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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 2 — Jan. 16, 2012
  • pp: 1530–1544

Use of numerical orthogonal transformation for the Zernike analysis of lateral shearing interferograms

Fengzhao Dai, Feng Tang, Xiangzhao Wang, Peng Feng, and Osami Sasaki  »View Author Affiliations


Optics Express, Vol. 20, Issue 2, pp. 1530-1544 (2012)
http://dx.doi.org/10.1364/OE.20.001530


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Abstract

A numerical orthogonal transformation method for reconstructing a wavefront by use of Zernike polynomials in lateral shearing interferometry is proposed. The difference fronts data in two perpendicular directions are fitted to numerical orthonormal polynomials instead of Zernike polynomials, and then the orthonormal coefficients are used to evaluate the Zernike coefficients of the original wavefront by use of a numerical shear matrix. Due to the fact that the dimensions of the shear matrix are finite, the high-order terms of the original wavefront above a certain order have to be neglected. One of advantages of the proposed method is that the impact of the neglected high-order terms on the outcomes of the lower-order terms can be decreased, which leads to a more accurate reconstruction result. Another advantage is that the proposed method can be applied to reconstruct a wavefront on an aperture of arbitrary shape from its difference fronts. Theoretical analysis and numerical simulations shows that the proposed method is correct and its reconstruction error is obviously smaller than that of Rimmer-Wyant method.

© 2012 OSA

OCIS Codes
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.3940) Instrumentation, measurement, and metrology : Metrology
(120.5050) Instrumentation, measurement, and metrology : Phase measurement

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: November 11, 2011
Revised Manuscript: December 15, 2011
Manuscript Accepted: December 26, 2011
Published: January 10, 2012

Citation
Fengzhao Dai, Feng Tang, Xiangzhao Wang, Peng Feng, and Osami Sasaki, "Use of numerical orthogonal transformation for the Zernike analysis of lateral shearing interferograms," Opt. Express 20, 1530-1544 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-2-1530


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