Measurement of Small-Angle Scatter from Smooth Surfaces

Abstract

Measurements of the scattering of reflected light as a function of angular separation from the specular direction were made on aluminum-coated flat glass samples with surface roughnesses ranging from 1.0 nm to 70 nm rms deviation from the mean surface. Small -angle scatter (measured between 0.33° and 1° away from the specular direction) was investigated using light that had passed through a narrow slit; a measure of the scattering magnitude was provided by comparison of the far -field diffraction patterns produced by the slit, reflected from the samples and without the samples in place. The slit used to produce the diffraction patterns was optically processed to be smooth enough so that without the sample in place the minima of the diffraction pattern would be well defined and of lower magnitude than the scattered flux produced when the samples were in place. By considering the effects of the scanning aperture, it was determined that the measured magnitude of the minima agreed with those predicted by the use of Kirchhoff theory to within a factor of three. Comparison of small-and large-angle scatter measurements made on the same set of samples indicated that a transition region between the two types of scatter may exist in the region of 1° to 5° away from the specular direction. Because separate instruments were used for the small-and large-angle measurements, the results are expressed in terms independent of the measuring instrument's geometry. The measured results were compared to a theory in which the choice of the scatter function, and by implication the autocorrelation function, could be arbitrary. This comparison revealed that the choice of the hyperbolic secant function, rather than a Gaussian function, provided a good fit to the small-angle data. By fitting a curve to the small -angle data, it was possible to estimate the autocorrelation length of the surface roughness as well as the peak value of the scattering profile. The scatter measurements for the smoothest sample ranged from approximately 3 X 10' per µsr near the specular direction to 10 -13 per µsr at wide angles. For the roughest sample, the range was from 3 X 10-4 per µsr to 10-10 per µsr.