A20 A40

in (7.44a), so obtaining with (7.45) an implicit relationship (t2/t1, a/b, v, i) which is valid for small to moderate values of the incidence angle i. As for centered systems, this fully defines the geometry of the circular vase, i.e. the dimensions of the ring with respect to the thickness of the clear aperture area.

For this non-centered system, because A20 and A40 are not exactly the same as in Sect. 7.6.1, the rigidity-ratio y must be slightly modified. In addition to the uniform r m load, the Astm 3 and Astm 5 flexure modes are also required by use of Fa,k and Fc,k forces. These forces act on the MDM via bridge-shaped Invar arms sealed on the ring rear side (Fig. 7.9-Down).

As a primary mirror of an f/5 reflective Schmidt telescope, a four-arm vase MDM (km = 4) has been designed with Zerodur vitroceram. Its geometry, the in situ partial vacuum q for Cv 1 and Sphe 3 modes, and the bending forces Fa,k, Fc,k for Astm 3 and Astm 5 modes are given in Table 7.2.

Table 7.2 Four-arm vase MDM as the primary mirror of an f/5 reflective Schmidt. Force distributions Fak and Fc k. Aperture 2rm = 2a = 400 mm. Field of view 2(m = 5°. Incidence angle of principal ray at M1i = ( + 1 /40. Coefficients A20 = 2.34410"5, A40 = -1.94510~10, A22 = -1.02910" 7 and A42 = 1.71510~12 in mm1"" from (7.49). Zerodur E = 90.6GPa, v = 0.240. MDM t1 = 20mm, t2/t1 = 2.791, b/a = 1.150, c/a = 1.5

Table 7.2 Four-arm vase MDM as the primary mirror of an f/5 reflective Schmidt. Force distributions Fak and Fc k. Aperture 2rm = 2a = 400 mm. Field of view 2(m = 5°. Incidence angle of principal ray at M1i = ( + 1 /40. Coefficients A20 = 2.34410"5, A40 = -1.94510~10, A22 = -1.02910" 7 and A42 = 1.71510~12 in mm1"" from (7.49). Zerodur E = 90.6GPa, v = 0.240. MDM t1 = 20mm, t2/t1 = 2.791, b/a = 1.150, c/a = 1.5

Angle

Arm

Cv 1

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