Gaussian-splatting ptychography via explicit and interpretable primitives

Abstract

Ptychography overcomes the limits of lenses by co-designing optics and computation. Yet prevailing implementations reconstruct on a pixel grid, where weakly-constrained modes drift and recovery demands redundant data. Here we introduce Gaussian-splatting ptychography, representing object and probe as Gaussian primitives. Relocation concentrates primitives where structure is dense, and overlapping primitives couple neighbouring pixels to suppress mode drift. The scheme unexpectedly restores the low-frequency phase that conventional approaches lose, enabling uniform phase transfer across spatial frequencies. The probe is represented and updated in its pupil plane from a random start. In Fourier ptychography, the pupil-plane model recovers severe aberrations where pixel-grid solvers fail. In conventional optical, X-ray and electron ptychography, the pupil-plane primitives also recover the real-space probes with no model of beam-forming optics. The representation cuts memory up to 14-fold and recovers specimens from fewer acquisitions. At electron wavelengths, it resolves atomic structure at tens of electrons per square angstrom.