Generic nonsinusoidal fringe model and gamma calibration in phase measuring profilometry

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)1047-1058
Journal / PublicationJournal of the Optical Society of America A: Optics and Image Science, and Vision
Issue number6
Publication statusPublished - Jun 2012


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.

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