The limited dynamic range of the detector can impede coherent diffractive imaging (CDI) schemes from achieving diffraction-limited resolution. To overcome this limitation, a straightforward approach is to utilize high dynamic range (HDR) imaging through multi-exposure image fusion (MEF). This method involves capturing measurements at different exposure times, spanning from under to overexposure and fusing them into a single HDR image. The conventional MEF technique in ptychography typically involves subtracting the background noise, ignoring the saturated pixels and then merging the acquisitions. However, this approach is inadequate under conditions of low signal-to-noise ratio (SNR). Additionally, variations in illumination intensity significantly affect the phase retrieval process. To address these issues, we propose a Bayesian MEF modeling approach based on a modified Poisson distribution that takes the background and saturation into account. To infer the model parameters, the expectation-maximization (EM) algorithm is employed. As demonstrated with synthetic and experimental data, our approach outperforms the conventional MEF method, offering superior phase retrieval under challenging experimental conditions. This work underscores the significance of robust multi-exposure image fusion for ptychography, particularly in imaging shot-noise-dominated weakly scattering specimens or in cases where access to HDR detectors with high SNR is limited. Furthermore, the applicability of the Bayesian MEF approach extends beyond CDI to any imaging scheme that requires HDR treatment. Given this versatility, we provide the implementation of our algorithm as a Python package.

翻译：探测器的有限动态范围会阻碍相干衍射成像方案实现衍射极限分辨率。为克服这一限制，一种直接方法是利用多曝光图像融合实现高动态范围成像。该方法通过在不同曝光时间（从欠曝光到过曝光范围）采集测量值，并将其融合为单张HDR图像。传统叠层成像中的MEF技术通常涉及扣除背景噪声、忽略饱和像素后进行数据合并。然而，该方法在低信噪比条件下效果欠佳。此外，照明强度的变化会显著影响相位恢复过程。为解决这些问题，我们提出了一种基于修正泊松分布的贝叶斯MEF建模方法，该方法同时考虑了背景噪声和饱和效应。为推断模型参数，我们采用了期望最大化算法。合成数据与实验数据表明，我们的方法优于传统MEF技术，能在挑战性实验条件下实现更优的相位恢复。本研究强调了鲁棒多曝光图像融合对叠层成像的重要性，特别是在成像受散粒噪声主导的弱散射样本，或无法获得高信噪比HDR探测器的情况下。此外，贝叶斯MEF方法的适用性可扩展至任何需要HDR处理的成像方案。基于该方法的通用性，我们将算法实现封装为Python软件包。