Alex Abramovici

LIGO: The Laser Interferometer Gravitational-Wave Observatory

The goal of the Laser Interferometer Gravitational-Wave Observatory (LIGO) Project is to detect and study astrophysical gravitational waves and use data from them for research in physics and astronomy. LIGO will support studies concerning the nature and nonlinear dynamics of gravity, the structures of black holes, and the equation of state of nuclear matter. It will also measure the masses, birth rates, collisions, and distributions of black holes and neutron stars in the universe and probe the cores of supernovae and the very early universe. The technology for LIGO has been developed during the past 20 years. Construction will begin in 1992, and under the present schedule, LIGOs gravitational-wave searches will begin in 1998.

IMPROVED SENSITIVITY IN A GRAVITATIONAL WAVE INTERFEROMETER AND IMPLICATIONS FOR LIGO

Sensitivity enhancements in the laser interferometer gravitational wave observatory (LIGO) projects 40 m interferometer have been achieved through two major instrumental improvements. Improved vibration isolation has reduced the noise due to ground motion. New test masses with less mechanical dissipation were installed to lower the thermal noise associated with mirror vibrations. The minimum interferometer noise (square root of the spectral density of apparent differential displacement) reached 3 x 10^(-19) m/Hz^(1/2) near 450 Hz.

The StarLight metrology subsystem

We describe a metrology subsystem for NASAs StarLight mission, a space-based separated-spacecraft stellar interferometer. It consists of dual-target linear metrology, based on a heterodyne interferometer with carrier phase modulation, and angular metrology designed to sense the pointing of the laser beam. The dual-target operation enables one metrology beam to sense displacement of two targets independently. We present the current design, breadboard implementation of the metrology subsystem in a stellar interferometer testbed and the present state of development of flight qualifiable subsystem components.

Photoelastic measurement of anelasticity and its implications for gravitational wave interferometers

We have developed a method to determine the internal friction over a wide range of frequencies in transparent materials such as fused silica. We measure the anelastic aftereffect, the relaxation of a sample after a steady stress is removed, by sensing the polarization of a beam of light that traverses the sample. The fractional relaxation of the sample on a given time scale is a direct measure of the anelastic loss angle of the material at the corresponding frequency. To date, we have achieved sensitivity to loss angles as small as 10−6. We discuss the relevance of these measurements for the design of interferometric detectors of gravitational waves.

Optical Metrology System for Radar Phase Correction on Large Flexible Structure

In aerospace applications there is an increasing interest in metrology systems. Metrology systems are used in applications such as wave front correction and formation flying, for measuring deployable structure deformation/oscillations, and as the crude stage for interferometer missions. In this paper we describe a concept for a metrology system. The metrology system concept will be able to determine the Cartesian (x,y,z) coordinates of 100+ fiducials to an accuracy of 1 mm with an update rate of 10 Hz. Considerable deployment uncertainty can be accepted. The system operates by laser illuminated fiducials feed through optical fibers. One fiducial is illuminated at a time. A camera reads the transverse position of the fiducial, and the distance to the fiducial is determined by modulating the laser light and measuring a phase difference. The inertial orientation of the structure is measured by imaging the stars. A metrology system as described is essential to a radar antenna on a large flexible structure.

Design and Troubleshooting

The steps of the design process, outlined in the previous Chapter, are explained in detail in what follows. The points where one has to chose between moving on or iterating some previous steps are highlighted. The design activity is considered complete when the new system has been tested and found to perform as specified. The structure of the FCS design flow has been discussed in Section 1.3 of the previous Chapter. Here it will be assumed that: 1 The top-level requirements for the system have been defined. In other words, it has been determined what the system is supposed to accomplish. 2 The frequency response of the passive plant has been simplified as much as it seemed possible with a reasonable level of effort1and the need to supplement it with a FCS has been established.

Flexible Elements and Stability

Practical control applications sometimes require that an object be moved. In the example of Fig. 11.1a, a mirror needs to be moved in order to maintain constant the optical path between it and another mirror. Changes in the optical path can be measured with an interferometric gauge. A FCS can be arranged by using the interferometer output as the error signal, which is processed by a compensator and then used to drive a piezo-electric (PZT) actuator supporting one of the mirrors. What can make this kind of arrangement tricky is the fact that the structure which connects the two mirrors is not infinitely rigid. When the PZT moves the mirror, a reaction force acts on the structure. If control is effected at frequencies at or close to structural resonances, the amplitude and phase of the open-loop frequency response is changed and instability may result. The negative effect of structure flexibility on FCS stability and some ways to mitigate it are discussed below.

Two Sensors for One Variable

In some cases, it may happen that one sensor has adequate low-frequency resolution, but cannot follow fast variations of the variable x while another sensor is fast enough, but has poor low-frequency resolution. The solution then is to combine the outputs of the two sensors as shown in Fig. 10.1 below. This is another special case of MIMO, called MISO (Multi-Input-Single-Output) which can be handled without having to call upon full-fledged MIMO formalism.

Multiple Signal Paths

In many applications, the loop configurations considered so far are insufficient for achieving the design goals. Often, adding new signal paths in parallel with the initial path can help. Three useful arrangements are presented in this section. The formal equivalence between these arrangements is emphasized, and is used to derive a stability criterion useful for designing loops with almost-maximum gain. In order to make it easier to carry out a unified discussion of control configurations with multiple paths, Fig. 2.1 is modified as shown in Fig. 7.1 on p. 100. The change consists of renaming the gain blocks, selecting a case with zero reference (control) input and rotating the various elements around the loop. These changes do not have any effect on the open-loop gainL.Therefore, reference tracking and disturbance suppression, as well as stability properties are the same for all diagrams shown in Fig. 7.1 Diagrams like the bottom one in Fig. 7.1 will be used throughout this chapter.

Active Null Measurements

In many applications where a parameter needs to be measured, available sensors are adequate in all respects, except that the range of variation of the parameter exceeds sensor range. For example, if a measurement of the angular coordinates of a flying aircraft needs to be carried out, a digital CCD camera is often appropriate, except for its field of view being to narrow to cover all possible positions of the aircraft in the sky. This shortcoming can be sidestepped by using a tracking arrangement like in Fig. 4.1, p. 37 to force the camera to follow the aircraft. As noted in Section 6.3, the correction signal is a measure of the disturbance, which in this case is the motion of the aircraft. Measuring a free-running parameter xfr.consisting of the plant output polluted by a disturbance, by sensing it, using the sensor in a FCS where an actuator nulls the value ofx fr and using the correction signalx, as a representation ofx fr is known as active null measurement. The system is set in the nulling mode by setting e r = 0. Another situation where an active null measurement may be useful is when the sensor has a strong nonlinearity, which makes calibration difficult. A better measurement can then be carried out if one can arrange for a more linear actuator and if it is possible to include all these parts into the same FCS.