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

A theoretical model for the interferogram from double beam interference mic roscopes, 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 obje ct beams a simplified expression is found for the defocus and path length d ependence of the interferogram. Based on this expression the characteristic s of the interferogram are studied and special attention is devoted to expl aining the dependence of the fringe size on the objective numerical apertur e, and the effect of the spatial and temporal coherence. For the Linnik mic roscope in which two objectives and a beam splitter cube are used, the effe ct 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 pre sented and they confirm the proposed model.