移相术中相移算法的窗函数整数近似方法分析

Window Function Integer Approximation Method of Phase Shifting Algorithms in Phase Shifting Technique

用离散傅里叶分析的方法将相移过程描述为频谱域滤波的过程,阐明了相移算法的窗函数整数近似法原理。由于相移的有限性会带来频谱泄露的问题,提出了好的移相算法窗函数应该满足主瓣窄、旁瓣小的观点,并给出了根据窗函数整数近似方法设计任意移相间距和任意移相步数移相算法的流程。选择矩形窗、三角窗、hanning窗和blackman窗生成4种11步移相算法,对振动误差和相移误差的分析验证了旁瓣小的hanning窗和blackman窗生成的算法对误差的灵敏度要小;再选择hanning窗生成了移相间距为π/2的5,11,15,39,51,76和101步7种移相算法,仿真验证了步数越多主瓣越小,对振动抑制能力越好,但需要更高的微位移器移动精度来获得有效的干涉条纹。在满足干涉条纹质量的前提下,步数多的移相算法对移相误差的抑制能力越好。最后模拟实验环境,验证了算法的性能。

Phase shift process is described as a filtering process in the frequency domain with the analysis of discrete Fourier and the theory of window function integer approximation method is also illustrated. In order to restrain the leakage problems from the finite phase shifting steps, a viewpoint that the algorithms should have narrow main lobe and small side lobes is presented. The flow of design phase shifting algorithms according to the integer approximation method is given, which can satisfy any phase shifting intervals and phase shifting steps. According to this method, four different 11-step algorithms with four different window functions which are rectangular window, triangle window, hanning window, and blackman window are designed. Analysis and simulation show that hanning window and blackman window with small lobes are less sensitive to errors. Seven different algorithms with the same phase shifting interval π/2 are designed by hanning window function, whose phase shifting steps are separately 5,11, 15,39,51,76 and 101 steps. Analysis of the relation between phase shifting algorithms and phase shift errors and vibration errors demonstrates that more phase steps lead to narrow main lobe and have higher resistance to vibration error （the 101 algorithm is virtually insensitive to vibration below 30 Hz）, but needs higher accuracy of displacement actuator to get effective fringe contrast （the accuracy of displace actuator for 101 is 4 nm）. If the enough signal strength is gotten, more steps mean better performance of phase shifting algorithms. Finally the result of stimulant experiment denominates the performance of phase shifting algorithms.