Pre-Phase A Report - Lisa - Nasa

100 Chapter 4 Measurement Sensitivity
4.3 Signal extraction
4.3.1 Phase measurement
Information is extracted from the beat signal as a time series of phase measurements. The
phase of the beat signal between the received and transmitted beams is measured with
the time base provided by the on-board USO in each of the spacecraft. The two laser
beams being beat together have different frequencies because of gradual changes in arm
length and because of the roughly 10 kHz offset frequencies used in the locking scheme.
The expected Doppler shifts for arms 1 and 2 (see Sections 3.1.1 and 3.1.2 and Figure 3.1)
are of the order of 1 MHz for annual orbit corrections, and could be kept below 20 kHz if
necessary by monthly orbit corrections. For arm 3, the Doppler shifts may be as high as
15 MHz.
The phase of the laser heterodyne signals needs to be measured with an accuracy much
better than the total error allocation of 40 pm/ √ Hz and with a dynamic range of roughly
109 in order to perform the laser phase noise cancellation scheme. Forty picometers
corresponds to 4×10−5 of a cycle, and the expected laser phase noise was estimated earlier
to be roughly 30 Hz/ √ Hz at 1 mHz (see Section 3.1.5). This corresponds to roughly
3000 cy/ √ Hz for the phase noise at 1 mHz . In order to measure the phase to the necessary
accuracy and with the desired dynamic range, the signal from each optical heterodyne
detector is beat again against a suitable reference frequency from a comb of frequencies
separated by intervals of 50 kHz, which are generated from the USO. The reference frequencies
are chosen to place the final beat frequencies in the range of 75 to 125 kHz. A
tracking filter is then used to remove phase noise above roughly 100 Hz in order to prevent
aliasing of such noise into the phase measurements.
The resulting signals are then sent to the phase meters, where they are strongly amplified,
clipped, differentiated, and clipped again to give positive-going zero-crossing pulses with
standard shapes. In each measurement interval, the delay between the USO clock pulse
defining the interval start and the next zero-crossing pulse is timed, and the total number
of zero-crossing pulses is counted. From this information the integer and fractional
numbers of zero crossings are determined for each interval. The results are then filtered
to remove phase variations at frequencies above about 1 Hz, and the data set is reduced
to a time delay and a count every 0.5 s.
4.3.2 Laser noise
The data are affected by the phase noise of the master laser in S/C 1, as well as orbital
motions and gravitational waves affecting the long arms. However, the variations in the
arm lengths in the frequency band of interest, roughly 0.1 mHz to 1 Hz, are small. Thus
the apparent variations in the length of any of the arms can be analyzed to determine the
laser phase noise as a function of time. For simplicity only arms 1 and 2 will be discussed
here, but similar results can be obtained for observables that include arm 3 also.
The accuracy of the phase noise measurements will be degraded near harmonics of the
frequencies corresponding to the round-trip travel times for the two arms. A weighted
mean of the results for the two arms can be used to avoid this problem, but we assume
3-3-1999 9:33 Corrected version 2.08