Point-spread function for a rotationally symmetric birefringent lens

Imaging properties of a birefringent lens, in which the fast (or the slow) axis is distributed in the radial direction whereas magnitude of birefringence varies as a quadratic function of the pupil radius, are investigated by calculating a point-spread function. It is found that the point image is analytically described by using the Lommel function as well as the zero-order Bessel function, and a localized intensity null surrounded by bright regions in all directions can be realized at a geometrical focus under certain conditions. The magnitude of birefringence that is tolerable in image formations is also discussed, assuming that the lens is applied to microlithography. (C) 2002 Optical Society of America.