Abstract

The synthesis of spherical computer-generated holograms is investigated. To deal with the staggering calculation times required to synthesize the hologram, a fast calculation method for approximating the hologram distribution is proposed. In this method, the diffraction integral is approximated as a convolution integral, allowing computation using the fast-Fourier-transform algorithm. The principles of the fast calculation method, the error in the approximation, and results from simulations are presented.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. Tricoles, "Computer generated holograms: an historical review," Appl. Opt. 26, 4351-4360 (1987).
    [CrossRef] [PubMed]
  2. O. D. D. Soares and J. C. A. Fernandes, "Cylindrical hologram of 360° field of view," Appl. Opt. 21, 3194-3196 (1982).
    [CrossRef] [PubMed]
  3. J. Rosen, "Computer-generated holograms of images reconstructed on curved surfaces," Appl. Opt. 38, 6136-6140 (1999).
    [CrossRef]
  4. D. Leseberg and C. Frère, "Computer-generated holograms of 3-D objects composed of tilted planar segments," Appl. Opt. 27, 3020-3024 (1988).
    [CrossRef] [PubMed]
  5. T. Tommasi and B. Bianco, "Computer-generated holograms of tilted planes by a spatial frequency approach," J. Opt. Soc. Am. A 10, 299-305 (1993).
    [CrossRef]
  6. K. Matsushima, H. Schimmel, and F. Wyrowski, "Fast calculation method for optical diffraction on tilted planes by use of the angular spectrum of plane waves," J. Opt. Soc. Am. A 20, 1755-1762 (2003).
    [CrossRef]
  7. Y. Sando, M. Itoh, and T. Yatagai, "Fast calculation method for cylindrical computer-generated holograms," Opt. Express 13, 1418-1423 (2005).
    [CrossRef] [PubMed]

2005

2003

1999

1993

1988

1987

1982

Bianco, B.

Fernandes, J. C. A.

Frère, C.

Itoh, M.

Leseberg, D.

Matsushima, K.

Rosen, J.

Sando, Y.

Schimmel, H.

Soares, O. D. D.

Tommasi, T.

Tricoles, G.

Wyrowski, F.

Yatagai, T.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Setup of the calculation method.

Fig. 2
Fig. 2

(a) Geometry of the approximation and (b) geometry to solve for α.

Fig. 3
Fig. 3

Relative distance error distributions for various object point locations.

Fig. 4
Fig. 4

(Color online) Distance error profiles for (a) ro = 1 cm, (b) ro = 3 cm, and (c) ro = 9 cm.

Fig. 5
Fig. 5

Computer-generated holograms for an object at (a) θ o = 0, (b) θ o = −π∕4, and (c) θ o = −π∕2.

Fig. 6
Fig. 6

(a) Amplitude distribution and (b) Fourier spectrum amplitude distribution of the point spread function.

Fig. 7
Fig. 7

Hologram of two point sources.

Fig. 8
Fig. 8

Reconstruction images of a small object at (a) θ o = 0, (b) θ o = −π∕4, and (c) θ o = −π∕2.

Fig. 9
Fig. 9

(a) Sample object and (b) reconstruction image.

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

f h ( ϕ h , θ h ) = C f o ( ϕ o , θ o ) exp ( i k d ) d  d ϕ o d θ o ,
d = { r o 2 + r h 2 2 r o r h [ sin ( θ h ) sin ( θ o ) + cos ( θ h ) cos ( θ o ) cos ( ϕ h ϕ o ) ] } 1 / 2 .
d = [ r o 2 + r h 2 2 r o r h cos ( ϕ h ϕ o ) cos ( θ h θ o ) ] 1 / 2 .
h ( ϕ , θ ) = exp { i k [ r o 2 + r h 2 2 r o r h cos ( ϕ ) cos ( θ ) ] 1 / 2 } [ r o 2 + r h 2 2 r o r h cos ( ϕ ) cos ( θ ) ] 1 / 2 .
f h ( ϕ h , θ h ) = C f o ( ϕ o , θ o ) h ( ϕ h ϕ o , θ h θ o ) d ϕ o d θ o ,
f h = C f o h ,
ν ϕ ( ϕ , θ ) = 1 2 π ϕ [ h ( ϕ , θ ) ] ,
ν ϕ ( ϕ , θ ) = 1 2 π ϕ { k [ r o 2 + r h 2 2 r o r h cos ( ϕ ) cos ( θ ) ] 1 / 2 }
= 1 2 π k r o r h sin ( ϕ ) cos ( θ ) [ r o     2 + r h     2 2 r o r h cos ( ϕ ) cos ( θ ) ] 1 / 2 .
| ν ϕ | max = k × min ( r o , r h ) 2 π ,
B W ϕ = 2 | ν ϕ | max = k × min ( r o , r h ) π ,
N ϕ > 4 π × min ( r o , r h ) λ ,
N θ > 2 π × min ( r o , r h ) λ ,
d = { r o 2 + r h 2 2 r o r h [ sin ( θ h ) sin ( θ o ) cos ( ϕ h ϕ o ) + cos ( θ h ) cos ( θ o ) cos ( ϕ h ϕ o ) ] } 1 / 2 ,
d = [ r o 2 + r h 2 2 r o r h cos ( ϕ h ϕ o ) cos ( θ h θ o ) ] 1 / 2 .
d = [ r o 2 + r h 2 2 r o r h cos ( θ h ) cos ( ϕ h ϕ o ) ] 1 / 2 ,

Metrics