Using integrating spheres with wavelength modulation spectroscopy: effect of pathlength distribution on 2nd harmonic signals

We have studied the effect on 2nd harmonic wavelength modulation spectroscopy of the use of integrating spheres as multipass gas cells. The gas lineshape becomes distorted at high concentrations, as a consequence of the exponential pathlength distribution of the sphere, introducing nonlinearity beyond that expected from the Beer-Lambert law. We have modelled this numerically for methane absorption at 1.651μm, with gas concentrations in the range of 0-2.5%vol in air. The results of this model compare well with experimental measurements. The nonlinearity for the 2f WMS measurements is larger than that for direct scan measurements; if this additional effect were not accounted for, the resulting error would be approximately 20% of the reading at a concentration of 2.5 %vol methane.