Methods of measuring the concentration of atmospheric pollutants by laser absorption spectroscopy, such as differential absorption lidar (DIAL) and integrated long-path techniques, all rely on the validity of Beer’s exponential absorption law. It is shown here that departures from this law occur if the probing laser has a bandwidth larger than the wavelength scale of structure in the absorption spectrum of the pollutant. A comprehensive experimental and theoretical treatment of the errors resulting from these departures is presented for the particular case of SO2 monitoring at ~300 nm. It is shown that the largest error occurs where the initial calibration measurement of absorption cross section is made at low pressure, in which case errors in excess of 5% in the cross section could occur for laser bandwidths >0.01 nm. Atmospheric measurements by DIAL or long-path methods are in most cases affected less, because pressure broadening smears the spectral structure, but when measuring high concentrations errors can exceed 5%.
D. J. Brassington, R. C. Felton, B. W. Jolliffe, B. R. Marx, J. T. M. Moncrieff, W. R. C. Rowley, and P. T. Woods, "Errors in spectroscopic measurements of SO2 due to nonexponential absorption of laser radiation, with application to the remote monitoring of atmospheric pollutants," Appl. Opt. 23, 469-475 (1984)