Optimal filter selection for quantitative gas mixture imaging

Abstract

We present a general technique to select optimal filters for a multispectral midwavelength infrared (MWIR) camera to quantify multiple components of a gas mixture. Filter sets are ranked in terms of the ratio of quantity-of-interest variance to noise variance, which is minimized by the optimal filter set. The suitability of this criterion is demonstrated using a numerical experiment in which we estimate the combustion efficiency (CE) of a gas flare from MWIR images of the flare. Synthetic hyperspectral intensity data are generated using the spatially-resolved thermochemical state of a simulated flare-in-crosswind. We then compute multispectral images for commercially-available filter sets and estimate the concentration of key species (CH4 and CO2) and temperature along lines-of-sight that correspond to sampled pixels. These distributions are converted to a CE and we compare the accuracy of CE estimates for a filter set to our selection criterion. We find that the selection criterion is a good proxy for CE accuracy. Moreover, the optimized filter set makes intuitive sense: the filters are aligned with the CH4 and CO2 absorption bands at 3.4 μm, with an emphasis on CH4 lines because the CE is highly sensitive to the presence of low concentrations of unburned fuel at low temperature. The selection technique can be applied to any number of quantitative multispectral gas imaging scenarios.