O20 O22 O31 O40 O33 O42 -317 jm, -155jm, -14jm, 29 nm, 203 nm, 19 nm.

The choice of the (N, Q) numbers always allows to minimize the Sphe 3 and Coma 5 modes, say reducing them to sags lower than AVis/20 or AVis/30 ptv, i.e.

which entails that the higher-order modes, not included in the above list (such as O60), become straightforwardly negligible.

• Determination of the elastic relaxation - Active optics co-addition law: The sphere generated by the figuring, with a tool of curvature 1/RS, is represented by zsph = X Sn0pn 2,4,6,...


since this single term representation comes from the fact that if O40 is negligible as stated in (7.34), then S40,S60,... are also negligible; within criterion (7.34), we cannot distinguish whether the surface zSph is a sphere or a paraboloid. The sag of the total flexure will be, of course, much smaller than that of any segment curvature.

The elastic relaxation and its anm coefficients are obtained from the active optics co-ddition law expressed by (7.24). This flexure is represented by

n,m from where we derive a„0 = On0 - Sn0 for m = 0, (7.37a)

Taking also into account the modes that have been given negligible values, the elastic relaxation is represented by the set a20 =

0 0

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