Modeling and Measuring the Effect of Refraction on the Depth Resolution of Confocal Raman Microscopy

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Abstract
A simple ray-tracing analysis has been used to predict the effect of refraction at the sample/air interface, on the depth resolution of confocal Raman microscopy. This analysis applies to the “z-scanning”, or “optical sectioning”, approach to obtaining depth profiles, where the laser beam is incident normal to the sample surface, and spectra are recorded sequentially as the focus is moved deeper into the material. It is shown that when a “dry” metallurgical objective (the most common configuration for commercial Raman microscopes) is used, both the position and the depth of focus increase dramatically as the beam is focused deeper into the sample. It quickly becomes impossible to obtain “pure” spectra of thin layers that are buried more than a few micrometers below the air interface. Equations are presented which model the intensity response expected when focusing through a coating into a substrate. The model requires knowledge of the sample refractive index, the numerical aperture, and the laser beam intensity distribution at the limiting aperture, of the objective. Given these values, one can predict the substrate Raman intensity as a function of the nominal focal point within the sample. For a 36 μm coating on a thick substrate, we predict that even for a perfectly sharp interface (<<1 μm), substrate bands rise slowly (over an apparent distance of 10 μm or more), and are strong when the focus is apparently only ∼ 18 μm below the air/coating interface. This prediction was confirmed through experimental observation. The model was also used to analyze literature data that had been interpreted previously as showing interfacial diffusion in polymer laminates. The model correctly reproduced the main features of the observed data without invoking interfacial penetration—the optical aberrations alone accounted for almost all the observed broadening and the fact that the apparent thickness of the buried layer is also distorted. It was concluded that, with the use of this illumination geometry, it is very difficult to detect or quantify interfacial broadening unless it occurs on a very large scale indeed (tens of micrometers). It is concluded that ‘optical sectioning’ cannot be recommended for quantitative depth profiling at significant depths using metallurgical objectives. The optimum practical solution is to cut a cross section and map laterally across the sample, thereby utilizing and maintaining the excellent (lateral) resolution of the Raman microprobe. An alternative solution is to use an immersion objective to minimize refraction at the sample surface.