23.1 INTRODUCTION

The focusing properties of zone plates were first discussed in the latter part of the nineteenth century,1 ^,2 ^,3 and their use as X-ray optical components was originally suggested by Baez.4 In their most common form, they are circular diffraction gratings with radially increasing line densities; linear,5 square,6 elliptical,7 and hyperbolic7 ^,8 zone plates (among others) have also been considered, but only the circular and, to a lesser extent, linear and elliptical forms have generally been used. The properties of zone plates may be described, without loss of generality, by considering the circular form (Fig. 1).

Figure 1: A circular zone plate.

A linear diffraction grating (see Chaps. 21 and 22) with a constant period, d, working in the first order diffracts radiation through an angle, ?= sin ^?1 ?/d, ? ?/d in the small-angle approximation. A circular grating with constant period could therefore be used to form an axial-line focus of a point source, as shown in Fig. 2a ; note that diffraction from opposite orders contributes either side of the axis. The distance from a radial point, r, on the grating to a point on the axis is z= r/tan ? ? rd/ ?. If the period is now made to decrease as the radius increases, then z can be made constant and the grating then acts as a lens,...