Pathlength calibration of integrating sphere based gas cells

Integrating sphere based multipass cells, unlike typical multipass cells, have an optically rough reflective surface, which produces multiple diffuse reflections of varying lengths. This has significant advantages, including negating scattering effects in turbid samples, removing periodicity of waves (often the cause of etalon fringes), and simple cell alignment. However, the achievable pathlength is heavily dependent on the sphere wall reflectivity. This presents a challenge for ongoing in-situ measurements as potential sphere wall contamination will cause a reduction in mean reflectivity and thus a deviation from the calibrated pathlength. With this in mind, two techniques for pathlength calibration of an integrating sphere were investigated. In both techniques contamination was simulated by creating low reflectivity tabs e.g. ≈5x7mm, that could be introduced into the sphere (and removed) in a repeatable manner. For the first technique, a four beam configuration, adapted from a turbidity method used in the water industry, was created using a 5cm diameter sphere with an effective pathlength of 1m. Detection of methane gas was carried out at 1650nm. A mathematical model was derived that corrected for pathlength change due to sphere wall contamination in situ, thus enabling gas measurements to continue to be made. For example, for a concentration of 1500ppm of methane where 1.2% of the sphere wall was contaminated with a low reflectivity material, the absorption measurement error was reduced from 41% to 2% when the model was used. However some scenarios introduced errors into the correction, including contamination of the cell windows which introduced errors of, for example, up to 70% if the particulate contamination size was on the order of millimetres. The second technique used high frequency intensity modulation with phase detection to achieve pathlength calibration. Two types of modulation were tested i.e. sinusoidal modulation and pulsed modulation. The technique was implemented using an integrated circuit board which allowed for generation of modulation signals up to 150MHz with synchronous signal processing. Pathlength calibration was achieved by comparison of iii the phase shift for a known length with the measured phase shift for the integrating sphere with unknown pathlength over a range of frequencies. The results for both modulation schemes showed that, over the range of frequencies detected, 3-48MHz, the resultant phase shift varied as an arctangent function for an integrating sphere. This differed from traditional single passes where frequency and phase have a linear relationship