Zuo Chao, Chen Qian, Yu Yingjie, Asundi Anand
Jiangsu Key Laboratory of Spectral Imaging & Intelligence Sense, Nanjing University of Science and Technology, Nanjing, Jiangsu Province 210094, China.
Opt Express. 2013 Mar 11;21(5):5346-62. doi: 10.1364/OE.21.005346.
Several existing strategies for estimating the axial intensity derivative in the transport-of-intensity equation (TIE) from multiple intensity measurements have been unified by the Savitzky-Golay differentiation filter--an equivalent convolution solution for differentiation estimation by least-squares polynomial fitting. The different viewpoint from the digital filter in signal processing not only provides great insight into the behaviors, the shortcomings, and the performance of these existing intensity derivative estimation algorithms, but more important, it also suggests a new way of improving solution strategies by extending the applications of Savitzky-Golay differentiation filter in TIE. Two novel methods for phase retrieval based on TIE are presented--the first by introducing adaptive-degree strategy in spatial domain and the second by selecting optimal spatial frequencies in Fourier domain. Numerical simulations and experiments verify that the second method outperforms the existing methods significantly, showing reliable retrieved phase with both overall contrast and fine phase variations well preserved.
通过Savitzky-Golay微分滤波器，统一了几种现有的从多个强度测量值估计强度传输方程（TIE）中轴向强度导数的策略，这是一种通过最小二乘多项式拟合进行微分估计的等效卷积解决方案。与信号处理中的数字滤波器不同的观点，不仅能深入了解这些现有强度导数估计算法的行为、缺点和性能，更重要的是，它还通过扩展Savitzky-Golay微分滤波器在TIE中的应用，提出了一种改进求解策略的新方法。提出了两种基于TIE的新型相位恢复方法——第一种是在空间域引入自适应阶数策略，第二种是在傅里叶域选择最佳空间频率。数值模拟和实验验证，第二种方法明显优于现有方法，能可靠地恢复相位，同时很好地保留整体对比度和精细相位变化。
