Abstract

The transmission properties of some bacteriorhodopsin-film spatial light modulators are uniquely suited to allow nonlinear optical image-processing operations to be applied to images with multiplicative noise characteristics. A logarithmic amplitude-transmission characteristic of the film permits the conversion of multiplicative noise to additive noise, which may then be linearly filtered out in the Fourier plane of the transformed image. I present experimental results demonstrating the principle and the capability for several different image and noise situations, including deterministic noise and speckle. The bacteriorhodopsin film studied here displays the logarithmic transmission response for write intensities spanning a dynamic range greater than 2 orders of magnitude.

© 1995 Optical Society of America

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References

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  1. J. D. Downie, J. F. Walkup, “Optimal correlation filters for images with signal-dependent noise,” J. Opt. Soc. Am. A 11, 1599–1609 (1994).
    [CrossRef]
  2. J. F. Walkup, R. C. Choens, “Image processing in signal-dependent noise,” Opt. Eng. 13, 258–266 (1974).
  3. C. Bräuchle, N. Hampp, D. Oesterhelt, “Optical applications of bacteriorhodopsin and its mutated variants,” Adv. Mater. 3, 420–428 (1991).
    [CrossRef]
  4. R. R. Birge, “Photophysics and molecular electronic applications of the rhodopsins,” Ann. Rev. Phys. Chem. 41, 683–733 (1990).
    [CrossRef]
  5. R. Thoma, N. Hampp, C. Bräuchle, D. Oesterhelt, “Bacteriorhodopsin films as spatial light modulators for nonlinear-optical filtering,” Opt. Lett. 16, 651–653 (1991).
    [CrossRef] [PubMed]
  6. Q. W. Song, C. Zhang, R. Gross, R. Birge, “Optical limiting by chemically enhanced bacteriorhodopsin films,” Opt. Lett. 18, 775–777 (1993).
    [CrossRef] [PubMed]
  7. T. Renner, N. Hampp, “Bacteriorhodopsin-films for dynamic time average interferometry,” Opt. Commun. 96, 142–149 (1993).
    [CrossRef]
  8. N. Hampp, R. Thoma, D. Oesterhelt, C. Bräuchle, “Biological photochrome bacteriorhodopsin and its genetic variant ASp96→Asn as media for optical pattern recognition,” Appl. Opt. 31, 1834–1841 (1992).
    [CrossRef] [PubMed]
  9. J. D. Downie, “Real-time holographic image correction using bacteriorhodopsin,” Appl. Opt. 33, 4353–4357 (1994).
    [CrossRef] [PubMed]
  10. J. D. Downie, “Optical logarithmic transformation of speckle images with bacteriorhodopsin films,” Opt. Lett. 20, 201–203 (1995).
    [CrossRef] [PubMed]
  11. A. Miller, D. Oesterhelt, “Kinetic optimization of bacteriorhodopsin by aspartic acid 96 as an internal proton donor,” Biochim. Biophys. Acta 1020, 57–64 (1990).
    [CrossRef]
  12. Q. W. Song, C. Zhang, R. Blumer, R. B. Gross, Z. Chen, R. R. Birge, “Chemically enhanced bacteriorhodopsin thin-film spatial light modulator,” Opt. Lett. 18, 1373–1375 (1993).
    [CrossRef] [PubMed]
  13. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 7, p. 142.
  14. A. V. Oppenheim, R. W. Schafer, T. G. Stockham, “Nonlinear filtering of multiplied and convolved signals,” Proc. IEEE 56, 1264–1291 (1968).
    [CrossRef]
  15. H. H. Arsenault, G. April, “Properties of speckle integrated with a finite aperture and logarithmically transformed,” J. Opt. Soc. Am. 66, 1160–1163 (1976).
    [CrossRef]
  16. H. Kato, J. W. Goodman, “Nonlinear filtering in coherent optical systems through halftone screen processes,” Appl. Opt. 14, 1813–1824 (1975).
    [CrossRef] [PubMed]
  17. J. Khoury, A. M. Biernacki, C. L. Woods, M. Cronin-Golomb, “Photorefractive quadratic processor for signal recovery from multiplicative complex noise,” Opt. Eng. 32, 2872–2876 (1993).
    [CrossRef]
  18. H. H. Arsenault, M. Denis, “Integral expression for transforming signal-dependent noise into signal-independent noise,” Opt. Lett. 6, 210–212 (1981).
    [CrossRef] [PubMed]
  19. P. R. Prucnal, B. E. A. Saleh, “Transformation of image-signal-dependent noise into image-signal-independent noise,” Opt. Lett. 6, 316–318 (1981).
    [CrossRef] [PubMed]
  20. R. B. Gross, K. C. Izgi, R. R. Birge, “Holographic thin films, spatial light modulators and optical associative memories based on bacteriorhodopsin,” in Image Storage and Retrieval Systems, A. A. Jamberdino, W. Niblack, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1662, 186–196 (1992).
  21. D. Zeisel, N. Hampp, “Spectral relationship of light-induced refractive index and absorption changes in bacteriorhodopsin films containing wild-type BRWT and the variant BRD96N,” J. Phys. Chem. 96, 7788–7792 (1992).
    [CrossRef]
  22. J. W. Goodman, Laser Speckle and Related Phenomena, J. C. Dainty, ed., Vol. 9 of Topics in Applied Physics (Springer-Verlag, New York, 1975), p. 10.
    [CrossRef]
  23. J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Chap. 7, p. 350.
  24. M. Tur, K. C. Chin, J. W. Goodman, “When is speckle noise multiplicative?” Appl. Opt. 21, 1157–1159 (1982).
    [CrossRef] [PubMed]

1995 (1)

1994 (2)

1993 (4)

Q. W. Song, C. Zhang, R. Gross, R. Birge, “Optical limiting by chemically enhanced bacteriorhodopsin films,” Opt. Lett. 18, 775–777 (1993).
[CrossRef] [PubMed]

T. Renner, N. Hampp, “Bacteriorhodopsin-films for dynamic time average interferometry,” Opt. Commun. 96, 142–149 (1993).
[CrossRef]

Q. W. Song, C. Zhang, R. Blumer, R. B. Gross, Z. Chen, R. R. Birge, “Chemically enhanced bacteriorhodopsin thin-film spatial light modulator,” Opt. Lett. 18, 1373–1375 (1993).
[CrossRef] [PubMed]

J. Khoury, A. M. Biernacki, C. L. Woods, M. Cronin-Golomb, “Photorefractive quadratic processor for signal recovery from multiplicative complex noise,” Opt. Eng. 32, 2872–2876 (1993).
[CrossRef]

1992 (2)

N. Hampp, R. Thoma, D. Oesterhelt, C. Bräuchle, “Biological photochrome bacteriorhodopsin and its genetic variant ASp96→Asn as media for optical pattern recognition,” Appl. Opt. 31, 1834–1841 (1992).
[CrossRef] [PubMed]

D. Zeisel, N. Hampp, “Spectral relationship of light-induced refractive index and absorption changes in bacteriorhodopsin films containing wild-type BRWT and the variant BRD96N,” J. Phys. Chem. 96, 7788–7792 (1992).
[CrossRef]

1991 (2)

R. Thoma, N. Hampp, C. Bräuchle, D. Oesterhelt, “Bacteriorhodopsin films as spatial light modulators for nonlinear-optical filtering,” Opt. Lett. 16, 651–653 (1991).
[CrossRef] [PubMed]

C. Bräuchle, N. Hampp, D. Oesterhelt, “Optical applications of bacteriorhodopsin and its mutated variants,” Adv. Mater. 3, 420–428 (1991).
[CrossRef]

1990 (2)

R. R. Birge, “Photophysics and molecular electronic applications of the rhodopsins,” Ann. Rev. Phys. Chem. 41, 683–733 (1990).
[CrossRef]

A. Miller, D. Oesterhelt, “Kinetic optimization of bacteriorhodopsin by aspartic acid 96 as an internal proton donor,” Biochim. Biophys. Acta 1020, 57–64 (1990).
[CrossRef]

1982 (1)

1981 (2)

1976 (1)

1975 (1)

1974 (1)

J. F. Walkup, R. C. Choens, “Image processing in signal-dependent noise,” Opt. Eng. 13, 258–266 (1974).

1968 (1)

A. V. Oppenheim, R. W. Schafer, T. G. Stockham, “Nonlinear filtering of multiplied and convolved signals,” Proc. IEEE 56, 1264–1291 (1968).
[CrossRef]

April, G.

Arsenault, H. H.

Biernacki, A. M.

J. Khoury, A. M. Biernacki, C. L. Woods, M. Cronin-Golomb, “Photorefractive quadratic processor for signal recovery from multiplicative complex noise,” Opt. Eng. 32, 2872–2876 (1993).
[CrossRef]

Birge, R.

Birge, R. R.

Q. W. Song, C. Zhang, R. Blumer, R. B. Gross, Z. Chen, R. R. Birge, “Chemically enhanced bacteriorhodopsin thin-film spatial light modulator,” Opt. Lett. 18, 1373–1375 (1993).
[CrossRef] [PubMed]

R. R. Birge, “Photophysics and molecular electronic applications of the rhodopsins,” Ann. Rev. Phys. Chem. 41, 683–733 (1990).
[CrossRef]

R. B. Gross, K. C. Izgi, R. R. Birge, “Holographic thin films, spatial light modulators and optical associative memories based on bacteriorhodopsin,” in Image Storage and Retrieval Systems, A. A. Jamberdino, W. Niblack, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1662, 186–196 (1992).

Blumer, R.

Bräuchle, C.

Chen, Z.

Chin, K. C.

Choens, R. C.

J. F. Walkup, R. C. Choens, “Image processing in signal-dependent noise,” Opt. Eng. 13, 258–266 (1974).

Cronin-Golomb, M.

J. Khoury, A. M. Biernacki, C. L. Woods, M. Cronin-Golomb, “Photorefractive quadratic processor for signal recovery from multiplicative complex noise,” Opt. Eng. 32, 2872–2876 (1993).
[CrossRef]

Denis, M.

Downie, J. D.

Goodman, J. W.

M. Tur, K. C. Chin, J. W. Goodman, “When is speckle noise multiplicative?” Appl. Opt. 21, 1157–1159 (1982).
[CrossRef] [PubMed]

H. Kato, J. W. Goodman, “Nonlinear filtering in coherent optical systems through halftone screen processes,” Appl. Opt. 14, 1813–1824 (1975).
[CrossRef] [PubMed]

J. W. Goodman, Laser Speckle and Related Phenomena, J. C. Dainty, ed., Vol. 9 of Topics in Applied Physics (Springer-Verlag, New York, 1975), p. 10.
[CrossRef]

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Chap. 7, p. 350.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 7, p. 142.

Gross, R.

Gross, R. B.

Q. W. Song, C. Zhang, R. Blumer, R. B. Gross, Z. Chen, R. R. Birge, “Chemically enhanced bacteriorhodopsin thin-film spatial light modulator,” Opt. Lett. 18, 1373–1375 (1993).
[CrossRef] [PubMed]

R. B. Gross, K. C. Izgi, R. R. Birge, “Holographic thin films, spatial light modulators and optical associative memories based on bacteriorhodopsin,” in Image Storage and Retrieval Systems, A. A. Jamberdino, W. Niblack, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1662, 186–196 (1992).

Hampp, N.

T. Renner, N. Hampp, “Bacteriorhodopsin-films for dynamic time average interferometry,” Opt. Commun. 96, 142–149 (1993).
[CrossRef]

D. Zeisel, N. Hampp, “Spectral relationship of light-induced refractive index and absorption changes in bacteriorhodopsin films containing wild-type BRWT and the variant BRD96N,” J. Phys. Chem. 96, 7788–7792 (1992).
[CrossRef]

N. Hampp, R. Thoma, D. Oesterhelt, C. Bräuchle, “Biological photochrome bacteriorhodopsin and its genetic variant ASp96→Asn as media for optical pattern recognition,” Appl. Opt. 31, 1834–1841 (1992).
[CrossRef] [PubMed]

R. Thoma, N. Hampp, C. Bräuchle, D. Oesterhelt, “Bacteriorhodopsin films as spatial light modulators for nonlinear-optical filtering,” Opt. Lett. 16, 651–653 (1991).
[CrossRef] [PubMed]

C. Bräuchle, N. Hampp, D. Oesterhelt, “Optical applications of bacteriorhodopsin and its mutated variants,” Adv. Mater. 3, 420–428 (1991).
[CrossRef]

Izgi, K. C.

R. B. Gross, K. C. Izgi, R. R. Birge, “Holographic thin films, spatial light modulators and optical associative memories based on bacteriorhodopsin,” in Image Storage and Retrieval Systems, A. A. Jamberdino, W. Niblack, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1662, 186–196 (1992).

Kato, H.

Khoury, J.

J. Khoury, A. M. Biernacki, C. L. Woods, M. Cronin-Golomb, “Photorefractive quadratic processor for signal recovery from multiplicative complex noise,” Opt. Eng. 32, 2872–2876 (1993).
[CrossRef]

Miller, A.

A. Miller, D. Oesterhelt, “Kinetic optimization of bacteriorhodopsin by aspartic acid 96 as an internal proton donor,” Biochim. Biophys. Acta 1020, 57–64 (1990).
[CrossRef]

Oesterhelt, D.

N. Hampp, R. Thoma, D. Oesterhelt, C. Bräuchle, “Biological photochrome bacteriorhodopsin and its genetic variant ASp96→Asn as media for optical pattern recognition,” Appl. Opt. 31, 1834–1841 (1992).
[CrossRef] [PubMed]

R. Thoma, N. Hampp, C. Bräuchle, D. Oesterhelt, “Bacteriorhodopsin films as spatial light modulators for nonlinear-optical filtering,” Opt. Lett. 16, 651–653 (1991).
[CrossRef] [PubMed]

C. Bräuchle, N. Hampp, D. Oesterhelt, “Optical applications of bacteriorhodopsin and its mutated variants,” Adv. Mater. 3, 420–428 (1991).
[CrossRef]

A. Miller, D. Oesterhelt, “Kinetic optimization of bacteriorhodopsin by aspartic acid 96 as an internal proton donor,” Biochim. Biophys. Acta 1020, 57–64 (1990).
[CrossRef]

Oppenheim, A. V.

A. V. Oppenheim, R. W. Schafer, T. G. Stockham, “Nonlinear filtering of multiplied and convolved signals,” Proc. IEEE 56, 1264–1291 (1968).
[CrossRef]

Prucnal, P. R.

Renner, T.

T. Renner, N. Hampp, “Bacteriorhodopsin-films for dynamic time average interferometry,” Opt. Commun. 96, 142–149 (1993).
[CrossRef]

Saleh, B. E. A.

Schafer, R. W.

A. V. Oppenheim, R. W. Schafer, T. G. Stockham, “Nonlinear filtering of multiplied and convolved signals,” Proc. IEEE 56, 1264–1291 (1968).
[CrossRef]

Song, Q. W.

Stockham, T. G.

A. V. Oppenheim, R. W. Schafer, T. G. Stockham, “Nonlinear filtering of multiplied and convolved signals,” Proc. IEEE 56, 1264–1291 (1968).
[CrossRef]

Thoma, R.

Tur, M.

Walkup, J. F.

J. D. Downie, J. F. Walkup, “Optimal correlation filters for images with signal-dependent noise,” J. Opt. Soc. Am. A 11, 1599–1609 (1994).
[CrossRef]

J. F. Walkup, R. C. Choens, “Image processing in signal-dependent noise,” Opt. Eng. 13, 258–266 (1974).

Woods, C. L.

J. Khoury, A. M. Biernacki, C. L. Woods, M. Cronin-Golomb, “Photorefractive quadratic processor for signal recovery from multiplicative complex noise,” Opt. Eng. 32, 2872–2876 (1993).
[CrossRef]

Zeisel, D.

D. Zeisel, N. Hampp, “Spectral relationship of light-induced refractive index and absorption changes in bacteriorhodopsin films containing wild-type BRWT and the variant BRD96N,” J. Phys. Chem. 96, 7788–7792 (1992).
[CrossRef]

Zhang, C.

Adv. Mater. (1)

C. Bräuchle, N. Hampp, D. Oesterhelt, “Optical applications of bacteriorhodopsin and its mutated variants,” Adv. Mater. 3, 420–428 (1991).
[CrossRef]

Ann. Rev. Phys. Chem. (1)

R. R. Birge, “Photophysics and molecular electronic applications of the rhodopsins,” Ann. Rev. Phys. Chem. 41, 683–733 (1990).
[CrossRef]

Appl. Opt. (4)

Biochim. Biophys. Acta (1)

A. Miller, D. Oesterhelt, “Kinetic optimization of bacteriorhodopsin by aspartic acid 96 as an internal proton donor,” Biochim. Biophys. Acta 1020, 57–64 (1990).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

J. Phys. Chem. (1)

D. Zeisel, N. Hampp, “Spectral relationship of light-induced refractive index and absorption changes in bacteriorhodopsin films containing wild-type BRWT and the variant BRD96N,” J. Phys. Chem. 96, 7788–7792 (1992).
[CrossRef]

Opt. Commun. (1)

T. Renner, N. Hampp, “Bacteriorhodopsin-films for dynamic time average interferometry,” Opt. Commun. 96, 142–149 (1993).
[CrossRef]

Opt. Eng. (2)

J. Khoury, A. M. Biernacki, C. L. Woods, M. Cronin-Golomb, “Photorefractive quadratic processor for signal recovery from multiplicative complex noise,” Opt. Eng. 32, 2872–2876 (1993).
[CrossRef]

J. F. Walkup, R. C. Choens, “Image processing in signal-dependent noise,” Opt. Eng. 13, 258–266 (1974).

Opt. Lett. (6)

Proc. IEEE (1)

A. V. Oppenheim, R. W. Schafer, T. G. Stockham, “Nonlinear filtering of multiplied and convolved signals,” Proc. IEEE 56, 1264–1291 (1968).
[CrossRef]

Other (4)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 7, p. 142.

R. B. Gross, K. C. Izgi, R. R. Birge, “Holographic thin films, spatial light modulators and optical associative memories based on bacteriorhodopsin,” in Image Storage and Retrieval Systems, A. A. Jamberdino, W. Niblack, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1662, 186–196 (1992).

J. W. Goodman, Laser Speckle and Related Phenomena, J. C. Dainty, ed., Vol. 9 of Topics in Applied Physics (Springer-Verlag, New York, 1975), p. 10.
[CrossRef]

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Chap. 7, p. 350.

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Figures (12)

Fig. 1
Fig. 1

Schematic of BR photocycle. The numbers in parentheses indicate peak wavelengths of the absorption spectra at the bR state and the M state. The transition time from bR→M is ~50 μs, and the thermal relaxation time from M→bR is ~10 ms for BR in its native form.

Fig. 2
Fig. 2

Schematic of the optical setup for making measurements of transmission characteristics of BR film. The wavelengths of the write beam and the readout beam were both 514.5 nm.

Fig. 3
Fig. 3

Transmittance of read-beam amplitude as a function of write-beam power density for wild-type bacteriorhodopsin film. Both beams have wavelengths of 514.5 nm. The square boxes are experimentally measured data points, and the solid black line is the best-fit logarithmic curve.

Fig. 4
Fig. 4

Optical setup for logarithmic transformation and subsequent Fourier-plane spatial filtering of images with multiplicative noise. Shutter A is opened during the image-recording process in BR film, and shutter B is opened during the read process and the image-processing operation. The argonion (Ar+) laser wavelength used is 514.5 nm.

Fig. 5
Fig. 5

(a) Original unfiltered input pattern of multiplicative crossed gratings; (b) unfiltered image of the logarithmically transformed crossed-gratings pattern transmitted by BR film.

Fig. 6
Fig. 6

(a) Fourier spectrum of the original multiplicative crossed-grating image; (b) Fourier spectrum of the logarithmically transformed crossed-grating image.

Fig. 7
Fig. 7

Fourier-plane filter used in image-processing experiments of the original and the logarithmically transformed versions of the crossed-gratings pattern.

Fig. 8
Fig. 8

(a) Output image after a filtering operation in the Fourier plane of the original multiplicative crossed-grating image; (b) output image after a filtering operation in the Fourier plane of the logarithmically transformed version of the crossed-grating image.

Fig. 9
Fig. 9

(a) Original unfiltered input pattern of an X multiplied by a horizontal grating; (b) unfiltered image of the logarithmically transformed version of the same pattern transmitted by BR film.

Fig. 10
Fig. 10

(a) Output image after a filtering operation in the Fourier plane of the original pattern of X multiplied by a horizontal grating; (b) output image after a filtering operation in the Fourier plane of the logarithmically transformed version of the same pattern.

Fig. 11
Fig. 11

(a) Original unfiltered input pattern of an X with speckle noise; (b) unfiltered image of the logarithmically transformed version of the same pattern transmitted by BR film.

Fig. 12
Fig. 12

(a) Output image after a filtering operation in the Fourier plane of the original pattern of X with speckle noise; (b) output image after a filtering operation in the Fourier plane of the logarithmically transformed version of the same pattern.

Equations (7)

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A trans , read = K log ( E write ) + c
r ( x , y ) = s ( x , y ) n ( x , y ) ,
R ( u , v ) = S ( u , v ) N ( u , v ) ,
log [ r ( x , y ) ] = log [ s ( x , y ) ] + log [ n ( x , y ) ] ,
r sp ( x , y ) = s ( x , y ) n sp ( x , y ) ,
p n [ n sp ( x , y ) ] = exp [ - n sp ( x , y ) ] .
log [ r sp ( x , y ) ] = log [ s ( x , y ) ] + log [ n sp ( x , y ) ] ,

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