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ECE/OPTI 531 – Image Processing Lab for Remote Sensing Fall 2005
Sensor Models
Reading: Chapter 3
Fall 2005Sensor Models 2
Sensor Models
• LSI System Model• Spatial Response• Spectral Response• Signal Amplification, Sampling, and
• Remote sensors are complex systems of optical,mechanical and electronic components– These components determine the quality of the data
from the sensor– The sensor may be considered a “black-box” that
converts at-sensor radiance to DNs
Fall 2005Sensor Models 4
LSI System Model
• Model the various systems as Linear Shift-Invariant (LSI)– A linear transformation of the input x results in a
similar transformation of the output y• Superposition principle• If T[f1] = g1 and T[f2] = g2 , then T[a1f1 + a2f2] = a1g1 + a2g2
– Shifting the input results in a similar shift of theoutput
• Shift invariance• If T[f(x)] = g(x) , then T[f(x-x0)] = g(x-x0)
• LSI model is generally applicable over thenominal range of operation for these systems– Model will break down as performance limits are
approached (i.e., system response becomes non-linear)
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Fall 2005Sensor Models 5
Instrument Response
• Any signal can be written as a sum of weighteddelta functions using the “sifting” property
• What happens when this input form is put intoa linear system?
• Knowing the transformation of a deltafunction, the “impulse response”, completelycharacterizes the LSI system
Fall 2005Sensor Models 6
Instrument Response (cont.)
• The precision of measurement is determined by theinstrument response, r
• The transformation from the input physical quantity tothe measurement is described mathematically by aconvolution
– where• i(α) is the input signal, a function of time, space, etc.• r(z0-α) is the instrument response, inverted and shifted by z0
• o(z0) is the output signal at z = z0
• W is the range over which the instrument response is significant• Shorthand notation, o(z) = i(z) ∗ r(z), read as “the output
signal is the input signal convolved with the instrumentresponse.”
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Fall 2005Sensor Models 7
Input and Impulse Response
Convolution Operation
Output
1-D Convolution Example
• The measured value at z0 is anaverage of the input signal inthe vicinity of z0, weighted overthe range W by the instrumentresponse
Fall 2005Sensor Models 8
Resolution
• Any instrument that measures a physicalquantity is limited in the amount of detail itcan capture– This limit is referred to as the instrument’s “resolution”– “Resolution” is a term that is widely used, but often
misunderstood• The width W of the instrument response defines
the spatial resolution, or effective GIFOV
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Fall 2005Sensor Models 9
Sensor Models
• LSI System Model• Spatial Response• Spectral Response• Signal Amplification, Sampling, and
• All remote sensing images are distorted relativeto a map– platform motion, especially airborne sensors– scanning distortion of the Ground Sample Interval (GSI)– topography Distortion caused by airplane
motion (ASAS airborne sensor)
cross-track ground distance from nadir (km)in-track
ground distance (km)
01.12.2
3.34.4
5.5
0 200 430 750 1400
1024 20481280 1536 1792
cross-track pixel numberorbital track
Bow-tie distortion in AVHRR data (Fig. 3–23)
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Fall 2005Sensor Models 25
Scanning Distortion
0
1
2
3
4
5
6
7
8
0 0.2 0.4 0.6 0.8 1
flat earthtrue earth
rela
tive
GS
I
off-nadir scan angle (radians)
!
FOV
nadir
H
"!
f
GSIe(!)
GSIf (!)
line and whiskbroom scanners (Fig. 3–22)
0.5
1
1.5
2
2.5
0 0.2 0.4 0.6 0.8 1
flat earthtrue earth
rela
tive
GS
I
off-nadir view angle (radians)
!
FOV
nadir
H
"!
W
f
GSIe(!)
GSIf (!)
pushbroom scanners (Fig. 3–24)
Fall 2005Sensor Models 26
Topographic Relief
• Image offset proportional to elevation abovebase plane, or “datum”
• Stereo pair of images can be used to findelevation
• Imagery corrected for topographic distortion iscalled “orthographic”