X-ray mirror module analytical design from field of view requirement and stray light tolerances

Abstract

The design of an X-ray mirror module is a critical issue. In general, the design depends on requirements such as the effective area on-axis, the angular resolution, and the field of view, meant as the angular diameter at which the effective area halves the on-axis one. One has also to come to terms with constraints such as the maximum mass and size allocated in the spacecraft, and the mirror module design consists of fulfilling all these requirements by populating the module with decreasing diameters until the total effective area on-axis is reached without exceeding the mass limit. However, the separation between consecutive shells has to be properly chosen, to avoid excessive obstruction off-axis that would limit the field of view. We already know, in fact, that it is possible to analytically determine a diameter population that is obstruction-free within the field of view. Even though this solution enhances the off-axis effective area, it is not always optimal because it often leaves too much spacing for stray light. The optimal choice for the spacing should hence be the necessary and sufficient one to allow for the required field of view; but, while the computation of the total vignetting from the spacing of mirrors in the module can be done by ray-tracing, the inverse problem is difficult because it should be approached by repeated attempts. Fortunately, the geometric vignetting of a mirror shell can be analytically determined as a function of the off-axis angle and the obstruction parameter, and the expression can be solved for the mirror shell spacing in order to set the field of view to the desired value. In this paper we show how this can be done and how the residual stray light contamination can be computed analytically. <P />