Fresnel detour-phase circular computer generated holograms

Abstract When a circularly symmetric wavefront has to be encoded onto a computer generated hologram, it is highly desirable to preserve the symmetry. The coding scheme must therefore be circularly symmetric itself. This paper introduces a particular kind of computer generated hologram which extends circular symmetry to the detour phase technique; this is obtained by working in Fresnel diffraction. The wavefront should be sampled using a circular sampling theorem such as the one derived from the Dini-Bessel expansion. The hologram then consists of weighted unit masses distributed on a set of circles, which in practice are replaced by annuli of suitable inner and outer radii. The approximations due to the detour phase method and to the annuli widths are discussed and an experimental example is shown.