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Fig. 3.7 Hybrid CTD-VTD configurations providing the Sphe 3 mode z = A40 r4 by uniform loads q applied all over the clear aperture diameter 2b. (Left) Same load q for the two zones. (Right) q (outer zone) > q (inner zone)

NB: Hybrid configurations using the CTD and VTD classes can be similarly derived for the Cv 1 mode. In this case, the uniform load applied to the central zone is suppressed for 0 < r < a.

3.3.4 Balance with a Curvature Mode

The best focussing of a wavefront containing a spherical aberration, i.e. the least confusion image, is located between its paraxial (Gauss) and marginal focii. Let Z(p) be a wavefront of biquadratic form whose dimensionless representation is Z = Z/R with respect to its radius of curvature R. The sum of the two modes Cv 1 and Sphe 3 may be written as

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