Using integrating spheres as absorption cells: path-length distribution and application of Beer's law

We have modeled the path-length distribution in an integrating sphere used as a multipass optical cell for absorption measurements. The measured radiant flux as a function of analyte concentration is nonlinear as a result, deviating from that expected for a single path length. We have developed a full numerical model and introduce a new analytical relationship that describes this behavior for high reflectivity spheres. We have tested both models by measuring the optical absorption of methane at 1651nm in a 50mm diameter sphere, with good agreement with experimental data in the absorption range 0-0.01cm -1 . Our results compare well with previous work on the temporal response of integrating spheres.