It is assumed that a preliminary design of an optical system has been completed and the characteristic rays traced through it to determine the aberrations which afflict it. The present article then starts with these data and offers a set of reduction formulae. These formulae are applied, surface by surface, from the image space forward until any particular parameter is reached. This is done for every parameter in the system. These results are finally substituted in differentiated aberration formulae to give a coefficient which, when multiplied by the change in the parameter, gives the change in the aberration in the final image space. When these coefficients are calculated for all parameters and all aberrations and recorded in a table, say, with the aberrations across the top and the parameters down the side, the designer has a complete picture of the, performance of that optical system. The table then enables him to quickly adjust all parameters so as to obtain the best results possible from the set-up as given.
WALDEMAR M. STEMPEL, "A Differential Adjustment Method of Refining Optical Systems," J. Opt. Soc. Am. 38, 935-935 (1948)