A fully-analytical treatment of stray light in silicon pore optics for the ATHENA X-ray telescope

Just like in any other X-ray telescope, stray light is expected to be a potential issue for the ATHENA X-ray telescope, with a significant impact on the scientific goals. The most prominent cause of stray light in Wolter-I type optics is represented by rays that did not undergo double reflection and were reflected only singly, on either the parabolic or the hyperbolic segment. A minor contribution may, additionally, arise from the diffuse reflections on the backside of the pore membrane and ribs. Aiming at determining whether the resulting background is tolerable or not, the effective area for stray light has to be calculated. While ray-tracing is a standard and well-assessed tool to perform this task, it usually takes a considerable amount of computation time to trace a number of rays sufficient to reach an appropriate statistical significance, because only a minority of stray rays emerge unobstructed from the mirror assembly. In contrast, approaching the stray light from the analytical viewpoint takes several upsides: it is faster than ray-tracing, does not suffer from any statistical uncertainties, and allows one to better understand the role of the parameters at play. The only approximation involved is the double cone geometry, which however is largely applicable to ATHENA as far as the sole effective area is concerned. In this paper, we show how the analytical approach can be successfully adopted to model the stray light effective area in the ATHENA mirror assembly, as a function of the X-ray energy and of the source off-axis angle.