We investigate the performance of ptychography with noisy data by analyzing the Cram'{e}r Rao Lower Bound. The lower bound of ptychography is derived and numerically computed for both top-hat plane wave and structured illumination. The influence of Poisson noise on the ptychography reconstruction is discussed. The computation result shows that, if the estimator is unbiased, the minimum variance for Poisson noise is mostly determined by the illumination power and the transmission function of the object. Monte Carlo analysis is conducted to validate our calculation results for different photon flux numbers. Furthermore, the performance of the maximum likelihood method and the approach of amplitude-based cost function minimization is studied in the Monte Carlo analysis.

中文翻译：

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CramérRao具有泊松噪声的谱图中的下界和最大似然估计

我们通过分析Cram'{e} r Rao Lower Bound，调查带有噪声数据的typography的性能。对于大礼帽平面波和结构化照明，推导了刻印术的下限并进行了数值计算。讨论了泊松噪声对码型重建的影响。计算结果表明，如果估计量是无偏的，则泊松噪声的最小方差主要由照明功率和物体的透射函数确定。进行了蒙特卡洛分析，以验证我们针对不同光子通量数的计算结果。此外，在蒙特卡洛分析中研究了最大似然方法的性能和基于幅度的成本函数最小化方法。