So far, the spectral plots displayed on the preceding page are mostly pure phases, irradiated under laboratory conditions. Even under ideal conditions, though, for the same species, notable physical and/or chemical variations can exist, e.g., ones related to color or from foreign coatings (such as iron rust). So, a single spectrum, while containing the dominant and diagnostic absorption features for a species, is a standard that we must generalize. Straightforward chemical changes can significantly modify the spectrum. Many minerals, for example, allow substitutions of one element or ion state at lattice sites by other elements, so that the formula for such materials is variable. Take, for instance, the progressive substitution of aluminum in certain octahedral sites that occurs in the common mica, Muscovite. Note how this affects the principal absorption trough at 2.2 µm. Again, the curves are offset.
The size range of individual mineral grains or crystals can have a major effect on the characteristic spectral curve of the same species. This usually influences the total reflectance but can also modify the depth of an individual absorption feature. Consider the effect of grain size (in µm) for finely ground samples of the same specimen of a pyroxene species (there is no offset applied to these curves).
As the grain size enlarges, the reflectance diminishes, although the absorption troughs remain relatively constant. Two factors control this effect: the larger grains allow more absorption and the smaller grains provide a higher proportion of surface area available as reflectors.
Rather unexpectedly, there is a broad reversal in the relative reflectance as a function of grain size when we examine the same material in the mid-IR region, as shown here:
As we saw earlier in this section, mixed pixels are the rule for most space images and become ever more troublesome as resolution becomes coarser, so that more diversity is expected as the ground area represented by a pixel increases. This problem can be a problem also when we acquire a single spectral curve that represents all the features and classes normally present in a pixel representing Landsat Multispectral Scanner or Thematic Mapper resolutions. Thus, for TM the spectrometer's Field of View would enclose a 30 meter square (this is hard to do from a cherry picker). The resulting spectral plot shows a variety of absorption troughs, some of which we can match to individual phases (classes), whereas others may lie in nearly the same wavelength positions, but are really other bands that are present in common with the phases. The reflectance at any given wavelength is also a composite average of the proportionalized phases contributing to the mixture. Because of the operational difficulties in encompassing large areas on the ground from a near surface position, to get a representative spectral curve one could point the spectrometer's view at a slant rather than straight down. Another way: take close-up spectra of each individual feature or class within the scene, weight the proportions of the various features, and calculate a composite spectral response (signature) curve (possible, but sometimes impractical). The best case scenario for obtaining relevant field spectra is where the scene within a pixel area contains only a few classes, these are small, and all appear close together (to illustrate: suppose the scene contained sagebrush, shortgrass, and bare soil; somewhere these would be together, allowing a spectral reading of their integrated response as though they could be described as "grassy brushland".
To illustrate this for two simple cases, inspect these curves. The first is just a series of a two-phase mix, in which the clay mineral Montmorillonite is progressively diluted with charcoal, which has a spectral curve with no absorption troughs and an overall low reflectance.
The reflectances are absolute (no offsets). The result of adding the black charcoal to the whitish Montmorillonite is to reduce the depths of the absorption troughs. Above 20% charcoal, the toughs nearly disappear due to the dominance of charcoal in reducing reflectance.
Now look what happens when we mix two very similar minerals, Alunite (a potassium sulphate also containing aluminum) and Jarosite (the same, except iron replaces the aluminum) in two different ways: Areal, which we compute as a linearly equal combination of the two end members, and Intimate,which we combine and thoroughly intermix and then irradiate under laboratory conditions. The darker (yellow-brown) Jarosite has a lower reflectance continuum at the shorter wavelengths but becomes higher at longer wavelengths. In a 50-50 mix, this darker phase predominates, so that the reflectances are (similar to the effect of charcoal) controlled almost entirely by Jarosite.
From the above considerations, we learn that practical remote sensing, which depends upon imaging spectrometers and hyperspectral data acquisition is especially sensitive to many variables, including foremost, the mixed pixel problem. Because the spectral curves that we can derive from sensors, such as AVIRIS. vary "all over the place," from pixel to pixel, as the combinations of surface features change in a scene, we need some method(s) of reducing the data to meaningful components that we can assign to their proper classes. We must simplify complex spectra, containing contributions from a variety of phases (in a single 30 meter square pixel soil, water, vegetation, buildings, etc. can mutually occur), so that we can extract the identity and proportions of each. Fortunately, with effective mathematical models and computer processing, we can do this task with surprising effectiveness.
This subject of hyperspectral data reduction and analysis is specialized and somewhat complicated, so that we offer only an outline of the approaches used.
The starting point (and the key) is to develop a Spectral Library. This library consists of literally thousands of individual spectral curves, obtained by spectrometers applied to discrete materials (as pure as possible,) and classes in laboratory and field settings. This library has built up over the years as a data collection developed from many observations by numerous groups. Best known in the U.S. is the library assembled by the Spectroscopy Lab of the U.S Geological Survey in Denver. (For more information, check their Home Page).
From such information, identification algorithms have been devised to quantitatively analyze hyperspectral data, acquired during aircraft overflights. The U.S.G.S. has put together such a program known as Tetracorder, which contains various routines that systematically reduce the raw data to specific identifications. It convolves individual fits of library curves to the hyperspectral data obtained from a mission. In some instances, it can analyze a complex (composite) curve by appropriate algorithms that break it into a set of "end member" curves, each representing a material or class that is a component of the curve. It calculates band locations (indexed to the wavelength at the bottom of the trough) and trough depths, using a continuum base as reference. The weighted fit leads to correlation coefficients that a least squares routine numerically fixes. Band ratios can also prove helpful.
Since spectral bandwidths may be broad, analysis of many individual channels (for AVIRIS, 224 spread continuously from 0.38 to 2.5 µm) is customary. However, an analysis need not sample all the channels for certain problems. If the task is to identify a group of minerals in an alteration zone in a mining district, located in a vegetation-sparse region, the critical interval between 2.1 and 2.5 µm containing a number of diagnostic absorption bands may suffice to identify them. For some identifications, data from two, three, or a few more channels may be sufficient to identify a particular class in compositional detail. From such data, one option is to devise correlation coefficients relating composition to wavelength using least-squares statistics.
Of course, it is usually not expedient to plot spectral curves for every pixel in a mission data set. Instead, the spectral data applicable to training sites containing the classes of interest serve as clues to the individual materials present in any given pixel. If the spatial resolution is high (a few meters), then commonly we assign a dominant class to each pixel. In the real world that we want to picture, that dominant class may extend over many pixels, leading to a hyperspectral image that has similar characteristics to typical Landsat scenes. But, the ability to fine-tune the class identities, and to record separately some of the nature of the mix, are the great advantages that emerge with imaging spectroscopy - certainly a significant improvement in sensor technology for remote sensing.
The writer (NMS) cannot resist closing this page with a non sequitur, the oddest spectral curves I've ever seen:
What these curves tell me: 1) at wavelengths encroaching on the thermal region, all the geese have about the same temperature; and 2) two of the birds are all white (Ross's Goose; Snow Goose) and two are much darker (the White-fronted Goose and its similar relative, the Cackling Goose). As a birdwatcher, I've seen all but the Cackling Goose - this last is rare in Pennsylvania but a few show up each winter.