Theory for double beam interference microscopes with coherence effects and verification using the Linnik microscope

A theoretical model for the interferogram from double beam interference microscopes, which takes into account the coherence effects, is presented. The model is based on the general imaging theory of a lens in defocus. For the case of zero relative lateral displacements between the reference and object beams a simplified expression is found for the defocus and path length dependence of the interferogram. Based on this expression the characteristics of the interferogram are studied and special attention is devoted to explaining the dependence of the fringe size on the objective numerical aperture, and the effect of the spatial and temporal coherence. For the Linnik microscope in which two objectives and a beam splitter cube are used, the effect of the mismatch between chromatic aberrations of the two objectives, and the effect of glass dispersions and misalignment of the beam splitter cube are investigated. Experimental results using the Linnik microscope are presented and they confirm the proposed model.