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.