Chapter 13 Tetracorder

Simple definition of band depth D = 1 - R b /R c where R b is reflectance in band center and R c is reflectance in continuum at band center. With 3 channels we can estimate R c as average of channels on wings on either side of band center. O.K. for narrow features, but not entirely satisfactory for more complex features where some form of interpolation may be desired.

Tetracorder (cont’d) Use specific bands to search for feature and estimate a relative concentration based on band depth. First generate a continuum removed spectra for library spectra and image-derived spectra.

Tetracorder (cont’d) Convolve library spectra with spectral response of sensor to generate an estimate of image derived reflectance spectra (i.e., assumes some form of atmospheric inversion has been applied to image data). Convert image DC spectra to approximate surface reflectance spectra.

Tetracorder (cont’d) Remove continuum according to where L c is the continuum removed spectra derived from library reflectance spectra (L), O c is the continuum removed spectra derived from image derived reflectance spectra, and C ( ) and C O ( ) are library and image derived continuum spectral estimated from a fit through the limbs. A fit is made through the limbs most simply using a straight line and several user-defined bands on either side of the absorption feature. cf. Figure 1 from paper

Tetracorder (cont’d) Fig. 1. A spectrum from the Canon City AVIRIS flight data is compared to a library reference kaolinite spectrum.

Tetracorder (cont’d) The difference in the continuum removed spectra may be due to areal or intimate mixtures (i.e., mixed pixels) or due to scattering differences due to grain size variations. A radiative transfer model could be used to model variations from library spectra and then fitted to the observed spectra.

Tetracorder (cont’d) In this case, a simple additive constant (k) is used to reduce the contrast in the continuum removed library spectra according to where L is the contrast reduced spectrum that best matches observation.

Tetracorder (cont’d) If we run a least squares fit on and solve for a and b, then for each library reference spectra.

Tetracorder (cont’d) Fig. 2. The kaolinite spectra from Figure 1B have had some continuum removed and the library spectrum fitted to the observed AVIRIS spectrum. While a single spectrum may not show the kaolinite doublet structure well, an average of several pixels from this region does.

Tetracorder (cont’d) Run this regression fit on each pixel and generate a goodness of fit (R 2 ) and compute a band depth. Band depth is proportional to abundance and R 2 yields a confidence. We can then generate relative abundance and confidence maps (set abundance to zero if confidence is below some threshold).

Tetracorder (cont’d) Note S/N can be improved by averaging spectra. This helps both continuum removal and curve fitting. Display of band depth *R 2 (cf. Figures) tends to highlight abundance and confidence simultaneously. (N.B. interesting opportunity for IHS … )

Tetracorder (cont’d) Fig. 2.

Tetracorder (cont’d) Fig. 3.

Tetracorder (cont’d) Fig. 6. An average spectrum of 32 pixels from the Canon City AVIRIS image compared to reference library spectra of kaolinite and geothite (dashed-dotted curves) and a spectrum of a rock sample from the sandstone unit seen in Figure 3d.