Pre-Phase A Report - Lisa - Nasa

3.1 The interferometer 63
signal should be stable enough to contribute a level of phase noise less than that from an
arm length change of 2×10−12 m/ √ Hz , i.e. δφ < 1.2×10−5 rad/ √ Hz . The noise δF of
the clock frequency F is related to the phase noise δφ at any frequency f by δF = f ×δφ,
so at 10−3 Hz we require a clock with a noise δF ≤ 1.2×10−8 Hz/ √ Hz .
If the clock frequency is, say, 15 MHz, the required relative stability of the clock is approximately
8×10−16 / √ Hz, an Allan variance2 of 3×10−17 at 10−3 Hz. This demand is
considerably stronger than can be fulfilled by any flight qualified USO currently available;
for example the one used on the Mars Observer had an Allan variance of 2×10−13 at 10−3 Hz. The stability of the USO can however be improved to the desired level by
modulating the clock frequency onto the laser light and stabilising this frequency to the
arm length in a scheme analogous to that used to stabilise the laser frequency. To be
more precise the USO in the master spacecraft is considered as the master oscillator in
the system, and its phase fluctuations are measured by comparing the phase of the outgoing
200 MHz modulation sidebands with the incoming ones in one arm, the incoming
ones being offset by a given frequency determined by an NPRO on the distant spacecraft.
The presence of this offset is essential to allow the phase measuring system to separate
the signals related to the beating of the sidebands from the signals related to the beating
of the carriers. It should be noted that the phase measuring system requires an accurate
measurement of the relevant Doppler signal also to be given to it.
Note that the USO on each craft is effectively phase locked to the master USO by controlling
an NPRO on the output of each by means of a signal derived from the beating
of the modulation sidebands on the incoming and outgoing light. This is elaborated in
Section 4.3.3 .
3.1.7 Thermal stability
A high level of thermal stability is required by the interferometer. Thermal variation
of the optical cavity to which the lasers are stabilized introduces phase variations in
the interferometer signal, which have to be corrected for by using data from the two
arms separately. Thermally induced variations in the dimensions of the transmit/receive
telescope will lead to changes in the optical path length. Variations in the dimensions of
the spacecraft will change the positions of components which cause a change in the mass
distribution and hence cause an acceleration of the proof mass.
The thermal stability needed is achieved by using structural materials with low thermal
expansion coefficient and by using multiple stages of thermal isolation. The spacecraft and
payload structural elements will be made of composite materials with thermal expansion
coefficient less than 1×10−6 /K. The optical bench and telescope are supported by the
payload cylinder which is weakly thermally coupled to the payload thermal shield which
in turn is weakly coupled to the spacecraft body. This provides three stages of thermal
isolation for the payload from solar and spacecraft electronics thermal input.
The main source of thermal variation is due to changes in the solar intensity around its
mean value of 1350 W m−2 . Observed insolation variations from 0.1 mHz to 10 mHz can
2For a clock with white frequency noise, the relationship between the Allan variance and the relative
frequency stability of the clock at a Fourier frequency f is given by σAllan = √
2ln2× δF/F × √ f .
Corrected version 2.08 3-3-1999 9:33