Vision transformer for multi-domain phase retrieval in coherent diffraction imaging

Bragg coherent diffraction imaging (BCDI) phase retrieval becomes difficult in the strong-phase regime, where a crystal contains distortions beyond half a lattice spacing. An important special case is the phase domain problem, where blocks of a crystal are displaced with sharp jumps at domain walls. This generates split Bragg peaks and dense fringe structures for which classical iterative solvers often stagnate or return different solutions from different initialisations. We introduce an unsupervised vision transformer (ViT) using Fourier attention to solve this block-phase, multi-domain phase retrieval problem directly from measured 2D Bragg diffraction intensities. Through token mixing and multiscale Fourier attention, Fourier ViT couples reciprocal-space information globally to improve convergence in the strong-phase regime. We have validated the approach on synthetic Voronoi multi-domain crystals with strong-phase contrast under realistic noise corruptions. We further tested it on experimental diffraction from weak-phase SrTiO₃, Fe₃O₄ across its phase transition, and strong-phase La_0.5Ca_0.5MnO₃ nanocrystals. For the cases studied here, we have achieved reciprocal-space mismatch (χ²) comparable to or lower than the compared baselines. Our method preserves domain-resolved phase reconstructions on synthetic data as the number of domains increases. On experimental data, the iterative method, Fourier ViT, and the complex convolutional neural network baseline reach similar χ² under the same fixed support.