Enhanced phase retrieval using nonlinear dynamics
Enhanced phase retrieval using nonlinear dynamics
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DOI：
10.1364/oe.24.025091
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发表时间：
2016-10-31
期刊：
影响因子：
3.8
通讯作者：
Fleischer, Jason W.
中科院分区：
文献类型：
--
作者：
Lu, Jen-Tang;Lu, Chien-Hung;Fleischer, Jason W.
历史上，相位恢复算法依赖于两个不同幅度（强度）测量之间的线性传播。虽然这些算法通常是成功的，但存在许多问题，包括对噪声的敏感性、局部极小值以及不确定的初始和最终条件。在这里，我们证明了非线性传播克服了这些问题，因为强度引起的折射率变化会对相位产生额外的约束。更具体地说，相位匹配条件（波能量和动量守恒）引起测量的振幅和未知相位之间的对象相关的共振。结果是重建算法中的非经典收敛曲线，其包含零交叉，其中幅度误差中的可观测最小值和相位误差中的不可观测最小值在相同的迭代次数处对齐。我们证明了这种收敛实验中的光折变晶体，有一个明确的规则停止迭代。我们发现，最佳相位恢复发生在线性和非线性输出幅度之间相关性最小的非线性强度下，即最大化线性和非线性传播之间信息多样性的条件。相应的算法大大改善了传统的Gerchberg-Saxton结果，并具有很大的潜力，以提高其他方法的衍射成像。(C)2016美国光学学会
Historically, phase retrieval algorithms have relied on linear propagation between two different amplitude (intensity) measurements. While generally successful, these algorithms have many issues, including susceptibility to noise, local minima, and indeterminate initial and final conditions. Here, we show that nonlinear propagation overcomes these issues, as intensity-induced changes to the index of refraction create additional constraints on the phase. More specifically, phase-matching conditions (conservation of wave energy and momentum) induce an object-dependent resonance between the measured amplitudes and the unknown phase. The result is a non-classical convergence profile in the reconstruction algorithm that contains a zero crossing, where the observable minimum in amplitude error and the unobservable minimum in phase error align at the same iteration number. We demonstrate this convergence experimentally in a photorefractive crystal, showing that there is a clear rule for stopping iterations. We find that the optimum phase retrieval occurs for a nonlinear strength that gives minimal correlation between the linear and nonlinear output amplitudes, i.e. a condition that maximizes the information diversity between linear and nonlinear propagation. The corresponding algorithm greatly improves the conventional Gerchberg-Saxton result and holds much potential for enhancing other methods of diffractive imaging. (C) 2016 Optical Society of America