REVIEW OF SCIENTIFIC INSTRUMENTS 83.044501(2012) Damping and local control of mirror suspensions for laser interferometric gravitational wave detectors K.A.Strain1.a)and B.N.Shapiro2.b) SUPA School of Physics Astronomy,University of Glasgow,Glasgow G12 8QQ.Scotland, United Kingdom 2LIGO-Massachusetts Institute of Technology,Cambridge,Massachusetts 02139,USA (Received 24 February 2012;accepted 2 April 2012;published online 18 April 2012) The mirrors of laser interferometric gravitational wave detectors hang from multi-stage suspensions. These support the optics against gravity while isolating them from external vibration.Thermal noise must be kept small so mechanical loss must be minimized and the resulting structure has high-Q resonances rigid-body modes,typically in the frequency range between about 0.3 Hz and 20 Hz.Op- eration of the interferometer requires these resonances to be damped.Active damping provides the design flexibility required to achieve rapid settling with low noise.In practice there is a compromise between sensor performance,and hence cost and complexity,and sophistication of the control algo- rithm.We introduce a novel approach which combines the new technique of modal damping with methods developed from those applied in GEO 600.This approach is predicted to meet the goals for damping and for noise performance set by the Advanced LIGO project.2012 American Institute of Physics.[http://dx.doi.org/10.1063/1.4704459] I.INTRODUCTION-SUSPENSIONS the optical wavelength:1.064 um.The mirrors must be posi- FOR INTERFEROMETRIC GRAVITATIONAL tioned to <1 pm in distance along the beam direction (modulo WAVE DETECTORS half the wavelength),and of order nanoradians in angle.Sta- Following initial searches for gravitational radiation car- ble,quiet suspensions are needed even to achieve the required ried out in recent years by a network of km-scale laser inter- operating point. ferometric gravitational wave detectors,-3 the detectors are The test-mass suspensions consist of 4 cascaded pendu- currently being upgraded.The sensitivity of the LIGO detec- lum stages,as sketched in Figure 1.The mirror is suspended tors is to be improved by an order of magnitude in the fre- on fused silica fibers for low thermal noise.6 The second stage quency range around 100 Hz,with the lower frequency limit up consists of a fused silica mass supported on loops of high for observing reduced from 40 Hz to 10 Hz.The project is carbon steel wire,while the (2 x 2)upper stages are made called Advanced LIGO(aLIGO),4 and the work reported here of metal and are also suspended on wires.Each of the wire- is designed to meet the project goals. hung stages includes high-stress,maraging-steel,cantilever- An interferometric gravitational wave detector is based mounted,triangular blade springs to provide a softer system on a set of sufficiently quiet,well-separated test masses whose and hence better isolation.'The upper end of each wire is local horizontal motion follows the oscillating gravitational attached to the tip of such a spring.The thick end of each field.Sensitive interferometric readout allows the evolution spring is attached to the previous suspension stage (or to the of the relative positions of the test masses to be recorded.The mounting structure in the case of the springs supporting the gravitational field acts on the bulk,or equivalently center of top mass).We refer to each set of wires or fibers and the mass mass,of the test masses. they support as a stage,numbered from I at the top to 4 at the To enable sensing,mirror coatings are applied to the sur- bottom. faces of the test masses.It is necessary to minimize thermal The masses are considered to be rigid bodies.We choose noise in the substrate and coatings.3 Low displacement noise Euler-basis local coordinates:x for the direction sensed by the can then be achieved by hanging each test mass on a suspen- interferometer,3 for local vertical,and y orthogonal to these. sion to provide isolation from the environment.Mechanical The angles about these axes are roll,yaw,and pitch.Of these dissipation in the materials of the suspension would also lead x,pitch and yaw are sensed by the interferometer,and the oth- to thermal noise and so must be limited.Low loss materials ers cross-couple weakly into interferometer signals.The max- are employed,such as fused silica for the suspension fibers imum acceptable displacement and angular noise at the test which support the mirrors. mass are given in Table I. Operation of the interferometer requires precise align- We describe the development of control methods and al- ment of its mirrors.The suspensions must allow control of gorithms required to meet the stated performance goals for test mass separation-4 km in aLIGO,to very much less than aLIGO.We show that a combination of two control methods provides best performance.One of these "modal damping" (Sec.V)was newly developed using modern control theory, a)Electronic mail:kenneth.strain@glasgow.ac.uk. the other(Sec.VI)is an extension and refinement of methods b)Electronic mail:bshapiro@MIT.EDU. applied in GEO 600,which has operated for almost a decade. 0034-6748/2012/83(4)/044501/9/$30.00 83,044501-1 2012 American Institute of Physics Reuse of AlP Publishing content is subject to the terms at:https://publishing.aip.org/authors/nghts-and-permis Downlo8dolP:183.195251.60:Fi.22Apr2016 00:5549REVIEW OF SCIENTIFIC INSTRUMENTS 83, 044501 (2012) Damping and local control of mirror suspensions for laser interferometric gravitational wave detectors K. A. Strain1,a) and B. N. Shapiro2,b) 1SUPA School of Physics & Astronomy, University of Glasgow, Glasgow G12 8QQ, Scotland, United Kingdom 2LIGO – Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA (Received 24 February 2012; accepted 2 April 2012; published online 18 April 2012) The mirrors of laser interferometric gravitational wave detectors hang from multi-stage suspensions. These support the optics against gravity while isolating them from external vibration. Thermal noise must be kept small so mechanical loss must be minimized and the resulting structure has high-Q resonances rigid-body modes, typically in the frequency range between about 0.3 Hz and 20 Hz. Op￾eration of the interferometer requires these resonances to be damped. Active damping provides the design flexibility required to achieve rapid settling with low noise. In practice there is a compromise between sensor performance, and hence cost and complexity, and sophistication of the control algo￾rithm. We introduce a novel approach which combines the new technique of modal damping with methods developed from those applied in GEO 600. This approach is predicted to meet the goals for damping and for noise performance set by the Advanced LIGO project. © 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4704459] I. INTRODUCTION—SUSPENSIONS FOR INTERFEROMETRIC GRAVITATIONAL WAVE DETECTORS Following initial searches for gravitational radiation car￾ried out in recent years by a network of km-scale laser inter￾ferometric gravitational wave detectors,1–3 the detectors are currently being upgraded. The sensitivity of the LIGO detec￾tors is to be improved by an order of magnitude in the fre￾quency range around 100 Hz, with the lower frequency limit for observing reduced from 40 Hz to 10 Hz. The project is called Advanced LIGO (aLIGO),4 and the work reported here is designed to meet the project goals. An interferometric gravitational wave detector is based on a set of sufficiently quiet, well-separated test masses whose local horizontal motion follows the oscillating gravitational field. Sensitive interferometric readout allows the evolution of the relative positions of the test masses to be recorded. The gravitational field acts on the bulk, or equivalently center of mass, of the test masses. To enable sensing, mirror coatings are applied to the sur￾faces of the test masses. It is necessary to minimize thermal noise in the substrate and coatings.5 Low displacement noise can then be achieved by hanging each test mass on a suspen￾sion to provide isolation from the environment. Mechanical dissipation in the materials of the suspension would also lead to thermal noise and so must be limited. Low loss materials are employed, such as fused silica for the suspension fibers which support the mirrors. Operation of the interferometer requires precise align￾ment of its mirrors. The suspensions must allow control of test mass separation—4 km in aLIGO, to very much less than a)Electronic mail: kenneth.strain@glasgow.ac.uk. b)Electronic mail: bshapiro@MIT.EDU. the optical wavelength: 1.064μm. The mirrors must be posi￾tioned to <1 pm in distance along the beam direction (modulo half the wavelength), and of order nanoradians in angle. Sta￾ble, quiet suspensions are needed even to achieve the required operating point. The test-mass suspensions consist of 4 cascaded pendu￾lum stages, as sketched in Figure 1. The mirror is suspended on fused silica fibers for low thermal noise.6 The second stage up consists of a fused silica mass supported on loops of high carbon steel wire, while the (2 × 2) upper stages are made of metal and are also suspended on wires. Each of the wire￾hung stages includes high-stress, maraging-steel, cantilever￾mounted, triangular blade springs to provide a softer system and hence better isolation.7 The upper end of each wire is attached to the tip of such a spring. The thick end of each spring is attached to the previous suspension stage (or to the mounting structure in the case of the springs supporting the top mass). We refer to each set of wires or fibers and the mass they support as a stage, numbered from 1 at the top to 4 at the bottom. The masses are considered to be rigid bodies. We choose Euler-basis local coordinates: x for the direction sensed by the interferometer, z for local vertical, and y orthogonal to these. The angles about these axes are roll, yaw, and pitch. Of these x, pitch and yaw are sensed by the interferometer, and the oth￾ers cross-couple weakly into interferometer signals. The max￾imum acceptable displacement and angular noise at the test mass are given in Table I. We describe the development of control methods and al￾gorithms required to meet the stated performance goals for aLIGO. We show that a combination of two control methods provides best performance. One of these “modal damping” (Sec. V) was newly developed using modern control theory, the other (Sec. VI) is an extension and refinement of methods applied in GEO 600, which has operated for almost a decade. 0034-6748/2012/83(4)/044501/9/$30.00 © 2012 American Institute of Physics 83, 044501-1 Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 183.195.251.6 On: Fri, 22 Apr 2016 00:55:49