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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) instruments 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, including spherical aberration of the hemispherical mirror, solid angle of the scattered light collected by a photodetector of a given size, and optimal size of the photodetector and its position with respect to the basal plane of the mirror.