title: Experimental and theoretical inspection of the phase-to-height relation in Fourier transform profilometry.
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.
authors.affiliation: Laboratoire Ondes et Acoustique, UMR CNRS 7587, Ecole Supérieure de Physique et Chimie Industrielles, 10 rue Vauquelin, 75005 Paris, France. agnes.maurel@espci.fr
authors.forename: Agnès
authors.initials: A
authors.lastname: Maurel
authors.forename: Pablo
authors.initials: P
authors.lastname: Cobelli
authors.forename: Vincent
authors.initials: V
authors.lastname: Pagneux
authors.forename: Philippe
authors.initials: P
authors.lastname: Petitjeans