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Fig. 3.95. Schiefspiegler achieved by off-axis sections of a centered, 2-mirror telescope

3.7.2 The significance of Schiefspiegler theory in the centering of normal telescopes: formulae for the effects of decentering of 2-mirror telescopes

3.7.2.1 Lateral decenter. The treatment above for the theory of Schief-spiegler can be taken over directly to analyse one of the most important errors in telescopes: field-uniform coma induced by decentering of the secondary relative to the primary.

Consider the special case of the Schiefspiegler of Fig. 3.93 in which the aspheric axes of the primary and secondary are parallel, but laterally translated by the amount S (Fig. 3.96). A principal ray is drawn at incident angle Upri, such that the reflected ray strikes the axis of the secondary. As above for the Schiefspiegler, we apply our general recursion formulae (3.336) in the

Fig. 3.96. Schiefspiegler interpretation of lateral decentering in a Cassegrain telescope

normal way for the paraxial aperture ray parameters yv, Av and A i and the formulae (3.334) for the paraxial principal ray to derive Av and (ypr)v as though the stop were at the mirror for both 'primary and secondary. This gives immediately ypri = ypr2 = 0 and (HE)i = (HE)2 = 0; or from (3.20) the consequence that the coma associated with the field angle upri in Fig. 3.96 is independent of the aspheric figure on both mirrors. This gives, with the suffix S, S implying decenter treated as a Schiefspiegler,

Now, applying the conditions (3.342) and (3.343) with A1 = A2 = upr1 (since

Upr2

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