Zone plates performing generalized Hankel transforms and their metrological applications

Abstract A modified computer-generated Fresnel zone plane with the zone distribution determined by a Fermat spiral is proposed for performing generalized Hankel transforms. The special case of these elements realizing the generalized Hankel transform of first order is of special interest from the point of view of alignment applications. The doughnut shaped focal pattern, characteristic for the whole family of proposed zone plates exhibits then the smallest diameter. Its diameter is also smaller than other solutions proposed previously for obtaining focal spots with a black dip in the centre.