FOCUSING PROPERTIES OF HEMISPHERICAL MIRRORS FOR TOTAL INTEGRATING SCATTERING INSTRUMENTS

Focusing properties are derived of a hemispherical mirror (also called a Coblentz sphere) used in total integrated scattering (TIS) instrume nts for the measurement of surface roughness. Analytical formulas for the scattered-light dependence on scattering angle and on the position of the photodetector and sample (with respect to the hemisphere) are given. From these formulas one can estimate useful parameters related to the construction and performance evaluation of TIS instruments, inc luding spherical aberration of the hemispherical mirror, solid angle o f the scattered Light collected by a photodetector of a given size, an d optimal size of the photodetector and its position with respect to t he basal plane of the mirror. (C) 1997 Optical Society of America.