in which upr/uprm gives the real semi-field compared with the normalized value uprm of 1 rad. Taking upr = 15 arcmin gives

(W'Ii)GF = —0.001 219 5 mm , which from Eq. (3.198) gives the angular tangential coma as

(Su'p)comat = — 3(Wyi)GF (206 265) arcsec = +0.4312 arcsec

This coma is not negligible for best quality but may be acceptable if we compare it with the residual astigmatism of the RC telescope without the corrector. We have from (4.36)

(£ Sii i)rc = —E2S = —E Sii and from (3.181) and (3.208)

(Su'p)ast,m = — ^ySiii (206 265) arcsec for the angular astigmatism at the mean focus. For upr = 15 arcmin, we deduce for the naked RC telescope

Since this declines with the square of the field and the coma only linearly, the use of such a singlet Gascoigne plate corrector with these parameters would be marginal: the astigmatism correction is paid for by a coma half as large at a semi-field of 15 arcmin. A more attractive solution would be to halve g to give f'/g = 70. From (4.42) the coma would be roughly halved. But the asphericity of the plate is increased, according to (4.38), although S is reduced. Quasi-RC (aplanatic) telescope. A more interesting possibility, in practice, is the optimization of the whole telescope system to fulfil all three conditions Sj = Sjj = Y1 Sjjj = 0 from (4.31) using all three aspheric parameters Z, £ and S. We can re-write these equations in the form

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