Depth Profiling by Confocal Raman Microspectroscopy: Semi-Empirical Modeling of the Raman Response

Abstract

It has been well documented that the use of dry optics in depth profiling by confocal Raman microspectroscopy significantly distorts the laser focal volume, thus negatively affecting the spatial resolution of the measurements. In that case, the resulting in-depth confocal profile is an outcome of several contributions: the broadening of the laser spot due to instrumental factors and diffraction, the spreading of the illuminated region due to refraction of the laser beam at the sample surface, and the influence of the confocal aperture in the collection path of the laser beam. Everall and Batchelder et al. developed simple models that describe the effect of the last two factors, i.e., laser refraction and the diameter of the pinhole aperture, on the confocal profile. In this work, we compare these theoretical predictions with experimental data obtained on a series of well-defined planar interfaces, generated by contact between thin polyethylene (PE) films (35, 53, 75, and 105 microm thickness) and a much thicker poly(methyl methacrylate) (PMMA) piece. We included two refinements in the above-mentioned models: the broadening of the laser spot due to instrumental factors and diffraction and a correction for the overestimation in the decay rate of collection efficiency predicted by Batchelder et al. These refinements were included through a semiempirical approach, consisting of independently measuring the Raman step-response in the absence of refraction by using a silicon wafer and the actual intensity decay of a thick and transparent polymer film. With these improvements, the model reliably reproduces fine features of the confocal profiles for both PE films and PMMA substrates. The results of this work show that these simple models can not only be used to assist data interpretation, but can also be used to quantitatively predict in-depth confocal profiles in experiments carried out with dry optics.

Confocal Raman Microscopy: Performance, Pitfalls, and Best Practice

“…This has been shown to be very successful in some circumstances, allowing accurate prediction of intensity-depth profiles for multilayer systems. 16,21 The overall conclusions that can be drawn from these studies are (a) the depth scale is significantly compressed (with at least two groups agreeing on a factor of~1.7 for NA = 0.9 and n = 1.5 21,23 ) and (b) the confocal aperture restricts the depth of field so that the resolution is better than predicted in our original treatment. Unfortunately, the resolution is still significantly worse than would be deduced from confocal…”

“…Unfortunately, as has been pointed out, 16,21 the Batchelder model greatly overestimates the fall in Raman intensity as a function of depth; consequently it does not accurately predict experimental depth profiles. Several workers have incorporated the effects of diffraction in a semi-empirical manner, 16,21,22 but the most rigorous theoretical treatment to date was by Sourisseau et al, who modeled axial and lateral diffraction and refraction as well as the effect of the confocal aperture. 23 They showed that diffraction is very important, introducing complex intensity variations both along and perpendicular to the zaxis (Fig.…”

“…Many workers have studied the depth scale compression; for example, Tomba et al 21 23 However, assessing the compression from the FWHM of the PE profile gives a larger value,~1.93 for the 35 and 53 lm films. Clearly, the compression deduced from the FWHM of the response from a single layer is greater than that obtained by measuring the point at which the signal from a These figures were not quoted by the authors, but were measured from the curves shown in Fig.…”

Raman Microspectroscopy as a Useful Tool for In Situ and Operando Studies of Water Transport in Perfluorosulfonic Membranes for PEMFCs

“…This model has then been refined by others, in order to reproduce experimental values and, more particularly, the gradual decreasing of the back-scattered Raman signal due to the progressive widening of the confocal volume with depth [63,65,68,69,73]. However, as far as the quantitative detection of sorbed water is concerned, the decreasing of the Raman intensity with depth can be assumed to be corrected by previous steps of the data treatment, namely by the normalization of the water signal by Raman bands from the polymer (Section 2.2).…”

The Role of ConfocalRaman Spectroscopy in Food Science

“…45 This, however, does not take into account the diffraction and the effect of the confocal aperture, which has been calculated by various authors to different levels. 41,42,46,47 The work of Sourisseau and Maraval, 48 generally thought to be the most complete model, reduces the compression to ×1.7. In general, it has usually been found to be between ×1.5 and ×2.…”