The contents include: 1) Brief history of related events; 2) Overview of original method used to establish absolute radiometric accuracy of remote sensing instruments using stellar sources; and 3) Considerations to improve the stellar calibration approach

Bowen, Howard S.

Cunningham, Douglas M.

NASA Technical Reports Server

Correction to Method of Establishing the 
Absolute Radiometric Accuracy of Remote 
Sensing Systems While On-orbit Using 
Characterized Stellar Sources
March 15, 2006
Howard S. Bowen and
Douglas M. Cunningham
https://ntrs.nasa.gov/search.jsp?R=20070038215 2019-08-29T18:37:00+00:00Z
2006 JACIE Stellar Calibration March 15, 2006 2
Presentation Outline
 Brief History of Related Events
 Overview of Original Method Used to Establish Absolute 
Radiometric Accuracy of Remote Sensing Instruments 
Using Stellar Sources
 Considerations to Improve the Stellar Calibration 
Approach
 Summary
Brief History of Related Events
2006 JACIE Stellar Calibration March 15, 2006 4
Historical Perspective
1999 2000 2001 2002 2003 2004 2005 2006
March 2004
3rd Stability Recheck
4 Non- & 7 G&S Stars
March 2005
4th Stability Recheck
4 Non- & 7 G&S Stars
2007 2008
March 2001
Stability Check
4 Non- & 11 G&S Stars
February 2000
IOC Completed
4  Non-G&S Stars
Sept 1994
IKONOS
Launch
March 2003
2nd Stability Recheck
4 Non- & 7 G&S Stars
March 2002
1st Stability Recheck
4 Non- & 7 G&S Stars
March 2006
5th Stability Recheck
4 Non- & 7 G&S Stars
July 2005 - Feb 2006
Independent
Re-evaluation of Stellar 
Calibration Method
November 2002
Stellar Calibration 
Method Presented at 
ISPRS Conference held 
in Denver, Colorado
March 2006
Stellar Calibration 
Correction 
Presented at 
JACIE Conference 
Washington DC
2006 JACIE Stellar Calibration March 15, 2006 5
Absolute Radiometric Calibration
The purpose of absolute radiometric calibration is to 
determine the expected response for any in-band entrance 
aperture radiance presented to the telescope.
L
DCCalCoef
j
j
j
=
where: CalCoef = In-Band Calibration Coefficient  (DC/(W/m2-sr))
DCj = Measured Digital Counts in the jth band (DC)
Lj = Entrance Aperture Radiance in the jth band (W/m2-sr)
Overview of Original Method Used to Establish 
Absolute Radiometric Accuracy of Remote 
Sensing Instruments Using Stellar Sources
2006 JACIE Stellar Calibration March 15, 2006 7
Original Method to Establish Absolute Radiometric 
Calibration Accuracy Using Stellar Sources
 Identify Acceptable Radiometrically Characterized Stars
– Compute Broadband Entrance Aperture Flux Density
 Gather Stellar Response Data
– Extract Stellar Scene Data (sum digital counts)
 Generate Calibration Coefficient
 Verify Results Using Independent Sources
 Determine System Stability
 Determine System Linearity
2006 JACIE Stellar Calibration March 15, 2006 8
Bright Star Catalogue Stars
-1.46 < Vmag < 8.0 = 9110 Items
HR7001
HR2491
-90
-60
-30
0
30
60
90
00010203040506070809101112131415161718192021222300
RA (hr) (J2000)
D
e
c
 
(
d
e
g
)
 
(
J
2
0
0
0
)
2006 JACIE Stellar Calibration March 15, 2006 9
Bright Stars most likely to be compatible with 
IKONOS-like Remote Sensing Instruments
Bright Star Catalogue Revision 5.0 Histogram
1 1 16 6 5 8 27 43 81 113
231
386
726
1257
2192
3323
646
40 6 0
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
-
1
.
5
 
-
 
-
1
-
1
 
-
 
-
0
.
5
-
0
.
5
 
-
 
0
0
 
-
 
0
.
5
0
.
5
 
-
 
1
1
 
-
 
1
.
5
1
.
5
 
-
 
2
2
 
-
 
2
.
5
2
.
5
 
-
 
3
3
 
-
 
3
.
5
3
.
5
 
-
 
4
4
 
-
 
4
.
5
4
.
5
 
-
 
5
5
 
-
 
5
.
5
5
.
5
 
-
 
6
6
 
-
 
6
.
5
6
.
5
 
-
 
7
7
 
-
 
7
.
5
7
.
5
 
-
 
8
8
 
-
 
8
.
5
Visual Magnitude Bins
S
t
a
r
s
 
p
e
r
 
M
a
g
n
i
t
u
d
e
2.0 < Vmag < 4.0
468 Stars
Remote Sensing
Compatible
2006 JACIE Stellar Calibration March 15, 2006 10
BSC Remote Sensing Compatible Stars (468)
and Spectrophotometric Standard Stars (28)
HR153
HR718
HR1996
HR3454
HR4468
HR4554
HR4963
HR5191
HR5501
HR7001
HR7596
HR7950
HR8634
GS7
GS142
GS127
GS134
GS83
GS109
GS8
GS86
GS135 GS152
GS158
GS6
GS149
HR1544
HR9087
GS150
GS118
-90
-60
-30
0
30
60
90
00010203040506070809101112131415161718192021222300
RA (hr) (J2000)
D
e
c
 
(
d
e
g
)
 
(
J
2
0
0
0
)
2006 JACIE Stellar Calibration March 15, 2006 11
RS ID BSC ID RA (J2000) DEC (J2000) Proper Name Vmag Spectral Type
HST 1 HR7001 18:36:56 38.7836 Alpha Lyrae -0.03 A0V
HST 2 HR718 2:28:09 8.4601 Xi 2 Ceti 4.28 B9III
HST 3 HR1544 4:50:36 8.9002 Pi 2 Orionis 4.36 A1V
HST 4 HR3454 8:43:13 3.3986 Eta Hydrae 4.30 B3V
HST 5 HR4468 11:36:40 -9.8023 Theta Crater 4.70 B9.5V
HST 6 HR4963 13:09:56 -5.5390 Theta Virginis 4.38 A1IV
HST 7 HR5501 14:45:30 0.7174 108 Virginis 5.68 B9.5V
HST 8 HR7596 19:54:44 0.2735 58 Aquilae 5.62 A0III
HST 9 HR7950 20:47:40 -9.4958 Eta Aquarii 3.78 A1V
HST 10 HR8634 22:41:27 10.8314 Zeta Pegasi 3.40 B8V
HST 11 HR9087 0:01:49 -3.0275 29 Piscium 5.12 B7III
HST 12 HR153 0:36:58 53.8969 Zeta Cassiopeiae 3.66 B2IV
HST 13 HR1996 5:45:59 -32.3065 Mu Columbae 5.17 O9V
HST 14 HR4554 11:53:49 53.6948 Gamma Ursae Majoris 2.44 A0V
HST 15 HR5191 13:47:32 49.3133 Eta Ursae Majoris 1.86 B3V
G&S 1 HR6787 18:08:45 20.8144 102 Her   4.36 B2IV
G&S 2 HR3454 8:43:13 3.3986 Eta Hydrae 4.30 B3V   
G&S 3 HR6588 17:39:27 46.0064 85 Iot Her 3.80 B3IV
G&S 4 HR6556 17:34:56 12.5600 55 Alp Oph 2.08 A5III 
G&S 5 HR6561 17:37:35 -15.3986 55 Xi Ser 3.54 F0IVDel Sct
G&S 6 HR1411 4:28:34 15.9622 77 The1 Tau 3.84 K0IIIbFe-0.5
G&S 7 HR4247 10:53:18 34.2150 46 LMI    3.83 K0+III-IV
G&S 8 HR4335 11:09:39 44.4986 52 Psi UMa 3.01 K1III 
G&S 9 HR5854 15:44:16 6.4256 24 Alp Ser 2.65 K2IIIbCN1
G&S 10 HR3905 9:52:45 26.0069 24 Mu Leo 3.88 K2IIICN1Ca1
G&S 11 HR3845 9:39:51 -1.1428 35 Iot Hya 3.91 K2.5III-IIIbBa0.3
G&S 12 HR2574 6:54:11 -12.0386 14 The CMa 4.07 K4III 
G&S 13 HR3003 7:46:07 18.5100 81 Gem 4.88 K4III-IIIb
G&S 14 HR2905 7:35:55 26.8958 69 Ups Gem 4.06 M0III-IIIb
G&S 15 HR1556 4:52:32 14.2506 4 Omi 1Ori 4.74 S3.5/1-
Remote Sensing Compatible Spectrophotometric 
Standard Stars (28) (Excluding Vega and 1 repeated star)
2006 JACIE Stellar Calibration March 15, 2006 12
VizieRRemote Sensing Compatible Spectrophotometric 
Standard Stars Spectral Data
0.0E+00
1.0E+06
2.0E+06
3.0E+06
4.0E+06
5.0E+06
6.0E+06
7.0E+06
8.0E+06
9.0E+06
1.0E+07
3000 4000 5000 6000 7000 8000 9000 10000 11000
Wavelength (Angstroms)
F
l
u
x
 
(
e
r
g
s
/
c
m
2
 
s
 
A
)
HR7001, V=0.03
HR718
HR1544
HR3454, V=4.3
HR4468
HR4963
HR5501
HR7596
HR7950
HR8634
HR9087
HR153
HR1996, V=5.17
HR4554, V=2.44
HR5191, V=1.86
G&S 6
G&S 7, V=4.134
G&S 8
G&S 83
G&S 86
G&S 109
G&S 118
G&S 127
G&S 134
G&S 135
G&S 142
G&S 149
G&S 150
G&S 152
G&S 158
2006 JACIE Stellar Calibration March 15, 2006 13
Hertzprung-Russell Diagram Showing Remote 
Sensing Characterized Star Categories
Star ID (s) Category
HR7596 A0III
HR7001, HR4554 A0V
HR4963 A1IV
HR1544, HR7950 A1V
HR6561 A5III
HR153, HR6787 B2IV
HR6556 B3IV
HR1591, HR3454 B3V
HR9087 B7III
HR8634 B8V
HR4468, HR550 B9.5V
HR718 B9III
HR1411 F0IV
HR4247 K0III
HR4335 K1III
HR3845 K2.5III
HR5854 K2IIIb
HR3095 K2IIIC
HR2574 K4III
HR3003 K4IIIb
HR2905 M0III
HR1996 O9V
HR1556 S3.5
Sun
2006 JACIE Stellar Calibration March 15, 2006 14
Brightest G&S Stars and Those Used for IKONOS 
Absolute Radiometric Accuracy Assessment (7)
GS7
GS142
GS127
GS134
GS83
GS109
GS8
GS86
GS118
GS135 GS152
GS158
GS6
GS149
GS150
HR7001
-90
-60
-30
0
30
60
90
00010203040506070809101112131415161718192021222300
RA (hr) (J2000)
D
e
c
 
(
d
e
g
)
 
(
J
2
0
0
0
)
2006 JACIE Stellar Calibration March 15, 2006 15
J.E. Gunn & L.L. Stryker – Stellar Spectrophotometric Atlas
3130 < λ < 10800 Ǻ (1983), Remote Sensing Stellar Subset
0.0E+00
3.0E+00
6.0E+00
9.0E+00
1.2E+01
1.5E+01
1.8E+01
7.50E+051.25E+061.75E+062.25E+062.75E+063.25E+06
Frequency (Hz)
F
l
u
x
 
(
m
W
/
m
2
-
H
z
)
Flux 6
Flux 7
Flux 8
Flux 83
Flux 86
Flux 109
Flux 118
Flux 127
Flux 134
Flux 135
Flux 142
Flux 149
Flux 150
Flux 152
Flux 158
2006 JACIE Stellar Calibration March 15, 2006 16
Un-normalized Stellar Spectral Data v. Frequency
Remote Sensing Stellar Subset
0.0E+00
2.0E-21
4.0E-21
6.0E-21
8.0E-21
1.0E-20
7.50E+051.25E+061.75E+062.25E+062.75E+063.25E+06
Frequency (Hz)
F
l
u
x
 
(
m
W
/
m
2
-
H
z
)
Flux 6
Flux 7
Flux 8
Flux 83
Flux 86
Flux 109
Flux 118
Flux 127
Flux 134
Flux 135
Flux 142
Flux 149
Flux 150
Flux 152
Flux 158
2006 JACIE Stellar Calibration March 15, 2006 17
Un-normalized Stellar Spectral Data v. Wavelength
Remote Sensing Stellar Subset
0.0E+00
2.0E-06
4.0E-06
6.0E-06
8.0E-06
1.0E-05
1.2E-05
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1
Wavelength (μm)
F
l
u
x
 
(
m
W
/
m
2
-
μ
m
)
Flux 6
Flux 7
Flux 8
Flux 83
Flux 86
Flux 109
Flux 118
Flux 127
Flux 134
Flux 135
Flux 142
Flux 149
Flux 150
Flux 152
Flux 158
2006 JACIE Stellar Calibration March 15, 2006 18
De-reddening Coefficients for Stellar Spectral Data
Remote Sensing Stellar Subset
1.00E+00
1.05E+00
1.10E+00
1.15E+00
1.20E+00
1.25E+00
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1
Wavelength (μm)
F
l
u
x
 
(
m
W
/
m
2
-
μ
m
)
G&S 6
G&S 7
G&S 8
G&S 83
G&S 86
G&S 109
G&S 118
G&S 127
G&S 134
G&S 135
G&S 142
G&S 149
G&S 150
G&S 152
G&S 158
2006 JACIE Stellar Calibration March 15, 2006 19
Re-reddened Stellar Spectral Data v. Wavelength
Remote Sensing Stellar Subset
0.0E+00
2.0E-06
4.0E-06
6.0E-06
8.0E-06
1.0E-05
1.2E-05
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1
Wavelength (μm)
F
l
u
x
 
(
m
W
/
m
2
-
μ
m
)
G&S 6
G&S 7
G&S 8
G&S 83
G&S 86
G&S 109
G&S 118
G&S 127
G&S 134
G&S 135
G&S 142
G&S 149
G&S 150
G&S 152
G&S 158
2006 JACIE Stellar Calibration March 15, 2006 20
Subset of G&S Stellar Spectra Used To Assess
IKONOS Absolute Radiometric Accuracy
0.0E+00
2.0E-06
4.0E-06
6.0E-06
8.0E-06
1.0E-05
1.2E-05
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1
Wavelength (μm)
F
l
u
x
 
(
m
W
/
m
2
-
μ
m
) G&S 7
G&S 83
G&S 109
G&S 127
G&S 134
G&S 142
G&S 150
2006 JACIE Stellar Calibration March 15, 2006 21
IKONOS MS Bands Relative Spectral Response (RSR) 
(http://www.spaceimaging.com/products/ikonos/spectral.htm)
Table 1 - IKONOS Spectral Band Characteristics
Band
Lower 50%
(nm)
Upper 50%
(nm)
Bandwidth
(nm)
Center
(nm)
Pan 525.8 928.5 403 727.1 
MS-1 (Blue) 444.7 516.0 71.3 480.3
MS-2 (Green) 506.4 595.0 88.6 550.7
MS-3 (Red) 631.9 697.7 65.8 664.8
MS-4 (VNIR) 757.3 852.7 95.4 805.0
Note: 
1. Spectral Bandwidths are Full-Width at Half-Max (FWHM)
2. Panchromatic Band does not incorporate spectral filtering - response is that of 
optics/detector only
Values Shown in Color are Bandpass Definitions Using 50nm-interval Datasets Without Interpolation
2006 JACIE Stellar Calibration March 15, 2006 22
IKONOS Multi-spectral Bands RSR - 50nm Intervals
(as published on GeoEye website)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1
Wavelength (μm)
2006 JACIE Stellar Calibration March 15, 2006 23
G&S Stellar Spectra and IKONOS MS Bands RSR
0.0E+00
2.0E-06
4.0E-06
6.0E-06
8.0E-06
1.0E-05
1.2E-05
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1
Wavelength (μm)
F
l
u
x
 
(
m
W
/
m
2
-
μ
m
)
0
0.5
1
G&S 7
G&S 83
G&S 109
G&S 127
G&S 134
G&S 142
G&S 150
Blue
Green
Red
NIR
2006 JACIE Stellar Calibration March 15, 2006 24
IKONOS Stellar Calibration Coefficients 2001 
Compared with JACIE 2001 Results
y = 63.3x - 46.6
y = 63.8x - 31.3
y = 79.8x - 38.1
y = 67.0x - 30.6
0
256
512
768
1024
1280
1536
1792
2048
0.0 5.0 10.0 15.0 20.0 25.0
Entrance-Aperture Radiance (W/m²-sr)
D
i
g
i
t
a
l
 
C
o
u
n
t
s
G&S BLU G&S GRN G&S RED G&S NIR JACIE BLU JACIE GRN
JACIE RED JACIE NIR Linear (G&S BLU) Linear (G&S GRN) Linear (G&S RED) Linear (G&S NIR)
JACIE 2001 Coefficients (dashed lines):
BLU:  y = 73.9x
GRN: y = 73.3x
RED: y = 99.3x
NIR:  y = 85.9x
2006 JACIE Stellar Calibration March 15, 2006 25
IKONOS Stellar Calibration Coefficients 2001 
Compared with JACIE 2001 Results
MS Band JACIE 2001 Stellar 2001FW
72.8 63.3x – 51
63.8x – 31
79.8x – 40
67.0 – 31
72.7
94.9
84.3
∆ Gain
Blue
445-516 nm ∆ = 14%
Green
506-595 nm ∆ = 13%
Red
632-698 nm ∆ = 20%
NIR
757-853 nm ∆ = 21%
Considerations to Improve the Stellar 
Calibration Approach
2006 JACIE Stellar Calibration March 15, 2006 27
Traditional Remote Sensing System Calibration 
Methods Determine Entrance Aperture Radiance
Remote
Sensing
System
Uniform
Extended
Source
Entrance Aperture
Radiance
(W/m2-sr)
Digital 
Counts
(DC)
2006 JACIE Stellar Calibration March 15, 2006 28
Typically the System Response Function Takes Into 
Consideration All of the Components of the System
Ao
Ad
Detector Amplifier A/D ConverterFilter
Reflective
Surfaces
Irradiance (E)
Photons
Gain A/D
Integration
Period
Electrons Voltage
Entrance
Aperture
Radiance (L)
Aperture
Counts
Output
(DC)
( ) ( ) ( ) ( )
( ) ( ) ( ) λλτλτλ
λλλτατ
Δ
Ω=
LDCDCDCR
TRTRtASRF
noiseNLDA
elecelecfp
,,,,
,,,
0/
detfltrotadeto
2006 JACIE Stellar Calibration March 15, 2006 29
System Response Function
Calibration Coefficient [DN/(W/m2-sr)]
( )
⎟⎠
⎞⎜⎝
⎛
−
=
⎟⎟
⎟⎟
⎠
⎞
⎜⎜
⎜⎜
⎝
⎛
− srm
WRadianceApertureEntrance
DCCountsDigital
srm
W
DCtCoefficiennCalibratio
22
Calibration Coefficient is the Relationship between 
Entrance Aperture Radiance and Digital Counts
Ao
Counts
Output
(DC)
Entrance
Aperture
Radiance (L)
2006 JACIE Stellar Calibration March 15, 2006 30
Stellar Calibration Uses Well-characterized Stellar 
Flux Densities Arriving at the Payload Aperture
Remote
Sensing
System
Radiometrically
Characterized
Star
Entrance Aperture
Radiant Spectral Flux Density
(W/m2)
Digital 
Counts
(DC)
2006 JACIE Stellar Calibration March 15, 2006 31
Stellar Calibration Method as Presented in 2002 
ISPRS Paper
 Assumed
– All of the energy was represented as if it was being captured within a 
single Instantaneous Field of View (IFOV) of the detector
 Did not consider Encircled Energy (εf) function for the optical system
– Encircled Energy Function determines the amount of energy falling on the 
focal plane that is higher than the response threshold of a detector circuit
 Did not consider compression artifacts imposed on stellar scene data
– Older Compression Algorithms and Points Sources don’t play well
 Did not include an absolute spectral reference associated with the 
vicarious ground calibration approach
– Stellar Spectral Content versus Solar/2xAtmosphere/Ground Spectral 
Content
2006 JACIE Stellar Calibration March 15, 2006 32
All Pixels with Measurable Response Summed to 
All Energy Contained Within Point Spread Function
Theoretical Area 
of Point Source 
at Image Plane 
(Ap)
Blurred Point 
Spread Function 
at Image Plane
Image Pixels Summed to Collect Total Response (DC)
Equivalent
Detector
Area
(Ad)
2006 JACIE Stellar Calibration March 15, 2006 33
Average Number of Detectors within 7x7 pixel Area 
Summed to Produce the Total Digital Counts
0
2
4
6
8
10
12
14
16
18
0 200 400 600 800 1000 1200 1400
Total Dn
N
u
m
b
e
r
 
o
f
 
V
a
l
i
d
 
P
i
x
e
l
s
BLU
GRN
RED
NIR
2006 JACIE Stellar Calibration March 15, 2006 34
Stellar Calibration Sensor Response Function 
Algorithm
λελλ dSCFARSRFL jimfj
nm
nm do
i
ji j
**)(*)(*)( ,
1100
350
, ∫ Ω=
where: Li,j(λ) = Equivalent Radiance of Star at the Aperture (W/m2-sr)
Fi(λ) = Spectral Flux Density at Entrance Aperture (W/m2-μm)Ωdo = Solid Angle of a single Detector (sr)
RSRj(λ) = Relative Spectral Response of jth Band (%)εfj (Am) = Encircled Energy Function of jth Band (%)
SCFi,j = Spectral Correction Function of jth Band (%)
2006 JACIE Stellar Calibration March 15, 2006 35
CRSS w/simulated stellar PSF (log scale)
15x15, 48um pixels, λ = 0.75 um, Focus at 700 km
2006 JACIE Stellar Calibration March 15, 2006 36
Point Source Illumination at Focal Plane Is 
Distributed According to Optical Transfer Function
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Detectors
Point Spread Function
-1 +1 +2 +3 +4 +5 +6 +7 +8 +90-9 -8 -7 -6 -5 -4 -3 -2
2006 JACIE Stellar Calibration March 15, 2006 37
Encircled Energy Function Describes Unaccounted 
Energy Due to Spatial Distribution at Focal Plane
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Detectors
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Encircled Energy Function (εf)
Point Spread Function
-1 +1 +2 +3 +4 +5 +6 +7 +8 +90-9 -8 -7 -6 -5 -4 -3 -2
2006 JACIE Stellar Calibration March 15, 2006 38
Discrete Detectors in the Focal Plane Under-
sample the Point Source Energy Distribution
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Detectors
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Encircled Energy Function (εf)
Point Spread Function
-1 +1 +2 +3 +4 +5 +6 +7 +8 +90-9 -8 -7 -6 -5 -4 -3 -2
Undersampled PSF
2006 JACIE Stellar Calibration March 15, 2006 39
Low-contrast Stellar Scenes Cause Compression 
Artifacts that Contribute to Algorithm Uncertainty
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Detectors
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Encircled Energy Function (εf)
Point Spread Function
Compression Algorithm Artifacts
-1 +1 +2 +3 +4 +5 +6 +7 +8 +90-9 -8 -7 -6 -5 -4 -3 -2
Undersampled PSF
Compression Algorithm Artifacts
2006 JACIE Stellar Calibration March 15, 2006 40
Empirical Encircled Energy Functions that Provide 
Match Between Stellar and Ground Results
0 200 400 600 800 1000 1200 1400
DC
E
n
c
i
r
c
l
e
d
 
E
n
e
r
g
y
 
F
u
n
c
t
i
o
n
BLU Emperical
GRN Empirical
RED Empirical
NIR Empirical
2006 JACIE Stellar Calibration March 15, 2006 41
Spectral Correction Function can be Employed to 
Reference the Stellar to a Solar/Ground Spectra 
∫
∫
∫
∫
=
h
l
h
l
dL
dRSRL
dL
dRSRL
SCF
gnd
nm
nm
gnd
star
nm
nm
star
j
λ
λ
λ
λ
λλ
λλλ
λλ
λλλ
)(
)()(
)(
)()(
1100
350
1100
350
where: Lstar(λ) = Equivalent Radiance of Star at the Aperture (W/m2-sr)
Lgnd(l) = Radiance of Reference Ground Scene at the Aperture (W/m2-sr)
RSRj(λ) = Relative Spectral Response of jth Band (%)
SCFi,j = Spectral Correction Function of jth Band (%)
2006 JACIE Stellar Calibration March 15, 2006 42
Correlation between Corrected Stellar Calibration 
and Vicarious Ground Calibration Results
0
5
10
15
20
25
30
0 256 512 768 1024 1280 1536 1792 2048
Digital Counts
R
a
d
i
a
n
c
e
 
 
(
W
/
m
2
s
r
)
BLU JACIE 2000 GRN JACIE 2000
RED JACIE 2000 NIR JACIE 2000
BLU JACIE 2001 GRN JACIE 2001
RED JACIE 2001 NIR JACIE 2001
BLU JACIE 2002 GRN JACIE 2002
RED JACIE 2002 NIR JACIE 2002
G&S BLU G&S GRN
G&S RED G&S NIR
2006 JACIE Stellar Calibration March 15, 2006 43
Topics for Future Investigations
 Add New Characterized Stars to Collection Plans
 Revisit Stellar Imaging Scenario
– Develop Encircled Energy Function
– Linear Array
– Push-broom Scanning Systems
– Separate data from compression noise
– Determine uncertainty of measurement
 Collect and Analyze Additional Stellar Imagery
– Analysis primarily uses only 7 stellar collects
2006 JACIE Stellar Calibration March 15, 2006 44
Summary
 Additional research needed to further refine the algorithm


Correction to Method of Establishing the Absolute Radiometric Accuracy of Remote Sensing Systems While On-orbit Using Characterized Stellar Sources

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