Analysis of illumination coherence properties in small-source systems such as synchrotrons

Modern synchrotron beamlines often take the form of critical illumination systems, where an incohrent source of limited spatial extent is re-imaged to an experimental plane of interest. Unique constraints of synchrotron sources and beamline, however, may preclude the use of the simple Zernike approximation for calculating the object-image coherence relationship. Here, we perform a rigorous analysis of the object-image coherence relationship valid for synhrotron beamlines. The analysis shows that beamline aberrations have an effect on the coherence properties. Effects of various low-order aberrations on the coherence properties are explicitly studied.