Figure 1. (a) Sampling with an imaging spectrometer from the 3-dimension spectral radiance cube, (b) A single full frame 
image of the CCD array of CASI extracted from the image of the tree shown in (c). The images (b) and (c) result 
from slicing the cube in (a) either perpendicular to the along track direction (b) or the spectral direction (c). 
The Imaging Spectrometer Data-cube 
Often when analyzing multispectral scanner data the analogy of 
image planes stacked on top of one another, but distinctly 
separated in space, is used to visualize the spatial and spectral 
relationships between the spectral bands. When using imaging 
spectrometer data we should refrain from thinking of 2-D 
sampling in distinct spectral bands but rather as sampling from 
a 3-D dimensional space where two dimensions are spatial 
dimensions and the third is spectral (Figure 1(a)). 
The image forming process can be thought of as a large square 
which is as wide as the sensor's swath and as tall as the 
spectral range. As the sensor's platform moves forward the 
square extrudes to become a parallelepiped which is as long as 
the flight-line. Partition the parallelepiped into tiny cubes by 
dividing the width into the number of pixels per line, the 
height into the number of spectral elements and the length 
along track into the number of image lines. Contained within 
each cube is the spectral radiance from that small area of the 
scene. The imaging spectrometer's CCD array can be thought 
of as imposing just such a grid on the incoming radiance distri 
bution. Further, it will integrate the spectral radiance over the 
volume of each cube and quantize it to a radiometrically 
scaleable value. Cross-sections through the cube give either a 
spectral-spatial image as shown in figure 1(b) or a familiar 2- 
dimensional spatial image as in figure 1(c). 
In contrast to a standard multispectral scanner, for an imaging 
spectrometer the sampling process must be considered in two 
stages; the first being the sampling of the spectral radiance 
field by the individual sensor elements of the spectrometer and 
the second being the sampling of the those elements into a 
workable subset. 
SAMPLING METHODS 
Consideration must be given to the method used to reduce the 
volume of imaging spectrometer data and which direction to 
reduce the data in. The trade-offs are undersampling vs 
averaging reduction and spatial vs spectral. 
Undersampling vs Averaging 
There are two categories for sampling techniques which are 
used to reduce image data: averaging and undersampling. 
They are not mutually exclusive and are often used in combi 
nation such as when averaging over a range of elements, then 
skipping others. 
Averaging includes all the elements by summing. It 
suppresses the high frequency component thereby minimizing 
the power in any aliased signal. This is the preferred method 
of sampling when using linear theory as the basis for signal 
reconstruction. If the high frequency component of the signal 
is unnecessary or undesirable then this is the best sampling 
method. 
Undersampling skips some elements of the CCD array which 
are not included directly or indirectly in the digital-levels 
recorded. It does not pass or reject components of the signal 
based on frequency alone, but rather by frequency and phase. 
Whether a feature in the signal will appear in the samples is 
determined by frequency if its frequency is below the Nyquist 
limit and by phase if it is above this limit. The samples then 
contain both high and low frequency components mixed 
inextricably together. 
Spatial vs Spectral Modes 
Conceptually, it is a vast simplification to neglect the along- 
track spatial dimension and consider a two-dimensional space 
which includes only the across track spatial and the spectral 
dimensions. Each cross-section through the cube perpen 
dicular to the flight direction is just the image of the CCD 
frame for a single scan-line, as in figure 1(b). 
The terms spatial and spectral modes are used to describe two 
general methods of reducing the vast volume of data that is 
generated by an imaging spectrometer rather than to any 
specific sampling strategy. Spatial mode will refer to data 
which is recorded with the full spatial resolution of the 
spectrometer, but reduced spectrally by some type of 
sampling. Figure 2(a) shows how this is done on the CCD 
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