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

Abstract

A theoretical model for the interferogram from double beam interference microscopes, which takes into account the coherence eVects, 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 simpli ed 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 eVect of the spatial and temporal coherence. For the Linnik microscope in which two objectives and a beam splitter cube are used, the eVect of the mismatch between chromatic aberrations of the two objectives, and the eVect of glass dispersions and misalignment of the beam splitter cube are investigated. Experimental results using the Linnik microscope are presented and they con rm the proposed model.

Spatial and temporal coherence effects in interference microscopy and full‐field optical coherence tomography

“…The distinction between the two techniques is somehow misleading as many researchers now refer to any doublebeam OCM as an OCT system. Coherence effects and interplay between spatial and temporal coherence are subjects of interest [36,[43][44][45] because they help to understand the physics behind the behavior of low-coherence interference microscopy (LCIM) systems. In recent studies [36,45] the present author concentrated on the distinction between the spatial versus temporal coherence effects showing that in fact each plays a different role in an OCT system.…”

“…Coherence effects and interplay between spatial and temporal coherence are subjects of interest [36,[43][44][45] because they help to understand the physics behind the behavior of low-coherence interference microscopy (LCIM) systems. In recent studies [36,45] the present author concentrated on the distinction between the spatial versus temporal coherence effects showing that in fact each plays a different role in an OCT system. It was shown that the coherence region is determined by the temporal coherence only when the path-length difference is scanned in a region where the reference and sample beams are perfectly longitudinally spatially coherent (collimated).…”

“…The CPM was the term coined to this technique by the optical metrology division of KLA-Tencor (a company based in Santa Clara, CA, USA) and it has many advantages over conventional microscopy or conventional interferometry in its ability to discriminate between different transparent layers in a multilayered stack. Very low coherence microscope (Linnik microscope) that uses high-NA objectives and broadband white light has been in use for many years within the metrology tools [34] of KLA-Tencor [5,[35][36][37] used for the inspection of the fabrication processes of microelectronic devices, particularly for autofocus purposes, the measurement of the critical dimension (CD) and the stepper misalignment errors between lithographically overlaid layers. Theoretical modeling of the interferogram from such microscopes has been established recently [36], based on the scalar imaging theory taking into account coherence effects following the treatment by Hopkins [38,39].…”

Measurement of thin film interfacial surface roughness by coherence scanning interferometry

“…The bandwidth of the light source and the numerical aperture (NA) of the objective lens mainly determines the coherence length. [19][20][21] Although a white light source such as a halogen light creates a shorter coherence length than those from LEDs making detection of the interference fringes on test surfaces less easy, a halogen light is used in this method. This is because this methodology involves a numerical optimization in the frequency domain, and thus a wider bandwidth in the region between 400 and 750 nm leads to a more accurate solution.…”

Biomedical Optical Applications of Liquid Crystal Devices

“…Figure 2 shows a good example of imaging system, the interferometric Linnik microscope [4,5]. It can be used as standard microscope when the reference path is blocked and it can be used as full field OCT system for deep imaging of biological tissue.…”