Imaging is indispensable for nearly every field of science, engineering, technology, and
medicine. However, measurement noise and stochastic distortions pose fundamental limits …

This paper develops uniqueness theory for 3D phase retrieval with finite, discrete
measurement data for strong phase objects and weak phase objects, including:(i) Unique …

Interest in atomic scale structures of individual specimens has invigorated developments of
high-resolution probes, which include single-particle imaging using x-ray free-electron …

X-ray imaging of soft materials is often difficult because of the low contrast of the
components. This particularly applies to frozen hydrated biological cells where the feature of …

A discrete framework of 3D tomographic phase retrieval with a coded aperture under the
Rytov and Born approximations is analyzed. With the introduction of a beam splitter together …

A general analytical model is established to study the change in the signal-to-noise ratio
(SNR) of the spatially noisy optical signal after passing through a subwavelength-aperture …

Simulations of radiation damage in single-molecule imaging using an x-ray free-electron
laser use atomic rates calculated in the lowest order. We investigate the difference in ion …

The notions of spatial resolution and signal-to-noise are central to most forms of imaging.
However, it appears that rigorous definitions of these quantities, which would be general …

The deterioration of both the signal-to-noise ratio and the spatial resolution in the electron-
density distribution reconstructed from diffraction intensities collected at different orientations …

Resolving the electronic structure of single biological molecules in their native state was
among the primary motivations behind X-ray free-electron lasers. The ultra-short pulses they …