Measurement of micro-roughness and effects of detector bandwidth and finite width

Surface micro-roughness of grazing incidence optics has long been recognized as a critical parameter in the control of the scattered X-ray intensity and its effects on the point spread function half-energy width. Accurate knowledge of the amplitude of surface micro-roughness is vital to assess optic predicted performance during the final stages of fabrication. This requires not only a knowledge of the spatial bandwidth over which surface features must be measured, but also knowledge of the bandwidth of the measurement instrument. We show that the standard assumption that instruments respond up to their Nyquist limit is an oversimplification which neglects the finite detector size and its bandwidth limiting effects when sampling a real (i.e., two-dimensional) surface.