Abstract
This paper represents an essay in Aspheric surface optics. Chretien's theory of the aplanatic telescope suggests that the theory of aplanatic single lenses can be worked out on similar lines. The polar equation of an aspheric surface of such a lens is given in series form, and two numerical examples are studied, one of these being an aplanat, the other an anastigmatic singlet free from primary and higher-order spherical aberration, offence against the sine condition, primary astigmatism, and curvature of field. The shape of the latter lens is, however, predicted by Burch's four-plate theorem, the results of which (as far as they concern primary aplanatism) are shown to agree with the formulae given in the paper.
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