Abstract

Phase retrieval has recently been experimentally demonstrated, using the irradiance transport equation. We show that this equation provides a unified description for incoherent wavefront sensing methods, bringing new insights and opening new prospects in this area.

© 1990 Optical Society of America

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References

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  1. M. R. Teague, “Irradiance Moments: Their Propagation and Use for Unique Phase Retrieval,” J. Opt. Soc. Am. 72, 1199–1209 (1982).
    [Crossref]
  2. M. R. Teague, “Deterministic Phase Retrieval: A Green’s Function Solution,” J. Opt. Soc. Am. 73, 1434–1441 (1983).
    [Crossref]
  3. N. Streibl, “Phase Imaging by the Transport Equation of Intensity,” Opt. Commun. 49, 6–10 (1984).
    [Crossref]
  4. K. Ichikawa, A. W. Lohmann, M. Takeda, “Phase Retrieval Based on the Irradiance Transport Equation and the Fourier Transform Method: Experiments,” Appl. Opt. 27, 3433–3436 (1988).
    [Crossref] [PubMed]
  5. M. Takeda, H. Ina, S. Kobayashi, “Fourier-Transform Method of Fringe-Pattern Analysis for Computer-Based Topography and Interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
    [Crossref]
  6. C. Roddier, F. Roddier, “Imaging with a Coherence Interferometer in Optical Astronomy,” in Proceedings, IAU Colloquium 49 on Formation of Images from Spatial Coherence Functions in Astronomy, Groningen, 1978, C. van Schooneveld, Ed. (Reidel, Norwell, MA, 1979).
  7. C. Roddier, F. Roddier, “Interferogram Analysis Using Fourier Transform Techniques,” Appl. Opt. 26, 1668–1673 (1987).
    [Crossref] [PubMed]
  8. F. Roddier, “Curvature Sensing and Compensation: a New Concept in Adaptive Optics,” Appl. Opt. 27, 1223–1225 (1988).
    [Crossref] [PubMed]
  9. F. Roddier, C. Roddier, N. Roddier, “Curvature Sensing: a New Wavefront Sensing Method,” Proc. Soc. Photo-Opt. Instrum. Eng. 976, 203–209 (1988).
  10. N. Roddier, F. Roddier, “Curvature Sensing and Compensation: a Computer Simulation,” Proc. Soc. Photo-Opt. Instrum. Eng. 1114, 92–96 (1989).

1989 (1)

N. Roddier, F. Roddier, “Curvature Sensing and Compensation: a Computer Simulation,” Proc. Soc. Photo-Opt. Instrum. Eng. 1114, 92–96 (1989).

1988 (3)

1987 (1)

1984 (1)

N. Streibl, “Phase Imaging by the Transport Equation of Intensity,” Opt. Commun. 49, 6–10 (1984).
[Crossref]

1983 (1)

1982 (2)

Ichikawa, K.

Ina, H.

Kobayashi, S.

Lohmann, A. W.

Roddier, C.

F. Roddier, C. Roddier, N. Roddier, “Curvature Sensing: a New Wavefront Sensing Method,” Proc. Soc. Photo-Opt. Instrum. Eng. 976, 203–209 (1988).

C. Roddier, F. Roddier, “Interferogram Analysis Using Fourier Transform Techniques,” Appl. Opt. 26, 1668–1673 (1987).
[Crossref] [PubMed]

C. Roddier, F. Roddier, “Imaging with a Coherence Interferometer in Optical Astronomy,” in Proceedings, IAU Colloquium 49 on Formation of Images from Spatial Coherence Functions in Astronomy, Groningen, 1978, C. van Schooneveld, Ed. (Reidel, Norwell, MA, 1979).

Roddier, F.

N. Roddier, F. Roddier, “Curvature Sensing and Compensation: a Computer Simulation,” Proc. Soc. Photo-Opt. Instrum. Eng. 1114, 92–96 (1989).

F. Roddier, C. Roddier, N. Roddier, “Curvature Sensing: a New Wavefront Sensing Method,” Proc. Soc. Photo-Opt. Instrum. Eng. 976, 203–209 (1988).

F. Roddier, “Curvature Sensing and Compensation: a New Concept in Adaptive Optics,” Appl. Opt. 27, 1223–1225 (1988).
[Crossref] [PubMed]

C. Roddier, F. Roddier, “Interferogram Analysis Using Fourier Transform Techniques,” Appl. Opt. 26, 1668–1673 (1987).
[Crossref] [PubMed]

C. Roddier, F. Roddier, “Imaging with a Coherence Interferometer in Optical Astronomy,” in Proceedings, IAU Colloquium 49 on Formation of Images from Spatial Coherence Functions in Astronomy, Groningen, 1978, C. van Schooneveld, Ed. (Reidel, Norwell, MA, 1979).

Roddier, N.

N. Roddier, F. Roddier, “Curvature Sensing and Compensation: a Computer Simulation,” Proc. Soc. Photo-Opt. Instrum. Eng. 1114, 92–96 (1989).

F. Roddier, C. Roddier, N. Roddier, “Curvature Sensing: a New Wavefront Sensing Method,” Proc. Soc. Photo-Opt. Instrum. Eng. 976, 203–209 (1988).

Streibl, N.

N. Streibl, “Phase Imaging by the Transport Equation of Intensity,” Opt. Commun. 49, 6–10 (1984).
[Crossref]

Takeda, M.

Teague, M. R.

Appl. Opt. (3)

J. Opt. Soc. Am. (3)

Opt. Commun. (1)

N. Streibl, “Phase Imaging by the Transport Equation of Intensity,” Opt. Commun. 49, 6–10 (1984).
[Crossref]

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

F. Roddier, C. Roddier, N. Roddier, “Curvature Sensing: a New Wavefront Sensing Method,” Proc. Soc. Photo-Opt. Instrum. Eng. 976, 203–209 (1988).

N. Roddier, F. Roddier, “Curvature Sensing and Compensation: a Computer Simulation,” Proc. Soc. Photo-Opt. Instrum. Eng. 1114, 92–96 (1989).

Other (1)

C. Roddier, F. Roddier, “Imaging with a Coherence Interferometer in Optical Astronomy,” in Proceedings, IAU Colloquium 49 on Formation of Images from Spatial Coherence Functions in Astronomy, Groningen, 1978, C. van Schooneveld, Ed. (Reidel, Norwell, MA, 1979).

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Equations (8)

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

I / z = - ( I · W + I 2 W ) ,
Δ ϕ = ( 2 π / a ) ( W / x ) Δ z ,
I = - I 0 n δ c .
I z = I 0 W n c - I 0 P 2 W ,
I 1 = I 0 + I z Δ z ,
I 2 = I 0 - I z Δ z .
S = I 1 - I 2 I 1 + I 2 = 1 I 0 I z Δ z .
S = ( W n δ c - P 2 W ) Δ z ,

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