Chapter 13

Tetracorder

Tetracorder

Simple definition of band depth D = 1 - Rb/Rc where

Rb is reflectance in band center and Rc is reflectance

in continuum at band center. With 3 channels we can

estimate Rc 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 Lc 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 CO() 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

 

)()(

)(

CL

LC )()(

)(

O

C CO

O

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.

where or 1 CCC

C bLaLkkL

L

)1(1

and )1(

1k

bk

a

Tetracorder (cont’d)

If we run a least squares fit on

and solve for a and b, then

for each library reference spectra.

bb

k1

CC bLaO

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 (R2) and compute a band depth.

Band depth is proportional to abundance and R2 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 *R2 (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.