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MOSPHERIC OPTICS GROUP
(Annex-Jom
rnals) hnical Note No. 263
3 3 1822 04429 0724
974.5
. T43
no. 263
Development of Techniques for Determination of
Nighttime Atmospheric Transmittance and Related
Analytic Support for the Whole Sky Imager
Published as Final Report for ONR Contract
N00014-01-D-0043-DO5
UNIVERSITY
OF
CALIFORNIA
SAN DIEGO
Janet E. Shields
Art R. Burden
Monette E. Karr
Richard W. Johnson
Justin G. Baker
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The material contained in this note is to be considered
proprietary in nature and is not authorized for distribution
without the prior consent of the Marine Physical Laboratory.
SCRIPPS
INSTITUTION
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MARINE PHYSICAL LAB San Diego, CA 92152-6400
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3 1822 04429 0724
Development of Techniques for Determination of
Nighttime Atmospheric Transmittance and Related
Analytic Support for the Whole Sky Imager
Published as Final Report for ONR Contract
N00014-01-D-0043-D05
Janet E. Shields, Art. R. Burden, Monette E. Karr,
Richard W. Johnson and Justin G. Baker

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5. Funding Numbers.
N00014-01-D-0043-D05
4. Title and Subtitle.
Development of Techniques for Determination of Nighttime Atmospheric
Transmittance and Related Analytic Support for the Whole Sky Imager
6. Author(s).
Janet E. Shields, Art R. Burden, Monnette E. Karr, Richard W. Johnson and
Justin G. Baker
11
Project No.
Task No.
8. Performing Organization
Report Number.
7. Performing Monitoring Agency Names(s) and Address(es).
University of California, San Diego
Marine Physical Laboratory
Scripps Institution of Oceanography
291 Rosecrans Street
San Diego, CA 92106
10. Sponsoring Monitoring Agency
Report Number
9. Sponsoring/Monitoring Agency Name(s) and Address(es).
Office of Naval Research
Department of the Navy
800 North Quincy Street
Arlington, VA 22217-5660
Atten: CDR Scott Tilden, Code 321
11. Supplementary Notes.
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Approved for public release; distribution is unlimited.
13. Abstract (Maximum 200 words).
This report describes the work done for the Air Force Research Lab, Kirtland Air Force Base under
Contract N00014-01-D-043 DO #5. The primary goal of this work was the development of techniques
for extracting the atmospheric transmittance distribution over the sky, from Whole Sky Imager
nighttime data.
14. Subject Terms.
atmospheric optics, Whole Sky Imager, atmospheric transmittance
15. Number of Pages
31
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of Report.
Unclassified
18. Security Classification
of This Page.
Unclassified
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of Abstract..
Unclassified
20. Limitation of Abstract.
None
:iconico
Development of Techniques for
Determination of Nighttime Atmospheric Transmittance
and Related Analytic Support
for the Whole Sky Imager
Table of Contents
1. Introduction.................................
2. Background.....
3. Statement of Work.
.........
4. Derivation of Star Irradiance Library and Equations for Extracting Beam
Transmittance ........
.............. 3
4.1 Spectral Irradiance of a Star - Definition ........
4.2 Using Visual Star Magnitude to Derive Visual Star Irradiance .... 5
4.3 Deriving Spectral Irradiance for the WSI Passbands..............
4.4 Definition of Earth-to-Space Beam Transmittance ................
4.5 The Measured Apparent Irradiance of the Star ..................... 11
4.6 Summary of Theoretical Derivation ........... ....................... 12
5. System Calibration.
l
..........................
6. Inherent Star Irradiance Library ................
7. Apparent Star Irradiance and Transmittance.
8. Results.
..................
9. Discussion of Transmittance Results ........
.............
10. Summary .........
.............................................
11. Acknowledgements..................
........................
12. References..
List of Illustrations
Fig. 1
........... 15
Fig. 2
Fig. 3
.60.0..0
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Calculated inherent spectral irradiances for stars found in the
NSSDCBright Star Catalog ........
Spectral irradiances for WSI passband, 32,714 stars ..................
Spectral irradiances for WSI passband, 1555 stars .....................
Transmittance for star HR1791 using various values of T(0) .... 19
Transmittance map for cloud-free image.......... .............. 20
Transmittance map for thin cloud image .........
Transmittance map for another thin cloud image........................
Transmittance map for partly cloudy image ..... ....................
Transmittance map for cloud-free image with aerosol corr ........ 24
Transmittance map for thin cloud image with aerosol corr ....... 25
Tables
Table 1 The Va Response in comparison with Photopic & Scotopic ........... 6
Table 2 Effective or Color Temperature vs. Star Class .....
Development of Techniques for
Determination of Nighttime Atmospheric Transmittance
and Related Analytic Support
for the Whole Sky Imager
Janet E. Shields, Art R. Burden, Monette E. Karr,
Richard W. Johnson, and Justin G. Baker
1. Introduction
This report describes the work done for the Air Force Research Lab, Kirtland Air Force
Base under Contract N00014-01-D-043 DO #5, between 24 May 01 and 17 Oct 03. The
primary goal of this work was the development of techniques for extracting the
atmospheric transmittance distribution over the sky, from Whole Sky Imager nighttime
data.
2. Background
The Atmospheric Optics Group at the Marine Physical Lab, Scripps Institution of
Oceanography, University of California San Diego, has been developing Whole Sky
Imagers (WSI) for many years. (Johnson 1989, 1991). A Day/Night WSI which had 24-
hour a day capability was initially developed in the early 1990's, and has been
significantly upgraded in capability since that time (Shields 1993, 1998). One
instruments, Day/Night WSI Unit 5, was delivered to the Air Force Research Lab,
Kirtland Air Force Base, in December 95 for fielding at a remote site. The WSI was
delivered to the sponsor under Contract N00014-93-D-0141 DO #11 (Shields, 1997a).
(At that time, AFRL was named Phillips Laboratory, PL/LIO.) The instrument was
operated under the sponsor's care at their site. The sponsor told us that the instrument “is
an excellent source of data and is a very reliable system.” Under follow-on contracts,
several developments to software and documentation took place (Shields, 1997b and
Shields, 2002).
Most recently, under funding from another sponsor, we evaluated and tested techniques
for identifying the presence of clouds in the starlight images. This starlight cloud
detection was based on the detection of stars in the image. Using the National Space
Science Data Center catalog of stars, the algorithm predicts the location of the stars in the
image, and attempts to detect each star. The point-spread function of the star is
represented by a Gaussian of width of approximately 0.5 pixels. If the algorithm is able
to detect this spatial signature at the appropriate location in the image, then the point is
identified as cloud free.
Approximately 2100 stars per image are evaluated to form a cloud decision in
approximately 237 regions (or cells) of the sky. Under subsequent funding from this
other sponsor, this algorithm was further refined (including increasing the number of
cells to 356), and converted to C code for processing efficiency.
Under funding from various sponsors, we had also developed techniques for providing
radiometric calibration of the WSI images. Essentially, each pixel is calibrated to
provide the radiance of the sky in the units of watt/92 m² um. The typical signal to noise
for the darkest part of the sky between stars is typically about 40, providing very high
quality raw data for calibration into the desired radiometric units.
By combining the techniques for star detection, and the techniques for absolute
calibration, we developed, under this contract, new techniques for determination of
optical beam transmittance of the atmosphere and semi-transparent clouds. Using a
technique similar to the Gaussian fit used in the star detection, it is possible to integrate
the area under the Gaussian, and relate this integrated signal to the star intensity. With an
appropriate library of inherent star intensity, determination of the earth-to-space beam
transmittance of the atmosphere and the semi-transparent clouds becomes possible.
3. Statement of Work
The Statement of Work from the proposal is as follows for the primary task:
The contractor shall, unless otherwise specified herein, supply the necessary personnel, facilities, services,
and materials to accomplish the following tasks within a one-year period following receipt of funding.
1. Develop a library of star irradiances for use by the transmittance algorithm.
2. Provide radiometric calibration of the sensor, contingent on the sponsor delivering the sensor to MPL.
3. Evaluate techniques for determining earth-to-space beam transmittance distribution from WSI starlight
imagery. Within the limits of funding, work toward development of these techniques in software code,
which can be fielded with the AFRL WSI.
4. Provide a final written report and interim verbal reports to the sponsor regarding the results of the
above work.
5. Other work such as minor repairs to the instrument are permissible under this task, if they are mutually
agreed upon by the sponsor and by MPL to be appropriate. In this case, the work toward the other
requirements in this statement of work would be lessened accordingly.
The primary task was fully funded (at $50,499), and in addition, a small increment of the
optional task was funded (for $14,501). The optional task was:
1. Coordinate with the sponsor regarding the most appropriate tasks and estimated costs for development.
2. Provide personnel trained in the Whole Sky Imager and its capabilities to address these tasks (at MPL)
to the limit of funding provided under the contract. These tasks may include analysis, software
development, documentation, minor hardware development, and other tasks related to the WSI that are
mutually agreed upon by the sponsor and by MPL to be appropriate.
3. Provide a final written report and interim verbal reports to the sponsor regarding the results of the
above work.
This additional funding was intended to supplement the development and programming
of the transmittance work.
All of the work was completed successfully, as will be discussed in the next sections.
4. Derivation of Star Irradiance Library and Equations for Extracting Beam
Transmittance
In order to determine the beam transmittance, a primary input is the irradiance of a star in
the absence of the atmosphere – which we will call the inherent irradiance of the star. In
the following sections, we will define and derive an equation for determining the spectral
irradiance of a star from known quantities. We will show how this can be used to
determine the effective spectral irradiance of a star over our sensor's wavebands. Then
we will derive the equation for the beam transmittance, and finally discuss how to use the
radiances measured by our system in the derivation of the beam transmittance.
4.1. Spectral Irradiance of a Star - Definition
We start with the basic blackbody equation (Budding, 1993), which gives the spectral
radiant emittance of a star.
=-
27 hc2 as
exp(hc/ak Tc)-1
W
"
Eq. 1
In this Blackbody equation (or Planck's equation), the terms are:
h = Planck's Constant = 6.626 10-34 J sec
c=speed of light = 2.998 108 m sec-?
a = wavelength in m
k=Boltzmann's constant = 1.381 10-23 J K1
Tc = Color Temperature of the star in degrees K
If the star is a perfect blackbody, the color temperature is equal to its physical
temperature. If the star is not a perfect blackbody, the color temperature is the
temperature for which the blackbody equation most closely predicts the actual emittance.
Physically, spectral emittance is the energy, in Watts per unit surface area per unit
wavelength, emitted by the star. In this case the surface involved is the surface of the
star. In radiometrics, this would commonly be given in the units of Watt /m'um. In
Equation 1, the units of the constants yield an emittance in J/sec mº, which is equivalent
to Watt/m". Thus if we want to convert the computed value to more standard radiometric
units, we must multiply the result of Eq. 1 by 10ºm/um.
Our sensor is calibrated to yield the absolute spectral radiance of an extended source.
Spectral radiance is defined as the energy received per solid angle, per surface area, and
We usually use the units of
per wavelength, by a surface in a given direction.
Watt/Sr m’um
All stars except the sun form effectively a point source, when sensed by the WSI. That
is, the surface area as seen from the earth by the WSI subtends less than a pixel. This
means that the radiance is undefined. For now, in this derivation we will therefore derive
the spectral irradiance of a star, rather than the spectral radiance, and deal with the
conversion of our signals to irradiance later in this memo.
Irradiance is defined as the energy received per unit area on a surface. Similarly, spectral
irradiance is the irradiance per wavelength. In this case, the surface involved is the
surface of the earth, or more specifically, the effective surface of the sensor. The
irradiance can be defined with respect to a horizontal surface, or a surface normal to the
star. For this derivation, we will use a surface normal to the star. This will be mentioned
again in Section V.
To derive the spectral irradiance E, created on a surface at a distance r by a star of
spectral emittance W. and radius R, we first recognize that the star is spherical, and its
surface is essentially Lambertian, meaning that its radiance is independent of viewing
angle (Boyd, 1983). In a Lambertian source, it can be shown that the emittance W is
related to the radiance L by
W = 1 L
Eq. 2
(Eq. 2.22 in the above reference). Further, the total flux emitted by the sphere of radius R
is given by Eq. 2.28 from the above,
0 = 41? R? L
Eq. 3
The irradiance on a surface at distance r is given by Eq. 2.29,
Err R? L/r?
Eq. 4
Combining Eq. 4 with Eq. 2, we see that the irradiance may be derived from the
emittance of a star by
E=R? W/r?
Eq. 5
and the spectral irradiance may similarly be derived from the spectral emittance by
E, =R? Wa/r?
Eq. 6
Unfortunately, Eq. 6 is not of much use to us unless we know the distance and radius of a
large set of stars. One of the references given to us by our sponsors in fact used this
method (Riker, 1993) both to calibrate the sensor and to determine the beam
transmittance to a few stars. (We have a very significant advantage over this method:
our sensor is small enough to be brought into a calibration room and be calibrated
directly. This significantly lowers the uncertainty in the calibration.) We could use Eq. 6
to determine the irradiance of a star, however our sponsors told us they do not have large
star libraries containing the star radius information. Therefore, we used an alternative
approach based in part on Riker 1997, which utilizes libraries of visual star magnitude,
which is documented for most of the stars in the standard star library we are using.
4.2. Using Visual Star Magnitude to Derive Visual Star Irradiance
The relative stellar magnitude is defined in a variety of ways. Budding defines it as
ml - m2 =-2.5 log (f/f,)
Eq. 7
where ml and m2 are the magnitude of two stars, and f1 and f2 are defined as their flux.
Flux is generally defined radiometrically as energy. Budding goes on to say that the
above is too imprecise for scientific use, and therefore standard magnitude is defined
using either V, B, or U, where V is the standard visual magnitude – a term he leaves
undefined. We believe the V refers to power of the source integrated over the visual
response curve. (B is Bolometric magnitude, which refers to the total power of the
source integrated over all wavelengths, and U is ultraviolet.) So far we know that stellar
magnitude refers to relative changes in energy from the star, such that a factor of 10
change in energy corresponds to a change of 2.5 in magnitude. This results from the
historical relationship that a change of 5 in magnitude corresponded to a factor of 100
change in energy.
Riker (1997) states that Eq. 7 refers to brightness. However, he also uses Eq. 7 to define
the relative change in visual irradiance, which he defines as
E, = \v (2) E, da
Eq. 8
Riker does not appear to define V(a) or list its values. However, Allen (1972) defines
m, as the apparent magnitude in the visual system as defined by the v(a) curve, which
he lists in Section 97. This curve is similar to the Photopic and Scotopic response curves,
which are the human visual response for day and night respectively, however, he states
that the v(a) curve includes aluminum reflectivity (but not atmospheric absorption).
The V(a), Photopic, and Scotopic response are shown in Table 1.
Riker then adds that the definition of a zero-magnitude source for visual magnitudes is
E (0)= 3.1623 10-9 Watt/m²
Eq. 9
Combining Eq. 9 and 7, we have the visual irradiance for a star of magnitude m is given
E,(m)=E,(0) 10-m/25
Eq. 10
Table 1
The V, Response in comparison with Photopic and Scotopic

0.08
-
-
| Mnm) | V | Photopic | Scotopic
400 0.00 0.00 0.02
420 0.00 0.00
440 0.00 0.02 0.21
460 0.00 0.06
0.41
480 0.01 0.14
0.65
500 0.36 0.32 0.90
520 0.91 0.71 0.96
540 0.98 0.95 0.68
560 0.80 1.00 0.35
580 0.59 0.87 0.14
600 0.39 0.63 0.05
620 0.22 0.38 0.02
640 | 0.09 0.18 0.01
660 0.03 0.06 0.00
680 0.01 0.02 0.00
Our star library includes visual magnitudes of the stars for nearly all the stars. Thus we
should be able to determine the visual irradiance of the star, or the spectral irradiance of
the star integrated over the V, curve.
There is some uncertainty in the value for the visual irradiance for a zero-magnitude
source. Riker lists his sources as Allen (1976) and Ramsey (1962). Ramsey lists the
value as 3.1, rather than 3.1623. He says he uses the “visible response curve (standard
observer)". This may be the Photopic curve than the Va curve given by Allen. We have
not been able to find the source of Riker's number in the Allen reference. Also, Riker
derives that the irradiance corresponding to the peak of the visual response curve is .0355
However, he states that others have obtained the values of .0380 and .0372.
Lena (1988) lists the value as .0392, and Zombeck (1990) gives .0364. These values
range to about 10% higher than the value given by Riker. The average value, .0373, is,
about 5% higher than Riker's value, indicating that a value closer to 3.32 10-Y may be
more appropriate in Eg. 9. We used Riker's value, because this is the one our sponsors
have historically used, so we should benefit from their experience with this issue.
4.3. Deriving Spectral Irradiance for the WSI Passbands
Because our sensor does not acquire information with a Va wavelength response, the
information on the visual irradiance of a star is not yet sufficient. We need to know the
effective spectral irradiance for our passbands. This is defined by
JE(m) SAT,da
E(m) ==
JS. Ta da
Eq. 11
where E(m) is the irradiance for star magnitude m, in a given spectral filter and neutral
density filter setting, and S,T, is the standard response in a given SP and ND filter.
Normally S, is the responsivity of the sensor, and Ta is the product of the transmittance
of all filters which are in place in a given SP and ND filter combination setting. The
calibration for all of our instruments are adjusted to provide the radiances for an
instrument of standard response, as defined in in-house Memo AV01-001t, and these
responses are designated by S,T, as noted above. We will normally be working in the
open hole configuration (Spectral 2, ND 1). Unless other specific designation is given,
the equations that follow will be assumed to apply to the open hole. By use of a different
S,Tcurve, however, these equations can be applied to any of our other filter
combinations.
To derive the value in Eq. 11, we need to derive a general equation for Ex. Combining
Eq. 8 and 6, we have
E,(m) = ſe, v(a) da = R I w.v(a) da=C Sw. v(a) da
Eq. 12
where C is a constant relating E, and W, as shown in Eq. 6 and defined below.
Ex =CW
Eq. 13
From Eq. 12 and 10, we have
C-E,(0) 10-m/25
Eq. 14
Wv(a) da
Thus, in order to derive spectral irradiance for the WSI open-hole band, we use the
defining equation 11, using the standard curves as input. The E, comes from Eq. 13,
where C is defined in Eq. 14, and Wa is defined in Eq. 1 (with the proper unit
conversions).
Use of Eq. 1 requires knowledge of the color temperature of the star. The star library
includes the “spectral types on the Morgan-Keenan (MK) classification system". The
color temperature is roughly correlated with the spectral class, although there is some
disagreement over the specific effective (or color) temperatures that correspond to each
class. Table 2 shows values from Riker, Allen, and Zombeck. Riker provides a fairly
complete list, but lists his source as “Davin, D., private communication”. Allen often
lists several temperatures for a given class. Where there are 3 temperatures for one class,
the first in the table is for the “Main sequence, V”, the second is for the “Giants, III”, and
the third is for “Super giants, I”. That is, his temperature values depend not only on the
spectral class but on a size class. Similarly, Zombeck lists values for the main sequence,
and a second set of values (given in parenthesis) for giants. We chose to use a spectral
OIL
class table with 133 classifications from the Jet Propulsion Lab, as will be discussed in
Section 6.
Clearly, there is a significant uncertainty in the derivation of the inherent irradiance from
information available in the star library. This may be our largest source of uncertainty.
However, if we use the existing information currently used by the sponsor, we should still
see a very significant increase in the extent and accuracy of the beam transmittance
values, for two reasons. First, because we are able to calibrate the WSI directly, we
should have a much more accurate measurement of apparent irradiance as sensed at the
earth surface. This should result in much more accurate transmittance estimates than was
previously possible. Secondly, we can sense many stars simultaneously, and provide a
distribution of transmittance estimates over the sky in place of a single estimate, thus
providing a much more extensive amount of information. We will still be subject to the
uncertainties in the inherent irradiance, but those uncertainties will at least be no worse
than they are currently.
In the future, it seems very reasonable to use the WSI to evaluate how much the inherent
irradiances should be changed. For example, by studying images taken throughout
several clear, reasonably stable nights, we should be able to identify stars that yield
consistently low or high results, and potentially adjust the inherent star irradiance library.
In fact, if accurate knowledge of the inherent star irradiances becomes more critical, the
possibility exists of using the WSI for a more detailed study. By using a photopic filter,
along with the red and blue filters, and taking more extensive measurements from high
altitude, it may be feasible to significantly improve the inherent star irradiance library for
use with other applications. In the meantime, for this project, we used the values
presented by Riker.
4.4. Definition of Earth-to-Space Beam Transmittance
Up until this point, the various irradiance values have all been for out of the atmosphere,
i.e. with no atmospheric losses. As noted earlier, this is called the inherent irradiance.
We will use the annotation E, to represent these inherent irradiances. As will be
discussed in Section V, we will also be determining a measured irradiance, which is the
irradiance from the ground. This includes the atmospheric transmission losses, and is
known as the apparent irradiance. We will designate it Ea where A represents Apparent.
(We would use M for Measured, however this could add confusion, since the star
magnitude is m.)
In McCartney's text, he treats beam transmittance as a function of spectral irradiance. He
states that a beam of spectral irradiance Ex in going through a lamina of thickness x is
attenuated according to
d
=B dx
Eq. 15
where ß is defined as the total scattering coefficient.
1
Тc
Тc
TC
G9
A6
K2
K5
Table 2
Effective or Color Temperature vs. Star Class
Class
Tc
Tc Class
Тc
Riker Allen Zombeck
Riker Allen
Zombeck
ΑΟ 11000 9900, 10800 1 G4 5578
12000
Al 10587
G5 5477 5520 5610 (5010)
5000, 4850
A2 10189
9730 G6 | 5378
A3 9806
G7 5281
A4 / 9438
G85186
5490 (4870)
A5 9083
8500
8620
5092
8742
KO 5000 4900, 5240 (4720)
4500, 4100
A7 8413
8190 K1 1 4825
(4580)
A8 8097
4656
4780 (4460)
A9 7793
K3 4493
(4210)
BO 25000 28000, 30000 K4 4335
(4010)
30000
B1 | 23030
24200
4183 4130,
(3780)
3800,3500
B2 21214
22100 K64037 |
B3 19542
18800
K7 | 3895
4410
B4 | 18002
K8 3759
B5 | 16583 15500 16400 K9 | 3627
B6 | 15276
15400 MO 3500 | 3480,3200 3920 (3660)
B7 14072
14500 M1 3407
3680 (3600)
B8 | 12963
13400
3317
3500 (3500)
B9 | 11941
124001 M3 3229
3360 (3300)
FO 7500 7400, 7240 M4 3143
3200 (3100)
7000
F1 7335
M5 3060 2800 3120 (2950)
F2 7173
6930 M6 | 2900
(2800)
7014
00 40000 |
| 6860
01 38163
F5 6708 6580
6540
36411
F6 6560
34740
F7 6415
| 33145
6274
6200
31623 40000
38000
F96135
30171
38000
GO 6000 6030,5600, 5920
28786
38000
5700
G1 5892
27464
35000
G2 5785
5780 09 26203
35000
G3 1 5681

-
M2
F3
F4
-
From this equation, we have the irradiance E, at distance x given by
E, = E, exp(-x)
Eq. 16
where E, is the initial irradiance. Here the à designation has been dropped, but it should
be understood that these are still spectral quantities.
McCartney then defines transmittance, which we will designate by T, as
T =
= exp(=Bx)
Eq. 17
The earth-to-space beam transmittance is the transmittance over a path from the earth
surface to outside the earth atmosphere. Thus the transmittance is a ratio of the inherent
spectral irradiance above the atmosphere E, to the apparent spectral irradiance at the
earth surface Ea. In our case, we will be determining the effective transmittance over our
passband, since we will be using the effective spectral irradiance of the star over our
passband. Thus the equation for beam transmittance becomes
Eq. 18
Whereas McCartney defines the beam transmittance in terms of the irradiance, Duntley
(1975) defines the beam transmittance in terms of radiance, as in the following equation
L, EL, T, +L*
Eq. 19
In this equation, L, is the apparent radiance at the end of a path of length r, L, is the
inherent radiance at the 0 point, Tr is the beam transmittance over the path, and Lr* is the
path radiance due to light scattered into the path. This is the transmittance we are far
more familiar with. If we remove the path radiance (as will be discussed in the next
section), this is similar in form to Eq. 17. For our geometry, the distance between the star
and a position on the earth's surface is nearly the same as the distance between the star
and a position above the earth's atmosphere. As seen in Eq. 4, this means that over the
distances we are dealing with, the change in irradiance due to the range change is
insignificant. As a result, the change in irradiance which is due to the atmosphere is
proportional to the change in radiance due to the atmosphere. This means that the beam
transmittance defined in terms of irradiance is equivalent to the beam transmittance
defined in terms of radiance, for this specific geometry, and using stars as the source.
This is shown in Eq. 20.
ET
Eq. 20
E.
E.
Note that in general the definition of beam transmittance based on irradiance may not be
equivalent to the definition of beam transmittance based on radiance. However, as shown
above, for the specific case of a star, the transmittances are equal. Had this not been the
case, we would have needed to find out what type of transmittance our sponsors need to
10
know. Since we are using stars for our sources, the transmittance we determine using the
irradiances will apply equally well to radiances as shown in Equation 20.
4.5. The Measured Apparent Irradiance of the Star
The WSI was designed to handle extended sources such as the sky, and it is calibrated to
yield the spectral radiance defined by
-
L=
JL, S,T, da
S, T, da
Eq. 21
where L is the total energy per solid angle and per unit surface area falling on a surface
from a given direction.
For a single pixel, the irradiance produced on a horizontal surface by the radiance in the
solid angle of the pixel is given by
E = SSL(0,0) cos 0 022
Eq. 22
Our sensor reports the actual radiance in the direction of a pixel, not the radiance
modified by the cos term. In a sense, it shows the radiance falling on a surface normal to
the direction sensed by the pixel. We will be evaluating the irradiance from a star. For
the inherent star irradiance, We have used the irradiance on a plane normal to the star,
rather than a horizontal plane. Since we are wishing to determine the irradiance on a
plane normal to the star for a single pixel or a few pixels, then the irradiance equation for
a single pixel reduces to
E=\ \L(0,0)d1=L AN
Eq. 23
where L is the measured radiance, and AS2 is the solid angle of the pixel.
Due to the slight defocusing of the optics and atmospheric turbulence the light from a star
is not collected by a single pixel, but is distributed over a few pixels. The typical light
distribution is approximately that of a Gaussian curve with a STD of approximately 0.5
pixel. The width of the Gaussian is reasonably constant over the image, but may vary
from system to system depending on how well focused the sensor is.
If there were only one star in a given image, it would be a simple process to multiply the
measured radiance in each pixel by that pixel's solid angle, and add the results. This
works because the pixels on the CCD are contiguous, so no flux falls between pixels. In
our images, with many stars, it may be possible to use a similar technique, perhaps
adding the weighted signals over a 4 x 4 array of pixels with no other stars within the
array. This is problematic in a crowded star field, so it may or may not be practical.
A second approach is to use the area under the Gaussian. Our current night cloud
algorithm program does this with uncalibrated signals. We would need to apply
11
radiometric calibrations, to yield a radiance image, and then multiply each pixel by its
solid angle, to yield irradiance for the pixel. Then the Gaussian algorithm could
determine the area under the curve for each star. This approach has the advantage that
the Gaussian best-fit technique already recognizes and removes nearby stars.
In both approaches outlined above, it is also necessary to subtract the background
radiance that is scattered into the field of view by the sky. This is the Lr* term in Eq. 19.
If we use the approach based on the Gaussian curve fit, this is already handled, because
the program determines the background level and subtracts this from the star signal. If
we use the approach of adding the signal from pixels near a star, we will similarly need to
determine the background level for the region of the star, and subtract it.
4.6. Summary of Theoretical Derivation
The approach we used to estimate earth-to-space beam transmittance depends on
knowing the inherent irradiance of a star above the atmosphere and determining the
apparent irradiance of the star at the surface from the calibrated measurements of the
WSI. The beam transmittance in the direction of that star can be determined from these
values, and the variation in beam transmittance over the sky can be determined from
using as many stars as is reasonable.
The inherent irradiance of a star on a surface normal to the star may be computed as
described in Section 4.3. That is, we use the star spectral type from the catalog to
determine color temperature, use Eq. 1 (with unit changes) to determine the emittance,
use Eq. 13 to determine spectral irradiance, and use Eq. 11 to determine the spectral
irradiance for the WSI passband. In Eq. 13, the constant C is determined from the visual
magnitude of the star given in the star library using Eq. 14 and 9. These steps could be
done once, to create a star spectral irradiance library to go with the star library.
The apparent irradiance of a star as measured by the WSI would be determined basically
by subtracting the background radiance, multiplying each measured radiance by the solid
angle of the pixel, and then combining the signals from those pixels affected by the star.
Section V discusses this approach in more detail.
When the inherent irradiance E, and the apparent irradiance Ea are known, the earth-to-
space beam transmittance is computed from Eq. 20. Note that in a clear atmosphere, the
vertical beam transmittance T(0=0) is typically about 0.70 in the photopic (a rule of
thumb from past experience), and the beam transmittance in the direction of a star should
vary roughly by
seco
T(O)= T(0) sce
Eq. 24
We will be determining the T value for each star, and so we should expect that on a clear
night these values will decrease toward the horizon. In other words, our sponsors told us
not to correct for the sec term, but rather to report the actual estimated transmittance in
each direction.
It should also be noted that in the future it would be reasonable to use several stars in a
region to estimate the beam transmittance for that region. It would also be reasonable to
add a feature which compares the signal from the star with the background signal, and
makes an automatic assessment of whether the star signal is bright enough to be useful.
5.0 System Calibration
The WSI was returned to MPL for calibration on 21 March 01. It was then sent to
Photometrics for routine maintenance. It turned out to be necessary to return it to
Photometrics again for replacement of a bad receiver card. We also replaced the shutter,
and checked the filters for aging. The system was calibrated in April and May 01, and
returned to the sponsor 29 May 01.
The system was calibrated using a 3 meter optical bench, and a FEL1000 lamp traceable
to NIST. Effective lamp irradiances in the WSI spectral filters were determined from the
measured lamp spectral irradiance, filter spectral transmittances, and sensor spectral
sensitivity. The calibrations included the following:
Linearity and Exposure Calibrations
Absolute Radiance in each filter combination
Aperture Calibration
Flat Field
Rolloff
Geometric Calibration
The calibrations are fully documented in in-house memoranda.
A program ImgCal was written in C, to process field images to yield fully calibrated
radiance distributions. This program is also documented in an in-house memo. This
program was used to process field data to produce the radiance images used for testing
the transmittance techniques.
A technique was developed by one of our sponsors for a higher precision geometric
calibration. With their permission, we modified this technique for easier application.
Our Air Force sponsors for the current project needed to extract the higher precision
calibration for Unit 5, so these programs and the tutorial were delivered to our sponsors.
The technique is not trivial, and further upgrades were developed and delivered.
The actual data for Unit 5 was not accessable to us due to security issues, so the
remainder of the analysis was done using data from the Air Force's SOR site. This SOR
data was acquired with one of our WSI units.
6. Inherent Star Irradiance Library
As discussed in Section 4, the first step in the determination of the beam transmittance
mapping with the WSI is determination of the inherent irradiance library. As discussed
in Section 4, there are several areas of potential error that may contribute to incorrect
values of inherent irradiance. Some of the error sources listed there include the definition
of a zero-magnitude source for visual magnitudes, the location of the peak in the visual
response curve, and a star's color temperature, which is estimated based on its spectral
class. The values of the first two variables are discussed in that memo, while the spectral
class - color temperature correspondence deserves further mentioning.
Each star is assigned a spectral class and subclass based on its spectra, which corresponds
to a specific star color temperature. For this study, a spectral class table with 133
classifications from the Jet Propulsion Lab was used:
http://spider.ipac.caltech.edu/staff/gerard/a refs/sptype temp.html. Because the spectral
classes and subclasses actually include a range of temperatures, a given star's spectral
class represents only an estimate of the actual color temperature. The varying color
temperatures assigned to specific stars by different sources can lead to inherent radiances
that differ by as much as 10% or more. For example, two sky map software packages list
Aldebaran as 3406 K and 4320 K, which leads to a calculated inherent irradiance of
1.67E-8 and 1.85E-8 W/m²-um, respectively (assuming the same star magnitude).
Aldebaran has been assigned a spectral class of K5, which, according to the spectral class
table used here has a corresponding color temperature of 3920 K.
Equation 13 was used to obtain the inherent spectral irradiance for each star. The
constant, C, in that equation was calculated in each case using Equation 14. The visual
response curve given in Table 1 was used for the integral in the bottom half of that
Effective blackbody emittances were calculated using a modified version of
the in-house software Program Filter. To system response for this instrument were also
correct to the standard WSI response, as documented in in-house memos. Figure 1 shows
the resulting inherent spectral irradiances calculated with this method as a function of
visual magnitude for all stars in the NASA star library.
7. Apparent Star Irradiance and Transmittance
While the inherent irradiance for a star need only be calculated a single time and stored
for later retrieval, the apparent irradiance is determined for stars during image processing.
In order to conduct the transmittance study, WSI imagery had to be radiometrically
calibrated. As noted in Section 5, software called ImgCal was written that calibrates
either a single image or a directory of images. Imgcal was used to calibrate several days
of WSI imagery used in the transmittance project.
The latest version of the nighttime cloud algorithm, called StarCloudAlgl, was used to
identify stars in each nighttime WSI image. The software is documented in in-house
memo AV03-030t. The NASA star catalog used in the software had to be modified to
include inherent spectral irradiances, which are described in Section 6. The night
14
algorithm software had to be modified to calculate and output measured spectral
irradiance and transmittance for identified stars.
10-6FTTTTTTTTTTTTTTTT

10-75
TTTT
Log(Spectral Irradiance) (W/m2-um)
10-9
10-10
por meio temas ini
10 ''L1 IIIIIIIIIIIIIIIII
10-11
Magnitude
Figure 1. Calculated inherent spectral irradiances for stars found in the NSSDC
Bright Star Catalog.
To convert image pixel values to star flux, it was decided that for the initial study, simply
adding pixels surrounding the predicted star location and correcting for the sky
background would suffice. The alternative method would be to integrate a best-fit
Gaussian curve placed at the star center. Anecdotal evidence suggests that the Gaussian
method works better, particularly in a crowded star field. Initial tests showed that the
results were similar when examining large datasets. We were concerned about
pixellation effects described below, so we decided to use the pixel addition method for
this study. This issue is one that could be examined further in the future.
One aspect of the determination of star energy from the Gaussian method that has not
been adequately addressed for this study is the pixellation effect mentioned in Memo
AV01-097t. Basically, if the star is centered on a pixel, we believe the best-fit procedure
used to locate stars handles the central pixel value as though it is equal to the star peak
value, rather than the star signal integrated over the area of the pixel. Methods were
15
developed to correct for this, however they did not improve the results. Therefore no
pixellation correction was used for this study.
The current method of calculating apparent star irradiance involves summing a 5 X 5
pixel array of signals surrounding the star center pixel. The signals are modified by
subtracting the background value (as determined by the Gaussian best-fit) and
multiplying by the solid angle for the pixel. The resulting sum equals the apparent star
irradiance.
As shown in Equation 24, transmittance in an isotropic atmosphere should drop off
toward the horizon. In the current version of the night algorithm containing these
irradiance calculations, the irradiances can be corrected for these atmospheric extin
effects using T(0) = 0.70 in order to estimate the cloud transmittance without the aerosol
effects. The correction can easily be removed or modified by using the following
multiplicative factor:
seco
E.= E.( 0,70)
EQ (25)
where Tm is the modified cloud-free transmittance, Eo is the irradiance computed using
T(0) = .7, and Em is the modified irradiance.
Estimated atmospheric transmittance at the location of a star may be calculated by
dividing the measured value of spectral irradiance by the inherent spectral irradiance
found in the star catalog. By combining the transmittance results over an image, a
transmittance map can be obtained.
8. Results
Results presented here were derived using cloud-free SOR imagery from February 14,
1999. In Figure 2, inherent and measured spectral irradiances are compared using catalog
stars up to magnitude 6 and star zenith angles < 60°, for a total of 32,714 stars. These
initial results clearly show a reasonable correlation (0.84) between inherent and measured
irradiances. The red line in the plot represents a simple best fit line. As Figure 1 shows,
higher spectral irradiances correspond with lower visual magnitudes, although the
relationship is not direct, as previously stated. Lower irradiances show significantly
higher variability than higher irradiances due to difficulties associated with determining
the measured (and inherent) irradiances for faint stars. Figure 3 shows similar data for
some of the brighter stars (spectral irradiances greater than 10-9 W/m²-um, for a total of
1555 stars). The correlation for these stars is much higher, 0.99, as expected.
It should be noted that although these were the results at the time of the completion of the
project, the transmittance work has been continued under funding from another sponsor.
This work resulted in a significant improvement in the correlations, from 0.84 correlation
to 0.96 correlation. We are continuing evaluating sources of uncertainties at the time of
this writing, however this work is not included in this contract report.

10-6 ETT
1
TTTT
Unit 12, February 14, 1999
10-15
Lih
TTTTTTT
Measured Spectral Irradiance (W/m²-um)
חזון
T
10-9
to
Linear Coefficients:
A = 1.27293e-011
B =
1.02694
Correlation Coeff =
0.842895
10-10
TTTT
10-10 10 9 10 8 10-7
Theoretical Spectral Irradiance (W/m2-um)
10-6
Figure 2. Spectral irradiances for WSI passband. Stars to Magnitude 6. Zenith
angles < 60°. Red line is linear best fit of data.
Results were also extracted for individual stars. Figure 4 shows how the transmittance
changes for a specific star as a function of zenith angle, as well as a function of changes
in T(0). We expect the transmittance to vary less when using the best estimate of T(0).
For this example, a vertical earth-to-space transmittance of 0.90 yields the most
consistent (flat) curve as a function of zenith angle. In most of the cases we examined,
T(0) = 0.8 yielded the most consistent transmittance results for zenith angles < 60°.
Although 0.7 is a nominal earth-to-space vertical beam transmittance for the photopic, we
would expect it to be closer to 1 for the WSI open hole configuration, which corresponds
most closely to a red filter.
Note that the curve for T(0) = 0.9 does not intersect the y axis at 0.9. This most probably
indicates a calibration offset. From multiple plots such as shown in Fig 4, we estimated
the calibration correction to be a factor of 0.89. This corresponds closely with a
calibration correction due to pixel cross-talk that we recently measured.

10-0 FTTTTT TTTTTTTT
TT
TTTT
Unit 12, February 14, 1999
10-7
LU
Measured Spectral Irradiance (W/m²-um)
TIT
TTT
Linear Coefficients:
A = 2.80535e-011
B =
1.02100
Correlation coeff =
0.987696
G
C
SL
10-9/
10-9
10-8
10-7
10-6
Theoretical Spectral Irradiance (W/m²-um)
Figure 3. Spectral irradiances for WSI passband. Stars with spectral irradiances
greater than 10-9 W/m²-um. Zenith angles < 60°. Red line is linear best fit of data.
Another possible source of error is the estimate of inherent irradiance. The zenith angle
dependence indicates that there may be stray light or rolloff issues to consider. The
variance in measured irradiance for a given star demonstrated here is also seen in Figures
2 and 3, where the measured irradiances for a given star line up along a line at constant
theoretical irradiance. Some of this variance in the corrected measured irradiances may
have to do with the aerosol correction, and some may be due to uncertainties in the
extraction of the measured irradiance.
Figures 5-10 show several preliminary transmittance maps that demonstrate the potential
of the technique using calibrated imagery from SOR. Each star in the dataset is identified
by a box with a color representative of the calculated transmittance. The key for the
colors is shown on each page. Only stars that were magnitude 6 or less were used.
Additionally, stars in a crowded field were eliminated. For all cases, a correction factor
was applied that accounts for an error in the calibration constant for Unit 12. The first
four cases present total transmittance, while the last two cases present cloud
transmittance including a correction for estimated aerosol transmittance (T(0) = 0.8).
18

SOR 19990214: Transmittance for Star HR1791
T
2.0
* Tfac =
* Tfac = 0.7
* Tfac
* Tfac
* Tfac =
0000-
ON000
1.5
Transmittance
*
*
*
*
*
*
*
*
0.5
*
0.0 LILI
L LL
20
40
60
80
100
Zenith Angle (degrees)
Figure 4. Transmittance for star HR1791 using various values of T(0). Results were
compiled from multiple images.
Figure 5 is a cloud-free image that was used to create the composite dataset used in
Figures 2 and 3. Because this plot is not corrected for aerosol transmittance, we would
expect the transmittances to be somewhat less than 1 and to drop off toward the horizon.
The transmittances at lower zenith angles (e.g. overhead) are mostly in the range 0.4-1.0.
There is clearly more variance than we would like, however the results appear to be in the
right ballpark. Where stray light from Albuquerque to the northwest exists, many stars
were not found (red squares). While the range of values is wide in this image, as thin
cloud moves into the field of view, it is apparent that the cloud-free portions of an image
can be distinguished, as demonstrated in the next three figures.
Figure 6 is a case with wispy thin cloud moving into most of the frame with somewhat
thicker cloud to the south. The difference in transmittance is seen throughout the image,
as green is predominant color (0.4-0.6) rather than the purple (0.6-0.8) from the previous
clear image. There are also many more yellow (0.2-0.4) and red (no star) cases here. In
cases with more cloud, as shown in Figure 7, transmittances drop even more. Figure 8 is

a nice example that includes a large semi-opaque cloud band that crosses the image. To
the southeast and northwest, where the sky is mostly clear, the pattern of colors resembles
that of Figure 5.
TRANSMITTANCE COLOR KEY
No Stars Found
0 0-0.2
0 0.2-0.4
0 0.4-0.6
0 0.6-0.8
0.8-1.0
01.0-2.0
90471000.cal
Transm = 1.0
CC_Cor = 0.89
26
XB
Figure 5. Transmittance map for cloud-free image. No aerosol correction applied.
Calibration correction of 0.89 applied.

TRANSMITTANCE COLOR KEY
No Stars Found
0 0-0.2
0 0.2-0.4
0.4-0.6
O 0.6-0.8
o 0.8-1.0
0 1.0-2.0
90480750.cal
Transm = 1.0
CC_Cor = 0.89
ch
her
Figure 6. Transmittance map for thin cloud image. No aerosol
correction applied. Calibration correction of 0.89 applied.
A couple of cases were also included that have an estimate of an aerosol transmittance
correction applied. This accounts for the reduction of clear sky transmittance toward the
horizon. Figure 9 is an aerosol-corrected cloud-free case, also used in Figure 5. The
transmittances here are higher, and the drop-off in transmittance at the horizon is no
longer apparent. Figure 10 shows similar results for the partly cloudy case also shown in
Figure 8.

TRANSMITTANCE COLOR KEY
No Stars Found
0 0-0.2
0 0.2-0.4
0 0.4-0.6
o 0.6-0.8
O 0.8-1.0
01.0-2.0
90470400.cal,
Transm = 1.0,
CC_Cor = 0.89
Figure 7. Transmittance map for another thin cloud image.
No aerosol correction applied. Calibration correction of 0.89
annlied

TRANSMITTANCE COLOR KEY
No Stars Found
0 0-0.2
0 0.2-0.4
O 0.4-0.6
0.6-0.8
0 0.8-1.0
01.0-2.0
90470740.cal
Transm = 1.0
CC_Cor = 0.89
si
The
Figure 8. Transmittance map for partly cloudy image. No aerosol correction
applied. Calibration correction of 0.89 applied.
23

TRANSMITTANCE COLOR KEY
No Stars Found
0 0-0.2
0 0.2-0.4
0.4-0.6
0 0.6-0.8
0 0.8-1.0
01.0-2.0
90471000.cal,
Transm = 0.8
CC_Cor = 0.89
s.
329
Figure 9. Transmittance map for cloud-free image (same image
as Fig 5). 0.8 aerosol correction applied. Calibration correction
24

TRANSMITTANCE COLOR KEY
No Stars Found
0 0-0.2
0 0.2-0.4
00.4-0.6
0 0.6-0.8
0 0.8-1.0
o 1.0-2.0
90470740.cal
Transm = 0.8
CC_Cor = 0.89
Se
AN
S
19
Figure 10. Transmittance map for thin cloud image (same image as Fig. 8). 0.8
aerosol correction applied. Calibration correction of 0.89 applied.
9. Discussion of Transmittance Results
With some reasonable results in hand that demonstrate that the instrument calibration and
the approach documented in Section 4 are both on target, we can now look toward how
errors in the results can be reduced. One observation that jumps out is the large variance
found in the measured irradiances for a given star under cloud-free conditions. It would
be a good idea to pick a few stars and take a closer look at why the variation occurs. One
possibility is to address the pixellation effect mentioned earlier, which is likely to be a
significant source of variance in the results. We may also be able to correct errors in the
calculated inherent spectral irradiances that were added to the star catalog by examining
results for individual stars over a number of days. The use of calibration stars for
determining the current vertical earth-to-space aerosol transmittance and generally
checking the calibration is another potentially fruitful approach. In general, we are very
pleased with these initial results, and feel that this technique has significant potential for
determining beam transmittance distribution over the sky dome.
10. Summary
Under this contract, we were primarily tasked to develop a library of inherent star
irradiances, calibrate the sensors to provide the absolute radiance field, evaluate
techniques for determining earth-to-space beam transmittance distribution from WSI
starlight imagery, and, within the limits of funding, work toward development of these
techniques in software code which can be fielded with the AFRL WSI. This work was
successfully completed.
The equations for extracting transmittance from WSI data were developed, and then
tested. The results were converted to a stand-alone program written in C, that produces
maps of transmittance over the full sky. While the results are not yet as precise as we
would like, we are pleased with the results. Work on these techniques is presently
continuing under funding from another sponsor.
11. Acknowledgements
We would like to express our appreciation to Capt. Dan Gisselquist, and Capt. Craig
Phillips of Air Force Research Labs, Kirtland Air Force Base, for their work with us on
this project. We would also like to thank Clint Campbell and Wil Gravemen of Logicon,
who were also working on our sponsor's project, and were a pleasure to work with.
Finally, thanks to Starfire Optical Range for the use of the data.
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8725 John J. Kingman Road
Suite 0944
Ft. Belvoir, VA 22060-6218