Abstract

An optimization-based strategy is introduced for suppressing errors due to vibration in phase-shifting-interferometry algorithms. A norm-square integral criterion of the error as a function of vibration frequency is used as the basis of the optimization procedure. Analytical results are obtained for certain classes of problems, and numerical algorithms are used when these are not available. It is also shown that the effect of vibration-induced errors in the computation of a time-averaged phase estimate diminishes as the measurements are averaged. Simulations are used to validate the analysis and demonstrate the overall efficacy of the approach. Generalizations to multiple objective optimization problems are briefly discussed.

© 2002 Optical Society of America

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  6. B. Zhao, Y. Surrel, “Phase shifting: six-sample self-calibrating algorithm insensitive to the second harmonic in the fringe signal,” Opt. Eng. 34, 2821–2822 (1995).
    [Crossref]
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    [Crossref]
  8. Y. Surrel, “Phase-stepping: a new self-calibrating algorithm,” Appl. Opt. 32, 3598–3600 (1993).
    [Crossref] [PubMed]
  9. M. Milman, S. Basinger, “White light fringe estimation: algorithms, error sources and mitigation strategies,” in Proceedings of the 2001 IEEE Aerospace Conference (Institute of Electrical and Electronics Engineers, New York, 2001), Paper 6.0811.
  10. W. Rudin, Real and Complex Analysis, McGraw-Hill, New York (1974).
  11. K. L. Chung, A Course in Probability Theory, 2nd ed. (Academic, New York, 1974).
  12. E. A. Coddington, N. Levinson, Theory of Ordinary Differential Equations (McGraw-Hill, New York, 1955).

2001 (1)

1995 (3)

1993 (1)

1992 (1)

1983 (1)

Basinger, S.

M. Milman, S. Basinger, “White light fringe estimation: algorithms, error sources and mitigation strategies,” in Proceedings of the 2001 IEEE Aerospace Conference (Institute of Electrical and Electronics Engineers, New York, 2001), Paper 6.0811.

Burrow, R.

Chung, K. L.

K. L. Chung, A Course in Probability Theory, 2nd ed. (Academic, New York, 1974).

Coddington, E. A.

E. A. Coddington, N. Levinson, Theory of Ordinary Differential Equations (McGraw-Hill, New York, 1955).

Coggrave, C. R.

Danner, R.

R. Danner, S. Unwin, “Space interferometry mission, taking the measure of the universe,” (Jet Propulsion Laboratory, Pasadena, Calif., 1999).

de Groot, P. J.

Elsner, K.-E.

Grzana, J.

Huntley, J. M.

Kaufmann, G. H.

Larkin, K. G.

Levinson, N.

E. A. Coddington, N. Levinson, Theory of Ordinary Differential Equations (McGraw-Hill, New York, 1955).

Merkel, K.

Milman, M.

M. Milman, S. Basinger, “White light fringe estimation: algorithms, error sources and mitigation strategies,” in Proceedings of the 2001 IEEE Aerospace Conference (Institute of Electrical and Electronics Engineers, New York, 2001), Paper 6.0811.

Oreb, B. F.

Rudin, W.

W. Rudin, Real and Complex Analysis, McGraw-Hill, New York (1974).

Ruiz, P. D.

Schwider, J.

Shen, Y.

Spolaczyk, R.

Surrel, Y.

B. Zhao, Y. Surrel, “Phase shifting: six-sample self-calibrating algorithm insensitive to the second harmonic in the fringe signal,” Opt. Eng. 34, 2821–2822 (1995).
[Crossref]

Y. Surrel, “Phase-stepping: a new self-calibrating algorithm,” Appl. Opt. 32, 3598–3600 (1993).
[Crossref] [PubMed]

Unwin, S.

R. Danner, S. Unwin, “Space interferometry mission, taking the measure of the universe,” (Jet Propulsion Laboratory, Pasadena, Calif., 1999).

Zhao, B.

B. Zhao, Y. Surrel, “Phase shifting: six-sample self-calibrating algorithm insensitive to the second harmonic in the fringe signal,” Opt. Eng. 34, 2821–2822 (1995).
[Crossref]

Appl. Opt. (4)

J. Opt. Soc. Am. A (2)

Opt. Eng. (1)

B. Zhao, Y. Surrel, “Phase shifting: six-sample self-calibrating algorithm insensitive to the second harmonic in the fringe signal,” Opt. Eng. 34, 2821–2822 (1995).
[Crossref]

Other (5)

M. Milman, S. Basinger, “White light fringe estimation: algorithms, error sources and mitigation strategies,” in Proceedings of the 2001 IEEE Aerospace Conference (Institute of Electrical and Electronics Engineers, New York, 2001), Paper 6.0811.

W. Rudin, Real and Complex Analysis, McGraw-Hill, New York (1974).

K. L. Chung, A Course in Probability Theory, 2nd ed. (Academic, New York, 1974).

E. A. Coddington, N. Levinson, Theory of Ordinary Differential Equations (McGraw-Hill, New York, 1955).

R. Danner, S. Unwin, “Space interferometry mission, taking the measure of the universe,” (Jet Propulsion Laboratory, Pasadena, Calif., 1999).

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