The potential to create a convex?concave lens (meniscus) with a spherical gradient of refractive index, transforming a divergent entrance homocentric beam into a convergent output homocentric beam, is shown. The lens has first aspherical and second spherical surfaces. The distribution law of the index of refraction for the lens material, the equation for the generatrix of the first aspherical surface, the basic parameters of the lens, and the magnification are obtained in analytical form.
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Vladimir Ivanovich Tarkhanov (2006) studied this question.
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