提出广义相移干涉术中结合广义四步公式改进最小二乘法抽取任意相移进而重建复波的方法。利用广义相移数字全息算法的物波重建公式替代传统最小二乘法来提取参考光相位和重建物体波前, 大幅减小迭代循环的计算量。使用该方法, 每一次迭代计算参考相位只需要一个最小二乘法, 同时利用物波前重建公式计算物光相位。这种方法的可行性和有效性已被计算机模拟证实。模拟结果表明, 相移值抽取误差保持在 0.004 rad左右, 同比传统的四步最小二乘法算法节省大约 10倍的计算时间, 精度完全满足物波再现要求。光学实验也取得了令人满意的结果。

An approach of unknown phase shifts extraction and complex wave reconstruction in generalized phase-shifting interferometry is proposed by the combination of least square methods and generalized four-step formulae. A much-simplified algorithm is suggested to extract reference phase and then reconstruct object wave-front by replacing the conventional least-square method in above process with our specially derived wave reconstruction formulae for generalized phase-shifting interferometry. In this method, only one least-square equation is needed for one iteration to retrieve the reference phase, and the object phase can be calculated simultaneously. The feasibility and effectiveness of this algorithm have been verified by computer simulations. The results show that this innovation can keep the phase extraction errors mostly in 0.004 rad and save computing time by about 10 times compared with previous four-step LSM algorithm while it still ensures its high precision. Optical experimental results are also satisfactory.