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. Verhoeven 1 // Christian Hellmann 2 // Mourad Idir 3 // Frank Wyrowski 2 // Jari Turunen 1 1 Institute of Photonics, University of Eastern Finland, 80101 Joensuu, Finland 2 Institute of Applied Physics, Friedrich-Schiller University, D-07745 Jena, Germany 3 Photonics Science Division, Brookhaven National Laboratory-NSL II, 11973-5000 New York, USA UNIVERSITY OF EASTERN FINLAND | INSTITUTE OF PHOTONICS 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 Fig. 2: X-ray gold coated grazing mirrors, = 3 mrad. Fig. 1: Gaussian Shell Model source [1], = 173 pm. Fig. 3: Mirror’s figure errors. Computation Fig. 4: Field trace diagram. Operator Description Propagation 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)