Thermal deformations of a cooled x-ray mirror

In order to minimize the deformation of cooled X-Ray mirrors, it is necessary to understand and to control several parameters: the mirror geometry, the cooling geometry, the power density variation in the beam, the mirror border line effects and the beam end effects. This paper gives an analysis of the influence that these parameters have on the thermal slope error by the use of both an analytical approach (for the understanding), and a finite element approach (for the accuracy). A distinction is made between the two basic contributions to the thermal slope: the flexion and the bump. Engineering guidelines are then provided for the designer willing to minimize the thermal slope error