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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 38, Iss. 23 — Aug. 10, 1999
  • pp: 5024–5031

Solution to the shearing problem

Clemens Elster and Ingolf Weingärtner  »View Author Affiliations


Applied Optics, Vol. 38, Issue 23, pp. 5024-5031 (1999)
http://dx.doi.org/10.1364/AO.38.005024


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Abstract

Lateral shearing interferometry is a promising reference-free measurement technique for optical wave-front reconstruction. The wave front under study is coherently superposed by a laterally sheared copy of itself, and from the interferogram difference measurements of the wave front are obtained. From these difference measurements the wave front is then reconstructed. Recently, several new and efficient algorithms for evaluating lateral shearing interferograms have been suggested. So far, however, all evaluation methods are somewhat restricted, e.g., assume a priori knowledge of the wave front under study, or assume small shears, and so on. Here a new, to our knowledge, approach for the evaluation of lateral shearing interferograms is presented, which is based on an extension of the difference measurements. This so-called natural extension allows for reconstruction of that part of the underlying wave front whose information is contained in the given difference measurements. The method is not restricted to small shears and allows for high lateral resolution to be achieved. Since the method uses discrete Fourier analysis, the reconstructions can be efficiently calculated. Furthermore, it is shown that, by application of the method to the analysis of two shearing interferograms with suitably chosen shears, exact reconstruction of the underlying wave front at all evaluation points is obtained up to an arbitrary constant. The influence of noise on the results obtained by this reconstruction procedure is investigated in detail, and its stability is shown. Finally, applications to simulated measurements are presented. The results demonstrate high-quality reconstructions for single shearing interferograms and exact reconstructions for two shearing interferograms.

© 1999 Optical Society of America

OCIS Codes
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.4630) Instrumentation, measurement, and metrology : Optical inspection
(120.5050) Instrumentation, measurement, and metrology : Phase measurement

History
Original Manuscript: February 3, 1999
Revised Manuscript: May 11, 1999
Published: August 10, 1999

Citation
Clemens Elster and Ingolf Weingärtner, "Solution to the shearing problem," Appl. Opt. 38, 5024-5031 (1999)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-38-23-5024

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