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)