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.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.
Psychological Depth Cues(Cont’d)• Occlusion• Shading Figures taken from Ref.
Psychological Depth Cues(Cont’d)• Texture Gradient Figure taken from Ref.
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.
Physiological Depth Cues (Cont’d)• Binocular Disparity/Stereospsis Dαθ 2 ∆D ≅ PO Figure taken from Ref.• Motion Parallax: different angular velocity of object at different depths the observer
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 x Figures taken from Ref.[1,2] θ= f
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
Three mechanisms of eyes in responding the incoming wavefront [12,26]1. Modifies and the focus the wavefront to retina→Accommodation2. Sample the wavefront from two slightly different positions andinterpreted as different position in two visual field→Convergence and Stereopsis3. Moving observer samples the wavefront from differentpositions and object’s position in visual field changes as theresult of observer’s motion→Motion ParallaxTo present all 4 physiological depth cues Provide or reconstruct the original object’s wavefront
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 waveformHolography is basically a technique to reconstruct the original wavefront through phase recording
Examples of Hologram• Transmission Hologram• Reflection hologram Figures taken from Refs.[6,8]
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]
Holographic Information Reduction Method• Rainbow Hologramhorizontal slit is to remove vertical parallax→reduce information content Figures taken from Ref.
Holographic Information Reduction Method (Cont’d)• Multiplex Hologram (Holographic Stereogram) – Proposed by De Bitteto Figures taken from Ref.
Holographic Stereogram (Cont’d)• Cross Hologram Figures taken from Ref.[3,4,6]→both hologram exhibit no vertical parallax
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. U p = e − j 2παx
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
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
Computer Generated Hologram (Cont’d) Figures taken from Ref.
Electronic Holography• Using dynamic electronically-controlled optical modulator1. 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 Figures taken from Ref.
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
Electronic Holography (Cont’d)Application: Haptic (Force Feedback) hologram Figures taken from http://www.media.mit.edu/spi/HHlathe.htm
Electronic Holography (Cont’d)– 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 athttp://www.academia.edu/1158381/Brief_Survey_on_Three-Dimensional_Displays_2001_
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