Phase Retrieval Microscope Based on Photon Counting Image Detection

从夫琅和费衍射图恢复相位的准确性和灵敏度在很大程度上取决于测量的夫琅和费衍射图的动态范围。在这项研究中，光子成像探测器被用来探测一个很弱的位相光栅的高阶衍射斑。利用夫琅和费衍射光强分布数据，包括三级衍射斑，采用迭代傅里叶变换算法，较好地实现了位相恢复。以较高的精度和灵敏度反演物相分布。文中还介绍了一种用单光子成像探测器测量整个衍射图的新方法，并研究了ML-EM(最大似然期望最大化)方法在处理只有光子计数相机才能检测到的极低强度图像中的应用。还定量地考察了光子噪声的影响。实验表明，在极低光强区域，每个像素的最大光子数小于100个，ML-EM算法比维纳滤波算法具有更好的复原效果。

The accuracy and sensitivity of the phase retrieval from a Fraunhofer diffraction pattern greatly depend on the dynamic range of the measured Fraunhofer diffraction pattern. In this study, the photon-imaging detector was adopted to detect higher order diffraction spots of a very weak phase grating. The phase retrieval was accomplished experimentally fairly well from the Fraunhofer diffraction intensity distribution data including up to the third order diffraction spots to which the iterative Fourier transform algorithms were applied. The object phase distribution was retrieved with fairly high accuracy and sensitivity. A newly introduced procedure for measuring the entire diffraction pattern with single photon-imaging detector is also described.The application of the ML-EM (maximum likelihood-expectation maximization) method to the processing of images of extremely low intensity, which is detectable only with a photon counting camera, is also examined. The influence of the photon noise is also quantitatively examined. It is experimentally shown that the ML-EM produces better restoration than the Wiener filter in the extremely low intensity region where the maximal number of photons per pixel is less than about one hundred.