Evaluating the Transfer of Information in Phase Retrieval STEM Techniques

Phase retrieval methods in scanning transmission electron microscopy (STEM) recover scattered phase information from far-field intensity measurements of a converged electron probe. We evaluate the performance of various phase retrieval techniques – including center-of-mass imaging (COM), tilt-corrected bright-field STEM (tcBF), and direct ptychographic methods such as single-side band (SSB) and Wigner distribution deconvolution (WDD) – under different experimental conditions. Through analytical derivation of contrast transfer functions (CTF) under the weak phase-object approximation and numerical validation using white-noise samples, we assess the impact of scan sampling, illumination aberrations, and detector geometries. Based on these findings, we develop a novel direct ptychographic algorithm that combines the relaxed scan-sampling advantages of tcBF while avoiding CTF zero-crossings through SSB recovery. Our analysis reveals fundamental limitations in using CTF as a performance metric and demonstrates the advantages of dose-invariant spectral signal-to-noise ratio (SSNR) for evaluating phase retrieval methods.