A method of evaluating the initial assumptions and uncertainties of the physical connection between Airborne Imaging Spectrometer (AIS) image data and laboratory/field spectrometer data was tested. The Tuscon AIS-2 image connects to lab reference spectra by an alignment to the image spectral endmembers through a system gain and offset for each band. Images were calibrated to reflectance so as to transform the image into a measure that is independent of the solar radiant flux. This transformation also makes the image spectra directly comparable to data from lab and field spectrometers. A method was tested for calibrating AIS images using the surface as a reference. The surface heterogeneity is defined by lab/field spectral measurements. It was found that the Tuscon AIS-2 image is consistent with each of the initial hypotheses: (1) that the AIS-2 instrument calibration is nearly linear; (2) the spectral variance is caused by sub-pixel mixtures of spectrally distinct materials and shade, and (3) that sub-pixel mixtures can be treated as linear mixtures of pure endmembers. It was also found that the image can be characterized by relatively few endmembers using the AIS-2 spectra

Adams, J. B.

Gillespie, A. R.

Roberts, D. A.

Shipman, H. M.

Smith, M. O.

Willis, S. C.

English

NASA Technical Reports Server

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N88- 1 3 f d O  
Calibrating AIS Images Using the Surface as a Reference 
M. 0. Smith, D. A. Roberts, H. M. Shipman, J. B. Adams, S. C. Willis and A. R. Gillespie 
University of Washington 
Seattle, WA. 98195 
ABSTRACT 
We have tested a method of evaluating the initial assumptions and uncertainties 
of the physical connection between AIS image data and laboratory / field spectrometer 
data. To first order, the Tuscon AIS-2 image (flight #601) connects to laboratory 
reference spectra by an alignment to the image spectral endmembers through a 
system gain and offset for each band. 
We have chosen to calibrate images to reflectance so as to transform the image 
into a measure that is independent of the solar radiant flux. This transformation also 
makes the image spectra directly comparable to data from laboratory and field 
spectrometers. Our objective in this paper is to test a method for calibrating AIS 
images using the surface as a reference. The surface heterogeneity is defined by 
laboratory / field spectral measurements. 
We have developed an approach to calibration that maps the n-dimensional 
volume defined by image spectra into the n-dimensional volume defined by laboratory/ 
field reference spectra. The dimension of the volume is equivalent to the number of 
image bandpasses. We assume that to first order 1) the image spectra are linear 
mixtures of the laboratory or field reference spectra and 2) that there is a set of system 
gains and offsets for each band. However, it is not necessary that the image spectra 
be mixtures of the reference spectra; they could be pure endmembers themselves. 
The system gains and offsets include all contributions from the entire system (e.g., 
atmosphere, solar spectrum, instrument, lighting geometry, etc.) not solely those due to 
the instrument. 
We tested these assumptions on an AIS-2 image (flight #601) obtained in 
September 1986 of the Tucson Mountains just west of Tucson, Arizonia. The 
instrument was flown in rock mode and included the wavelength range from 1200 nm 
to 2500 nm. We used only bandpasses where the signal to noise ratio was near 100 
or better, which resulted in a reduction of the original 128 bands (rock mode) to 64 
bands. Prior to analysis the image was destriped by adjusting gains for each column 
to equalize the column means. 
Representative spectra of surface samples were measured on a Beckman DK-2A 
spectrometer. We term this set of spectra the reference endmembers, since they 
describe pure surface components (Figure 1). Other reference spectra could be 
modeled as linear mixtures of these spectra. In addition to these three spectra the 
reference endmembers also include the spectrum shade which has 0% reflectance. A 
precise definition of the endmember shade is given in Adams et al. 1986. These 
reference spectra are used to define the n-dimensional volume of all reference spectral 
measurements. 
To complement the reference endmembers, we need to determine a set of image 
endmembers such that they define the n-dimensional volume of the image. The image 
volume is defined by single pixel image endmembers that, when linearly mixed, 
63 
https://ntrs.nasa.gov/search.jsp?R=19880004378 2020-03-20T09:20:00+00:00Z
adequately fit the iqage spectral variance and yield fractions between 0 and 1. The 
spectral image endmembers do not necessarily have any physical identity. For the 64 
selected AIS-2 bands we found the linear mixtures of four image endmember spectra 
could model the fans south of the Desert Museum (Figure 2) to within 10 DN rms error. 
The rms error is computed as the difference between the measured image data and 
that predicted by a least square fit of mixtures of the four endmembers. Only random 
spatial patterns were present in the rms error image indicating the four image 
endmembers adaquately defined the image n-dimensional volume. 
The connection between the image endmembers and laboratory reference 
endmembers is made using the following equation: 
Gb DNiem,b -t Ob = Re,b 
subject to the constraint : C Fern = 1 
where DNiem,b is the digital number for each image endmember for each band, Gb 
the system gain to convert image digital numbers to total hemispherical reflectance for 
each band b, ob the offset in reflectance for each band b, Fern the fractional 
contribution of each reference spectral endmember, and Re,b the total hemispherical 
reflectance for each reference spectral endmember for each band b. The summation 
in Equation 1 is over the number of relevant spectral endmembers. The equation is 
solved iteratively first for the gains and offsets and then for the fractions Fern. 
Equation 1 formalizes our hypothesis that the primary connection between the 
imaged surface and laboratory reference spectra involves first an alignment of mixed 
pixels in the image to unmixed reference spectra, and secondly a calibration between 
image digital numbers and total hemispherical reflectance. The calibration model uses 
a simple linear equation consisting of a single gain and offset for each band. However, 
imbedded in the gains and offsets are more than the instrument calibration; in addition, 
there are effects caused by the solar spectrum, the atmosphere, and differences in 
lighting geometry between image and laboratory measurement systems. We are 
testing whether or not the entire system including the atmosphere, solar spectrum, and 
conversion of bidirectional to total hemispherical reflectance can, to first order, be 
approximated by a linear equation. 
The solution consists of finding the fractions Fern that align the mixed pixel 
endmember spectra from the image to the unmixed reference endmembers. The 
results of the alignment (Table 1) are physically realizable, Le., the image endmember 
set consists of fractions between 0 and 1 for each reference endmember spectrum, and 
each image endmember spectrum fits well to linear combinations of the reference 
spectra (rms errors are all < 0.3'10 reflectance). Table 1 now makes possible a physical 
identification of the image endmembers from the reference spectra. For example, em-1 
is predominantly equivalent to an arkose spectrum (f=0.6 arkose), but unlike the 
reference spectrum of arkose, is mixed with vegetation, shade, and rhyolite. Similarly, 
each of the other image endmembers connect predominantly to an equivalent 
reference endmember spectrum. 
64 
BURSAGE 
ARKOSE 
o J  , 
500 1000 1500 2000 2500 
Wavelengtn (nml 
Figure 1. 
Measurements were made with a Beckman 2K-DA spectrometer. 
Total hemispherical reflectance of the field spectral endmembers. 
El- 
Arkose I I- 
I j -  Rhyolite J -____--- 
. > .. :.. .. . (. 
I .. . .  . .  
-.... ; 
0 1 I I I 
1600 1800 2000 2200 2400 1200 1400 
Wavelength (nm) 
Figure 2. Raw digital numbers of the image spectral endmembers. Wavelengths 
shown were those with high signal to noise ratios used in our analysis. Note abscissas 
for Figures 1 and 2 are different. 
65 
Table I. Results of Image Endmember Alignment to Reference Spectra 
Fraction of Reference Endmember 
arkose rhyolite bursage shade rms error 
Image 
Endmember 
em-1 
em-2 
em-3 
em-4 
0.60 0.14 0.24 0.03 0.002 
0.01 0.52 0.21 0.27 0.001 
0.36 0.02 0.42 0.19 0.002 
0.03 0.32 0.1 4 0.51 0.002 
The gains and offsets from Equation 1 characterize the total system response to a 
linear calibration. The predominant pattern in the gain curves (Figure 3) is an inverted 
response to the water bands at 1400 and 1900 nm. In addition, the C02 absorption 
bands near 2000 nm are evident. These characteristics are resolved in the gains 
because they are constant for the en-tire image. Similarly, the offsets for most bands 
(Figure 4) typically were below 1 % reflectance. However, many bands near 1200 nm 
have erratic scatter and high offsets. This type of pattern is indicative of faulty detector 
elements in the two-dimensional CCD array of the AIS-2 instrument. 
To test the appropriateness of the reference endmembers with respect to the 
image endmembers, we determined the quality of fit (correlation) between each of the 
four image and reference endmembers for each band independently (Figure 5). The 
wavelengths between 1200 nm and 1300 nm exhibit some of the variability observed 
in the offsets (Figure 5) and gains (Figure 3). This does not fit the pattern of variation 
we observe in the reference endmembers (Figure 1). We interpret the almost random 
variation in corrlelations between 1200nm and 1300nm, and the significantly lower 
correlations at 1900 nm to be typical of that caused by the instrumentation. 
In contrast, the systematic lack of fit near 2200 nm corresponds to the absorption 
feature of the arkose reference spectra (Figure 1). A plot of the image and reference 
endmembers for the 2200 nm wavelength (Figure 6) illustrates the deviation of the 
arkose from a linear calibration. We interpret this lack of fit at 2200 nm as a mismatch 
between the image and reference arkose endmember spectrum. What we have 
interpreted as an arkose for the image endmember has the general shape of the 
reference arkose spectrum, but lacks the 2200 nm absorption band. Even though the 
arkose reference spectrum does not fit the image data at 2200 nm we can use the 
other three reference endmembers to determine the gains and offsets in this 
wavelength region to maintain calibration integrity. 
To determine if areas in the image contained the 2200 nm clay absorption band 
found in the arkose reference spectrum, we examined the difference images between 
that predicted by mixtures of the calibrated image endmembers and the raw image. 
Three of the difference images corresponding to the bands of the 2200 nm clay 
absorption contained distinct spatial patterns relating to the reference arkose spectrum. 
Distinct spatial patterns in the difference images provide a means of determining if 
subtle absorption features present in the surface mineralogy can be detected over that 
of the AIS-2 instrument noise. Further resolution of the 2200 nm 
66 
1200 1400 1600 1800 2000 2200 2400 
Wavelength (nm) 
Figure 3. System gains (Gb) obtained by solving Equation 1. 
1200 1400 1600 1800 2000 2200 2400 
Wavelength (nm) 
Figure 4. System offsets (ob) obtained by solving Equation 1. 
67 
1200 1400 1600 1800 2000 2200 2400 
Wavelength (nm) 
600 
APICOae * 
- 500 - 
0 - 
Rnyolite 
m 
2 400 . 
a 
!i, 300 . 
n 
0 
0 
m 
/* : vegetation z 0 
W 
01 
100 
it Snade 
2oo 0 /*  
Figure 5. The fit (correlation) between each of the four image and reference 
endmembers for each band is computed independently. 
Figure 6. The departure of the reference arkose spectrum from that of the unmixed 
image arkose endmember spectrum is inferred from the deviation of the arkose 
endmember from a linear calibration from the other endmembers. 
68 
absorption feature can be accomplished by spectrally unmixing the background 
continium spectrum from that of the arkose (Shipman and Adams 1987). 
In summary, we have found that the Tucson AIS-2 image is consistent with each 
of our initial hypotheses; 1) that the A S 2  instrument calibration is nearly linear, 2)the 
spectral variance is caused primarily by sub-pixel mixtures of spectrally distinct 
materials and shade, and 3) that sub-pixel mixtures can be treated as linear mixtures of 
pure endmembers. In addition, we have found that the image can be characterized by 
relatively few spectral endmembers using the AIS-2 high resolution spectra. The 
resulting patterns in fractions, gains, offsets, and overall fit of Equation 1 to the data 
make possible the separation of surface effects from those of the instrument, 
atmosphere, and solar spectrum. 
REFERENCES 
Adams, J. B., M. 0. Smith and P. E. Johnson. 1986. Spectral mixture modeling: A new 
analysis of rock and soil types at the Viking Lander I Site, J. GeoDhvs. Res. 9 1, 
8098-81 12. 
Shipman H. M., and J. B. Adams, Detectability of mineral on desert alluvial fans using 
reflectance spectra, J. Geophvs. Res,, in press 1987. 
69 


Calibrating AIS images using the surface as a reference

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