Towards Low-Photon Nanoscale Imaging: Holographic Phase Retrieval via Maximum Likelihood Optimization

A new algorithmic framework is presented for holographic phase retrieval via maximum likelihood optimization, which allows for practical and robust image reconstruction. This framework is especially well-suited for holographic coherent diffraction imaging in the \textit{low-photon regime}, where data is highly corrupted by Poisson shot noise. Thus, this methodology provides a viable solution towards the advent of \textit{low-photon nanoscale imaging}, which is a fundamental challenge facing the current state of imaging technologies. Practical optimization algorithms are derived and implemented, and extensive numerical simulations demonstrate significantly improved image reconstruction versus the leading algorithms currently in use. Further experiments compare the performance of popular holographic reference geometries to determine the optimal combined physical setup and algorithm pipeline for practical implementation. Additional features of these methods are also demonstrated, which allow for fewer experimental constraints.