ATR III: How Wavenumber Impacts DP

The first parameter to consider in the ATR depth of penetration (DP) equation is W, the wavenumber. At first glance the presence of this parameter in the equation should strike you as bizarre. In a transmission sampling experiment the infrared beam passes through a thin film of sample and all wavenumbers of light see the same sample thickness. Since wavenumber appears in the denominator of the DP equation, as W goes up DP goes down. This means, for example, that in an ATR experiment 1000 cm-1 light penetrates further into samples than 3000 cm-1 light does. Since peak size is proportional to pathlength, the relative intensities in ATR spectra are different than in spectra taken via other sampling techniques. In general in ATR spectra the peaks at high wavenumber are smaller than the peaks at low wavenumber.

This point is illustrated in the figure pasted into this blog post which shows the ATR and non-ATR spectra of sucrose (table sugar). Note in the ATR spectrum (top) the peaks at low wavenumber are much bigger than the peaks at high wavenumber, whereas in the non-ATR spectrum (bottom) the peaks at low and high wavenumber are about the same size.

This phenomenon has important implications for how we use ATR spectra. Since ATR spectra look different than non-ATR spectra it is best to only compare ATR spectra to each other. This also means you will get better library searching results by only searching ATR spectra against ATR libraries. If you own an ATR I strongly suggest you to build ATR libraries of your own samples and/or buy a commercial ATR library.