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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