Optimum Zone Plate Theory and Design

Abstract

Transmission zone plates composed of materials describable by the complex index of refraction ñ(ñ = (1 − δ)+ ik) modulate both the amplitude and phase of the light passing through them. In this monograph, a general variational approach to the design of zon plate profiles which maximize system transfer functions like I^(m)/I_IN or I^(m)/I_OUT (where I_IN and I_OUT are the total input and output powers and I^(m) is the diffracted power of the m^th order) is presented in terms of the real and imaginary components of ñ. The variational problem, as formulated here, is shown to generate some important classical zone plate configurations as special solutions and to lead naturally to the derivation of the most general zone plate configurations possible. Some specific optimum solutions are derived for gold in the soft x-ray range and tabulated for convenient reference.