Related papers: Dressing the Cusp: How Sharp-Edge Diffraction Theo…
Scattering of light in complex media scrambles optical wavefronts and breaks the principles of conventional imaging methods. For decades, researchers have endeavored to conquer the problem by inventing approaches such as adaptive optics,…
The high energy physics unfolding problem is an important statistical inverse problem in data analysis at the Large Hadron Collider (LHC) at CERN. The goal of unfolding is to make nonparametric inferences about a particle spectrum from…
The inability of standard models to explain the flux ratios in many 4-image gravitational lenses has been cited as evidence for significant small-scale structure in lens galaxies. That claim has generally relied on detailed lens modeling,…
For over a century diffraction theory has been thought to limit the resolution of focusing and imaging in the optical domain. The size of the smallest spot achievable is inversely proportional to the range of spatial wavevectors available.…
In this paper, we consider the obstacle scattering problem for biharmonic equations with a Dirichlet boundary condition in both two and three dimensions. Some basic properties are first derived for the biharmonic scattering solutions, which…
Intrinsic image decomposition is an important and long-standing computer vision problem. Given an input image, recovering the physical scene properties is ill-posed. Several physically motivated priors have been used to restrict the…
We develop embedding formulae for all possible diffraction problems with Dirichlet scatterers on square lattices using the Wiener--Hopf perspective. The embedding formula expresses solutions for arbitrary plane-wave incidence in terms of a…
Detecting if and when objects change is difficult in passive sub-diffraction imaging of dynamic scenes. We consider the best possible tradeoff between responsivity and accuracy for detecting a change from one arbitrary object model to…
Kirchhoff's scalar diffraction theory is applied throughout photon and electron optics. It is based on the stationary electromagnetic or Schr\"odinger wave equation, and is useful in describing interference phenomena for both light and…
We present a new computational near-eye display method that addresses the vergence-accommodation conflict problem in stereoscopic displays through accommodation-invariance. Our system integrates a refractive lens eyepiece with a novel…
In this thesis I discuss combinatorial optimization problems, from the statistical physics perspective. The starting point are the motivations which brought physicists together with computer scientists and mathematicians to work on this…
In this work, we present and investigate the novel blind inverse problem of position-blind ptychography, i.e., ptychographic phase retrieval without any knowledge of scan positions, which then must be recovered jointly with the image. The…
Based on the ideas of arXiv:1710.06612, we consider the problem of minimization of the Holder-continuous non-smooth functional $f$ with non-positive convex (generally, non-smooth) Lipschitz-continuous functional constraint. We propose some…
Overcoming diffraction limit is crucial for obtaining high-resolution image and observing fine microstructure. With this conventional difficulty still puzzling us and the prosperous development of wave dynamics of light interacting with…
Image segmentation is a central topic in image processing and computer vision and a key issue in many applications, e.g., in medical imaging, microscopy, document analysis and remote sensing. According to the human perception, image…
We consider the geometric optics problem of finding a system of two reflectors that transform a spherical wavefront into a beam of parallel rays with prescribed intensity distribution. Using techniques from optimal transportation theory, it…
Optical tweezers exploit light--matter interactions to trap particles ranging from single atoms to micrometer-sized eukaryotic cells. For this reason, optical tweezers are a ubiquitous tool in physics, biology, and nanotechnology. Recently,…
This dissertation is concerned with understanding and analyzing some of the effects of diffraction in the near field. The contributions of homogeneous and of evanescent waves to two-dimensional near-field diffraction patterns of scalar…
A comprehensive convergence and stability analysis of some probabilistic numerical methods designed to solve Cauchy-type inverse problems is performed in this study. Such inverse problems aim at solving an elliptic partial differential…
The interaction of optical vortices (or phase singularities, screw dislocations) with ordinary matter is treated with simple approach. Using total internal reflection phenomenon and superposition of four plane waves incident on a material…