Aberrations of anamorphic optical systems. I: The first-order foundation and method for deriving the anamorphic primary aberration coefficients

We suggest that, in the paraxial region, a double-plane symmetric optical system (anamorphic system) can be treated as two associated rotationally symmetric optical systems (RSOS). We find that paraxial quantities in the anamorphic system can be expressed as linear combinations of the paraxial marginal and chief rays traced in the two associated RSOS. As a result, we provide a set of equations that are key to derive the primary aberration coefficients for various anamorphic optical system types. By applying the generalized Aldis theorem to anamorphic optical systems, we build up the anamorphic total ray aberration equations. These equations can be reduced to third-order form, that is, the anamorphic primary ray aberration equations. We find that the terms in the anamorphic primary ray aberration equations can be expressed as paraxial marginal and chief ray-trace data in the two associated RSOS, together with normalized object and stop coordinates. More importantly, we build up a novel method for deriving the anamorphic primary aberration coefficients for anamorphic optical systems of various types.