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Fig. 9.1 B values defining the bending or cambrure of a lens: meniscus, plano-convex, equiconvex, convexo-plane, and meniscus

where H is the Lagrange invariant (cf. Sect. 1.6.1). Since we have assumed that the entrance pupil coincides with the lens, the distortion SV is null because the principal ray which passes through the vertex of the lens is undeviated.

If the power and conjugates are fixed, the variation of the primary spherical aberration, Sphe 3, is quadratic with the shape. For opposite conjugates (C = 0, i.e. z' = -z), the minimum value is for the equiconvex lens i.e. B = 0. The quantity 4Sif '3/x4 in (9.5a) is plotted in Fig. 9.2 with respect to B and n for opposite conjugates C = 0i.e. M = -1 .

• Lenses with minimal spherical aberration: If both conjugates are real, it can be shown that, whatever the bending B, the amount of spherical aberration of a thin lens cannot be cancelled. Setting minimal the above expression of the Si coefficient in writing dSi/dB = 0 entails

and the minimal value for Sphe 3 is

0 0

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