pharos 1991

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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.

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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.

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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

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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

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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.

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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).

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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.

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