Zheng Shiling, Xue Bindang, Xue Wenfang, Bai Xiangzhi, Zhou Fugen
School of Astronautics, Beihang University, Beijing, China.
Opt Express. 2012 Jan 16;20(2):972-85. doi: 10.1364/OE.20.000972.
The noise problem is generally inevitable for phase retrieval by solving the transport of intensity equation (TIE). The noise effect can be alleviated by using multiple intensities to estimate the axial intensity derivative in the TIE. In this study, a method is proposed for estimating the intensity derivative by using multiple unevenly-spaced noisy measurements. The noise-minimized intensity derivative is approximated by a linear combination of the intensity data, in which the coefficients are obtained by solving a constrained optimization problem. The performance of the method is investigated by both the error analysis and the numerical simulations, and the results show that the method can reduce the noise effect on the retrieved phase. In addition, guidelines for the choice of the number of the intensity planes are given.
对于通过求解强度传输方程（TIE）进行相位恢复而言，噪声问题通常是不可避免的。通过使用多个强度来估计TIE中的轴向强度导数，可以减轻噪声影响。在本研究中，提出了一种利用多个非均匀间隔的噪声测量值来估计强度导数的方法。通过强度数据的线性组合来近似噪声最小化的强度导数，其中系数通过求解一个约束优化问题获得。通过误差分析和数值模拟对该方法的性能进行了研究，结果表明该方法可以降低噪声对恢复相位的影响。此外，还给出了强度平面数量选择的指导原则。
