%0 Journal Article %1 Maurel:09 %A Maurel, Agnès %A Cobelli, Pablo %A Pagneux, Vincent %A Petitjeans, Philippe %D 2009 %I OSA %J Appl. Opt. %K Fourier Fringe Geometric analysis optics phase profilometry %N 2 %P 380--392 %T Experimental and theoretical inspection of the phase-to-height relation in Fourier transform profilometry %U http://ao.osa.org/abstract.cfm?URI=ao-48-2-380 %V 48 %X 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)APOPAI0003-6935 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)JOAOF81464-425810.1088/1464-4258/9/6/S10. 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 History Original Manuscript: September 11, 2008 Manuscript Accepted: October 29, 2008 Revised Manuscript: October 28, 2008 Published: January 8, 2009

@article{Maurel:09, 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)]APOPAI0003-6935 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)JOAOF81464-425810.1088/1464-4258/9/6/S10]. 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 History Original Manuscript: September 11, 2008 Manuscript Accepted: October 29, 2008 Revised Manuscript: October 28, 2008 Published: January 8, 2009}, added-at = {2009-01-22T08:47:34.000+0100}, author = {Maurel, Agn\`{e}s and Cobelli, Pablo and Pagneux, Vincent and Petitjeans, Philippe}, biburl = {https://www.bibsonomy.org/bibtex/2a53de82fc056bdb6b0ee6a5f8b6f1eeb/pick600}, interhash = {8be47a0f8b336170e20aa5a8bc39f53e}, intrahash = {a53de82fc056bdb6b0ee6a5f8b6f1eeb}, journal = {Appl. Opt.}, keywords = {Fourier Fringe Geometric analysis optics phase profilometry}, number = 2, pages = {380--392}, publisher = {OSA}, timestamp = {2009-01-22T10:08:44.000+0100}, title = {Experimental and theoretical inspection of the phase-to-height relation in Fourier transform profilometry}, url = {http://ao.osa.org/abstract.cfm?URI=ao-48-2-380}, volume = 48, year = 2009 }