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

Full Article  |  PDF Article
OSA Recommended Articles
Multi-frequency color-marked fringe projection profilometry for fast 3D shape measurement of complex objects

Chao Jiang, Shuhai Jia, Jun Dong, Qingchen Bao, Jia Yang, Qin Lian, and Dichen Li
Opt. Express 23(19) 24152-24162 (2015)

Empirical mode decomposition profilometry: small-scale capabilities and comparison to Fourier transform profilometry

Guillaume Lagubeau, Pablo Cobelli, Tomasz Bobinski, Agnès Maurel, Vincent Pagneux, and Philippe Petitjeans
Appl. Opt. 54(32) 9409-9414 (2015)

Uneven fringe projection for efficient calibration in high-resolution 3D shape metrology

Zonghua Zhang, Catherine E. Towers, and David P. Towers
Appl. Opt. 46(24) 6113-6119 (2007)

References

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Figures (16)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Equations (49)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Metrics

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription