# Patent

## Title
Stereoscopic displays with addressable focus cues

## Abstract

The present invention relates generally to stereoscopic displays, and more particularly, but not exclusively, to stereoscopic displays with addressable focus cues. A stereoscopic display system with the addressable focus cues, comprises: a microdisplay for providing a virtual image for display to a user; a reflective active optical element configured to provide a variable optical power; a relay lens disposed along an optical path between the microdisplay and the active optical element, the relay lens positioned therebetween such that the microdisplay and the active optical element are disposed at conjugate planes of the relay lens; a beamsplitter disposed along the optical path between the microdisplay and the active optical element at an orientation to receive optical radiation from the active optical element; and a see-through eyepiece comprising a selected surface configured to receive optical radiation from the beamsplitter and reflect the received radiation to an exit pupil of the system to provide a virtual display path, the selected surface also configured to receive optical radiation from a source other than the microdisplay and to transmit such optical radiation to the exit pupil to provide a see-through optical path.

## Background
RELATED APPLICATIONS
This present application is a 371 application of International Application No. PCT/US2013/065422 filed Oct. 17, 2013, which claims the benefit of priority of U.S. Provisional Application No. 61/795,500, filed on Oct. 18, 2012, the entire contents of which application(s) are incorporated herein by reference.


GOVERNMENT LICENSE RIGHTS
This invention was made with government support under IIS0915035 awarded by NSF. The government has certain rights in the invention.


FIELD OF THE INVENTION
The present invention relates generally to stereoscopic displays, and more particularly, but not exclusively, to stereoscopic displays with addressable focus cues.
BACKGROUND OF THE INVENTION
Conventional stereoscopic 3D displays create the illusion of depth based on binocular disparities, rendering 3D scenes from a single pair of 2D perspective images at a fixed distance to the viewer. Therefore conventional stereoscopic displays force an unnatural decoupling of the accommodation and convergence cues, which may contribute to various visual artifacts in stereoscopic displays, such as distortion in perceived depth, diplopic vision, visual discomfort, and fatigue. Many approaches have been proposed which may overcome the drawbacks of conventional stereoscopic displays, including volumetric displays, holographic displays, and multi-focal-plane displays. However, a need exists to develop an optical see-through stereoscopic display which solves the fundamental accommodation-convergence problems and also renders large volumes of continuous 3D scene at high image quality and flickering-free speed.
A stereoscopic display with addressable focus cues is one of the most promising approaches to solving the fundamental accommodation-convergence problems of providing the capability of rendering correct or near-correct focus cues for virtual 3D objects. Unlike traditional stereoscopic displays, stereoscopic displays with addressable focus cues enable the ability to either dynamically vary the focal distance of the virtual display through an active optical element in accordance to the viewer's region of interest, known as vari-focal display mode, or present multiple focal planes at a flickering-free speed through with no need to track a viewer's region of interest, known as multi-focal display mode. For instance, multi-focal-plane displays present perspective 2D images at multiple carefully placed, discrete focal distances along the visual axis. These discrete focal planes sample a 3D scene volume into multiple zones, and objects within a zone are rendered by the corresponding pair of adjacent focal planes, as shown in FIG. 1. Therefore multi-focal-plane displays are able to render correct or near-correct focus cues for virtual objects at different depths. Contrary to multi-viewpoint displays such as holographic displays and volumetric displays, the multi-focal-plane display is a fixed-viewpoint display. By restricting the viewing position, multi-focal-plane display systems only need to display a small number of viewpoints. Also multi-focal-point displays can preserve disparity, occlusion and perspective in conventional 2D displays as well as rendering viewing-dependent lighting effects such as specular reflection and shading. In practice, the implementations of multi-focal-plane displays can be categorized into two categories: spatially multiplexed or temporally multiplexed. In a spatial-multiplexed system, multi-focal capability is achieved by stacking multiple 2D displays. In the alternative and more elegant, time-multiplexed system, the focal distances of images from a single 2D display are fast switched by an active optical element in synchronization with the frame rendering of multiple focal planes. In general, a multi-focal plane display can be readily adapted for use in a vari-focal mode without much change to the optics layout.
In addition, progress has recently been made in the field of stereoscopic displays that can be head-mounted and that have addressable focal planes for improved depth perception but require substantially less computational power than existing methods, as reflected in commonly owned U.S. Patent Application Publication. No. 2011/0075257, the contents of which are incorporated herein by reference. However, a need still exists for optical imaging systems which can provide enhanced imaging performance in stereoscopic displays with addressable focus cues.
SUMMARY OF THE INVENTION
In one of its aspects, the present invention may provide a virtual display system with addressable focus cues comprising a microdisplay for providing a virtual image for display to a user. A reflective active optical element, configured to provide a variable optical power, may also be provided. A relay lens may be disposed along an optical path between the microdisplay and the active optical element, with the relay lens positioned therebetween such that the microdisplay and active optical element are disposed at conjugate planes of the relay lens. A beamsplitter may be disposed along the optical path between the microdisplay and the active optical element at an orientation to receive optical radiation from the active optical element. In addition, a see-through eyepiece may be provided which includes a selected surface configured to receive optical radiation from the beamsplitter and reflect the received radiation to an exit pupil of the system to provide a virtual display path. The selected surface may also be configured to receive optical radiation from a source other than the microdisplay (such as the real world) and to transmit such optical radiation to the exit pupil to provide a see-through optical path. The eyepiece may include a freeform prism shape, and, in particular, may include a first surface configured to receive and refract optical radiation from the beamsplitter and may include a second surface configured to receive the refracted optical radiation from the first surface, with the second surface configured to reflect the optical radiation to the selected surface of the eyepiece. The second surface may be configured to total internally reflect the optical radiation, and one or more of the surfaces of the eyepiece may comprise a rotationally asymmetric surface.
In another of its aspects, the present invention may provide a virtual display system with addressable focus cues comprising a microdisplay for providing a virtual image for display to a user, and an eyepiece comprising a reflective optical element configured to reflect optical radiation from the microdisplay to an exit pupil of the system. A relay lens, comprising a refractive active optical element configured to provide a variable optical power, may be disposed along an optical path between the microdisplay and the eyepiece to relay an image from the microdisplay to the eyepiece. The relay lens may include first and second lens groups disposed along the optical path with the active optical element located between the first and second lens groups. In addition, a beamsplitter may be disposed along the optical path between the microdisplay and the eyepiece, with the beamsplitter configured to receive and transmit optical radiation from a source other than the microdisplay (such as the real world) to the exit pupil to provide a see-through optical path. The eyepiece may comprise a spherical mirror, and the system may be telecentric in the microdisplay. The system may also have an f-number less than 3.



BRIEF DESCRIPTION OF THE DRAWINGS
The foregoing summary and the following detailed description of exemplary embodiments of the present invention may be further understood when read in conjunction with the appended drawings, in which:
FIG. 1 schematically illustrates 3D objects rendered by multiple focal planes relative to a viewer;
FIG. 2 schematically illustrates the unfolded optical path of an exemplary display system in accordance with the present invention;
FIG. 3A schematically illustrates a 2D layout of virtual display optics of an exemplary display system in accordance with the present invention;
FIG. 3B schematically illustrates a 2D layout of the exemplary display system of FIG. 3A but having a field lens comprising two optical elements rather than a singlet;
FIG. 3C schematically illustrates the free-form eyepiece and compensator of FIGS. 3A-3B showing the see-through optical path;
FIG. 3D schematically illustrates the free-form eyepiece and compensator of FIGS. 3A-3B showing both the see-through and display paths;
FIGS. 4A-4E illustrate the polychromatic MTF through the display path for the virtual display system of FIG. 3B;
FIG. 4F illustrates a distortion grid through the display path for the virtual display system of FIG. 3B;
FIGS. 5A-5E illustrate the polychromatic MTF through the see-through path for the virtual display system of FIG. 3B;
FIG. 5F illustrates a distortion grid through the see-through path for the virtual display system of FIG. 3B;
FIG. 6A schematically illustrates a 3D layout of the free-form eyepiece with relay optics of the display system of FIG. 3B;
FIG. 6B schematically illustrates a 3D Solidworks model of the assembled free-form eyepiece and compensator of the display system of FIG. 6A;
FIG. 7A illustrates a depth-fused 6-focal-plane 3D scene of 40 degrees of field of view and 3 diopters of depth, captured through the eyepiece for a prototype built according to the design of FIG. 3B;
FIGS. 7B-7C illustrate 6-focal-plane 3D scenes captured by a camera focused at 2 m and 30 cm, respectively, for a prototype built according to the design of FIG. 3B;
FIG. 8A illustrates a retinal image MTF as a function of accommodations in a dual-focal-plane display, with two focal planes placed at 1.2D and 1.8D, respectively, and with a luminance ratio of 1:1;
FIG. 8B illustrates a retinal image contrast as a function of accommodation showing the contrast gradient for different spatial frequencies;
FIGS. 9A-9B illustrate that the spatial frequency of a transition point decreases when the focal plane separation increases and when the eye pupil size increases, respectively;
FIGS. 10A, 10B schematically illustrate 2D and 3D layouts, respectively, of the virtual display optics of a further exemplary display system in accordance with the present invention;
FIG. 11 schematically illustrates a 2D layout and element descriptions of the relay lens group of FIG. 10A along with an optional display illumination path; and
FIGS. 12A, 12B illustrate polychromatic MTF and field curves, respectively, of the system of FIGS. 10A-11.



DETAILED DESCRIPTION OF THE INVENTION
Referring now to the figures, wherein like elements are numbered alike throughout, in accordance with one aspect of the present invention, FIG. 2 schematically illustrates the first-order unfolded optical path of an exemplary optical system which is particularly suited for providing high imaging quality in depth-fused multi-focal-plane stereoscopic displays with addressable focus cues. FIGS. 3A, 3B schematically illustrate particular designs according to the layout of FIG. 2, with a first optical system 100 having a single field lens 18, FIG. 3A, and an alternative system 200 having a two-element 17, 19 field lens 18, FIG. 3B. (While a single set of optics for a single viewer's eye is illustrated, it is understood that in a final stereoscopic device, two such sets of optics will be provided, one for each eye.)
A relevant feature of the designs is the inclusion of a relay lens group 20 which relays the image from a microdisplay, such as a digital micro-mirror device (DMD) 60, to the front of an eyepiece 12. The relay lens group 20 may include a traditional, non-deformable lens 21 and a reflective active optical element, such as a deformable membrane mirror 80, FIG. 2. The relay lens 21 may include a pair of doublets 22, 24 and lens 26, FIGS. 3A, 3B. The deformable membrane mirror device (DMMD) 80 may be placed at the focal plane of the relay lens 21 and may serve as the system stop. Together the lens 21, FIG. 2, (or lenses 22, 24, 26, FIGS. 3A, 3B) and the DMMD 80 may provide a folded double-telecentric system particularly suited to depth-fused multi-focal-plane stereoscopic displays. An advantage of designing a double-telecentric relay 20 is that the change of optical power on the DMMD 80 changes only the location of the intermediate image without changing the image magnification, so that the field of view of the system and the angular resolution in eye space remain constant, and so that the corresponding pixels on multiple focal planes overlap with each other one-to-one. Thus, the designs of FIGS. 3A, 3B are well suited for a depth fusing technique without the need for correcting misaligned multiple focal images otherwise resulting from different image magnifications. These benefits may be further understood by analysis of the focus cue and accommodation range.
The focus cue or accommodation range, ΔDaccommodation, which implies the depth range of the 3D volume the system can render, is determined by




  
    
      Δ
      ⁢
      
        
      
      ⁢
      
        D
        accommodation
      
    
    =
    
      
        
          Φ
          eye
          2
        
        
          Φ
          1
          2
        
      
      ×
      Δ
      ⁢
      
        
      
      ⁢
      
        Φ
        DMMD
      
    
  
  ,




where Φeye is the power of the eyepiece 12, Φ1 is the power of the relay lens 21, and ΔΦDMMD denotes the range of power by which the deformable mirror 80 can change. The above equation gives and the relationship between the focal length of the relay lens 20 and the eyepiece 12. Since the eyepiece 12 will relay the system stop, i.e., the DMMD 80, to form an exit pupil, the ratio between the size of the exit pupil Dxp and the size of the DMMD 80, is fixed once the desired accommodation range is determined:





  
    D
    XP
  
  =
  
    
      
        D
        DMMD
      
      
        
          f
          1
        
        /
        
          f
          eye
        
      
    
    .
  




One drawback of the folded double-telecentric relay design is that it provides no magnification to the image of the DMD display 60. Therefore to get a desired system field of view, a field lens 18 may be added in front of the DMD display 60 to magnify the image. (The display 60 may be an emissive display, or maybe a reflective display that is illuminated through an illumination path.) The magnification introduced by the field lens 18 is




  m
  =
  
    
      1
      
        
          
            z
            0
          
          
            f
            field
          
        
        -
        1
      
    
    .
  




The system half field of view is then:





  HFOV
  =
  
    
      
        y
        DMD
        ′
      
      
        f
        eye
      
    
    =
    
      
        
          
            y
            DMD
          
          ×
          m
        
        
          f
          eye
        
      
      .
    
  




Based on the design goal, device specifications, and mechanical considerations, Table 1 lists the first-order system specifications for the designs of FIGS. 3A, 3B.







TABLE 1





First-order system specifications for virtual display.
















Microdisplay
0.7′′ DMD, XGA resolution, 14 μm pixel









Deformable mirror defocus range
0~1.2 
diopters


Accommodation Range
0~3 
diopters








Field of view
40° (32.5° H × 24.5° V)









Relay lens focal length, f1
43.9 
mm


Eyepiece focal length, feye
27.8 
mm


Exit pupil diameter
6 
mm









Free Form Eyepiece and Compensator

The optical see-through capabilities of the systems 100, 200 may be realized by using beamsplitters to fold the virtual display optics (e.g., DMD 60, field lens 18, relay lens group 20) out of the way. However, given that the eyepiece 12 in the present design has a short focal length, it was very difficult to design the system conventionally.
In the instant exemplary design, a more elegant solution was pursued. As shown in FIGS. 3C, 3D, the eyepiece 12 was designed as a wedge-shaped free-form plastic lens. The free-form prism eyepiece 12 may include three rotationally asymmetric surfaces, labeled as S1, S2, and S3, respectively. Considering the virtual display path, FIG. 3D, a ray from the intermediate image of the display 60 is first refracted by the surface S3. After two consecutive reflections by surfaces S1 and S2, the ray is transmitted through the surface S1 and reaches the exit (eye) pupil of the system. The surface S1 desirably satisfies the condition of total internal reflection for all rays reflected on the surface S1. The surface S2 of the eyepiece 12 may be coated as a half mirror in order to facilitate the optical see-through capability. A free-form compensator 14, which may include two rotationally asymmetric surfaces, S2 and S4, may be cemented to the eyepiece 12 to compensate for the aberrations and distortions introduced to the rays from the real-world scene when the two pieces 12, 14 are combined together, FIG. 3C. In addition, an optional cylindrical lens 13 may be included with the free-form compensator 14 to help minimize aberrations and distortion for the see-through path.
To achieve the desired optical performance, MTF values were selected to evaluate the overall image sharpness. Since the virtual display system 100 was designed backwards from the eyepiece 12 to the display 60, the goal was to have MTF values no less than 20% at spatial frequency of 36 lp/mm on the display 60, which is the cut-off frequency for pixel size of 14 μm. The human eye has an angular resolution of 1 arcmin. Therefore the compensator 14 was optimized such that the MTF values at 30 cycles/degree are greater than 0.2 to minimize degradation of the real-world scene. Another important optical performance factor of the system 100, 200 was image distortion. In conventional system, distortion is regular and can be compensated easily electronically or computationally. However in systems with off-axis freeform optics, the distortion can be very large and irregular. Therefore the design of the systems 100, 200 should have tight constraints on distortion sampled over the entire FOV. The distortion is especially important for the see-through optical path, because it can change the sizes and shapes of objects seen through the see-through view, thus greatly affecting 3D perception.
Design and Optimization Procedures
The design of the systems 100, 200 involved two steps, the virtual display path and the optical see-through path. For the virtual display path, the freeform eyepiece 12 was setup with the relay lens 20 and field lens 18 in CodeV and optimized together. The display performance was balanced for fields sampled across the 40-degrees of FOV and across the desired accommodation range of 3 diopters. After the virtual display optimization was finished, the freeform eyepiece 12 was setup alone with the compensator 14 and the compensator's back surface S4 was optimized for see-through performance. The see-through performance was optimized for 60 degrees of field of view while emphasizing the central 40 degrees. A progressive optimization strategy was adopted in both steps by gradually increasing the number of variable surface coefficients of the freeform surfaces as the system performance improved.
In the final design, the freeform eyepiece and compensator surfaces S1, S2, S3, S4 were described by XY-polynomials to the 10th order and prototyped by single-point diamond turning on PMMA. In the system 200 of FIG. 3B, one of the field lenses elements, element 17, was optimized, and a diffractive optical feature was added to correct for chromatic aberrations introduced by the freeform eyepiece 12. All other lenses 19, 22, 24, 26 are all off-the-shelf components to reduce the prototyping costs.
The polychromatic MTF values of the virtual display, evaluated for a 3 mm pupil, are greater than 0.2 at 36 lp/mm across the 40 degrees of field of view with a central field value of 0.5, FIGS. 4A-4E. The virtual display also shows minimal distortion, FIG. 4F. The polychromatic MTF values of the see-through optical path, evaluated for 3 mm pupil, are greater than 0.4 at 30 cycles/degree across the 40 degrees of field of view, FIGS. 5A-5E. The distortion of the see-through scene was also very well corrected, FIG. 5F. The prescription for the particular design of FIG. 3B is provided as follows.
System Prescription for Virtual Display Path
In Table 2, surfaces #2-#4 specify the free-form eyepiece 12. Surface #2 and #4 represent the same physical surface and is also denoted as eyepiece surface S1. Surface #3 is also denoted as eyepiece surface S2, and Surface #5 is also denoted as eyepiece surface S3. Surfaces #8-#15 and surfaces #17-#24 are the same group of relay lenses 22, 24, 26 modeled in double path. The deformable mirror 80 is modeled at Surface #16. Surfaces #25-#26 model the beam splitter 16 at 45 degrees. Surfaces #27-#28 represent the field lens element 17, and Surfaces #29-#30 represent the field lens element 19.







TABLE 2







System prescription for virtual display path.













Ele-








ment








num-








ber
Sur-







used in
face
Surface
Y 
Thick-

Refract


figures
No.
Type
Radius
ness
Material
Mode

















 1 
Sphere
Infinity
   0.000

Refract



(Stop)







12, S1
 2
XY Poly
−185.496
   0.000
PMMA
Refract


12, S2
 3
XY Poly
−67.446
   0.000
PMMA
Reflect


12, S1
 4
XY Poly
−185.496
   0.000
PMMA
Reflect


12, S3
 5
XY Poly
−830.046
   0.000

Refract



 6
Sphere
Infinity
   0.000

Refract



 7
Sphere
Infinity
  53.933

Refract


24
 8
Sphere
435.850
   4.000
NSF10
Refract



 9
Sphere
36.730
  12.070
NBAF10
Refract



10
Sphere
−53.760
  18.079

Refract


22
11
Sphere
53.760
  12.070
NBAF10
Refract



12
Sphere
−36.730
   4.000
NSF10
Refract



13
Sphere
−435.850
  19.826

Refract


26
14
Sphere
Infinity
   2.000
NBK7
Refract



15
Sphere
38.900
   3.502

Refract


80
16
Sphere
−4000.000
 −3.502

Reflect


26
17
Sphere
38.900
 −2.000
NBK7
Refract



18
Sphere
Infinity
−19.826

Refract


22
19
Sphere
−435.850
 −4.000
NSF10
Refract



20
Sphere
−36.730
−12.070
NBAF10
Refract



21
Sphere
53.760
−18.079

Refract


24
22
Sphere
−53.760
−12.070
NBAF10
Refract



23
Sphere
36.730
 −4.000
NSF10
Refract



24
Sphere
435.850
−23.000

Refract


16
25
Sphere
Infinity
 −1.600
471400.6541
Refract



26
Sphere
Infinity
−10.513

Refract


19
27
Sphere
−46.700
 −6.500
NBK7
Refract



28
Sphere
Infinity
 −1.896

Refract


17
29
Asphere
−102.223
 −2.800
PMMA
Refract



30
Asphere
−61.641
 −7.655

Refract









System Prescription for Optical See-Through Path

In Table 3 surfaces #2 and #3 are eyepiece surfaces S1 and S3, modeled the same as in the virtual display path. Surfaces #4, #5 specify the free-form compensator 14. Surface #4 is, it an exact replica of Surface #3 (eyepiece surface S3).







TABLE 3







System prescription for see-through path.














Ele-









ment









num-









ber









used 









in
Sur-








fig-
face
Surface
Y 
X
Thick-
Ma-
Refract


ures
No.
Type
Radius
Radius
ness
terial
Mode


















1 
Sphere
Infinity
Infinity
 0.000

Refract



(Stop)








12, S1
2
XY Poly
−185.496
−185.496
 0.000
PMMA
Refract


12, S3
3
XY Poly
−67.446
−67.446
 0.000
PMMA
Refract


14, S2
4
XY Poly
−67.446
−67.446
 0.000
PMMA
Refract


14, S4
5
XY Poly
−87.790
−87.790
10.000

Refract


13
6
Cylin-
Infinity
−103.400
 6.5
NBK7
Refract




drical







13
7
Sphere
Infinity
Infinity
 0.000

Refract









As used in the system prescription Tables, e.g., Table 2 or Table 3, the term “XY Poly” refers to a surface which may be represented by the equation



  
    z
    =
    
      
        
          cr
          2
        
        
          1
          +
          
            
              1
              -
              
                
                  (
                  
                    1
                    +
                    k
                  
                  )
                
                ⁢
                
                  c
                  2
                
                ⁢
                
                  r
                  
                    2
                    ⁢
                    
                      
                    
                  
                
              
            
          
        
      
      +
      
        
          ∑
          
            j
            =
            2
          
          66
        
        ⁢
        
          
            C
            j
          
          ⁢
          
            x
            m
          
          ⁢
          
            y
            n
          
        
      
    
  




  
    
      j
      =
      
        
          
            
              
                (
                
                  m
                  +
                  n
                
                )
              
              2
            
            +
            m
            +
            
              3
              ⁢
              n
            
          
          2
        
        +
        1
      
    
    ,
  



where z is the sag of the free-form surface measured along the z-axis of a local x, y, z coordinate system, c is the vertex curvature (CUY), r is the radial distance, k is the conic constant, and Cj is the coefficient for xmyn. The term “Asphere” in the Tables refers to an aspherical surface which may be represented by the equation





  
    z
    =
    
      
        
          cr
          2
        
        
          1
          +
          
            
              1
              -
              
                
                  (
                  
                    1
                    +
                    k
                  
                  )
                
                ⁢
                
                  c
                  2
                
                ⁢
                
                  r
                  2
                
              
            
          
        
      
      +
      
        Ar
        4
      
      +
      
        Br
        6
      
      +
      
        Cr
        8
      
      +
      
        Dr
        10
      
      +
      
        Er
        12
      
    
  
  ,




where z is the sag of the surface measured along the z-axis of a local x, y, z coordinate system, c is the vertex curvature, r is the radial distance, k is the conic constant, A through E are the 4th, 6th, 8th, 10th and 12th order deformation coefficients, respectively.








TABLE 4





Optical surface prescription of Surface #2 and #4 of Table 2.


















Y Radius
−1.854965E+02
X**2 * Y**5
−1.505674E−10


Conic Constant
−2.497467E+01
X * Y**6
 0.000000E+00


X
 0.000000E+00 
Y**7
−4.419392E−11


Y
 0.000000E+00
X**8
 4.236650E−10


X**2
−2.331157E−03
X**7 * Y
 0.000000E+00


X * Y
 0.000000E+00
X**6 * Y**2
−1.079269E−10


Y**2
 6.691726E−04 
X**5 * Y**3
 0.000000E+00


X**3
 0.000000E+00 
X**4 * Y**4
−1.678245E−10


X**2 * Y
−1.066279E−04
X**3 * Y**5
 0.000000E+00


X Y**2
 0.000000E+00 
X**2 * Y**6
 2.198604E−12


Y**3
−2.956368E−05
X * Y**7
 0.000000E+00


X**4
−1.554280E−06
Y**8
−2.415118E−12


X**3 * Y
 0.000000E+00 
X**9
 0.000000E+00


X**2 * Y**2
 1.107189E−06
X**8 * Y
 4.113054E−12


X * Y**3
 0.000000E+00
X**7 * Y**2
 0.000000E+00


Y**4
 1.579876E−07
X**6 * Y**3
−1.805964E−12


X**5
 0.000000E+00 
X**5 * Y**4
 0.000000E+00


X**4 * Y
 1.789364E−07
X**4 * Y**5
 9.480632E−13


X**3 * Y**2
 0.000000E+00
X**3 * Y**6
 0.000000E+00


X**2 * Y**3
−2.609879E−07
X**2 * Y**7
 2.891726E−13


X * Y**4
 0.000000E+00
X * Y**8
 0.000000E+00


Y**5
−6.129549E−10
Y**9
−2.962804E−14


X**6
−3.316779E−08
X**10
−6.030361E−13


X**5 * Y
 0.000000E+00 
X**9 * Y
 0.000000E+00


X**4 * Y**2
 9.498635E−09 
X**8 * Y**2
−7.368710E−13


X**3 * Y**3
 0.000000E+00
X**7 * Y**3
 0.000000E+00


X**2 * Y**4
 9.042084E−09
X**6 * Y**4
 9.567750E−13


X * Y**5
 0.000000E+00
X**5 * Y**5
 0.000000E+00


Y**6
−4.013470E−10
X**4 * Y**6
 4.280494E−14


X**7
 0.000000E+00
X**3 * Y**7
 0.000000E+00


X**6 * Y
−8.112755E−10
X**2 * Y**8
−7.143578E−15


X**5 * Y**2
 0.000000E+00 
X * Y**9
 0.000000E+00


X**4 * Y**3
 1.251040E−09
Y**10
 3.858414E−15


X**3 * Y**4
 0.000000E+00
N-Radius
 1.000000E+00
















TABLE 5







Decenter of Surface #2 and #4 of Table 2, relative to Surface #1 of Table 2.









Y DECENTER
Z DECENTER
ALPHA TILT





6.775E+00
2.773E+01
7.711E+00
















TABLE 6





Optical surface prescription of Surface #3 of Table 2.


















Y Radius
−6.744597E+01
X**2 * Y**5
−3.464751E−11


Conic Constant
−1.258507E+00
X * Y**6
 0.000000E+00


X
 0.000000E+00
Y**7
−8.246179E−12


Y
 0.000000E+00
X**8
−2.087865E−11


X**2
−1.300207E−03
X**7 * Y
 0.000000E+00


X * Y
 0.000000E+00
X**6 * Y**2
 2.845323E−11


Y**2
 4.658585E−04 
X**5 * Y**3
 0.000000E+00


X**3
 0.000000E+00 
X**4 * Y**4
−5.043398E−12


X**2 * Y
−1.758475E−05
X**3 * Y**5
 0.000000E+00


X Y**2
 0.000000E+00 
X**2 * Y**6
 2.142939E−14


Y**3
−1.684923E−06
X * Y**7
 0.000000E+00


X**4
−1.463720E−06
Y**8
 1.607499E−12


X**3 * Y
 0.000000E+00
X**9
 0.000000E+00


X**2 * Y**2
−1.108359E−06
X**8 * Y
−1.922597E−12


X * Y**3
 0.000000E+00
X**7 * Y**2
 0.000000E+00


Y**4
−1.098749E−07
X**6 * Y**3
 1.100072E−13


X**5
 0.000000E+00 
X**5 * Y**4
 0.000000E+00


X**4 * Y
−7.146353E−08
X**4 * Y**5
−4.806130E−14


X**3 * Y**2
 0.000000E+00 
X**3 * Y**6
 0.000000E+00


X**2 * Y**3
−1.150619E−08
X**2 * Y**7
−2.913177E−14


X * Y**4
 0.000000E+00
X * Y**8
 0.000000E+00


Y**5
 5.911371E−09 
Y**9
 9.703717E−14


X**6
−5.406591E−10
X**10
 2.032150E−13


X**5 * Y
 0.000000E+00 
X**9 * Y
 0.000000E+00


X**4 * Y**2
−1.767107E−09
X**8 * Y**2
−1.037107E−13


X**3 * Y**3
 0.000000E+00 
X**7 * Y**3
 0.000000E+00


X**2 * Y**4
−7.415334E−10
X**6 * Y**4
 3.602862E−14


X * Y**5
 0.000000E+00
X**5 * Y**5
 0.000000E+00


Y**6
−5.442400E−10
X**4 * Y**6
−8.831469E−15


X**7
 0.000000E+00
X**3 * Y**7
 0.000000E+00


X**6 * Y
 6.463414E−10 
X**2 * Y**8
 2.178095E−15


X**5 * Y**2
 0.000000E+00 
X * Y**9
 0.000000E+00


X**4 * Y**3
 1.421597E−10
Y**10
 1.784074E−15


X**3 * Y**4
 0.000000E+00
N-Radius
 1.000000E+00
















TABLE 7





Decenter of Surface #3 of Table 2 relative to Surface #1 of Table 2.

















Y DECENTER
Z DECENTER
ALPHA TILT


1.329E+01
4.321E+01
−8.856E+00
















TABLE 8





Optical surface prescription of Surface #5 of Table 2.


















Y Radius
−8.300457E+02
X**2 * Y**5
 4.051880E−08


Conic Constant
−9.675799E+00
X * Y**6
 0.000000E+00


X
 0.000000E+00
Y**7
−3.973293E−09


Y
 0.000000E+00 
X**8
−1.881791E−10


X**2
−1.798206E−04
X**7 * Y
 0.000000E+00


X * Y
 0.000000E+00
X**6 * Y**2
 5.519986E−09


Y**2
−2.606383E−03
X**5 * Y**3
 0.000000E+00


X**3
 0.000000E+00 
X**4 * Y**4
 3.822268E−09


X**2 * Y
−7.767146E−05
X**3 * Y**5
 0.000000E+00


X Y**2
 0.000000E+00
X**2 * Y**6
−3.024448E−09


Y**3
−8.958581E−05
X * Y**7
 0.000000E+00


X**4
 1.978414E−05
Y**8
 2.673713E−11


X**3 * Y
 0.000000E+00
X**9
 0.000000E+00


X**2 * Y**2
 2.081156E−05 
X**8 * Y
 1.006915E−10


X * Y**3
 0.000000E+00 
X**7 * Y**2
 0.000000E+00


Y**4
−1.073001E−06
X**6 * Y**3
−2.945084E−10


X**5
 0.000000E+00 
X**5 * Y**4
 0.000000E+00


X**4 * Y
 2.585164E−07
X**4 * Y**5
 5.958040E−10


X**3 * Y**2
 0.000000E+00 
X**3 * Y**6
 0.000000E+00


X**2 * Y**3
−2.752516E−06
X**2 * Y**7
−3.211903E−10


X * Y**4
 0.000000E+00
X * Y**8
 0.000000E+00


Y**5
−1.470053E−06
Y**9
 2.296303E−11


X**6
−1.116386E−07
X**10
 5.221834E−12


X**5 * Y
 0.000000E+00
X**9 * Y
 0.000000E+00


X**4 * Y**2
−3.501439E−07
X**8 * Y**2
 1.135044E−11


X**3 * Y**3
 0.000000E+00
X**7 * Y**3
 0.000000E+00


X**2 * Y**4
 1.324057E−07
X**6 * Y**4
−1.050621E−10


X * Y**5
 0.000000E+00
X**5 * Y**5
 0.000000E+00


Y**6
−9.038017E−08
X**4 * Y**6
 5.624902E−11


X**7
 0.000000E+00 
X**3 * Y**7
 0.000000E+00


X**6 * Y
 3.397174E−10
X**2 * Y**8
 5.369592E−12


X**5 * Y**2
 0.000000E+00 
X * Y**9
 0.000000E+00


X**4 * Y**3
−1.873966E−08
Y**10
 2.497657E−12


X**3 * Y**4
 0.000000E+00 
N-Radius
 1.000000E+00
















TABLE 9







Decenter of Surface #5 of Table 2 relative to Surface #1 of Table 2.









Y DECENTER
Z DECENTER
ALPHA TILT





.427E+01
3.347E+01
7.230E+01









Turning to the prescription of the second field lens element 17, both surfaces of the field lens element 17 are aspheric surfaces. Additionally, Surface #29 (Table 2) of field lens element 17 has a kinoform diffractive optical feature which may be represented according to the following equation

φ=Ar2+Br4+Cr6+Dr8+Er10,

where φ is the phase function of the diffractive element, r is the radial distance, A through E are the 4th, 6th, 8th, 10th and 12th order phase coefficients, respectively. The surface prescriptions of second field lens element 17 are provide in Table 10-Table 12.








TABLE 10





Surface Prescription for Surface #29 of Table 2.

















Y Radius

1.022230E+02


Conic Constant 
(K)
1.091191E+01


 4th Order Coefficient 
(A)
4.372314E−06


 6th Order Coefficient 
(B)
−6.940740E−08


 8th Order Coefficient 
(C)
8.588869E−11


10th Order Coefficient 
(D)
2.348571E−14


12th Order Coefficient 
(E)
−1.463306E−16
















TABLE 11





Diffractive Optical Element Phase 


Data for Surface #29 of Table 2.


















Construction Wavelength (nm)
525











R**2 
(HCO C1)
−1.295858E−03



R**4 
(HCO C2)
−3.879339E−07



R**6 
(HCO C3)
8.494999E−09



R**8 
(HCO C4)
−1.771348E−13



R**10
(HCO C5)
−3.584229E−15

















TABLE 12





Surface Prescription for Surface #30 of Table 2.



















Y Radius

6.164108E+01



Conic Constant
(K)
9.828641E+00



 4th Order Coefficient
(A)
5.898651E−05



 6th Order Coefficient
(B)
−2.951081E−07



 8th Order Coefficient
(C)
−3.440910E−10



10th Order Coefficient
(D)
1.785109E−13



12th Order Coefficient
(E)
2.803121E−15

















TABLE 13





Optical surface prescription of Surface #5 of Table 3.


















Y Radius
−8.779024E+01
X**2 * Y**5
−8.011955E−11


Conic 
−7.055198E+00
X * Y**6
  0.000000E+00


Constant





X
  0.000000E+00
Y**7
  3.606142E-11


Y
  0.000000E+00
X**8
  3.208020E-11


X**2
−3.191225E−03
X**7 * Y
  0.000000E+00


X * Y
  0.000000E+00
X**6 * Y**2
−2.180416E−11


Y**2
  4.331992E−03
X**5 * Y**3
  0.000000E+00


X**3
  0.000000E+00
X**4 * Y**4
−3.616135E−11


X**2 * Y
−9.609025E−05
X**3 * Y**5
  0.000000E+00


X Y**2
  0.000000E+00
X**2 * Y**6
−5.893434E−12


Y**3
−2.432809E−05
X * Y**7
  0.000000E+00


X**4
−2.955089E−06
Y**8
  3.081069E−12


X**3 * Y
  0.000000E+00
X**9
  0.000000E+00


X**2 * Y**2
  2.096887E−07
X**8 * Y
  1.267096E−12


X * Y**3
  0.000000E+00
X**7 * Y**2
  0.000000E+00


Y**4
−9.184356E−07
X**6 * Y**3
−1.848104E−12


X**5
  0.000000E+00
X**5 * Y**4
  0.000000E+00


X**4 * Y
  3.707556E-08
X**4 * Y**5
  5.208420E−14


X**3 * Y**2
  0.000000E+00
X**3 * Y**6
  0.000000E+00


X**2 * Y**3
−1.535357E−07
X**2 * Y**7
  1.198597E-13


X * Y**4
  0.000000E+00
X * Y**8
  0.000000E+00


Y**5
−1.445904E−08
Y**9
−6.834914E−14


X**6
−4.440851E−09
X**10
−1.706677E−14


X**5 * Y
  0.000000E+00
X**9 * Y
  0.000000E+00


X**4 * Y**2
  1.686424E−09
X**8 * Y**2
−1.614840E−14


X**3 * Y**3
  0.000000E+00
X**7 * Y**3
  0.000000E+00


X**2 * Y**4
  6.770909E-09
X**6 * Y**4
  8.739087E−14


X * Y**5
  0.000000E+00
X**5 * Y**5
  0.000000E+00


Y**6
−3.713094E−10
X**4 * Y**6
  3.940903E−15


X**7
  0.000000E+00
X**3 * Y**7
  0.000000E+00


X**6 * Y
−1.316067E−10
X**2 * Y**8
  5.435162E−15


X**5 * Y**2
  0.000000E+00
X * Y**9
  0.000000E+00


X**4 * Y**3
  7.924387E−10
Y**10
−2.259169E−15


X**3 * Y**4
  0.000000E+00
N-Radius
  1.000000E+00
















TABLE 14







Decenter of Surface #5 relative to Surface #1 of Table 3.









Y DECENTER
Z DECENTER
ALPHA TILT





3.358E+00
4.900E+01
6.765E+00









Alternative Exemplary Design without Cylindrical Lens

In the designs of FIGS. 3A, 3B above, an optional cylindrical lens 13 has been included with the free-form compensator 14 to help minimize aberrations and distortion. An alternative design is also provided without the cylindrical lens 13, in which the virtual display path is the same as shown in FIG. 3B and Table 2. The only difference among the remaining surfaces of the see-through path in the absence of the cylindrical lens 13 is the eyepiece/compensator surface S2 (Surface #5 in the optical see-through path of Table 3). In Table 15, Surfaces #2 and #3 are eyepiece surfaces S1 and S3, modeled the same as in the virtual display path. Surfaces #4-5 describe the free-form compensator 14. Surface #4 is a exact replica of Surface #3.







TABLE 15







Alternative eyepiece optics prescription without cylindrical lens.














Surface 
Y 
X 


Refract 



Type 
Radius
Radius
Thickness
Material
Mode





Object
Sphere
Infinity
Infinity
−666.700

Refract


1 
Sphere
Infinity
Infinity
   0.000

Refract


(Stop)








2
XY 
−185.496
−185.496
   0.000
PMMA
Refract



Polynomial







3
XY 
 −67.446 
 −67.446
   0.000
PMMA
Refract



Polynomial







4
XY 
 −67.446 
 −67.446
   0.000
PMMA
Refract



Polynomial







5
XY 
−492.346
−492.346
   0.000

Refract



Polynomial







Image
Sphere
Infinity
Infinity 
   0.000

Refract
















TABLE 16





Optical surface prescription of Surface #5 of Table 15.


















Y Radius
−4.923462E+02
X**2 * Y**5
−1.476237E−10


Conic 
  3.982960E+00
X * Y**6
  0.000000E+00


Constant





X
  0.000000E+00
Y**7
  2.044705E−11


Y
  0.000000E+00
X**8
  2.971746E−11


X**2
−3.001720E−03
X**7 * Y
  0.000000E+00


X * Y
  0.000000E+00
X**6 * Y**2
−6.199724E−12


Y**2
−5.233825E−04
X**5 * Y**3
  0.000000E+00


X**3
  0.000000E+00
X**4 * Y**4
−2.279723E−11


X**2 * Y
−6.009699E-05
X**3 * Y**5
  0.000000E+00


X Y**2
  0.000000E+00
X**2 * Y**6
−1.041364E−12


Y**3
−2.244921E−05
X * Y**7
  0.000000E+00


X**4
−6.379076E-07
Y**8
  1.125487E−12


X**3 * Y
  0.000000E+00
X**9
  0.000000E+00


X**2 * Y**2
  2.968752E-06
X**8 * Y
  1.210373E−12


X * Y**3
  0.000000E+00
X**7 * Y**2
  0.000000E+00


Y**4
  3.771516E−07
X**6 * Y**3
−1.331110E−12


X**5
  0.000000E+00
X**5 * Y**4
  0.000000E+00


X**4 * Y
  5.359865E-08
X**4 * Y**5
−9.781602E−14


X**3 * Y**2
  0.000000E+00
X**3 * Y**6
  0.000000E+00


X**2 * Y**3
−1.965407E−07
X**2 * Y**7
  4.515428E−13


X * Y**4
  0.000000E+00
X * Y**8
  0.000000E+00


Y**5
−7.301859E−09
Y**9
−5.050786E−14


X**6
−6.841269E−09
X**10
−1.058279E−14


X**5 * Y
  0.000000E+00
X**9 * Y
  0.000000E+00


X**4 * Y**2
−2.507411E−09
X**8 * Y**2
−2.975833E−14


X**3 * Y**3
  0.000000E+00
X**7 * Y**3
  0.000000E+00


X**2 * Y**4
  4.627014E−10
X**6 * Y**4
  6.309574E−14


X * Y**5
  0.000000E+00
X**5 * Y**5
  0.000000E+00


Y**6
−4.841692E−10
X**4 * Y**6
  1.214005E−15


X**7
  0.000000E+00
X**3 * Y**7
  0.000000E+00


X**6 * Y
−3.343485E−10
X**2 * Y**8
  1.180350E−14


X**5 * Y**2
  0.000000E+00
X * Y**9
  0.000000E+00


X**4 * Y**3
  7.999315E−10
Y**10
−5.938353E−16


X**3 * Y**4
  0.000000E+00
N-Radius
  1.000000E+00
















TABLE 17







Decenter of Surface #5 of Table 15


relative to Surface #1 of Table 15.









Y DECENTER
Z DECENTER
ALPHA TILT





4.618E+00
4.853E+01
7.007E+00









Prototype of System of FIG. 3B

A prototype of the multi-focal-plane display system 200 of FIG. 3B was built with off-the-shelf lenses and customized optics, 3D views of which are provided in FIGS. 6A, 6B. The system 200 was folded to avoid conflicting with the viewer's head. Custom electronics were also developed to control and synchronize the display images on the DMD 60 (LUXBEAM® 4500, VISITECH, Drammen, Norway.), the illumination of the LED (not shown), and focal-plane switching of the deformable mirror 80 (OKO® Technologies MMDM10-1-focus, Flexible Optical B.V., Rijswijk, Netherlands).
A continuous 3D scene was rendered which was composed of a slanted planar object and a green floor grid, both extending from 0 to 2.5 diopters. The scene was decomposed onto 6 focal planes, placed at 3 diopter, 2.4 diopter, 1.8 diopter, 1.2 diopter, 0.6 diopter and 0 diopter, based on the targets' depth values, and a depth-fusing technique was used to blend the 6 focal planes into a smooth continuum. The whole 3D scene was refreshed at about 60 Hz; thus, flickering was not visible. FIG. 7A shows the actual 6-focal-plane scene as seen through the system; the image was sharp and had very low distortion. Without special algorithms, the pixels on different focal planes overlap and fuse smoothly due to the constant field of view design. In addition, a camera lens with shallow depth of field was used and manually focused at different parts of the scene. In FIG. 7B, the resolution target was displayed on the back wall, and the camera was focused at about 2 m. The near end of the floor grid was out of focus and the back grids as well as the logos were in sharp focus. In FIG. 7C, the resolution target was displayed on the front focal plane, the camera was focused at 30 cm, and now the near scene was in focus and the content on the back was blurred. Thus, the prototype was demonstrated to be capable of rendering 6 or more focal planes of high quality, high resolution color images at a flickering-free speed. It also had very good optical see-through performance for augmented reality applications, and has the potentially to provide higher depth perception accuracy, higher stereoacuity, and lower user fatigue.
Alternative Exemplary Tunable Lens
In another of its aspects, the present invention provides an exemplary multi-focal-plane display system 300 combining high-speed display technologies, such as Liquid Crystal on Silicon (LCOS) and Ferroelectric Liquid Crystal On Silicon (FLCoS) and a high-speed active refractive optical element, such as an electrical tunable lens 380. The Specific design is based on a 0.8′′ WXGA LCOS/FLCOS display 360 and a 10 mm aperture electrical tunable lens 380 (Optotune EL-10-30, Optotune AG, Dietikon, Switzerland.)). The tunable lens 380 changes shape when electrical current flows through the lens 380 to produce a change in optical power. The Optotune lens 380 has a response time of about 2.5 ms and therefore potentially can be used in multi-focal-plane displays.







TABLE 18





Design specification for tunable lens system.
















Microdisplay
0.8” LCOS/FLCOS WXGA, 14, μm pixel


Tunable Lens
10 mm aperture, 12 diopter, focus range


Virtual Display Field of view
50° (43.6° H x 26.4° V)


Pupil size
10 mm


Eye Clearance
20 mm (accommodates low-profile glasses)


Image Quality (DMD space)
MTF > 0.2 at 36 lp/mm (5 mm pupil)


Display Distortion
< 2.0 %


Virtual Image Distance
33 cm~Infinity


f-number
2.2









The final layout of the design is shown in FIGS. 10A-11. A relay lens group (lenses 302, 304, 306, 380, 308, 310) relays the image to a spherical mirror 318, which acts as an eyepiece and forms a virtual image for a user. Optionally, the mirror 318 may be aspherical. A beamsplitter 316 is used to enable see-through capability. The tunable lens 380 may provide the system stop and the system may be telecentric to the microdisplay 360 due to the requirements of LCOS/FLCoS. Enough space is also given for an illumination beamsplitter 317, FIG. 11. The prescription of the system 300 is provided in Table 19-Table 26. (In Table 19, surfaces #9-12 model the Optotune electric tunable lens 380.) The performance of the system is illustrated in FIGS. 12A, 12B.







TABLE 19







Tunable lens system prescription.













Ele-








ment








num-








ber
Sur-







used in
face
Surface
Y 
Thick-

Refract


figures
No.
Type
Radius
ness
Material
Mode






 1 
Sphere
Infinity
  44.000

Refract



(Stop)








 2
Sphere
Infinity
−24.000

Reflect


318
 3
Sphere
68.000
  34.000

Reflect


316
 4
Sphere
Infinity
  17.371

Refract


310
 5
Asphere
−23.777
   6.000
PMMA
Refract



 6
Asphere
363.193
   0.100

Refract


308
 7
Sphere
39.587
   6.000
NSF11
Refract



 8
Sphere
−119.109
   4.385

Refract


380
 9
Sphere
Infinity
   0.500
BK7
Refract


380
10
Sphere
Infinity
   4.377

Refract


380
11
Sphere
30.270
   2.023
′OL1024′
Refract


380
12
Sphere
Infinity
   0.500
BK7
Refract



13
Sphere
Infinity
   3.724

Refract


306
14
Asphere
−24.004
   5.999
Polystyrene
Refract



15
Asphere
27.079
   0.251

Refract


304
16
Sphere
38.710
   5.944
Zeonex
Refract







ZE48R




17
Sphere
−21.557
   5.631

Refract


302
18
Asphere
33.959
   9.698
Zeonex
Refract







ZE48R




19
Asphere
−21.555
  29.000

Refract
















TABLE 20





Surface Prescription for Surface #5 of Table 19.



















Y Radius

−23.777



Conic Constant
(K)
2.040996E+00



 4th Order Coefficient
(A)
1.385342E−04



 6th Order Coefficient
(B)
−1.022594E−06



 8th Order Coefficient
(C)
8.784855E−09



10th Order Coefficient
(D)
−2.891372E−11

















TABLE 21





Surface Prescription for Surface #6 of Table 19.



















Y Radius

363.193



Conic Constant
(K)
−1.060606E+01



 4th Order Coefficient
(A)
6.247531E−05



 6th Order Coefficient
(B)
−8.622953E−07



 8th Order Coefficient
(C)
9.037984E−09



10th Order Coefficient
(D)
−4.513968E-11

















TABLE 22





Surface Prescription for Surface #14 of Table 19.



















Y Radius

−24.004



Conic Constant
(K)
2.609562E+00



 4th Order Coefficient
(A)
−1.053175E−04



 6th Order Coefficient
(B)
3.126004E−07



 8th Order Coefficient
(C)
−2.716200E−08



10th Order Coefficient
(D)
2.112687E−10

















TABLE 23





Surface Prescription for Surface #15 of Table 19.



















Y Radius

27.079



Conic Constant
(K)
−6.178694E+00



 4th Order Coefficient
(A)
−1.075797E−05



 6th Order Coefficient
(B)
−1.383769E−07



 8th Order Coefficient
(C)
4.641779E−10



10th Order Coefficient
(D)
9.831856E−13

















TABLE 24





Surface Prescription for Surface #16 of Table 19.


















Construction (nm)
589



Wavelength




R**2 (HCO C1)
−1.543448E−03



R**4 (HCO C2)
 7.864956E−06



R**6 (HCO C3)
−1.080042E−07



R**8 (HCO C4)
 1.272753E−09



R**10 (HCO C5)
−5.114979E−12

















TABLE 25





Surface Prescription for Surface #18 of Table 19.



















Y Radius

33.959



Conic Constant
(K)
2.310849E+00



4th Order Coefficient
(A)
4.222932E−06



6th Order Coefficient
(B)
−2.501786E−08



8th Order Coefficient
(C)
3.154900E−11



10th Order Coefficient
(D)
2.517705E−13

















TABLE 26





Surface Prescription for Surface #19 of Table 19.



















Y Radius

−21.555



Conic Constant
(K)
−1.347355E+00



4th Order Coefficient
(A)
1.944341E−05



6th Order Coefficient
(B)
3.600425E−08



8th Order Coefficient
(C)
−1.998220E−11



10th Order Coefficient
(D)
6.798072E−13










Overall Design Considerations

In another of its aspects the present invention relates to new criteria for determining depth-fused display (DFD) system design parameters. The optical quality of a fused pixel in DFD displays is quantified by the point spread function (PSF) of its retinal image, or, equivalently, by the modulation transfer function (MTF) which is characterized by the ratio of the contrast modulation of the retinal image to that of a sinusoidal object on the 3D display. For instance, when the eye is accommodated at a rendered depth, z, the PSF of a fused pixel, PSF12, by two pixels on a pair of adjacent focal planes located at z1 and z2, respectively, may be described as the weighted sum of the PSFs from the front and the back pixels as:




  
    
      
        
          
            
              PSF
              12
            
            ⁡
            
              (
              z
              )
            
          
          =
          
            
              
                
                  w
                  1
                
                ⁡
                
                  (
                  z
                  )
                
              
              ⁢
              
                
              
              ⁢
              
                
                  
                    PSF
                    1
                  
                  ⁡
                  
                    (
                    
                      z
                      ,
                      
                        z
                        1
                      
                    
                    )
                  
                
                
                  
                    
                      ∫
                      ∫
                    
                    
                      x
                      ,
                      y
                    
                  
                  ⁢
                  
                    
                      PSF
                      1
                    
                    ⁡
                    
                      (
                      
                        z
                        ,
                        
                          z
                          1
                        
                      
                      )
                    
                  
                  ⁢
                  d
                  ⁢
                  
                    
                  
                  ⁢
                  x
                  ⁢
                  
                    
                  
                  ⁢
                  d
                  ⁢
                  
                    
                  
                  ⁢
                  y
                
              
            
            +
            
              
                
                  w
                  2
                
                ⁡
                
                  (
                  z
                  )
                
              
              ⁢
              
                
                  
                    PSF
                    2
                  
                  ⁡
                  
                    (
                    
                      z
                      ,
                      
                        z
                        2
                      
                    
                    )
                  
                
                
                  
                    
                      ∫
                      ∫
                    
                    
                      x
                      ,
                      y
                    
                  
                  ⁢
                  
                    
                      PSF
                      2
                    
                    ⁡
                    
                      (
                      
                        z
                        ,
                        
                          z
                          2
                        
                      
                      )
                    
                  
                  ⁢
                  d
                  ⁢
                  
                    
                  
                  ⁢
                  x
                  ⁢
                  
                    
                  
                  ⁢
                  d
                  ⁢
                  
                    
                  
                  ⁢
                  y
                
              
            
          
        
        ,
      
    
    
      
        (
        1
        )
      
    
  




where PSF1(z, z1) and PSF2(z, z2) are the point spread functions of the front and back pixels when the eye is accommodated at distance z. The PSFs in Eq. (1) are normalized so that front and back pixels have the same luminance before calculating the weighted sum. w1 and w2 are the depth-weighted fusing functions modulating the luminance of the front and back pixels and typically w1(z)+w2(z)=1 is enforced so that the total luminance of the fused image stays the same when the simulated depth changes. The MTF of the display can then be calculated via Fourier Transform of PSF12(z).

An example of the MTF plots of simulated retinal images of a dual-focal-plane DFD display is shown in FIG. 8A. In the simulation, the two focal planes were placed at 1.2 diopters and 1.8 diopters, respectively, and the luminance ratio between the two focal planes was 1:1, indicating that the fused pixel was being simulated at the dioptric midpoint of the front and back focal planes, i.e., 1.5 diopters. To concentrate on the effects of depth fusion, an eye model was selected with a 3 mm pupil, with all residual aberrations removed. FIG. 8A shows how the MTF of the retinal image changes as the eye accommodates at various positions between the two focal planes. FIG. 8B shows the contrast gradient as a function of eye accommodation distance for different spatial frequencies, and the peak contrast for each frequency was marked by a black square marker. A transition frequency of around 17 cycles/degree (cpd) is observed from both plots. Below that transition frequency, the MTF of the retinal image is maximized at the dioptric midpoint of 1.5 diopters, which is the simulated depth by the 1:1 luminance ratio in the dual-focal plane system. Furthermore, as the eye approaches the simulated depth from either the far or near focal planes, the MTF values increase smoothly, providing the appropriate contrast gradient required for driving the eye accommodation. For frequencies higher than 17 cpd, however, the contrast of the fused pixel is always highest when the eye is accommodated at or near the physical focal planes, meaning that the contrast gradient has the tendency to drive the accommodation away from the simulated pixel depth, therefore creating a conflict accommodation cue.
FIGS. 9A, 9B show how the transition frequency varies as a function of focal plane separation and as a function of pupil size. FIG. 9A assumes a 3 mm eye pupil, and FIG. 9B assumes a constant focal plane separation of 0.6 diopters. The results suggest that the smaller the focal plane separation and the smaller the designed eye pupil size, the higher in frequency the transition point is. Therefore a critical criterion for designing a DFD display is that the focal plane separation and the display's working pupil size should be determined such that the contrast gradient reverse point is higher than the system's cut-off frequency to avoid presenting a conflicting accommodation cue to the viewer. For instance, a 0.6-diopter separation between adjacent focal planes can be considered adequate for a DFD display affording an angular resolution of 1.8 arc minutes per pixel (approximately a spatial frequency of 17 cpd) and luminance greater than 10 cd/m2. The stimulation of 10 cd/m2 display luminance leads to approximately a 3 mm eye pupil diameter. A 0.45-diopter spacing or smaller would be desired for displays affording an angular resolution of 1 arc minute per pixel (i.e., 30 cpd). The smaller the angular resolution per pixel or the lower the image brightness, the smaller the required focal-plane separation would be.
These and other advantages of the present invention will be apparent to those skilled in the art from the foregoing specification. Accordingly, it will be recognized by those skilled in the art that changes or modifications may be made to the above-described embodiments without departing from the broad inventive concepts of the invention. It should therefore be understood that this invention is not limited to the particular embodiments described herein, but is intended to include all changes and modifications that are within the scope and spirit of the invention as set forth in the claims.

## Claims

1. A virtual display system with addressable focus cues, comprising:
a microdisplay for providing a virtual image for display to a user;
a reflective active optical element configured to provide a variable optical power;
a double-telecentric relay lens, with focal length f1, disposed along an optical path between the microdisplay and active optical element;
a beamsplitter disposed along the optical path between the microdisplay and the active optical element at an orientation to receive optical radiation from the active optical element; and
a see-through eyepiece, with focal length feye, comprising a selected surface configured to receive optical radiation from the beamsplitter and reflect the received radiation to an exit pupil of the system to provide a virtual display path which relays a stop of the virtual display system defined by the reflective active optical element therewith to form the exit pupil, and wherein the selected surface is also configured to receive optical radiation from a source other than the microdisplay and to transmit such optical radiation to the exit pupil to provide a see-through optical path,
wherein the ratio of the size of the exit pupil, Dxp to the size of the reflective active optical element, DDMMD, is





  
    D
    XP
  
  =
  
    
      
        D
        DMMD
      
      
        
          f
          1
        
        /
        
          f
          eye
        
      
    
    .

2. The display system of claim 1, wherein the eyepiece comprises a freeform prism shape.

3. The display system of claim 1, wherein the eyepiece comprises a first surface configured to receive and refract optical radiation from the beamsplitter and comprises a second surface configured to receive the refracted optical radiation from the first surface, the second surface configured to reflect the optical radiation to the selected surface of the eyepiece.

4. The display system of claim 3, wherein the second surface is configured to total internally reflect the optical radiation.

5. The display system of claim 1, wherein one or more of the surfaces of the eyepiece comprise a rotationally asymmetric surface.

6. The display system of claim 1, comprising an eyepiece compensator disposed along the see-through path adjacent the selected surface of the eyepiece.

7. The display system of claim 1, comprising a field lens disposed adjacent the microdisplay configured to provide magnification of the display.

8. The display system of claim 7, wherein the field lens comprises an aspheric surface and a diffractive optical feature.

9. The display system of claim 1, wherein the relay lens and active optical element are configured to provide a folded, doubly telecentric system.