Regular papers

Image formation in a multilayer using the extended Nijboer-Zernike theory

¹ Optics Research Group, Faculty of Applied Sciences, Delft University of Technology, Lorentzweg 1, NL-2628 CJ Delft, The Netherlands
² Philips Research Europe, HTC-36, NL 5656 AE Eindhoven, The Netherlands

^* s.vanhaver@tudelft.nl

Received: 22 June 2009

Abstract

We study the image formation by a high-numerical-aperture optical imaging system in the presence of a multilayer structure in the region around the image plane. Earlier references to this subject in the literature use numerical solutions of the diffraction integrals. In this paper, we use a numerical approach based on the semi-analytic Extended Nijboer-Zernike (ENZ) theory to solve the diffraction integrals in the presence of a multilayer structure. The specific ENZ calculation scheme uses the complex Zernike expansion of the complex amplitudes of forward and backward propagating plane wave components in a certain layer of the multilayer stack. By its nature, the ENZ approach enables an accurate and fast calculation of the vector field in the stratified image region. Examples of multilayer imaging that are encountered in high-numerical-aperture optical systems and in optical lithography for semiconductor manufacturing are presented and the accuracy of the ENZ approach is examined.