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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 48, Iss. 2 — Jan. 10, 2009
  • pp: 380–392

Experimental and theoretical inspection of the phase-to-height relation in Fourier transform profilometry

Agnès Maurel, Pablo Cobelli, Vincent Pagneux, and Philippe Petitjeans  »View Author Affiliations


Applied Optics, Vol. 48, Issue 2, pp. 380-392 (2009)
http://dx.doi.org/10.1364/AO.48.000380


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Abstract

The measurement of an object’s shape using projected fringe patterns needs a relation between the measured phase and the object’s height. Among various methods, the Fourier transform profilometry proposed by Takeda and Mutoh [Appl. Opt. 22, 3977–3982 (1983)] is widely used in the literature. Rajoub et al. have shown that the reference relation given by Takeda is erroneous [ J. Opt. A. Pure Appl. Opt. 9, 66–75 (2007)]. This paper follows from Rajoub’s study. Our results for the phase agree with Rajoub’s results for both parallel- and crossed-optical-axes geometries and for either collimated or noncollimated projection. Our two main results are: (i) we show experimental evidence of the error in Takeda’s formula and (ii) we explain the error in Takeda’s derivation and we show that Rajoub’s argument concerning Takeda’s error is not correct.

© 2009 Optical Society of America

OCIS Codes
(080.0080) Geometric optics : Geometric optics
(120.2650) Instrumentation, measurement, and metrology : Fringe analysis

History
Original Manuscript: September 11, 2008
Revised Manuscript: October 28, 2008
Manuscript Accepted: October 29, 2008
Published: January 8, 2009

Citation
Agnès Maurel, Pablo Cobelli, Vincent Pagneux, and Philippe Petitjeans, "Experimental and theoretical inspection of the phase-to-height relation in Fourier transform profilometry," Appl. Opt. 48, 380-392 (2009)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-48-2-380

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