M2 M3 M3

Putting si =0 and applying these formulae to the paraxial principal ray, the quantities ypr and Av can be checked for any of the systems given in Tables 3.2 and 3.3. With the normalization used there, we set up upri = +1.

The above general form is, in practice, of more direct use for the principal ray for which spri is normally finite, often zero. For astronomical telescopes, of course, the normal case is si = ro, and si = ro has little practical significance. Because of the singularity introduced with si = ro, the general recursion form of (3.333) requires modification. The recursion formulae resulting break down for v =1, but are generally valid for v > 1:

236 3 Aberration theory of telescopes Recursion formulae for si = ro

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