Abstract

Laser light, which is doubly phase modulated by an ultrasonic wave, can be utilized for speckle reduction. The double phase modulation is found to be more effective for speckle reduction than single phase modulation, since the doubly modulated laser beam for illumination is much degraded in spatial coherence with the same ultrasonic conditions. Average contrast is discussed analytically and experimentally as a measure of image-speckle reduction. Agreement between the measured and calculated results are recognized to the extent that the ultrasonic wave can be regarded as a pure phase grating. The average contrasts for two kinds of diffuser decrease similarly down to a minimum of ~0.4 by increasing the ultrasonic power.

© 1980 Optical Society of America

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References

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1980

1979

1978

Y. Imai, Y. Ohtsuka, Opt. Commun. 27, 18 (1978).
[CrossRef]

1976

F. P. Chiang, R. M. Juang, Appl. Opt. 15, 2199 (1976).
[CrossRef] [PubMed]

P. J. Chandley, Opt. Quantum. Electron. 8, 323 (1976).
[CrossRef]

H. Fujii et al., Opt. Commun. 16, 68 (1976).
[CrossRef]

1975

1974

H. Fujii, T. Asakura, Opt. Commun. 4, 32 (1974).
[CrossRef]

1973

1972

T. Asakura et al., Opt. Acta 19, 273 (1972).
[CrossRef]

1971

J. C. Dainty, W. T. Welford, Opt. Commun. 3, 289 (1971).
[CrossRef]

S. Lowenthal, D. Joyeux, J. Opt. Soc. Am. 69, 847 (1971).
[CrossRef]

E. Schröder, Opt. Commun. 3, 68 (1971).
[CrossRef]

1968

1967

W. R. Klein, B. D. Cook, IEEE Trans. Sonics Ultrason. SU-14, 123 (1967).
[CrossRef]

Asakura, T.

H. Fujii, T. Asakura, Opt. Commun. 4, 32 (1974).
[CrossRef]

T. Asakura et al., Opt. Acta 19, 273 (1972).
[CrossRef]

Chandley, P. J.

P. J. Chandley, Opt. Quantum. Electron. 8, 323 (1976).
[CrossRef]

Chiang, F. P.

Cloud, G.

Cook, B. D.

W. R. Klein, B. D. Cook, IEEE Trans. Sonics Ultrason. SU-14, 123 (1967).
[CrossRef]

Dainty, J. C.

J. C. Dainty, W. T. Welford, Opt. Commun. 3, 289 (1971).
[CrossRef]

Davenport, W. B.

W. B. Davenport, W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1968).

Fujii, H.

H. Fujii et al., Opt. Commun. 16, 68 (1976).
[CrossRef]

H. Fujii, T. Asakura, Opt. Commun. 4, 32 (1974).
[CrossRef]

George, N.

Goodman, J. W.

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

Imai, Y.

Y. Imai, Y. Ohtsuka, Appl. Opt. 19, 542 (1980).
[CrossRef] [PubMed]

Y. Ohtsuka, Y. Imai, J. Opt. Soc. Am. 69, 684 (1979).
[CrossRef]

Y. Imai, Y. Ohtsuka, Opt. Commun. 27, 18 (1978).
[CrossRef]

Y. Ohtsuka, Y. Imai, in Proceedings, ICO-11 Conference (1978), p. 515.

Jain, A.

Joyeux, D.

Juang, R. M.

Klein, W. R.

W. R. Klein, B. D. Cook, IEEE Trans. Sonics Ultrason. SU-14, 123 (1967).
[CrossRef]

Leith, E. N.

Lowenthal, S.

Ohtsuka, Y.

Y. Imai, Y. Ohtsuka, Appl. Opt. 19, 542 (1980).
[CrossRef] [PubMed]

Y. Ohtsuka, Y. Imai, J. Opt. Soc. Am. 69, 684 (1979).
[CrossRef]

Y. Imai, Y. Ohtsuka, Opt. Commun. 27, 18 (1978).
[CrossRef]

Y. Ohtsuka, Y. Imai, in Proceedings, ICO-11 Conference (1978), p. 515.

Root, W. L.

W. B. Davenport, W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1968).

Schröder, E.

E. Schröder, Opt. Commun. 3, 68 (1971).
[CrossRef]

Upatnieks, J.

Wang, E. Y.

Welford, W. T.

J. C. Dainty, W. T. Welford, Opt. Commun. 3, 289 (1971).
[CrossRef]

Yu, F. T. S.

Appl. Opt.

IEEE Trans. Sonics Ultrason.

W. R. Klein, B. D. Cook, IEEE Trans. Sonics Ultrason. SU-14, 123 (1967).
[CrossRef]

J. Opt. Soc. Am.

Opt. Acta

T. Asakura et al., Opt. Acta 19, 273 (1972).
[CrossRef]

Opt. Commun.

H. Fujii, T. Asakura, Opt. Commun. 4, 32 (1974).
[CrossRef]

H. Fujii et al., Opt. Commun. 16, 68 (1976).
[CrossRef]

E. Schröder, Opt. Commun. 3, 68 (1971).
[CrossRef]

J. C. Dainty, W. T. Welford, Opt. Commun. 3, 289 (1971).
[CrossRef]

Y. Imai, Y. Ohtsuka, Opt. Commun. 27, 18 (1978).
[CrossRef]

Opt. Quantum. Electron.

P. J. Chandley, Opt. Quantum. Electron. 8, 323 (1976).
[CrossRef]

Other

Y. Ohtsuka, Y. Imai, in Proceedings, ICO-11 Conference (1978), p. 515.

W. B. Davenport, W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1968).

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

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram for the observation of the image-speckle pattern.

Fig. 2
Fig. 2

Experimental arrangements for measuring the average contrasts by using doubly ultrasound-modulated laser light.

Fig. 3
Fig. 3

Image-speckle patterns. Photographs (a) and (b) were taken without and with ultrasonic modulation of υ = 1.2.

Fig. 4
Fig. 4

Calculated and measured average contrasts. Variances of phase are 5.0 and 10.0 for (a) and (b), respectively. Solid lines and dots are results of computer calculations and experiments, respectively.

Fig. 5
Fig. 5

Spatial coherence conditions of the doubly ultrasound-modulated laser light. Solid lines and dots denote the theoretical and experimental values, respectively.

Fig. 6
Fig. 6

Comparison of the calculated average contrasts obtained by singly (broken line) and doubly (solid line) ultrasound-modulated laser light. Variance of phase is 10.0.

Equations (10)

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E ( z ) = E 0 ( x ) 0 ( x ) h ( z x ) d x ,
I ( z ) = E ( z ) E * ( z ) = Γ ( x 1 , x 2 ) R ( x 1 , x 2 ) h ( z x 1 ) h * ( z x 2 ) d x 1 d x 2 ,
R ( x 1 , x 2 ) = A 2 exp { i [ ϕ ( x 1 ) ϕ ( x 2 ) ] } = A 2 exp { ϕ 2 [ 1 ϕ ( x 1 ) ϕ ( x 2 ) / ϕ 2 ] } ,
I 2 ( z ) = Γ ( x 1 , x 2 ) Γ ( x 3 , x 4 ) R ( x 1 , x 2 , x 3 , x 4 ) × h ( z x 1 ) h * ( z x 2 ) h ( z x 3 ) h * ( z x 4 ) × d x 1 d x 2 d x 3 d x 4 ,
R ( x 1 , x 2 , x 3 , x 4 ) = 0 ( x 1 ) 0 * ( x 2 ) 0 ( x 3 ) 0 * ( x 4 ) = A 4 exp [ 2 ϕ 2 + ϕ ( x 1 ) ϕ ( x 2 ) + ϕ ( x 3 ) ϕ ( x 4 ) ϕ ( x 1 ) ϕ ( x 3 ) ϕ ( x 2 ) ϕ ( x 4 ) + ϕ ( x 1 ) ϕ ( x 4 ) + ϕ ( x 2 ) ϕ ( x 3 ) ] .
C = [ I 2 I 2 I 2 ] 1 / 2
Γ ( x p , x q ) = Γ 0 ( x p , x q ) J 0 [ 4 υ | sin ( K / 2 ) ( x p x q ) | ] .
ϕ ( x 1 ) ϕ ( x 2 ) / ϕ 2 = exp [ ( x 1 x 2 ) 2 l 2 ] ,
h ( z x ) = sinc [ B ( z x ) ] ,
C = [ J 0 [ 4 υ | sin ( K / 2 ) ( x 1 x 2 ) | ] J 0 [ 4 υ | sin ( K / 2 ) ( x 3 x 4 ) | ] × exp ( ϕ 2 { exp [ ( x 1 x 2 ) 2 / l 2 ] + exp [ ( x 3 x 4 ) 2 / l 2 ] } ) × [ exp ( ϕ 2 { exp [ ( x 1 x 3 ) 2 / l 2 ] + exp [ ( x 2 x 4 ) 2 / l 2 ] exp [ ( x 1 x 4 ) 2 / l 2 ] exp [ ( x 2 x 3 ) 2 / l 2 ] } ) 1.0 ] × sinc [ B ( z x 1 ) ] sinc [ B ( z x 2 ) ] sinc [ B ( z x 3 ) ] sinc [ B ( z x 4 ) ] × d x 1 d x 2 d x 3 d x 4 } 1 / 2 × [ J 0 [ 4 υ | sin ( K / 2 ) ( x 1 x 2 ) | ] × exp ( ϕ 2 { exp [ ( x 1 x 2 ) 2 / l 2 ] } ) × sinc [ B ( z x 1 ) ] sinc [ B ( z x 2 ) ] d x 1 d x 2 ] 1 .

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