G. Rangarajan et M. Sachidanand, SPHERICAL-ABERRATION AND ITS CORRECTION USING LIE ALGEBRAIC METHODS, Pramana journal of physics, 49(6), 1997, pp. 635-643
We discuss three methods to correct spherical aberration for a point t
o point imaging system. First, results obtained using Fermat's princip
le and the ray tracing method are described briefly. Next, we obtain s
olutions using Lie algebraic techniques. Even though one cannot always
obtain analytical results using this method, it is often more powerfu
l than the first method. The result obtained with this approach is com
pared and found to agree with the exact result of the first method.