When , the photoacoustic signal increases linearly with because as increases, more infrared absorption occurs within layer thickness, L, which is efficient in transporting heat into the gas. The photoacoustic signal loses linearity (the onset of saturation) as the infrared absorption continues to increase and as a high fraction of the absorption occurs within the layer. At very high infrared absorption, heating occurs very close to the sample surface and the photoacooustic signal no longer increases with infrared absorption (full saturation). After full saturation some spectral features may still be observed due to spectral variations in the (1-R) term of the photoacoustic signal expression.
FTIR-PAS spectra usually contain bands with infrared absorption coefficients in the ranges both before and after the onset of saturation are a very minor presence and often are not discernible. The onset of saturation can be moved to higher absorption by increasing modulation frequency and thereby decreasing the sampling depth. In most quantitative analyses, however, signal saturation does not present a problem due to the presence of weaker bands that are linear with concentration and the tolerance of commercial FTIR factor analysis software to nonlinearities in spectra.

B. Variation of Sampling Depth

In the analysis of samples with concentration gradients or layers it is particularly desirable to be able to vary the sampling depth. The most straight forward situation in one where: (i) the thermal diffusivity is homogeneous, (ii) the weak absorption bands (such that values at absorbance band peaks are ) can be used both for monitoring the depth-varying concentration and (iii) an internal standard absorbance is available which is associated with a species that doesn't vary with depth. Furthermore, the sample's thermal diffusivity D and the modulation frequency f must allow the sampling depth to be adjusted over the range of interest by setting f via the mirror velocity or the step-scan modulation.^8,11
Table 1 gives sampling depths for typical values of thermal diffusivities and modulation frequencies. The thermal-wave decay coefficient, which should be larger than the analysis peak absorption coefficient value, is just the reciprocal of the sampling depth as discussed in the last section. FTIR-PAS sampling depths for polymers are typically in the micrometer to hundreds of micrometers range. This range nicely compliments ATR measurements which typically have sampling depths ranging from fractions of micrometers to micrometers.¹²