Analysis On An Improved Fourier Transforms Profilometry

With the advantages of non-contact, only one fringe needed besides of the reference plane fringe, full field analysis and high precision, Fourier transform profilometry(FTP) has been widely applied to measure 3D shape.In order to obtain the correct height reconstruction of a measured object through the traditional Fourier transform profilometry(FTP), the connecting-line between the exit pupil of the projecting lens and the entrance pupil of the imaging lens must be horizontal and set to parallel to the reference plane. Here an improved optical geometry of FTP is discussed, and a strict theoretical analysis about an improved phase-height mapping formula based on a new description of a reference fringe and a deformed fringe in FTP is proposed in this paper when the location of the exit pupil of the projecting lens and that of the entrance pupil of the imaging lens do not meet the conditions. We focus on resolving the following problems in FTP, that is how to guarantee the measurement accuracy of FTP when the connect line between the exit pupil of the projecting lens and that of the entrance pupil of the imaging lens is not parallel to the reference, or the two pupils are not coplanar, or neither the connect line parallel to the reference nor the two pupils coplanar.Employing the new theory, it is easier to obtain the full-field fringe through adjusting either the location of the projector or imaging device. Especially, in some cases, where the required conditions that the connecting-line of the two pupils parallel to the reference plane and the projecting and imaging axes must be horizontal can not be met, the new method offers a flexible way to obtain the reliable height distribution of a measured object. Computer simulations and experiments have proved its correctness.Finally, some further suggestions for the improved Fourier transform profilometry measuring device are presented.