Related papers: Stability estimates for linearized near-field phas…
This paper focuses on stability estimates of the inverse random source problems for the polyharmonic, electromagnetic, and elastic wave equations. The source is represented as a microlocally isotropic Gaussian random field, which is defined…
The ill-posed problem of phase retrieval in optics, using one or more intensity measurements, has a multitude of applications using electromagnetic or matter waves. Many phase retrieval algorithms are computed on pixel arrays using discrete…
In coherent X-ray diffraction microscopy the diffraction pattern generated by a sample illuminated with coherent x-rays is recorded, and a computer algorithm recovers the unmeasured phases to synthesize an image. By avoiding the use of a…
The displacement field in highly non uniformly strained crystals is obtained by addition of constraints to an iterative phase retrieval algorithm. These constraints include direct space density uniformity and also constraints to the sign…
The mutual intensity and its equivalent phase-space representations quantify an optical field's state of coherence and are important tools in the study of light propagation and dynamics, but they can only be estimated indirectly from…
These tutorials introduce some basics of imaging with coherent X-rays, focusing on phase contrast. We consider the transport-of-intensity equation, as one particular method for X-ray phase contrast imaging among many, before passing on to…
The problem of phase retrieval, i.e., the problem of recovering a function from the magnitudes of its Fourier transform, naturally arises in various fields of physics, such as astronomy, radar, speech recognition, quantum mechanics and,…
X-ray phase-contrast tomography (XPCT) is widely used for high contrast 3D imaging using either synchrotron or laboratory microfocus X-ray sources. XPCT enables an order of magnitude improvement in image contrast of the reconstructed…
The problem of optimization of propagation-based phase-contrast imaging setups is considered in the case of projection X-ray imaging and three-dimensional tomography with phase retrieval. For two-dimensional imaging, a simple model for a…
This paper concerns the inverse source problems for the time-harmonic elastic and electromagnetic wave equations. The goal is to determine the external force and the electric current density from boundary measurements of the radiated wave…
We describe near-field imaging of sample sheet resistance via frequency shifts in a resonant coaxial scanning microwave microscope. The frequency shifts are related to local sample properties, such as surface resistance and dielectric…
The challenge of imaging low-density objects in an electron microscope without causing beam damage is significant in modern TEM. This is especially true for life science imaging, where the sample, rather than the instrument, still…
We are concerned with the inverse scattering problem of recovering an inhomogeneous medium by the associated acoustic wave measurement. We prove that under certain assumptions, a single far-field pattern determines the values of a…
In the last five decades, iterative phase retrieval methods draw large amount of interest across the research community as a non-interferometric approach to recover quantitative phase distributions from one (or more) intensity measurement.…
In this work we study the inverse boundary value problem of determining the refractive index in the acoustic equation. It is known that this inverse problem is ill-posed. Nonetheless, we show that the ill-posedness decreases when we…
One of the most prominent challenges in the field of diffractive imaging is the phase retrieval (PR) problem: In order to reconstruct an object from its diffraction pattern, the inverse Fourier transform must be computed. This is only…
The structural complexity and instability of many interference phase microscopy methods are the major obstacles toward high-precision phase measurement. In this vein, improving more efficient configurations as well as proposing new methods…
We study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequencies as the data. A conditional Lipschitz stability estimate for the inverse problem holds in the case of…
Phase retrieval is concerned with recovering a function $f$ from the absolute value of its Fourier transform $|\widehat{f}|$. We study the stability properties of this problem in Lebesgue spaces. Our main results shows that $$ \|…
A method for estimating the relative content of crystalline phases of a multiphase sample, based on probabilistic analysis of the intensities of the diffraction pattern reflexes, has been developed. The method is based on the introduction…