A procedure was developed and used to obtain the optimal shape of corrected aspheric geodesic lenses for F-numbers ranging from 3 to 15. This optimization procedure allows the (constant) refractive index, lens radius, and focal length to be used as independent design parameters. Results of the increase in size of the first diffraction spot and shift in the focal plane caused by perturbations in a lens's shape have been included for several lenses with F-numbers between 3 and 10.
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Betts et al. (1978) studied this question.
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