Pjz

amYm(K)

where the harmonic m of the lateral force distribution leads to the associated flexural mode m represented by the product of the square of a dimensionless amplitude am -depending on the force distribution type - with the dimensionless function Ym(K) (Table 8.3).

For the mode m = 0, it appears from the Yo-value that the piston, Cv 1, Sphe 3 and higher-order spherical aberration modes have a negligible resulting effect. For m = 1, which represent a lateral displacement of the field of view, the effect is extremely small. The dominant effect is the all-order astigmatism mode given by m = 2. The next aberration mode m = 3, representing coma, is much smaller than astigmatism, whilst the influence of the higher modes decreases continuously.

Whether a plano-concave or a meniscus shape of the mirror, use of parallel and equal push-pull forces Fx,n = —W/Nl uniformly distributed at the contour provide a smaller residual flexure than that of the radial push force distribution fr = —(W/na)(1 + cos 9). In practice, direct axial astatic levers can easily generate such a push-pull distribution either with equatorial or altazimuth telescope mount, the latter mount requiring the levels to pivot only around one direction. The lateral support of the meniscus mirror of the 3.5-m Eso-Ntt is with Nl = 24 parallel and equal push-pull forces uniformly distributed at the contour in the plane of the center of gravity [69].

Table 8.3 Value of coefficients Ym(k) for the various flexure modes in cosm6 of a vertical planoconcave mirror supported at its edge. Geometrical ratio to /2a _ 1/8. Poisson's ratio v _ 0.25. Radial push force distribution fr 1 + cos 6 [75]

Flexure mode

K — 0.0(*)

0 0

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