On decentred aspheric plates

Abstract

The main purpose of the paper is to discuss the effects of errors of centring on the optical performance of plate-mirror systems. Such errors may occur during the aspheric grinding of the plates and also in the lining up of the system. It is first shown that if a grinding technique is used which builds up the asphericity at a proportionately equal rate all over the surface, the result of a large number of small centring errors at different stages of the grinding is very nearly equivalent to a simple decentring of the asphericity on the surface, combined with a small amount of primary astigmatism. Next, general formulae are obtained for the effects on the Seidel errors of a centred system of decentring and tilting its components, and it is shown that in the case of a plate-mirror system the formulae can be used to estimate the practical tolerances for disturbances of this kind. Lastly, the general formulae are applied to discuss the lining up of a two-sphere one-plate Schmidt-Cassegrain camera