A differential equation is obtained for the shape of an aspherical lens which is aplanatic for an object at infinity. Numerical integration of this equation for a range of lenses shows the variation in the shape and properties of such a lens for a range of adjustable parameters. A differential equation is also derived for the shape of a lens which exactly corrects the spherical aberration and coma of an arbitrary optical system.
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A. K. Head (1959) studied this question.
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