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Satellite borne laser for adaptive optics reference
A.H. Greenaway.
Royal Signals and Radar Establishment,
St. Andrews Rd. ,
MALVERN,
WR14 3PS, U.K.
ABSTRACT
Low
power (2mW) lasers mounted on a small satellite in a highly
eccentric orbit can provide a bright and spectrally welF-defined
reference
source for calibration of ground-based adaptive optic
systems.
Because the reference is spectrally welldefined it can be
efficiently filtered in broadband imaging applications and yet can
provide a very bright ( +5 mag) reference source for wavefront
detectors when imaging faint sources. Dependent on the size of the
atmospheric isoplanatic patch, the satellite reference may be useful
for calibrating observations of selected objects for periods in excess
of 1 hour, leading to limiting magnitudes for detection of up to +30.
The area of sky for which the reference is valid is restricted (order 1
sq degree of sky per telescope per year) .
The
reference is valid for
phasing aperture synthesis telescope arrays of kilometric scale.
Orbital manoeuvers for target selection and to increase the sky
coverage will be considered.
:.
INTRODUCTION
Whilst the spectral coverage available from the ground can never
compete with that available to a space telescope, the large collecting
area available to terrestrial telescopes makes such telescopes equipped
with adaptive optics a serious alternative to a space telescope for
observations in the visible and near infra-red wavelength region. For
this reason, and to increase the observing efficiency of existing
telescopes, interest in using adaptive optic techniques for full or
partial correction of atmospheric turbulence is steadily increasing
[1-3].
The increasing interest in partial correction arises for several
reasons.
Firstly, it is very expensive to build an adaptive optic
system with a large number of actuators (or high order of correction)
and the associated electronics.
Secondly, the perturbation impressed on the starlight has to be
assessed in realtime and for this a reference source is used. The
estimation of the parameters associated with low order modes can be
made on fainter sources since, crudely, there are more photons per
parameter for lower order modes. For the same reason, a relatively
bright reference source is required. Asthe light from the reference
and that from the source under study has propagated through a different
portion of the atmosphere,
the distortion suffered by the two
wavefronts will not be identical. The angle over which the distortions
of two wavefronts decorrelate is referred to as the isoplanatic angle
and, not surprisingly, this angle is larger for lower order modes.
386
/ SPIE Vol 1494 Space Astronomical Telescopes
and
Instruments (1991)
O-8194-0603-1/91/$4.OO
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Given the relatively low Uensity of suitably bright reference sources,
the isoplanatic angle must be large if a significant fraction of the
sky is to be available for successful imaging using an adaptive optic
system.
Thirdly, the number of actuators required to achieve a given order
of correction scales as the inverse of the wavelength to a power
exceeding two, and the isoplanatic angle and relaxation time of the
atmospheric perturbations scale as the inverse of the wavelength to a
power greater than unity.
For this reason the near infrared
wavelengths are the favoured regime for adaptive optics, the longer
wavelengths being an unfavourable regime due to the increase in thermal
background radiation
[
4
1
. As has been pointed out [
5
1
, systems
designed to achieve full correction at near infra-red wavelengths will
still
achieve at least partial wavefront correction at shorter
wavelengths and this situation should be exploited.
When using adaptive optics for wavefront correction the quality of
the images obtained will be influenced by several factors.
Firstly, imperfection in the wavefront correction will reduce the
Strehi ratio in the corrected image. This will lead to leakage of
light from the image core into the wings of the point spread function,
although the expected profile for partially corrected images is still a
matter of some disagreement [
5
)
.
Whatever
the form of such leakage,
the reduced Strehl ratio will seriously impair the dynamic range
achievable from such images, as evidenced from the performance of HST.
Thus sensitivity close to the reference will be damaged by leakage from
the bright reference source and further from the reference will be
damaged by the decorrelation between the reference wavefront and that
from the source under study.
Secondly, in most cases it will not be possible to use spectral or
other differences between the source and the reference to increase the
dynamic range. An exception here is the proposed use of an artificial
reference star generated by laser excitation of the sodium ions at
about 100km altitude [
6
]
.
However
,
the narrowband source so generated
is broad in intensity profile and, being close to the ground, its
apparent direction changes by about 2 seconds of arc for every metre
the observer moves across the telescope mirror.
An alternative is to use a low power laser mounted on a small
satellite in a highly eccentric orbit.
Such a source may be kept
within two seconds of arc of selected faint sources for periods
exceeding 5000s, gives a bright, narrowband source that may be
spectrally filtered to dramatically reduce the problem of light
pollution from the reference and may be used to cophase telescope
arrays of kilometric dimensions (thus permitting extremely high angular
resolution imaging to be performed). The main disadvantages of such a
proposal (PHAROS -
{7J)
are difficulty in scheduling targets for
observation, the relatively small area of sky within the isoplanatic
angle of the satellite (order one square degree of sky per telescope
per year) and the cost associated with a satellite mission.
SPIE
Vol. 1494
Space Astronomical Telescopes and Instruments
1991)
387
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2 SUMMARY OF PERFORMANCE OF PHAROS
If
one assumes that the technological difficulties and cost
associated with development of adaptive optics capable of high order
correction will be solved over the following decade, the performance
achieved from PHAROS will be limited by anisoplanatism, the accuracy
with which the wavefront errors can be measured and the ability to
place and to maintain the apparent position of the satellite relative
to the celestial sphere.
It has been shown [7], that a 2mW laser at cislunar altitudes can
provide a reference source with apparent magnitude of +5, provided
that the diameter of the laser source at the satellite exceeds 6.3cm,
thus that beam divergence is restricted to 2 seconds of arc. To direct
the laser beam at .a co-operating ground-based telescope the pointing of
the beam must be achieved with the same level of accuracy. This
probably implies a three axis stabilised satellite, but does not appear
to be unreasonable. The position of the satellite in orbit would need
to be known by dead reckoning to about 1km.
If this level of
performance can be obtained from the satellite system, active control
of the laser pointing would not be required. Ground-based observations
would permit the satellite position to be determined to within a few
tens of metres and infrequent telemetric corrections could be used to
guide the beam or, alternatively, the satellite could intelligently
track a low power laser directed from the observatory. A reference of
magnitude +5 would facilitate estimation of the wavefront perturbation
to better than one radian accuracy.
Because a laser reference is
narrow band, it may be easily and effectively filtered from the image
so alleviating the reduction in dynamic range caused by leakage of
light due to imperfect compensation of the reference wavefront.
Attenuation of the laser by a factor of one million seems feasible
whilst
still
retaining
80
of the continuum for scientific
observations.
Calculations using simple Keplerian orbits, ignoring luni-solar
perturbations and accounting for perturbations due to the geoid shape
only at perigee, show that a satellite in a highly eccentric, 5 day
period orbit, may be kept within 2 seconds of arc of a selected target
for at least l000s. These figures refer to observations from La Palma
and object declinations between -10 and +45 degrees (figure 1).
6000
U
Ui
-
Fig
1.
Effect of declination of
target on integration time. Longest
time within 1.5 seconds of arc of
target as seen from La Palma, for
various
target
declinations
(in
degrees).
0
60
For
sources at declinations of a few degrees, the satellite may be
kept within 2 seconds of arc of a selected target for periods exceeding
5000s, giving a threshold for detection of stellar sources of +30 if
388
/ SPIE Vol. 1494 Space Astronomical Telescopes and Instruments (1991)
10
DECLINATION
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the Strehi ratio of the corrected images is assumed to approach unity
when using an 8m telescope (
figure
2).
r
Fig
2.
Limiting
magnitudes.
Diffractionlimited
limiting
1HOUR
,
magnitudes
for stellar sources against
log integration time, for detection
with signal to noise ratio 5, with
total efficiency q= 0.05 and bandpass
200nm. The three curves correspond to
telescopes of diameter 2, 4 and 8m.
The curves change slope at the point
where variations in flux from the sky
0
background,
subtracted from
the
20
STELLAR MAGNITUDE
30
1 begins
to dominate the noise.
These long integration times are achieved by matching the velocity
of the satellite at apogee to that of the ground-based observer due to
earth rotation. If the satellite were in an orbit with curvature equal
to that of the earth's surface and with velocity matching that produced
by earth rotation the satellite would appear stationary to a
terrestrial observer.
Clearly it is not possible to match the
curvature in this way, but by using a highly eccentric orbit in which
the satellite velocity at apogee is slightly slower than that produced
at the earth's surface by diurnal rotation, it may be arranged that a
terrestrial observer sees the satellite apparently execute a tight loop
around the target of interest (
figure
3 )
.
For
an observer on La Palma
and a satellite in a 5day orbit such a loop, of 1.5 second of arc
radius, can take over 5000s to complete.
Fig 3.
Effect on satellite track of
small
changes in eccentricity and
inclination.
...
e
=
0.9012;
i =
1.7210.
e
=
0.9018;
i =
1.7207.
e
=
0.9026;
i =
1.7205.
A satellite following the solid drawn
track stays within 1.5 seconds of arc
of the target for 5040 sec. The plot
shows a 4 second of arc square area of
sky centred on a target of declination
+1 degree.
Unless one is prepared to countenance major orbital manoeuvres, the
targets around which the satellite is to perform such loops would need
to be carefully prescheduled and would be few in number [7 ]
.
For
the
remainder of the time the satellite appears to wander relatively slowly
across the celestial sphere. Given this situation, it is important to
justify PHAROS in terms of the high angular resolution survey that
could be achieved by following this wandering reference. For any given
patch of sky, the satellite is only useful as a reference for adaptive
optics when it is within an isoplanatic angle centred on that patch of
sky. For any given elemental patch of the celestial sphere, the length
SPIE
Vol. 1494 Space Astronomical Telescopes
air Instruments (1991)1 389
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RA
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of time for which PHAROS co1d provide a useful reference depends on
the distance of the patch from the apparent orbit and the apparent
motion of the satellite along its track.
The limiting niagnitude
observable depends on the length of time for which the reference is
available and the size and efficiency of the telescope ( figure 2).
These considerations have been combined together to produce figure 4,
which shows the area of sky for which PHA.ROS provides a useful
reference
against the magnitude of the stellar source that is
detectable in that patch of sky.
Fig 4.
Area of sky surveyed per year
against limiting magnitude. The curves
correspond to isoplanatic patches of
semi-diameter 0.5, 1.5, 2.5 and 3.5
seconds of arc. All curves are for an
8m telescope, SNR =
5
and for a 5 day
orbit with e = 0.902
and i =
+10.98
degrees (corresponding to a target of
declination +10.5 degrees).
Each telescope using the satellite reference would achieve the level
of
sky
coverage
indicated
by
figure
4,
yielding
a
I I
unbiased
survey of approximately 1 square degree
of sky per telescope per year.
The limiting magnitude for this
hypothetical mission is +29, with most of the area surveyed having a
detection threshold of +24 magnitudes. Partial correction of wavefront
distortions would be valid over larger angles than the isoplanatic
angle mentioned bo, but would give poorer Strehi ratios [ 1 J .
The
combination of these effects would move the curves in figure 4 upward
and to the left.
The
sky
coverage obtained consists of a series of narrow,
diffraction-limited strips, with extended areas on either side for
which only partial correction would be achieved. Unless major orbital
manoevres were undertaken, the satellite orbit is essentially inertial
with respect to the sun, as a result of which the satellite is
available as a night-time reference object every night for 135 nights
and for some nights over a 245 day period ( figure 5).
Fig 5.
Histogram showing the number
of
minutes
per
night
that the
satellite has a zenith angle less than
45 degrees as seen by an observer on
La Palma. The ticks on the horizontal
axis
correspond
to the satellite
apogee every 5 days. On day 122 the
apogee
is
synchronized
with the
observer' s midnight.
390
/ SPIE Vol. 1494 Space
Astronomical
Telescopes aix Instruments (1991)
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Fig 6. The satellite orbit is almost
inertial with respect to the solar
system and, in consequence, for half
of the year is at apogee during the
observer's daytime.
The short lines
indicate the angles within 45 degrees
of the observer's zenith at midnight.
Two velocity impulses could be used to
rotate the axes of the orbit by 180
degrees, but the impulses required are
too large to be of practical value.
This may be understood by reference to figure 6, where the
relationship
between the
orbit
and the observer's night-time
observation cone is shown and to figure 7, where it is shown that a
satellite in an appropriate orbit is within 45 degrees of the
observer's meridian for every night when the satellite perigee is time
to coincide with the observer's midday.
Fig. 7. The satellite spends only 12
hours to the left of the dotted lines.
When apogee is synchronized to the
observer's midnight the satellite will
be within 45 degrees of the midnight
zenith for several hours every night.
The footprint of the laser beam at the observatory would be a few
kilometres in diameter and, if several lasers of different colour were
used to reduce the coherence length of the reference beam, the
satellite could be used to cophase the wavefronts in an interferometric
system with kilometric baselines. Using several laser would offer the
additional
advantage that different observatories could use the
satellite simultaneously in order to increase sky coverage (figure 8).
1202
DEC
( MINS)
______________________________
940
1121
RA(HRSMINS)
1036
Fig
8. Apparent positions of the satellite from 13 observatories over
a 24 hr period. The heavy marks indicate when the satellite has zenith
angles less than 45 degrees during an observer's nighttime (defined as
20h00 to 04h00 local solar time).
SPIE Vol. 1494 Space Astronomical Telescopes
aix
Instruments (1991) 391
I-
': -: ..
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3 MANOEUVRES DURING ORBIT
The satellite could be made available for use as a reference
throughout the whole year if a velocity impulse were applied at apogee
to convert the orbit to a circular orbit, followed by an equal and
opposite impulse half an orbit later. This inanoeuver would effectively
rotate the semi axes of the orbit through 180 degrees in the orbital
plane. To achieve such a manoeuvre would require a velocity impulse in
excess of 2km per sec, hardly a minor manoeuvre and thus rather
impractical.
Suitable orbits have periods of 4 days or more. A period of 5 days
and eccentricity of 0.910.005 appears to be most suitable. Changes in
eccentricity of this magnitude can be achieved with velocity impulses
of a few metres per sec applied at apogee and such minor manoeuvres
should therefore be quite practical. In addition, minor orbital
corrections to position the satellite for selected targets should be
possible using relative low thrust engines. To accurately compute the
impulses required for orbital manoeuvres would require perturbations
from luni-solar effects and from the earth's shape to be taken into
account.
However, such orbits have a perigee altitude of several
thousand kilometres and thus atmospheric drag should be negligible.
Velocity impulses to change the orbital inclination are most
efficiently applied at a node of the orbit
[
8
,
but
even so are
expensive manoeuvres and would not be practical.
For these reasons, minor re-positioning of the satellite to optiinise
the orbit for a small number of target objects would appear quite
feasible, but this would restrict the choice of specific targets to a
few objects over an hour or so in right ascension and a few degrees in
declination (
figure
8).
4 DISCUSSION
A satellite at apogee in the proposed orbit suffers an apparent
change in direction of one second of arc for a 1km shift iii the
observer's position.
Thus the reference provided by the satellite
would be within the isoplanatic patch for a ground-based aperture
synthesis array of kilometric diameter.
To permit such a dilute
aperture instrument to be accurately cophased it would be necessary to
reduce the coherence length of the reference beam. This could be
achieved by using lasers of differing wavelength.
Matching the
separation of the laser wavelengths to the free spectral range would
permit use of a single Fabry-Perot etalon to filter all the laser
reference beams from the continuum used for scientific observations
[
7
:i
.
Used
in cooperation with groundbased telescope arrays currently
considered or under construction
[
9
3 ,
the
laser reference would
facilitate a very high angular resolution survey of the sky with a very
faint magnitude limit. Unfortunately, only a small pre-defined portion
of the sky would be available to such a survey. Use of several lasers
would be necessary if several qbservatories were to use the satellite
simultaneously to image different sources or to increase sky coverage.
392
/ SPIE Vol. 1494 Space
Astronomical
Telescopes aix/Instruments (1991)
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