Except for some special cases, a spherical incident wavefront does not remain spherical after refraction through the spherical surfaces of a thin lens. The resulting shape of the emerging wavefront can be represented by Seidel's primary aberration coefficients Si to SV such as shown for the general case of the aberration wavefront function (cf. eq. (1.41) in Sect. 1.80). The calculation of Seidel coefficients representing the sum of the aberration contribution of the two surfaces is lengthy but not particularly difficult. From Welford [1], the resulting Seidel sums for a lens in air and a pupil at the lens are

4f n1

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