Error analysis for estimation of trace vapor concentration pathlength in stack plumes

Near-infrared hyperspectral imaging is finding utility in remote sensing applications such as detection and quantification of chemical vapor effluents in stack plumes. Optimizing the sensing system or quantification algorithms is difficult because reference images are rarely well characterized. The present work uses a radiance model for a down-looking scene and a detailed noise model for dispersive and Fourier transform spectrometers to generate well-characterized synthetic data. These data were used with a classical least-squares-based estimator in an error analysis to obtain estimates of different sources of concentration-pathlength quantification error in the remote sensing problem. Contributions to the overall quantification error were the sum of individual error terms related to estimating the background, atmospheric corrections, plume temperature, and instrument signal-to-noise ratio. It was found that the quantification error depended strongly on errors in the background estimate and second-most on instrument signal-to-noise ratio. Decreases in net analyte signal (e.g., due to low analyte absorbance or increasing the number of analytes in the plume) led to increases in the quantification error as expected. These observations have implications on instrument design and strategies for quantification. The outlined approach could be used to estimate detection limits or perform variable selection for given sensing problems.