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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 37, Iss. 34 — Dec. 1, 1998
  • pp: 7983–7987

Polynomial Fitting of Interferograms with Gaussian Errors on Fringe Coordinates. III. Nonlinear Solution

Alberto Cordero-Dávila, Octavio Cardona-Nuñez, and Alejandro Cornejo-Rodríguez  »View Author Affiliations


Applied Optics, Vol. 37, Issue 34, pp. 7983-7987 (1998)
http://dx.doi.org/10.1364/AO.37.007983


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Abstract

Assuming that the measured coordinates of the fringes of an interferogram have random errors and that they are considered Gaussian, the system of normal equations that is obtained on application of the least-squares method is converted into a nonlinear set of equations. We present an algorithm to estimate the coefficients of the nonlinear system by applying the Newton–Raphson method and starting the iteration from the standard classic solution. This algorithm is applied to a pattern of straight and equally spaced fringes, obtaining not only the right coefficients but also the adequate election of the terms to be included in the model, to show the contrast with the results of the classic method.

© 1998 Optical Society of America

OCIS Codes
(100.2650) Image processing : Fringe analysis
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(190.0190) Nonlinear optics : Nonlinear optics

Citation
Alberto Cordero-Dávila, Octavio Cardona-Nuñez, and Alejandro Cornejo-Rodríguez, "Polynomial Fitting of Interferograms with Gaussian Errors on Fringe Coordinates. III. Nonlinear Solution," Appl. Opt. 37, 7983-7987 (1998)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-37-34-7983


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References

  1. D. Malacara, “Twymann Green interferometer,” in Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley, New York, 1992), Chap. 2.
  2. A. Cordero-Dávila, A. Cornejo-Rodríguez, and O. Cardona-Nuñez, “Polynomial fitting of interferograms with Gaussian errors on fringe coordinates. I: Computer simulations,” Appl. Opt. 33, 7339–7342 (1994).
  3. A. Cordero-Dávila, A. Cornejo-Rodríguez, O. Cardona-Nuñez, and Rufino Díaz-Uribe, “Polynomial fitting of interferograms with Gaussian errors on fringe coordinates. II: Analytical study,” Appl. Opt. 31, 7343–7349 (1994).
  4. W. H. Jefferys, “On the method of least squares,” Astron. J. 85, 177–181 (1980).
  5. W. H. Jefferys, “On the method of least squares II,” Astron. J. 86, 149–155 (1981).
  6. A. W. Ross, “Regression line analysis,” Am. J. Phys. 48, 409 (1980).
  7. D. Malacara, ed., Optical Shop Testing, 2nd ed. (Wiley, New York, 1992).

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