1. 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
2. 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
3. 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
4. Psychological Depth Cues
• Retinal Image Size:
different image size
appearance on
retina
• Aerial Perspective
• Linear Perspective
Figure taken from Ref.[1]
7. Physiological Depth Cues
• Accommodation:
Change of eye
muscular tension to
adjust the focal length
• Convergence: eyes
ability to fixate a point
on the object
dα PO
= 2
da a
P0 = two pupil separation
a = object distance
Figure taken from Ref.[1]
8. Physiological Depth Cues (Cont’d)
• Binocular Disparity/Stereospsis
Dαθ
2
∆D ≅
PO
Figure taken from Ref.[1]
• Motion Parallax: different angular velocity of
object at different depths the observer
9. Example of Three-Dimensional Displays
• Integral Photography: using lenslet array to sample
the object
Figures taken from Refs.[1,8]
11. Example of Three-Dimensional Displays(Cont’d)
• Parallax Barrier
Figures taken from Refs.[1,2]
viewing distance = .25 m, p < .08 mm → for slit width
1/10 of pitch = 8 µm or only 15 x λvisible
12. 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
13. Wavefront Reconstruction
1
1
0.9
0.8 0.8
0.7
0.6
0.6
0.5
0.4
0.4
0.2 0.3
0.2
0
0.1
-0.2 0
-10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10
Intensity reconstruction (waveform shape disappears)
Original waveform
1.6
inten. of raised ampl.
1.2
orig. wavefront
1.4
1
1.2
0.8 1
0.8
0.6
0.6
0.4 0.4
0.2
0.2
0
0
-0.2
-10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10
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
14. Examples of Hologram
• Transmission Hologram
• Reflection hologram
Figures taken from Refs.[6,8]
15. Information Content in a Hologram [23,28]
• Grating equation λf h = sin θ
– fh highest frequency comp. of object
• Required sampling freq sin θ
fs = 2 fh = 2
– fs = sampling frequency λ
• N= Number of sampling (in horizontal direction) 2d sin θ
N = df s =
– d = width of hologram in horizontal direction λ
• Nt= Total number of sample in both horizontal and vertical direction
– w=width of hologram in vertical direction 4dw sin θ
Nt =
λ2
• 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]
16. Holographic Information Reduction Method
• Rainbow Hologram
horizontal slit is to remove vertical parallax
→reduce information content Figures taken from Ref.[8]
17. Holographic Information Reduction Method (Cont’d)
• Multiplex Hologram (Holographic Stereogram)
– Proposed by De Bitteto
Figures taken from Ref.[8]
19. Computer Generated Hologram
• Binary Detour Phase Method: to create Fourier
Hologram
– Final image must be in the form of
N X −1 N Y −1 2π
( up∆x + vq∆y )
∑ ∑a
j
jφ pq λf
U f ( u, v ) = pq e e
p=0 q =0
– Cell aperture transmittance
x − x0 y − y0
t A ( x , y ) = rect
w X wY
– Inclined plane wave illumination
Figures taken from Ref.[4]
U p = e − j 2παx
20. Computer Generated Hologram (Cont’d)
• After illumination
− j 2 παx x − x0 y − y0
U t ( x, y) = e rect
wx
w
y
• At Fourier Plane
2π
w w w ( u + λfα ) w v j [ ( u + fλα ) x0 + vy0 ]
U f (u, v ) = X Y sin c X sin c Y e λf
λf λf λf
• After some assumptions, simplifications and
setting the offset ( x ) = p∆x & ( y ) = q∆y 0 pq 0 pq
N X −1 N Y −1 2π
( up∆x + vq∆y )
∑ ∑ (w
j
U f ( u, v ) = X ) pq ( wY ) pq e j 2πp e λf
p=0 q =0
21. Computer Generated Hologram (Cont’d)
• Shifting the aperture center ( x ) 0 pq = p∆x + (δx ) pq
( δx ) pq 2π
N X −1 N Y −1
j 2π (
up∆x + u ( δx ) pq + vq∆y )
∑ ∑ ( wX ) pq ( wY ) pq e
j
λf
U f ( u, v ) = ∆x
e
p=0 q =0
• With several assumption, the above expression
can be simplified as δ π
N X −1 N Y −1 ( ) ( x ) pq 2
up∆x + vq∆y
π
U ( u, v ) = ∑ ∑ ( w ) ( w ) e
j2 j
λ ∆x f
f e
X pq Y pq
p=0 q =0
• Compared with the desired form
π
N X −1 N Y −1 2
( ) up∆x + vq∆y
U ( u, v ) = ∑ ∑ a e e
j
φ λ j pq f
f pq
p=0 q =0
• Phase and amplitude relation to the cell aperture
2π (δx ) pq
φ pq = − & ( wY ) pq ∝ a pq
∆x
23. 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]
24. 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
Figures taken from Ref.[29]
25. 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
27. Electronic Holography (Cont’d)
– Potential application: telesurgery,
telemanufacturing, etc
Figure taken from http://www.media.mit.edu/spi/HHlathe.htm
28. 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
29. 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
30. Full paper available at
http://www.academia.edu/1158381/Brief_Survey_on_Three-Dimensional_Displays_2001_
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