Circles in diffraction

TL;DR

This paper derives a formula for the intensity of the Fourier transform of a measure along circles, linking diffraction patterns to autocorrelation, with applications in analyzing diffraction phenomena.

Contribution

It introduces a new formula for diffraction intensity along circles for Fourier transformable measures, connecting diffraction measures to autocorrelation in two dimensions.

Findings

Derived a formula for diffraction intensity along circles.

Connected diffraction measure to autocorrelation measure.

Presented applications demonstrating the formula's utility.

Abstract

Given a Fourier transformable measure in two dimensions, we find a formula for the intensity of its Fourier transform along circles. In particular, we obtain a formula for the diffraction measure along a circle in terms of the autocorrelation measure. We look at some applications of this formula.