Light scattering by sinusoidal surfaces: illumination windows and harmonics in standards

Sinusoidal surfaces can be used as material standards to help calibrate instruments that measure the angular distribution of the intensity of light scattered by arbitrary surfaces, because the power in the diffraction peaks varies over several orders of magnitude. The calculated power in the higher-order diffraction peaks from sinusoidal surfaces expressed in terms of Bessel functions is much smaller than the values determined from angular distributions that are measured or computed from measured profiles, both of which are determined mainly by the harmonic contents of the profile. The finite size of the illuminated area, represented by an illumination window, gives rise to a background that is much larger than the calculated power in the higher-order peaks. For a rectangular window of a size equal to an even number of periods of the sinusoid, a computation of the power distribution produces minima at or near the location of the diffraction angles for higher-order diffraction angles.