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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 30, Iss. 7 — Jul. 1, 2013
  • pp: 1448–1459

Improving wavefront reconstruction accuracy by using integration equations with higher-order truncation errors in the Southwell geometry

Guanghui Li, Yanqiu Li, Ke Liu, Xu Ma, and Hai Wang  »View Author Affiliations

JOSA A, Vol. 30, Issue 7, pp. 1448-1459 (2013)

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Least-squares (LS)-based integration computes the function values by solving a set of integration equations (IEs) in LS sense, and is widely used in wavefront reconstruction and other fields where the measured data forms a slope. It is considered that the applications of IEs with smaller truncation errors (TEs) will improve the reconstruction accuracy. This paper proposes a general method based on the Taylor theorem to derive all kinds of IEs, and finds that an IE with a smaller TE has a higher-order TE. Three specific IEs with higher-order TEs in the Southwell geometry are deduced using this method, and three LS-based integration algorithms corresponding to these three IEs are formulated. A series of simulations demonstrate the validity of applying IEs with higher-order TEs in improving reconstruction accuracy. In addition, the IEs with higher-order TEs in the Hudgin and Fried geometries are also deduced using the proposed method, and the performances of these IEs in wavefront reconstruction are presented.

© 2013 Optical Society of America

OCIS Codes
(010.7350) Atmospheric and oceanic optics : Wave-front sensing
(100.5070) Image processing : Phase retrieval
(220.4840) Optical design and fabrication : Testing

ToC Category:
Image Processing

Original Manuscript: March 4, 2013
Revised Manuscript: June 7, 2013
Manuscript Accepted: June 11, 2013
Published: June 28, 2013

Guanghui Li, Yanqiu Li, Ke Liu, Xu Ma, and Hai Wang, "Improving wavefront reconstruction accuracy by using integration equations with higher-order truncation errors in the Southwell geometry," J. Opt. Soc. Am. A 30, 1448-1459 (2013)

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