Abstract

Coherent imaging techniques rely on the coherence properties of backscattered radiation to form an image of an illuminated object. These techniques are sensitive to the degree of coherence of the illuminating source. We present an approach for simulating the effects that partial temporal coherent illumination has on these techniques. Computer simulation and laboratory experimental results are presented that illustrate illumination coherence effects on imagery obtained with the technique known as imaging correlography.

© 1997 Optical Society of America

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References

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  1. P. S. Idell, J. R. Fienup, R. S. Goodman, “Image synthesis from nonimaged laser-speckle patterns,” Opt. Lett. 12, 858–860 (1987).
    [CrossRef] [PubMed]
  2. P. S. Idell, J. D. Gonglewski, “Image synthesis from wavefront sensor measurements of a coherent diffraction field,” Opt. Lett. 15, 1309–1311 (1990).
    [CrossRef] [PubMed]
  3. D. G. Voelz, J. D. Gonglewski, P. S. Idell, D. C. Dayton, “Coherent image synthesis using a Shack–Hartmann wavefront sensor,” in Digital Image Synthesis and Inverse Optics, A. F. Gmitro, P. S. Idell, I. J. LaHaie, eds., Proc. SPIE1351, 780–786 (1990).
  4. R. A. Hutchin, “Sheared Coherent Interferometric Photography, A Technique for Lenless Imaging,” in Digital Image Recovery and Synthesis, P. S. Idell, ed., Proc. SPIE2029, 161–168 (1994).
  5. D. G. Voelz, D. B. Rider, J. D. Gonglewski, “Detection analysis for a heterodyne imaging system,” in Proceedings of 1992 Meeting of the IRIS Specialty Group on Active Systems, Vol. 1, 59–66 (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1993).
  6. G. Parry, “Speckle patterns in partially coherent light,” in Laser Speckle and Related Phenomena Vol. 9 of Topics in Applied Physics, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984).
  7. G. Parry, “The scattering of polychromatic light from rough surfaces: first order statistics,” Opt. Quantum Electron. 7, 311–318 (1975).
    [CrossRef]
  8. H. M. Pedersen, “On the contrast of polychromatic speckle patterns and its dependence on surface roughness,” Opt. Acta 22, 15–24 (1975).
    [CrossRef]
  9. D. G. Voelz, J. D. Gonglewski, P. S. Idell, “Image synthesis from nonimaged laser-speckle patterns: comparison of theory, computer simulation, and laboratory results,” Appl. Opt. 30, 3333–3344 (1991).
    [CrossRef] [PubMed]

1991 (1)

1990 (1)

1987 (1)

1975 (2)

G. Parry, “The scattering of polychromatic light from rough surfaces: first order statistics,” Opt. Quantum Electron. 7, 311–318 (1975).
[CrossRef]

H. M. Pedersen, “On the contrast of polychromatic speckle patterns and its dependence on surface roughness,” Opt. Acta 22, 15–24 (1975).
[CrossRef]

Dayton, D. C.

D. G. Voelz, J. D. Gonglewski, P. S. Idell, D. C. Dayton, “Coherent image synthesis using a Shack–Hartmann wavefront sensor,” in Digital Image Synthesis and Inverse Optics, A. F. Gmitro, P. S. Idell, I. J. LaHaie, eds., Proc. SPIE1351, 780–786 (1990).

Fienup, J. R.

Gonglewski, J. D.

D. G. Voelz, J. D. Gonglewski, P. S. Idell, “Image synthesis from nonimaged laser-speckle patterns: comparison of theory, computer simulation, and laboratory results,” Appl. Opt. 30, 3333–3344 (1991).
[CrossRef] [PubMed]

P. S. Idell, J. D. Gonglewski, “Image synthesis from wavefront sensor measurements of a coherent diffraction field,” Opt. Lett. 15, 1309–1311 (1990).
[CrossRef] [PubMed]

D. G. Voelz, J. D. Gonglewski, P. S. Idell, D. C. Dayton, “Coherent image synthesis using a Shack–Hartmann wavefront sensor,” in Digital Image Synthesis and Inverse Optics, A. F. Gmitro, P. S. Idell, I. J. LaHaie, eds., Proc. SPIE1351, 780–786 (1990).

D. G. Voelz, D. B. Rider, J. D. Gonglewski, “Detection analysis for a heterodyne imaging system,” in Proceedings of 1992 Meeting of the IRIS Specialty Group on Active Systems, Vol. 1, 59–66 (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1993).

Goodman, R. S.

Hutchin, R. A.

R. A. Hutchin, “Sheared Coherent Interferometric Photography, A Technique for Lenless Imaging,” in Digital Image Recovery and Synthesis, P. S. Idell, ed., Proc. SPIE2029, 161–168 (1994).

Idell, P. S.

Parry, G.

G. Parry, “The scattering of polychromatic light from rough surfaces: first order statistics,” Opt. Quantum Electron. 7, 311–318 (1975).
[CrossRef]

G. Parry, “Speckle patterns in partially coherent light,” in Laser Speckle and Related Phenomena Vol. 9 of Topics in Applied Physics, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984).

Pedersen, H. M.

H. M. Pedersen, “On the contrast of polychromatic speckle patterns and its dependence on surface roughness,” Opt. Acta 22, 15–24 (1975).
[CrossRef]

Rider, D. B.

D. G. Voelz, D. B. Rider, J. D. Gonglewski, “Detection analysis for a heterodyne imaging system,” in Proceedings of 1992 Meeting of the IRIS Specialty Group on Active Systems, Vol. 1, 59–66 (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1993).

Voelz, D. G.

D. G. Voelz, J. D. Gonglewski, P. S. Idell, “Image synthesis from nonimaged laser-speckle patterns: comparison of theory, computer simulation, and laboratory results,” Appl. Opt. 30, 3333–3344 (1991).
[CrossRef] [PubMed]

D. G. Voelz, D. B. Rider, J. D. Gonglewski, “Detection analysis for a heterodyne imaging system,” in Proceedings of 1992 Meeting of the IRIS Specialty Group on Active Systems, Vol. 1, 59–66 (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1993).

D. G. Voelz, J. D. Gonglewski, P. S. Idell, D. C. Dayton, “Coherent image synthesis using a Shack–Hartmann wavefront sensor,” in Digital Image Synthesis and Inverse Optics, A. F. Gmitro, P. S. Idell, I. J. LaHaie, eds., Proc. SPIE1351, 780–786 (1990).

Appl. Opt. (1)

Opt. Acta (1)

H. M. Pedersen, “On the contrast of polychromatic speckle patterns and its dependence on surface roughness,” Opt. Acta 22, 15–24 (1975).
[CrossRef]

Opt. Lett. (2)

Opt. Quantum Electron. (1)

G. Parry, “The scattering of polychromatic light from rough surfaces: first order statistics,” Opt. Quantum Electron. 7, 311–318 (1975).
[CrossRef]

Other (4)

D. G. Voelz, J. D. Gonglewski, P. S. Idell, D. C. Dayton, “Coherent image synthesis using a Shack–Hartmann wavefront sensor,” in Digital Image Synthesis and Inverse Optics, A. F. Gmitro, P. S. Idell, I. J. LaHaie, eds., Proc. SPIE1351, 780–786 (1990).

R. A. Hutchin, “Sheared Coherent Interferometric Photography, A Technique for Lenless Imaging,” in Digital Image Recovery and Synthesis, P. S. Idell, ed., Proc. SPIE2029, 161–168 (1994).

D. G. Voelz, D. B. Rider, J. D. Gonglewski, “Detection analysis for a heterodyne imaging system,” in Proceedings of 1992 Meeting of the IRIS Specialty Group on Active Systems, Vol. 1, 59–66 (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1993).

G. Parry, “Speckle patterns in partially coherent light,” in Laser Speckle and Related Phenomena Vol. 9 of Topics in Applied Physics, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984).

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Figures (9)

Fig. 1
Fig. 1

Computer simulation flowchart.

Fig. 2
Fig. 2

Comparison of computer simulation and theoretical contrast results for intensity speckle patterns created with partially coherent light.

Fig. 3
Fig. 3

Theoretical probability density functions for intensity speckle patterns created with partially coherent light.

Fig. 4
Fig. 4

Comparison of computer simulation histograms and theoretical probability density functions for intensity speckle patterns created with partially coherent light: (a) no bias adjustment, (b) with bias adjustment.

Fig. 5
Fig. 5

Line-shape function approximating a single-color argon laser line.

Fig. 6
Fig. 6

Simulation target.

Fig. 7
Fig. 7

Computer simulated imaging correlography results using partially coherent illumination: (a) truth object; (b) truth half-object piece; (c) image recovered with pieces separated in depth 0.0 cm; (d) 2.5 cm; and (e) 5.0 cm.

Fig. 8
Fig. 8

Laboratory schematic for the imaging correlography experiment.

Fig. 9
Fig. 9

Imaging correlography results generated from laboratory data: (a) image recovered with object pieces separated in depth 0.0 cm; (b) 1.25 cm; (c) 2.5 cm; (d) 3.75 cm; and (e) 5.0 cm.

Equations (21)

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Ix= SkIx, kdk.
Sk=n=1NSknδk-kn,
Ix= n=1NSknδk-knIx, kdk,
Ix=n=1NSknIx, kn.
pI=1Iexp-II, for I0, pI=0, otherwise,
ρ=σII.
I=n=1NSknIx, kn.
σI2=n=1Nm=1NSknSkmAx, knA*x, km2,
Γkn, km=Ax, knA*x, km.
pI=12π-exp-iItn=11-itλndt,for I0,pI=0,otherwise.
λnΨnk=0SkΨnkΓk, kdk.
Ax, k=n=1anΨnk.
Ix=n=1an2, Ix=n=1λn, σI2=n=1λn2.
pI=n=1Ncn/λnexp-I/λn,
cn=m=1mnN λnλn-λm-1.
Γkn, km=C exp-kn-km2σz2/2,
Au, k=ruPuexpi2kH˜u,
H˜u=Hu+hu,
Ix, k=Au, k2,
Ix=n=1NSknAu, kn2.
Skn=exp-4n-N22Δνσ2ln 2, for n=1 to n=N,

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