The Effect of Surface Errors on Optical Performance

Abstract

Surface irregularities range in lateral dimensions from those usually associated with optical figure error through values associated with zonal errors to those usually described as microroughness and extending to submicron dimensions. Typically, the irregularities are a small fraction of a wavelength in height so that physical, not geometrical, optics must be used to calculate their contribution to optical performance. The total integrated scatter (TIS) from irregularities is given by the expression (4πδ/λ)2, where λ is the wavelength and δ is the rms roughness of the surface. TIS is defined as the total reflectance of the surface minus the specular reflectance, i.e., the fraction of the total reflected light that is scattered into a hemisphere. The amount of scattered light is proportional to the mean square of the heights of the surface irregularities. No upper limiting value of lateral dimensions of the surface irregularities appears in this scalar theory, although, for normal incidence, the scattering becomes virtual when the lateral dimension ℓ of the irregularities becomes less than λ. The more closely spaced the irregularities are, the larger is the angle into which light is scattered. When ℓ ≈ λ, as is true for zonal irregularities, the scattered light is very close to the specular direction (typically a few minutes of arc), and, for still larger lateral dimensions such as are associated with figure errors, its main effect is to decrease the on-axis intensity of the focused beam. It follows that if near-angle scattering is of primary importance, as for example in a system projecting a light beam, the most important surfacing parameters may be zonal and figure errors. Large-angle scattering may also be important but becomes of particular concern for an imaging system such as a telescope where light may enter the optical system from large off-axis angles, strike the optical component, and be scattered into the focal plane. When large-angle scattering is important, the height of the more closely spaced irregularities beomes critical. A calculation of the effect of microirregularities having a range of autocovariance lengths on the performance of a typical mirror telescope will be given to demonstrate the possible degradation effects of both near- and large-angle scattering. Vignetting effects that occur when the mirror is illuminated at off-axis angles are also considered. (It should be pointed out that we are discussing scattering of light into the optical path by the optical components themselves. No arrangement of baffles will have any effect on this type of scattered intensity. Programs such as APART or GUERAP are designed to prevent light scattered from the mounting system from reaching the focal plane, not light scattered directly into the focal plane by the components themselves.)