Confocal Raman microspectrometry: a vectorial electromagnetic treatment of the light focused and collected through a planar interface and its application to the study of a thin coating.

In-depth confocal Raman microspectrometry (CRM) studies through a planar interface between materials of mismatched refraction indices are known to be affected by a decrease of both the collected Raman intensity and the axial resolution as a function of the penetration depth. Following a previous model, which takes the refraction, diffraction, and spherical aberration effects into account when focusing a Gaussian incident laser beam with a high numerical aperture objective lens, a complete vectorial treatment of these phenomena is considered. It is demonstrated that off-axis refraction effects cannot be neglected and that the dimension of the confocal pinhole aperture plays a crucial role on the effective focal plane position and on the collection efficiency. We thus propose a more rigorous and complete approach to the problem, and we find a very good agreement between experimental and theoretical Raman intensity variations for a thick polyethylene sample as a function of the penetration depth. As compared with calculations where only refraction was considered, we confirm that the lengthening of the focus even for a large penetration depth is significantly reduced upon diffraction effects. As an illustrative example, the theoretical Raman responses for a thin coating of approximately 20 microns on a polymer substrate were investigated and compared to experimental results already published. Even though the interfacial region is spread over approximately 5-6 microns when using a 100x objective and a confocal pinhole of 200 microns diameter, it is definitively concluded that the apparent axial resolution is not drastically deteriorated with increasing depth and that the coating thickness may be directly estimated with a precision of approximately 1.0 micron (5%).