ABSTRACT
When one wish to calculate the Seidel aberration terms, that is the expressions with coefficients, they could naturally led to consider whether they can be expressed similarly as sums through the system. Many different derivations of the Seidel sum formulae are to be found in the literature; of these the simplest to follow are perhaps those which start by deriving the spherical aberration. This chapter illustrates the fact that the Seidel sum formulae can be put in many alternative forms. The Seidel sums represent, apart from simple numerical factors, the wavefront aberration for each of the primary aberration at full aperture and field. They arise naturally in this form because the summation theorem for aberrations applies specifically to optical path terms. The choice of the appropriate measure of aberration depends on the nature of the problem. Wavefront aberrations arise naturally in the development of the subject because of the summation theorem for primary aberrations.
