Wave vector integral method for design of Fresnel zone plates with different focusing manners

We present an approach for design of Fresnel zone plates (FZPs) with different focusing manners. By re-performing the formula for calculating the half-wave zones of a conventional FZP into wave vector domain, we get a wave vector integral formula, by which the half-wave zones of a generalized FZP could be derived from the wave vector distribution of the expected focusing beams. As examples, we analyzed the situations with, respectively, a circular focusing manner and a line focusing manner, and successfully derived, for the first time to our knowledge, the analytic expressions for calculating the corresponding half-wave zones of the expected FZPs. Some simulations in X-ray domain demonstrated the feasibility of the method and the derived formulas.