Phase Retrieval Microscope Based on Photon Counting Image Detection

从夫琅和费衍射图中恢复相位的精度和灵敏度在很大程度上取决于所测量的夫琅和费衍射图的动态范围。本研究采用光子成像探测器对微弱相位光栅的高阶衍射光斑进行探测。从Fraunhofer衍射强度分布数据（包括应用迭代傅里叶变换算法的三阶衍射点）中，实验上相当好地完成了相位恢复。该方法具有较高的精度和灵敏度。本文还介绍了一种用单光子成像探测器测量整个衍射图样的新方法，并研究了ML-EM（maximum likelihood-expectation maximization）方法在处理只有光子计数照相机才能探测到的极低强度图像中的应用。光子噪声的影响也定量检查。实验结果表明，ML-EM产生更好的恢复比维纳滤波器在极低的强度区域，其中每像素的光子的最大数量是小于约一百。

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.