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The co-addition of Cv 1 and Sphe 3 modes allows avoiding the radial arms if verifying the condition

For the primary mirror of a reflective Schmidt, (7.43) provides the relationship between A20 and A40, that is

which does not depend on the f-ratio, and where a = rm i.e. a clear aperture corresponding to the inner radius of the perimeter ring. After substitution of (7.46) in (7.45), the resulting condition for the reciprocal rigidity ratio is

1 _ 16 [2a - 1 - (1 + v) ln ยง] - (5 + v) Y (1 - v2) (1 - g)

This condition fully defines the geometry of the vase form as an implicit relationship (t2/t\, a/b, v) and provides effective solutions without radial arms. An example of a vase-form primary mirror in Zerodur vitroceram is displayed by Fig. 7.9-Up.

For this centered system used off-axis, the co-addition of the Cv 1 and Sphe 3 flexure modes are simultaneously achieved by the appropriate vase-form geometry and uniform loading q = 64D\A40. An inner enclosure plate is sealed into the vase. The aspherization can be obtained either by air pressure and stress polishing or by air depressure inside the mirror during observations i.e. in situ stressing.

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