Error Balancing in fast Schmidt Cameras

Abstract

An approximate solution is obtained to the problem of designing the Schmidt camera so as to obtain best performance, in an agreed sense, over the field surface taken as a whole. The approximation consists in neglecting small quantities of the seventh and higher orders and basing the discussion on the fifth-order aberrations of the system. The optimization covers arbitrary variations of the plate profile and of the adopted field surface ; it also takes account of the spectral characteristics of the light in which the camera is to work. In all cases, the best field surface turns out to be spherical and the best corrector plate profile such as would give axial stigmatism to fifth-order accuracy when the refractive index of the corrector plate is assigned a suitable fictitious value. In a system intended to work in monochromatic light, the best position of the neutral zone is at the edge of the plate aperture and the root mean square image radius is then |$\frac{3}{5}$| of that of a dassical Schmidt camera. When the light is not monochromatic, the best radius of the neutral zone always lies between |$H\sqrt\frac{2}{3}$| and H , where H is the radius of the aperture stop. Its value is given by a simple expression depending only on the angular diameter of the field and the effective index-spread of the corrector plate for the given spectral distribution. In the last section of the paper it is shown that a slightly better root mean square performance can be obtained by the use of the modified Schmidt system described in a previous paper ( I ), and the relation between the properties of the classical and modified Schmidt systems is analysed.