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Equations that relate photothermal lens focal lengths and photothermal deflection angles to saturation absorption coefficients are derived. These equations are derived for two-level absorbers with both homogeneously and inhomogeneously broadened transitions. Initial and time-dependent photothermal lens signals are calculated. Equations describing the zero-time signals are exact to within the simplifying assumptions of the derivation, while the time-dependent signals are approximate. The approximation is performed by the use of a finite series of Gaussian functions to model the temperature change profile distorted by nonlinear absorption. The excitation irradiance-dependent signal behavior for rectangular and exponential excitation pulse time profiles for homogeneously and inhomogeneously broadened transitions are compared. Absorbed energies are used to calculate effective absorbances obtained by the use of conventional and photothermal lensing spectrometry. The conclusions drawn from these comparisons are tha pulsed laser photothermal spectroscopy is sensitive to the excitationlaser's pulse temporal profile and the transition broadening mechanism.
Stephen E. Bialkowski (1993) studied this question.