beam's intensity is modulated at frequencies, , by the FTIR interferometer when the mirror moves with optical path difference velocity v resulting in a unique modulation frequency corresponding to each wavenumber . Alternatively, the modulation frequency can be set independent of v and if the FTIR interferometer has step-scan capability.^6,7,8.
After the infrared beam passes through the detector window and a transparent gas (typically helium), a fraction, R, is reflected at the sample's surface. The infrared beam intensity is given by at a depth of x=0 inside the sample and decays to a value at depth x due to absorption of infrared radiation in the sample which has an absorption coefficient .

Fig. 1. Schematic of photoacoustic signal generation showing the infrared beam intensity changes upon reflection and absorption by the sample.

Each layer dx of the sample that absorbs infrared radiation experiences an oscillatory heating at frequencies f with temperature change amplitudes proportional to as shown in Fig 2. Each sample layer that oscillates in temperature is a source of thermal-waves.⁹ In the one-dimensional energy flow schematic of Fig. 2, thermal-waves propagate from the sample's bulk to the irradiated surface and into the adjacent gas. During propagation thermal-waves decay with a coefficient where D is the sample's thermal diffusivity.¹⁰ Consequently, the surface temperature oscillation amplitude is proportional to for the thermal-wave generated at depth x just before it crosses into the gas adjacent to the sample surface. A fraction, , of the thermal-wave is reflected back into the sample at the surface resulting in a temperature oscillation amplitude in the gas proportional to .