FlowTIE: Flow-based Transport of Intensity Equation for Phase Gradient Estimation from 4D-STEM Data

The introduction of FlowTIE marks a significant advancement in the field of electron microscopy, particularly in phase reconstruction from 4D-Scanning Transmission Electron Microscopy (STEM) data. By integrating the Transport of Intensity Equation with a flow-based representation of the phase gradient, FlowTIE enhances the accuracy and speed of phase reconstruction, especially for thick specimens. This framework not only demonstrates improved performance over classical TIE and gradient-based optimization methods but also showcases the potential of combining data-driven learning with physics-based approaches. The validation on simulated datasets of crystalline materials further underscores its effectiveness, making FlowTIE a promising tool for researchers dealing with complex materials and conditions.