## Application of S-transform profilometry in eliminating nonlinearity in fringe pattern |

Applied Optics, Vol. 51, Issue 5, pp. 577-587 (2012)

http://dx.doi.org/10.1364/AO.51.000577

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### Abstract

The S-transform, conceptually viewed as an extension of the short-time Fourier transform and the wavelet transform, features a time-frequency representation known for its local spectral property and multiresolution strategy. It has been introduced in optical three-dimensional shape measurement based on a fringe projection technique recently. In this paper, an application of S-transform for demodulating fringe patterns affected by the nonlinearity has been discussed. Two methods based on the S-transform, called S-transform ridge method and S-transform filtering method, are used to eliminate the phase errors caused by nonlinear factors of the projector and CCD camera. The theoretical representations of S-transform ridge method and S-transform filtering method in fringe analysis are given. The computer simulation and experiment are carried out to verify our research. Compared with the reconstructions of the windowed Fourier transform, the wavelet transform and the S-transform ridge method, the S-transform filtering method gives a better result under considering the influence of the fringe nonlinearity.

© 2012 Optical Society of America

**OCIS Codes**

(070.2590) Fourier optics and signal processing : ABCD transforms

(070.4790) Fourier optics and signal processing : Spectrum analysis

(120.6650) Instrumentation, measurement, and metrology : Surface measurements, figure

(190.2620) Nonlinear optics : Harmonic generation and mixing

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: July 25, 2011

Revised Manuscript: October 24, 2011

Manuscript Accepted: October 25, 2011

Published: February 7, 2012

**Citation**

Min Zhong, Wenjing Chen, and Mohua Jiang, "Application of S-transform profilometry in eliminating nonlinearity in fringe pattern," Appl. Opt. **51**, 577-587 (2012)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-51-5-577

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