T T4010 with T40 v 13[lp83v 1p

The infinite slope at the null thickness of the mirror edge allows use of a simply supported edge as the boundary condition, while the infinite thickness at the center is due to the imposed null paraxial curvature. The central thickness can be made finite (Fig. 5.12) in agreement with Rayleigh's quarterwave criterion (Lemaitre [14, 16]).

Tulip-form mirrors of the VTD class in Sect. 3.2 can exactly generate an Astm 5 mode. Setting q = 0, n = 4, and m = 2 in (3.14), the roots obtained for generating the Astm5 mode, i.e. coefficient A42, are ai = 3 + v and a2 = 0; this leads to the variable thickness

where the flexure is achieved by applying an angular modulated force F = F42 cos20 at the mirror perimeter. The thickness profile difference between T40 in (5.24a) and above T42 is within a few percent for practical applications. Hence, the simultaneous corrections of the two modes Sphe 3 and Astm 5 can be achieved by superposition of the two loading systems by use of the T40 thickness profile. This is quite valid because Astm 5 is much smaller than Sphe 3.

The aspherization is directly achieved from a plane mirror shape. Then, starting conditions are

0 0

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