An Investigation into the Lambert-Beer Law in Incoherent Broad-Band Cavity-Enhanced Absorption Spectroscopy

Zane Thornburg


Absorbance values measured using incoherent broad-band cavity-enhance absorption spectroscopy (IBBCEAS) were confirmed to have a non-linear dependence on concentration in contrast to the expected linear dependence from Beer’s Law. A liquid-phase sample in a cuvette is placed within an optical cavity created by two highly reflective mirrors to increase the number of optical passes through the sample, enhancing the sensitivity of absorption measurement. The nonlinear behavior was observed in absorbance measurements for both a weak absorber, toluene, and a strong absorber, the dye 1,1-diethyl-4,4-carbocyanine iodide. Tracking losses of intensity within the mirror cavity, models to describe the behavior in certain absorbance ranges were found. Two models were found that could be used to predict absorbance measurements made between 0 and 0.3. The first model predicts a finite number of passes within the mirror cavity, specifically around 60 passes, as a good fit to the experimental data in the range of 0 to 0.3. The second model predicts an infinite number of passes through the cuvette and incorporates a constant non-absorptive loss. The non-absorptive loss is difficult to predict, but can be empirically determined and used later for unknown samples to predict absorbance measurements. Above absorbance 0.3, the number of passes occurring appears to decrease for higher concentrations/absorbances. The effects causing the apparent fewer passes likely include factors such as reflection off the cuvette-air interface within the mirror cavity, complicating the equations needed to describe the behavior at higher absorbance values. While a complete model was not achieved, models that are good approximations for cavity-enhanced absorbance measurements between 0 and 0.3 were found.