A Formula for determining the Wave-Surface if the Spherical Aberrations are Known

Abstract

IF the spherical aberrations of a cylindrical symmetrical optical system are known in the form of a series: it is possible to deduce the equation of the orthotomic wave-surfaces to the rays defined by (1), as has been shown by Picht¹. Picht gives a recursion formula proceeding from the higher terms to the lower, which is very inconvenient if the constants a, b, c, ... increase rapidly, as is ordinarily the case. It is possible, however, to obtain a recursion formula proceeding from the lower terms to the higher, which has been found very useful for practical purposes while analysing the concentration of light near the geometrical focus² by the Debye–Picht method.