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The FT-IR interferometer modulates the intensity of the infrared beam that is incident on the sample.  The beam is partially reflected (RI₀) at the front face of the sample but this reflection is ignored in the simple model.  The beam then decays exponentially with an absorption coefficient, ,as it propagates within the sample.  The wavenumber of the infrared radiation is denoted by .  In most cases all of the absorbed radiation is converted into heat, causing the temperature of each absorbing layer to oscillate at the beam modulation frequency with an amplitude proportional to the amount of light absorbed in it.  Each of these layers becomes a source for launching propagating temperature oscillations called thermal waves.  
       Thermal waves have three important properties affecting photoacoustic signal generation.  They have a short decay length called the thermal diffusion depth or thermal wave decay length, L, given by equation (1):  

            L = (D/pf)^1/2                                                                                  (1)

where D and f denote the sample’s thermal diffusivity and the infrared beam modulation frequency, respectively.  Thermal waves decay to 37% (i.e. 1/e) of their original amplitude over a distance of L.  If the decay of thermal waves did not define an active signal-generation layer that is smaller than the optical decay length, photoacoustic spectra of opaque samples would be just as hopelessly saturated and impractical for measurement as transmission spectra are for such samples.  Fortunately, as long as the thin layer is partially transmitting, the photoacoustic signal increases with absorption coefficient and spectra can be readily measured by PAS, regardless of sample thickness. 
            After the thermal waves are launched, those that propagate to the front face of the sample contribute to the PAS signal, but most of their amplitude is not detected because it is reflected back into the sample and decays.  The strong back reflection of thermal waves in the solid is the second important property of thermal waves in photoacoustic signal generation, but it is not as fortuitous for the signal generation process as is their short decay length.  In fact, if the high back reflection were not present, photoacoustic signals would have significantly higher amplitudes and signal-to-noise ratios.
            The small thermal-wave amplitude that does transmit into the gas results in thermal expansion and a pressure oscillation in the gas, which increases with and that is detected as an acoustic signal containing both phase and magnitude information by a sensitive microphone.  The phase of the PAS signal is equal to the phase lag between the signal and the waveform of the IR beam that excites it.  The lag is caused by the finite propagation time of thermal waves during signal generation.  This is the third important property of thermal waves in signal generation and it results in the phase angle being a measure of the depth from which the signal evolves within the sample.  The maximum phase angle that can be measured is one cycle, or 360°, corresponding to a maximum depth of 2pL on the length scale.
               In many instances, PAS data are analyzed in the form of magnitude spectra.  These spectra are commonly used for qualitative and quantitative analysis of