Abstract:
A display device has a display, operable to generate a real image, and an optical system. In the optical system are at least two free-form reflective surfaces, S I and S 2 . At least one of the reflective surfaces is convex in one direction at substantially all points of its optically active area. Light rays from the display are reflected on SI before they are reflected on S 2 . The reflective surfaces SI and S 2  are arranged to generate a virtual image from the real image on the display, by projecting light from the display to an eye position. The field of view occupied by the virtual image as seen from the eye position is greater than 50 degrees in at least one direction, preferably the direction linking the two eyes of an intended user.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application claims benefit of commonly assigned U.S. Provisional Patent Applications No. 62/105,905, filed on 21 Jan. 2015, and No. 62/208,235 filed on 21 Aug. 2015, both with common inventors, both for “Immersive Compact Display Glasses.” Both of those applications are incorporated herein by reference in their entirety. This application is related to commonly assigned International Patent Application No. WO 2015/077718 with common inventors, published 28 May 2015, for “Immersive compact display glasses,” which is incorporated herein by reference in its entirety. 
     
    
     FIELD OF THE INVENTION 
       [0002]    The application relates to visual displays, and especially to head-mounted display technology. 
       BACKGROUND 
     1. Definitions 
       [0003]      
         [0000]    
       
         
               
               
             
           
               
                   
               
             
             
               
                 Concave reflective 
                 Consider a reflective surface whose normal vectors are oriented 
               
               
                 surface at a point 
                 pointing towards the volume where the rays impinge on it, and a 
               
               
                   
                 point P with normal vector N on the surface. We say a surface is 
               
               
                   
                 concave at the point P if the centers of curvature C 1  and C 2  of the 
               
               
                   
                 two principal curvature lines passing through that point fulfil that 
               
               
                   
                 (C 1  − P) · N and (C 2  − P) · N are both positive (the dot indicates vector 
               
               
                   
                 scalar product). 
               
               
                 Convex reflective 
                 Consider a reflective surface whose normal vectors are oriented 
               
               
                 surface in at least 
                 pointing towards the volume where the rays impinge on it, and a 
               
               
                 one direction of 
                 point P with normal vector N on the surface. We say a surface is 
               
               
                 principal curvature 
                 convex in at least one direction of principal curvature at the point 
               
               
                 at a point. 
                 P if the center of curvature C 1  of at least one of the two principal 
               
               
                   
                 curvature lines passing through that point fulfils that (C 1  − P) · N is 
               
               
                   
                 negative (the dot indicates vector scalar product). 
               
               
                 display 
                 Component, usually electronic, that modulates light spatially, 
               
               
                   
                 which can be self-emitting, such as an OLED display, or 
               
               
                   
                 externally illuminated by a front or a backlight system, such as an 
               
               
                   
                 LCD or an LCOS. 
               
               
                 eye pupil 
                 Image of the interior iris edge through the eye cornea seen from 
               
               
                   
                 the exterior of the eye. In visual optics, it is referenced as the input 
               
               
                   
                 pupil of the optical system of the eye. Its boundary is typically a 
               
               
                   
                 circle from 3 to 7 mm diameter depending on the illumination 
               
               
                   
                 level. 
               
               
                 eye sphere 
                 Sphere centered at the approximate center of the eye rotations and 
               
               
                   
                 with radius the average distance of the eye pupil to that center 
               
               
                   
                 (typically 13 mm). For practical reasons the eye(s) of the user may 
               
               
                   
                 be represented by an imaginary representation of a typical eye or 
               
               
                   
                 pair of eyes. 
               
               
                 field of view 
                 The horizontal and vertical full angles subtended by the virtual 
               
               
                   
                 screen from the eye pupil center when the two eyes rest looking 
               
               
                   
                 frontwards, or the region within those angles. 
               
               
                 fixation point 
                 Point of the scene that is imaged by the eye at center of the fovea, 
               
               
                   
                 which is the highest resolution area of the retina and typically has 
               
               
                   
                 a diameter of 1.5 mm. 
               
               
                 gaze vector 
                 Unit vector of the direction linking the center of the eye pupil and 
               
               
                   
                 the fixation point. 
               
               
                 gazed region of 
                 Region of the virtual screen containing the fixation points for all 
               
               
                 ImageSurface 
                 positions of the eye pupil within the union of the pupil ranges. It 
               
               
                   
                 contains all the ipixels that can be gazed. 
               
               
                 ipixel 
                 Virtual image of the opixels belonging to the same web. 
               
               
                   
                 Preferably, this virtual image is formed at a certain distance from 
               
               
                   
                 the eye (from 2 m to infinity). It can also be considered as the 
               
               
                   
                 pixel of the virtual screen seen by the eye. 
               
               
                 opixel 
                 Physical pixel of the digital display. There are active opixels, 
               
               
                   
                 which are lit to contribute to the displayed image, and inactive 
               
               
                   
                 opixels, which are never lit. An inactive opixel can be physically 
               
               
                   
                 nonexistent, for instance, because the display lacks at that opixel 
               
               
                   
                 position at least one necessary hardware element (OLED material, 
               
               
                   
                 electrical connection) to make it functional, or it can be 
               
               
                   
                 unaddressed by software. The use of inactive opixels reduces the 
               
               
                   
                 power consumption and the amount of information to be managed. 
               
               
                 peripheral angle 
                 Angle formed by a certain direction and the gaze vector. 
               
               
                 virtual screen 
                 Surface containing the ipixels, preferably being a region of the 
               
               
                   
                 surface of a sphere concentric with the eye and with radius in the 
               
               
                   
                 range from 2 m to infinity. 
               
               
                   
               
             
          
         
       
     
       2. State of the Art 
       [0004]    Head mounted display technology is a rapidly developing area. One aspect of head mounted display technology is that it can provide a full immersive visual environment (which can be described as virtual reality), such that the user observes only the images provided by one or more displays, while the outside environment is visually blocked. These devices have application in areas such as entertainment, gaming, military, medicine and industry. In US 2010/0277575 A1 by Ismael et al. there is a description of one of such device. The basic optical function of a Head Mounted Display (HMD) is that of a stereo-viewer such as the one described in U.S. Pat. No. 5,390,047 by Mizukawa. 
         [0005]    A head mounted display consists typically of one or two displays, with their corresponding optical systems, which image the displays into a virtual screen to be visualized by the user&#39;s eye. The display may also have a pupil tracker and/or a head tracker, such that the image provided by the display changes according to the user&#39;s movement. 
         [0006]    The displays may be of the type called Light Field Displays (F. Huang, K. Chen, G. Wetzstein. “The Light Field Stereoscope: Immersive Computer Graphics via Factored Near-Eye Light Field Displays with Focus Cues”, ACM SIGGRAPH (Transactions on Graphics 33, 5), 2015) implemented by stacked (transmisive) LCDs. Particularly interesting because of its thickness is the case of just 2 stacked LCDs with a separator between them. Light Field Displays support focus cues which together with the rest of the device help to solve the vergence-accommodation conflict at a reasonable cost and volume. This conflict may lead to visual discomfort and fatigue, eyestrain, diplopic vision, headaches, nausea, compromised image quality, and it may even lead to pathologies in the developing visual system of children. 
         [0007]    An ideal head mounted display combines a high resolution, a large field of view, a low and well-distributed weight, and a structure with small dimensions. Although some technologies successfully achieve these desired features individually, so far no known technology has been able to combine all of them. That results in an incomplete or even uncomfortable experience for the user. Problems may include a low degree of realism and eye strain (low resolution or optics imaging quality), failure to create an immersive environment (small field of view), or excessive pressure on the user&#39;s head (excessive weight). 
         [0008]    There are two types of HMDs, one in which the user observes only the information from displays (virtual reality, VR) and another in which the virtual objects are mixed with the real environment (augmented reality, AR). Additionally, the information presented to each eye may be the same (2D) or different to include the stereoscopic vision (3D). 
         [0009]    The typical VR system shows a stereoscopic immersive virtual reality with large field of view and occupies a large volume. 
         [0010]    Compared to VR systems, the typical AR systems have better ergonomics, show higher resolution (measured in pixels per degree) and have a much smaller field of view, so only small portion of the user&#39;s natural field of vision is superimposed with the virtual information. 
         [0011]    A prior art device with application to AR is described in WO 2015/088468A1 by Moskalenko et al. That device consists of a single concave rotational mirror whose axis of revolution passes through the center of revolution of the eye, and a curved display whose surface approximates points that are optically conjugated with specified points of the image observed by the eye though the reflection. This device is integrated in spectacles produced by Kverve Optics AS, who report that they provide a vertical field of view (FoV) of 43 degrees and 200 degrees horizontal FoV with full binocular superposition inside 50 degrees. 
         [0012]    Another device for AR, described in U.S. Pat. No. 5,838,490 by Fritz et al. comprises a partially reflective 45° tilted flat filter, a Mangin mirror having a curved reflecting surface to receive the light reflected from the filter and reflect it back through the filter to the eye, and a transparent element mated to the curved surface of the Mangin mirror allowing the light from a remote scene passing undistorted through the optical system to the eye. 
         [0013]    Another HMD design, shown in  FIG. 1 , is based on a free-form wedge-shaped prism, and was first presented by Morishima (H. Morishima, T. Akiyama, N. Nanba, and T. Tanaka, “The design of off-axial optical system consisting of aspherical mirrors without rotational symmetry,” in 20th Optical Symposium, Extended Abstracts, 1995, Vol. 21, pp. 53-56), while the fabrication and evaluation method were explored by Inoguchi et al. (“Fabrication and evaluation of HMD optical system consisting of aspherical mirrors without rotation symmetry,” Japan Optics &#39;95, Extended Abstracts, 20pB06, pp. 19-20, 1995). Free-form here means that the optically active surfaces have neither rotational nor linear symmetry. Following these pioneering efforts, many attempts have been made to design HMD optics using free-form wedge-shaped prisms. For instance, U.S. Pat. Nos. 5,699,194, 5,701,202, both by Takahashi, U.S. Pat. No. 5,706,136 by Okuyama &amp; Takahashi, D. Cheng, et al., “Design of a lightweight and wide field-of-view HMD system with free form surface prism,” Infrared and Laser Engineering, Vol. 36, 3, 2007). Also, Hoshi et al. presented a free form surface (FFS) prism offering a FoV of 34° and a thickness of 15 mm (H. Hoshi, N. Taniguchi, H. Morishima, T. Akiyama, S. Yamazaki, and A. Okuyama, “Off-axial HMD optical system consisting of aspherical surfaces without rotational symmetry,” Proc. SPIE 2653, 234-242, 1996); Yamazaki et al. described a 51° Optical-See-Through HMD design consisting of a free-form prism and an auxiliary lens attached to the prism (S. Yamazaki, K. Inoguchi, Y. Saito, H. Morishima and N. Taniguchi,“Thin wide-field-of-view HMD with free-form-surface prism and applications”, Proc. SPIE 3639, 453, 1999). More recently, U.S. Pat. No. 8,605,008 to Prest et al. includes a similar wedge-shaped prism optics in his description. There are also several commercially available HMD products based on the FFS prism concept. For instance, Olympus released their Eye-Trek series of HMDs based on free-form prisms. Emagin carried Z800 with the optical module WFOS, Daeyang carried i-Visor FX series (GEOMC module, A3 prism) products; Rockwell Collins announced the ProView SL40 using the prism technology of OEM display optics. US Patent Application No. 2012/0081800 “Optical see-through free-form head-mounted display” by D. Cheng et al., also proposes an optical design for HMD applications, where in particular a see-through free-form head-mounted display including a wedge-shaped prism-lens having free-form surfaces and low F-number is presented. 
         [0014]    There are several differences of these wedge shaped prisms from the devices disclosed herein (such as the one shown in  FIG. 8 ). First, the type (i.e. refraction, reflection, total internal reflection) and number of deflections that rays suffer on their way from the digital display to the eye are different. Second, the first reflective surface in those prior art wedge-shaped prisms has a concave surface, while in the present embodiments the first reflective surface is convex in at least one direction of principal curvature at substantially all points of its optically active area. This gives the present devices the capacity of providing larger focal lengths in the same occupied space. These larger focal lengths permit the use of low cost displays based on non-crystalline backplane technologies (with diagonals typically over 1.5 inches, 38.1 mm), while those prior art wedge shaped prisms, with their shorter focal lengths, are only suitable for small displays, which are made of more expensive crystalline backplanes (with diagonals typically below 1 inch, 25.4 mm). Third, an additional refractive lens is introduced in the present embodiments to enlarge the field of view for VR applications. 
         [0015]    U.S. Pat. No. 7,689,116 by Ho Sik You et al., applicable to a mobile camera, presents an optical lens system which assures a wide field of view (FoV) by dividing an original FoV into a plurality of FoVs and by providing separate off-axis lens systems corresponding to each one of the new FoVs, thereby achieving a thinner mobile camera optical lens system.  FIG. 2  explains the basis of You&#39;s system, particularized for the case where we only have two different view angles, i.e. two different ranges of field of view. In  FIG. 2 , the light emitted by the object (in the example, the flower  201 ) is transmitted through the optical system and impinges on the image plane  202 , where a light sensor is placed. The light corresponding to the top half of the FoV enters the system through refractive surface  203 , while the bottom half of the FoV enters the system through refractive surface  204 . Both halves of the optical system are symmetrical, as shown in  FIG. 2 . The rays belonging to the top half are deflected successively by four different surfaces: first refracted on entrance surface  203 , then reflected on back surface  207 , again reflected on front surface  208 , then refracted by exit surface  209 , and finally impinge on the top half of the image plane  202 . Due to the particular optical architecture used in this device, each half of the image obtained on the image plane is inverted  205 . This situation is corrected electronically, in order to finally obtain the desired image  206 . 
         [0016]    There are several differences between our embodiment shown in  FIG. 7  and You&#39;s system. First, the present embodiment is for a different application, i.e. head-mounted displays, while You&#39;s device is a mobile camera optical lens. That requires major differences in the optical geometry. Then, the physical object in You&#39;s optical system (which is the scene to take the picture of) is located at a far distance from the lens, while our equivalent element (the digital display) is at a very short distance from the lens, even touching it. On the other hand, You&#39;s image is real (projected onto the camera sensor  202 ) and is located very close to the lens, while our equivalent element (the virtual screen) is virtual and is located far from the lens. The output pupil in our case is real, located on the right side of the lens and is defined as the pupil range to allow for eye movements, while in You&#39;s case the equivalent pupil (which is the exit one) is virtual and is located at the opposite side of the lens. 
       SUMMARY 
       [0017]    One aspect of the present disclosure provides a display device comprising a display, operable to generate a real image comprising a plurality of object pixels, and an optical system, comprising at least two surfaces at which the rays are reflected (by a mirror or being reflected by TIR), designed to generate a virtual image from the real image. 
         [0018]    Another aspect provides a display device comprising a display, operable to generate a real image, and an optical system, comprising at least two free-form reflective surfaces, S 1  and S 2 , such that at least one of surfaces S 1  and S 2  is convex in at least one direction at substantially all points of its optically active surface. Those reflective surfaces are arranged to generate a virtual image from the real image on the display, by projecting light from the display to an eye position. The field of view occupied by the virtual image as seen from the eye position is greater than 50 degrees in at least one direction. The optical system is arranged to produce a virtual image that contains a foveal part projected by a normal human eye onto a 1.5 mm fovea of said eye when said eye is at the eye position with a pupil of the eye within a pupil range, the foveal part of said virtual image having a higher resolution than a peripheral part. 
         [0019]    The one of surfaces S 1  and S 2  that is convex in at least one direction at substantially all optically active points may be surface S 1 , with surface S 2  concave at substantially all optically active points, and where the light rays from the display are reflected on S 1  before they are reflected on S 2 . 
         [0020]    The display device may further comprise a lens in the optical path between the display and the eye position. The field of view in the at least one direction may be more than 80 degrees. 
         [0021]    The lens may be between the display and mirror S 1 . 
         [0022]    The lens may be between mirror S 1  and mirror S 2 . 
         [0023]    The reflective surface S 2  may be semitransparent and be on a transparent substrate, permitting a direct view of an external environment from the eye position. 
         [0024]    The reflective surface S 2  may then be on a surface of the transparent substrate nearer to the eye position or may be adjacent to an additional transparent substrate further from the eye than the reflective surface S 2 . A frontward entrance surface of the transparent substrate or the additional transparent substrate, through which light from the external environment enters the optical system, may be so formed that light rays from the external environment exiting the optical system to the eye position exit the optical system substantially parallel to directions in which the respective rays entered the optical system. 
         [0025]    The display may be offset laterally from a direct line of view of the eye. 
         [0026]    The optical system may be placed at a distance between 5 and 40 mm from an imaginary 13 mm radius sphere at the eye position, the optical system may subtend a solid angle from a closest point of the imaginary sphere comprising a cone with 40 degrees whole angle, and the display may be on a side of the optical system remote from the imaginary sphere, at a distance from the optical system of no more than 40 mm. 
         [0027]    The focal lengths may be from 15 to 60 mm. The monocular horizontal field of view may be larger than 50 degrees. 
         [0028]    The embodiments designed for Augmented Reality applications (AR) may have at least one semi-transparent mirrored surface allowing the user to see through that surface, as well as reflecting the projected virtual images. In the case of AR, at least one additional free form refractive surface is usually designed to correct distortion of the images coming from real environment. 
         [0029]    An embodiment for Virtual Reality applications (VR) may comprise an additional refractive surface, and may provide monocular horizontal and vertical fields of view of 100 degrees and 70 degrees, respectively. 
         [0030]    Another aspect provides a headgear comprising the display device according to any of the above aspects and/or embodiments, with a mount for positioning the display device on a human head with the eye position of the display device coinciding with an eye of the human. 
         [0031]    The at least one direction in which the field of view occupied by the virtual image as seen from the eye position is greater than 50 degrees may be parallel to a direction joining the eyes of a person wearing the headgear. 
         [0032]    The headgear may further comprise a second display device according to any of the above aspects and/or embodiments, mounted with the eye position of the second display device coinciding with a second eye of the human. 
     
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         [0033]    The above and other aspects, features and advantages will be apparent from the following more particular description of certain embodiments, presented in conjunction with the following drawings. In the drawings: 
           [0034]      FIG. 1  shows a Head Mounted Display (HMD) with a free-form wedge-shaped prism designed by Morishima et al. in 1995 (prior art). 
           [0035]      FIG. 2  shows a mobile camera optical lens system designed by Ho Sik You et al., in 2010 (prior art). 
           [0036]      FIG. 3  shows a two-mirror free-form HMD for Virtual Reality. 
           [0037]      FIG. 4  shows a two-mirror free-form HMD with an additional lens providing a larger field of view. 
           [0038]      FIG. 5  shows a two-mirror free-form HMD with an additional lens between the display and the mirrors. 
           [0039]      FIG. 6  shows a two-mirror free-form HMD with an additional lens between the mirrors. 
           [0040]      FIG. 7  shows a configuration for Virtual Reality (VR) applications with four free-form optical surfaces. 
           [0041]      FIG. 8  shows an HMD with a free-form wedge-shaped prism lens with an additional free-form lens providing a larger field of view. 
           [0042]      FIG. 9  shows a two-mirror free-form HMD for Augmented Reality (AR) applications. 
           [0043]      FIG. 10  shows a two-mirror free-form HMD for AR with an additional lens. 
           [0044]      FIG. 11  shows an embodiment for AR with four free-form optical surfaces. 
           [0045]      FIG. 12  shows an HMD for AR with a free-form wedge-shaped prism and with an additional free-form lens. 
       
    
    
     DETAILED DESCRIPTION 
       [0046]    The embodiments to be described here are designed for HMD devices, suitable for augmented reality (AR) or virtual reality (VR) applications. These embodiments aim to provide simultaneously a wide field of view, high resolution, low weight, and small volume. 
         [0047]    For an effective immersive experience, this wide field of view must to be provided independently of the eye pupil orientation relative to the head. This approach considers the pupil range as a design parameter. The maximum pupil range is the region of the eye sphere formed by the union of all physically accessible pupil positions for an average human. It is then a spherical shell in good approximation. The boundary of the maximum pupil range is approximately an ellipse with angular horizontal semi-axis of 60 degs and vertical semi-axis of 45 degs relative to the front direction, subtended at the center of rotation of the eye. However, for a practical immersive design, an elliptical cone of semi-axis in the 15 to 30 degrees range can be considered sufficient for the pupil range definition. 
         [0048]    Human vision resolution peaks on the part of the scene imaged at the fovea (which is about 1.5 mm in diameter) and decreases rapidly away from that part. Therefore, the angular resolution of a typical human eye is a decreasing function of the peripheral angle (according to J. J. Kerr, “Visual resolution in the periphery”, Perception &amp; Psychophysics, Vol. 9 (3), 1971). Since the human eye resolution is much coarser in peripheral vision than close to the gazing direction, the embodiments in this specification have been designed to match the imaging quality so that the ipixels of the virtual screen are no finer than strictly needed (because the eye will not appreciate further increase in fineness). 
         [0049]    Embodiments shown here consist of: 
         [0050]    A display whose surface coincides preferably with a plane or a cylinder, and which is composed by a multiplicity of physical pixels called object pixels or “opixels”. 
         [0051]    An optical system, which can contain various numbers of refractive/reflective surfaces, providing a virtual image composed by pixels on a virtual screen, called “ipixels”. The virtual screen is preferably spherical, lying at a certain distance from the eye; and the virtual image is defined by a mapping from opixels to ipixels. 
         [0052]      FIG. 3  shows a two-mirror embodiment together with user&#39;s eye  314  and nose  315  shown for orientation purpose. This design is denoted an XX (which means that the lens consists of two surfaces, both being reflective) design. Rays  305 ,  306 ,  307  and  308  emitted by the digital display  301  undergo 2 reflections: first on freeform mirror surface  302  and then on the see-through free-form mirror  303  to be directed to the eye  314 . After 2 reflections, rays  306  and  308  are directed towards the eye sphere center  310 . The rays  305  and  307  define the vertical FoV of this mirror device as these are edge rays of the eye input pupil center  309  when eye rests looking forward and these rays come from the edges of the display  301 . The embodiment generates a virtual image from the real image that appears on the display. The distortions of the virtual image, if any, are corrected electronically by imparting a contrary distortion to the real image on display  301 . 
         [0053]      FIG. 3  shows an example of an XX design with focal length f=52 mm, and 35° of vertical FoV and 60° of horizontal FoV.  FIG. 3  left shows a vertical cross-section at the x=0 plane. Surfaces are described with the equation z=P m (x,y): 
         [0000]    
       
         
           
             
               
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         [0054]    where Pm(x,y) is the 10 th  order polynomial, i.e. m=10, c 2i,j  are surface coefficients listed in Table 1 below, and P 2i ((x−(x max +x min )/2)/x max ) and P j ((y−(y max +y min )/2)/y max ) are Legendre-polynomials that are orthogonal inside the rectangle x min &lt;x&lt;x max , and y min &lt;y&lt;y max . All surfaces are symmetric respect to the plane x=0 (the plane of the drawing shown in  FIG. 3 ) so Legendre polynomial P 2i  ((x−(x max +x min )/2)/x max ) has only pair order monomials. The Legendre polynomial P n (x) can be expressed as: 
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         [0000]    Where the latter expresses the Legendre polynomials by simple monomials and involves the multiplicative formula of the binomial coefficient, and where 
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                     ! 
                   
                 
               
               . 
             
           
         
       
     
         [0055]    The origin of the global coordinate system (x,y,z)=(0, 0, 0) is placed in the eye center  310 . The local coordinate system for a display  311 , with 2.5″ (63.5 mm) diagonal and aspect ratio 16:9, has coordinates (x,y,z)=(0, 32.6943, 44.2473) and it is rotated 20° around the x axis in negative (clockwise) direction with respect to the global coordinate system. The local coordinate system  312  for mirror  302  has its origin at (x,y,z)=(0, 23.7419, 34.8724) and is rotated 11.6039° around the x axis in positive (counterclockwise) direction respect to the global coordinate system. The local coordinate system  313  for mirror  303  has its origin at (x,y,z)=(0, 0, 45), and is rotated 33.4493° around the x axis in positive direction respect to the global coordinate system. Coordinates are given in mm. Coefficients of all surfaces&#39; polynomials are listed in Table 1. The first four rows are x min , x max , y min  and y max  that describe rectangular area between x min  and x max  in x-direction, and y min  and y max  in y-direction where every Legendre polynomial P m (x,y) is orthogonal. The subsequent rows of Table 1 are the coefficients of 10 th  order Legendre polynomial P m (x,y) for each surface we have designed. “Mirror-1” in Table 1 corresponds to the mirror  302  in  FIG. 3 . “Mirror-2” in Table 1 corresponds to the mirror  303  in  FIG. 3 . 
         [0000]    
       
         
               
               
               
               
             
               
               
               
               
             
           
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 Parameter 
                 Mirror-1 
                 Mirror-2 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 x min   
                 −18 
                 −27 
               
               
                   
                 x max   
                 18 
                 27 
               
               
                   
                 y min   
                 −16 
                 −16 
               
               
                   
                 y max   
                 16 
                 16 
               
               
                   
                 c 0,0   
                 −1.42507 
                 −2.59056 
               
               
                   
                 c 0,1   
                 0.0451835 
                 0.143174 
               
               
                   
                 c 0,2   
                 −0.72009794 
                 −1.06388171 
               
               
                   
                 c 0,3   
                 −0.01547969 
                 0.01484046 
               
               
                   
                 c 0,4   
                 0.00206765 
                 −0.00346054 
               
               
                   
                 c 0,5   
                 −0.00028542 
                 −0.0012447 
               
               
                   
                 c 0,6   
                 0.00064372 
                 −0.00035631 
               
               
                   
                 c 0,7   
                 0.00029827 
                 −0.00175909 
               
               
                   
                 c 0,8   
                 0.00076968 
                 −0.0005269 
               
               
                   
                 c 0,9   
                 −0.00289666 
                 −0.00057807 
               
               
                   
                 c 0,10   
                 −0.0009011 
                 −0.00041103 
               
               
                   
                 c 2,0   
                 −2.17547149 
                 −4.19354056 
               
               
                   
                 c 2,1   
                 0.04495347 
                 0.20853189 
               
               
                   
                 c 2,2   
                 −0.0315604 
                 −0.07086542 
               
               
                   
                 c 2,3   
                 −0.02546096 
                 −0.00760281 
               
               
                   
                 c 2,4   
                 −8.14E−05 
                 −0.00087688 
               
               
                   
                 c 2,5   
                 0.00194202 
                 0.00111976 
               
               
                   
                 c 2,6   
                 0.00036391 
                 −0.00406823 
               
               
                   
                 c 2,7   
                 −0.00263027 
                 −0.00127324 
               
               
                   
                 c 2,8   
                 −0.00388143 
                 −0.00244588 
               
               
                   
                 c 2,9   
                 0 
                 0 
               
               
                   
                 c 2,10   
                 0 
                 0 
               
               
                   
                 c 4,0   
                 −0.01848644 
                 −0.0570722 
               
               
                   
                 c 4,1   
                 −0.02417861 
                 −0.04399492 
               
               
                   
                 c 4,2   
                 0.01349926 
                 −0.01382028 
               
               
                   
                 c 4,3   
                 0.00473022 
                 −0.0034179 
               
               
                   
                 c 4,4   
                 −0.00384481 
                 −0.00095022 
               
               
                   
                 c 4,5   
                 −0.00295132 
                 0.00035308 
               
               
                   
                 c 4,6   
                 0.00010286 
                 −0.00039971 
               
               
                   
                 c 4,7   
                 0 
                 0 
               
               
                   
                 c 4,8   
                 0 
                 0 
               
               
                   
                 c 4,9   
                 0 
                 0 
               
               
                   
                 c 4,10   
                 0 
                 0 
               
               
                   
                 c 6,0   
                 0.00470142 
                 −0.01049631 
               
               
                   
                 c 6,1   
                 0.00667805 
                 −0.01978286 
               
               
                   
                 c 6,2   
                 −0.03062507 
                 −0.01824176 
               
               
                   
                 c 6,3   
                 −0.00213372 
                 0.00212772 
               
               
                   
                 c 6,4   
                 −0.00256455 
                 −0.00131309 
               
               
                   
                 c 6,5   
                 0 
                 0 
               
               
                   
                 c 6,6   
                 0 
                 0 
               
               
                   
                 c 6,7   
                 0 
                 0 
               
               
                   
                 c 6,8   
                 0 
                 0 
               
               
                   
                 c 6,9   
                 0 
                 0 
               
               
                   
                 c 6,10   
                 0 
                 0 
               
               
                   
                 c 8,0   
                 −0.00682394 
                 −0.0082152 
               
               
                   
                 c 8,1   
                 0.01123838 
                 −0.00529108 
               
               
                   
                 c 8,2   
                 −0.00589758 
                 −0.01197266 
               
               
                   
                 c 8,3   
                 0 
                 0 
               
               
                   
                 c 8,4   
                 0 
                 0 
               
               
                   
                 c 8,5   
                 0 
                 0 
               
               
                   
                 c 8,6   
                 0 
                 0 
               
               
                   
                 c 8,7   
                 0 
                 0 
               
               
                   
                 c 8,8   
                 0 
                 0 
               
               
                   
                 c 8,9   
                 0 
                 0 
               
               
                   
                 c 8,10   
                 0 
                 0 
               
               
                   
                 c 10,0   
                 −0.00240235 
                 0.0005887 
               
               
                   
                 c 10,1   
                 0 
                 0 
               
               
                   
                 c 10,2   
                 0 
                 0 
               
               
                   
                 c 10,3   
                 0 
                 0 
               
               
                   
                 c 10,4   
                 0 
                 0 
               
               
                   
                 c 10,5   
                 0 
                 0 
               
               
                   
                 c 10,6   
                 0 
                 0 
               
               
                   
                 c 10,7   
                 0 
                 0 
               
               
                   
                 c 10,8   
                 0 
                 0 
               
               
                   
                 c 10,9   
                 0 
                 0 
               
               
                   
                 c 10,10   
                 0 
                 0 
               
               
                   
                   
               
             
          
         
       
     
         [0056]    Reversed rays for different ipixels are traced from a notional eye pupil (displaced to the center  310  of the eye  314 ) towards the display  301 , impinging on different opixels. This eye pupil allows us to simulate the performance of the ipixels when they are gazed while the eye is rotated, which are the ipixels whose performance should be the best. Raytrace simulation results indicate that the average rms spot diameter on the display  301  for the ipixels inside the gazed region of the virtual screen when they are gazed is about 70 microns. However, if the reversed rays from different ipixels are traced from the eye pupil at  310  when the eye is gazing frontwards, the image quality for these rays can be progressively relaxed when the peripheral angle increases, as permitted by the decreasing human eye resolution. As an example, the rms spot diameter of the reversed rays impinging on the display for an ipixel at a peripheral angle of 12° is about 160 microns, much higher than the value of the rms spot diameter for that ipixel when it is gazed, which is 56 microns. Since the focal length is about 52 mm, the forward ray-trace gives the result that the angular rms spot diameter of that ipixel seen through the pupil gazing frontwards is 10.3 arcmin. This is not perceived as blurred by the human eye, because it is smaller than 12 arcmin, which is what can be resolved by the human eye at 12 degrees peripheral angle (according to J. J. Kerr, “Visual resolution in the periphery”, Perception &amp; Psychophysics, Vol. 9 (3), 1971) 
         [0057]    The field of view of the design shown in  FIG. 3  can be increased by putting a lens  404  between the second mirror  403  and the eye  400 , as shown in  FIG. 4 . The rays  405 , and  406 , emitted by the display  401  undergo 2 reflections: first on freeform mirror surface  402  then on see-through free-form mirror  403 . After the 2 reflections, these rays are refracted twice at the lens  404  being directed towards the eye center  408 . The field of view is increased due to additional collimation at the lens  404 , thus for the same distance between the mirror surfaces and the eye, a bigger angular spread of rays can be directed from the digital display to the eye. With this configuration, we have a monocular vertical and horizontal FoV of 70 degrees and 100 degrees, respectively, with a 16:9 display with a diagonal of 2.1″, 55 mm. As an alternative embodiment, the lens  404  can be designed with low optical power (closer to a plano parallel plate) with the purpose of correcting non-chromatic aberrations. 
         [0058]    The position of the lens can be changed along the ray trajectory.  FIG. 5  shows an embodiment with a lens  504  placed between a digital display  501  and first mirrored surface  502 . Rays  505  and  506 , emitted by the display  501 , undergo two refractions at the lens  504 , and then 2 reflections: a first reflection on the free-form mirror surface  502  and a second reflection on the see-through freeform mirror  503 . After the 4 deflections, these rays are directed towards the eye center  508 . In this case the field of view is not increased compared with the design presented in  FIG. 3 . However, since the lens provides more degrees of freedom in the optical design (compared to the design from  FIG. 3 ), the geometrical aberrations can be reduced. 
         [0059]    Another embodiment is presented in  FIG. 6 . The lens  604  is placed between two mirrored surfaces  602  and  603 . The rays  605  and  606  coming from digital display  601  first reflect on the mirrored surface  602 , then refract twice at the lens  604 , and finally reflect at the see-through freeform mirror  603 . After the 4 deflections, these rays are directed towards the eye center  608 . Here, as in  FIG. 5 , only the aberrations are reduced while the field of view is the same as in  FIG. 3 . 
         [0060]      FIG. 7  shows a configuration consisting essentially of a tilted display  701  and a lens  714 . All the optical surfaces are surfaces of the lens  714 , as explained in more detail below. The user&#39;s nose  713  and eye  712  are shown for orientation. With this configuration, we have monocular vertical and horizontal fields of view of 70 degrees and 100 degrees, respectively, with a display diagonal of 2.1″ (55 mm). This configuration contains 4 freeform optical surfaces, 2 refractive and 2 reflective. Rays  706 ,  707 ,  708  and  709  emitted by tilted display  701  suffer 4 deflections in total: first they refract on entrance surface  702 , then reflect on surface  703 , remaining inside lens  714 , reflect on surface  704 , remaining inside lens  714 , refract on exit surface  705 , and finally reach the eye  712 . The rays  706  and  708  are directed towards the eye sphere center  711 . The rays  706  and  709  define the vertical FoV of this mirror device as these are edge rays of the eye pupil center  710  when eye rests looking forward. 
         [0061]    Another design is presented in  FIG. 8 . This design has two solid lenses separated by a narrow air-gap  805 . The rays emitted by a digital display  802  are first refracted by entrance surface  803  of the first lens, then some rays are reflected by mirrored surface  804  and other rays are reflected by TIR thanks to the air-gap (or gap filled with low-refractive-index material such as fluoropolymer FEP)  805 . All the rays are then reflected by mirrored surface  806 . Afterwards, the rays go across the low-index-gap without experiencing major changes in their directions, and finally are refracted by exit surface  807  towards the eye  801 . The ray  810  impinges on the mirrored part of surface  804 , while the rays  808  and  809  are reflected by TIR by the air-gap  805 . Compared to the prior art in  FIG. 1 , the field of view is increased due to additional collimation at surface  807 , thus for the same distance between the optical system and the eye, a bigger angular spread (defined by the angle between rays  810  and  809 ) of rays can be directed from the digital display to the eye. Surface  804 , which looks concave in  FIG. 8 , is convex at substantially all of its points in the direction perpendicular to the drawing. 
         [0062]    Embodiments shown up to here are designed for virtual reality applications. From this point forward we show embodiments to be used for augmented reality (AR) applications allowing the user to see the surrounding reality through the optics. 
         [0063]    The design shown in  FIG. 3  can be easily adapted for AR application if mirror  303  is a “see-through” mirror, in which the substrate of mirror  303  is transparent and the reflective coating is partially transmissive. This is shown in  FIG. 9 , where the surface  914  of mirror  903  nearer to the eye  911  is preferably the one that is mirror coated. If the substrate is thin (&lt;1 mm), then the distance between the surfaces  914  and  913  can just be a constant value, and any distortion of the see-through live view will be minimal. If a fine correction of the see-though quality is desired, particularly for thicker substrates, the frontward surface  913  can be designed with the condition that rays  907 ,  908  coming from the environment exit surface  914  in same direction they had before impinging on surface  913 . The embodiments presented in  FIG. 5  and  FIG. 6  can be adapted for AR in the same way as shown in  FIG. 9 . Rays  905 ,  906 , coming from display  901  via first mirror  902  behave in the same way as the corresponding rays in  FIG. 3 . The nose  912  is shown for orientation.  910  is the center of the eye  911 , and  909  is the pupil range. 
         [0064]    The design shown in  FIG. 4  can be adapted for AR as shown in  FIG. 10 . The substrate of mirror  1003  is transparent and the reflective coating  1011 , which is on the surface nearer to the eye  1000 , is partially transmissive. The rays  1005  and  1006  coming from the display  1001  are reflected on mirror  1002  and reflective surface  1011 , then refracted twice by lens  1004  being directed towards the eye center  1009 . The substrate of mirror  1003  is a lens, and the frontward surface  1010  is designed with the condition that rays  1007 ,  1008  coming from the environment and refracted at surfaces  1010  and  1011  and also after two refractions at lens  1004  come to the eye in a direction parallel to the direction they have before impinging on  1010 . In  FIG. 10  the substrate of mirror  1003  is a biconcave lens, but that is not required in the general case. 
         [0065]    The embodiment shown in  FIG. 11  is an adaptation of the embodiment in  FIG. 7  to Augmented Reality applications.  FIG. 11  shows a tilted display  1101 , a lens  1114 , and an additional piece of transparent material  1116 . The user&#39;s nose  1115  and the eye  1112  are shown for orientation. The rays  1107  and  1108  emitted by the display  1101  suffer 4 deflections in total: first they refract at entrance surface  1102 , then reflect on back surface  1103 , reflect on semi-transparent surface  1104 , which is at the boundary between the main lens  1114  and the additional piece  1116 , refract at exit surface  1105 , and finally reach the center  1113  of eye  1112 . Thus a virtual image of a real image from the digital display  1101  is formed. On the other hand, rays  1110  and  1111  coming from the environment are first refracted at entrance surface  1109  of piece  1116 , then refracted twice at the connection between piece  1116  and lens  1114 . Since the two pieces of transparent material  1114 ,  1116  are very close to each other and the surfaces are parallel, this double refraction does not change the ray path considerably. The rays  1110 ,  1111  are then finally refracted at exit surface  1105 , being redirected towards the eye. The entrance surface  1109  is designed so that after these refractions the rays  1110 ,  1111  preserve their directions, so the user is able to see through the optical system. As the result the user perceives both a virtual image of the digital display  1101  and the environment that surrounds the user. 
         [0066]    The embodiment shown in  FIG. 12  is the adaptation of the embodiment in  FIG. 8  to AR. Rays  1208  and  1209  coming from a tilted display  1202  have the same trajectories as in  FIG. 8 . The rays  1208 ,  1209  are refracted at entrance surface  1203 , reflected on back surface  1204  (partly at a metallic reflector and partly by TIR at low-index gap  1206 ), reflected on semitransparent surface  1205 , pass across low-index gap  1206 , are then refracted at exit surface  1207 , and finally reach the eye  1201 . An additional piece  1214  of transparent material (lens) is placed with its eyeward surface on the back of semitransparent mirror  1205 . The frontward entrance surface of additional piece  1214  is designed with the condition that rays  1210 ,  1211  coming from the environment reach the eye in direction parallel to the one they have before impinging on  1213 . These rays are refracted at entrance surface  1213 , pass through semitransparent mirror  1205 , pass across thin air gap  1206 , and are finally refracted at exit surface  1207 . 
         [0067]    Although specific embodiments have been described, the preceding description of presently contemplated modes of practicing the invention is not to be taken in a limiting sense, but is made merely for the purpose of describing certain general principles of the invention. Variations are possible from the specific embodiments described. For example, the patents and applications cross-referenced above describe systems and methods that may advantageously be combined with the teachings of the present application. Although specific embodiments have been described, the skilled person will understand how features of different embodiments may be combined. 
         [0068]    The full scope of the invention should be determined with reference to the claims, and features of any two or more of the claims may be combined.