Geometrical and wave optics of paraxial beams

Most calculational techniques used to evaluate beam propagation are geared towards either fully coherent or fully incoherent beams. The intermediate p artial-coherence regime, while in principle known for a long time, has rece ived comparably little attention so far. The resulting shortage of adequate calculational techniques is currently being felt in the realm of x-ray opt ics where, with the advent of third generation synchrotron light sources, p artially coherent beams become increasingly common. The purpose of this pap er is to present a calculational approach which, utilizing a "variance matr ix" representation of paraxial beams, allows for a straightforward evaluati on of wave propagation through an optical system. Being capable of dealing with an arbitrary degree of coherence, this approach covers the whole range from wave to ray optics, in a seamless fashion. [S1063-651X(99)03506-0].