# 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

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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

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I. Introduction
Motivation of three-dimensional directional display

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

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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.

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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.

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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.

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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.

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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.

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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

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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)

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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

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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

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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

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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

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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

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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

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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

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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

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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 − ∆′ ) + ∆′ )

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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 )

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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
⎣                 ⎦

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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

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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

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

Proposed uniformly cross-sectional display

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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

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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.

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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).

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II. Three-dimensional directional display
2.3 Hologram-like projection display

Embodiment of hologram-like display

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II. Three-dimensional directional display
2.3 Hologram-like projection display

Labview programs for hologram-like display

Image synthesis program                   Display driving program

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II. Three-dimensional directional display
2.3 Hologram-like projection display

Experimental results

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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

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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

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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

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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

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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).

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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

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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).

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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
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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

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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

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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

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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.

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