Abstract

A fast calculation method for computer generation of cylindrical holograms is proposed. The calculation method is based on wave propagation in spectral domain and in cylindrical co-ordinates, which is otherwise similar to the angular spectrum of plane waves in cartesian co-ordinates. The calculation requires only two FFT operations and hence is much faster. The theoretical background of the calculation method, sampling conditions and simulation results are presented. The generated cylindrical hologram has been tested for reconstruction in different view angles and also in plane surfaces.

© 2010 OSA

Full Article  |  PDF Article
Related Articles
Reconstruction of in-line digital holograms from two intensity measurements

Yan Zhang, Giancarlo Pedrini, Wolfgang Osten, and Hans J. Tiziani
Opt. Lett. 29(15) 1787-1789 (2004)

Simplified electroholographic color reconstruction system using graphics processing unit and liquid crystal display projector

Atsushi Shiraki, Naoki Takada, Masashi Niwa, Yasuyuki Ichihashi, Tomoyoshi Shimobaba, Nobuyuki Masuda, and Tomoyoshi Ito
Opt. Express 17(18) 16038-16045 (2009)

References

  • View by:
  • |
  • |

  1. Tung H. Jeong, “Cylindrical holography and some proposed applications,” J. Opt. Soc. Am.57, 31396–1398 (1967), http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-57-11-1396 .
    [Crossref]
  2. O. D. D. Soares and J. C. A. Fernandes, “Cylindrical hologram of 360° field of view,” Appl. Opt.21,3194–3196 (1982), http://www.opticsinfobase.org/abstract.cfm?URI=ao-21-17-3194 .
    [Crossref] [PubMed]
  3. A. W. Lohmann and D. P. Paris, “Binary Fraunhofer holograms, generated by computer,” Appl. Opt.6, 739–1748 (1967), http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-6-10-1739 .
    [Crossref]
  4. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).
  5. T. Tommasi and B. Bianco, “Computer-generated holograms of tilted planes by a spatial frequency approach,” J. Opt. Soc. Am. A10, 299–305 (1993), http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-10-2-299 .
    [Crossref]
  6. Y. Sakamoto and M. Tobise, “Computer generated cylindrical hologram,” in Practical Holography XIX: Materials and Applications, Tung H. Jeong and Hans I. Bjelkhagen, eds., Proc.SPIE5742, 267–274 (2005).
  7. A. Kashiwagi and Y. Sakamoto, “A Fast calculation method of cylindrical computer-generated holograms which perform image reconstruction of volume data,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, OSA Technical Digest (CD) (Optical Society of America, 2007), paper DWB7, http://www.opticsinfobase.org/abstract.cfm?URI=DH-2007-DWB7 .
    [PubMed]
  8. T. Yamaguchi, T. Fujii, and H. Yoshikawa, “Fast calculation method for computer-generated cylindrical holograms,” Appl. Opt.47, D63–D70 (2008), http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-47-19-D63 .
    [Crossref] [PubMed]
  9. T. Yamaguchi, T. Fujii, and H. Yoshikawa, “Computer-generated cylindrical rainbow hologram,” in Practical Holography XXII: Materials and Applications, Hans I. Bjelkhagen and Raymond K. Kostuk, eds., Proc.SPIE6912, 69121C (2009).
  10. Y. Sando, M. Itoh, and T. Yatagai, “Fast calculation method for cylindrical computer-generated holograms,” Appl. Opt.13, 1418–1423 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-5-1418 .
  11. G. E. Williams, Fourier Acoustics, Sound Radiation, and Near-field Acoustical Holography (Academic Press, 1999).
  12. N. N. Lebedev, Special Functions and Their Applications (Prentice Hall, 1965), pp. 98–160.
  13. G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists (Academic Press, 2001), pp. 702–705.

Arfken, G. B.

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists (Academic Press, 2001), pp. 702–705.

Fujii, T.

T. Yamaguchi, T. Fujii, and H. Yoshikawa, “Computer-generated cylindrical rainbow hologram,” in Practical Holography XXII: Materials and Applications, Hans I. Bjelkhagen and Raymond K. Kostuk, eds., Proc.SPIE6912, 69121C (2009).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

Lebedev, N. N.

N. N. Lebedev, Special Functions and Their Applications (Prentice Hall, 1965), pp. 98–160.

Sakamoto, Y.

Y. Sakamoto and M. Tobise, “Computer generated cylindrical hologram,” in Practical Holography XIX: Materials and Applications, Tung H. Jeong and Hans I. Bjelkhagen, eds., Proc.SPIE5742, 267–274 (2005).

Tobise, M.

Y. Sakamoto and M. Tobise, “Computer generated cylindrical hologram,” in Practical Holography XIX: Materials and Applications, Tung H. Jeong and Hans I. Bjelkhagen, eds., Proc.SPIE5742, 267–274 (2005).

Weber, H. J.

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists (Academic Press, 2001), pp. 702–705.

Williams, G. E.

G. E. Williams, Fourier Acoustics, Sound Radiation, and Near-field Acoustical Holography (Academic Press, 1999).

Yamaguchi, T.

T. Yamaguchi, T. Fujii, and H. Yoshikawa, “Computer-generated cylindrical rainbow hologram,” in Practical Holography XXII: Materials and Applications, Hans I. Bjelkhagen and Raymond K. Kostuk, eds., Proc.SPIE6912, 69121C (2009).

Yoshikawa, H.

T. Yamaguchi, T. Fujii, and H. Yoshikawa, “Computer-generated cylindrical rainbow hologram,” in Practical Holography XXII: Materials and Applications, Hans I. Bjelkhagen and Raymond K. Kostuk, eds., Proc.SPIE6912, 69121C (2009).

Other (13)

Tung H. Jeong, “Cylindrical holography and some proposed applications,” J. Opt. Soc. Am.57, 31396–1398 (1967), http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-57-11-1396 .
[Crossref]

O. D. D. Soares and J. C. A. Fernandes, “Cylindrical hologram of 360° field of view,” Appl. Opt.21,3194–3196 (1982), http://www.opticsinfobase.org/abstract.cfm?URI=ao-21-17-3194 .
[Crossref] [PubMed]

A. W. Lohmann and D. P. Paris, “Binary Fraunhofer holograms, generated by computer,” Appl. Opt.6, 739–1748 (1967), http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-6-10-1739 .
[Crossref]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

T. Tommasi and B. Bianco, “Computer-generated holograms of tilted planes by a spatial frequency approach,” J. Opt. Soc. Am. A10, 299–305 (1993), http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-10-2-299 .
[Crossref]

Y. Sakamoto and M. Tobise, “Computer generated cylindrical hologram,” in Practical Holography XIX: Materials and Applications, Tung H. Jeong and Hans I. Bjelkhagen, eds., Proc.SPIE5742, 267–274 (2005).

A. Kashiwagi and Y. Sakamoto, “A Fast calculation method of cylindrical computer-generated holograms which perform image reconstruction of volume data,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, OSA Technical Digest (CD) (Optical Society of America, 2007), paper DWB7, http://www.opticsinfobase.org/abstract.cfm?URI=DH-2007-DWB7 .
[PubMed]

T. Yamaguchi, T. Fujii, and H. Yoshikawa, “Fast calculation method for computer-generated cylindrical holograms,” Appl. Opt.47, D63–D70 (2008), http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-47-19-D63 .
[Crossref] [PubMed]

T. Yamaguchi, T. Fujii, and H. Yoshikawa, “Computer-generated cylindrical rainbow hologram,” in Practical Holography XXII: Materials and Applications, Hans I. Bjelkhagen and Raymond K. Kostuk, eds., Proc.SPIE6912, 69121C (2009).

Y. Sando, M. Itoh, and T. Yatagai, “Fast calculation method for cylindrical computer-generated holograms,” Appl. Opt.13, 1418–1423 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-5-1418 .

G. E. Williams, Fourier Acoustics, Sound Radiation, and Near-field Acoustical Holography (Academic Press, 1999).

N. N. Lebedev, Special Functions and Their Applications (Prentice Hall, 1965), pp. 98–160.

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists (Academic Press, 2001), pp. 702–705.

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 (12)

Fig. 1
Fig. 1

Coordinate system.

Fig. 2
Fig. 2

Recording setup: (a) schematic and (b) geometry.

Fig. 3
Fig. 3

Object.

Fig. 4
Fig. 4

Hologram.

Fig. 5
Fig. 5

Reconstruction-Cylindrical surface.

Fig. 6
Fig. 6

Planar reconstruction: (a) schematic and (b) geometry.

Fig. 7
Fig. 7

Planar Reconstruction (z=1).

Fig. 8
Fig. 8

Planar Reconstruction (z=−1).

Fig. 9
Fig. 9

Variable angle reconstruction - Schematic.

Fig. 10
Fig. 10

120° (−60° to 60°) view angle.

Fig. 11
Fig. 11

90° (90° to 180°) view angle.

Fig. 12
Fig. 12

45° (−180° to −135°) view angle.

Tables (1)

Tables Icon

Table 1 Calculation time

Equations (21)

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

( 2 + k ) p = 0 ,
p ( r , ϕ , y ) = R ( r ) Φ ( ϕ ) Y ( y ) ,
R ( r ) = R 1 H n ( 1 ) ( k r r ) + R 2 H n ( 2 ) ( k r r ) ,
Φ ( ϕ ) = ϕ 1 e i n ϕ + ϕ 2 e in ϕ ,
Y ( y ) = Y 1 e ik y y + Y 2 e ik y y ,
p ( r , ϕ , y ) = n = e i n ϕ 1 2 π [ A n ( k y ) e i k y y H n ( 1 ) ( k r r ) + B n ( k y ) e ik y y H n ( 2 ) ( k r r ) ] dk y ,
p ( a , ϕ , y ) = n = e in ϕ 1 2 π A n ( k y ) e ik y y H n ( 1 ) ( k r a ) d k y ,
P n ( r , k y ) 1 2 π 0 2 π d ϕ p ( r , ϕ , y ) e i n ϕ e i k y y d y ,
p ( r , ϕ , y ) = n = e i n ϕ 1 2 π p n ( r . k y ) e i k y y d k y ,
P n ( a , k y ) = A n ( k y ) H n ( 1 ) ( k r a ) ,
p ( r , ϕ , y ) = n = e i n ϕ 1 2 π p n ( a , k y ) e i k y y H n ( 1 ) ( k r r ) H n ( 1 ) ( k r a ) d k y ,
p ( x , y , z ) = 1 4 π 2 d k x d k y P ( k x , k y , z 0 ) e i ( k x x + k y y ) e i k z ( z z 0 ) .
P n ( a , k y ) = 1 2 π 0 2 π d ϕ p ( a , ϕ , y ) e in ϕ e i k y y d y ,
T ( a , k a , r , k r ) = H n ( 1 ) ( k r r ) H n ( 1 ) ( k r a ) ,
n | k r 1 ( λ k y ) 2 | n = N / 2 π ,
| k λ 2 r n Δ L 0 2 1 λ 2 n 2 Δ L 0 2 | n = N / 2 π ,
2 n r λ Δ L 0 Δ L 0 2 λ 2 ( N 2 ) 2 ,
Δ L 0 N r λ ( or ) N Δ L 0 2 r λ .
Hologram = | I F F T [ F F T ( Object ) × T F ] + I F F T [ F F T ( Reference ) × T F ] | 2
Reconstruction = | I F F T [ F F T ( Hologram × Conjugate [ Reference ] ) × T F ] | 2
U ( a , ϕ , z ) = U ( r , θ , z ) exp ( ikr ) r d ϕ d z .

Metrics