Abstract

This paper proposes a new displacement method for measuring speckles using a 2-D level-crossing technique. The crossing points in space of the speckle intensity traversing a specified level are analyzed twodimensionally by using a TV-computer system. In an actual analysis, an occurrence rate histogram of the distance vectors determined by connecting the crossing points obtainable before and after displacement of speckles is investigated. It is found that the vectorial displacement of speckles can be measured from the position of the maximum occurrence in the bivariate histogram with respect to the magnitude and angle by which the displacement vector is characterized. The vectorial displacement of speckles is related to the movement of an object.

© 1983 Optical Society of America

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References

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  1. K. J. Ebeling, Opt. Acta 26, 1505 (1979).
    [Crossref]
  2. K. J. Ebeling, Opt. Acta 26, 1345 (1979).
    [Crossref]
  3. N. Takai, T. Iwai, T. Asakura, J. Opt. Soc. Am. 70, 450 (1980).
    [Crossref]
  4. N. Takai, T. Iwai, T. Asakura, Opt. Eng. 20, 320 (1981).
    [Crossref]
  5. T. Iwai, N. Takai, T. Asakura, Opt. Acta 28, 857 (1981).
    [Crossref]
  6. E. Archbold, J. M. Burch, A. E. Ennos, Opt. Acta 17, 883 (1970).
    [Crossref]
  7. A. E. Ennos, “Speckle Interferometry,” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer, Berlin, 1975), pp. 203–253.
    [Crossref]
  8. T. Asakura, N. Takai, Appl. Phys. 25, 179 (1981).
    [Crossref]
  9. S. Jutamulia, H. Fujii, T. Asakura, Opt. Laser Technol. 15, 101 (1983).
    [Crossref]

1983 (1)

S. Jutamulia, H. Fujii, T. Asakura, Opt. Laser Technol. 15, 101 (1983).
[Crossref]

1981 (3)

T. Asakura, N. Takai, Appl. Phys. 25, 179 (1981).
[Crossref]

N. Takai, T. Iwai, T. Asakura, Opt. Eng. 20, 320 (1981).
[Crossref]

T. Iwai, N. Takai, T. Asakura, Opt. Acta 28, 857 (1981).
[Crossref]

1980 (1)

1979 (2)

K. J. Ebeling, Opt. Acta 26, 1505 (1979).
[Crossref]

K. J. Ebeling, Opt. Acta 26, 1345 (1979).
[Crossref]

1970 (1)

E. Archbold, J. M. Burch, A. E. Ennos, Opt. Acta 17, 883 (1970).
[Crossref]

Archbold, E.

E. Archbold, J. M. Burch, A. E. Ennos, Opt. Acta 17, 883 (1970).
[Crossref]

Asakura, T.

S. Jutamulia, H. Fujii, T. Asakura, Opt. Laser Technol. 15, 101 (1983).
[Crossref]

T. Asakura, N. Takai, Appl. Phys. 25, 179 (1981).
[Crossref]

T. Iwai, N. Takai, T. Asakura, Opt. Acta 28, 857 (1981).
[Crossref]

N. Takai, T. Iwai, T. Asakura, Opt. Eng. 20, 320 (1981).
[Crossref]

N. Takai, T. Iwai, T. Asakura, J. Opt. Soc. Am. 70, 450 (1980).
[Crossref]

Burch, J. M.

E. Archbold, J. M. Burch, A. E. Ennos, Opt. Acta 17, 883 (1970).
[Crossref]

Ebeling, K. J.

K. J. Ebeling, Opt. Acta 26, 1505 (1979).
[Crossref]

K. J. Ebeling, Opt. Acta 26, 1345 (1979).
[Crossref]

Ennos, A. E.

E. Archbold, J. M. Burch, A. E. Ennos, Opt. Acta 17, 883 (1970).
[Crossref]

A. E. Ennos, “Speckle Interferometry,” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer, Berlin, 1975), pp. 203–253.
[Crossref]

Fujii, H.

S. Jutamulia, H. Fujii, T. Asakura, Opt. Laser Technol. 15, 101 (1983).
[Crossref]

Iwai, T.

T. Iwai, N. Takai, T. Asakura, Opt. Acta 28, 857 (1981).
[Crossref]

N. Takai, T. Iwai, T. Asakura, Opt. Eng. 20, 320 (1981).
[Crossref]

N. Takai, T. Iwai, T. Asakura, J. Opt. Soc. Am. 70, 450 (1980).
[Crossref]

Jutamulia, S.

S. Jutamulia, H. Fujii, T. Asakura, Opt. Laser Technol. 15, 101 (1983).
[Crossref]

Takai, N.

T. Asakura, N. Takai, Appl. Phys. 25, 179 (1981).
[Crossref]

N. Takai, T. Iwai, T. Asakura, Opt. Eng. 20, 320 (1981).
[Crossref]

T. Iwai, N. Takai, T. Asakura, Opt. Acta 28, 857 (1981).
[Crossref]

N. Takai, T. Iwai, T. Asakura, J. Opt. Soc. Am. 70, 450 (1980).
[Crossref]

Appl. Phys. (1)

T. Asakura, N. Takai, Appl. Phys. 25, 179 (1981).
[Crossref]

J. Opt. Soc. Am. (1)

Opt. Acta (4)

K. J. Ebeling, Opt. Acta 26, 1505 (1979).
[Crossref]

K. J. Ebeling, Opt. Acta 26, 1345 (1979).
[Crossref]

T. Iwai, N. Takai, T. Asakura, Opt. Acta 28, 857 (1981).
[Crossref]

E. Archbold, J. M. Burch, A. E. Ennos, Opt. Acta 17, 883 (1970).
[Crossref]

Opt. Eng. (1)

N. Takai, T. Iwai, T. Asakura, Opt. Eng. 20, 320 (1981).
[Crossref]

Opt. Laser Technol. (1)

S. Jutamulia, H. Fujii, T. Asakura, Opt. Laser Technol. 15, 101 (1983).
[Crossref]

Other (1)

A. E. Ennos, “Speckle Interferometry,” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer, Berlin, 1975), pp. 203–253.
[Crossref]

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Figures (8)

Fig. 1
Fig. 1

One-dimensional level-crossing technique for displacement measurement of speckles. The upper and middle figures indicate the speckle intensity variations with their average levels before and after displacement, while the lower figure denotes a sequence of pairs of crossing points before and after displacement.

Fig. 2
Fig. 2

Basic principle of the 2-D level-crossing technique for displacement measurements of speckles; si and Ai with i = 1,2,…, M indicate the crossing points before and after displacement and the distance vector from si to one crossing point after displacement is shown by its magnitude | d | and angle θ.

Fig. 3
Fig. 3

Experimental setup together with the detecting and analyzing system used for displacement measurements of speckles caused by in-plane object movement.

Fig. 4
Fig. 4

Typical 2-D level-crossing maps obtained in the 20 × 20 sampling array (a) before and (b) after displacement. The crossing points are shown by s and A.

Fig. 5
Fig. 5

Bivariate histogram with respect to the magnitude | d | and angle θ of the displacement vectors obtained from the superposed level-crossing map of Figs. 4(a) and (b).

Fig. 6
Fig. 6

Typical level-crossing maps and resultant displacement vectors of speckles. In measurements, map (a) was used as the standard for maps (b)–(d) which were obtained after displacements with different magnitudes and directions; (e)–(g) show the displacement vectors obtained from the combinations of (a)–(b), (a)–(c), and (a)–(d).

Fig. 7
Fig. 7

Level-crossing maps and resultant displacement vectors: (a) is the standard crossing maps, (b) and (c) are the crossing maps before and after displacement, and (d) and (e) are the displacement vectors obtained from the combinations of (a)–(b) and (a)–(c).

Fig. 8
Fig. 8

Comparison between the theoretical and experimental results for the speckle displacement Δdspeckle as a function of the object displacement Δdobject.

Equations (4)

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D = { d 11 d 12 . . . . . d 1 M d 21 d 22 . . . . . d 2 M d M 1 d M 2 . . . . . d MM } .
r = Δ θ 2 π M ( M 1 ) N .
σ SN = the number of d 0 in D the occurrence rate of d ij with i j in D = 2 π Δ θ N M 1
Δ d speckle = ( 1 + R / ρ ) Δ d object ,

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