Ptychography is a powerful imaging technique that is used in a variety of fields, including materials science, biology, and nanotechnology. However, the accuracy of the reconstructed ptychography image is highly dependent on the accuracy of the recorded probe positions which often contain errors. These errors are typically corrected jointly with phase retrieval through numerical optimization approaches. When the error accumulates along the scan path or when the error magnitude is large, these approaches may not converge with satisfactory result. We propose a fundamentally new approach for ptychography probe position prediction for data with large position errors, where a neural network is used to make single-shot phase retrieval on individual diffraction patterns, yielding the object image at each scan point. The pairwise offsets among these images are then found using a robust image registration method, and the results are combined to yield the complete scan path by constructing and solving a linear equation. We show that our method can achieve good position prediction accuracy for data with large and accumulating errors on the order of $10^2$ pixels, a magnitude that often makes optimization-based algorithms fail to converge. For ptychography instruments without sophisticated position control equipment such as interferometers, our method is of significant practical potential.

The problem of phase retrieval, or the algorithmic recovery of lost phase information from measured intensity alone, underlies various imaging methods from astronomy to nanoscale imaging. Traditional methods of phase retrieval are iterative in nature, and are therefore computationally expensive and time consuming. More recently, deep learning (DL) models have been developed to either provide learned priors to iterative phase retrieval or in some cases completely replace phase retrieval with networks that learn to recover the lost phase information from measured intensity alone. However, such models require vast amounts of labeled data, which can only be obtained through simulation or performing computationally prohibitive phase retrieval on hundreds of or even thousands of experimental datasets. Using a 3D nanoscale X-ray imaging modality (Bragg Coherent Diffraction Imaging or BCDI) as a representative technique, we demonstrate AutoPhaseNN, a DL-based approach which learns to solve the phase problem without labeled data. By incorporating the physics of the imaging technique into the DL model during training, AutoPhaseNN learns to invert 3D BCDI data from reciprocal space to real space in a single shot without ever being shown real space images. Once trained, AutoPhaseNN is about one hundred times faster than traditional iterative phase retrieval methods while providing comparable image quality.

Phase retrieval, the problem of recovering lost phase information from measured intensity alone, is an inverse problem that is widely faced in various imaging modalities ranging from astronomy to nanoscale imaging. The current process of phase recovery is iterative in nature. As a result, the image formation is time-consuming and computationally expensive, precluding real-time imaging. Here, we use 3D nanoscale X-ray imaging as a representative example to develop a deep learning model to address this phase retrieval problem. We introduce 3D-CDI-NN, a deep convolutional neural network and differential programming framework trained to predict 3D structure and strain solely from input 3D X-ray coherent scattering data. Our networks are designed to be "physics-aware" in multiple aspects; in that the physics of x-ray scattering process is explicitly enforced in the training of the network, and the training data are drawn from atomistic simulations that are representative of the physics of the material. We further refine the neural network prediction through a physics-based optimization procedure to enable maximum accuracy at lowest computational cost. 3D-CDI-NN can invert a 3D coherent diffraction pattern to real-space structure and strain hundreds of times faster than traditional iterative phase retrieval methods, with negligible loss in accuracy. Our integrated machine learning and differential programming solution to the phase retrieval problem is broadly applicable across inverse problems in other application areas.