![]() ![]() Specific to the problem of phase retrieval, neural networks have been trained to learn to retrieve phases in holographic imaging 25, lensless computational imaging 26, X-ray ptychography 27, 28, 29, Fourier ptychography 30 and in BCDI 31, 32, 33, 34, 35. Neural network (NN) models have been developed to rapidly solve inverse problems across a variety of disciplines including magnetic resonance imaging (MRI) 19, image denoising 20, 21, super-resolution 22, 23, 24, etc. ![]() Iterative phase retrieval typically requires thousands of iterations and often multiple starts to arrive at a robust solution, often taking longer than a single dataset acquisition time. More broadly, while coherent imaging techniques have grown to become an integral part of electron and X-ray materials characterization 2, 3, 18, their dependence on iterative phase retrieval to recover sample images prevents real-time feedback, which is particularly crippling for in-situ and operando experiments. Examples include defect dynamics in battery electrodes 6, in-situ catalysis 7, 8, photon transport 9, 10, 11, phase transformation 12, 13, 14, and plastic deformation 15, 16, 17. ![]() This capability of BCDI to provide nanoscale structural information as well as picometer sensitivity to strain has had profound implications for the materials science, chemistry and solid-state physics communities. Consequently, in addition to being a fundamental requirement to recovering the object’s 3D structure, phase recovery also provides a 3D map of the strain state within the crystal, encoded as a phase of the complex image. Additionally, when measured at a Bragg peak, the phase is influenced by the local strain within the crystal. ![]() Hence, the 3D image of the object cannot be recovered from a simple inverse FT and we must resort to phase retrieval algorithms that can recover this lost phase information to recover an image of the object. The measured intensities represent the modulus of the complex Fourier transform (FT) of the object, but the phase of the wave is lost. In BCDI for example, a nanocrystalline sample is illuminated with a coherent X-ray beam from a synchrotron source or X-ray free electron lasers (XFEL) and the scattered intensities are measured in the far-field at a Bragg peak. Phase retrieval is the algorithmic process of recovering phases from measured scattered intensities alone. The problem of phase retrieval is a central problem in many imaging techniques including X-ray Bragg coherent diffraction imaging (BCDI) and ptychography 1, electron ptychography 2, Lorentz transmission electron microscopy (LTEM) 3, super-resolution optical imaging 4, and astronomy 5. Once trained, AutoPhaseNN can be effectively used in the 3D BCDI data inversion about 100× faster than iterative phase retrieval methods while providing comparable image quality. By incorporating the imaging physics into the DL model during training, AutoPhaseNN learns to invert 3D BCDI data in a single shot without ever being shown real space images. Using 3D X-ray Bragg coherent diffraction imaging (BCDI) as a representative technique, we demonstrate AutoPhaseNN, a DL-based approach which learns to solve the phase problem without labeled data. However, such models require vast amounts of labeled data, which can only be obtained through simulation or performing computationally prohibitive phase retrieval on experimental datasets. Deep learning (DL) models have been developed to either provide learned priors or completely replace phase retrieval. Traditional phase retrieval methods are iterative and are therefore computationally expensive. The problem of phase retrieval underlies various imaging methods from astronomy to nanoscale imaging. ![]()
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