Experimental photoacoustic (PA) magnitude spectra of a coated paper and the uncoated basepaper are presented. The normalized and scaled PA magnitude spectra are used to calculate difference magnitude spectra. It was decided to scale all PA magnitude spectra to (low) equal intensity at the approximately optically thin spectral range before subtraction. Then no infrared (IR) bands of identical band shape and height (as needed for common difference spectroscopy) in either PA magnitude spectrum are needed. Contributions of the two individual layers to the IR-PA magnitude spectrum of the coated paper are separated in the difference spectrum by their sign. An increasing relative contribution of the coating layer with an increasing phase modulation frequency is found. On decreasing the thermal length to a value near the coating thickness, the difference spectra increasingly show positive coating bands and negative bulk signals. The extension of the Rosencwaig-Gersho theory to a double-layered system introduced by N. C. Fernelius [J. Opt. Soc. Am . 70, 480 (1980) and J. Appl. Phys. 50, 650 (1980)] applied to synthetic spectra confirms the experimental observation. It is found that photoacoustic difference spectroscopy may provide quantitative depth-resolved spectral information due to the presented scaling procedure, and photoacoustic difference magnitude spectra of any polymeric laminate may therefore be calculated.
M. W. C. Wahls, E. Kentta, and J. C. Leyte, "Depth Profiles in Coated Paper: Experimental and Simulated FT-IR Photoacoustic Difference Magnitude Spectra," Appl. Spectrosc. 54, 214-220 (2000)