Basic thermal perturbations are considered for a fused-silica primary mirror in an orbiting space telescope within 800 km of the earth’s surface. In such an orbit, the change of thermal environment with pointing direction leads almost inevitably to an axial temperature gradient dT/dz through the primary mirror, and to a consequent bending of the mirror and a change ΔF of focal length. If ΔF is constant across the mirror to within about ±3 f2λ, where f is the focal ratio and λ the wavelength, the rms deviation of the mirror surface from a paraboloid will not exceed λ/50, and diffraction-limited performance is possible. Nonuniformities of ΔF can result either from lateral changes of dT/dz across the face of the mirror or from axial changes of dT/dz, i.e., from nonlinear gradients. A numerical analysis of the radiation transfer in the telescope tube, when this is illuminated from one side, shows that even in the unfavorable case of a two-dimensional telescope the lateral variation of dT/dz can be kept sufficiently small if the telescope tube is substantially longer than the mirror diameter, and if the sunlit earth does not shine directly on the mirror at any time. Analysis of the thermal distortion near the edge of a flat disk subject to a nonlinear axial gradient and of a spherical cap subject to a radial gradient dT/dR indicates that the likely distortions are certainly within optical tolerance for a 1-m telescope and probably also for a 3-m telescope. Deviations from uniformity resulting from the mirror supports or from inhomogeneities in the mirror itself are not considered.
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