Towards M Axis

4.3.2 Non-Centered Optical Systems

Considering non-centered systems, the basic mounting inclinations i of the primary mirror are also given by (4.19a) for two-mirror systems or by (4.19b) with an additional flat folding mirror. Theoretically, the exact shape of the primary mirror has only one symmetry plane. The mirror Bn,m coefficients in Table 4.2-column 4 provide a perfect stigmatism at the center of the field.

In the case of moderate f-ratios up to f/1.7-f/1.5, the coma terms of Bn,m with n odd are negligible. Therefore, the mirror surface assimilates to a biaxial symmetric shape generated by quasi-homothetical ellipses obtained by coupling B n,m with Bn,0 for n even. The first term pair expressing the mirror shape is

Zopt = B2,o r2 + B2,2 r2 cos 29 +... From coefficients in Table 4.2, column 4, we obtain sÄ2

Zopt:

4R cos i

With x = r cos 9, y = r sin 9 and the next coupled terms B40 and B42

ZOpt s

2 cos i

A4 r3

Cn sAn

By substitution of A2 and A4 (Table 4.1), the series becomes s

ZOpt x

Considering now the free parameter k = r^/r^, the best resolution in the field is obtained for a null-power zone ratio \fk = \J3/2, as for centered systems. Then, from (4.8), M = k/25Q2 = 3/26Q2 where Q = R/4ym is the telescope f-ratio and the y-axis is perpendicular to the telescope symmetry plane. Hence we may represent the optical surface of the primary mirror, with its elliptic pupil receiving cylindrical incident beams, by the first approximation

cos i

0 0