Abstract

A method of optical image subtraction is proposed. It provides parallel and real-time amplitude subtraction of two images by using holographic interference in photorefractive media. This new method provides an automatic phase shift of 180 deg between the two images and may be viewed as a real-time implementation of Gabor’s image-subtraction technique. Some experimental results are presented and discussed.

© 1988 Optical Society of America

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References

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  1. D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 116 (1965).
    [CrossRef]
  2. See, for example, J. F. Ebersole, Opt. Eng. 14, 436 (1975).
  3. See, for example, H. K. Liu, T. H. Chao, Proc. Soc. Photo-Opt. Instrum. Eng. 638, 55 (1986).
  4. M. D. Ewbank, P. Yeh, J. Feinberg, Opt. Lett 10, 282 (1985).
    [CrossRef] [PubMed]
  5. A. E. T. Chiou, P. Yeh, Opt. Lett. 11, 306 (1986).
    [CrossRef] [PubMed]
  6. A. E. T. Chiou, P. Yeh, M. Khoshnevisan, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 201 (1986).
  7. S. K. Kwong, G. A. Rakuljuc, A. Yariv, Appl. Phys. Lett. 48, 201 (1986).
    [CrossRef]
  8. G. G. Stokes, Camb. Dubl. Math. J. 4, 1 (1849).
  9. J. Feinberg, Opt. Lett. 7, 486 (1982).
    [CrossRef] [PubMed]

1986 (4)

See, for example, H. K. Liu, T. H. Chao, Proc. Soc. Photo-Opt. Instrum. Eng. 638, 55 (1986).

A. E. T. Chiou, P. Yeh, M. Khoshnevisan, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 201 (1986).

S. K. Kwong, G. A. Rakuljuc, A. Yariv, Appl. Phys. Lett. 48, 201 (1986).
[CrossRef]

A. E. T. Chiou, P. Yeh, Opt. Lett. 11, 306 (1986).
[CrossRef] [PubMed]

1985 (1)

M. D. Ewbank, P. Yeh, J. Feinberg, Opt. Lett 10, 282 (1985).
[CrossRef] [PubMed]

1982 (1)

1975 (1)

See, for example, J. F. Ebersole, Opt. Eng. 14, 436 (1975).

1965 (1)

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 116 (1965).
[CrossRef]

1849 (1)

G. G. Stokes, Camb. Dubl. Math. J. 4, 1 (1849).

Brumm, D.

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 116 (1965).
[CrossRef]

Chao, T. H.

See, for example, H. K. Liu, T. H. Chao, Proc. Soc. Photo-Opt. Instrum. Eng. 638, 55 (1986).

Chiou, A. E. T.

A. E. T. Chiou, P. Yeh, M. Khoshnevisan, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 201 (1986).

A. E. T. Chiou, P. Yeh, Opt. Lett. 11, 306 (1986).
[CrossRef] [PubMed]

Ebersole, J. F.

See, for example, J. F. Ebersole, Opt. Eng. 14, 436 (1975).

Ewbank, M. D.

M. D. Ewbank, P. Yeh, J. Feinberg, Opt. Lett 10, 282 (1985).
[CrossRef] [PubMed]

Feinberg, J.

M. D. Ewbank, P. Yeh, J. Feinberg, Opt. Lett 10, 282 (1985).
[CrossRef] [PubMed]

J. Feinberg, Opt. Lett. 7, 486 (1982).
[CrossRef] [PubMed]

Funkhouser, A.

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 116 (1965).
[CrossRef]

Gabor, D.

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 116 (1965).
[CrossRef]

Khoshnevisan, M.

A. E. T. Chiou, P. Yeh, M. Khoshnevisan, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 201 (1986).

Kwong, S. K.

S. K. Kwong, G. A. Rakuljuc, A. Yariv, Appl. Phys. Lett. 48, 201 (1986).
[CrossRef]

Liu, H. K.

See, for example, H. K. Liu, T. H. Chao, Proc. Soc. Photo-Opt. Instrum. Eng. 638, 55 (1986).

Rakuljuc, G. A.

S. K. Kwong, G. A. Rakuljuc, A. Yariv, Appl. Phys. Lett. 48, 201 (1986).
[CrossRef]

Restrick, R.

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 116 (1965).
[CrossRef]

Stokes, G. G.

G. G. Stokes, Camb. Dubl. Math. J. 4, 1 (1849).

Stroke, G. W.

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 116 (1965).
[CrossRef]

Yariv, A.

S. K. Kwong, G. A. Rakuljuc, A. Yariv, Appl. Phys. Lett. 48, 201 (1986).
[CrossRef]

Yeh, P.

A. E. T. Chiou, P. Yeh, M. Khoshnevisan, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 201 (1986).

A. E. T. Chiou, P. Yeh, Opt. Lett. 11, 306 (1986).
[CrossRef] [PubMed]

M. D. Ewbank, P. Yeh, J. Feinberg, Opt. Lett 10, 282 (1985).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

S. K. Kwong, G. A. Rakuljuc, A. Yariv, Appl. Phys. Lett. 48, 201 (1986).
[CrossRef]

Camb. Dubl. Math. J. (1)

G. G. Stokes, Camb. Dubl. Math. J. 4, 1 (1849).

Opt. Eng. (1)

See, for example, J. F. Ebersole, Opt. Eng. 14, 436 (1975).

Opt. Lett (1)

M. D. Ewbank, P. Yeh, J. Feinberg, Opt. Lett 10, 282 (1985).
[CrossRef] [PubMed]

Opt. Lett. (2)

Phys. Lett. (1)

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 116 (1965).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

A. E. T. Chiou, P. Yeh, M. Khoshnevisan, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 201 (1986).

See, for example, H. K. Liu, T. H. Chao, Proc. Soc. Photo-Opt. Instrum. Eng. 638, 55 (1986).

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Figures (3)

Fig. 1
Fig. 1

Schematic of a real-time optical image-subtraction system. Transparencies T1 and T2 imprinted with images are backilluminated by mutually incoherent light sources with amplitudes A and B, and the throughputs are directed to the input ports of a Mach–Zehnder interferometer. Beam splitter BS1 mixes this light into two beams, E1 and E2, which are then interfered in a photorefractive BaTiO3 crystal. Spatial information on E2 is removed by pinhole PH. The interference pattern containing image information T1 is 180 deg out of phase with respect to the pattern containing image information T2. When read out by a reference beam that is then sampled through beam splitter BS2, the intensity pattern will correspond to an algebraic subtraction of the two complex image amplitudes.

Fig. 2
Fig. 2

Experimental setup used to demonstrate real-time optical image subtraction. The laser output is isolated and then split into a reference and a main beam by wedge W. The main beam is split into two components that are made mutually incoherent by having a sufficiently large path-length difference. These beams illuminate two transparencies T1 and T2. The image-bearing beams are mixed on beam splitter BS1 and made to interfere in the BaTiO3 crystal. Spatial information is removed from one of the beams by the lens L3 and pinhole PH arrangement. The reference beam reading the holograms written in the crystal is sampled at the output of beam splitter BS2 and imaged onto the screen. FR, Faraday rotator; P’s, polarizers; L1–L6, lenses; M1–M9, mirrors. An alternative scheme using self-pumping of the input beams (with no pinhole or reference beam) can also be used for the subtraction.

Fig. 3
Fig. 3

Photographs of the original images impressed on the input beams to the Mach–Zehnder interferometer and the output subtraction observed at the screen (referring to Fig. 2). In the first case two uniform Gaussian beams are subtracted (exposure time for the subtraction photo is 25 times longer). In the second case a resolution chart image is subtracted from a Gaussian beam.

Equations (7)

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E 1 = ( t T 1 A + r T 2 B ) exp ( - i k 1 · r ) , E 2 = ( r T 1 A + t T 2 B ) exp ( - i k 2 · r ) ,
I = ( r t * T 1 2 A 2 + t r * T 2 2 B 2 ) exp ( - i K · r ) + c . c . ,
r t * + t r * = 0 ,
I = r t * ( T 1 2 A 2 - T 2 2 B 2 ) exp ( - i K · r ) + c . c .
E 2 = ( r A + t B ) exp ( - i k 2 · r ) ,
I = ( r t * T 1 * A 2 + t r * T 2 * B 2 ) exp ( - i K · r ) + c . c . ,
I = r t * ( T 1 * A 2 - T 2 * B 2 ) exp ( - i K · r ) + c . c .

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