Abstract
Abstract Phase holographic optical elements (HOEs) such as reflective HOEs and transmissive phase HOEs have the advantage of almost 100% theoretical diffraction efficiency, but the calculation of phase function is very complicated and time consuming by numerically handling equations and the intensity distribution of a focal curve is very difficult to control by the Fresnel transforming theory. In this paper we are concerned primarily with seeking an analytic solution to calculate the phase function of a phase HOE for generating a focal curve of an arbitrary shape with controllable intensity distribution so as to simplify calculations and save the calculating time. At the same time, we discuss the phase functions of focusers for generating on-axis and off-axis (or large) focal curves, respectively. Our calculation will be carried out within the framework of geometrical optics. Finally, two practical examples are given.
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