基于傅里叶变换的Gamma因子快速自标定方法

Fast Self-Calibration Method of Gamma Factor Based on Fourier Transform

为减少测量系统中由非线性响应引起的相位误差,提出一种基于傅里叶变换的Gamma因子快速自标定方法。首先,对捕获的光栅条纹进行傅里叶变换,将图像由灰度值域转换到频率值域;其次,在频率值域找到畸变光栅条纹的高次谐波分量与基波分量,通过优化函数在实数范围内搜索最佳预编码Gamma值,使高次谐波分量与基波分量的功率比值最小,完成测量系统的Gamma值自标定,进而有效减小实际测量过程中的相位误差;最后,在标准平面及实际测量物体上对所提方法进行实验验证,并与经典的相位误差校正算法进行对比。实验结果表明,所提方法能极大地抑制Gamma非线性响应,比已有相位误差校正方法更简单高效,具有更高的测量精度和测量效率。

To reduce the phase error caused by the nonlinear response in the measurement system,this paper proposed a fast self-calibration method of the Gamma factor based on the Fourier transform.In this method,Fourier transform of the captured grating fringes was performed to convert the image from the gray-scale domain to the frequency domain.Then,the high-order harmonic components and fundamental components of the distorted grating fringes were found in the frequency domain.The optimal pre-encoded Gamma value within the real number range was searched by an optimization function to minimize the power ratio of the high-order harmonic components to the fundamental components and complete the Gamma value self-calibration of the measurement system,which thereby effectively reduced the phase error in the actual measurement process.On standard planes and actual measurement objects,the method in this paper was verified by experiments and compared with classic phase-error correction algorithms.Experimental results prove that this method can suppress Gamma nonlinear response to a great extent.It is simpler and more efficient than existing phase-error correction methods and improves measurement accuracy and measurement efficiency.