Analytical expressions for field astigmatism in decentered two mirror telescopes and application to the collimation of the ESO VLT

Abstract

We derive formulae for all parameters defining the field astigmatism of misaligned two mirror telescopes with arbitrary geometries and with stop positions anywhere on the line connecting the vertices of the two mirrors. The formulae show explicitly the dependence of the field astigmatism on the fundamental design parameters and characteristics of the telescope and on the stop position. Special attention is given to the particular case where such a schiefspiegler has been corrected for coma at the field center. In addition, we study the effects of the practical definition that the center of the field is the center of the adapter. Following a recent paper by McLeod, where the field dependence of astigmatism is used to collimate a Ritchey-Chretien telescope with the stop at the primary mirror, we apply our formulae to the Cassegrain focus of the ESO Very Large Telescope (VLT), where the stop is at the secondary mirror and the telescope is only corrected for spherical aberration. We present measurements of the field astigmatism and discuss the accuracy of the collimation method.