1. Digital Imaging and Remote Sensing Laboratory thermal infrared data 1 Processing of TIMS data to emissivity spectra TIMS bands for this analysis 8.407, 8.801, 9.204, 9.933, 10.703, and 11.625  m. Given 6 channels calibrated to surface-leaving spectral radiance, we have 7 unknowns: temperature (T) and 6 spectral emissivity values, so the problem is undetermined.

2. Digital Imaging and Remote Sensing Laboratory thermal infrared data 2 Hook compares three techniques for computing spectral radiance, only 2 will be presented here. 1.The “assumed channel 6 emittance model” developed by Kahle (1980) (ref). – This method assumes the emissivity in one channel (usually #6) is a known constant for all materials, and therefore, the temperature can be calculated using that channel. Then the emissivity in all other channels can be found. This method is simple and intuitive but prone to errors when the assumption is violated. It also tends to propagate any noise in the reference channel to all the other channels.

3. Digital Imaging and Remote Sensing Laboratory thermal infrared data 3 2.The alpha residuals technique attempts to eliminate the temperature dependence and generate spectral values that are proportional, though not necessarily equal to emissivities. It proceeds as follows: a.Assume Wien’s blackbody approximation to the Planck equation (˜1% error is introduced in the 300 K region).

4. Digital Imaging and Remote Sensing Laboratory thermal infrared data 4 where L ij is the surface-leaving radiance for pixel i in channel j, C 1, and C 2 are radiation constants j is the central wavelength for channel j and, T i is the temperature for pixel i. Taking the log of both sides and including emissivity  ij yields weighting by j isolates a temperature term

5. Digital Imaging and Remote Sensing Laboratory thermal infrared data 5 Taking the average of the X ij values for each pixel and subtracting yields where K j is known Comment: Hook points out that the alpha residuals should exhibit the same spectral features as the laboratory spectra and that the laboratory spectra can be converted to alpha residuals.

6. Digital Imaging and Remote Sensing Laboratory thermal infrared data 6

7. Digital Imaging and Remote Sensing Laboratory thermal infrared data 7 The image derived alpha residuals and laboratory derived alpha residuals could then be analyzed using many of the spectral analysis tools developed for the reflectance channels.