Apodizing of an achromatic lens by a gray-glass negative lens element

The apodizing performance of a plano-concave lens made of gray glass was analyzed numerically. It was found that apodizing performance depends solely on the edge transmittance of the lens (a zero center thickness is assumed here) for any reasonable ratio of radius of curvature of the concave surface and the lens radius. If a modest increase in the size of the central diffraction peak and light losses introduced by such a lens can be accepted, it is possible to reduce energy diffracted into diffraction rings approximately tenfold.