Stationary-phase analysis of generalized axicons

Simple asymptotic expressions based on diffraction and the method of stationary phase are derived for the axial line images produced by generalized axicons. It is shown that many of the previously numerically established results concerning the logarithmic uniform-intensity axicons readily follow from these expressions. The role of the radial and azimuthal hologram variations in axicon image formation is elucidated. In particular, the generation of hollow uniform-intensity axicon Lines of finite length is demonstrated. Linear holographic axicons are shown to produce a uniform axial line of high transverse definition if the illumination intensity is suitably varied along the radial direction. The connection of axicon images with nondiffracting wave fields is also discussed. (C) 1996 Optical Society of America