Creating von Laue patterns in crystal scattering with partially coherent sources

When spatially coherent radiation is diffracted by a crystalline object, the field is scattered in specific directions, giving rise to so-called von Laue patterns. We examine the role of spatial coherence in this process. Using the first-order Born approximation, a general analytic expression for the far-zone spectral density of the scattered field is obtained. This equation relates the coherence properties of the source to the angular distribution of the scattered intensity. We apply this result to two types of sources. Quasihomogeneous Gaussian Schell-model sources are found to produce von Laue spots whose size is governed by the effective source width. Delta-correlated ring sources produce von Laue rings and ellipses instead of point-like spots. In forward scattering, polychromatic ellipses are created, whereas in backscattering striking, overlapping ring patterns are formed. We show that both the directionality and the wavelength-selectivity of the scattering process can be controlled by the state of coherence of the illuminating source