Background noise generated by planets is the dominant noise source in most deep space direct detection optical communications systems. Earlier approximate analyses of this problem are based on simplified blackbody calculations and can yield results that may be inaccurate by up to an order of magnitude. Various other factors that need to be taken into consideration, such as the phase angle and the actual spectral dependence of the planet albedo, in order to obtain a more accurate estimate of the noise magnitude are examined

Katz, J.

English

NASA Technical Reports Server

TDA Progress Report 42-85
N86-28277
January-March 1986
Planets as Background Noise Sources in
Free Space Optical Communications
J. Katz
Advanced Electronic Materiels and Devices Section
Background noise generated by planets is the dominant noise source in most deep
space direct detection optical communications systems. Earlier approximate analyses of
this problem are based on simplified blackbody calculations and can yield results that
may be inaccurate by up to an order of magnitude. This article points out various other
factors that need to be taken into consideration, such as the phase angle and the actual
spectral dependence of the planet albedo, in order to obtain a more accurate estimate of
._the noise magnitude.
I. Introduction
Optical communications is considered as an alternative to
conventional microwave links in future planetary (and exo-
solar) space missions (Ref. 1). For many typical deep space
communications scenarios, the optical receiver which achieves
maximum link sensitivity employs direct detection with a
photon counting detector (e.g., photomultiplier tube) at the
front end (Ref. 2). The performance of such receivers is
limited by either the photon statistics of the received signal
light or by background noise photons that appear in the
receiving telescope field of view. In planetary space missions,
the dominant background noise sources are the planets. Not
only are they the brightest objects in the solar system (except
the sun), but the highest demand on the communication link
usually occurs during the planetary fly-by phase, where they
are almost certain to be in the receiver field of view.
A first order approximation to the planet background noise
is based on simplified blackbody calculations (for the spectral
dependence), including the planet albedo as a single unique
parameter (Refs. 3, 4, 5). As will be discussed in the follow-
ing sections, the problem is much more involved, and the
actual result can vary by more than an order of magnitude as
compared to this simplified calculation. The purpose of this
article is to point out the other parameters that need to be
taken into account and to demonstrate their effect through
some illustrative examples. This article is not meant to be an
exhaustive study of the problem. Such a detailed analysis is
relevant only in the context of an actual planned mission.
Section II will briefly review the approximate basic theory.
The following sections will consider the effects of the planet
being an extended or a point source (Section III), phase angle
(Section IV), and spectral dependence (Section V). Two other
effects (polarization and temporal variations) will be briefly
mentioned in Section VI.
II. Basic Theory
For the visible and near-infrared regions of the spectrum,
virtually all the planet radiation is from reflected sunlight. The
situation is different in the mid and far infrared (Ref. 3), but
these cases will not be considered here:
If the planet is replaced by an ideal lambertian disk with a
unit reflectivity facing the sun and with the same radius as the
planet, the irradiance at the receiver plane is:
13
https://ntrs.nasa.gov/search.jsp?R=19860018805 2020-03-23T07:28:44+00:00Z
( 12 w
Ex R 2 cm 2/am
Pe
where H x is the solar flux at 1 AU (see Fig. 1 and Table 1),
Rpo is the sun-planet distance in AU, R e is the planet radius
(in km), and Z is the distance between the planet and the
receiver - usually earth - in km. Since the planets' orbits are
not circular, there will be some variations due to the orbit
eccentricity. The magnitude of this effect, with other basic
parameters of the planets, are listed in Table 2. The ratio
between the actual irradiance to the one predicted by Eq. (1)
is the geometric albedo, p, of the planet.
By multiplying the actual irradiance by the receiver aper-
ture area and by the bandwidth of its optical filter we obtain
the background power level at the detector.
The simplified worst case calculations are given in Refs. 3,
4, and 5 (it should be noted that there is error in those refer-
ences where the curves corresponding to Mars and Mercury are
interchanged), where a single number is used to represent the
albedo of each planet. In the following sections we will con-
sider the various factors affecting the geometric albedo.
III. Planets as Extended Sources or
Point Sources
Planetary optical communication receivers are usually
envisioned to have narrow fields of view, usually in the micro-
radian regime. Thus in many cases where the angular extent
of the planet, Or, exceeds the receiver field of view, 0r, the
planet appears as an extended background source. Table 3 lists
the approximate minimum, maximum and typical values of
Op of each planet for near-earth reception. For uniformly
reflecting planets the background irradiance dependence on
0r is as shown in Fig. 2. Some planets, though, do not reflect
uniformly, as shown, for example, for the planet Mars in
Fig. 3, and thus when Or < 0p, planetary features may have
to be considered in greater detail. Of course, when Or > Op
(i.e., the planet is entirely encompassed by the receiver field
of view) all the planet spatial features are averaged out.
IV. Phase-Angle Dependence
The phase angle is defined as the sun-planet-receiver (earth)
angle. Even if the geometric albedo did not depend on the
phase angle, the background contribution from the planet will
vary because at the various phases different portions of the
illuminated planet are seen from earth. This effect, which is
most important for the inner planets(and the moon), is ana-
lyzed in more detail in Appendix A and is depicted in Fig. 4.
In addition, there is a basic dependence of the geometric
albedo on the phase angle a, because planets are not ideal
lambertian reflectors. This dependence is expressed by a
phase function ¢(a), which is shown in Fig. 5 for the planet
Mars (Ref. 8) and the moon (Ref. 9). The typical features
of the phase function are a linear part for phase angles exceed-
ing approximately 10 deg, and a higher order component for
phase angles smaller than approximately 5 deg. This enhanced
reflectivity at small phase angles is called the "opposition
effect." The exact shape of the phase function depends on
the detailed light scattering properties at the planet (Refs. 8
and 9). Generally, albedos of planets with atmospheres have a
smaller dependence on the phase angle than atm0sphereless
planets.
V. Spectral Dependence
In many cases the geometric albedo depends strongly on
the wavelength. This may be caused, for example, by absorp-
tion lines in the planet's atmosphere or other processes such as
Raman Scattering. Examples of the spectral variations of the
albedo are shown in Fig. 3 (for Mars), Fig. 6 (for several
planets in general low resolution detail) and in Fig. 7 for some
other planets in more detail (Venus, Jupiter, Uranus, and
Neptune). It is clearly seen that with all other parameters
equal, a judicious choice of the communications link wave-
length can significantly reduce the background noise by even
more than an order of magnitude. For example, the Mars
albedo at X = 1 /am is three to four times larger than at ;k =
0.5 /am (this is somewhat offset by the fact that the photon
irradiance of the sun is 1.5 times larger at 0.5 /am than at
1/am). Furthermore,/other outer planets which have atmo-
spheres appear very dark at several wavelength regions, and
they will contribute negligibly low background noise levels if
these wavelengths are utilized in the communication link.
VI. Other Factors
In addition to the parameters discussed in the earlier sec-
tions, there are other factors that are usually of secondary
importance, and are mentioned here for the sake of Complete-
ness. The first is the fact that planets - like most other objects -
do not reflect equally both light polarizations. This effect is
small (see data for Venus and Earth in Fig. 8) and completely
unimportant in systems using unpolarized light or light with
unknown polarization. The second factor is various temporal
variations that can be caused by planetary climate patterns,
solar flares, and other phenomena. Again, these are minor
14
effects compared with the effects of the Earth-Planet distance
variation, phase angle and spectral dependence discussed
earlier.
VII. Conclusion
As shown in the earlier sections, the simplified calculations
of background noise generated by planets (Refs. 3, 4, 5) pre-
dict worst case situations and can thus serve in many cages
only as a first order approximation to the actual magnitude
of the background. While exact results can be obtained only
when all the mission parameters are known (e.g., Planet and
Earth location with respect to the Sun), this article points out
the various parameters that play a role in determining this
final result. The most important conclusion is that the noise
magnitude strongly depends on the wavelength used for
communication.
Acknowledgment
Discussions with S. Dolinar were helpful in ascertaining the dependence of received
background noise from Venus on the Earth-Sun-Venus angle.
15
References
1. Posner, E. C., Grant, T., and Hortor, R., "Communications and Navigation for Galileo
and Future Outer Planets Spacecraft," IEEE Spectrum (to be published), June 1986.
2. Lesh, J. R., Katz, J., Tan, H. H., and Zwillinger, D., "2.5 Bit/Detected Photon
Demonstration Program: Description, Analysis, and Phase I Results," TDA Progress
Report 42-66, Jet Propulsion Laboratory, Pasadena, Calif., pp. 115-132, 1981.
3. Ramsey, R. C., "Spectral Irradiance from Stars and Planets, above the Atmosphere,
from 0.1 to 100.0 Microns,"Appl. Opt. 1,465-471, 1962.
4. Katz, J., "The Deep-Space Optical Channel: I. Noise Mechanisms," TDA Progress
Report 42-64, Jet Propulsion Laboratory, Pasadena, Calif., 180-186, 1981.
5. Vilnrotter, V. A., "Background Sources in Optical Communications.," JPL Publica-
tion 82-73, Jet Propulsion Laboratory, Pasadena, Calif., 1983.
6. "Solar Electromagnetic Radiation," NASA SP-8005, Washington, D.C., 1971.
7. "Surface Models of Mars (1975)," NASA SP-8020, Washington, D.C., 1975.
8. Egan, W. G., Photometry and Polarization in Remote Sensing, New York: Elsevier,
1985.
9. Lumme, K., and Bowell, E., "Radiative Transfer in the Surfaces of Atmosphereless
Bodies," Astron. J. "I. Theory," 86 1694-1704, 1981;"II. Interpretation of Phase
Curves," 86, 1705-1771, 1981; "III. Interpreation of Lunar Photometry," 87,
1076-1082, 1982.
10. Hartmann, W. K., Moons and Planets: An Introduction to Planetary Science, Tarry-
town-on-Hudson, New York: Bogden and Quigley, 1972.
11. Moroz, V. I., "Stellar Magnitude and Albedo Data of Venus" (Ch. 3) in Venus,
D. M. Hunten et al., Eds. Tucson: The U. of Arizona Press, 1983.
12. Taylor, D.J., "Spectrophotometry of Jupiter's 34100-1000A Spectrum and a
Bolometric Albedo for Jupiter," lcarus, 4, 362-373, 1965.
13. Irvine, W. M., and Lane, A. P., "Monochromatic Albedos for the Disk of Saturn,"
lcarus, 15, 18-26, 1971.
14. Neff, J. S., et al., "Absolute Spectrophotometry of Titan, Uranus and Neptune:
3500-10,500A," lcarus, 60, 221-235, 1984.
15. Coffeen, D. L., and Hansen, J. E., "Polarization Studies of Planetary Atmospheres,"
from Planets, Stars and Nebulae, Studied with Photopolarimetry, T. Gehrels, Ed.
Tuscon: The U. of Arizona Press, 1974.
16
Table I. Solar spectral irradlance at I AU (from Ref. 6)
Wavelength (h), Average
_m Irradiance*
(Ph), W cm -2 _m -1
0.120 0.000010
0.140 0.000003
0.150 0.000007
0.160 0.000023
0.170 0.000063
0.180 0.000125
0.190 0.000271
0.200 0.00107
0.210 0.00229
0.220 0.00575
0.225 0.00649
0.230 0.00667
0.235 0.00593
0.240 0.00630
0.245 0.00723
0.250 0.00700
0.255 0.0100
0.260 0.0130
0.265 0.0185
0.270 0.0232
0.275 0,0204
0.280 0.0222
0.285 0.0315
0.290 0.0482
0.295 0.0584
0.300 0.0514
0.305 0.0603
0.310 0.0689
0.315 0.0764
0.320 0.0830
0.325 0.0975
0.330 0.1059
0.335 0.1081
0.340 0.1074
0.345 0.1069
0.350 0.1093
0.355 0.1083
0.360 0.1068
0.365 0.1132
0.370 0.1181
0.375 0.1157
0.380 0.1120
0.385 0.1098
0.390 0.1098
0.395 0.1189
0.400 0.1429
0.405 0.1644
0.410 0.1751
0.415 0.1774
0.420 0.1747
Wavelength (h), Average
/_m Irradiance*
(Ph), W cm -2 um -1
0.425 0.1693
0.430 0.1639
0.435 0.1663
0.440 0.1810
0.445 0.1922
0.450 0.2006
0.455 0.2057
0.460 0.2066
0.465 0.2048
0.470 0.2033
0.475 0.2044
0.480 0.2074
0.485 0.1976
0.490 0.1950
0.495 0.1960
0.500 0.1942
0.505 0.1920
0.510 0.1882
0.515 0.1833
0.520 0.1833
0.525 0.1852
0.530 0.1842
0.535 0.1818
0.540 0.1783
0.545 0.1754
0.550 0.1725
0.555 0.1720
0.560 0.1695
0.565 0.1705
0.570 0.1712
0.575 0.1719
0.580 0.1715
0.585 0.1712
0.59O 0.1700
0.595 0.1682
0.600 0.1666
0.605 0.1647
0.610 0.1635
0.620 0.1602
0.630 0.1570
0.640
0.650
0.660
0.670
0.680
0.690
0.700
0.710
0".720
0.730
*Special irradiance averaged over small bandwidth centered at h:
and 1.0 to 5.0 _m (bandwidth, 1000A)
Wavelength (h), Average
Irradmnce*
um (pX),Wcm_2 um_l
0.740 0.1260
0.750 0.1235
0.800 0.1107
0.850 0.0988
0.900 0.0889
0.950 0.0835
1.000 0.0746
1.100 0.0592
1.200 0.0484
1.300 0.0396
1.400 0.0336
1.500 0.0287
1.600 0.0244
1.700 0.0202
1.800 0.0159
1.900 0.0126
2.000 0.0103
2.100 0.0090
2.200 0.0079
2.300 0.0068
0.1544
0.1511
0.1486
0.1456
0.1427
0.1402
0.1369
0.1344
0.1314
0.1290
2.400 0.0064
2.500 0.0054
2.600 0.0048
2.700 0.0043
2.800 0.00390
2.900 0.00350
3.000 0.00310
3.100 0.00260
3.200 0.00226
3.300 0.00192
3.400 0.00166
3.500 0.00146
3.600 0.00135
3.700 0.00123
3.800 0.00111
3.900 0.00103
4.000 0.00095
4.100 0.00087
4.200 0.00078
4.300 0.00071
4.400 0.00065
4.500 0.00059
4.600 0.00053
4.700 0.00048
4.800 0.00045
4.900 0.00041
5.000 0.0003830
6.000 0.0001750
7.000 0.0000990
8.000 0.0000600
0.3 to 0.75 um (bandwidth, 100A), 0.75 to 1.0 um (bandwidth, 500A),
17
Table 2. Orbital constants of the planets and solar irradlance at planetary distances (from Ref. 6)
Planet
Semi-Major Axis Solar Irradiance at Ratio of Max
Distance of to Min
of Orbit Sidereal Eccentricity
Period, of Semi-Major Axis* Irradiance,**
AU 106km days Orbit 1971, e Solar [1 + et2
Constant mW cm -2 \1 - e]
Mercury 0.387 099 57.91 87.9686 0.205 629 6.673 5 902.9 2.303
Venus 0.723 332 108.21 224.700 0.006 787 1.911 3 258.6 1.028
Earth 1.000 149.60 365.257 0.016 721 1.000 0 135.3 1.069
Mars 1.523 69 227.94 686.980 0.093 379 0.430 7 58.28 1.454
Jupiter 5.2028 778.3 4 332.587 0.048 122 0.036 95 4.999 1.212
Saturn 9.540 1427 I0 759.20 0.052 919 0.010 99 1.487 1.236
Uranus 19.18 2869 30 685 0.049 363 0.002 718 0.3678 1.218
Neptune 30.07 4498 60 188 0.004 362 0.001 106 0.1496 1.018
Pluto 39.44 5900 90 700 0.252 330 0.000 643 0.0870 2.806
*Solar irradiance is 1/R 2 in units of the solar constant and 135.3/R 2 in mW cm -2 where R is the semi-major axis of the planetary orbit.
**Values of eccentricity change with time; the ratio of solar irradiance at perihelion to that at aphelion in the last column is computed on the
assumption of constant eccentricity.
Table 3. Approximate angles (in microradlans) subtended by planets 1
Planet Minimum 2 Maximum 3 Typical 4
Mercury 23 53 33
Venus 47 292 81
Mars 18 87 30
Jupiter 153 225 182
Saturn 76 94 84
Uranus 19 17 18
Neptune 6 6 6
Pluto 2 2 2
1 Does not include the partially lit area effect which is primarily important for the inner planets as
discussed in Appendix A.
2At maximum Earth-Planet distance.
aAt minimum Earth-Planet distance.
4Earth-Planet distance equals 1 AU for the inner planets and Sun-Planet distance of the outer planets.
18
0.5 I I t I I
O
c3
o.4
0.24 I I I
_ _ 0.3
o16 ==
o 0.2
_- o.12
_o.o8 "<
< _ 0.1
oc
__ 0.04 _.
o1_ I I I I I I I I -"]_ I I _<
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1,6 1.8 2.0 2.2 2,4 2.6
0
WAVELENGTH,/._m
Fig. 1. Solar spectral Irradlance (after Re/. 6)
BRIGHT DESERT AREAS
_AVERAGE DESERT AREAS
-
i I I I I I
0,4 0.5 0.6 0,7 0.8 0.9 1.0
WAVELENGTH, Fm
Fig. 3. Estimates of Mars surface normal albedo (after fief. 7)
.J
LU
>
0
Z
a
z
o
40 dBldec_
8p
RECEIVER FIELD OF VIEW, e r
Fig. 2. Background noise power level from a planet vs. receiver
field o/view
1.8 I
VENUS
,6 EARTH S_N
EARTH
TO VENUS
DISTANCE,
arbitraryunit$
FRACTION
OFSUNLIT
AREA OF
VENUS
VENUS
IRRADIANCE,
arbitrary units
o I I I
0 30 60 90 120 150
8, deg
t
180
Fig. 4. Dependence of the received background noise from
Venus on the Earth-Sun-Venus angle
19
1.00
(a)
I I I I / -14 / I Id L (b)
MARS
• 0.3926 p.m
+ 0.5012 p.m
O 0.7297 p,m
0.50
0,25 --
0
0
-10 tl
l l I I -8 I I
10 20 30 40 50 0 50 100 150
PHASE ANGLE, deg PHASE ANGLE, deg
Fig. 5. Phase function (a) for Mars (after Fig. 16.4, Rid. 8) and (b) for Moon (in logarithmic magnitude units, after Fig. 2 in Fief. 9 [111])
2O
0
a
,<
I-
0
uJ
0.8
0.7 P
0.6--
0.5--
0.4--
0.3--
0.2-
0.1-
0
0.3
I I I I I I I
ICES?
,,/
JUPITER
(_ EARTH
BLUE RED
I I I I I I I
0.4 0.5 0.6 0.7 0.8 0.9 1.0
WAVELENGTH,/,.¢m
Rg. 6. Geometric allxtdo (low resolution) wavelength dependence for vadous
planetary bodies (after Rg. 11.7 in Ref. 10 and Table IV in Fief. 13)
21
>X
<
0
I.-
a
Lu
N
.J
<
5
Z
0
<
0
a
w
<
1-
0.50
0.25
0.8
(a)
• 40 °
• 100
13 • 155
1:2_ n _ 40-100
O 3
• 76
n 95
0.2 0.4 0.6
WAVELENGTH,/.,_m
r o
vVwv =D I i
v I'1 I I
ill I I
- _. ,_1 -
i I iI I
,,:,x× ' ,,,
II I l •II I1_ %
t I I
,,0 i
;
× !
|| X
||
||
I!
||
||
||
||
||
I!
(1 I!
A 155 °
X 13-38
.... 86
I I
1 2
_,,, ;,_xx xX
3
I ' I i 1
(b) i
' I I I I
0.6
0.4
0.2
I I L [ [ I n
0.4 0.5 0.6 0.7
WAVELENGTH, p.m
I I I I I I I I
L I I I I _ L...L.,/J
0.4 0.6 0.8 1.0
I [ ] i
0.8 0.9 1.0
I I I I I I I |
(d)
0.4 0.6 0.8 1.0
WAVELENGTH, #m
Fig. 7. Detailed geometric albedo for various planets: (a) Venus (after Fig. 1 in Re/. 11); (b) Jupiter
(from data in Re/. 12); (c) Uranus (after Fig. 7 In Re/. 14); (d) Neptune (after Fig. 8 in Re/. 14)
22
0.3 I I I ] I I ] I
(a)
0.5 -2
0.6 3
0.8
2
I I I I i
50
4O
30
I
(b)
20
10
o ) I
20
o_
L I I
I I I I I I I
o00
o•
° o
oo
I I I
40 60 80
o •
q
I I I I
100 120 140 160 180
PHASE ANGLE, deg
Fig. 8. Polarization: (a) degree of polarization (in percent) of Venus as a function of phase angle
and wavelength (after Fig. 16 in Fief. 15) and (b) global earth degree of polamization (after Fig. 24
in Ref. 15)
23
Appendix A
Phase-Angle Dependence
Consider the sun-planet-earth system shown in Fig. A-1
(for an inner planet in this particular case). The lit angle of
the cross sectional disc is lr - a, where a is the phase angle.
Choosing 0 (planet-sun-earth angle) as the natural coordinate
for this problem, it is clearly seen that
7r- a = 0 + 3'(0) (A-l)
where 3'(0) is the Sun-Earth-Planet angle, given by
"frO) = _ - cos 0 (A-2)
Simple trigonometric calculations show that the fraction of the
lit planetary disc is o
sm _ = sin 2 (A-3)
and that the Earth-Planet distance is given by
[ sin 0 ] = Rp® sin 0 (A-4)
Z = RE® Lsin[0 + 3'(0)]j sin[7(0)]
As long as the planet appears as an extended background
source, its noise contribution is not affected by the above con-
siderations. However, when the planet is small enough to be
considered as a point source, its actual noise is proportional to
the ratio of the fractional area lit (Eq. [A-3]) to the distance
(Eq. [A-4] ). This dependence is strongest for the inner planets,
as shown in Fig. 4. For the outer planets, though, the frac-
tional area lit is always close to unity (for Mars the minimum
is approximately 87% and the planets from Jupiter and beyond
are always more than 99% lit), so the main effect on the noise
variation is the Earth-Planet distance.
-- SUNLIT SECTOR
SUNLIT SECTOR
SEEN FROM EARTH
/t '_" "_",_. PLANET
/,, \x
/ \ X\
iiiii
/ _
EARTH SUN
REO
Fig. A-1. Sun-planet-earth system (for Inner planet)
24


Planets as background noise sources in free space optical communications

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