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Three-dimensional directional display and pickup

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					Three-dimensional directional display and pickup




                    Joonku Hahn

                    NCRCAPAS
           School of Electrical Engineering
              Seoul National University
CONTENTS



   I. Introduction

   II. Three-dimensional directional display
    2.1 Uniform angular resolution integral imaging with boundary folding mirrors
    2.2 Uniformly cross-sectional display using multiple shear projection
    2.3 Hologram-like projection display

   III. Pickup suitable for three-dimensional directional display
    3.1 Direct pickup of elemental images
    3.2 Undistorted pickup method of both virtual and real objects for integral imaging
    3.3 Pixel matched pickup for hologram-like display

   IV. Conclusion
I. Introduction
 Classification of three-dimensional display


                  Directional display
                  : Directional emission



3D display




                  Volumetric display
                  : Nondirectional scattering
                    or emission



                                            1/52
I. Introduction
 Properties of three-dimensional display
 1. Volume occupation
     Some directional displays + All volumetric displays




 2. One focused image plane
     Some directional displays with incoherent light source




 3. Multi focused image plane
     Some directional displays with coherent light source




                                           2/52
I. Introduction
 Motivation of three-dimensional directional display




                  When we want to watch different channels at the same time,
                  What is the best solution?



                                              3/52
I. Introduction
 Motivation of three-dimensional directional display


                       DRAMA                  SPORTS




                                                                VIDEO
                                 GAME




                  Multi-view display can give us the solution
                  that whole family exist at the same place.

                                               4/52
I. Introduction
 Motivation of pixel matched pickup for three-dimensional display




            Sometimes, we meet an mysterious scene that is unintelligible.
            And someone wants to record this scene.


                                             5/52
I. Introduction
 Motivation of pixel matched pickup for three-dimensional display

                  Let’s assume that there exists a Dracula really,
                  And intermediate view should be generated form two cameras.




                    1st camera                                     2nd camera


                                       Dracula Human




                                             Mirror
  Then, what is a correct solution?
  Since a Dracula has no reflection image, the existence of a mirror results in the contradiction.


                                               6/52
I. Introduction
 Motivation of pixel matched pickup for three-dimensional display

    Similar problems occur on the surface emitting different colors according to directions.
    As you know, a three-dimensional directional display also has these properties.




                  Pickup                                    Display

     Therefore, for correct and efficient pickup for a directional display,
     a pickup method with pixel matching between pickup and display is necessary.

                                              7/52
I. Introduction
 Motivation of pixel matched pickup for three-dimensional display




                               1:1 pixel matching




                  Multi pickup                       Multi projection

                  Pixel matched pickup is not only efficient but also correct.


                                             8/52
               II. Three-dimensional directional display




2.1 Uniform angular resolution integral imaging with boundary folding mirrors
2.2 Uniformly cross-sectional display using multiple shear projection
2.3 Hologram-like projection display




                                       9/52
II. Three-dimensional directional display
 2.1 Uniform angular resolution integral imaging with boundary folding mirrors

Conventional integral imaging display




                              Unit horizontal length
                              of spatial resolution




                                                       of spatial resolution
                                                       Unit vertical length
  Directions of
  perspectives




      Horizontal
      viewing angle
                                               Unit horizontal angle
           Vertical                            of angular resolution
           viewing angle

      Unit vertical angle                                 Central depth plane
      of angular resolution


           Spatial and angular resolutions                                              View volume and directions of perspectives


   J. Hahn, Y. Kim, and B. Lee, Appl. Opt. 48, pp. 504-511 (2009)


                                                                                10/52
II. Three-dimensional directional display
 2.1 Uniform angular resolution integral imaging with boundary folding mirrors

Proposed integral imaging display with boundary folding mirrors



                                                                   Lens array
                                                                   with focal
                                                                   length f




                  Elemental
                  images


                Elemental
                image plane d
                              gap
                                                     Boundary folding
                    Lens array    d mirror           mirrors
                    plane
                           Central depth
                           plane




                                             11/52
II. Three-dimensional directional display
 2.1 Uniform angular resolution integral imaging with boundary folding mirrors

Conventional integral imaging display




            Imbricate view volumes                  Directions of perspectives on CDP

                                            12/52
II. Three-dimensional directional display
 2.1 Uniform angular resolution integral imaging with boundary folding mirrors

Proposed integral imaging display




          Folded imbricate view volumes             Directions of perspectives on CDP

                                            13/52
II. Three-dimensional directional display
 2.1 Uniform angular resolution integral imaging with boundary folding mirrors

Conventional integral imaging display
                 Angular resolution                                  Distribution of
                                                                      perspectives




        Lower boundary       Upper boundary
                                                           Lower boundary        Upper boundary
        of InIm display      of InIm display
                                                           of InIm display       of InIm display

Proposed integral imaging display
                                                                     Distribution of
                  Angular resolution                                  perspectives       Boundary
                                        Boundary                                         folded
                                        folded




                                                           Lower boundary        Upper boundary
         Lower boundary       Upper boundary               of InIm display       of InIm display
         of InIm display      of InIm display



                                                   14/52
II. Three-dimensional directional display
 2.1 Uniform angular resolution integral imaging with boundary folding mirrors

Movement of field of view by boundary folding mirrors




              Boundaries
              of InIm display                              Field of view


                                                                     Total
                                                                     viewing
                                                                     angle Ω



                                                                 Viewing zone
                   Elemental
                   images                 Lens     Central
                                          array    depth plane


                          Field of view in the conventional InIm display


                                              15/52
II. Three-dimensional directional display
 2.1 Uniform angular resolution integral imaging with boundary folding mirrors

Movement of field of view by boundary folding mirrors

                                                       Boundary
          Mirror folded             w folded           folding
          region                                       mirrors
          Boundaries                  w
                                                                  Field of view
          of InIm display

                                                                             Total
                                                                             viewing
                                                                             angle Ω


             Elemental
                                                                         Viewing zone
             images
          Mirror folded
          region                       Lens    Central
                                       array   depth plane
                            d gap
                            Field of view in the proposed InIm display


                                               16/52
II. Three-dimensional directional display
 2.1 Uniform angular resolution integral imaging with boundary folding mirrors

Reorganization for generating set of elemental images



                                                                    Elemental images
                                                                    in mirror folded regions




           Reorganized relation                     Reorganized set of elemental images




                                            17/52
II. Three-dimensional directional display
 2.1 Uniform angular resolution integral imaging with boundary folding mirrors

Experimental results




                                     Full HD Projector
                               Magnification lens




       Projection screen




             Boundary
             folding mirrors               Lens array




                Experimental setup                               Perspective views




                                                         18/52
II. Three-dimensional directional display
 2.2 Uniformly cross-sectional display using multiple shear projection

3D display with both global and local stops based on integral imaging

                    EI plane        Local stops with                Global stop with             Display
                                    effective focal length f1       effective focal length f 2   image plane




                                               Local optical axis

               ∆                                        ∆′
                                                                                Global optical axis

                           CS EI               CS1                            CS 2                         CS display

              wEI              Slocal



                               d1                       d2                              d3
                                          +0

                      X                 A ( X − ∆′ ) + ∆′                                        B ( A ( X − ∆′ ) + ∆′ )




                                                                19/52
II. Three-dimensional directional display
  2.2 Uniformly cross-sectional display using multiple shear projection

Step.1 The condition that one view is generated by one elemental image
       B22 = 0

         ⎛ 1 d3 ⎞ ⎛ 1       0 ⎞ ⎛ 1 d2 ⎞
       B=⎜       ⎟⎜           ⎟⎜       ⎟
         ⎝ 0 1 ⎠ ⎝ −1 f 2 1 ⎠ ⎝ 0 1 ⎠
         ⎛1 − d3 f 2 d 2 + d3 − d 2 d3 f 2 ⎞
        =⎜                                 ⎟
         ⎝ −1 f 2         1 − d2 f2        ⎠

        d2 = f2
Step.2 The condition that light emissions from elemental image are focused on image plane

       ( ΒΑ )12 = 0
             ⎛1 − d3 f 2 f 2 ⎞ ⎛ 1      0 ⎞ ⎛ 1 d1 ⎞
        BA = ⎜                ⎟⎜          ⎟⎜        ⎟
             ⎝ −1 f 2      0 ⎠ ⎝ −1 f1 1 ⎠ ⎝ 0 1 ⎠
             ⎛1 − d3 f 2 − f 2 f1 f 2 + d1 − d1 f 2 f1 − d1d3 f 2 ⎞
           =⎜                                                     ⎟
             ⎝      −1 f 2                     − d1 f 2           ⎠

        d3 = f 2 (1 + f 2 d1 − f 2 f1 )



                                                          20/52
II. Three-dimensional directional display
  2.2 Uniformly cross-sectional display using multiple shear projection

Step.3 The condition that the cross-sectional size in display maintains uniformly
       d3 = 0

       d1 = f1 f 2   ( f 2 − f1 )


Step.4 The calculation of the amount of shear projections

       ∆ = ( ∆x, α )
                      T




                                ⎛f f −f d                 f 2 ⎞ ⎡⎛ 1       d1 ⎞ ⎛ ∆x − ∆x′ ⎞ ⎛ ∆x′ ⎞ ⎤
       B ⎡ A ( ∆ − ∆′ ) + ∆′⎤ = ⎜ 2 1 2 1
         ⎣                  ⎦                                 ⎟ ⎢⎜               ⎟⎜        ⎟+⎜     ⎟⎥
                                ⎝   −1 f 2                0 ⎠ ⎣⎝ −1 f1 1 − d1 f1 ⎠ ⎝ α     ⎠ ⎝ 0 ⎠⎦
                                     ⎛ f f − f d f2 ⎞ ⎛                    ∆x + α d1               ⎞
                                    =⎜ 2 1 2 1              ⎟⎜                                     ⎟
                                     ⎝     −1 f 2         0 ⎠ ⎝ − ( ∆x − ∆x′ ) f1 + α (1 − d1 f1 ) ⎠
                                     ⎛ ∆x′ f 2 f1 − ∆x f 2 d1 ⎞
                                    =⎜                         ⎟
                                     ⎝ − ( ∆x + α d1 ) f 2 ⎠

       ∆x′ = ( f1 d1 ) ∆x = ⎡( f 2 − f1 ) f 2 ⎤ ∆x
                            ⎣                 ⎦


                                                                    21/52
II. Three-dimensional directional display
 2.2 Uniformly cross-sectional display using multiple shear projection

3D display with both global and local stops with d1 > f1




                                            22/52
II. Three-dimensional directional display
 2.2 Uniformly cross-sectional display using multiple shear projection

3D display with both global and local stops with d1 < f1




                                            23/52
II. Three-dimensional directional display
 2.2 Uniformly cross-sectional display using multiple shear projection

Proposed uniformly cross-sectional display




                                             24/52
II. Three-dimensional directional display
 2.2 Uniformly cross-sectional display using multiple shear projection

Experimental results



                             Optics for multiple
     EI plane                shear projections
                             on local stops




       Lens on global stop



                Experimental setup                         Perspective views



                                                   25/52
II. Three-dimensional directional display
 2.3 Hologram-like projection display (previous research)

Directional emission screen




Field of view and angular resolution




   T. Balogh et al., EUROGRAPHICS 2005.

                                            26/52
II. Three-dimensional directional display
 2.3 Hologram-like projection display

Embodiment of hologram-like display




                                                       Folding mirrors

                                                                   Asymmetric diffusing screen
                                                                   188 × 141mm 2


                                                                             8 LCDs




                                                     Projection lenses
                                                     f = 50.0mm

                                                                                                 LCD:
                                                                                                 Monochromatic XGA
                                                                 Irises                          Pixel Size: 14 µ m

   Samsung SDI project (Mar. 2006 ~ Feb. 2007).

                                                  27/52
II. Three-dimensional directional display
 2.3 Hologram-like projection display

Embodiment of hologram-like display




                                            28/52
II. Three-dimensional directional display
 2.3 Hologram-like projection display

Labview programs for hologram-like display




          Image synthesis program                   Display driving program




                                            29/52
II. Three-dimensional directional display
 2.3 Hologram-like projection display

Experimental results




                                            30/52
    III. Pickup suitable for three-dimensional directional display




3.1 Direct pickup of elemental images
3.2 Undistorted pickup method of both virtual and real objects for integral imaging
3.3 Pixel matched pickup for hologram-like display




                                     31/52
III. Pickup suitable for three-dimensional directional display
 3.1 Direct pickup of elemental images

Inverted perspective projection view volume of integral photography




  Elemental                                                      Directio
  Image                                                                  n   of camer
                                                                                        a view

          Projection                 Rectangular
          Reference                  Frustum
          Point      Far clipping    View volume
                     Plane
                          Clipping                  Near clipping
                          Window                    Plane


                                           32/52
III. Pickup suitable for three-dimensional directional display
 3.1 Direct pickup of elemental images

Inverted perspective projection view volume of hologram-like display




                                                                             Viewing volume
                                                                             from one elemental image
                                                   Source of             Asymmetric diffraction screen
                                                   one elemental image   of hologram-like display




                                           33/52
III. Pickup suitable for three-dimensional directional display
 3.1 Direct pickup of elemental images

Two types of inverted perspective projection view volumes




   Inverted perspective symmetric view volume       Inverted perspective asymmetric view volume




                                            34/52
III. Pickup suitable for three-dimensional directional display
 3.1 Direct pickup of elemental images

Camera with an inverted asymmetric perspective view volume for hologram-like display


                                           Cylindrical lens

                                                      Telecentric lens




                    Inverted perspective
                    view volume
                                                          CCD

    CCD: 4.65µ m pixel size (Sony XCD-SX910)
                                                                           ⎛ 0.00465 ×1280 ⎞
                                                         FOV = −2 × arctan ⎜                 ⎟ = −14.0 ( degree )
    Telecentric lens: X0.16 (Edmund Optics)
    Cylindrical lens: 152mm focal length                                   ⎝  0.16 × 2 × 152 ⎠
    HPO FOV

    J. Hahn, Y. Lim, G. Park, and B. Lee, COOC, 214-215 (2007).


                                                     35/52
III. Pickup suitable for three-dimensional directional display
 3.1 Direct pickup of elemental images

Experimental results




              perspective view volume          telecentric view volume




            Elemental image synthesized        inverted asymmetric
            by conventional method             perspective view volume

                                           36/52
III. Pickup suitable for three-dimensional directional display
 3.2 Undistorted pickup method of both virtual and real objects for integral imaging

Distortion in conventional pickup of both virtual and real objects with a large convex lens




            View volumes of pickup                                View volumes of InIm display




  J. Hahn, Y. Kim, E.-H. Kim, and B. Lee, Opt. Express 16, 13969-13978 (2008).


                                                      37/52
III. Pickup suitable for three-dimensional directional display
 3.2 Undistorted pickup method of both virtual and real objects for integral imaging

Sub-view volume of an individual lens in InIm display




                                           38/52
III. Pickup suitable for three-dimensional directional display
 3.2 Undistorted pickup method of both virtual and real objects for integral imaging

Imbricate view volumes of InIm display




                                           39/52
III. Pickup suitable for three-dimensional directional display
 3.2 Undistorted pickup method of both virtual and real objects for integral imaging

Pickup system with imbricate view volumes




                                           40/52
III. Pickup suitable for three-dimensional directional display
 3.2 Undistorted pickup method of both virtual and real objects for integral imaging

Relationship between demanded elemental images and pickup image




                                           41/52
III. Pickup suitable for three-dimensional directional display
 3.2 Undistorted pickup method of both virtual and real objects for integral imaging

Pickup and reconstructed images




                                                                    Upper view



                                                   Left view                         Right view


                                                                    Lower view
              Raw pickup image




        Set of flipped elemental images                        Reconstructed image

                                           42/52
III. Pickup suitable for three-dimensional directional display
 3.2 Undistorted pickup method of both virtual and real objects for integral imaging

Experimental results


                          4f optics                                                          Virtual object
                                                               Object on                     z = −30mm
             Lens array                                        the critical plane
                                                               z = 0mm

     Telecentric lens
                                                                                                  Object moving
                                                                                                  from virtual to
  CCD                                 Fresnel lenses                                              real field


                                                                                                                    ˆ
                                                                                                                    y
                                                                                    Real object                         ˆ
                                                                                                                        x
                                                                                    z = 30mm                  ˆ
                                                                                                              z


    Photograph of embodied pickup system                                  Configuration of objects
    with imbricate view volumes                                           with different positions




                                                       43/52
III. Pickup suitable for three-dimensional directional display
 3.2 Undistorted pickup method of both virtual and real objects for integral imaging

Conventional pickup with the movable object




              z = −30mm                       z = 0mm                z = 30mm




              Virtual object    Real object       Movable object   Movable object
                                                  at z = −30mm     at z = 30mm



                                              44/52
III. Pickup suitable for three-dimensional directional display
 3.2 Undistorted pickup method of both virtual and real objects for integral imaging

Proposed pickup with the movable object




              z = −30mm                       z = 0mm                z = 30mm




              Virtual object    Real object       Movable object   Movable object
                                                  at z = −30mm     at z = 30mm



                                              45/52
III. Pickup suitable for three-dimensional directional display
 3.2 Undistorted pickup method of both virtual and real objects for integral imaging

Pickup and reconstructed images




                                                   Perspective views of reconstructed images




                                           46/52
III. Pickup suitable for three-dimensional directional display
 3.3 Pixel matched pickup for hologram-like display

Folded imbricate view volumes in hologram-like display




                                                                                  Cylindrical lens

                                                                                            Telecentric lens




                                                                 Inverted perspective
                                                                 view volume
                             Viewing volume                                                    CCD
                             from one elemental image
   Source of             Asymmetric diffraction screen
   one elemental image   of hologram-like display

     View volumes in hologram-like display                   Camera with an inverted perspective view volume




                                                         47/52
III. Pickup suitable for three-dimensional directional display
 3.3 Pixel matched pickup for hologram-like display

Flip effect in 4f system

                                                                    Cameras




                                   4f system


                       Inverted view volumes
        1234                                                     3412
                                               48/52
III. Pickup suitable for three-dimensional directional display
 3.3 Pixel matched pickup for hologram-like display

The problem in folded imbricate view volumes resulting from flip effect

                                                                           Cameras


                                                                  Mirror




                                                                  Mirror




                                           49/52
III. Pickup suitable for three-dimensional directional display
 3.3 Pixel matched pickup for hologram-like display

Correction of flipping effect using Amici-roof prisms




                                         Amici
                                         Roof prism
           width=1             width=3                  width=3   width=1




                                           50/52
III. Pickup suitable for three-dimensional directional display
 3.3 Pixel matched pickup for hologram-like display

Design of pixel matched pickup for hologram-like display




                                           51/52
IV. Conclusion


     Three-dimensional directional display
     - Uniform angular resolution is achieved using boundary folding mirrors
       based on integral imaging, which is regarded as the full-parallax expansion
       of a hologram-like projection display.
     - Uniformly cross-sectional display is realized using multiple shear projection
       with both global and local stops.


     Pickup suitable for three-dimensional directional display
     - For direct pickup of elemental images, camera with an inverted perspective
       view volume is embodied.
     - Undistorted pickup method of both virtual and real objects for integral
       imaging is realized by generating imbricate view volumes in 4f system.
     - Pixel matched pickup for hologram-like display is proposed and under
       manufacture.




                                        52/52

				
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