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Characterizations of optical surfaces by measurement of scattering distribution.

The micropolish of good quality optical surfaces can be characterized by measuring the scattered light distribution. Very often the surface defects are not isotropic but display preferred orientations that are translated into an anisotropy of the scattered light distribution. The total amount of light scattered by very high quality surfaces, coated or uncoated, scarcely exceeds a few hundred parts per million. Precise measurement of the distribution of the scattered light is always a task requiring great care and attention to detail. The apparatus is described. All the necessary degrees of freedom have been included so that the scattering may be completely analyzed. It is possible to make measurements out of the plane of incidence so that the complete spatial distribution of the scattered light can be obtained, whatever the angle of incidence of the primary beam. Thus to characterize the geometry of the system we use four fundamental parameters: the angle of incidence i, the two angles θ and ϕ that define the scattering direction, and the angle α that defines the orientation of the scattering surface in its own plane. Only two free parameters need exist because the surface roughness itself, which is the source of the scattered light, only depends on two variables. We have verified experimentally the validity of the relationships linking i, θ, ϕ, and α. In these relationships the expression for the intensity scattered in a particular direction (θ,ϕ) for an uncoated surface at angle of incidence i can be written in the form of the product of a coefficient, depending only on illumination and observation conditions, and of the 2-D Fourier transform of the autocorrelation functions of the surface roughness. Experimental measurements with uncoated surfaces of black glass have accorded with the theory. When the surfaces are coated with one or several layers the problem is more complicated, but it should be possible to derive information on the autocorrelation functions of each of the interfaces and the degree of correlation between them.