Design of diffractive phase elements that produce focal annuli: a new method.

A new optimization method based on the general theory of amplitude-phase retrieval is proposed for designing the diffractive phase elements (DPE's) that produce focal annular patterns. A set of equations for determining the phase distribution of the DPE is given. The profile of a surface-relief DPE can be designed with an iterative algorithm. Numerical calculations are carried out for several examples. A comparison of the performance of the DPE's designed with the Gerchberg-Saxton algorithm and the new algorithm is presented. The effect of quantization of the phase distribution of the DPE's on the results is also investigated. The results show that the new algorithm can successfully achieve the design of the DPE's that convert the uniform incident beam into the focal annular patterns.