The NOAA-20 (formerly the Joint Polar Satellite System-1) satellite was launched on November 18, 2017. One of the five scientific instruments aboard the NOAA-20 satellite (N20) is the Visible Infrared Imaging Radiometer Suite (VIIRS). The VIIRS scans the earth surface in 22 spectral bands, of which 14 are denoted as the reflective solar bands (RSBs) with design band central wavelengths from 412 to 2250 nm. The VIIRS regularly performs on-orbit radiometric calibration of its RSBs, primarily through observations of an onboard sunlit solar diffuser (SD). The on-orbit change of the SD bidirectional reflectance distribution function (BRDF) value, denoted as the H-factor, is determined by an onboard solar diffuser stability monitor (SDSM). We have shown that the H-factor for the SD on the VIIRS instrument on the Suomi National Polar-orbiting Partnership (SNPP) satellite is both incident and outgoing sunlight direction dependent. This angular dependence profoundly affects the on-orbit radiometric calibration process and results. Here, we give preliminary results for the angular dependence for the N20 VIIRS SD H-factor, and compare the dependence with that for the SNPP VIIRS

Lei, Ning

Xiong, Xiaoxiong

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Initial investigation of the angular
dependence of the NOAA-20 VIIRS
solar diffuser BRDF change factor
Ning Lei, Xiaoxiong Xiong
Ning Lei, Xiaoxiong Xiong, "Initial investigation of the angular dependence of
the NOAA-20 VIIRS solar diffuser BRDF change factor," Proc. SPIE 10781,
Earth Observing Missions and Sensors: Development, Implementation, and
Characterization V, 1078116 (23 October 2018); doi: 10.1117/12.2324530
Event: SPIE Asia-Pacific Remote Sensing, 2018, Honolulu, Hawaii, United
States
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https://ntrs.nasa.gov/search.jsp?R=20190027363 2019-09-26T19:09:56+00:00Z
  
 
 
 
Initial Investigation of the Angular Dependence of the NOAA-20  
VIIRS Solar Diffuser BRDF Change Factor   
Ning Lei*a and Xiaoxiong Xiongb 
 
 
aScience Systems and Applications, Inc., 10210 Greenbelt Road, Suite 600, Lanham, MD 20706 
USA  
bSciences and Exploration Directorate, NASA Goddard Space Flight Center, Greenbelt, MD 20771 
USA 
*  Corresponding author: ning.lei@ssaihq.com, tel: +1-301-867-2066 
ABSTRACT 
The NOAA-20 (formerly the Joint Polar Satellite System-1) satellite was launched on November 18, 2017. One of the five 
scientific instruments aboard the NOAA-20 satellite (N20) is the Visible Infrared Imaging Radiometer Suite (VIIRS). The 
VIIRS scans the earth surface in 22 spectral bands, of which 14 are denoted as the reflective solar bands (RSBs) with 
design band central wavelengths from 412 to 2250 nm.  The VIIRS regularly performs on-orbit radiometric calibration of 
its RSBs, primarily through observations of an onboard sunlit solar diffuser (SD). The on-orbit change of the SD 
bidirectional reflectance distribution function (BRDF) value, denoted as the H-factor, is determined by an onboard solar 
diffuser stability monitor (SDSM). We have shown that the H-factor for the SD on the VIIRS instrument on the Suomi 
National Polar-orbiting Partnership (SNPP) satellite is both incident and outgoing sunlight direction dependent. This 
angular dependence profoundly affects the on-orbit radiometric calibration process and results. Here, we give preliminary 
results for the angular dependence for the N20 VIIRS SD H-factor, and compare the dependence with that for the SNPP 
VIIRS. 
Index Terms: N20 VIIRS, radiometric calibration, solar diffuser, BRDF, H-factor, angular dependence 
1.  INTRODUCTION 
The Visible Infrared Imaging Radiometer Suite (VIIRS) instrument is a passive earth observing scanning sensor. Fourteen 
of the 22 spectral bands are denoted as the reflective solar bands (RSBs) with design band central wavelengths from 412 
to 2250 nm. The RSBs, by design, are radiometrically calibrated on-orbit primarily by observing the onboard sunlit solar 
diffuser (SD)1. The second VIIRS is on the NOAA-20 (N20) satellite launched on November 18, 2017. The N20 satellite 
has the same equator crossing time of 13:30±10 min as the Suomi National Polar-orbiting Partnership (SNPP) satellite on 
which the first VIIRS instrument resides, and has the same nominal orbital time period of 101.5 min. 
Fig. 1 illustrates the physical components related to the on-orbit RSB calibration. The sunlight goes through the SD screen 
and then is diffusely scattered by the SD to provide a radiance source. The spectral radiance of the SD scattered sunlight 
is proportional to the SD BRDF at the mission start and the change factor of the BRDF since launch. The on-orbit BRDF 
change factor, commonly denoted as the H-factor, is determined by the onboard solar diffuser stability monitor (SDSM)1. 
Earth Observing Missions and Sensors: Development, Implementation, and Characterization V
 edited by Xiaoxiong Xiong, Toshiyoshi Kimura, Proc. of SPIE Vol. 10781, 1078116
 © 2018 SPIE · CCC code: 0277-786X/18/$18 · doi: 10.1117/12.2324530
Proc. of SPIE Vol. 10781  1078116-1
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RTA
/ \/ /
SDSM
I
I
I
I
1
SD screen
Solar Diffuser (SD)
sunlight
SDSM screen
sunlight
 
 
 
 
 
Figure 1. A sketch that shows the components related to the VIIRS on-orbit radiometric calibration. The SDSM and the SD screens 
are otherwise opaque plates with through holes. The RTA stands for the rotating telescope assembly that directs incoming light to 
the detector focal planes. 
When in operation, the eight SDSM detectors, with design band central wavelengths from 412 to 926 nm, receive photons 
from the Sun through an attenuation screen denoted as the SDSM screen and the SD reflected sunlight almost at the same 
time. The ratio of the SDSM signal strengths adjusted for the SD and the SDSM screen transmittance and the sun-sensor 
distance is a direct measure of the H-factor. 
However, the H-factor directly measured by the SDSM is along the SD-to-SDSM direction and what we need is the H-
factor along the SD-to-RTA direction. It has been discovered that the H-factor for the first VIIRS instrument onboard the 
SNPP satellite2-3 is angle dependent. Here we determine whether the H-factor for the second VIIRS is angle dependent.  
2.  METHODOLOGY 
To determine whether the H-factor is angle dependent, we use the SDSM SD observations, as we did for the SNPP 
VIIRS2,4. As shown in Fig. 2, for the two points 1 and 2, if the solar angles are the same, the ratio of the digital counts from 
the SD view cancels the SD screen transmittance and the BRDF at the mission start to yield 
SR(𝑡2)HSDSM(𝑡2,?⃗⃗⃗? (𝑡1))
SR(𝑡1)HSDSM(𝑡1,?⃗⃗⃗? (𝑡1))
=
𝑑𝑐SD,p(𝑡2,?⃗⃗⃗? (𝑡1))
𝑑𝑐SD(𝑡1,?⃗⃗⃗? (𝑡1))
  ,                                                                                                                              (1) 
where the SR is the spectral response function for an SDSM detector, ?⃗?  is the solar angle, and 𝑑𝑐SD represents the digital 
count with background subtracted from the SD view. In equation (1), we use HSDSM to indicate the H-factor along the SD-
to-SDSM direction. We use 𝑑𝑐SD,p to indicate the digital count at time t2 with the solar angle at time t1. In general, it is 
impossible to have a digital count that happens at a later time t2 and at the exact solar angle for an early time t1. Hence we 
use a subscript “p” to indicate that the digital count at the later time is a pseudo-digital count that must be constructed 
through interpolations of measured values. Equation (1) assumes that the spectral response function is sharp enough in the 
wavelength space to be regarded as a Dirac delta function. The advantage in using equation (1) is the removal of the SD 
screen transmission function that may not be exactly known. Additionally, equation (1) uses the property that the H-factor 
at the early mission is very close to one and thus is not particularly angle dependent. Note that the small angular dependence 
at an early mission time can be taken into account as we did for the SNPP VIIRS4. 
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ai 30v
o
`° 25
ñ
tll
,5 20
I. 10
0 1000 2000 3000 4000 5000
Orbit
19
18
orbit 8
d X
orbit 4284 -O X
17 R +O
X16 ++\O xx5.
S
4; 15
14
13
+ p X orbit 42980
++O Xx
22.0 22.2 22.4 22.6
(PH, VIIRS (deg)
22.8 23.0
 
 
 
 
 
Figure 2. Circles indicate the solar angles in the VIIRS coordinate system when the SDSM sees the sunlit SD. The VIIRS coordinate 
system is such defined so that the z axis is along the RTA to the center of the earth view port and the x axis is along the normal of 
the SD screen. The solar azimuth angle 𝜙H,VIIRS is defined as the negative of the angle that the solar vector projected onto the xy 
plane makes with the x axis, and the solar declination angle 𝜙V,VIIRS is defined as the angle that the solar vector projected onto the 
xz plane makes with the x axis. 
To find 𝑑𝑐SD,p(𝑡2, ?⃗? (𝑡1)), we rely on the fact that 
𝑑𝑐SD,p (𝑡, ?⃗? (𝑡)) = 𝑑𝑐SD (𝑡, ?⃗? (𝑡)) .                                                                                                                                  (2) 
 
Figure 3. Circles, pluses, and crosses are for the solar angles in the VIIRS coordinate system when the SDSM sees the sunlit SD at 
orbits 681, 4284, and 4298, respectively. 
We select t1 as satellite orbit 681. Note that the nominal satellite orbit time period is 101.5 min. To find a 𝑡2 and 
𝑑𝑐SD,p(𝑡2, ?⃗? (𝑡1)), we examine the solar angles shown in Fig. 3. The figure shows that the solar angles at orbit 681 are in 
between those at orbits 4284 and 4298. As a result, we can use 𝑑𝑐SD (𝑡3, ?⃗? (𝑡3)) and 𝑑𝑐SD (𝑡4, ?⃗? (𝑡4)) to calculate 
𝑑𝑐SD,p(𝑡2, ?⃗? (𝑡1)) where, 𝑡3 and 𝑡4 are respective times on orbits 4284 and 4298. We define ?⃗? (𝑡3) and ?⃗? (𝑡4) to have the 
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op
0.888
ó 0.886
.- 0.884vvv
Ñ 0.8820
= 0.880
33 34 35 36 37 38
$v, SD (deg)
 
 
 
 
same solar declination angle as 𝜙V,VIIRS(𝑡1) and 𝜙H,VIIRS(𝑡3) ≤ 𝜙H,VIIRS(𝑡1) ≤  𝜙H,VIIRS(𝑡4). Fig. 3 reveals that the solar 
angular curve for orbit 681 is parallel to those of orbits 4284 and 4298 and thus presents a simpler case4 since we can set 
 𝑡2 = 𝑡3 +
𝑡4−𝑡3
𝜙H,VIIRS(𝑡4)−𝜙H,VIIRS(𝑡3)
× (𝜙H,VIIRS(𝑡1) − 𝜙H,VIIRS(𝑡3))                                                                                   (3) 
to obtain 
𝑑𝑐SD,p (𝑡2, ?⃗? (𝑡1)) =
(𝑡4−𝑡2)×𝑑𝑐SD(𝑡3,?⃗⃗⃗? (𝑡3))+(𝑡2−𝑡3)×𝑑𝑐SD(𝑡4,?⃗⃗⃗? (𝑡4))
𝑡4−𝑡3
  .                                                                                     (4) 
We calculate the ratio of the SDSM detector response functions in equation (1) from the sun view data through 
𝑑𝑐Sun (𝑡, ?⃗? (𝑡)) = 𝜏SDSM
eff (?⃗? (𝑡)) × SR(𝑡)Esun(𝜆𝑑 , 𝑡) ,                                                                                                      (5) 
where t indicates a time on a particular orbit,  𝜏SDSM
eff  is the effective SDSM screen transmittance refined with both the yaw 
maneuver and regular on-orbit SDSM data5, 𝜆𝑑 indicates band central wavelength for SDSM detector d, and Esun is the 
solar spectral irradiance at the VIIRS. 
3.  RESULTS 
Assuming HSDSM at 𝑡1 is not solar angle dependent since 𝑡1 is early in the mission, we use equation (1) to calculate HSDSM 
at 𝑡2 that is determined by equation (3) to be about orbit 4288. To give an example, in Fig. 4 we plot the HSDSM at 𝑡2 for 
SDSM detector 1. The obtained HSDSM, indicated as the circles, follows a linear function of the solar angle 𝜙V,SD defined  
 
Figure 4. Circles indicate HSDSM at 𝑡2 calculated by using equation (1), versus 𝜙V,SD for SDSM detector 1 with 𝑡2 =orbit 4288, 
where 𝜙V,SD is the angle between the incident sunlight and the SD surface. The solid line indicates the best fit of a linear polynomial 
of 𝜙V,SD to the measured HSDSM. 
as the angle between the sunlight and the SD surface. The slope of the linear function is 0.00053 deg-1. We calculate the 
HSDSM at 𝑡2 for all eight SDSM detectors and plot the slopes versus 1- HSDSM at 𝜙V,SD = 35.5 deg in the left chart of Fig. 
5. To compare, we also plot the slopes for the SNPP VIIRS versus 1- HSDSM in the right chart4 of Fig. 5. Fig. 5 reveals that 
at the same 1 – HSDSM, both SDs on the N20 and SNPP VIIRS instruments yield about the same amount of solar angular 
dependence at least along the solar angles of satellite orbits. 
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j 0.0006ó 0.0004
oî
-o 0.0002
0
>é- 0.0000
a
-0.0002
-o
o
N20
o
o
0.00 0.02
1 -
0.04 0.06 0.08 0.10
NOW (95v, so =35.5 deg)
-^ 0.0015
0,
a)U
á 0.0010 -
0
O
[
O
0.0005
s'
0.0000
SNPP
X
0400 +700 A1088 02992 X3389 -
0
o -
0.12 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
1 - Hs,s,,(0, ,=35.5 deg)
0.90
0.89
0.88
0.87
0.86
0.85
0.84
tock=e4S
11 12 M1 M2 M3 M4 M5 M6 M7
0 50 100 150 200 250 300
Days since launch
0.90
V_
0.84
hiemea."^
11 12 M1 M2M3M4M5M6M7
0 50 100 150 200 250 300 350
Doys since launch
 
 
 
 
 
 
Figure 5. 𝑑HSDSM/𝑑𝜙V,SD along the solar angles of satellite orbits at 𝜙V,SD = 35.5 deg. (Left) for the N20 VIIRS and (right) for 
the SNPP VIIRS. 
4.  AN APPLICATION OF THE H-FACTOR ANGULAR DEPENDENCE 
In the last section, we showed that the amounts of the solar angular dependence of the N20 and SNPP VIIRS SD HSDSM 
along the satellite orbits are about the same at the same HSDSM. Since both the SNPP and N20 satellites orbit the Earth in 
the same plane, the nearly same amount of solar angular dependence at the same HSDSM for both the SDs indicates that the 
SNPP VIIRS SD H-factor angular dependence may be valid to the N20 VIIRS SD H-factor. 
 
Figure 6. The SNPP VIIRS VISNIR band F-factors calculated from (left) the measured HSDSM and (right) from the HRTA that is 
determined through equation (6) with the RSR de-convoluted HSDSM. The F-factors are averaged over all the detectors in a band 
and are for half-angle-mirror side A, and high-gain stage for dual-gain bands. 
For the SNPP VIIRS, we have6 
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HRTA = HSDSM ×
1+𝛼RTA(𝜆)∗(1−HSDSM)
1+𝛼H(𝜆)∗(1−HSDSM)∗(𝜙H,SD−𝜙H0)
 ,                                                                                                            (6) 
where 𝜙H0=48.0 deg, 𝜙H,SD is the solar azimuth angle in the SD plane
6. In equation (6) 
𝛼H(𝜆) = 0.0033 × (1 −
0.076
𝜆2.48
) ,                                                                                                                                        (7) 
where λ is the band central wavelength in microns6 and 𝛼RTA(𝜆) is obtained from matching the lunar F-factor with the SD 
F-factor calculated with the SNPP HSDSM, where the F-factor is a correction factor to the initially calculated scene spectral 
radiance1. Fig. 6 shows the N20 VIIRS visible near infrared (VISNIR) band F-factors using HSDSM (left) and HRTA (right). 
In generating the right chart of Fig. 6, we have de-convoluted the measured N20 HSDSM7, using the SNPP VIIRS SDSM 
detector RSRs as approximations. The F-factors calculated with the HRTA show that since launch the F-factor moves up 
about 0.5% for the M1 band, 0.3% for the M2 band, 0.2% for the M3 band, stays nearly flat for the M4, I1, and M5 bands, 
and decreases about 0.2% for the I2 and M7 bands. 
5. SUMMARY 
We have obtained the initial solar declination angular dependence of the measured HSDSM at day 302 after launch (orbit 
number 4288) along the solar angles on satellite orbit 681 (day 48). As for the SNPP VIIRS, the dependence is stronger at 
a shorter wavelength. At the wavelength of the SDSM detector 1 with the design wavelength of 412 nm that is the shortest 
among the 8 SDSM detectors, the derivative of the HSDSM over the solar declination angle along the satellite orbit has a 
value of 0.00053 deg-1. Very importantly, we have found that at the same HSDSM, the dependence has nearly the same 
amount as the SNPP VIIRS. Since the SNPP and N20 share the same orbital plane, the finding indicates that the H-factor 
angular dependence for the N20 VIIRS may be the same as that for the SNPP VIIRS. Applying the SNPP VIIRS H-factor 
angular dependence for the N20 VIIRS, we have obtained the N20 VIIRS HRTA from the RSR de-convoluted HSDSM and 
applied the HRTA to calculate the F-factors. 
ACKNOWLEDGMENTS 
We thank Kevin Twedt of Science Systems and Applications, Inc. (SSAI), Lanham, MD, USA, for many useful comments. 
REFERENCES 
1. Joint Polar Satellite System (JPSS) VIIRS Radiometric Calibration Algorithm Theoretical Basis Document (ATBD); 
NASA Goddard Space Flight Center: Greenbelt, MD, USA, 2013. 
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degradation factor”, Proc. SPIE, vol. 9218, paper ID: 9218-1N, 2014. 
3. J. Sun and M. Wang, “Visible Infrared Imaging Radiometer Suite solar diffuser calibration and its challenges using a 
solar diffuser stability monitor”, Applied Optics, vol. 53, pp. 8571-8584, 2014, DOI: 10.1364/AO.53.008571. 
4. N. Lei and X. Xiong, “Products of the SNPP VIIRS SD Screen Transmittance and the SD BRDFs from Both Yaw 
Maneuver and Regular On-orbit Data”, IEEE Trans. Geosci. Remote Sens. vol. 55(4), pp. 1975-1987, 2017; DOI: 
10.1109/TGRS.2016.2633967. 
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Initial Investigation of the Angular Dependence of the NOAA-20 VIIRS Solar Diffuser BRDF Change Factor

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