Design, manufacture and experiment of Axilens

In this paper,a methodology of produc ing a line focus by Axilens is presented.The surface differential equation of an Axilens is generated and its approximate solutions are derived.The diffraction properties of the Axilens are analyzed theoretically and numerically.The errors in the approximate solutions are analyzed.A Fourier series expansion of the solutions of the surface differential equation is given.Experiments are then performed on two Axilenses that are designed and manufactured by a Taylor Hobson Nanoform 300 Ultra-precision Lathe.The experimental results confirm that the desired line focus by Axilens can be achieved by the developed method.