Abstract

A modified Levenberg-Marquardt (MLM) algorithm is proposed to substitute for modified G-S (MGS) algorithm in some situations of phase-diverse phase retrieval wavefront sensing (WFS), such as the obstructed pupil, in which the second derivative information is specifically employed to eliminate the local minimum stagnation. Experiments have been performed to validate MLM algorithm in WFS accuracy (less than λ/30 RMS) referring to ZYGO interferometer results and in WFS repeatability (less than λ/200 RMS), even the dynamic range is more than 7λ PV. Moreover, experiments have shown the MLM algorithm is superior to the MGS algorithm both in WFS accuracy and repeatability.

© 2009 Optical Society of America

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  1. R. W. Gerchberg and W. O. Saxton, " A Practical Algorithm for the Determination of Phase from Image and Diffraction Plane Pictures, " OPTIK 35, 237-246 (1972).
  2. B. H. Dean, D. L. Aronstein, J. S. Smith, R. Shiri, and D. S. Acton, "Phase Retrieval Algorithm for JWST Flight and Testbed Telescope," Proc. SPIE 6265, 626511-1 (2006).
    [CrossRef]
  3. R. A. Gonsalves, "Phase Retrieval from Modulus Data," J. Opt. Soc. Am. 66, 961-964 (1976).
    [CrossRef]
  4. R. A. Gonsalves, "Phase Retrieval and Diversity in Adaptive Optics," Opt. Eng. 21, 829-832 (1982).
  5. C. Roddier and F. Roddier, "Combined Approach to the Hubble Space Telescope Wave-Front Distortion Analysis," Appl. Opt. 32, 2992-3008 (1993).
    [CrossRef] [PubMed]
  6. J. R. Fienup, "Phase-retrieval algorithms for a complicated optical system," Appl. Opt. 32, 1737-1746 (1993).
    [CrossRef] [PubMed]
  7. D. C. Redding, P. Dumont, and J. Yu, "Hubble Space Telescope prescription retrieval," Appl. Opt. 32, 1728-1736 (1993).
    [CrossRef] [PubMed]
  8. D. C. Redding, S. Basinger, A. Lowman, A. Kissil, P. Bely, R. Burg, R. Lyon, G. Mosier, M. Femiano, M. Wilson, G. Schunk, L. Craig, D. Jacobson, J. Rakoczy, and J. Hadaway, "Wavefront Sensing and Control for a Next Generation Space Telescope," Proc. SPIE 3356, 758-772 (1998).
    [CrossRef]
  9. D. C. Ghiglia and M. D. Pritt, "Minimum-norm methods," in Two-Dimensional Phase Unwrapping (Wiley Press, 1998), pp. 178-278.
  10. D. Cohen and D. C. Redding, "NGST High Dynamic Range Unwrapped Phase Estimation," Proc. SPIE 4850, 336-344 (2003).
    [CrossRef]
  11. D. S. Acton, P. Atcheson, M. Cermak, L. Kingsbury, F. Shi, and D. C. Redding, "James Webb Space Telescope Wavefront Sensing and Control Algorithms," Proc. SPIE 5487, 887-896 (2004).
    [CrossRef]
  12. C. M. Ohara, D. C. Redding, F. Shi, and J. J. Green, "PSF monitoring and in-focus wavefront control for NGST," Proc. SPIE 4850, 416-427 (2003).
    [CrossRef]
  13. D. Malacara and S. DeVore, "Interferogram evaluation and wavefront fitting," in Optical Shop Testing 2nd Ed. (Wiley Press, 1992), pp. 455-487.
  14. G. R. Brady and J. R. Fienup, "Nonlinear optimization algorithm for retrieving the full complex pupil function," Opt. Express 14, 474-486 (2006).
    [CrossRef] [PubMed]
  15. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, "Nonlinear models," in Numerical Recipes in C++: The Art of Scientific Computing 2nd Ed. (Cambridge University Press, 2002), pp. 686-694.
  16. J. J. Green, D. C. Redding, S. Shaklan, and S. A. Basinger, "Extreme wavefront sensing accuracy for the Eclipse Coronagraphic Space Telescope," Proc. SPIE 4860, 266-276 (2003).
    [CrossRef]
  17. Heng Mao, Xiao Wang, and Dazun Zhao, "Application of phase-diverse phase retrieval to wavefront sensing in non-connected complicated pupil optics", Chinese Opt. Lett. 5, 397-399 (2007).
  18. J. J. Green, D. C. Redding, Y. Beregovski, A. E. Lowman, and C. M. Ohara, "Interferometric validation of image-based wavefront sensing for NGST," Proc. SPIE 4850, 345-352 (2003).
    [CrossRef]

2007 (1)

Heng Mao, Xiao Wang, and Dazun Zhao, "Application of phase-diverse phase retrieval to wavefront sensing in non-connected complicated pupil optics", Chinese Opt. Lett. 5, 397-399 (2007).

2006 (2)

B. H. Dean, D. L. Aronstein, J. S. Smith, R. Shiri, and D. S. Acton, "Phase Retrieval Algorithm for JWST Flight and Testbed Telescope," Proc. SPIE 6265, 626511-1 (2006).
[CrossRef]

G. R. Brady and J. R. Fienup, "Nonlinear optimization algorithm for retrieving the full complex pupil function," Opt. Express 14, 474-486 (2006).
[CrossRef] [PubMed]

2004 (1)

D. S. Acton, P. Atcheson, M. Cermak, L. Kingsbury, F. Shi, and D. C. Redding, "James Webb Space Telescope Wavefront Sensing and Control Algorithms," Proc. SPIE 5487, 887-896 (2004).
[CrossRef]

2003 (4)

C. M. Ohara, D. C. Redding, F. Shi, and J. J. Green, "PSF monitoring and in-focus wavefront control for NGST," Proc. SPIE 4850, 416-427 (2003).
[CrossRef]

J. J. Green, D. C. Redding, S. Shaklan, and S. A. Basinger, "Extreme wavefront sensing accuracy for the Eclipse Coronagraphic Space Telescope," Proc. SPIE 4860, 266-276 (2003).
[CrossRef]

D. Cohen and D. C. Redding, "NGST High Dynamic Range Unwrapped Phase Estimation," Proc. SPIE 4850, 336-344 (2003).
[CrossRef]

J. J. Green, D. C. Redding, Y. Beregovski, A. E. Lowman, and C. M. Ohara, "Interferometric validation of image-based wavefront sensing for NGST," Proc. SPIE 4850, 345-352 (2003).
[CrossRef]

1998 (1)

D. C. Redding, S. Basinger, A. Lowman, A. Kissil, P. Bely, R. Burg, R. Lyon, G. Mosier, M. Femiano, M. Wilson, G. Schunk, L. Craig, D. Jacobson, J. Rakoczy, and J. Hadaway, "Wavefront Sensing and Control for a Next Generation Space Telescope," Proc. SPIE 3356, 758-772 (1998).
[CrossRef]

1993 (3)

1982 (1)

R. A. Gonsalves, "Phase Retrieval and Diversity in Adaptive Optics," Opt. Eng. 21, 829-832 (1982).

1976 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, " A Practical Algorithm for the Determination of Phase from Image and Diffraction Plane Pictures, " OPTIK 35, 237-246 (1972).

Acton, D. S.

B. H. Dean, D. L. Aronstein, J. S. Smith, R. Shiri, and D. S. Acton, "Phase Retrieval Algorithm for JWST Flight and Testbed Telescope," Proc. SPIE 6265, 626511-1 (2006).
[CrossRef]

D. S. Acton, P. Atcheson, M. Cermak, L. Kingsbury, F. Shi, and D. C. Redding, "James Webb Space Telescope Wavefront Sensing and Control Algorithms," Proc. SPIE 5487, 887-896 (2004).
[CrossRef]

Aronstein, D. L.

B. H. Dean, D. L. Aronstein, J. S. Smith, R. Shiri, and D. S. Acton, "Phase Retrieval Algorithm for JWST Flight and Testbed Telescope," Proc. SPIE 6265, 626511-1 (2006).
[CrossRef]

Atcheson, P.

D. S. Acton, P. Atcheson, M. Cermak, L. Kingsbury, F. Shi, and D. C. Redding, "James Webb Space Telescope Wavefront Sensing and Control Algorithms," Proc. SPIE 5487, 887-896 (2004).
[CrossRef]

Basinger, S.

D. C. Redding, S. Basinger, A. Lowman, A. Kissil, P. Bely, R. Burg, R. Lyon, G. Mosier, M. Femiano, M. Wilson, G. Schunk, L. Craig, D. Jacobson, J. Rakoczy, and J. Hadaway, "Wavefront Sensing and Control for a Next Generation Space Telescope," Proc. SPIE 3356, 758-772 (1998).
[CrossRef]

Basinger, S. A.

J. J. Green, D. C. Redding, S. Shaklan, and S. A. Basinger, "Extreme wavefront sensing accuracy for the Eclipse Coronagraphic Space Telescope," Proc. SPIE 4860, 266-276 (2003).
[CrossRef]

Bely, P.

D. C. Redding, S. Basinger, A. Lowman, A. Kissil, P. Bely, R. Burg, R. Lyon, G. Mosier, M. Femiano, M. Wilson, G. Schunk, L. Craig, D. Jacobson, J. Rakoczy, and J. Hadaway, "Wavefront Sensing and Control for a Next Generation Space Telescope," Proc. SPIE 3356, 758-772 (1998).
[CrossRef]

Beregovski, Y.

J. J. Green, D. C. Redding, Y. Beregovski, A. E. Lowman, and C. M. Ohara, "Interferometric validation of image-based wavefront sensing for NGST," Proc. SPIE 4850, 345-352 (2003).
[CrossRef]

Brady, G. R.

Burg, R.

D. C. Redding, S. Basinger, A. Lowman, A. Kissil, P. Bely, R. Burg, R. Lyon, G. Mosier, M. Femiano, M. Wilson, G. Schunk, L. Craig, D. Jacobson, J. Rakoczy, and J. Hadaway, "Wavefront Sensing and Control for a Next Generation Space Telescope," Proc. SPIE 3356, 758-772 (1998).
[CrossRef]

Cermak, M.

D. S. Acton, P. Atcheson, M. Cermak, L. Kingsbury, F. Shi, and D. C. Redding, "James Webb Space Telescope Wavefront Sensing and Control Algorithms," Proc. SPIE 5487, 887-896 (2004).
[CrossRef]

Cohen, D.

D. Cohen and D. C. Redding, "NGST High Dynamic Range Unwrapped Phase Estimation," Proc. SPIE 4850, 336-344 (2003).
[CrossRef]

Craig, L.

D. C. Redding, S. Basinger, A. Lowman, A. Kissil, P. Bely, R. Burg, R. Lyon, G. Mosier, M. Femiano, M. Wilson, G. Schunk, L. Craig, D. Jacobson, J. Rakoczy, and J. Hadaway, "Wavefront Sensing and Control for a Next Generation Space Telescope," Proc. SPIE 3356, 758-772 (1998).
[CrossRef]

Dean, B. H.

B. H. Dean, D. L. Aronstein, J. S. Smith, R. Shiri, and D. S. Acton, "Phase Retrieval Algorithm for JWST Flight and Testbed Telescope," Proc. SPIE 6265, 626511-1 (2006).
[CrossRef]

Dumont, P.

Femiano, M.

D. C. Redding, S. Basinger, A. Lowman, A. Kissil, P. Bely, R. Burg, R. Lyon, G. Mosier, M. Femiano, M. Wilson, G. Schunk, L. Craig, D. Jacobson, J. Rakoczy, and J. Hadaway, "Wavefront Sensing and Control for a Next Generation Space Telescope," Proc. SPIE 3356, 758-772 (1998).
[CrossRef]

Fienup, J. R.

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, " A Practical Algorithm for the Determination of Phase from Image and Diffraction Plane Pictures, " OPTIK 35, 237-246 (1972).

Gonsalves, R. A.

R. A. Gonsalves, "Phase Retrieval and Diversity in Adaptive Optics," Opt. Eng. 21, 829-832 (1982).

R. A. Gonsalves, "Phase Retrieval from Modulus Data," J. Opt. Soc. Am. 66, 961-964 (1976).
[CrossRef]

Green, J. J.

J. J. Green, D. C. Redding, Y. Beregovski, A. E. Lowman, and C. M. Ohara, "Interferometric validation of image-based wavefront sensing for NGST," Proc. SPIE 4850, 345-352 (2003).
[CrossRef]

J. J. Green, D. C. Redding, S. Shaklan, and S. A. Basinger, "Extreme wavefront sensing accuracy for the Eclipse Coronagraphic Space Telescope," Proc. SPIE 4860, 266-276 (2003).
[CrossRef]

C. M. Ohara, D. C. Redding, F. Shi, and J. J. Green, "PSF monitoring and in-focus wavefront control for NGST," Proc. SPIE 4850, 416-427 (2003).
[CrossRef]

Hadaway, J.

D. C. Redding, S. Basinger, A. Lowman, A. Kissil, P. Bely, R. Burg, R. Lyon, G. Mosier, M. Femiano, M. Wilson, G. Schunk, L. Craig, D. Jacobson, J. Rakoczy, and J. Hadaway, "Wavefront Sensing and Control for a Next Generation Space Telescope," Proc. SPIE 3356, 758-772 (1998).
[CrossRef]

Jacobson, D.

D. C. Redding, S. Basinger, A. Lowman, A. Kissil, P. Bely, R. Burg, R. Lyon, G. Mosier, M. Femiano, M. Wilson, G. Schunk, L. Craig, D. Jacobson, J. Rakoczy, and J. Hadaway, "Wavefront Sensing and Control for a Next Generation Space Telescope," Proc. SPIE 3356, 758-772 (1998).
[CrossRef]

Kingsbury, L.

D. S. Acton, P. Atcheson, M. Cermak, L. Kingsbury, F. Shi, and D. C. Redding, "James Webb Space Telescope Wavefront Sensing and Control Algorithms," Proc. SPIE 5487, 887-896 (2004).
[CrossRef]

Kissil, A.

D. C. Redding, S. Basinger, A. Lowman, A. Kissil, P. Bely, R. Burg, R. Lyon, G. Mosier, M. Femiano, M. Wilson, G. Schunk, L. Craig, D. Jacobson, J. Rakoczy, and J. Hadaway, "Wavefront Sensing and Control for a Next Generation Space Telescope," Proc. SPIE 3356, 758-772 (1998).
[CrossRef]

Lowman, A.

D. C. Redding, S. Basinger, A. Lowman, A. Kissil, P. Bely, R. Burg, R. Lyon, G. Mosier, M. Femiano, M. Wilson, G. Schunk, L. Craig, D. Jacobson, J. Rakoczy, and J. Hadaway, "Wavefront Sensing and Control for a Next Generation Space Telescope," Proc. SPIE 3356, 758-772 (1998).
[CrossRef]

Lowman, A. E.

J. J. Green, D. C. Redding, Y. Beregovski, A. E. Lowman, and C. M. Ohara, "Interferometric validation of image-based wavefront sensing for NGST," Proc. SPIE 4850, 345-352 (2003).
[CrossRef]

Lyon, R.

D. C. Redding, S. Basinger, A. Lowman, A. Kissil, P. Bely, R. Burg, R. Lyon, G. Mosier, M. Femiano, M. Wilson, G. Schunk, L. Craig, D. Jacobson, J. Rakoczy, and J. Hadaway, "Wavefront Sensing and Control for a Next Generation Space Telescope," Proc. SPIE 3356, 758-772 (1998).
[CrossRef]

Mao, Heng

Heng Mao, Xiao Wang, and Dazun Zhao, "Application of phase-diverse phase retrieval to wavefront sensing in non-connected complicated pupil optics", Chinese Opt. Lett. 5, 397-399 (2007).

Mosier, G.

D. C. Redding, S. Basinger, A. Lowman, A. Kissil, P. Bely, R. Burg, R. Lyon, G. Mosier, M. Femiano, M. Wilson, G. Schunk, L. Craig, D. Jacobson, J. Rakoczy, and J. Hadaway, "Wavefront Sensing and Control for a Next Generation Space Telescope," Proc. SPIE 3356, 758-772 (1998).
[CrossRef]

Ohara, C. M.

C. M. Ohara, D. C. Redding, F. Shi, and J. J. Green, "PSF monitoring and in-focus wavefront control for NGST," Proc. SPIE 4850, 416-427 (2003).
[CrossRef]

J. J. Green, D. C. Redding, Y. Beregovski, A. E. Lowman, and C. M. Ohara, "Interferometric validation of image-based wavefront sensing for NGST," Proc. SPIE 4850, 345-352 (2003).
[CrossRef]

Rakoczy, J.

D. C. Redding, S. Basinger, A. Lowman, A. Kissil, P. Bely, R. Burg, R. Lyon, G. Mosier, M. Femiano, M. Wilson, G. Schunk, L. Craig, D. Jacobson, J. Rakoczy, and J. Hadaway, "Wavefront Sensing and Control for a Next Generation Space Telescope," Proc. SPIE 3356, 758-772 (1998).
[CrossRef]

Redding, D. C.

D. S. Acton, P. Atcheson, M. Cermak, L. Kingsbury, F. Shi, and D. C. Redding, "James Webb Space Telescope Wavefront Sensing and Control Algorithms," Proc. SPIE 5487, 887-896 (2004).
[CrossRef]

J. J. Green, D. C. Redding, Y. Beregovski, A. E. Lowman, and C. M. Ohara, "Interferometric validation of image-based wavefront sensing for NGST," Proc. SPIE 4850, 345-352 (2003).
[CrossRef]

D. Cohen and D. C. Redding, "NGST High Dynamic Range Unwrapped Phase Estimation," Proc. SPIE 4850, 336-344 (2003).
[CrossRef]

C. M. Ohara, D. C. Redding, F. Shi, and J. J. Green, "PSF monitoring and in-focus wavefront control for NGST," Proc. SPIE 4850, 416-427 (2003).
[CrossRef]

J. J. Green, D. C. Redding, S. Shaklan, and S. A. Basinger, "Extreme wavefront sensing accuracy for the Eclipse Coronagraphic Space Telescope," Proc. SPIE 4860, 266-276 (2003).
[CrossRef]

D. C. Redding, S. Basinger, A. Lowman, A. Kissil, P. Bely, R. Burg, R. Lyon, G. Mosier, M. Femiano, M. Wilson, G. Schunk, L. Craig, D. Jacobson, J. Rakoczy, and J. Hadaway, "Wavefront Sensing and Control for a Next Generation Space Telescope," Proc. SPIE 3356, 758-772 (1998).
[CrossRef]

D. C. Redding, P. Dumont, and J. Yu, "Hubble Space Telescope prescription retrieval," Appl. Opt. 32, 1728-1736 (1993).
[CrossRef] [PubMed]

Roddier, C.

Roddier, F.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, " A Practical Algorithm for the Determination of Phase from Image and Diffraction Plane Pictures, " OPTIK 35, 237-246 (1972).

Schunk, G.

D. C. Redding, S. Basinger, A. Lowman, A. Kissil, P. Bely, R. Burg, R. Lyon, G. Mosier, M. Femiano, M. Wilson, G. Schunk, L. Craig, D. Jacobson, J. Rakoczy, and J. Hadaway, "Wavefront Sensing and Control for a Next Generation Space Telescope," Proc. SPIE 3356, 758-772 (1998).
[CrossRef]

Shaklan, S.

J. J. Green, D. C. Redding, S. Shaklan, and S. A. Basinger, "Extreme wavefront sensing accuracy for the Eclipse Coronagraphic Space Telescope," Proc. SPIE 4860, 266-276 (2003).
[CrossRef]

Shi, F.

D. S. Acton, P. Atcheson, M. Cermak, L. Kingsbury, F. Shi, and D. C. Redding, "James Webb Space Telescope Wavefront Sensing and Control Algorithms," Proc. SPIE 5487, 887-896 (2004).
[CrossRef]

C. M. Ohara, D. C. Redding, F. Shi, and J. J. Green, "PSF monitoring and in-focus wavefront control for NGST," Proc. SPIE 4850, 416-427 (2003).
[CrossRef]

Shiri, R.

B. H. Dean, D. L. Aronstein, J. S. Smith, R. Shiri, and D. S. Acton, "Phase Retrieval Algorithm for JWST Flight and Testbed Telescope," Proc. SPIE 6265, 626511-1 (2006).
[CrossRef]

Smith, J. S.

B. H. Dean, D. L. Aronstein, J. S. Smith, R. Shiri, and D. S. Acton, "Phase Retrieval Algorithm for JWST Flight and Testbed Telescope," Proc. SPIE 6265, 626511-1 (2006).
[CrossRef]

Wang, Xiao

Heng Mao, Xiao Wang, and Dazun Zhao, "Application of phase-diverse phase retrieval to wavefront sensing in non-connected complicated pupil optics", Chinese Opt. Lett. 5, 397-399 (2007).

Wilson, M.

D. C. Redding, S. Basinger, A. Lowman, A. Kissil, P. Bely, R. Burg, R. Lyon, G. Mosier, M. Femiano, M. Wilson, G. Schunk, L. Craig, D. Jacobson, J. Rakoczy, and J. Hadaway, "Wavefront Sensing and Control for a Next Generation Space Telescope," Proc. SPIE 3356, 758-772 (1998).
[CrossRef]

Yu, J.

Zhao, Dazun

Heng Mao, Xiao Wang, and Dazun Zhao, "Application of phase-diverse phase retrieval to wavefront sensing in non-connected complicated pupil optics", Chinese Opt. Lett. 5, 397-399 (2007).

Appl. Opt. (3)

Chinese Opt. Lett. (1)

Heng Mao, Xiao Wang, and Dazun Zhao, "Application of phase-diverse phase retrieval to wavefront sensing in non-connected complicated pupil optics", Chinese Opt. Lett. 5, 397-399 (2007).

J. Opt. Soc. Am. (1)

Opt. Eng. (1)

R. A. Gonsalves, "Phase Retrieval and Diversity in Adaptive Optics," Opt. Eng. 21, 829-832 (1982).

Opt. Express (1)

OPTIK (1)

R. W. Gerchberg and W. O. Saxton, " A Practical Algorithm for the Determination of Phase from Image and Diffraction Plane Pictures, " OPTIK 35, 237-246 (1972).

Proc. SPIE (7)

B. H. Dean, D. L. Aronstein, J. S. Smith, R. Shiri, and D. S. Acton, "Phase Retrieval Algorithm for JWST Flight and Testbed Telescope," Proc. SPIE 6265, 626511-1 (2006).
[CrossRef]

D. C. Redding, S. Basinger, A. Lowman, A. Kissil, P. Bely, R. Burg, R. Lyon, G. Mosier, M. Femiano, M. Wilson, G. Schunk, L. Craig, D. Jacobson, J. Rakoczy, and J. Hadaway, "Wavefront Sensing and Control for a Next Generation Space Telescope," Proc. SPIE 3356, 758-772 (1998).
[CrossRef]

D. Cohen and D. C. Redding, "NGST High Dynamic Range Unwrapped Phase Estimation," Proc. SPIE 4850, 336-344 (2003).
[CrossRef]

D. S. Acton, P. Atcheson, M. Cermak, L. Kingsbury, F. Shi, and D. C. Redding, "James Webb Space Telescope Wavefront Sensing and Control Algorithms," Proc. SPIE 5487, 887-896 (2004).
[CrossRef]

C. M. Ohara, D. C. Redding, F. Shi, and J. J. Green, "PSF monitoring and in-focus wavefront control for NGST," Proc. SPIE 4850, 416-427 (2003).
[CrossRef]

J. J. Green, D. C. Redding, S. Shaklan, and S. A. Basinger, "Extreme wavefront sensing accuracy for the Eclipse Coronagraphic Space Telescope," Proc. SPIE 4860, 266-276 (2003).
[CrossRef]

J. J. Green, D. C. Redding, Y. Beregovski, A. E. Lowman, and C. M. Ohara, "Interferometric validation of image-based wavefront sensing for NGST," Proc. SPIE 4850, 345-352 (2003).
[CrossRef]

Other (3)

D. Malacara and S. DeVore, "Interferogram evaluation and wavefront fitting," in Optical Shop Testing 2nd Ed. (Wiley Press, 1992), pp. 455-487.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, "Nonlinear models," in Numerical Recipes in C++: The Art of Scientific Computing 2nd Ed. (Cambridge University Press, 2002), pp. 686-694.

D. C. Ghiglia and M. D. Pritt, "Minimum-norm methods," in Two-Dimensional Phase Unwrapping (Wiley Press, 1998), pp. 178-278.

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Figures (14)

Fig. 1.
Fig. 1.

Second PDPR propagation model.

Fig. 2.
Fig. 2.

Flowchart of modified L-M algorithm.

Fig. 3.
Fig. 3.

Layout of experimental setup.

Fig. 4.
Fig. 4.

Pupil module and Lens L1 module.

Fig. 5.
Fig. 5.

GUI in systematic errors calibration.

Fig. 6.
Fig. 6.

Systematic errors calibration: MLM estimate vs MGS estimate (actual map).

Fig. 7.
Fig. 7.

Sample 1: MLM estimate vs MGS estimate (actual map) for whole aberrations.

Fig. 8.
Fig. 8.

Sample 1: MLM estimate vs ZYGO result (actual map).

Fig. 9.
Fig. 9.

Sample 1: MGS estimate vs ZYGO result (actual map).

Fig. 10.
Fig. 10.

Sample 2: all related images in MLM WFS.

Fig. 11.
Fig. 11.

Sample 2: MLM estimate vs MGS estimate (actual map) for whole aberrations.

Fig. 12.
Fig. 12.

Sample 2: MLM estimate vs ZYGO result (actual map).

Fig. 13.
Fig. 13.

Sample 2: MGS estimate vs ZYGO result (actual map).

Fig. 14.
Fig. 14.

Sample 2: obstructed MLM estimate vs circular MLM estimate (actual map).

Tables (2)

Tables Icon

Table 1. Zernikes decomposed from MLM estimate and MGS estimate (in radians).

Tables Icon

Table 2. Summarization of all WFS results in sample 1 and 2 (in waves).

Equations (10)

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U pupil ( i , j ) = I ( i , j ) · exp [ i · ϕ pupil ( i , j , α ) ] = I ( i , j ) · exp [ i · ( u = 1 S α u · Z u ( i , j ) ) ] ,
U defocus ( m , n , Δ f , α ) = FFT { U pupil ( i , i , α ) · exp [ i · ϕ defocus ( i , j , Δ f ) ] } ,
I de cal ( m , n , Δ f , α ) = FFT { W · exp [ i · ( ϕ pu + ϕ de ) ] } · FFT * { W · exp [ i · ( ϕ pu + ϕ de ) ] } ,
F ( α ) = m = 1 M n = 1 N h 2 ( m , n , Δ f , α ) = m = 1 M n = 1 N [ I ̂ de sen ( m , n , Δ f ) I ̂ de cal ( m , n , Δ f , α ) ] 2 ,
h ( r , Δ f , α ) α u = [ FFT { U total · i · Z u } · FFT * { U total } + FFT { U total } · FFT * { U total · i · Z u } ] Max [ I de cal ( r , Δ f , α ) ] ,
α ( k + 1 ) α ( k ) = [ J T ( α ( k ) ) · J ( α ( k ) ) + λ ( k ) · I ] 1 · J T ( α ( k ) ) · H ( α ( k ) ) ,
α ( k + 1 ) α ( k ) = [ J T ( α ( k ) ) · J ( α ( k ) ) + S ( α ( k ) ) ] 1 · J T ( α ( k ) ) · H ( α ( k ) ) ,
2 h r ( α ) α u α v = FFT { U total · Z u · Z v } · FFT * { U total } + FFT { U total } · FFT * { U total · Z u · Z v } Max [ I de cal ( r , Δ f , α ) ]
FFT { U total · i · Z u } · FFT * { U total · i · Z v } + FFT { U total · i · Z v } · FFT * { U total · i · Z u } Max [ I de cal ( r , Δ f , α ) ] .
Weighting ( i ) = [ Metric 3 ( α i * ) ] γ / i = 1 3 [ Metric 3 ( α i * ) ] γ ,

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