Focal shift and astigmatism for a circular zone plate Shaomin Wang , Xiaoqing Jiang , Qiang Lin Department of Physics , Hangzhou University, 310028 Hangzhou, CHINA Eusebio Bernabéu , Javier Alda , Victor Martin Optics Department , University Complutense of Madrid 28040 Madrid, SPAIN ABSTRACT Focal shift of zone plate is completely different from corresponding circular and annular apertures. Focal powers of zone plate are constant under some condition but for the latter they are always variables. Astigmatism for a zone plate is also investigated. The sagittal focal surfaces are unchanged but the tangential focal surfaces are changed as a function : cos20 , besides , it has neither spherical aberration , nor coma. They are also completely different from conventional imaging devices. 1. INTRODUCTION The concept of focal shift for a circular hard aperture was given by Li and Wolf about one decade ago'2. It is also suitable for an annular aperture3. Based on the concept of focal shift , an equivalent transfer matrix for a circular aperture was defind4, 1 0 M10== 1/(r2/12)Np1 1 (1) Where , N1 = a2/A p I is Fresnel number before the aperture , p is the radius of curvature of the incident spherical wave. p' is set negative if the incident wave is converging. Note that the focal power for an aperture is a variable. For a Fresnel zone plate, we can use eikonal function and complete Fresnel number56 to find another matrix M = ( 0) with i = (2) Where f= f1/i , = a2/?. Note that the focal power for a Fresnel zone plate is a constant, i. e. not depend on the incident wave. On the other hand, there has been a series of papers and books to describe various phenomena of the Fresnel zone plate, see the examples7'. However, the astigmatism of a circular Fresnel zone plate has not been investigated, at least to our knowledge. But the astigmatism for some other imaging devices are well—know, e. g. 456 ISPIE Vol. 1979 Lasers and Optoelectronics (1992) o-8194-1225-2/93/$4.OO Downloaded From: http://opticalengineering.spiedigitallibrary.org/ on 10/24/2014 Terms of Use: http://spiedl.org/terms