Post on 08-Aug-2020
Field modeling for partially coherent X-ray
imaging system
The statistical properties of a synchrotron source is described by the cross-spectral density
function as a superposition of mutually uncorrelated, spatially localized modes (Fig. 1). This
description is applied to model the propagation of spatially partially coherent light beams in
an X-ray imaging system (Fig. 2) with non-ideal grazing-incidence mirrors (Fig. 3).
Antonie D. Verhoeven1 // Christian Hellmann2 // Mourad Idir3 // Frank Wyrowski2 // Jari Turunen1
1Institute of Photonics, University of Eastern Finland, 80101 Joensuu, Finland2Institute of Applied Physics, Friedrich-Schiller University, D-07745 Jena, Germany3Photonics Science Division, Brookhaven National Laboratory-NSL II, 11973-5000 New York, USA
U N I V E R S I T Y O F E A S T E R N F I N L A N D | I N S T I T U T E O F P H O T O N I C S
Introduction
[1] J. Turunen, ‘Elementary-field representations in partially coherent optics’, J. Mod. Opt.58, 509–527, 2011.[2] A. T. Friberg, and R. J. Sudol, ‘Propagation parameters of gaussian Schell-model beams’, Optics Commun. 41,
383–387, 1982.[3] F. Wyrowski, and C. Hellman, ‘ The geometric Fourier Transform’, Proc. DGaO 118, A37, 2017.[4] F. Wyrowski, and M. Kuhn, ‘Introduction to field tracing,’ J. Mod. Opt. 58, 449–466, 2011.
Setup
Friedrich
Schiller
Universität
Jena
𝜃
Fig. 2: X-ray gold coated grazing mirrors, 𝜃= 3 mrad. Fig. 1: Gaussian Shell Model
source [1], 𝜆 = 173 pm.
Fig. 3: Mirror’s figure errors.
Computation
Fig. 4: Field trace diagram.
Operator DescriptionPropagation by analytical equations [2]
Propagation by Geometric Field Tracing* [3].
Propagation by angular spectrum approach [4]
Mirror reflection by local plane wave/interface* [4]
Table 1: Operators used; *requires smooth wave front.
Results
Fig. 6: a) Focal spot with figure errors,
b) cross-section of elementary modes.
Fig. 5: a) Focal spot without figure errors,
b) cross-section of elementary modes.
(a) (b) (a) (b)