Brief survey on Three-Dimensional Displays

Brief survey on Three-Dimensional Displays: from Our Eyes to Electronic Hologram*

Taufiq Widjanarko

*Presented at ECPE 4144 Optical Information Processing, Project Term Paper, Virginia Tech, Fall 2001. Last modified 19 March 2013

Outline • Depth Cues • Examples of Three-Dimensional Displays • Wavefront Reconstruction • Examples of Hologram

– Off-axis Hologram – Reflection Hologram

• Information Content in Hologram • Method to reduce profuse information content

– Rainbow Hologram – Multiplex Hologram

• Computer Generated Hologram • Electronic Hologram

– Optical Scanning Holography – Holographic Video

Depth Cues • Visual depth sense is often taken for granted until we

encounter the problem that can be solved if depth cues are present

• Depth Cues can be grouped into two major categories [1]:

1.Psychological (Pictorial) Depth Cues: depth cues influenced by the mental and prior knowledge of the observer

2.Physiological Depth Cues: depth cues related to the

physiology of our eyes

Psychological Depth Cues

• Retinal Image Size: different image size appearance on retina

• Aerial Perspective • Linear Perspective

Figure taken from Ref.[1]

Psychological Depth Cues(Cont’d)

• Occlusion

• Shading

Figures taken from Ref.[1]

Psychological Depth Cues(Cont’d)

• Texture Gradient


Physiological Depth Cues • Accommodation:

Change of eye muscular tension to adjust the focal length

• Convergence: eyes ability to fixate a point on the object

P0 = two pupil separation a = object distance

dda

Pa

Oα= 2


Physiological Depth Cues (Cont’d) • Binocular Disparity/Stereospsis

• Motion Parallax: different angular velocity of object at different depths the observer

∆D DPO

≅ αθ2


Example of Three-Dimensional Displays • Integral Photography: using lenslet array to sample

the object

Figures taken from Refs.[1,8]

Example of Three-Dimensional Displays(Cont’d)

• Lenticular Sheet

θ =xf

Figures taken from Ref.[1,2]

Example of Three-Dimensional Displays(Cont’d)

• Parallax Barrier

viewing distance = .25 m, p < .08 mm → for slit width 1/10 of pitch = 8 µm or only 15 x λvisible


Three mechanisms of eyes in responding the incoming wavefront [12,26]

1. Modifies and the focus the wavefront to retina →Accommodation 2. Sample the wavefront from two slightly different positions and

interpreted as different position in two visual field →Convergence and Stereopsis 3. Moving observer samples the wavefront from different

positions and object’s position in visual field changes as the result of observer’s motion

→Motion Parallax To present all 4 physiological depth cues Provide or reconstruct the original object’s wavefront

Wavefront Reconstruction

-10 -8 -6 -4 -2 0 2 4 6 8 10

-0.2

0

0.2

0.4

0.6

0.8

1

-10 -8 -6 -4 -2 0 2 4 6 8 10

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-10 -8 -6 -4 -2 0 2 4 6 8 10

0

0.2

0.4

0.6

0.8

1

1.2

-10 -8 -6 -4 -2 0 2 4 6 8 10-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6 inten. of raised ampl.orig. wavefront

Original waveform Intensity reconstruction (waveform shape disappears)

Original waveform + reference wave (flatline below the waveform) Intensity reconstruction of Original waveform + reference wave

Intensity reconstruction of Original waveform + reference wave maintains the original shape of the waveform

Holography is basically a technique to reconstruct the original wavefront through phase recording

Examples of Hologram

• Transmission Hologram

• Reflection hologram


Information Content in a Hologram [23,28]

• Grating equation – fh highest frequency comp. of object

• Required sampling freq

– fs = sampling frequency

• N= Number of sampling (in horizontal direction) – d = width of hologram in horizontal direction

• Nt= Total number of sample in both horizontal and vertical direction

– w=width of hologram in vertical direction

• 100 x 100 mm2, 30° view angle →2.5x1010 samples/frame • Real time hologram of 60 frames per second requires →1.2x1012 bit/sec (fastest conventional display rate 2 Gbits/s) [23,28]

λ θfh = sin

f fs h= =2 2 sinθλ

N df ds= =

2 sinθλ

N dwt =

42

sinθλ

Holographic Information Reduction Method

• Rainbow Hologram

horizontal slit is to remove vertical parallax →reduce information content


Holographic Information Reduction Method (Cont’d)

• Multiplex Hologram (Holographic Stereogram) – Proposed by De Bitteto


Holographic Stereogram (Cont’d)

• Cross Hologram

→both hologram exhibit no vertical parallax Figures taken from Ref.[3,4,6]

Computer Generated Hologram • Binary Detour Phase Method: to create Fourier

Hologram – Final image must be in the form of

– Cell aperture transmittance

– Inclined plane wave illumination

( )U u v a e ef pq

j

q

N jf

up x vq y

p

Npq

YX

( , ) ==

− +

=

−

∑∑ φπ

λ

0

1 2

0

1 ∆ ∆

t x y rect x xw

y ywA

X Y

( , ) =−

−

0 0

U epj x= − 2πα


Computer Generated Hologram (Cont’d)

• After illumination

• At Fourier Plane

• After some assumptions, simplifications and

setting the offset

U x y e rect x xw

y ywt

j x

x y

( , ) =−

−

− 2 0 0πα

[ ]U u v w w

fc w u f

fc w v

fef

X Y X Yj

fu f x vy

( , ) sin ( ) sin( )

=+

+ +

λλ α

λ λ

πλ

λα20 0

( ) ( )x p x & y q y pq pq0 0= =∆ ∆

( )U u v w w e ef X pq Y pq

j p

q

N jf

up x vq y

p

N YX

( , ) ( ) ( )==

− +

=

−

∑∑ 2

0

1 2

0

1π

πλ

∆ ∆


• Shifting the aperture center

• With several assumption, the above expression

can be simplified as

• Compared with the desired form

• Phase and amplitude relation to the cell aperture

( ) ( )x p x xpq pq0 = ∆ + δ


jx

x

q

N jf

up x u x vq y

p

N pqY pqX

( , ) ( ) ( )( ) ( )

==

− + +

=

−

∑∑2

0

1 2

0

1 πδ π

λδ

∆∆ ∆

( )U u v a e ef pq

j

q

N jf

up x vq y

p

Npq

YX

( , ) ==

− +

=

−

∑∑ φπ

λ

0

1 2

0

1 ∆ ∆


jx

x

q

N jf

up x vq y

p

N pqYX

( , ) ( ) ( )( )

==

− +

=

−

∑∑2

0

1 2

0

1 πδ π

λ∆∆ ∆

φπ δ

pqpq

Y pq pq

xx

w a= − ∝2 ( )

( )∆

&



Electronic Holography

• Using dynamic electronically-controlled optical modulator 1. Optical Scanning Holography: scanning TDFZP to obtain the

scanned holographic pattern of the object

Application in fluorescence microscopy: for image region 2 x 2 mm2, the system can reveal lateral and axial resolution of 7.7 and 200 µm, respectively

Figures taken from Ref.[5,16]

Electronic Holography (Cont’d)

– Holographic video (Media Lab MIT) • inspired by binary detour phase, holographic

stereogram and rainbow hologram • using AOM to diffract light into desired point in

volume space • fringe calculation is similar to computer

graphics


Electronic Holography (Cont’d) • A single hologram lines is decomposed into pre-

computed ‘basis fringe’ → orthogonal basis function decomposition

• First generation: full color 25x25x25 mm3, 15°viewing angle, 20 frames/second

• Second generation: 80x140x150 mm3, 2.5 frames/second

Figure taken from http://www.media.mit.edu/spi/HVmark2.htm


Application: Haptic (Force Feedback) hologram

Figures taken from http://www.media.mit.edu/spi/HHlathe.htm


– Potential application: telesurgery,

telemanufacturing, etc

Figure taken from http://www.media.mit.edu/spi/HHlathe.htm

Conclusion • Depth Cues:

– Psychological or Pictorial cues (based on mental and prior knowledge of observer): retinal image size, aerial and linear perspective, occlusion, shading and texture gradient

– Physiological depth cues: accommodation, binocular disparity, convergence and motion parallax

– 3-D displays prior to hologram can only provide the last three physiological cues

– Hologram can naturally provide all physiological & psychological depth cues due to its nature to reconstruct object wavefront

• Off axis hologram can solve initial Gabor’s hologram problem • Information content in a hologram is tremendously profuse→ 100 x 100

mm2, 30° view angle requires 2.5x1010 samples/frame • Some proposed method to reduce information content are rainbow

hologram and multiplex hologram (holographic stereogram) →sacrificing vertical parallax to reduce information content

Conclusion (Cont’d) • The earliest Computer Generated Hologram method: the Binary

Detour Phase Hologram uses aperture within a cell to encode the amplitude (from aperture area) and phase (from center of aperture shift). Plotted pattern quality is determined by resolution of the writing device

• Recent Electronic Holograms use dynamic optical modulator, such as AOM, LCD as a light diffracting component.AOM are used in optical scanning holography and holographic video

Full paper available at http://www.academia.edu/1158381/Brief_Survey_on_Three-Dimensional_Displays_2001_

http://www.academia.edu/1158381/Brief_Survey_on_Three-Dimensional_Displays_2001_




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Brief survey on Three-Dimensional Displays