It has been proposed to use a high energy pulsed laser to beam power into space for satellites or a lunar base. The effects of atmospheric transmission are critical to such a system. Thermal blooming in the atmosphere can cause the beam to spread rapidly. Atmospheric turbulence can cause beam bending or beam spreading, resulting in the loss of transmitted energy that fails to hit the target receiver

Leland, Robert P.

English

NASA Technical Reports Server

1992
NASA/ASEE SUMMER FACULTY FELLOWSH-P PROGRAM
MARSHALL SPACE FLIGHT CENTER
THE UNIVERSITY OF ALABAMA
ADAPTIVE OPTICS FOR LASER POWER BEAMING
Prepared By:
Academic Rank:
Institution and
Department:
Robert P. Leland, Ph.D.
Assistant Professor
The University of Alabama
Department of Electrical Engineering
NASA/MSFC:
Division:
Branch:
MSFC Colleague:
Guidance, Control, and Optical Systems
Optical Systems
James Bilbro
XXVIII
https://ntrs.nasa.gov/search.jsp?R=19930008118 2020-03-17T09:11:55+00:00Z

It has been proposed to use a high energy pulsed laser to beam
power into space for satellites or a lunar base. The effects of
atmospheric transmission are critical to such a system. Thermal
blooming in the atmosphere can cause the beam to spread rapidly.
Atmospheric turbulence can cause beam bending or beam spreading,
resulting in the loss of transmitted energy that fails to hit the
target receiver.
If the laser beam is expanded to a width of 12 m using a
Cassegrain beam expander, and the beam is collimated, thermal
blooming will be minimized. An adaptive optics system has been
proposed to compensate for the effects of turbulence. The
primary mirror is made up of hexagonal segments which can each
be moved in a piston or two axis tilt manner. A Hartmann Shack
sensor is used to measure the wavefront of radiation from a distant
source, called a beacon. In our case, the beacon is a ''spot''
formed by the reflection of a laser beam by atmospheric aerosols,
referred to as an artificial guide star. A laser pulse is
transmitted into the atmosphere, and the wavefront of the radiation
reflected by aerosols at a desired altitude is measured and used
to impose a wavefront correction on the shape of the primary mirror.
The next laser pulse is transmitted with this correction, which
compensates for the effects of turbulence. The system is shown in
Figure 1 below.
Laser
Primary Mirror /_ Aer@sol
/k
/_) / / Target
> o
Pri_a_ user A _ "_.'. G_ia.
• • . Star
'_,
) " .'
Wavefront Sensor [
coherent Detector [Control ler _ SFingsUrso:
Figure I.
The goal of the adaptive optics system is to obtain a
diffraction limited 12 meter collimated beam at a given altitude.
We consider three schemes for creating beacons using artificial
guide stars, and the resulting system performance.
XXVIII-I
Case I. Entire 12 m Beam Used as Guide Star.
Suppose the reflection from the 12 meter beam itself is used
as a beacon. This idea is attractive, since we will be getting
a return signal from all points of the 12 m beam at the chosen
altitude. However the beacon occupies an area larger than the
isoplanatic patch. To calculate the isoplanatic patch, we assume
the mean turbulence profile of the Hufnagel-Valley-Boundary model:
C_(h) = .374"(2.2E-53 hl%xp(-h/1000) + I.E-16 exp(-h/1500)
-_I_
+ 1.7E-14 exp(-hll00)) m
This turbulence profile corresponds to a value of the Fried
coherence length of r0 = 23 cm for a I_ wavelength, which would be
i0 cm for visible light. The isoplanatic angle _p and isoplanatic
patch D2p are shown in Table 1 for several guide star altitudes.
Altitude kln _2_ arc sec D_p m
7 29.3 1.99
12 12.2 1.42
30 8.2 2.38
60 8.2 4.76
90 8.2 7.13
Table i. Isoplanatic angle _p and patch diameter D2p
The data in Figure 2 assumes the laser is pointed vertically, and
that there is no significant turbulence layer at tropopause (about
12 - 15 km). A significant turbulence layer at tropopause would
greatly reduce the isoplanatic angle for guide stars above 15 km,
as would deflection of the beam from vertical. At 90 km the guide
star is assumed to be formed by exciting the sodium layer. At 60 km
the concentration of aerosols is extremely low.
Since the beam diameter is larger than the isoplanatic patch,
we cannot use the return from the entire beam for wavefront
correction. Since the Hartmann wavefront sensor will use coherent
detection, the signal to noise ratio in the wavefront measurement
will be decreased due to speckle from the 12 m beacon. Hence use of
the entire 12 m beam for wavefront correction appears infeasible.
Case 2. Single Guide Star with Small Radius.
An alternative approach is to produce a smaller guide star
with a second laser. This avoids the problems of signal loss due
to speckle. Anisoplanatism is still a problem, however, since the
primary mirror aperture is larger than the isoplanatic patch at any
of the altitudes under consideration. Hence a single guide star
cannot be used to correct the effects of turbulence over a 12 m
aperture.
XXVIII-2
Case 3. Multiple Guide Stars.
For ground based large aperture telescopes it has been
proposed to use multiple guide stars, and to correct the wavefront
on the subaperture of the mirror directly below a guide star based
on the return from that star. In this manner, the effects of
anisoplanatism are greatly reduced. This technique could be used
for the laser power beaming problem. Each guide star would be used
to correct the part of the beam expander mirror within an area that
is a fraction of the the isoplanatic patch around the guide star.
In this way the part of the beam in the isoplanatic patch around the
guide star will be corrected for turbulence effects, relative to
the position of the guide star. The number of _aide stars needed
depends on the diameter of the primary mirror aperture and the size
of the isoplanatic patch. For wavefront correction with rms error
of _ /I0, it is required that
Ngs = (1.25 D/mip)_
where Ngs is the number of guide stars, and D is the mirror
aperture, 12 m in this case. The number of guide stars required
at several altitudes is given in Table 2 below.
Altitude km Number of Guide Stars (Ngs)
7 57
12 112
30 40
60 I0
90 5
Table 2. Multiple Guide Star Requirements
Power Considerations:
Each guide star at a given altitude requires sufficient
brightness, or laser power, in order to provide enough photons
for each cell of the Hartmann sensor to produce a wavefront slope
measurement. If the guide stars are created at higher altitudes,
we require more power per star, since the density of aerosols is
lower, however we need fewer stars. Hence the _mount of power
needed to produce 57 guide stars at 7 km is less than that needed
to produce 40 guide stars at 30 km. However, guide stars at 30 km
could be used to correct for turbulence at tropopause, whereas
wavefront correction based on a star at 7 km would be limited to
turbulence in the boundary layer and a few kilometers above.
Since the most intense turbulence is in the boundary layer, a guide
star at 7 km may yield good performance. In addition, it is easier
to precisely position the guide stars at the lower altitude, since
the angular separation between them is greater.
XXVIII-3
Referencing and Positioning of Multiple Guide Stars
Since our beacon is in the atmosphere, and not on the target,
no correction can be made for pointing errors, or overall tilt of
the wavefront. When using multiple guide stars, the average tilt
of the wavefront over the subaperture around each guide star
cannot be corrected. If the guide stars are positioned correctly
with respect to each other, this does not present a problem.
However if the guide stars spread out, then the corrected beam will
also spread. Hence it is required that the guide stars
be positioned accurately with respect to each other. In an
experiment on Mt. Haleakala, Maul, Hawaii [2], two guide stars were
produced about 30 cm apart at an altitude of 6 km. A second
telescope was used to verify the position of two guide stars.
Production and Sensing of Multiple Guide Stars
In the Mt. Haleakala experiment, the guide stars were produced
by two staggered pulsed lasers, and a switching tip-tilt mirror. In
this manner, by gating the returns from the guide stars, the returns
from each star could be separated and associated with the
corresponding primary mirror subaperture. This approach is not
practical for larger numbers of guide stars, since the delay time
between sensing the wavefront and transmitting the corrected laser
pulse must be less than about I0 ms. In the multidither
approach the wavelength of each guide star is shifted about _ /15
so that each star has its own frequency, and can be discriminated
using coherent detection. A third approach is to produce an array
of guide stars, and use appropriate stopping and vignetting in the
optical path so that each cell in the Hartmann sensor sees a single
guide star through an appropriate subaperture of the primary
mirror. The wavefront sensor would be located behind the primary
mirror in the optical path and a beam splitter would be required in
the path of the primary laser. Wavefront sensors could not be
integrated into the primary mirror segments, as is currently being
discussed. The multidither approach would allow the wavefront
sensors to be integrated into the mirror segments.
Conclusions
Turbulence compensation for a 12 m laser beam will require
multiple guide stars produced by a second laser. The number of
guide stars required at various altitudes was calculated. The
potential costs and benefits of using low or high altitude guide
stars were discussed in terms of power requirements, positioning
and wavefront correction.
References
I. Gardner, C.S., Welsh, B.M., _Design and Performance Analysis
of Adaptive Optical Telescopes Using Laser Guide Stars'',
IEEE Procedings, Vol. 78, No. II, Nov. 1990.
2. Murphy, D., Primmerman, C., Zollars, B., Barclay, H.,
'' Experimental Demonstration of Atmospheric Compensation
Using Multiple Synthetic Beacons'', submitted for publication.
XXVIII-4


Adaptive optics for laser power beaming

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