If Eqs. (3.59), (3.60) and (3.61) are compared with the stop-shift formulae of (3.22), it will be seen that there is exact equivalence, the quantities Si and Sii in (3.22) being the normalized quantities (—f + L£) and (—di£ — f '/2) in (3.59) and (3.60) respectively and (HdE) being the normalized stop shift
The form of the above equations (3.32) for the primary mirror and (3.59) to (3.62) for a 2-mirror telescope is essentially that given by Bahner [3.5] except that the formulae given here are general and not limited to normalized parameters as used in Table 3.3. Also, the sign convention differs with our use of the general Cartesian system of optical design defined in Tables 2.1, 2.2 and 2.3. Equations of this sort were first set up by K. Schwarzschild [3.1] in his classic paper of 1905, arguably the most fundamental and important paper ever written in telescope optics. Schwarzschild's formulation retained parameters equivalent to A and A, so that certain properties were less evident than they are in the form given in Eqs. (3.59) to (3.62) above. We shall return to this matter in § 3.2.6, where individual solutions arising from the equations are considered.
In § 220.127.116.11 it was pointed out that the initial layout of a 2-mirror telescope is usually established with the parameters yi, fi, m-2 (giving f') and P, whereby the resulting axial obstruction ratio Ra must also be acceptable. The parameters d 1 and L used in Eqs. (3.59) to (3.62) are therefore derived parameters resulting from the basic ones. The conversion from d 1 and L to the basic parameters above, if these are preferred, is easily performed from two relations derived from Eq. (2.72):
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