Descartes Ovoids

Fig. 9.3 Descartes ovoids for various values of k = b/a. These curves provide stigmatic lenses at all orders. The thick curve is the Pascal limacon kn = 1 associated with the refractive index n

9.1.3 Aplanatic and Anastigmatic Singlet Lenses

A special case of a singlet lens with spherical surfaces is when one of the conjugates is virtual. Then the emergent beam has a convergence angle u'2 of the same sign as u1 of the incident beam, and it is possible to obtain thin and thick lenses which, for one wavelength, satisfy the sine condition and even are anastigmatic at all orders. This corresponds to a limit case of the ovoids (Fig. 9.4).

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