Hi Panini,

Seidel sums come from the evaluation of the Optical Path difference (OPD) between a marginal and principal ray from the object respect to a reference ray. This OPD is approximated to a third order for on axis object as well as for off axis object. This often done for full field object. Since OPD is related with wavefront aberration (W), if we compare this calulated OPD (W)  with its Taylor expansion in terms of pupil and object coordinates, we conclude that Seidel sums (SI to SV) are related with the corresponding coeffcients expansion except for some numerical factors, i.e., 1/8 for SI or 1/2 for SII as you point out.

Be advised that we are talking about rotationally invariant optical systems for which Seidel theory is applied. Some additional considerations and a more complete theory should be applied for a general system.

Seidel theory is important in a predesign of any optical system in a first approach to aberration correction. Finite raytracing is needed for further optimization.

I suggest you read the W.T. Welford "Aberrations of Optical Systems" from Adam Hilger Publishing, particularly Chapter 8.

Hope this helps.

José Antonio

While comparing seidel aberration terms with the wave aberrations,  spherical aberration and coma, SI/2 and SII/8 corresponds to the above receptively.

So, we use SI/2 and SII/8 instead of SI and SII for spherical aberration and coma.