任意正弦调制的正弦移相干涉波面测量方法

针对正弦移相干涉（SinPSI）中位相调制无法精确控制的问题，提出了一种从时域频谱提取波面信息的任意正弦调制SinPSI方法（ASM-SinPSI）。首先，根据SinPSI信号频谱的第一、三个谱峰强度关系确定调制幅度，并采用空间随机点的方法避免了分母零值的问题，然后从SinPSI信号的前三个谱峰中获得波面位相的正切数值与符号信息，最后以反正切计算波面位相。数值仿真表明:在未知调制信息情况下，ASM-SinPSI的波面位相提取误差为0.016 rad。在调制幅度为1.6、2、2.5、3 rad时的测量实验中，ASM-SinPSI均可精确提取波面位相，与真实波面偏差的最大值为0.058 7 rad。在1.5~3.5 rad区间内的任意调制幅度下，ASM-SinPSI无需精确预知调制信息即可高精度提取波面位相，放宽了对移相器的严苛要求。

Sinusoidal phase-shifting interferometry with arbitrary sinusoidal modulation for wavefront measurement

Sinusoidal phase-shifting interferometry (SinPSI) suffered from modulation error. To cope with this problem, an arbitrary sinusoidal modulation SinPSI (ASM-SinPSI) method was proposed, which extracted wavefront phase from Fourier spectrum of the interferometric signal. In ASM-SinPSI, firstly the modulation amplitude was determined from the strength ratio of the first and third spectrum peaks. To avoid being divided by zero in calculating the ratio, a spatially random sampling strategy was adopted. Then the absolute values and signs of sine and cosine of wavefront phase were determined from the first three spectrum peaks, and the phase was calculated with arctangent. Simulations demonstrated that the wavefront phase retrieval error is 0.016 rad without prior knowledge of the modulation. In experiments with modulation amplitudes of 1.6, 2, 2.5 and 3 rad, wavefront phases were accurately measured with ASM-SinPSI, and the maximum deviation from the exact phase was 0.058 7 rad. ASM-SinPSI, having the benefit of extracting wavefront phase with arbitrary unknown modulation amplitude between 1.5-3.5 rad, relaxed the demanding requirement on the phase shifter of interferometers.