Lens axicons: systems composed of a diverging aberrated lens and a perfect converging lens

Abstract

A description is given of axicons obtained as a tandem of one diverging lens that has third-order spherical aberration and one perfect converging lens. The asymptotic representation obtained with the help of the nonuniform stationary phase method allows the determination of such principal features of the focal segment as the intensity distribution and the width of the central core along the optical axis. The obtained results are compared with the numerical evaluation of the corresponding diffraction integral. The analyzed system contains four special cases: the doublet of both lenses, the setup of the perfect converging lens placed in the front of the aberrated diverging lens, the setup of the aberrated diverging lens placed in the primary focal plane of the perfect converging lens, and the defocused Galilean telescope. A short discussion of the aberrated-lens bending factor as well as of choice of the most convenient system geometry is also included.