Effects of Wavelength Calibration Mismatch on Temperature-Emissivity Separation Techniques

Accurate estimation or retrieval of surface emissivity from long-wave infrared hyperspectral imaging data acquired by airborne or space-borne sensors is necessary for many scientific and defense applications. This process consists of two interwoven steps: atmospheric compensation and temperature-emissivity separation (TES). The most widely used TES algorithms for hyperspectral imaging data assume that the emissivity spectra for solids are smooth compared to the atmospheric transmission function. In this paper, we develop a model to explain and evaluate the performance of TES algorithms using a smoothing approach. Based on this model we identify four sources of error: the smoothing error of the emissivity spectrum, the emissivity error from using the incorrect temperature, and the errors caused by sensor noise and wavelength calibration. For the TES smoothing technique used in the automatic retrieval of temperature and emissivity using spectral smoothness algorithm, we analyze the bias in the temperature errors caused by wavelength calibration errors under varying ground temperatures and emissivities. It turns out that an increase in calibration error leads to an additional temperature error, which leads to a further increase in the emissivity error. Furthermore, the performance model explains how the errors interact to generate the final temperature errors. We assume exact knowledge of the atmosphere, so that the only causes of error are calibration errors and the smoothing error of the emissivity spectrum.