The characteristics of the earth's atmosphere and its effects upon laser beams was investigated in a series of balloon borne, optical propagation experiments. These experiments were designed to simulate the space to ground laser link. An experiment to determine the amplitude fluctuation, commonly called scintillation, caused by the atmosphere was described

Bufton, J. L.

Grolemund, D. A.

Minott, P. O.

Schaefer, W. H.

English

NASA Technical Reports Server

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X-723-74-123
VERTICAL LASER BEAM PROPAGATION
THROUGH THE TROPOSPHERE
P. O. Minott, J. L. Bufton,
W. H. Schaefer, and D. A. Grolemund
April 1974
Goddard Space Flight Center
Greenbelt, Maryland
/
CONTENTS
Page
PURPOSE ........................................... 1
OBJECTIVES ......................................... 1
THEORY AND ANALYSIS ................................. 2
METHOD ........................................... 4
RESULTS. .................... ...................... 5
CONCLUSION ........................................ 6
ACKNOWLEDGMENTS .................................. 7
REFERENCES ........................................ 7
LIST OF ILLUSTRATIONS
Figure Page
1 Propagation Path ................................ 8
2 Stellar Scintillation ............................... 9
3 System Parameters .............................. 10
4 Flight Profile .................................. 11
5 Turbulence Profile... ............................ 12
6 Scintillation vs. Aperture ........................... 13
7 Power Spectral Density ....................... .... 14
PRECEDING PAGE BLANK NOT FILMED
iii
PURPOSE
The development of larger and more sophisticated satellites has led to an
expanding need for increased data transmission capabilities to transfer the
information obtained by these satellites to earth based data receiving facilities.
Estimates of NASA's future needs indicate that telemetry channels with a capac-
ity of 300 megabits per second will be required on advanced earth observation
satellites. Due to the high cost of the network of tracking stations which would
be required to keep a low orbiting satellite in view, the data will first be trans-
ferred to one of several synchronously orbiting data relay satellites which can
be constantly seen by a few ground data receiver terminals. Because of their
short wavelength compared to microwaves, laser communications systems offer
a great improvement in size, weight, and power consumption over microwaves,
and, therefore, NASA is actively developing laser communications for space to
space and space to ground data transfer.
As part of this effort, the characteristics of the earth's atmosphere and its
effects upon laser beams has been investigated in a series of balloon borne,
optical propagation experiments. These, experiments have been designed to
simulate the space to ground laser link. In this paper, an experiment to deter-
mine the amplitude fluctuation, commonly called scintillation, caused by the
atmosphere will be described.
OBJECTIVES
The objective of the experiment was to simulate a space to earth laser data
transmission link by directing a balloon borne laser transmitter from an altitude
well above all significant turbulence to an instrumented ground receiving station.
1
Specific objectives were as follows,
1. Measure the statistics of scintillation as a function of receiver aperture.
2. Compare the statistics of the laser scintillation to available data on
stellar scintillation.
3. Compare the statistics of daytime scintillation with existing data on
nighttime scintillation.
THEORY AND ANALYSIS
Consider Figure 1 which shows a spherical wave souroe at altitude H above
the earths atmosphere, and a receiver of diameter D pointed at the source.
Between source and receiver is an arbitrary distribution of turbulence which
we will assume is isotropic when measured in any plane parallel to the earth,
but which will vary in some fashion as a function of altitude. Characterizing
the strength of scintillation for a small aperture by the normalized standard
deviation of irradiance, and the strength of turbulence by the refractive-index-
structure constant the scintillation may be calculated for the case of weak
scintillation by the following expression,
(rI  H= 22
= 2 [C6(0)] 1/2 2 .56 k7/6 sec11 / 6  dh CN (h) (hbL)s/6]
where
C (0) = log-amplitude variance
k = wave number = 27/A
0 = zenith angle
C2 (h) = refractive-index-structure constant at altitude h
.= 1 - h/H
2
We immediately see that for small apertures the scintillation is aperture
independent, but has a pronounced dependence upon wavelength, zenith angle and
the vertical distribution of turbulence. The factor is p used to account for the
spherical wave nature of the source. By using the artifice of allowing the source
to recede to infinity, the source can be made to approximate an infinite plane
wave, and the factor u becomes unity leaving us with the standard plane wave
equation for scintillation.
As the aperture is increased, the magnitude of the normalized signal stand-
ard deviation will decrease below the normalized irradiance standard deviation
due to the averaging effect of the receiver aperture upon the random optical
distribution of irradiance in the receiver plane. This effect is usually accounted
for by a term known as an aperture averaging factor which relates the two
normalized standard deviations.
=S = 1/2
SI
In the limiting case for very large apertures, Fried 2 has derived an ex-
pression for the aperture averaging factor under conditions of weak scintillation
= 4.313 D- 7 / 3 sec 3  dh C(h) h / 38   2 (h) 2 /Z /
'C(o) JoC N
Combining the expressions for normalized standard deviation of irradiance
and aperture averaging factor, we obtain the scintillation for large apertures
S= 4.15 -IT' / 6 sec3 / 2 01 dh C2 (h) h2 - 1/3
3
We immediately see that for large aperture there is, a distinct aperture
dependence, a new zenith angle and turbulence profile dependence, but no wave-
length dependence. In the range of aperture sizes between very large and very
small, there is no theoretical derivation for the aperture dependence, and there-
fore, experimental data must be used to fabricate an empirical equation for the
aperture averaging factor. While there is no data on laser propagation from
space to earth, there is an extensive amount of aperture dependence data which
has been obtained from stellar scintillation studies. We have plotted this data
in Figure 2 and fitted an empirical equation for the aperture averaging factor
suggested by Fried 8.
= + ('7/6 +
where do is JI •3/7
d h C (h) h 2 1 E1/ 3
do = 2.399 k-1/ 2 sec 1 / 2 6<_II
fdh C 2 (h) (h/t)/6
The above aperture averaging factor has the virtues of fitting the equations
for the limiting values as well as the experimental values for intermediate
apertures. It represents our best estimate of aperture averaging.
METHOD
In order to simulate a space to earth laser propagation link, a helium-neon
laser transmitter was installed in a gimballed platform aboard the gondola of a
high altitude research balloon. The balloon was launched and flown by the Air
4
For3e Cambridge Research Laboratories Balloon Detachment at White Sands
Missile Range, and tracked by an optical theodolite of 76 cm aperture. An argon
laser beacon directed at the balloon from the theodolite allowed a star tracker
mounted on the gimballed platform to direct the helium-neon laser beam at the
theodolite optics. A variable aperture stop system allowed the effective collect-
ing diameter of the theodolite to be changed in steps of two from 8 cm to 64 cm
with an additional stop used for the full 76 cm aperture. The signal received
was detected by a photomultiplier and recorded for later processing. Significant
system parameters are shown in Figure 3.
RESULTS
The flight profile is shown in Figure 4, data presented in this paper came
from the third interval of laser operation between 1200 and 1300 Mountain
Standard Time on October 19, 1973. A device known as a thermosonde9 was
used to measure the vertical profile of turbulence shortly before the experiment.
Results are shown in Figure 5 together with standard Rawinsonde plots of the
vertical profiles of temperature and wind speed. Using this data, we obtain a
value of d o of
do = 0.137 sec
1 / 2 9
for the wavelength 0.63 x 10-6 meters.
The next graph illustrates the major results of the experiment (Figure 6).
In this plot, the ordinate is the normalized standard deviation of received signal
on a logarithmic scale and the abscissa is the receiver diameter in meters also
on a logarithmic scale. Data points are represented by the small circles and
5
each represents a value taken from a one minute sample of scintillation. The
variation in observed values is due to the non-stationarity of the atmospheric
turbulence rather than experimental difficulties, and is of approximately the
same magnitude as seen for stellar scintillation. A curve of the same shape as
that for stellar scintillation, but with the magnitude adjusted for best fit has been
drawn through the data. The corresponding asymptotic limits for very small and
very large apertures are shown by the dashed lines. The previous stellar
scintillation curve is shown for reference and demonstrates that the laser scin-
tillation was approximately 46% higher than average stellar scintillation. This
slight increase does not necessarily indicate any systematic difference between
stellar and laser scintillation as the limits of the day to day variation in stellar
scintillation easily include all of the observed laser data. All data has been
corrected to a zenith angle of 45'. The normalized power spectral density of
the scintillation is a function of aperture with large apertures acting as low pass
filter to remove the high frequencies. Figure 7 shows the spectral density for
the largest and smallest apertures used in the experiment. Results are similar
to stellar scintillation spectra.
CONCLUSION
The major conclusions we can draw from the experiment are that the scin-
tillation of a space to ground laser link is similar to that of stellar scintillation,
and that there are only minor differences between day and night. We have found
nothing to indicate that the statistics of laser scintillations are in anyway differ-
ent from those of an incoherent stellar source. However due to the limited
amount of data, further work needs to be done in this area.
6
ACKNOWLEDGMENTS
The authors would like to express their appreciation for the support given
by Air Force Cambridge Research Laboratories, H. Wischnia of Perkin Elmer
Corp., and D. L. Fried of Optical Services Consultants in the execution of this
experiment.
REFERENCES
1. D. L. Fried "Theoretical Analysis of Aperture Averaging" Report No. DR-015
Optical Science Consultants, Yorba Linda, Cal. (October 1973).
2. Ibid. Ref. 1.
3. W. M. Protheroe, "Preliminary Report on Stellar Scintillation," Scientific
Report 4, AF 19 (604)-41 ASTIA No. AD 56040, Figure 86 (Physics and
Astronomy Dept., Ohio State University, Nov. 1964).
4. A. T. Young, Astron. Journ., 72, 747 (1967).
5. J. L. Bufton, "An Investigation of Atmospheric Turbulence by Stellar Obser-
vations," NASA TR R-369 (National Aeronautics and Space Administration
Washington, D. C., August 1971).
6. M. A. Ellison and H. Seddon, Monthly Notices Ray. Astron. Soc. 112, 73
(1952).
7. P. O. Minott, J. Opt. Soc. Am. 62, 885 (1972).
8. Ibid. Ref. 1.
9. J. L. Bufton, "Comparison of Vertical Profile Turbulence Structure with
Stellar Observations" Applied Optics 12, 1785 (1973).
7
SPHERICAL WAVE SOURCE--
ATMOSPHERIC
TURBULENCE H
C2 (h)
I
h
RECEIVER
Figure 1. Propagation Path
8
100_
Uo O
10-1 0 X3 ° x
xO
10-2 1l11
0.01 0.1 1.0 3.0
RECEIVER APERTURE - METERS
Figure 2. Stellar Scintillation
9
SOURCE
HEIGHT 26.8 KILOMETERS
RANGE 42.5 - 92.9 KILOMETERS
ZENITH ANGLES 53 - 74 DEGREES
BEAM DIVERGENCE 20 MILLIRADIANS
POINTING ERROR 0.50 MILLIRADIANS (rms)
WAVELENGTH 0.63 MICROMETERS
POWER 1.5 MILLIWATTS
RECEIVER
APERTURES . 8,16, 32, 64, 76 CENTIMETERS
OBSCURATION 20 (ON 64 AND 76) CENTIMETERS
RECEIVER FIELD 2 MILLIRADIANS
POINTING ERROR 0.5 MILLIRADIANS (PEAK)
Figure 3. System Parameters
ZA AND ALT. VS. TIME (MST)
FOR FLIGHT NO. 5
3 0 ' I ' I ' 'I ' I I I ' I
LASER ON ON OFF ON
OPERATION LOG
- 90
/+ --- +
+ +
25 /
S+ \ - 80
7 +
E+ 70
20 /" \ m
E \ z
20-60
LU.
E> z/ 0
- 15 - +. - 50 m"- II
< TROPOPAUSE _/_m
z z
Z i -40
0 5m0
-J10
_o - m,;_
5-
/ C/
/ - 10
GROUND /
LEVEL _/
0 , , , I l i I , , , I i i i 1 i I l , , I , 0
07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00
TIME OF DAY (MST)
Figure 4. Flight Profile
11
8 'lli 'I I I '' 'I
10:00 MST 19 OCT 73
6-
E
0 4-o
'-f
CIZ 2 
-
300 30
S,--WIND SPEED E20
< 250- u
x25 TEMPERATURE
uJ 10
zuJl
200 0
0 5 10 15 20 25
ALTITUDE MSL (km)
Figure 5. Turbulence Profile
ZENITH ANGLE 450 -WAVELENGTH 0.63 MICROMETERS
1.0 1 ' ' ' ' ' I
S 0.8- 0 LASER SCINTILLATION EQUATION
00
I--S /
< o-
> 0.6 = 0.7 
tu S\ S 1/2
O C/ \/ x 1/2e7/k do= 0.137 sec 8
_ 0.4 - S -L -- Q/o 063xlO-6
b8< 0C,')
z 0.2 0
0L.
N
_j
< 0.1 -
0.08
0
z
0.04 0.06 0.08 0.1 0.2 0.4 0.6 0.8 1.0 2.0
RECEIVER DIAMETER - METERS
Figure 6. Scintillation vs. Aperture
He Ne SCINTILLATION
10:20 MST 19 OCT 73
0.1 I I
-" 0.08
N
m
S0.06 - APERTURE DIAMETER 73 cm0.06 -
N 0.04
<APERTURE DIAMETER 8 cm
0
z 0.02
0 1 i I I
0 20 40 60 80 100
FREQUENCY (Hz)
z
>Figure 7. Power Spectral Density
0
cn


Vertical laser beam propagation through the troposphere

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