Multilayer coatings can be used as broad-band reflecting layer in X-ray focusing optics. The effective area over
the field of view is determined by the energetic and angular dependence of the coating reflectivity, with a different
behavior in dependence of the coating structure, that can be designed in order to enhance the effective area.
Often the best design is selected to maximize the on-axis effective area, but this does not ensure the performances
off-axis, where the most of the detector area is allocated.
We demonstrate the possibility of optimizing the coating over the whole field of view by means of a new
method, that does not require the use of ray-tracing procedures, being based on the computation of a simple
analytical expression computed over a limited number of points.
Our method is used to optimize a multilayer structure over the field of view. The effectiveness of the method
is tested by comparison with ray-tracing results. The performances of the multilayer structure resulting from the
optimization are then compared with a not optimized broad-band multilayer and with a multilayer optimized
for on-axis effective area.
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