As another example of physics essentially .inaccessible to .the .classical tests, gravitational waves can provide polarization information equivalent to identifying the spin content of the gravitational interaction. The operation of the Caltech interferometer (its optics, electronics and sensitivity) is described in Chapter 2.
THE CALTECH 40 MEI'ER INTERFEROMETER
Noise Sources
I will discuss some of the sources of noise that the CIT interferometer faces - from the standard quantum limit which is currently irrelevant, to the thermal noise of the test mass. Where thermal noise poses more of a ditiiculty is in the vibrational modes of the test mass itself.
PERIODIC SOURCES
The gain of the gain brought the signal to a few volts rms so that. 6 Hz, is given by the capacitance of the fast piezo mirror and the series resistance.
FREQUENCY STANDARD
LOCK C>----1 CAVITY 2 CPU
30 mins of DATA
Timing Verification and .Monitoring
To check whether the synthesizer's rubidium standard or phase lock is out of standard, a 1 MHz sinusoid generated by the synthesizer was mixed with a signal from a furnace-controlled quartz crystal. The secular increase in frequency during the experiment is part of a larger periodic variation due to Earth's orbit around the Sun. The resulting beat note was recorded on a strip chart recorder for the duration of the experiment.
Each time the CPU changed the synthesizer frequency, the old value was read from the synthesizer and printed along with the new value and the clock. At every million (106) pulse cycles (min), the time in microseconds from the beginning of the observation period was stored in a register and displayed by a 12-digit LED array. From each recorded record, I calculated the cGmplex amplitude of the interferometer motion at the pulsar frequency and its first harmonic.
This involved a change of units from ADC volts to differential length change, as described in the previous chapter, and a calculation of the Fourier sine and cosine components.
Records from Tape
The calculation of the Fourier component was complicated by the speed and size limitations of the HP-85 computer. Finally, the conversion from volts to meters of differential motion in both arms of the interferometer was used. The result is a 1024-sample longitude difference time record synchronized with the pulsar and averaged over a 30-minute period.
Memory and speed limitations of the small desktop computer used forced a clumsy calculation. Instead of multiplying the 1024 sample vector by cosine and sine the simple way, I folded it into a sfugle 16 sample vector that represents about 1 cycle of the fundamental. The uncertainty in the real and imaginary parts of the amplitude calculated above is therefore given by.
If the two arms of the interferometer are directed along mutually orthogonal unit vectors, H and L, then this response is given by.
APPARENT LATITUDE
In terms of the pulsar's declination, 6, the apparent latitude of the detector, A, and the phase of the Earth's rotation, rp, (rp=O when the detector is closest to the pulsar), the response: . This was possible with our single detector due to the orthogonality of the response functions for the independent polarizations and the fact that our observation period uniformly covered an essentially integer number. The sensitivity of the detector to each polarization of gravitational radiation as a function of time.
The center of the plot is 12 side hours later with the detector on the other side of the Earth. This can be thought of as the change in units from the differential strain in the detector orientation to the differential strain in the x, y, z coordinates. The slight reduction in magnitudes is a systematic effect introduced by calculating the complex amplitudes from each time record, as discussed earlier in this chapter.
When making comparisons between the data described in the next chapter and pulsar models or electromagnetic pulse data, these phases can be important.
RESULTS AND CONCLUSIONS
The Run
During the first 24 hours of work, the temperature in the laboratory was particularly stable due to the prevailing cloudy weather. The air conditioner was also more efficient due to the light load on the cold water supply over the weekend. The effect of these temperature changes is clearly visible in the quality of the data collected (Figure 6.1).
Shown are the magnitudes of the 642 Hz Fourier component of each tape recording saved during the run. Increased demand on the campus cooling water supply during the hot hours of the day reduced the efficiency of both the air conditioning and the laser cooling water heat exchanger. The weighted sizes are noticeably larger during the first and last days of the experiment than during the intermediate days.
The line thickness is due to low-frequency changes in the orientation of the test masses.
FIRST CAVITY
The uncertainty represented by 0', the mean of CTRe and CTim· is consistent with the variance used to weight the time domain data. Assuming that the distribution of complex amplitudes is Gaussian, in the real and imaginary part, with variance a2 and negligible offset from the origin, the magnitude distribution is given by the Rayleigh distribution.
Magnitude I Sigma
Magnitude Distribution
The same as in Figure 6.8 except that for each point in the spectrum, indexed by a shift of i, the 1284Hz magnitudes at 2i+1 were included in the sum of squares instead of the magnitudes at 2i. The same as in Figure 6.8 except that for each point in the spectrum, indexed by a shift of i, the 1284Hz magnitudes at 2i-1 were included in the sum of squares instead of the magnitudes at 2i. However, systematic variations in the weighting of the data may allow a constant signal to appear in the "cross" polarization.
A higher precession frequency would shift the gravitational radiation from the center frequency of 1284 Hz. Interestingly, the maximized ratio sets the angle of inclination of the angular momentum to the sky at 94° (90° being in the plane of the sky). This is surprising because the profile of the electromagnetic pulse shows that the angular momentum vector may indeed be almost in the plane of the sky.
This is most easily explained by an angular momentum in the plane of the sky and a perpendicularly aligned dipole field.
DESIGN OF THE TESf MASS AND POINTING CONTROL SYSI'EM
Control Block
The high Q mode of the suspension pendulum can be artificially damped by applying suitable forces to the test mass. Two piezoelectric flexing discs pull two of the three suspension wires to a location a few centimeters below the control block (Figure A.3). The wires are attached to the centers of the adjacent sides of the control block and are held under tension by opposing springs (Figure A.4).
One corner of the control block is connected to the cone of a speaker by a thin wire. The spring that opposes the translational restriction on the same side is offset to compensate for the tension in the speaker cone. Two thin wires clamp to adjacent sides of the control block and ultimately connect to two additional speaker cones above.
TILT LOUDSPEAKER
MOVABLE CLAMP
7 shows details of the converter support along with its relationship to the control block and lead/rubber isolation assembly. These restraints precisely determine the position of the transducer mount so that it cannot rock or slide. The inside of the transducer mount shows its relationship to the control block and test mass.
The rubber bottoms rest on an aluminum frame which is bolted to the bottom of the tank. I believe this is representative of frequencies above the resonant frequencies of the building, around 10 Hz. Conservative estimates of quality factors place test mass drift due to ambient ground noise below 5xl0-29m/..JHZ at 1kHz.
The closed-loop effect on the error signal is shown in Figure A.10.
HELIUM NEON LASER
LOUDSPEAKER ROTATION FEEDBACK
PIEZOELECTRIC LONGITUDINAL TRANSDUCER
SENSITIVE PHOTOOIODE
TILT FEEDBACK
Auxiliary Michelson Interferometer
The pendulum mode of the suspension also loads the dynamic range of the interferometer cavity loops. For this reason, a small speed-dependent voltage is applied to some of the PETs at the pendulum suspension point to damp the differential length change between the two cavities. The quarter-wave plate (A./4) in front of the 130-foot radius of curvature mirror on Louie rotates the linear polarization of the light in the second arm by 90 inches so that it is distinguishable from the light flowing through the first arm.
Light exiting a Michelson beam splitter gate is split according to polarization and provides global orientation information to position-sensitive photodiodes. To obtain a quadrature signal, one of the polarizations is modulated in phase before combining in the polarizer. The photodiode signal contains a fringe signal at DC and its quadrature at the modulation frequency.
The sign of the quadrature signal determines whether the differential length is increasing or decreasing.
AUXILIARY MICHELSON INTERFEROMETER POSITION SENSITIVE PHOTODIODES TO LOUIE GLOBAL POINTING I -
POLARIZING BEAM
LOCK-IN AMPLIFIERI
It differs and acts weakly on two of the pusher PET wires - one in each cavity. I have devoted this last part of the appendix to a subject which demonstrates the effectiveness of the design described up to this point. The control block, however, will rotate around the intersection of the lines defined by the limit wires.
If that point does not coincide with the support wire contact, the center of the control block will translate. Misalignment of one restraint wire causes coupling to only one of the PETs, so it was a simple matter to minimize the effect. When misadjusted, rotation of the control block causes it to translate horizontally in both directions, which in turn creates a mechanical resonance (dashed lines).
1979, ed., Sources of Gra:uitational Radiation, Proceedings of the Battelle Seattle Workshop, 24 juli - 4 augustus 1978 (Cambridge University Press).
