相关论文: A Glimpse at Mathematical Diffraction Theory

Discrete sampling theorem is formulated that refers to discrete signals specified by a finite number of their samples and band-limited in a domain of a certain orthogonal transform. Conditions of the recoverability of such signals from…

We introduce a class of integral theorems based on cyclic functions and Riemann sums approximating integrals. The Fourier integral theorem, derived as a combination of a transform and inverse transform, arises as a special case. The…

I review various theory issues in diffraction that have been presented and discussed in the working group on diffractive interactions, and a few points concerning the comparison of theory with data.

For more than a century and a half it has been widely-believed (but was never rigorously shown) that the physics of diffraction imposes certain fundamental limits on the resolution of an optical system. However our understanding of what…

We study the multifractal properties of diffusion in the presence of an absorbing polymer and report the numerical values of the multifractal dimension spectra for the case of an absorbing self avoiding walk or random walk.

The theory of measurement is employed to elucidate the physical basis of general relativity. For measurements involving phenomena with intrinsic length or time scales, such scales must in general be negligible compared to the (translational…

Fourier Transforms is a first in a series of monographs we present on harmonic analysis. Harmonic analysis is one of the most fascinating areas of research in mathematics. Its centrality in the development of many areas of mathematics such…

Optical diffraction tomography is an indispensable tool for studying objects in three-dimensions due to its ability to accurately reconstruct scattering objects. Until now this technique has been limited to coherent light because spatial…

Transmission matrices are valuable tools to describe and control light transport through scattering media. There are only a few cases where the transmission matrix can be compared to microscopic theories. Here we measure the…

How could the Fourier and other transforms be naturally discovered if one didn't know how to postulate them? In the case of the Discrete Fourier Transform (DFT), we show how it arises naturally out of analysis of circulant matrices. In…

When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model, for example, the orders of the fractional derivative or the source term, are often unknown,…

The Fourier transform is typically seen as closely related to the additive group of real numbers, its characters and its Haar measure. In this paper, we propose an alternative viewpoint; the Fourier transform can be uniquely characterized…

The interest in using optical transition radiation (OTR) in high energy (multiGeV) beam diagnostics has motivated theoretical and experimental investigations on the limitations brought by diffraction on the attainable resolution. This paper…

We use machine learning to provide a tractable measure of the amount of predictable variation in the data that a theory captures, which we call its "completeness." We apply this measure to three problems: assigning certain equivalents to…

Fraunhofer diffraction plays a vital role in experimental physics not only because it accurately describes the behaviour of light in the usual propagation limit, but also because it links the diffracted light with the scattering object…

An appeal for symmetry is made to build established notions of specific representation and specific nonlinearity of measurement (often called model error) into a canonical linear regression model. Additive components are derived from the…

The Fourier transform is naturally defined for integrable functrions. Otherwise, it should be stipulated in which sense the Fourier transform is understood. We consider some class of radial and, generally saying, nonintegrable functions.…

We define hyperbolic fractional-order Fourier transformations by replacing the circular trigonometric functions in the integral expressions of conventional fractional-order Fourier transformations with hyperbolic trigonometric functions. We…

The change of the effective dimension of spacetime with the probed scale is a universal phenomenon shared by independent models of quantum gravity. Using tools of probability theory and multifractal geometry, we show how dimensional flow is…

We derive a semiclassical theory for the detection of matter-waves. This theory draws on the theories of semiclassical optical detection and fluid mechanics. We observe that the intrinsically dispersive nature of matter-waves is important…