Abstract

The random-walk model is employed to simulate modulated speckle patterns. We demonstrate that the geometrical image approximation fails to describe the modulated speckle pattern. A new approach to analyzing this phenomenon is proposed. The validity of the approximations employed is verified by comparison of the simulation with the experimental results. Speckle metrological applications and phase measurement techniques could be improved by taking advantage of this model.

© 2003 Optical Society of America

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References

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  1. A. Zardecki, Inverse Source Problems, H. P. Baltes, ed. (Springer-Verlag, Berlin, 1985), p. 155.
  2. J. C. Dainty, ed., Laser Speckle and Related Phenomena (Springer-Verlag, Berlin, 1975).
    [CrossRef]
  3. M. Tebaldi, A. Lencina, and N. Bolognini, Opt. Commun. 202, 257 (2002).
    [CrossRef]
  4. L. Angel, M. Tebaldi, M. Trivi, and N. Bolognini, Opt. Lett. 27, 506 (2002).
    [CrossRef]
  5. R. P. Khetan and F. P. Chiang, Appl. Opt. 15, 2205 (1976).
    [CrossRef] [PubMed]
  6. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996), p. 111.
  7. E. Jakeman, Opt. Eng. 23, 453 (1984).
    [CrossRef]
  8. G. Marsaglia and A. Zaman, Ann. Appl. Probab. 1, 462 (1991).
    [CrossRef]
  9. K. Uno, J. Uozumi, and T. Asakura, Opt. Commun. 114, 203 (1995).
    [CrossRef]
  10. M. Tebaldi, L. Ángel, M. Trivi, and N. Bolognini, J. Opt. Soc. Am. A 20, 116 (2003).
    [CrossRef]

2003 (1)

2002 (2)

M. Tebaldi, A. Lencina, and N. Bolognini, Opt. Commun. 202, 257 (2002).
[CrossRef]

L. Angel, M. Tebaldi, M. Trivi, and N. Bolognini, Opt. Lett. 27, 506 (2002).
[CrossRef]

1996 (1)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996), p. 111.

1995 (1)

K. Uno, J. Uozumi, and T. Asakura, Opt. Commun. 114, 203 (1995).
[CrossRef]

1991 (1)

G. Marsaglia and A. Zaman, Ann. Appl. Probab. 1, 462 (1991).
[CrossRef]

1985 (1)

A. Zardecki, Inverse Source Problems, H. P. Baltes, ed. (Springer-Verlag, Berlin, 1985), p. 155.

1984 (1)

E. Jakeman, Opt. Eng. 23, 453 (1984).
[CrossRef]

1976 (1)

1975 (1)

J. C. Dainty, ed., Laser Speckle and Related Phenomena (Springer-Verlag, Berlin, 1975).
[CrossRef]

Angel, L.

Ángel, L.

Asakura, T.

K. Uno, J. Uozumi, and T. Asakura, Opt. Commun. 114, 203 (1995).
[CrossRef]

Bolognini, N.

Chiang, F. P.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996), p. 111.

Jakeman, E.

E. Jakeman, Opt. Eng. 23, 453 (1984).
[CrossRef]

Khetan, R. P.

Lencina, A.

M. Tebaldi, A. Lencina, and N. Bolognini, Opt. Commun. 202, 257 (2002).
[CrossRef]

Marsaglia, G.

G. Marsaglia and A. Zaman, Ann. Appl. Probab. 1, 462 (1991).
[CrossRef]

Tebaldi, M.

Trivi, M.

Uno, K.

K. Uno, J. Uozumi, and T. Asakura, Opt. Commun. 114, 203 (1995).
[CrossRef]

Uozumi, J.

K. Uno, J. Uozumi, and T. Asakura, Opt. Commun. 114, 203 (1995).
[CrossRef]

Zaman, A.

G. Marsaglia and A. Zaman, Ann. Appl. Probab. 1, 462 (1991).
[CrossRef]

Zardecki, A.

A. Zardecki, Inverse Source Problems, H. P. Baltes, ed. (Springer-Verlag, Berlin, 1985), p. 155.

Ann. Appl. Probab. (1)

G. Marsaglia and A. Zaman, Ann. Appl. Probab. 1, 462 (1991).
[CrossRef]

Appl. Opt. (1)

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

Opt. Commun. (2)

K. Uno, J. Uozumi, and T. Asakura, Opt. Commun. 114, 203 (1995).
[CrossRef]

M. Tebaldi, A. Lencina, and N. Bolognini, Opt. Commun. 202, 257 (2002).
[CrossRef]

Opt. Eng. (1)

E. Jakeman, Opt. Eng. 23, 453 (1984).
[CrossRef]

Opt. Lett. (1)

Other (3)

A. Zardecki, Inverse Source Problems, H. P. Baltes, ed. (Springer-Verlag, Berlin, 1985), p. 155.

J. C. Dainty, ed., Laser Speckle and Related Phenomena (Springer-Verlag, Berlin, 1975).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996), p. 111.

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Figures (1)

Fig. 1
Fig. 1

(a) Experimental modulated speckle pattern. Theoretically modulated speckle pattern obtained by use of (b) geometrical image approximation and (c) local phase approximation.

Equations (8)

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UiX,Y=U0x,yexp-jkRλRPu,v×expjk2fu2+v2exp-jkRλRdxdydudv,
UiX,Y=1λ2Z0ZCh=1nU0x,yahuh,vh×exp-jk2ZCdh sin αh-Y2+dh cos αh-X2×exp-jk2Z0dh sin αh-y2+dh cos αh-x2×expjkuhxZ0+XZC+vhyZ0+YZC×expjkdh22f-Z0+ZCdxdyduhdvh.
UiX,Y=1λ2Z0ZCq=1r h=1nUqhX,Y×expjϕq+ϕhX,Y,
ϕhX,Y=-2kdhZCY sin αh+X cos αh,
UqhX,Y=dxdyUqx,yAhx,y;X,Y,
Ahx,y;X,Y=ahuh,vh×expjkuhxZ0+YZC+yhyZ0+YZCduhdvh.
IiX,Y=2λ2Z0ZC21+cos2kdXZC×q=1rUq2+2q=1r-1 s>qrUqUs cosϕq-ϕs.
IiX,Yλ2d0di22=q=1rUq21+coskdxqZ0+XZC+q=1r-1 s>qrUqUs cosϕq-ϕs+k2Z0yq2-ys2+xq2-xs2×coskd2Z0xq-xs+coskdxq+xs2Z0+XZC.

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