Analytical computation of the effective area and of the stray light in the NewAthena x-ray telescope

The assessment of the effective area and of the stray light is a crucial step in the design and the tests of optical systems for x-ray telescopes. While the effective area for focused x-rays determines the telescope sensitivity, stray light has the potential to severely hinder observations with ghost images and a diffuse background. The root cause of stray light is represented by rays that undergo a single reflection instead of the two canonical reflections in sequence. In the NewAthena telescope, the tight nesting of Silicon Pore Optics (SPO) helps blocking a relevant fraction of the stray light, but some unobstructed rays coming from off-axis x-ray sources can anyway impact the sensitive area of the WFI. Determination of the effective area for double and single reflection as a function of the off-axis angle and the x-ray energy is a task that can be effectively accomplished by ray-tracing; nevertheless, the same issue can also be faced analytically, i.e., computing it from the geometric parameters of the pores, the position they occupy in the mirror module assembly, and the coating reflectivity. In a previous paper, we have described the formalism that enables a fast and effective computation of the effective area for focused and stray light, including the obstruction in the mirror module structures, with the only assumption that the mirror profile can be approximated as a double cone, a widely acceptable approximation for NewAthena as far as the sole effective area is concerned. In this paper, we recall the formalism and present a validation by comparing the outcomes of the analytical method with those of a detailed ray-tracing routine, finding excellent agreement.