Related papers: Absolute Uniqueness of Phase Retrieval with Random…
Assuming the Bousso bound, we prove a singularity theorem: if the light rays entering a hyperentropic region contract, then at least one light ray must be incomplete. "Hyperentropic" means that the entropy of the region exceeds the…
A standardized phase retrieval algorithm is presented and applied to an industry-grade high-energy ultrashort pulsed laser to uncover its spatial phase distribution. We describe in detail how to modify the well-known algorithm in order to…
In this paper we consider the following real-valued and finite dimensional specific instance of the 1-D classical phase retrieval problem. Let ${\bf F}\in\mathbb{R}^N$ be an $N$-dimensional vector, whose discrete Fourier transform has a…
We present a new method for real- and complex-valued image reconstruction from two intensity measurements made in the Fourier plane: the Fourier magnitude of the unknown image, and the intensity of the interference pattern arising from…
A theory is presented (and supported by numerical simulations) for phase-coherent reflection of light by a disordered medium which either absorbs or amplifies radiation. The distribution of reflection eigenvalues is shown to be the Laguerre…
Previous criteria for the feasibility of reconstructing phase information from intensity measurements, both in x-ray crystallography and more recently in coherent x-ray imaging, have been based on the Maxwell constraint counting principle.…
The possibility of making an optically large (many wavelengths in diameter) object appear invisible has been a subject of many recent studies. Exact invisibility scenarios for large (relative to the wavelength) objects involve…
Ptychography involves a sample being illuminated by a coherent, localised probe of illumination. When the probe interacts with the sample, the light is diffracted and a diffraction pattern is detected. Then the probe or sample is shifted…
Unconstrained partial-wave amplitudes obtained at discrete energies from fits to complete sets of experimental data may not vary smoothly with energy, and are in principle non-unique. We demonstrate how this behavior can be ascribed to the…
This paper considers the recovery of continuous signals in infinite dimensional spaces from the magnitude of their frequency samples. It proposes a sampling scheme which involves a combination of oversampling and modulations with complex…
Singularities that symbolize abrupt changes and exhibit extraordinary behavior are of broad interest. We experimentally study optomechanically induced singularities in a compound system consisting of a three-dimensional aluminum…
Ptychography has risen as a reference X-ray imaging technique: it achieves resolutions of one billionth of a meter, macroscopic field of view, or the capability to retrieve chemical or magnetic contrast, among other features. A…
Resolution enhancements are often desired in imaging applications where high-resolution sensor arrays are difficult to obtain. Many computational imaging methods have been proposed to encode high-resolution scene information on…
The reconstruction of a function from its spectrogram (i.e., the absolute value of its short-time Fourier transform (STFT)) arises as a key problem in several important applications, including coherent diffraction imaging and audio…
We show that an arbitrary spatial distribution of complex refractive index inside an object can be exactly represented as a sum of two "monomorphous" complex distributions, i.e. the distributions with the ratios of the real part to the…
A phenomenological approach is proposed to the problem of universe accelerated expansion and of the dark energy nature. A general class of models is introduced whose energy density depends on the redshift $z$ in such a way that a smooth…
By suitably generalizing the Fourier constraint projection in the difference map phasing algorithm, an object can be reconstructed from its diffraction pattern even when the latter has been incoherently averaged over a discrete group of…
A simple method of phase-and-amplitude extraction is derived that corrects for image blurring induced by partially spatially coherent incident illumination using only a single intensity image as input. The method is based on Fresnel…
The problem of phase retrieval is revisited and studied from a fresh perspective. In particular, we establish a connection between the phase retrieval problem and the sensor network localization problem, which allows us to utilize the vast…
Using the subdivision schemes theory, we develop a criterion to check if any natural number has at most one representation in the $n$-ary number system with a set of non-negative integer digits $A=\{a_1, a_2,\ldots, a_n\}$ that contains…