Zhang Xu, Zhu Limin, Li Youfu, Tu Dawei
School of Mechatronic Engineering and Automation, Shanghai University, Shanghai Key Laboratory of Manufacturing Automation and Robotics, Shanghai, China.
J Opt Soc Am A Opt Image Sci Vis. 2012 Jun 1;29(6):1047-58. doi: 10.1364/JOSAA.29.001047.
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.
伽马畸变是相位测量轮廓术的主要误差源。它使理想正弦波形的单一频率具有无限宽的频谱。此外，投影仪 - 相机系统的散焦，就像一个空间低通滤波器，会衰减高频谐波的幅度。本文提出了一种通用的畸变条纹模型，该模型表示为傅里叶级数。推导了谐波系数的数学模型。基于所提出的模型，引入了一种鲁棒的伽马校准方法。它采用多频相移法来消除散焦的影响，并保留伽马畸变的影响。然后，提出了一种伽马校正方法，用校准后的伽马值校正伽马畸变。所提出的校正方法具有高信噪比的优点。通过实验验证了所提出的模型。结果证实相位误差取决于散焦和间距。将所提出的伽马校准方法与现有技术进行比较，结果表明该方法对间距和散焦变化更具鲁棒性。采用所提出的伽马校正方法后，测量表面的相位精度大大提高，质量更高。
