Abstract

We present the results of applying lossless and lossy data compression to a three-dimensional object reconstruction and recognition technique based on phase-shift digital holography. We find that the best lossless (Lempel–Ziv, Lempel–Ziv–Welch, Huffman, Burrows–Wheeler) compression rates can be expected when the digital hologram is stored in an intermediate coding of separate data streams for real and imaginary components. The lossy techniques are based on subsampling, quantization, and discrete Fourier transformation. For various degrees of speckle reduction, we quantify the number of Fourier coefficients that can be removed from the hologram domain, and the lowest level of quantization achievable, without incurring significant loss in correlation performance or significant error in the reconstructed object domain.

© 2002 Optical Society of America

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References

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  1. A. Vander Lugt, “Signal detection by complex spatial filtering,” IEEE Trans. IT-10, 139–145 (1964).
  2. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).
  3. A. D. McAulay, Optical Computer Architectures (Wiley, New York, 1991).
  4. A. Pu, R. F. Denkewalter, D. Psaltis, “Real-time vehicle navigation using a holographic memory,” Opt. Eng. 36, 2737–2746 (1997).
    [CrossRef]
  5. R. Bamler, J. Hofer-Alfeis, “Three- and four-dimensional filter operations by coherent optics,” Opt. Acta 29, 747–757 (1982).
    [CrossRef]
  6. J. Rosen, “Three-dimensional joint transform correlator,” Appl. Opt. 37, 7538–7544 (1998).
    [CrossRef]
  7. J. J. Esteve-Taboada, D. Mas, J. García, “Three-dimensional object recognition by Fourier transform profilometry,” Appl. Opt. 38, 4760–4765 (1999).
    [CrossRef]
  8. J. Guerrero-Bermúdez, J. Meneses, O. Gualdrón, “Object recognition using three-dimensional correlation of range images,” Opt. Eng. 39, 2828–2831 (2000).
    [CrossRef]
  9. B. Javidi, E. Tajahuerce, “Three-dimensional object recognition by use of digital holography,” Opt. Lett. 25, 610–612 (2000).
    [CrossRef]
  10. Y. Frauel, E. Tajahuerce, M.-A. Castro, B. Javidi, “Distortion-tolerant three-dimensional object recognition with digital holography,” Appl. Opt. 40, 3887–3893 (2001).
    [CrossRef]
  11. Ph. Réfrégier, F. Goudail, “Statistical processing of polarization diversity images,” in Optoelectronic Information Processing: Optics for Information Systems, Ph. Réfrégier, B. Javidi, C. Ferreira, S. Vallmitjana, eds., Proc. SPIECR81-13, 262–288 (2001).
  12. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt. 13, 2693–2703 (1974).
    [CrossRef] [PubMed]
  13. I. Yamaguchi, T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
    [CrossRef] [PubMed]
  14. M. Rabbani, Selected Papers on Image Coding and Compression, SPIE Milestone SeriesMS48 (SPIE Press, 1992).
  15. L. P. Yaroslavsky, N. S. Merzlyakov, Methods of Digital Holography (Consultants Bureau, New York, 1980).
    [CrossRef]
  16. O. Bryngdahl, F. Wyrowski, “Digital holography—computer-generated holograms,” Prog. Opt. 28, 1–86 (1990).
    [CrossRef]
  17. J. W. Goodman, R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
    [CrossRef]
  18. J. W. Goodman, A. Silvestri, “Digital reconstruction of holographic images,” Nerem Record 10, 118 (1968).
  19. A. Bilgin, G. Zweig, M. W. Marcellin, “Three-dimensional image compression with integer wavelet transforms,” Appl. Opt. 39, 1799–1814 (2000).
    [CrossRef]
  20. S. Qian, A. B. Hollinger, D. J. Williams, D. Manak, “Fast three-dimensional data compression of hyperspectral imagery using vector quantization with spectral-feature-based binary coding,” Opt. Eng. 35, 3242–3249 (1996).
    [CrossRef]
  21. G. J. Ewing, C. J. Woodruff, “Comparison of JPEG and fractal-based image compression on target acquisition by human observers,” Opt. Eng. 35, 284–288 (1996).
    [CrossRef]
  22. C. A. Morioka, M. P. Eckstein, J. L. Bartroff, J. Hausleiter, G. Aharanov, J. S. Whiting, “Observer performance for JPEG vs. wavelet image compression of x-ray coronary angiograms,” Opt. Express 5, 8–19 (1999).
    [CrossRef] [PubMed]
  23. M. W. Farn, J. W. Goodman, “Bounds on the performance of continuous and quantized phase-only matched filters,” J. Opt. Soc. Am. A 7, 66–72 (1990).
    [CrossRef]
  24. A. Mahalanobis, C. Daniell, “Data compression and correlation filtering,” in Smart Imaging Systems, B. Javidi, ed. SPIE PM91 (SPIE Press, 2001), pp. 111–132.
  25. J. Vago, H. Vermeulen, A. Verga, “Fast Fourier transform based image compression algorithm optimized for speckle interferometer measurements,” Opt. Eng. 36, 3052–3063 (1997).
    [CrossRef]
  26. R. Shahnaz, J. F. Walkup, T. F. Krile, “Image compression in signal-dependent noise,” Appl. Opt. 38, 5560–5567 (1999).
    [CrossRef]
  27. F. Murtagh, J.-L. Starck, M. Louys, “Very-high-quality image compression based on noise modeling,” Int. J. Imaging Syst. Technol. 9, 38–45 (1998).
    [CrossRef]
  28. F. Wyrowski, O. Bryngdahl, “Speckle-free reconstruction in digital holography,” J. Opt. Soc. Am. A 6, 1171–1174 (1989).
    [CrossRef]
  29. T. Nomura, A. Okazaki, M. Kameda, Y. Morimoto, B. Javidi, “Digital holographic data reconstruction with data compression,” Algorithms and Systems for Optical Information Processing V, B. Javidi, D. Psaltis, ed., Proc. SPIE4471 (2001).
  30. E. Y. Lam, J. W. Goodman, “Discrete cosine transform domain restoration of defocused images,” Appl. Opt. 37, 6213–6218 (1998).
    [CrossRef]
  31. J. W. Goodman, A. M. Silvestri, “Some effects of Fourier domain phase quantization,” IBM J. Research and Dev. 14, 478–484 (1970).
    [CrossRef]
  32. W. J. Dallas, A. W. Lohmann, “Phase quantization in holograms,” Appl. Opt. 11, 192–194 (1972).
    [CrossRef] [PubMed]
  33. H. J. Caulfield, Handbook of Optical Holography (Academic Press, San Diego, Calif., 1979).
  34. D. A. Huffman, “A method for the construction of minimum redundancy codes,” Proc. IRE 40, 1098–1101 (1952).
    [CrossRef]
  35. J. Ziv, A. Lempel, “A universal algorithm for sequential data compression,” IEEE Trans. IT-23, 337–343 (1977).
  36. T. A. Welch, “A technique for high performance data compression,” IEEE Computer 17, 8–19 (1984).
    [CrossRef]
  37. M. Burrows, D. J. Wheeler, “A block-sorting lossless data compression algorithm,” Digital SRC Report 124, (1994).
  38. B. Javidi, “Nonlinear joint power spectrum based optical correlation,” Appl. Opt. 28, 2358–2367 (1989).
    [CrossRef] [PubMed]

2001 (1)

2000 (3)

1999 (3)

1998 (3)

1997 (3)

J. Vago, H. Vermeulen, A. Verga, “Fast Fourier transform based image compression algorithm optimized for speckle interferometer measurements,” Opt. Eng. 36, 3052–3063 (1997).
[CrossRef]

A. Pu, R. F. Denkewalter, D. Psaltis, “Real-time vehicle navigation using a holographic memory,” Opt. Eng. 36, 2737–2746 (1997).
[CrossRef]

I. Yamaguchi, T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
[CrossRef] [PubMed]

1996 (2)

S. Qian, A. B. Hollinger, D. J. Williams, D. Manak, “Fast three-dimensional data compression of hyperspectral imagery using vector quantization with spectral-feature-based binary coding,” Opt. Eng. 35, 3242–3249 (1996).
[CrossRef]

G. J. Ewing, C. J. Woodruff, “Comparison of JPEG and fractal-based image compression on target acquisition by human observers,” Opt. Eng. 35, 284–288 (1996).
[CrossRef]

1990 (2)

O. Bryngdahl, F. Wyrowski, “Digital holography—computer-generated holograms,” Prog. Opt. 28, 1–86 (1990).
[CrossRef]

M. W. Farn, J. W. Goodman, “Bounds on the performance of continuous and quantized phase-only matched filters,” J. Opt. Soc. Am. A 7, 66–72 (1990).
[CrossRef]

1989 (2)

1984 (1)

T. A. Welch, “A technique for high performance data compression,” IEEE Computer 17, 8–19 (1984).
[CrossRef]

1982 (1)

R. Bamler, J. Hofer-Alfeis, “Three- and four-dimensional filter operations by coherent optics,” Opt. Acta 29, 747–757 (1982).
[CrossRef]

1977 (1)

J. Ziv, A. Lempel, “A universal algorithm for sequential data compression,” IEEE Trans. IT-23, 337–343 (1977).

1974 (1)

1972 (1)

1970 (1)

J. W. Goodman, A. M. Silvestri, “Some effects of Fourier domain phase quantization,” IBM J. Research and Dev. 14, 478–484 (1970).
[CrossRef]

1968 (1)

J. W. Goodman, A. Silvestri, “Digital reconstruction of holographic images,” Nerem Record 10, 118 (1968).

1967 (1)

J. W. Goodman, R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

1964 (1)

A. Vander Lugt, “Signal detection by complex spatial filtering,” IEEE Trans. IT-10, 139–145 (1964).

1952 (1)

D. A. Huffman, “A method for the construction of minimum redundancy codes,” Proc. IRE 40, 1098–1101 (1952).
[CrossRef]

Aharanov, G.

Bamler, R.

R. Bamler, J. Hofer-Alfeis, “Three- and four-dimensional filter operations by coherent optics,” Opt. Acta 29, 747–757 (1982).
[CrossRef]

Bartroff, J. L.

Bilgin, A.

Brangaccio, D. J.

Bruning, J. H.

Bryngdahl, O.

O. Bryngdahl, F. Wyrowski, “Digital holography—computer-generated holograms,” Prog. Opt. 28, 1–86 (1990).
[CrossRef]

F. Wyrowski, O. Bryngdahl, “Speckle-free reconstruction in digital holography,” J. Opt. Soc. Am. A 6, 1171–1174 (1989).
[CrossRef]

Burrows, M.

M. Burrows, D. J. Wheeler, “A block-sorting lossless data compression algorithm,” Digital SRC Report 124, (1994).

Castro, M.-A.

Caulfield, H. J.

H. J. Caulfield, Handbook of Optical Holography (Academic Press, San Diego, Calif., 1979).

Dallas, W. J.

Daniell, C.

A. Mahalanobis, C. Daniell, “Data compression and correlation filtering,” in Smart Imaging Systems, B. Javidi, ed. SPIE PM91 (SPIE Press, 2001), pp. 111–132.

Denkewalter, R. F.

A. Pu, R. F. Denkewalter, D. Psaltis, “Real-time vehicle navigation using a holographic memory,” Opt. Eng. 36, 2737–2746 (1997).
[CrossRef]

Eckstein, M. P.

Esteve-Taboada, J. J.

Ewing, G. J.

G. J. Ewing, C. J. Woodruff, “Comparison of JPEG and fractal-based image compression on target acquisition by human observers,” Opt. Eng. 35, 284–288 (1996).
[CrossRef]

Farn, M. W.

Frauel, Y.

Gallagher, J. E.

García, J.

Goodman, J. W.

E. Y. Lam, J. W. Goodman, “Discrete cosine transform domain restoration of defocused images,” Appl. Opt. 37, 6213–6218 (1998).
[CrossRef]

M. W. Farn, J. W. Goodman, “Bounds on the performance of continuous and quantized phase-only matched filters,” J. Opt. Soc. Am. A 7, 66–72 (1990).
[CrossRef]

J. W. Goodman, A. M. Silvestri, “Some effects of Fourier domain phase quantization,” IBM J. Research and Dev. 14, 478–484 (1970).
[CrossRef]

J. W. Goodman, A. Silvestri, “Digital reconstruction of holographic images,” Nerem Record 10, 118 (1968).

J. W. Goodman, R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

Goudail, F.

Ph. Réfrégier, F. Goudail, “Statistical processing of polarization diversity images,” in Optoelectronic Information Processing: Optics for Information Systems, Ph. Réfrégier, B. Javidi, C. Ferreira, S. Vallmitjana, eds., Proc. SPIECR81-13, 262–288 (2001).

Gualdrón, O.

J. Guerrero-Bermúdez, J. Meneses, O. Gualdrón, “Object recognition using three-dimensional correlation of range images,” Opt. Eng. 39, 2828–2831 (2000).
[CrossRef]

Guerrero-Bermúdez, J.

J. Guerrero-Bermúdez, J. Meneses, O. Gualdrón, “Object recognition using three-dimensional correlation of range images,” Opt. Eng. 39, 2828–2831 (2000).
[CrossRef]

Hausleiter, J.

Herriott, D. R.

Hofer-Alfeis, J.

R. Bamler, J. Hofer-Alfeis, “Three- and four-dimensional filter operations by coherent optics,” Opt. Acta 29, 747–757 (1982).
[CrossRef]

Hollinger, A. B.

S. Qian, A. B. Hollinger, D. J. Williams, D. Manak, “Fast three-dimensional data compression of hyperspectral imagery using vector quantization with spectral-feature-based binary coding,” Opt. Eng. 35, 3242–3249 (1996).
[CrossRef]

Huffman, D. A.

D. A. Huffman, “A method for the construction of minimum redundancy codes,” Proc. IRE 40, 1098–1101 (1952).
[CrossRef]

Javidi, B.

Kameda, M.

T. Nomura, A. Okazaki, M. Kameda, Y. Morimoto, B. Javidi, “Digital holographic data reconstruction with data compression,” Algorithms and Systems for Optical Information Processing V, B. Javidi, D. Psaltis, ed., Proc. SPIE4471 (2001).

Krile, T. F.

Lam, E. Y.

Lawrence, R. W.

J. W. Goodman, R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

Lempel, A.

J. Ziv, A. Lempel, “A universal algorithm for sequential data compression,” IEEE Trans. IT-23, 337–343 (1977).

Lohmann, A. W.

Louys, M.

F. Murtagh, J.-L. Starck, M. Louys, “Very-high-quality image compression based on noise modeling,” Int. J. Imaging Syst. Technol. 9, 38–45 (1998).
[CrossRef]

Mahalanobis, A.

A. Mahalanobis, C. Daniell, “Data compression and correlation filtering,” in Smart Imaging Systems, B. Javidi, ed. SPIE PM91 (SPIE Press, 2001), pp. 111–132.

Manak, D.

S. Qian, A. B. Hollinger, D. J. Williams, D. Manak, “Fast three-dimensional data compression of hyperspectral imagery using vector quantization with spectral-feature-based binary coding,” Opt. Eng. 35, 3242–3249 (1996).
[CrossRef]

Marcellin, M. W.

Mas, D.

McAulay, A. D.

A. D. McAulay, Optical Computer Architectures (Wiley, New York, 1991).

Meneses, J.

J. Guerrero-Bermúdez, J. Meneses, O. Gualdrón, “Object recognition using three-dimensional correlation of range images,” Opt. Eng. 39, 2828–2831 (2000).
[CrossRef]

Merzlyakov, N. S.

L. P. Yaroslavsky, N. S. Merzlyakov, Methods of Digital Holography (Consultants Bureau, New York, 1980).
[CrossRef]

Morimoto, Y.

T. Nomura, A. Okazaki, M. Kameda, Y. Morimoto, B. Javidi, “Digital holographic data reconstruction with data compression,” Algorithms and Systems for Optical Information Processing V, B. Javidi, D. Psaltis, ed., Proc. SPIE4471 (2001).

Morioka, C. A.

Murtagh, F.

F. Murtagh, J.-L. Starck, M. Louys, “Very-high-quality image compression based on noise modeling,” Int. J. Imaging Syst. Technol. 9, 38–45 (1998).
[CrossRef]

Nomura, T.

T. Nomura, A. Okazaki, M. Kameda, Y. Morimoto, B. Javidi, “Digital holographic data reconstruction with data compression,” Algorithms and Systems for Optical Information Processing V, B. Javidi, D. Psaltis, ed., Proc. SPIE4471 (2001).

Okazaki, A.

T. Nomura, A. Okazaki, M. Kameda, Y. Morimoto, B. Javidi, “Digital holographic data reconstruction with data compression,” Algorithms and Systems for Optical Information Processing V, B. Javidi, D. Psaltis, ed., Proc. SPIE4471 (2001).

Psaltis, D.

A. Pu, R. F. Denkewalter, D. Psaltis, “Real-time vehicle navigation using a holographic memory,” Opt. Eng. 36, 2737–2746 (1997).
[CrossRef]

Pu, A.

A. Pu, R. F. Denkewalter, D. Psaltis, “Real-time vehicle navigation using a holographic memory,” Opt. Eng. 36, 2737–2746 (1997).
[CrossRef]

Qian, S.

S. Qian, A. B. Hollinger, D. J. Williams, D. Manak, “Fast three-dimensional data compression of hyperspectral imagery using vector quantization with spectral-feature-based binary coding,” Opt. Eng. 35, 3242–3249 (1996).
[CrossRef]

Rabbani, M.

M. Rabbani, Selected Papers on Image Coding and Compression, SPIE Milestone SeriesMS48 (SPIE Press, 1992).

Réfrégier, Ph.

Ph. Réfrégier, F. Goudail, “Statistical processing of polarization diversity images,” in Optoelectronic Information Processing: Optics for Information Systems, Ph. Réfrégier, B. Javidi, C. Ferreira, S. Vallmitjana, eds., Proc. SPIECR81-13, 262–288 (2001).

Rosen, J.

Rosenfeld, D. P.

Shahnaz, R.

Silvestri, A.

J. W. Goodman, A. Silvestri, “Digital reconstruction of holographic images,” Nerem Record 10, 118 (1968).

Silvestri, A. M.

J. W. Goodman, A. M. Silvestri, “Some effects of Fourier domain phase quantization,” IBM J. Research and Dev. 14, 478–484 (1970).
[CrossRef]

Starck, J.-L.

F. Murtagh, J.-L. Starck, M. Louys, “Very-high-quality image compression based on noise modeling,” Int. J. Imaging Syst. Technol. 9, 38–45 (1998).
[CrossRef]

Tajahuerce, E.

Vago, J.

J. Vago, H. Vermeulen, A. Verga, “Fast Fourier transform based image compression algorithm optimized for speckle interferometer measurements,” Opt. Eng. 36, 3052–3063 (1997).
[CrossRef]

Vander Lugt, A.

A. Vander Lugt, “Signal detection by complex spatial filtering,” IEEE Trans. IT-10, 139–145 (1964).

Verga, A.

J. Vago, H. Vermeulen, A. Verga, “Fast Fourier transform based image compression algorithm optimized for speckle interferometer measurements,” Opt. Eng. 36, 3052–3063 (1997).
[CrossRef]

Vermeulen, H.

J. Vago, H. Vermeulen, A. Verga, “Fast Fourier transform based image compression algorithm optimized for speckle interferometer measurements,” Opt. Eng. 36, 3052–3063 (1997).
[CrossRef]

Walkup, J. F.

Welch, T. A.

T. A. Welch, “A technique for high performance data compression,” IEEE Computer 17, 8–19 (1984).
[CrossRef]

Wheeler, D. J.

M. Burrows, D. J. Wheeler, “A block-sorting lossless data compression algorithm,” Digital SRC Report 124, (1994).

White, A. D.

Whiting, J. S.

Williams, D. J.

S. Qian, A. B. Hollinger, D. J. Williams, D. Manak, “Fast three-dimensional data compression of hyperspectral imagery using vector quantization with spectral-feature-based binary coding,” Opt. Eng. 35, 3242–3249 (1996).
[CrossRef]

Woodruff, C. J.

G. J. Ewing, C. J. Woodruff, “Comparison of JPEG and fractal-based image compression on target acquisition by human observers,” Opt. Eng. 35, 284–288 (1996).
[CrossRef]

Wyrowski, F.

O. Bryngdahl, F. Wyrowski, “Digital holography—computer-generated holograms,” Prog. Opt. 28, 1–86 (1990).
[CrossRef]

F. Wyrowski, O. Bryngdahl, “Speckle-free reconstruction in digital holography,” J. Opt. Soc. Am. A 6, 1171–1174 (1989).
[CrossRef]

Yamaguchi, I.

Yaroslavsky, L. P.

L. P. Yaroslavsky, N. S. Merzlyakov, Methods of Digital Holography (Consultants Bureau, New York, 1980).
[CrossRef]

Zhang, T.

Ziv, J.

J. Ziv, A. Lempel, “A universal algorithm for sequential data compression,” IEEE Trans. IT-23, 337–343 (1977).

Zweig, G.

Appl. Opt. (9)

Appl. Phys. Lett. (1)

J. W. Goodman, R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

IBM J. Research and Dev. (1)

J. W. Goodman, A. M. Silvestri, “Some effects of Fourier domain phase quantization,” IBM J. Research and Dev. 14, 478–484 (1970).
[CrossRef]

IEEE Computer (1)

T. A. Welch, “A technique for high performance data compression,” IEEE Computer 17, 8–19 (1984).
[CrossRef]

IEEE Trans. (2)

J. Ziv, A. Lempel, “A universal algorithm for sequential data compression,” IEEE Trans. IT-23, 337–343 (1977).

A. Vander Lugt, “Signal detection by complex spatial filtering,” IEEE Trans. IT-10, 139–145 (1964).

Int. J. Imaging Syst. Technol. (1)

F. Murtagh, J.-L. Starck, M. Louys, “Very-high-quality image compression based on noise modeling,” Int. J. Imaging Syst. Technol. 9, 38–45 (1998).
[CrossRef]

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

Nerem Record (1)

J. W. Goodman, A. Silvestri, “Digital reconstruction of holographic images,” Nerem Record 10, 118 (1968).

Opt. Acta (1)

R. Bamler, J. Hofer-Alfeis, “Three- and four-dimensional filter operations by coherent optics,” Opt. Acta 29, 747–757 (1982).
[CrossRef]

Opt. Eng. (5)

J. Guerrero-Bermúdez, J. Meneses, O. Gualdrón, “Object recognition using three-dimensional correlation of range images,” Opt. Eng. 39, 2828–2831 (2000).
[CrossRef]

A. Pu, R. F. Denkewalter, D. Psaltis, “Real-time vehicle navigation using a holographic memory,” Opt. Eng. 36, 2737–2746 (1997).
[CrossRef]

S. Qian, A. B. Hollinger, D. J. Williams, D. Manak, “Fast three-dimensional data compression of hyperspectral imagery using vector quantization with spectral-feature-based binary coding,” Opt. Eng. 35, 3242–3249 (1996).
[CrossRef]

G. J. Ewing, C. J. Woodruff, “Comparison of JPEG and fractal-based image compression on target acquisition by human observers,” Opt. Eng. 35, 284–288 (1996).
[CrossRef]

J. Vago, H. Vermeulen, A. Verga, “Fast Fourier transform based image compression algorithm optimized for speckle interferometer measurements,” Opt. Eng. 36, 3052–3063 (1997).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Proc. IRE (1)

D. A. Huffman, “A method for the construction of minimum redundancy codes,” Proc. IRE 40, 1098–1101 (1952).
[CrossRef]

Prog. Opt. (1)

O. Bryngdahl, F. Wyrowski, “Digital holography—computer-generated holograms,” Prog. Opt. 28, 1–86 (1990).
[CrossRef]

Other (9)

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

A. D. McAulay, Optical Computer Architectures (Wiley, New York, 1991).

Ph. Réfrégier, F. Goudail, “Statistical processing of polarization diversity images,” in Optoelectronic Information Processing: Optics for Information Systems, Ph. Réfrégier, B. Javidi, C. Ferreira, S. Vallmitjana, eds., Proc. SPIECR81-13, 262–288 (2001).

M. Rabbani, Selected Papers on Image Coding and Compression, SPIE Milestone SeriesMS48 (SPIE Press, 1992).

L. P. Yaroslavsky, N. S. Merzlyakov, Methods of Digital Holography (Consultants Bureau, New York, 1980).
[CrossRef]

T. Nomura, A. Okazaki, M. Kameda, Y. Morimoto, B. Javidi, “Digital holographic data reconstruction with data compression,” Algorithms and Systems for Optical Information Processing V, B. Javidi, D. Psaltis, ed., Proc. SPIE4471 (2001).

H. J. Caulfield, Handbook of Optical Holography (Academic Press, San Diego, Calif., 1979).

A. Mahalanobis, C. Daniell, “Data compression and correlation filtering,” in Smart Imaging Systems, B. Javidi, ed. SPIE PM91 (SPIE Press, 2001), pp. 111–132.

M. Burrows, D. J. Wheeler, “A block-sorting lossless data compression algorithm,” Digital SRC Report 124, (1994).

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Figures (8)

Fig. 1
Fig. 1

Experimental setup for PSI: M, mirror; BS, beam splitter; SF, spatial filter; L, lens; RP, retardation plate.

Fig. 2
Fig. 2

Illustration of the problem statement: (a) digital hologram H 0 must be compressed and transmitted such that (b) decompressed and reconstructed U 0′ compares closely with the approximation of the original complex amplitude distribution U(x, y, d). PSI, image capture and interferometry stage; DP, digital propagation (reconstruction) stage; ⊗, normalized cross-correlation operation.

Fig. 3
Fig. 3

Set of holograms used in these experiments: (a) through (e) are the amplitudes of the reconstructed wavefronts for holograms No. 1 through No. 5, respectively. Image (f) shows the amplitudes of an example 512 × 512 subset of digital hologram No. 1.

Fig. 4
Fig. 4

Resampling of the digital hologram: (a) a plot of hologram side length (relative to the original side length) against linear and nonlinear correlation performance for three interpolation strategies; (b) searching the z axis for an appropriate d 0 offset for a hologram resize of 0.97 and bilinear interpolation.

Fig. 5
Fig. 5

Resizing hologram No. 1 with three different interpolation strategies and then using only the amplitude information in the reconstructed object plane. Plots for (a) normalized RMS difference, and (b) normalized cross-correlation peak height, show the effect of resizing both without filtering and with 11 × 11 pixel median filtering.

Fig. 6
Fig. 6

Quantization with hologram No. 1: (a) normalized rms difference, and (b) normalized cross-correlation peak height, plotted against the number of bits in each of the real and imaginary values.

Fig. 7
Fig. 7

Reconstructed amplitudes for hologram No. 1 for various numbers of quantization levels and with 11 × 11 pixel median filtering: (a) 4 bits (15 quantization levels); (b) 3 bits (7 quantization levels); (c) 5 quantization levels; (d) 2 bits (3 quantization levels).

Fig. 8
Fig. 8

Removing Fourier coefficients from hologram No. 1: (a) normalized rms difference, and (b) normalized cross-correlation peak height, as functions of DFT coefficients retained, for various median filter neighborhoods.

Tables (2)

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Table 1 Compression with LZ77, LZW, Huffman, and BWa

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Table 2 Compression with LZ77, LZW, Huffman, and BWa

Equations (5)

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Ux, y, z=H0x, y  hx, y, z,
hx, y, z=- iλzexpi 2πλ zexpiπ x2+y2λz
r=uncompressed sizecompressed size,
D=1PU01NxNym=0Nx-1n=0Ny-1U0m, n-U0m, n21/2,
PU0= 1NxNym=0Nx-1n=0Ny-1U0m, n21/2.

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