upr 1

From the definitions above Eq. (3.19), we have 2 y2

ypr2 and y2 are given in Eqs. (3.44) and (3.33) respectively. Substituting again from (3.34) and (2.55) for /, these equations reduce easily to

upr 1

For the field curvature (S/y)2, we require (Pc)2. From the definitions above Eq. (3.19), this is simply

The second equation of (3.24) can now be applied to the calculation of the coma contribution (Sii)2 using Eqs. (3.42) for (Si)° and (Si)2 and (3.48) and (3.50) for (a) and (HE) 2. The reduction is made quite simple by the fact that the form of the equation (3.48) is the same as (3.50) except for an additional term, and that and have a common factor. The result is

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