## Info

Zopt ~ 2903

cos i

2 2 • 2 / 2 2 . 2 \ 21 3 x2cos2 i+y2 /x2cos2 i+y2 x y2m y2m ym, (5.20d)

where ym = rm is the mirror half clear aperture in perpendicular direction to the telescope symmetry plane, and f-ratio O = R/4ym = R/4rm. The semi-axes of the clear aperture elliptic contour are (xm, ym) with xm = ym/cos i. The representation (5.20d) applies with x < xm, y < ym.

• Accurate representations: Use of the exact expressions for An(M) and Bn,m coefficients in Tables 4.1 and 4.2 provides a precise shape of the primary mirror (cf. Chap. 4).

If a positive singlet lens is implemented before the focus for flat fielding, then a slight homothetic increase of the coefficients allows maintaining the mirror geometry with k = constant. This overcorrection of spherical aberration is easily achieved by setting the s-factor in (4.10) slightly larger than unity.

5.3.2 Axisymmetric Circular Primaries with k = 3/2 - Vase Form

• Centered systems: From Sect. 4.3.1, the mirror figure for best images in the field is obtained for k = 3/2. Although the optical surface can be approximated by (5.20b), let us consider the shape ZOpt of the axisymmetric primary such as represented by (4.18) with exact coefficients Cv 1 and Sphe3.

For a constant thickness plate bent by uniform load q, whatever is the perimeter boundary - simply supported or built-in edge -, the particular solution of Poisson's equation always appears in the general solution ZElas, in (5.5), as showing the same fourth-degree term; this term is (q/64D) r4. The aspherization process can be directly carried out from a flat polished surface (ZSphe = 0). Then the active optics co-addition law writes

where p= ±1 is depending on the choice of stress figuring or in-situ stressing.

The identification of the elasticity ZEias( r4) term with the optical Zopt( r4) term in (4.18) provides the first part of the opto-elastic coupling. Let Q = R/4rm be the f-ratio and t1 the optical mirror thickness, after simplifications, the uniform load is q =

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