Abstract

We describe various techniques to synthesize three types of computer-generated hologram (CGH): the Fresnel–Fourier CGH, the Fresnel CGH, and the image CGH. These holograms are synthesized by fusing multiple perspective views of a computer-generated scene. An initial hologram is generated in the computer as a Fourier hologram. Then it can be converted to either a Fresnel or an image hologram by computing the desired wave propagation and imitating an interference process of optical holography. By illuminating the CGH, a 3D image of the objects is constructed. Computer simulations and experimental results underline the performance of the suggested techniques.

© 2006 Optical Society of America

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References

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  1. C. D. Cameron, D. A. Pain, M. Stanley, and C. W. Slinger, "Computational challenges of emerging novel true 3D holographic displays," in Critical Technologies for the Future of Computing, S. Bains and L. J. Irakliotis, eds., Proc. SPIE 4109, 129-140 (2000).
  2. D. Abookasis and J. Rosen, "Computer-generated holograms of three-dimensional objects synthesized from their multiple angular viewpoints," J. Opt. Soc. Am. A 20, 1537-1545 (2003).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  8. A. P. Hariharan, Optical Holography, 2nd ed. (Cambridge U. Press, 1996), Chap. 2, pp. 19-21.
  9. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996), Chap. 4, pp. 65-72.
  10. D. Leseberg, "Computer-generated three-dimensional image holograms," Appl. Opt. 31, 223-229 (1992).
    [CrossRef] [PubMed]

2003 (2)

2002 (1)

2001 (1)

2000 (1)

C. D. Cameron, D. A. Pain, M. Stanley, and C. W. Slinger, "Computational challenges of emerging novel true 3D holographic displays," in Critical Technologies for the Future of Computing, S. Bains and L. J. Irakliotis, eds., Proc. SPIE 4109, 129-140 (2000).

1992 (1)

1976 (1)

1964 (1)

A. B. VanderLugt, "Signal detection by complex spatial filtering," IEEE Trans. Inf. Theory IT-10, 139-145 (1964).
[CrossRef]

Abookasis, D.

Cameron, C. D.

C. D. Cameron, D. A. Pain, M. Stanley, and C. W. Slinger, "Computational challenges of emerging novel true 3D holographic displays," in Critical Technologies for the Future of Computing, S. Bains and L. J. Irakliotis, eds., Proc. SPIE 4109, 129-140 (2000).

Gillet, J.-N.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996), Chap. 4, pp. 65-72.

Hariharan, A. P.

A. P. Hariharan, Optical Holography, 2nd ed. (Cambridge U. Press, 1996), Chap. 2, pp. 19-21.

Itoh, M.

Leseberg, D.

Li, Y.

Pain, D. A.

C. D. Cameron, D. A. Pain, M. Stanley, and C. W. Slinger, "Computational challenges of emerging novel true 3D holographic displays," in Critical Technologies for the Future of Computing, S. Bains and L. J. Irakliotis, eds., Proc. SPIE 4109, 129-140 (2000).

Rosen, J.

Sando, Y.

Sheng, Y.

Slinger, C. W.

C. D. Cameron, D. A. Pain, M. Stanley, and C. W. Slinger, "Computational challenges of emerging novel true 3D holographic displays," in Critical Technologies for the Future of Computing, S. Bains and L. J. Irakliotis, eds., Proc. SPIE 4109, 129-140 (2000).

Stanley, M.

C. D. Cameron, D. A. Pain, M. Stanley, and C. W. Slinger, "Computational challenges of emerging novel true 3D holographic displays," in Critical Technologies for the Future of Computing, S. Bains and L. J. Irakliotis, eds., Proc. SPIE 4109, 129-140 (2000).

VanderLugt, A. B.

A. B. VanderLugt, "Signal detection by complex spatial filtering," IEEE Trans. Inf. Theory IT-10, 139-145 (1964).
[CrossRef]

Yatagai, T.

Appl. Opt. (3)

IEEE Trans. Inf. Theory (1)

A. B. VanderLugt, "Signal detection by complex spatial filtering," IEEE Trans. Inf. Theory IT-10, 139-145 (1964).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Lett. (1)

Other (3)

A. P. Hariharan, Optical Holography, 2nd ed. (Cambridge U. Press, 1996), Chap. 2, pp. 19-21.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996), Chap. 4, pp. 65-72.

C. D. Cameron, D. A. Pain, M. Stanley, and C. W. Slinger, "Computational challenges of emerging novel true 3D holographic displays," in Critical Technologies for the Future of Computing, S. Bains and L. J. Irakliotis, eds., Proc. SPIE 4109, 129-140 (2000).

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Figures (5)

Fig. 1
Fig. 1

CGH algorithm. f m , n = exp [ i 2 π b ( x p   sin   φ m + y p   sin   θ n ) ] .

Fig. 2
Fig. 2

(a) Enlarged portion ( 300 × 300 pixels of 601 × 601 ) of the color-inverted Fresnel–Fourier CGH. (b)–(d) Digital reconstruction images from the hologram appear in (a), along the optical axis. (e)–(g) The optical reconstruction in the vicinity of the back of an imaging lens for three transverse planes at 470, 510, and 550  mm for the C, G, and H planes, respectively. We used the imaging lens to bring the far reconstruction plane nearer and for better visualization.

Fig. 3
Fig. 3

(a) Enlarged portion of the Fresnel CGH. (b)–(d) Digitally reconstructed images for three successive transverse planes along the optical axis. (e)–(g) The optical reconstruction for three transverse planes at 145, 160, and 177  mm from the SLM for the C, G, and H balls, respectively.

Fig. 4
Fig. 4

Nine out of 201 × 201 projections of the 3D object.

Fig. 5
Fig. 5

(a) Enlarged portion of the intensity distribution of the image CGH. (b) and (c) The digital reconstructed images from (a). (d) and (e) The optical reconstruction. In (d) the G cube was observed at 230   mm from the lens and in (e) the U cube was observed at 270   mm from the lens.

Equations (11)

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s ( m , n ) = p m n ( x p , y p ) × exp [ i 2 π b ( x p   sin   φ m + y p   sin   θ n ) ] × d x p d y p ,
s ( u , v ) t ( x s , y s , z s ) × exp { i 2 π α [ u x s + v y s + σ z s ( u 2 + v 2 ) ] } × d x s d y s d z s ,
H FF ( u , v ) = { s ( u , v ) exp ( i π r 2 λ z 𝔍 ) × exp ( i 2 π   sin   ψ λ v ) } + c ,
H FF ( u , v ) = { exp [ i 8 π γ ( r d N ) 2 + i 4 π β v d N ] } ,
Z 𝔍 = ( d N ) 2 8 λ γ ,
sin   ψ = 2 λ β d N .
[ 2 π γ ( 2 r d N ) 2 + 2 π β 2 v d N ] v , r = dN / 2 [ 2 π γ ( 2 r d N ) 2 + 2 π β 2 v d N ] v , r = ( dN / 2 ) 2 d 2 π .
z 𝔍 d λ ( N d + 2 r o ) ,
H Fr ( x , y ) = { 𝔍 1 { s ( u , v ) }   exp [ i π λ z F ( x 2 + y 2 ) ] × exp ( i 2 π sin   ψ λ y ) } + c ,
z F  ≥  d 2 N λ .
H I ( x , y ) = { 𝔍 1 { s ( u , v ) } exp ( i 2 π sin ψ λ y ) } + c .

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