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