Assume, as before, that AS/// ^ 2EAS// and that E « f'/g = 35. Then (4.84) leads, when combined with the E S/v = 0 condition from (4.71), to f ' +
in which the second term on the left has been added compared with (4.79) for the strict RC. Setting the same values from Table 3.2 as before with n' = 1.5 gives
« -0.143/' , which should be compared with the equivalent result of ASjj ~ +0.300/' from (4.77) for the quasi-classical Cassegrain. Bearing in mind that the classical Cassegrain has (ES//)Tei = -0.5/', we see that, within our rough approximations, the two solutions are about the same, being (from the point of view of coma) about one third of the way from the RC back to the classical Cassegrain. This, then, is the optimum amount of coma from a 2-mirror telescope to favour a thin one-glass corrector with E « 35. Practical designs will confirm this advantage.
Implicitly, the theory of Violette [4.3] contains both the above relaxation possibilities (2 different glasses and variation of the asphericities of the mirrors), although Violette introduced two glasses for reasons of achromatism. It was thus a very far-sighted analysis. He recognised, too, that he had more variables than necessary and proposed a corrector form minimising a further condition, distortion.
Up to now, we have considered solutions with a "thin" corrector in the sense that all its surfaces have effectively the same value of E. We must now consider the possibility of separated lenses, in particular a separated doublet. We will consider the case of a strict RC with two separated corrector lenses of the same glass. (An equivalent formulation and conclusion applies to the case of a classical Cassegrain). Then Eqs. (4.78) become:
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