Coma Tolerances for Photographic Star Images

Abstract

The question of alignment tolerances in large Cassegrain-type telescopes led us to consider the problem: how much coma can be tolerated in photographic star images intended for high-accuracy positional astronomy? In the present paper this problem is attacked computationally for a 150-in. Ritchey-Chrétien telescope with a 50-in. secondary mirror. A star image, distorted by coma, possible focus error and astigmatism, blurred by seeing spread, and super-posed on a uniform sky background, is received on a model photographic emulsion of specified characteristic curve. The mean centres of the resulting density and blackness distributions each vary with the star magnitude; their variations are taken as an estimate of the ‘astrometric magnitude errors’. If the tolerance for these errors is set at 0.003 arc sec it appears that a geometrical coma tolerance of 0.75 arc sec is a reasonable value for a large Ritchey–Chrétien telescope. In general, the ‘magnitude errors’ diminish when the seeing deteriorates (though random errors of measurement would then increase); they are increased by a slight focusing error and also by a decrease in the total scale of the emulsion, such as is generally associated with increasing contrast γ . Of particular interest is the conclusion that the alignment tolerances for photographic astrometry are probably less stringent than those for visual double star measurement.