Abstract

We studied the diffraction halo function of partially coherent speckle photography, using the theory of partial coherence of light and speckle statistics. Numerical calculations were made on the basis of the derived expression. It was shown that the anisotropic coherence of the illumination induced by the source could lead to the inhomogeneity of the halo distribution. An experiment was performed to prove the theoretical predictions.

© 1999 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. Meynart, “Diffraction halo in speckle photography,” Appl. Opt. 23, 2235–2236 (1984).
    [CrossRef] [PubMed]
  2. F. P. Chiang, D. W. Li, “Diffraction halo functions of coherent and incoherent speckle patterns,” Appl. Opt. 24, 2166–2170 (1985).
    [CrossRef]
  3. R. P. Khetan, F. P. Chiang, “Strain analysis by one-beam laser speckle interferometry. 1. Single aperture method,” Appl. Opt. 15, 2205–2215 (1976).
    [CrossRef] [PubMed]
  4. F. P. Chiang, R. P. Khetan, “Strain analysis by one-beam laser speckle interferometry. 2. Multiaperture method,” Appl. Opt. 18, 2175–2186 (1979).
    [CrossRef] [PubMed]
  5. K. Hinsch, “Fringe position in double-exposure speckle photography,” Appl. Opt. 28, 5298–5304 (1989).
    [CrossRef] [PubMed]
  6. H. D. Novone, G. H. Kaufman, “Two-dimensional digital processing of speckle photography fringes. 3. Accuracy in angular determination,” Appl. Opt. 26, 154–156 (1987).
    [CrossRef]
  7. C. F. Cheng, J. H. Jiang, Y. Z. Shen, “Partially coherent speckle shearing interferometry with the source encoded,” Acta Sin. Optica (Guangxue Xuebao) 10, 938–944 (1990) (in Chinese).
  8. C. F. Cheng, J. H. Jiang, Y. Z. Shen, “The theory of partially coherent photography and its applications,” Chin. J. Exp. Mech. (Shiyan Lixue) 8, 207–213 (1993) (in Chinese).
  9. J. H. Jiang, C. F. Cheng, Y. Z. Shen, “Techniques of partially coherent speckle on image plane,” Chin. J. Exp. Mech. (Shiyan Lixue) 5, 164–169 (1990) (in Chinese).
  10. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980), Chap. 10.
  11. J. C. Dainty, ed., Laser Speckle and Related Phenomena (Springer-Verlag, Berlin, 1975), p. 37.

1993 (1)

C. F. Cheng, J. H. Jiang, Y. Z. Shen, “The theory of partially coherent photography and its applications,” Chin. J. Exp. Mech. (Shiyan Lixue) 8, 207–213 (1993) (in Chinese).

1990 (2)

J. H. Jiang, C. F. Cheng, Y. Z. Shen, “Techniques of partially coherent speckle on image plane,” Chin. J. Exp. Mech. (Shiyan Lixue) 5, 164–169 (1990) (in Chinese).

C. F. Cheng, J. H. Jiang, Y. Z. Shen, “Partially coherent speckle shearing interferometry with the source encoded,” Acta Sin. Optica (Guangxue Xuebao) 10, 938–944 (1990) (in Chinese).

1989 (1)

1987 (1)

1985 (1)

1984 (1)

1979 (1)

1976 (1)

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980), Chap. 10.

Cheng, C. F.

C. F. Cheng, J. H. Jiang, Y. Z. Shen, “The theory of partially coherent photography and its applications,” Chin. J. Exp. Mech. (Shiyan Lixue) 8, 207–213 (1993) (in Chinese).

J. H. Jiang, C. F. Cheng, Y. Z. Shen, “Techniques of partially coherent speckle on image plane,” Chin. J. Exp. Mech. (Shiyan Lixue) 5, 164–169 (1990) (in Chinese).

C. F. Cheng, J. H. Jiang, Y. Z. Shen, “Partially coherent speckle shearing interferometry with the source encoded,” Acta Sin. Optica (Guangxue Xuebao) 10, 938–944 (1990) (in Chinese).

Chiang, F. P.

Hinsch, K.

Jiang, J. H.

C. F. Cheng, J. H. Jiang, Y. Z. Shen, “The theory of partially coherent photography and its applications,” Chin. J. Exp. Mech. (Shiyan Lixue) 8, 207–213 (1993) (in Chinese).

C. F. Cheng, J. H. Jiang, Y. Z. Shen, “Partially coherent speckle shearing interferometry with the source encoded,” Acta Sin. Optica (Guangxue Xuebao) 10, 938–944 (1990) (in Chinese).

J. H. Jiang, C. F. Cheng, Y. Z. Shen, “Techniques of partially coherent speckle on image plane,” Chin. J. Exp. Mech. (Shiyan Lixue) 5, 164–169 (1990) (in Chinese).

Kaufman, G. H.

Khetan, R. P.

Li, D. W.

Meynart, R.

Novone, H. D.

Shen, Y. Z.

C. F. Cheng, J. H. Jiang, Y. Z. Shen, “The theory of partially coherent photography and its applications,” Chin. J. Exp. Mech. (Shiyan Lixue) 8, 207–213 (1993) (in Chinese).

C. F. Cheng, J. H. Jiang, Y. Z. Shen, “Partially coherent speckle shearing interferometry with the source encoded,” Acta Sin. Optica (Guangxue Xuebao) 10, 938–944 (1990) (in Chinese).

J. H. Jiang, C. F. Cheng, Y. Z. Shen, “Techniques of partially coherent speckle on image plane,” Chin. J. Exp. Mech. (Shiyan Lixue) 5, 164–169 (1990) (in Chinese).

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980), Chap. 10.

Acta Sin. Optica (Guangxue Xuebao) (1)

C. F. Cheng, J. H. Jiang, Y. Z. Shen, “Partially coherent speckle shearing interferometry with the source encoded,” Acta Sin. Optica (Guangxue Xuebao) 10, 938–944 (1990) (in Chinese).

Appl. Opt. (6)

Chin. J. Exp. Mech. (Shiyan Lixue) (2)

C. F. Cheng, J. H. Jiang, Y. Z. Shen, “The theory of partially coherent photography and its applications,” Chin. J. Exp. Mech. (Shiyan Lixue) 8, 207–213 (1993) (in Chinese).

J. H. Jiang, C. F. Cheng, Y. Z. Shen, “Techniques of partially coherent speckle on image plane,” Chin. J. Exp. Mech. (Shiyan Lixue) 5, 164–169 (1990) (in Chinese).

Other (2)

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980), Chap. 10.

J. C. Dainty, ed., Laser Speckle and Related Phenomena (Springer-Verlag, Berlin, 1975), p. 37.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Typical optical setup for PCSP

Fig. 2
Fig. 2

Calculated one-dimensional halo functions for different sizes of light source. L s , length of the source in millimeters.

Fig. 3
Fig. 3

Calculated two-dimensional halo functions of PCSP. (a) v axis to the front, (b) u axis to the front.

Fig. 4
Fig. 4

Halo function in defocused PCSP.

Fig. 5
Fig. 5

One-dimensional halo distribution at different values of defocus Δ and source size L s : (a) L s = 2 mm, (b) L s = 5 mm, (c) comparison of the PCSP with different values of the product of Δ and L s .

Fig. 6
Fig. 6

Experimental picture of the PCSP halo

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

Ix=-+ Jξ1-ξ2Aξ1A*ξ2hx-ξ1×h*x-ξ2dξ1dξ2,
JΔξ=FTSq|fq=Δξ/λ0R,
hx-ξ=1/λ02di2-+ Pβ×exp-j2πβx-ξ/λ0didβ.
Ifu=aua*u=-+ IxIxexp-j2πux-x/λfdxdx,
IxIx=-+-+ Jξ1-ξ2Jξ3-ξ4×hx-ξ1h*x-ξ2hx-ξ3h*x-ξ4×Aξ1A*ξ2Aξ3A*ξ4dξ1dξ2dξ3dξ4.
IxIx=I0+-+  Jx-x+ξ3-ξ1×Jx-x+ξ1-ξ1hξ1h*x-x+ξ3×hξ3h*x-x+ξ1dξ1dξ3,
Ifu=I0δu+-+-+ JΔx+ΔξJ-Δx-Δξhξ1×h*Δx+ξ1+Δξhξ1+Δξ×h*-Δx-ξ1exp-j2πuΔx/λf×dxdΔxdξ1dΔξ.
Ihu=R2C1/λ02di4-+ S-λ0Rv2/λfSλ0Rv3/λf×Pλ0div1-v2-u/λfP*λ0divi-v2/λf×Pλ0div1+v3/λfP*-λ0diu-v1-v3/λf×dv1dv2dv3,
Ihu=C2-+-+ SRϕ2/diPϕ1+ϕ2×P*ϕ1+ϕ2-λ0diu/λfdϕ22dϕ1,
Ihu, v=C -+  -+  SRϕ2/di, Rψ2/di×Pϕ1+ϕ2, ψ1+ψ2×P*ϕ1+ϕ2-λ0diu/λf, ψ1+ψ2-λ0div/λfdϕ2dψ2|2dϕ1dψ1,

Metrics