Understanding transverse coherence properties of X-ray beams in third generation Synchrotron Radiation sources

TL;DR

This paper develops a comprehensive theory for the transverse coherence of X-ray undulator radiation, providing practical formulas and methods to accurately predict and manipulate coherence properties in third-generation synchrotron sources.

Contribution

It introduces a general technique to calculate the cross-spectral density of undulator radiation beyond the quasi-homogeneous approximation, improving coherence predictions for beamline design.

Findings

Derived an analytical expression for the cross-spectral density up to the undulator exit.

Provided simple formulas for transverse coherence length applicable to various sources.

Demonstrated manipulation of coherence properties using a vertical slit to enlarge the coherent spot.

Abstract

This paper describes a theory of transverse coherence properties of Undulator Radiation. Our study is of very practical relevance, because it yields specific predictions of Undulator Radiation cross-spectral density in various parts of the beamline. On the contrary, usual estimations of coherence properties assume that the undulator source is quasi-homogeneous, like thermal sources, and rely on the application of van Cittert-Zernike (VCZ) theorem, in its original or generalized form, for calculating transverse coherence length in the far-field approximation. The VCZ theorem is derived in the frame of Statistical Optics using a number of restrictive assumptions: in particular, the quasi-homogeneous assumption is demonstrated to be inaccurate in many practical situations regarding undulator sources. We propose a technique to calculate the cross-spectral density from undulator sources in the most general case. Also, we find the region of applicability of the quasi-homogeneous model and we present an analytical expression for the cross-spectral density which is valid up to the exit of the undulator. For the case of more general undulator sources, simple formulas for the transverse coherence length, interpolated from numerical calculations and suitable for beamline design applications are found. Finally, using a simple vertical slit, we show how transverse coherence properties of an X-ray beam can be manipulated to obtain a larger coherent spot-size on a sample. This invention was devised almost entirely on the basis of theoretical ideas developed throughout this paper.