Abstract We present a novel approach of phase retrieval using a 4f-imaging system, for the specific case of spatially partially coherent illumination. The theoretical investigation presented in Part I is based on scalar diffraction theory in combination with a heuristic approach. We find that the intensity of the de-focused speckle fields across the image plane shows sufficient contrast for phase retrieval, as long as the radius of the point spread function of the imaging system is well below the radius of the correlation area (spatial coherence) in the object plane. We also derive a useful relation, which allows to determine the requirements towards the essential parameters of an experimental setup, such as maximum propagation distance, diameter of the source, illumination distance and the numerical aperture of the imaging system. The consecutive paper, Part II, describes shape measurement based on the present treatise.

中文翻译：

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空间部分相干照明下基于透镜的相位恢复——第一部分：理论

摘要 我们提出了一种使用 4f 成像系统进行相位检索的新方法，适用于空间部分相干照明的特定情况。第一部分中介绍的理论研究基于标量衍射理论与启发式方法相结合。我们发现，只要成像系统的点扩散函数的半径远低于相关区域的半径（空间相干性），图像平面上散焦散斑场的强度就显示出足够的对比度来进行相位检索在物体平面。我们还推导出一个有用的关系，它允许确定对实验设置的基本参数的要求，例如最大传播距离、光源直径、照明距离和成像系统的数值孔径。