基于最小二乘迭代的多表面干涉条纹分析

Multiple-Surface Interference Fringes Analysis Based on Least-Squares Iteration

为了准确地测量透射平行平板,提出了基于最小二乘迭代的多表面干涉条纹分析方法。依据波长调谐相移的原理,通过最小二乘迭代准确地求得每组双表面干涉条纹的实际相移值,从而准确地提取平板前后表面面形及厚度变化等信息。模拟计算结果表明,当相移值有微小偏差(小于0.2 rad)时,通过10次迭代后求得相位的峰值(PV)误差为0.005 rad,均方根(RMS)误差为0.002 rad,而相应Okada算法的PV误差为0.512 rad,RMS误差为0.103 rad。实验结果验证了该算法的有效性。

To accurately profile transparent elements with parallel surfaces, a method based on least-squares iteration is presented to extract the phase information from multiple-surface interference fringes, According to the principle of wavelength-tuned phase shifting, the least-squares iteration is applied to obtain the actual phase shifts of the different two-beam interference fringes in each frame. Therefore, it allows extraction of front surface, back surface and thickness variation from multiple-surface interference fringes with high precision. The simulation results show that when the phase-shifting error is less than 0.2 rad, the proposed algorithm needs only 10 iterations and reduces the residual phase errors from 0. 512 rad （peak value, PV） and 0. 103 rad （root-mean-square, RMS） obtained by Okada＇s algorithm to 0. 005 rad （PV） and 0. 002 rad （RMS）. Its validation is also demonstrated by the experiment of three-surface fringes analysis.