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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 29, Iss. 6 — Jun. 1, 2012
  • pp: 1047–1058

Generic nonsinusoidal fringe model and gamma calibration in phase measuring profilometry

Xu Zhang, Limin Zhu, Youfu Li, and Dawei Tu  »View Author Affiliations


JOSA A, Vol. 29, Issue 6, pp. 1047-1058 (2012)
http://dx.doi.org/10.1364/JOSAA.29.001047


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Abstract

Gamma distortion is a dominant error source of phase measuring profilometry. It makes a single frequency for the ideal sinusoidal waveform an infinite width of spectrum. Besides, the defocus of the projector-camera system, like a spatial low-pass filter, attenuates the amplitudes of the high-frequency harmonics. In this paper, a generic distorted fringe model is proposed, which is expressed as a Fourier series. The mathematical model of the harmonic coefficients is derived. Based on the proposed model, a robust gamma calibration method is introduced. It employs the multifrequency phase-shifting method to eliminate the effect of defocus and preserve the influence of gamma distortion. Then, a gamma correction method is proposed to correct the gamma distortion with the calibrated gamma value. The proposed correction method has the advantage of high signal-to-noise ratio. The proposed model is verified through experiments. The results confirm that the phase error is dependent on the defocus and the pitch. The proposed gamma calibration method is compared with the state of the art and proves to be more robust to pitch and defocus variations. After adopting the proposed gamma correction method, the phase precision is much enhanced with higher quality in the measured surfaces.

© 2012 Optical Society of America

OCIS Codes
(000.3110) General : Instruments, apparatus, and components common to the sciences
(110.6880) Imaging systems : Three-dimensional image acquisition
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
(150.6910) Machine vision : Three-dimensional sensing
(330.1400) Vision, color, and visual optics : Vision - binocular and stereopsis

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: November 28, 2011
Revised Manuscript: February 11, 2012
Manuscript Accepted: March 14, 2012
Published: May 29, 2012

Citation
Xu Zhang, Limin Zhu, Youfu Li, and Dawei Tu, "Generic nonsinusoidal fringe model and gamma calibration in phase measuring profilometry," J. Opt. Soc. Am. A 29, 1047-1058 (2012)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-29-6-1047

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