Fractal Zone Plates for X-ray Microscopy

Fresnel zone plates are diffractive elements that are essential to form images in X-ray microscopy[1,2]. One of the main shortcomings of Fresnel zone plates their high chromatic aberration. Recently presented, Fractal Zone Plates (FZPs) [3] are diffractive lenses characterized by a fractal focal structure with an extended focal depth, as compared with Fresnel lenses. This behaviour predicts an improved performance of FZPs as image forming devices with an extended depth of field and a reduced chromatic aberration. Here we examine the incoherent imaging characteristics of these elements using polychromatic light in the visible range. The performance of FZPs is cotrasted with conventional Fresnel zone plates of the same focal distances. We have demonstrated experimentally that the FZP provides an extended depth of field and a reduction of chromatic aberration. This finding is confirmed objectively using the modulation transfer function as a merit function. We show that the polychromatic modulation transfer function (MTF) of a FZP affected by defocus is about two times better than one corresponding to a Fresnel zone plate. The reason for the good performance of FZP lies on its focal structure. The principal lobes of the different foci provided by a FZP coincide in the axial position with those obtained with a conventional Fresnel zone plate, but the FZP produce a sequence of subsidiary foci around each major focus following the fractal structure of the FZP itself. Precisely these subsidiary foci of the FZP provide an extended depth of focus for each wavelength that partially overlap with the other ones creating an overall extended depth of focus which is less sensitive to the chromatic aberration. We have experimentally tested the imaging capabilities of FZPs under white light illumination, and compared their performance against a conventional Fresnel zone plate of the same main focal distance (see Fig.1). We believe that the improved imaging capabilities (i.e. an increased in the depth of field and a reduction in the chromatic aberration) that FZP offer in polychromatic imaging could be profited across a broad range of applications where conventional Fresnel zone plates are currently applied mainly in X-ray microscopy (where narrow-band sources are hardly available).