  One of the most important parameters determining the sensitivity of X-ray
telescopes is their effective area as a function of the X-ray energy. The
computation of the effective area of a Wolter-I mirror, with either a single
layer or multilayer coating, is a very simple task for a source on-axis at
astronomical distance. Indeed, when the source moves off-axis the calculation
is more complicated, in particular for new hard X-ray imaging telescopes
(NuSTAR, ASTRO-H, NHXM, IXO) beyond 10 keV, that will make use of multilayer
coatings to extend the reflectivity band in grazing incidence. Unlike
traditional single-layer coatings (in Ir or Au), graded multilayer coatings
exhibit an oscillating reflectivity as a function of the incidence angle, which
makes the effective area not immediately predictable for a source placed
off-axis within the field of view. For this reason, the computation of the
off-axis effective area has been so far demanded to ray- tracing codes, able to
sample the incidence of photons onto the mirror assembly. Even if this approach
should not be disdained, it would be interesting to approach the same problem
from an analytical viewpoint. This would speed up and simplify the computation
of the effective area as a function of the off-axis angle, a considerable
advantage especially whenever the mirror parameters are still to be optimized.
In this work we present the application of a novel, analytical formalism to the
computation of the off-axis effective area and the grasp of the NHXM optical
modules, requiring only the standard routines for the multilayer reflectivity
computation.
