Kory J. Priestley
Figures
142
Optical
Axis
ξ
η
θ
Field
Stop
Cross-Scan
Direction
φ
Scan
Direction
Figure 5.14 Definition of various angles used in the discretization of the field-of-view into
discrete solid angles.
Kory J. Priestley
Figures
143
1.0
0.9
0.8
Ray Trace Scan Direction
Normalized Optical Throughput
Ray Trace Cross-scan Direction
0.7
PFM total channel
0.6
0.5
0.4
0.3
0.2
0.1
0.0
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
Angle from Edge of Field Stop (deg)
Figure 5.15 Predicted and measured attenuation at the edge of the optical field for the PFM
total channel.
Kory J. Priestley
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144
1.0
0.9
Normalized Optical Throughput
0.8
0.20 deg radius
0.25 deg radius
0.7
0.30 deg radius
Ray Trace
0.6
0.5
0.4
0.3
0.2
0.1
0.0
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
Angle from Edge of Field Stop (deg)
Figure 5.16 Comparison of attenuation for a theoretical effective blur circle and the predicted
attenuation in the scan direction from the ray-trace module.
Kory J. Priestley
Figures
145
1.6
1.4
Outline of
Field-stop
1.2
1
0.8
0.6
0.9-1.0
0.4
0.8-0.9
0.2
Cross-Scan Angle
(Deg)
0
-0.2
0.7-0.8
0.6-0.7
0.5-0.6
-0.4
0.4-0.5
-0.6
0.3-0.4
-0.8
0.2-0.3
-1
0.1-0.2
-1.2
0.0-0.1
-1.4
1.0795
0.9525
0.8255
0.6985
0.5715
0.4445
0.3175
0.1905
0.0635
-0.0635
-0.1905
-0.3175
-0.4445
-0.5715
-0.6985
-0.8255
-0.9525
-1.0795
-1.6
Scan Angle (Deg)
(a )
1.0
0.9
0.8
50-percent
Contour
OPSF
0.7
0.6
0.9-1.0
0.8-0.9
0.5
0.7-0.8
1.4
0.9
0.4
0.3
0.5-0.6
0.4
0.2
-0.1
0.1
-0.6
-1.6
0.9525
0.4445
0.1905
0.6985
Scan Angle (Deg)
-0.0635
-0.3175
-0.5715
-1.1
-0.8255
-1.0795
0.0
0.6-0.7
Cross-Scan Angle
(Deg)
0.4-0.5
0.3-0.4
0.2-0.3
0.1-0.2
0.0-0.1
(b)
Figure 5.17 The predicted Optical Point Spread Function (OPSF) for the CERES PFM total
channel in (a) topographical, and (b) three-dimensional representations.
Kory J. Priestley
Figures
146
Cross-scan
Direction
-1.00°
-0.75°
-0.50°
-0.25°
0.00°
Scan
Direction
0.25°
0.50°
0.75°
1.00°
Figure 5.18 Illustration of trace lines used by TRW to measure the PFM total channel
instrument point spread function.
Kory J. Priestley
Figures
147
Instantaneous
Optical
FOV
80%
Scan
Direction
60%
40% 20% 0%
Axis of
Symmetry
Figure 5.19 Topographical representation of a point spread function for a generic scanning
instrument.
Kory J. Priestley
Figures
50-percent
Profile
148
95-percent
Profile
Instantaneous
Optical
FOV
Scan
Direction
Axis of
Symmetry
Figure 5.20 Discretization of the instrument point spread function with an equi-angular
16-by-16 grid.
Kory J. Priestley
Figures
149
1.6
1.4
1.2
1
Outline of
Field-stop
0.8
0.6
0.9-1.0
0.4
0.8-0.9
0.2
Cross-Scan Angle
(deg)
0
-0.2
0.7-0.8
0.6-0.7
0.5-0.6
-0.4
0.4-0.5
-0.6
0.3-0.4
-0.8
0.2-0.3
-1
0.1-0.2
-1.2
0.0-0.1
-1.4
4.699
5.1435
3.81
4.2545
2.921
3.3655
2.032
2.4765
1.5875
1.143
0.254
0.6985
-0.635
-0.1905
-1.0795
-1.6
Scan Angle
(deg)
(a)
1.0
0.9
0.8
0.7
0.9-1.0
0.6
PSF
0.8-0.9
50-percent
Contour
0.7-0.8
0.5
0.6-0.7
0.4
0.5-0.6
0.4-0.5
0.3
0.3-0.4
0.2-0.3
0.2
1.4
0.8
0.2
Cross-Scan Angle
-0.4
(deg)
0.1
0.0-0.1
4.953
4.6355
4.318
4.0005
3.683
3.3655
-1
3.048
2.413
1.778
2.7305
Scan Angle
(deg)
2.0955
1.143
1.4605
0.508
0.8255
0.1905
-0.127
-0.762
-0.4445
-1.0795
0.0
0.1-0.2
-1.6
(b )
Figure 5.21 Predicted dynamic instrument point spread function of the CERES PFM total
channel for a nominal scan rate of 63.5 deg/s in (a) topographical, and (b) threedimensional representations.
Kory J. Priestley
Figures
150
1.0
0.9
Numerically Predicted
0.8
Experimentally Measured
0.7
PSF
0.6
0.5
0.4
0.3
0.2
0.1
0.0
-1
0
1
2
3
4
5
Scan Angle (deg)
Figure 5.22 Comparison between an experimentally measured and numerically predicted point
spread function trace line taken along the 0-deg cross-scan plane.
Kory J. Priestley
Figures
151
Outline of
Field-stop
16.1925
15.1765
14.1605
13.1445
12.1285
11.1125
10.0965
9.0805
8.0645
7.0485
6.0325
5.0165
4.0005
2.9845
1.9685
0.9525
-0.0635
-1.0795
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0 Cross-Scan Angle (deg)
-0.2
-0.4
-0.6
-0.8
-1
-1.2
-1.4
-1.6
0.9-1.0
0.8-0.9
0.7-0.8
0.6-0.7
0.5-0.6
0.4-0.5
0.3-0.4
0.2-0.3
0.1-0.2
0.0-0.1
Scan Angle
(deg)
(a)
1.0
0.9
0.8
0.9-1.0
0.7
50-percent
Contour
PSF
0.6
0.8-0.9
0.7-0.8
0.6-0.7
0.5
0.5-0.6
0.4
0.4-0.5
0.3
0.3-0.4
1.4
0.9
0.2
0.1
0.4
-0.1
0.0-0.1
Cross-Scan Angle (deg)
-1.6
16.7005
15.4305
14.1605
12.8905
11.6205
9.0805
7.8105
0.1-0.2
-1.1
10.3505
Scan Angle
(deg)
6.5405
5.2705
2.7305
-0.6
4.0005
1.4605
0.1905
-1.0795
0.0
0.2-0.3
(b)
Figure 5.23 Predicted dynamic instrument point spread function of the CERES PFM total
channel for a nominal scan rate of 254 deg/s in (a) topographical, and (b) threedimensional representations.
Kory J. Priestley
Figures
152
1
0.9
Predicted Rapid Retrace Trace Line
0.8
Scaled Normal Scan Trace Line
0.7
PSF
0.6
0.5
0.4
0.3
0.2
0.1
0
-1
1
3
5
7
9
11
13
15
17
Scan Angle (deg)
Centroid Location
Figure 5.24 Comparison of trace lines from the rapid retrace, 254 deg/s, and normal,
63.5 deg/s, point spread functions. The trace lines correspond to a crossscan angle of 0 deg.
19
Kory J. Priestley
Figures
153
Outline of
Field-stop
1.6
1.4
1.2
1
0.8
0.6
0.4
0.9-1
0.2 Cross-Scan
Angle
0
(deg)
-0.2
0.8-0.9
-0.4
0.4-0.5
-0.6
0.3-0.4
0.7-0.8
0.6-0.7
0.5-0.6
0.2-0.3
-0.8
0.1-0.2
-1
0-0.1
-1.2
14.351
14.9225
13.208
13.7795
12.065
12.6365
10.922
11.4935
9.779
10.3505
8.636
9.2075
7.493
8.0645
6.35
6.9215
5.207
5.7785
4.064
4.6355
2.921
3.4925
1.778
2.3495
0.635
1.2065
-0.508
0.0635
-1.0795
-1.4
-1.6
Scan Angle (deg)
(a )
Outline of
Field-stop
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
Cross-Scan
Angle
(deg)
-0.2
0
-0.4
-0.6
-0.8
-1
0.9-1
0.8-0.9
0.7-0.8
0.6-0.7
0.5-0.6
0.4-0.5
0.3-0.4
0.2-0.3
0.1-0.2
0-0.1
-1.2
14.9225
14.1605
13.3985
12.6365
11.8745
11.1125
10.3505
9.5885
8.8265
8.0645
7.3025
6.5405
5.7785
5.0165
4.2545
3.4925
2.7305
1.9685
1.2065
0.4445
-0.3175
-1.0795
-1.4
-1.6
Scan Angle (deg)
(b)
Figure 5.25 Topographical comparison of the instrument point spread function for the (a)
normal scan rate of 63.5 deg/s and the (b) rapid retrace rate of 254 deg/s.
Kory J. Priestley
Figures
154
0
Bessel
Pre-amp
Instrument
Gain (db)
-5
-10
-15
-20
-25
-30
1
10
100
Frequency (Hz)
(a)
Phase Angle (Deg)
-10
-60
Bessel
Pre-amp
Instrument
-110
-160
-210
-260
-310
-360
1
10
100
Frequency (Hz)
(b)
Figure 5.26 Predicted (a) Bode and (b) phase angle diagram for the CERES PFM total channel
sensor based on the numerical end-to-end model.
Kory J. Priestley
Figures
155
Superimposed 10 and 30 Hz sinusoidal waves
1
0.9
normalized input
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.1
0.2
0.3
0.4
0.5
time (s)
(a)
Predicted output of the CERES instrument
1
normalized input, output
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
Bessel
Instrument
0.1
Pre-amp
0
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
time (s)
(b)
Figure 5.27 (a) Normalized input used to assess the effectiveness of the low-pass filtering, and
(b) end-to-end model output corresponding to the input seen in (a).
Kory J. Priestley
Figures
156
Comparison of 10 Hz sinusoidally varying scene to
superimposed 10 & 30 Hz sinusoidally varying scene
voltage output
10
9
8
7
10 Hz
10 & 30 Hz
6
0
0.1
0.2
0.3
0.4
0.5
time (s)
Figure 5.28 Comparison of the predicted output of the end-to-end model for a 10-Hz
input and a superimposed 10- and 30-Hz input.
Kory J. Priestley
Figures
157
a) 30% Stratocumulus
b) 10% Cumulus
c) 20% Cumulus
d) 30% Cumulus
e) Clear sky
Figure 5.29 50-by-50 km Earth scene modules used in Villeneuve’s Atmospheric Radiative
Transfer model [32].
Kory J. Priestley
Figures
158
250
500 km
200
450
150
400
100
350
50
300
Scan
Direction
0
250
Figure 5.30 500-km mosaic TOA strip constructed from ten 50-by-50 km modules [32].
Kory J. Priestley
Figures
159
Solar Radiation
incident at 45 deg
Satellite
3
2
1
Scan
Earth Scene
0
100
200
300
400
500
Figure 5.31 Virtual satellite scanning a 500-km TOA strip from three different orbital positions
[32].
Kory J. Priestley
Figures
160
18
10% Contour
16
50% Contour
90% Contour
Radiance/Power in
14
12
10
8
6
4
0
50
100
150
200
250
300
350
400
450
TOA Position (km)
Figure 5.32 Ratios of average radiance arriving at the aperture to the power arriving at
the active flake for three effective fields-of-view for the CERES sensors.
500
Kory J. Priestley
Figures
161
1.6
1.4
Orbit 1
Orbit 2
stdev(Radiance/P flake )
1.2
Orbit 3
1.0
0.8
0.6
0.4
0.2
0.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
OPSF Cutoff Contour
Figure 5.33 Determination of the optimal instantaneous field-of-view for the CERES flight
sensors.
0.9
Kory J. Priestley
Figures
162
Instantaneous
Optical
FOV
Axis of
Symmetry
Scan
Direction
(a)
Instantaneous
Optical
FOV
Axis of
Symmetry
Scan
Direction
(b)
Figure 5.34 Illustration of two extreme weightings of the dynamic instrument point spread
function used to assess the sensitivity of recovered TOA flux to point spread
function weighting. In (a) all 16-by-16 bins are assigned a weighting of 1/256, in
(b) the four central bins are assigned a weighting of ¼.
Kory J. Priestley
Figures
0
200
400
163
600
800 W/m2
Figure 5.35 ERBE shortwave TOA fluxes (Wm-2) determined using ERBE Pathfinder CERESlike data processing algorithms and an equally weighted 16-by-16 PSF array.
Kory J. Priestley
-100
Figures
-62
-25
164
12
50 W/m2
Figure 5.36 Difference in calculated ERBE SW TOA flux (Wm-2) for the two weightings of the
PSF displayed in Fig. 5.34.
Kory J. Priestley
Figures
5.E-05
165
Incident Power
Recovered Power
Power (W)
4.E-05
3.E-05
2.E-05
1.E-05
0.E+00
0.4
0.41
0.42
0.43
0.44
0.45
0.46
0.47
0.48
0.49
0.5
Time (s)
Figure 5.37 Results of using an autoregressive model to recover a 20-Hz scene. The model was
formulated with n=4, N=12, and the Ai coefficients determined with a 10-Hz
source.