In this paper a new kind of modulated circular zone plates is presented. Its focal curve is contained in a plane parallel to that of the zone plate, and can be described as a gentle deformation of a ring. The transmittance is obtained in a explicit form by encoding a suitably modulated toroidal wavefront in a hologram. Usually this encoding requires the use of digital techniques. A method for obtaining more general two-dimensional focal curves is also outlined. © 1991 Taylor & Francis Ltd.