The three-interferometer configuration provides redundancy
against component failure, gives better detection probability,
and allows the determination of polarisation of the incoming
radiation. The spacecraft in which they are accommodated shields
each pair of proof masses from external disturbances (e.g. solar
radiation pressure). Drag free control servos enable the
spacecraft to follow the proof masses to a high level of
precision, the drag compensation being effected using
proportional electric thrusters. Illumination of the
interferometers is by highly stabilised laser light from Nd:YAG
lasers at a wavelength of 1.064 microns, laser powers of
1 W being available from monolithic, non planar ring
oscillators which are diode pumped. For each interferometer -
consisting of a central spacecraft and two distant spacecraft -
two lasers in the central spacecraft, each pointing along one of
the arms, are phase locked together so they effectively behave as
a single laser. For LISA to achieve its design performance,
adjacent arm lengths have to be sensed to an accuracy of better
than
. Because of the long distances involved and the spatial extent
of the laser beams (the diffraction limited laser spot size,
after travelling
km, is approximately 50 km in diameter), the low
photon fluxes make it impossible to use standard mirrors for
reflection; thus active mirrors with phase locked laser
transponders on the spacecraft will be implemented. Telescope
mirrors will be used to reduce diffraction losses on transmission
of the beam and to increase the collecting area for reception of
the beam. Given that the available laser power in each arm is of
the order of 1 W, and that arguments similar to those
already discussed for ground based detectors can be made,
photoelectron shot noise considerations suggest that the
diameters of the transmitting and receiving mirrors on the space
craft need to be
30 cm.
Further, just as in the case of the ground based detectors,
the presence of laser frequency noise is a limiting factor. It
leads to an error in the measurement of each arm length. If the
arms are equal these errors cancel out but if they are unequal,
the comparison of lengths used to search for gravitational waves
may be dominated by frequency noise. For the
m long arms of LISA, a difference in arm length of
m is likely. Then for a relative arm length measurement of
(the error budget level allowed in the LISA design for this
noise source), equation (12
) suggests that a laser stability of
is required, a level much better than can be achieved from the
laser on its own. Thus frequency stabilisation has to be
provided. The primary method of stabilisation is to lock the
frequency of one laser in the system on to a Fabry-Perot cavity
mounted on one of the craft - see for example [66] - and then to effectively transfer this stability to other
lasers in the system by phase locking techniques. With the
temperature fluctuations inside each craft limited in the region
of
Hz to approximately
by three stages of thermal insulation, a cavity formed of
material of low expansion coefficient such as ULE allows a
stability level of approximately
. This level of laser frequency noise is clearly much worse than
the required
and a further correction scheme is needed. Further frequency
correction is provided by comparing the phase of the light
returning in each arm with the phase of the transmitted light.
The phase difference, measured over the time of flight in the
arm, allows an estimate of laser frequency noise to be
made [92,
34,
40]. For the arm of length
L
and thus if the spectral density
is measured, the spectral density
can be estimated. This estimate can then be used to correct the
signal obtained by subtracting the phase difference measurements
in two adjacent arms, allowing the search for gravitational waves
to be carried out. This correction is made easier if each arm
length is known to a few km and the difference in arm length is
known to a few tens of metres. These quantities should be
available from radar and optical ranging measurements. If however
they are not well enough known then they can be found by
searching through a range of possible values to minimise the
effect of frequency noise on the `gravitational wave' signal.
There are many other issues associated with the laser interferometry for LISA which are not dealt with here and the interested reader should refer to [48] for a discussion of some of these.
LISA has been adopted by ESA as a Cornerstone project in their post Horizon 2000 programme and the possibility of it being a joint ESA/NASA collaborative mission is being enthusiastically addressed at present.
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Gravitational Wave Detection by Interferometry (Ground
and Space)
Sheila Rowan and Jim Hough http://www.livingreviews.org/lrr-2000-3 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |