Image formation of confocal microscopes using Lorentz's reciprocity theorem

Abstract

A general expression for the image formation of confocal scanning microscopes is derived within the framework of vector optics. The derivation is based on a reciprocity principle in the form of a closed surface integral over electromagnetic fields, the so-called Lorentz reciprocity theorem. The approach comprises the reflection- and the transmission-type setup. It is assumed that single-mode optical fibers serve as pinholes. Different types of polarization of both, illumination and detection and the non-polarized case are investigated. It shows that, with the help of Lorentz's reciprocity theorem, the detection characteristics are given by emission characteristics and vice versa, although the assumptions concerning the optical setup are very general. The result is formulated with the help of angular spectrum decomposition. As the spectra may contain evanescent waves, the approach may be applied also to scanning near-field microscopes working in the illumination mode.