Generic nonsinusoidal fringe model and gamma calibration in phase measuring profilometry

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.

Phase error correction for fringe projection profilometry by using constrained cubic spline

“…With the constrained cubic spline fitting algorithm, an issue worth discussing is the amplitude of the output intensity. As indicated in the previous literature, the uncertainty of the measured phase is inversely proportional to the amplitude [10]. Thus, the small amplitude of the fringe pattern makes the phase more sensitive to the noise.…”

Micro-phase measuring profilometry: Its sensitivity analysis and phase unwrapping

“…The detailed methods on system calibration and gamma calibration can be found in Refs. [35,36] respectively.…”

Generic exponential fringe model for alleviating phase error in phase measuring profilometry

“…These methods can be categorized in two main types: a) calibration based methods and b) defocusing based methods [4]. As the name suggests, calibration based compensation methods depend on a calibration procedure to quantify the nonlinearity of system response by using techniques like response curve fitting [5], phase benchmark building [6,7], and gamma model derivation [8][9][10][11][12]. Huang et al [5] pre-coded the projection grating to reduce measurement error caused by the nonlinear gamma.…”

“…Li et al [10] developed a theoretical model of the gamma-distorted fringe image to calculate the gamma factor. Zhang et al [11] combined the methods proposed by Liu [9] and Li [10], and developed a universal gamma model to eliminate phase error. Cai et al [12] introduced two methods to realize robust active and passive phase-error compensation that could adapt to dynamic measurement conditions.…”