                 NA 
                 Infinity 
                 0.000 
               
               
                 ST 
                 Standard 
                 Infinity 
                 10.000 
                 NA 
                 3.542 
                 0.000 
               
               
                 2 
                 Even 
                 36.671 
                 5.000 
                 Poly- 
                 15.000 
                 −20.921 
               
               
                   
                 Asphere 
                   
                   
                 carbonate 
               
               
                 3 
                 Even 
                 −66.536 
                 2.261 
                 NA 
                 15.391 
                 13.841 
               
               
                   
                 Asphere 
               
               
                 4 
                 Even 
                 −37.346 
                 −2.261 
                 Mirror 
                 15.589 
                 2.644 
               
               
                   
                 Asphere 
               
               
                 5 
                 Even 
                 −66.536 
                 2.261 
                 Mirror 
                 14.989 
                 13.841 
               
               
                   
                 Asphere 
               
               
                 6 
                 Even 
                 −37.346 
                 6.000 
                 E48R 
                 14.931 
                 2.644 
               
               
                   
                 Asphere 
               
               
                 7 
                 Even 
                 −7.233 
                 6.001 
                 NA 
                 15.167 
                 −3.173 
               
               
                   
                 Asphere 
               
               
                 IM 
                 Standard 
                 Infinity 
                 NA 
                 NA 
                 12.205 
                 0.000 
               
               
                   
               
            
           
         
       
     
     In the above table, OB refers to the object and the surfaces are listed order from the stop surface (ST) to the image surface (IM). The aspheric polynomial coefficients were taken to be zero except for surface  7  which had second, fourth, sixth, eight, and tenth order coefficients of 0.000, −2.805×10 −5 , 1.232×10 −7 , −1.936×10 −10 , and −3.088×10 −13 , respectively. 
     The lens was imported into LightTools, where a display plane was created with a central and peripheral emissive element. Each element was immersed in an NBK7 lens with a 0.1 mm diameter and a 0.05 mm radius. The emissive elements were designed to have a 0.004 mm square emissive area. Placement of the lens relative to the emissive element was optimized so as to provide the best combination of uniformity and brightness at the pupil. The near eye display with the microlens array was 8.1 times brighter than without the lens array (710 percent increase in brightness). 
     Example 2 
     An optical system similar to optical system  200  was modeled using ray tracing as follows. Optical stack  210  included a quarter wave retarder on the outer surface (surface facing panel  232 ) of lens  212  and partial reflector on the inner surface (surface facing exit pupil  235 ) of lens  212 . Optical stack  220  included a linear polarizer on the outer surface (surface facing lens  212 ) of lens  222  and included a quarter wave retarder disposed on the linear polarizer. The quarter wave retarders were modeled as ideal retarders, the partial reflector was modeled as having a transmissivity of 50 percent and a reflectivity of 50 percent, and the linear polarizer was modeled as having a 1 percent transmissivity and a 99 percent reflectivity for light polarized along a linear block axis, and a 99 percent transmissivity and a 1 percent reflectivity for light polarized along an orthogonal linear pass axis. The lenses were as specified in the following table: 
                                                                     Thick-       Semi-               Surface   Radius   ness       Diameter           Type   (mm)   (mm)   Material   (mm)   Conic                                                                OB   Standard   Infinity   Infinity   NA   Infinity   0.0000000       ST   Standard   Infinity   15.000   NA   3.424   0.0000000       2   Even   −23.172   2.500   Poly-   12.500   0.0000000           Asphere           carbonate       3   Even   −18.852   4.691   NA   13.316   0.5582269           Asphere       4   Standard   Infinity   0.000   NA   21.709   0.0000000       5   Even   −19.441   −4.691   Mirror   15.345   −9.5827826           Asphere       6   Even   −18.852   4.691   Mirror   12.193   0.5582269           Asphere       7   Even   −19.441   2.000   E48R   15.500   −9.5827826           Asphere       8   Even   −19.441   1.820   NA   15.500   −9.5827826           Asphere       9   Standard   Infinity   0.281   PMMA   14.520   0.0000000       10   Standard   Infinity   0.010   NA   14.547   0.0000000       11   Standard   Infinity   0.700   N-BK7   14.548   0.0000000       12   Standard   Infinity   0.000   NA   14.620   0.0000000       IM   Standard   Infinity   NA   NA   14.000   0.0000000                    
The second through eight order aspheric polynomial coefficients used for the lens surfaces are given in the following table:
 
                                                     2nd Order   4th Order   6th Order   8th Order                                                        OB   NA   NA   NA   NA       ST   NA   NA   NA   NA       2   0.0000E+00    0.0000E+00   0.0000E+00    0.0000E+00       3   0.0000E+00    1.2455E−05   1.3936E−07    1.8601E−09       4   NA   NA   NA   NA       5   0.0000E+00   −1.4624E−04   9.5699E−07   −6.0196E−09       6   0.0000E+00    1.2455E−05   1.3936E−07    1.8601E−09       7   0.0000E+00   −1.4624E−04   9.5699E−07   −6.0196E−09       8   0.0000E+00   −1.4624E−04   9.5699E−07   −6.0196E−09       9   NA   NA   NA   NA       10   NA   NA   NA   NA       11   NA   NA   NA   NA       12   NA   NA   NA   NA       IM   NA   NA   NA   NA                    
The tenth and higher order aspheric polynomial coefficients used for the lens surfaces are given in the following table:
 
     
       
         
           
               
               
               
               
             
               
                   
                   
               
               
                   
                 10th Order 
                 12th Order 
                 14th Order 
               
               
                   
                 (mm −9 ) 
                 (mm −11 ) 
                 (mm −13 ) 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 OB 
                 NA 
                 NA 
                 NA 
               
               
                   
                 ST 
                 NA 
                 NA 
                 NA 
               
               
                   
                 2 
                 0.0000E+00 
                  0.0000E+00 
                 0.0000E+00 
               
               
                   
                 3 
                 2.4079E−11 
                 −1.2664E−13 
                 2.8533E−16 
               
               
                   
                 4 
                 NA 
                 NA 
                 NA 
               
               
                   
                 5 
                 2.3733E−11 
                 −5.3312E−14 
                 4.9018E−17 
               
               
                   
                 6 
                 2.4079E−11 
                 −1.2664E−13 
                 2.8533E−16 
               
               
                   
                 7 
                 2.3733E−11 
                 −5.3312E−14 
                 4.9018E−17 
               
               
                   
                 8 
                 2.3733E−11 
                 −5.3312E−14 
                 4.9018E−17 
               
               
                   
                 9 
                 NA 
                 NA 
                 NA 
               
               
                   
                 10 
                 NA 
                 NA 
                 NA 
               
               
                   
                 11 
                 NA 
                 NA 
                 NA 
               
               
                   
                 12 
                 NA 
                 NA 
                 NA 
               
               
                   
                 IM 
                 NA 
                 NA 
                 NA 
               
               
                   
                   
               
            
           
         
       
     
     The display panel  235  was modeled as producing a checker-board pattern of bright and dark squares, each squares having a dimension of 6 mm×6 mm. The display panel had dimensions of 2.4 cm×2.4 cm. The light output was modeled as having a central ray normal to the surface of the display panel and having a cone angle of 5 degrees half width at half maximum (HWHM). This was chosen to simulate a display panel with a partially collimating backlight or with a light redirecting layer that partially collimates the light output. For comparison, a conventional display panel having a cone angle of 35 degrees HWHM was also modeled. Receivers were position an exit pupil  235 . The contrast ratio was calculated as the average power of received at a bright square to the average power received at a dark square. For the partially collimated (5 degree HWHM) case, the contrast ratio was determined to be 747, while for the conventional case (35 degree HWHM), the contrast ratio was determined to be 100. 
     Example 3 
     The relative efficiency of optical system  1600  (depicted in  FIG. 16A ) and similar optical systems with backlight  1636  replaced with different backlight units were calculated. The relative efficiency of the optical system utilizing a backlight unit with a Lambertian output was defined to be unity. The relative efficiency of other optical systems was then defined as the ratio of the brightness at the exit pupil  1635  of the optical system to the brightness at the exit pupil  1635  of the optical system with the backlight unit having a Lambertian output. When the backlight unit included one Brightness Enhancement Film (BEF available from 3M Company, St. Paul, Minn.), the output from the backlight unit had a Full-Width and Half Maximum (FWHM) in a horizontal direction (width direction of the display) of 44 degrees and in a vertical direction (height direction of the display) of 80 degrees and the optical system had a relative efficiency of 1.4 (40 percent increase in brightness). When the backlight unit included two crossed BEFs, the output from the backlight unit had a FWHM of 44 degrees in both the horizontal and vertical directions and the optical system had a relative efficiency of 1.6 (60 percent increase in brightness). When the backlight unit included a structured surface  1667  adapted to provide a high degree of collimation in a direction normal to the display (in the minus z-direction), the output from the backlight unit had a FWHM of 16 degrees in the horizontal direction and 12 degrees in the vertical direction and the optical system had a relative efficiency of 2.4 (140 percent increase in brightness). When the backlight unit included a structured surface  1667  adapted to provide a high degree of collimation in directions turned towards the lens system  1619 , the output from the backlight unit had a FWHM of 12 degrees in the horizontal direction and 11 degrees in the vertical direction and the optical system had a relative efficiency of 3 (200 percent increase in brightness). The results are summarized in the following table. 
                                             FWHM-Horizontal   FWHM-Vertical   Relative       Backlight Unit   (degrees)   (degrees)   Efficiency                                                Lambertian   90   90   1       BEF   44   80   1.4       Crossed BEF   44   44   1.6       Collimated   16   12   2.4       Collimated and   12   11   3       angle optimized                    
The following is a list of exemplary embodiments of the present description.
 
Embodiment 1 is a display system, comprising:
 
an imager for forming an image, the imager comprising a plurality of discrete spaced apart pixels; and
 
a projection lens system for projecting the image formed by the imager,
 
wherein for each pixel in the plurality of pixels, the imager is configured to emit a cone of light having a central ray, the central ray having a direction that varies with location of the pixel in the imager, the variation increasing a brightness of an image projected through the projection lens system by at least 30 percent.
 
Embodiment 2 is the display system of Embodiment 1, wherein the projection lens system comprises a folded optical system.
 
Embodiment 3 is the display system of Embodiment 2, wherein the folded optical system comprises:
 
a first partial reflector having an average optical reflectance of at least 30% in a desired plurality of wavelengths; and
 
a second partial reflector adjacent to and spaced apart from the first partial reflector.
 
Embodiment 4 is the display system of Embodiment 3, wherein the second partial reflector is a reflective polarizer substantially transmitting light having a first polarization state and substantially reflecting light having an orthogonal second polarization state.
 
Embodiment 5 is the display system of Embodiment 3, wherein the second partial reflector has an average optical reflectance of at least 30% in the desired plurality of wavelengths.
 
Embodiment 6 is the display system of Embodiment 1, wherein the projection lens system comprises a refractive optical system.
 
Embodiment 7 is the display system of Embodiment 1, wherein the projection lens system has an acceptance angle and the variation in the central ray direction increases light emitted by the imager that is within the acceptance angle by at least 30 percent.
 
Embodiment 8 is the display system of Embodiment 1, wherein the projection lens system has an optical axis and an angle between the central ray and the optical axis varies with location of the pixel in the imager.
 
Embodiment 9 is the display system of Embodiment 1, wherein imager has a surface normal and an angle between the central ray and the surface normal varies with location of the pixel in the imager.
 
Embodiment 10 is the display system of Embodiment 1, wherein the imager is substantially planar.
 
Embodiment 11 is the display system of Embodiment 1, wherein the imager includes a plurality of planar portions disposed at oblique angles relative to one another.
 
Embodiment 12 is the display system of Embodiment 1, wherein the imager is curved.
 
Embodiment 13 is the display system of Embodiment 1, wherein the projection lens system has a largest lateral optically active dimension less than one half of a largest optically active dimension of the imager.
 
Embodiment 14 is the display system of Embodiment 1 further comprising a light guide having a light insertion portion and a light extraction portion in optical communication with the light insertion portion and with the imager.
 
Embodiment 15 is the display system of Embodiment 14, wherein the light insertion portion and the light extraction portion are spaced apart along an optical axis of the lens system.
 
Embodiment 16 is the display system of Embodiment 15, wherein the light guide further comprises a light transport portion configured to receive light from the light insertion portion and transport the light to the light extraction portion.
 
Embodiment 17 is the display system of Embodiment 16, wherein the optical axis intersects each of the light insertion portion, the light transport portion and the light extraction portion.
 
Embodiment 18 is the display system of Embodiment 14, wherein the light guide is folded such that the light extraction portion faces the light insertion portion.
 
Embodiment 19 is the display system of Embodiment 14, wherein light received by the light insertion portion propagates predominately along a first direction, the light received by the light extraction portion propagating predominately along a second direction, and an included angle between the first and second directions is less than 40 degrees or greater than 140 degrees.
 
Embodiment 20 is the display system of Embodiment 14, wherein the imager comprises a transmissive spatial light modulator disposed proximate the light extraction portion opposite the light insertion portion.
 
Embodiment 21 is the display system of Embodiment 14, wherein the imager comprises a reflective spatial light modulator disposed between the light extraction portion and the light insertion portion.
 
Embodiment 22 is a display system comprising:
 
a projection lens system having one or more lenses centered on an optical axis;
 
a light guide comprising:
         a light insertion portion adapted to receive light;   a light transport portion disposed to receive light from the light insertion portion; and a light extraction portion disposed to receive light from the light transport portion, the light extraction portion configured to provide a light output central ray direction having an angle with respect to the optical axis that varies with location on an output surface of the light extraction portion, the light extraction portion being separated from the light insertion portion along the optical axis forming a space between the light extraction portion and the light insertion portion; and
 
a spatial light modulator in optical communication with the light extraction portion,
 
wherein the light guide is folded such that the light extraction portion faces the light insertion portion.
 
Embodiment 23 is the display system of Embodiment 22, wherein the optical axis intersects the light insertion portion and the light extraction portion.
 
Embodiment 24 is the display system of Embodiment 23, wherein the optical axis intersects the light transport portion.
 
Embodiment 25 is the display system of Embodiment 22, wherein the spatial light modulator is disposed between the lens system and the light extraction portion.
 
Embodiment 26 is the display system of Embodiment 25, wherein the spatial light modulator is a transmissive liquid crystal panel.
 
Embodiment 27 is the display system of Embodiment 25, wherein a reflector is disposed in the space between the light extraction portion and the light insertion portion.
 
Embodiment 28 is the display system of Embodiment 22, wherein the spatial light modulator is disposed in the space between the light extraction portion and the light insertion portion.
 
Embodiment 29 is the display system of Embodiment 28, wherein the spatial light modulator is a reflective liquid crystal panel.
 
Embodiment 30 is the display system of Embodiment 29, wherein the reflective liquid crystal panel is a Liquid Crystal on Silicon (LCoS) panel.
 
Embodiment 31 is the display system of Embodiment 22, wherein the projection lens system comprises a folded optical system.
 
Embodiment 32 is the display system of Embodiment 31, wherein the projection lens system comprises:
 
a partial reflector having an average optical reflectance of at least 30% in a desired plurality of wavelengths; and
 
a reflective polarizer substantially transmitting light having a first polarization state and substantially reflecting light having an orthogonal second polarization state.
 
Embodiment 33 is the display system of Embodiment 22, wherein the projection lens system is a refractive optical system.
 
Embodiment 34 is the display system of Embodiment 22, wherein the optical lens system has a largest lateral optically active dimension less than one half of a largest lateral optically active dimension of the spatial light modulator.
 
Embodiment 35 is a display system comprising:
 
a projection lens system having one or more lenses and having a largest lateral optically active dimension; an imager having a largest lateral optically active dimension, an image formed by the imager projected by the projection lens system;
 
a light guide for receiving light from a light source and comprising a light extraction portion disposed between the projection lens system and the imager, the light extraction portion comprising a plurality of discrete spaced apart light extraction features for extracting and directing the received light toward the imager,
 
wherein the largest lateral optically active dimension of the projection lens system is no more than 80 percent of the largest lateral optically active dimension of the imager.
 
Embodiment 36 is the display system of Embodiment 35, wherein the largest lateral optically active dimension of the projection lens system is no more than 60 percent of the largest lateral optically active dimension of the imager.
 
Embodiment 37 is the display system of Embodiment 35, wherein the largest lateral optically active dimension of the projection lens system is no more than 50 percent of the largest lateral optically active dimension of the imager.
 
Embodiment 38 is the display system of Embodiment 35, wherein the largest lateral optically active dimension of the projection lens system is no more than 40 percent of the largest lateral optically active dimension of the imager.
 
Embodiment 39 is the display system of Embodiment 35, wherein the light guide further comprises a light insertion portion in optical communication with the light extraction portion.
 
Embodiment 40 is the display stem of Embodiment 39, where the light guide is folded such that the light insertion portion faces the light extraction portion.
 
Embodiment 41 is the display system of Embodiment 39, wherein the light guide further comprises a light transport portion disposed to receive light from the light insertion portion through a first fold and to transport the light to the light extraction portion though a second fold.
 
Embodiment 42 is the display system of Embodiment 41, wherein the lens has an optical axis, the optical axis intersecting the light insertion portion and the light extraction portion.
 
Embodiment 43 is the display system of Embodiment 42, wherein the optical axis intersects the light transport portion.
 
Embodiment 44 is the display system of Embodiment 39, wherein the imager is disposed between the light extraction portion and the light insertion portion.
 
Embodiment 45 is the display system of Embodiment 44, wherein the spatial light modulator is a reflective liquid crystal panel.
 
Embodiment 46 is the display system of Embodiment 45, wherein the reflective liquid crystal panel is a Liquid Crystal on Silicon (LCoS) panel.
 
Embodiment 47 is the display system of Embodiment 38, wherein the light insertion portion comprises an optical element configured to at least partially collimate light injected into the light insertion portion.
 
Embodiment 48 is a light guide comprising:
 
a light insertion portion adapted to receive light;
 
a light transport portion disposed to receive light from the light insertion portion through a first fold; and
 
a light extraction portion disposed to receive light from the light transport portion through a second fold, wherein the light extraction portion is spaced apart from and faces the light insertion portion.
 
Embodiment 49 is the light guide of Embodiment 48, wherein the light insertion portion comprises an optical element configured to at least partially collimate light received into the light insertion portion.
 
Embodiment 50 is the light guide of Embodiment 48, wherein the light extraction portion has opposing first and second major surfaces, the first major surface comprising a plurality of discrete spaced apart light extraction features disposed to extract light from the light extraction portion through the second major surface toward the light insertion portion.
 
Embodiment 51 is the light guide of Embodiment 50, wherein a reflective polarizer is disposed on the first major surface.
 
Embodiment 52 is the light guide of Embodiment 48, further comprising a reflector disposed between the light extraction portion and the light insertion portion, the reflector receiving light extracted from the light extraction portion and reflecting the light back through the light extraction portion.
 
Embodiment 53 is a display system comprising the light guide of Embodiment 52 and a transmissive spatial light modulator disposed to receive the light reflected from the reflector through the light extraction portion.
 
Embodiment 54 is a display system comprising the light guide of Embodiment 48 and a reflective spatial light modulator disposed between the light extraction portion and the light insertion portion.
 
Embodiment 55 is a light guide comprising:
 
a light insertion portion adapted to receive light, the light received by the light insertion portion propagating predominately along a first direction;
 
a light transport portion disposed to receive light from the light insertion portion, the light transport portion having a first segment, the light received by the light transport portion propagating predominately along a second direction in the first segment; and
 
a light extraction portion disposed to receive light from the light transport portion, the light received by the light extraction portion propagating predominately along a third direction,
 
wherein a first included angle between the first and second directions is at least 140 degrees and a second included angle between the first and third directions is less than 40 degrees.
 
Embodiment 56 is the light guide of Embodiment 55, wherein the first included angle is at least 160 degrees and the second included angle is less than 20 degrees.
 
Embodiment 57 is the light guide of Embodiment 55, wherein the light transport portion receives light from the light insertion portion through a first fold and the light extraction portion receives light from the light transport portion through a second fold.
 
Embodiment 58 is the light guide of Embodiment 55, wherein the light extraction portion has opposing first and second major surfaces, the first major surface comprising a plurality of discrete spaced apart light extraction features disposed to extract light from the light extraction portion through the second major surface toward the light insertion portion.
 
Embodiment 59 is a display system comprising the light guide of Embodiment 55 and a transmissive spatial light modulator disposed proximate the light extraction portion opposite the light insertion portion.
 
Embodiment 60 is a display system comprising the light guide of Embodiment 55 and a reflective spatial light modulator disposed between the light extraction portion and the light insertion portion.
 
Embodiment 61 is a display system comprising:
 
a projection lens system;
 
a light guide comprising:
   a light insertion portion adapted to receive light, the light received by the light insertion portion propagating predominately along a first direction;   a light extraction portion disposed to receive light from the light insertion portion, the light received by the light extraction portion propagating predominately along a second direction, an included angle between the first direction and the second direction being at least 120 degrees,
 
wherein the light extraction portion includes a plurality of light extraction features adapted to extract light from the light extraction portion towards the projection lens system.
 
Embodiment 62 is the display system of Embodiment 61, wherein the included angle is at least 140 degrees.
 
Embodiment 63 is the display system of Embodiment 61, wherein the included angle is at least 160 degrees.
 
Embodiment 64 is the display system of Embodiment 61, wherein the included angle is about 180 degrees.
 
Embodiment 65 is the display system of Embodiment 61, wherein the light extraction portion receives light from the light insertion portion through a fold.
 
Embodiment 66 is the display system of Embodiment 61, wherein the light extraction portion faces the light insertion portion.
 
Embodiment 67 is the display system of Embodiment 61, further comprising a spatial light modulator in optical communication with the light extraction portion.
 
Embodiment 68 is the display system of Embodiment 61, wherein the spatial light modulator is disposed between the projection lens system and the spatial light modulator.
 
Embodiment 69 is the display system of Embodiment 61, wherein the light extraction portion is disposed between the spatial light modulator and the projection lens system.
 
Embodiment 70 is the display system of Embodiment 61, wherein the projection lens system comprises a folded optical system.
 
Embodiment 71 is the display system of Embodiment 61, wherein the projection lens system comprises a refractive optical system.
       

     Related optical systems are described in the following U.S. patent application which is hereby incorporated herein by reference in its entirety: OPTICAL SYSTEM (Ser. No. 62/347,650) filed on an even date herewith. 
     Descriptions for elements in figures should be understood to apply equally to corresponding elements in other figures, unless indicated otherwise. Although specific embodiments have been illustrated and described herein, it will be appreciated by those of ordinary skill in the art that a variety of alternate and/or equivalent implementations can be substituted for the specific embodiments shown and described without departing from the scope of the present disclosure. This application is intended to cover any adaptations or variations of the specific embodiments discussed herein. Therefore, it is intended that this disclosure be limited only by the claims and the equivalents thereof