The Virgo automatic alignment system - Noise in Physical System

INSTITUTE OF PHYSICS PUBLISHING Class. Quantum Grav. 23 (2006) S91–S101

CLASSICAL AND QUANTUM GRAVITY

doi:10.1088/0264-9381/23/8/S13

The Virgo automatic alignment system F Acernese1, P Amico2, M Al-Shourbagy3, S Aoudia4, S Avino1, D Babusci5, G Ballardin6, R Barillé6, F Barone1, L Barsotti3, M Barsuglia7, F Beauville8, M A Bizouard7, C Boccara9, F Bondu4, L Bosi2, C Bradaschia3, S Braccini3, A Brillet4, V Brisson7, L Brocco10, D Buskulic8, E Calloni1, E Campagna11, F Cavalier7, R Cavalieri6, G Cella3, E Chassande-Mottin4, C Corda3, A-C Clapson7, F Cleva4, J-P Coulon4, E Cuoco6, V Dattilo6, M Davier7, R De Rosa1, L Di Fiore1, A Di Virgilio3, B Dujardin4, A Eleuteri1, D Enard6, I Ferrante3, F Fidecaro3, I Fiori3, R Flaminio8,6, J-D Fournier4, S Frasca10, F Frasconi6,3, A Freise6, L Gammaitoni2, A Gennai3, A Giazotto3, G Giordano5, L Giordano1, R Gouaty8, D Grosjean8, G Guidi11, S Hebri6, H Heitmann4, P Hello7, L Holloway6, S Kreckelbergh7, P La Penna6, V Loriette9, M Loupias6, G Losurdo11, J-M Mackowski12, E Majorana10, C N Man4, M Mantovani3, F Marchesoni2, F Marion8, J Marque6, F Martelli11, A Masserot8, M Mazzoni11, L Milano1, C Moins6, J Moreau9, N Morgado12, B Mours8, A Pai10, C Palomba10, F Paoletti6,3, S Pardi1, A Pasqualetti6, R Passaquieti3, D Passuello3, B Perniola11, F Piergiovanni11, L Pinard12, R Poggiani3, M Punturo2, P Puppo10, K Qipiani1, P Rapagnani10, V Reita9, A Remillieux12, F Ricci10, I Ricciardi1, P Ruggi6, G Russo1, S Solimeno1, A Spallicci4, R Stanga11, R Taddei6, D Tombolato8, M Tonelli3, A Toncelli3, E Tournefier8, F Travasso2, G Vajente3, D Verkindt8, F Vetrano11, A Viceré11, J-Y Vinet4, H Vocca2, M Yvert8 and Z Zhang6 1 INFN, Sezione di Napoli and/or Universit` a di Napoli ‘Federico II’ Complesso Universitario di Monte S Angelo, and/or Università di Salerno, Fisciano (Sa), Italy 2 INFN, Sezione di Perugia and/or Universit` a di Perugia, Perugia, Italy 3 INFN, Sezione di Pisa and/or Universit` a di Pisa, Pisa, Italy 4 Departement Artemis—Observatoire de la Cˆ ote d’Azur, BP 42209 06304 Nice, Cedex 4, France 5 INFN, Laboratori Nazionali di Frascati, Frascati (Rm), Italy 6 European Gravitational Observatory (EGO), Cascina (Pi), Italy 7 Laboratoire de l’Acc´ elérateur Linéaire (LAL), IN2P3/CNRS—Université de Paris-Sud, Orsay, France 8 Laboratoire d’Annecy-le-Vieux de Physique des Particules, Annecy-le-Vieux, France 9 ESPCI, Paris, France 10 INFN, Sezione di Roma and/or Universit` a ‘La Sapienza’, Roma, Italy 11 INFN, Sezione di Firenze/Urbino, Sesto Fiorentino, and/or Universit` a di Firenze, and/or Università di Urbino, Italy 12 LMA, Villeurbanne, Lyon, France

E-mail: [email protected] and [email protected]

Received 30 August 2005, in final form 8 December 2005 Published 24 March 2006 Online at stacks.iop.org/CQG/23/S91 0264-9381/06/080091+11$30.00 © 2006 IOP Publishing Ltd Printed in the UK

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Abstract The automatic alignment system of the Virgo interferometer differs substantially from those used in similar experiments, since it uses a variant of the Anderson technique. This implies a completely different control topology with respect to other detectors, and the main feature is a strong coupling of different degrees of freedom in the optical signals. It also provides two extra output ports in which differential wave-front sensors can be placed, namely the light transmitted by the Fabry–Perot arm cavities. We report on the first experimental demonstration of this technique on a large scale recycled interferometer, and on the present status of the automatic alignment system. PACS numbers: 04.80.Nn, 95.55.Ym (Some figures in this article are in colour only in the electronic version)

1. Introduction Virgo is a large-scale interferometric gravitational wave detector consisting of a Michelson interferometer with 3 km long Fabry–Perot cavities in its arms. Figure 1 shows a simplified scheme of the Virgo optical layout. Like other similar experiments, we use a power recycling mirror (PR) to enhance the circulating light power. We operated the interferometer in two different configurations: the recombined mode, with the PR mirror largely misaligned in order to prevent its reflected beam interfering with the light inside the interferometer, and the recycled mode, which is the final configuration with an aligned PR mirror. (See [4] for a more detailed description of the detector.) The interferometer can operate with high sensitivity only if all its degrees of freedom are actively controlled. This includes the longitudinal and angular positions of the optical components. The purpose of the automatic alignment (AA) system is exactly to reduce the fluctuation of the mirror angular motions with respect to the beam, in order to have good long-term stability and to minimize the noise coupling into the main detection port. Angular fluctuations of input beam and of the mirrors do not directly introduce noise to the dark fringe but through quadratic coupling. In particular, the main contributions come from the coupling of total RMS angular motions of the mirrors with high frequency beam jitter of the input beam and from coupling high frequency angular mirror motion with a constant miscentring of the input beam. The current design requirements for the AA system have been derived from noise computations for these two forms of coupling. In brief, summarizing the results of [8, 9], if we assume, for example, that the beam is centred on the end mirror with an accuracy of 1 mm, then the requirement for the residual RMS motion of the end mirror is 10−6 rad. However, more stringent requirements are obtained from computing the coupling with the input beam jitter. Taking into account a jitter of the input beam of the order of 10−11 1 rad Hz− 2 , the limits for the residual RMS motion of all mirrors are shown in table 1. The mirrors are suspended as multiple pendulums (superattenuators) in order to reduce the longitudinal and angular mirror motion for frequencies above the resonance frequencies of the pendulums (around 2 Hz). During the acquisition of the longitudinal control (also called lock acquisition) the angular positions of the main mirrors and of the beam splitter are controlled by local control systems (LC) [1], which maintain the pointing of the mirrors with respect to local references, with an accuracy of about 1 µrad and a bandwidth of about 4 Hz. It is however apparent that this is not sufficient to fulfil the requirements.

The Virgo automatic alignment system

S93 B8 Q82 Q81 WE

IMC B2

3 km

144 m WI

Q22

IB

Q71 Q72

PR

BS

Q21

NE

NI 3 km

B7

Laser

EOM RFC

OMC

B1p

B1

B5

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Figure 1. A simplified optical scheme of Virgo in the recycled configuration. The photodiodes used for longitudinal (with names starting with B) and alignment (starting with Q) control systems are shown. Table 1. Requirement for RMS residual motion of all mirrors. Mirror

RMS (rad)

Power recycling Arm input mirrors Arm end mirrors

10−7 2 × 10−8 3 × 10−9

2. The Anderson–Giordano technique After lock acquisition, the alignment control systems have to be switched from local control to a globally acting automatic alignment system, designed to be able to control five mirrors (PR, NI, NE, WI or BS13 , WE). All longitudinal and angular control systems of the main Virgo interferometer generate their error signals with standard modulation–demodulation techniques. They are designed to share the same modulation frequency which imposes additional constraints on the lengths of the optical cavities. First of all, the modulation sidebands must be resonant in the input mode cleaner (IMC, figure 1), i.e., the modulation frequency must be a multiple of the IMC free spectral range (FSR). This condition is crucial since a mismatch of a few Hz can couple IMC length noise into the dark fringe. Furthermore, for the longitudinal control system the sidebands must be resonant in the power recycling cavity and anti-resonant in the arm cavities. Hence, the modulation frequency must not be an integer multiple of the arm cavity FSR, while it must be a half multiple of the recycling cavity FSR. For angular control we use a variant of the Anderson technique [6, 8, 9], the Anderson–Giordano technique, which requires the upper sideband first transverse modes 13 The angular motions of these two mirrors, from the point of view of wave-front sensing, are essentially the same degree of freedom.

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(TEM01 and TEM10 ) to be resonant in the arm cavities. Therefore the modulation frequency must also satisfy c arccos 1 − L/RC (1) fMOD = N · FSRarm + 2π L with N a positive integer, L being the length of the Fabry–Perot arm cavities and RC the radius of curvature of the end mirrors. The modulation frequency we actually use is ≈6.264 200 MHz. The alignment error signals are obtained using the wavefront sensing technique [13, 14]: the sensors are quadrant split photo detectors (quadrant photodiodes in short), made of four sensitive elements. The sum over these four elements gives the same signal as a normal photodiode. Alignment control signals can be obtained by demodulating at fMOD the differences between the upper and lower elements, or the left and right. Demodulation with two local oscillator phases which differ by 90◦ gives two outputs: the in-phase and quadrature signal; both contain (possibly independent) information about the angle of the carrier wave front with respect to that of the sidebands. In the Anderson–Giordano scheme four sets of two quadrants each are located in four of the interferometer outputs (see figure 1): in reflection from the PR mirror (Q21, Q22), from the anti-reflection coated surface of the main beam splitter (Q51, Q52) and in transmission of the arm cavities (Q71, Q72, Q81, Q82, north and west respectively). Telescopes are used to create a local Gouy phase difference of 90◦ between the two quadrants of each pair, in order to achieve the best possible separation of the various degrees of freedom visible in each port. In conclusion, for each angular direction (pitch and yaw) we generate 16 signals for controlling five degrees of freedom. 3. Sensing and control scheme The most notable difference of the Anderson–Giordano technique with respect to other methods [7, 11, 12] is that the angular motions of all mirrors creates optical output signals of similar magnitude in all output ports, as shown by our simulations. This can be intuitively explained by the fact that the upper sidebands first transverse modes, which are created by any misalignment, resonate in both arm cavities and can thus be detected with a substantial amplitude in all output ports. We performed several simulations (in the frequency domain, using Finesse [10]) to investigate the frequency behaviour of the alignment error signals. It turned out that there is no significant dependence on the frequency in the control band of the automatic alignment system and further up to around 50 Hz (figure 2). Therefore, the design of the control system can be based on frequency independent coefficients. To quantify this coupling of error signals we use optical matrices, with each element being the low-frequency limit of the transfer function between one mirror motion and one quadrant diode demodulated signal. The optical response of the interferometer with respect to angular mirror motion can thus be described using two 16 × 5 matrices, one for the pitch degrees of freedom (θx ) and another one for yaw (θy ). These optical matrices depend on the status of the interferometer (we recall that in Virgo it is possible to lock the interferometer with an offset from the dark fringe; see [5]) and on the setting demodulation phases of the quadrant diodes. Since we have 16 signals to control five degrees of freedom, we are faced with the task of solving an over-determined linear system. We use a χ 2 -reconstruction algorithm: if A is the measured optical matrix, yi are the quadrant signals, δyi the corresponding noise levels

Simulated transfer function [W/rad]


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101

102 Frequency [Hz]

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Figure 2. Results of frequency domain simulations, showing the behaviour of the transfer functions between mirror motions and demodulated quadrant diode signals (one of Q8 quadrants). The optical matrix is frequency independent in the AA control bandwith and up to 50 Hz.

and xi the mirror positions, the best reconstruction of the latter is obtained by minimizing the following quantity: 2 16 yi − 5j =1 Aij xj 2 . (2) χ = δyi2 i=1 The result, written in a more compact matrix form, is C = (AT V −1 A)−1 AT V −1 (3) 2 2 V being the diagonal matrix V = diag δy1 , . . . , δy16 . Here C is the 5 × 16 reconstruction matrix giving those linear combinations of the optical signals that provide an optimized reconstruction of the mirror’s angular position. In order to measure the matrix coefficients Aij , we inject sinusoidal excitations (lines) at the marionette level of the mirror suspensions (see [4]), with frequencies in the range between 5 and 9 Hz (outside the control band) or around 100–150 mHz (inside). As an example, figure 3 shows a set of measurements of the optical-matrix coefficients, performed while changing the demodulation phase of the quadrant photo-diode signals, in the recombined configuration. The circles are the experimental data and the continuous lines represent fits of the theoretical signal shape to the data. The best signal decoupling is obtained when the ratio of the two signal amplitudes is maximized. This measurement has been completely automated and permits one to check the linearity of the system by looking at the sine behaviour of the matrix coefficients, to estimate the level of noise by observing the coherence between the excitation and the signal, and most importantly, to tune the demodulation phases of the quadrant diodes in order to optimize the signal diagonalization. The actual computation for reconstruction of the mirror angular positions is managed by the global control (GC) system that has the duty of gathering and processing any main interferometer output signal. The AA error signals are serviced by the GC, passed to the last-stage suspension digital-control chain to be sent to the coil-magnet actuators of the mirror marionette [4].

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Matrix Coefficient [V/µrad]

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0 0

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60 75 90 105 120 Demodulation Phase [deg]

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Figure 3. Behaviour of the low frequency limit of the transfer functions between the signals from one of the Q8 quadrant diodes and the west cavity mirror motions, as a function of the demodulation phase of the quadrant diode.

4. Experimental results The first configuration for which the AA system has been installed was the recombined mode. This optical layout was the first one to be commissioned and provided a good test bed as it represents a comparably simple control task. The implementation of this automatic alignment system was completed in May 2004 [2]. This control system is still in use as part of the standard pre-alignment procedure for Virgo in the recycled configuration. The first step in the commissionig of the AA system for the final Virgo configuration (recycled) has been the development of the drift control system, which is a very low-bandwidth (few mHz) servo. Its purpose is to maintain the overall mean alignment for long periods. This system was implemented in July 2005 and tested during the C6 commissioning run (from 29 July to 12 August). The second step has been the development of the full bandwidth AA system. This task was completed in September 2005 and the system was tested during the last commissioning run (C7, from 14–19 September). 4.1. Recombined configuration The automatic alignment system for the recombined configuration has proven to be very stable and robust (tested during more than 32 h of continuous lock). The system uses two 4 × 2 matrices to reconstruct the mirror angular positions independently for the two arm cavities. When the AA is active, the in-loop error signals show, as expected, much less noise than the corresponding local control system signal (obtained by means of optical levers and cameras [1]). A comparison is shown in figure 4. The noise level is different especially at high frequencies, where the local position measurement system is limited by sensor electronic noise, and at low frequencies where the global signal is subject to the residual misalignment of the input beam. The fluctuation of the power stored in the cavity is strongly reduced when the AA system is used (figure 5): the residual power noise is dominated at all frequencies by the input power fluctuations. However, the total residual RMS motions of the mirrors are still higher than the


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Error signal [µrad/√Hz]

LC error signal AA error signal AA error signal RMS -1

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Figure 4. Comparison between the in-loop error signals from local control and automatic alignment for the input mirror of the north cavity (recombined configuration). The total residual RMS motion for this mirror is 0.16 µrad, which is still above the requirements.

Power fluctuat ions [W/√Hz]

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10-9 Transmitted power (AA) Transmitted power (LC) Input beam power 10-1

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Frequency [Hz]

Figure 5. Reduction of fluctuations of the power transmitted through the north cavity when the automatic alignment system is active (recombined configuration). The residual fluctuations are dominated by the input beam power fluctuations, which are mainly due to input beam jitter.

requirements. This is due to the fact that the error signals are dominated by input beam jitter, mainly between 2 and 7 Hz. 4.2. Drift control system for the recycled configuration When the mirrors are controlled by LC, the duration of the stable operation of the interferometer is limited mainly by slow drifts of the mirror positions, which cannot be corrected by a control system based on local references only. This motivated our effort to implement a slow drift control system before the full automatic alignment. Using the optical signals of the quadrants we implemented control loops with a very low bandwidth (a few mHz) to correct the setpoint of the local control system, which remain active

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Arbitrary counts

0.8

0.6

0.4

0.2

0 15

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25

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50

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Figure 6. A comparison of the power fluctuations in the dark fringe when the north end mirror is controlled by the local control system and by the automatic alignment loop with full bandwidth. The mean value of the power in the dark fringe, in this second configuration, is compatible with only sidebands being present in this port. Table 2. Normal modes of the mirror angular motions. The direction of rotation is referred to the front side of the optical component defined by the high-reflective coating. θx

θy

NE − WE PR − NI − WI NI − WI −PR − NI − WI + NE + WE PR + NI + WI + NE + WE

NE + WE PR − NI + WI NI + WI −PR − NI + WI + NE − WE PR + NI − WI + NE − WE

all the time. In this way the local control reduces the high frequency angular fluctuations and compensates for the suspension resonances [3], while the slow motions are controlled by the global control system. At the same time the global system is relatively easy to implement because, due to its low bandwidth, it is less sensitive to signal couplings and not much affected by control stability issues. Our studies showed that it is better to describe the angular misalignment of the interferometer not using the motion of single mirrors but combinations of them that can be described using physical normal modes (see table 2). Not all these combined degrees of freedom have the same relevance for the stability of the interferometer: for example, the first one of table 2 (differential motion of end mirrors) is the most important one for the power stability inside the recycling cavity, due to power loss through the dark fringe. To obtain a better control of this degree of freedom we changed the readout scheme of our system, moving one quadrant from the secondary reflected beam from the beam splitter (Q52) to the dark fringe beam. We then used this quadrant’s signals to control the differential motion of the end mirrors, acting for simplicity on the north end mirror alone. For this degree of freedom, we managed also to implement a full bandwidth AA control loop, switching off the corresponding local control. In this way we could reduce the power fluctuations in the dark fringe by one order of magnitude so that the carrier light leakage at the output port was decreased considerably (see figure 6).


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Arbitrary counts

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2.3 2.4 Recycling cavity pickoff power [mW]

2.5

Figure 7. A comparison of the power level and stability of the recycling cavity pick-off beam with and without drift control. The larger maximum power and the narrow distribution indicate a better overall alignment which reduces the sensitivity to the residual angular motions of all mirrors.

During the C6 commissioning run, the entire interferometer was kept continuously well aligned and locked on the dark fringe for slightly less than 40 h. Furthermore, after the event of an unlock (due to reasons not related to AA) there was no need for the pre-alignment procedure. During these long locking periods the power stored in the recycling cavity remained very stable (see figure 7); the residual long-term fluctuations were mainly due to input beam jitter. The overall corrections to the mirror positions during this time were typically of the order of a few µrad. The drift control also allowed us to improve the accuracy of the measurement of the optical matrix by keeping the system more stable during the measurements. 4.3. Full Virgo configuration For reasons of stability and simplicity, the first attempt at the implementation of an automatic alignment system with full complexity has been carried out in an intermediate step of commissioning of the longitudinal control system. At that time the interferometer was not held at exactly the dark fringe but with an offset of 8% away from it [5]. In this configuration we were able to control seven degrees of freedom out of a total of ten, before moving on to the final configuration. The reduction of noise in the error signal (figure 8) is similar to what we obtained in the recombined configuration. Due to the automatic alignment control the residual RMS motion of the mirrors can be reduced below the limits of the local control system. From a preliminary analysis performed using data when the seven loops were active, it turned out that the residual RMS motions of the mirrors are comparable with the requirements (slightly less than 20 nrad for input mirrors). Taking advantage of the stability obtained using the drift control system at the dark fringe (without any dark fringe locking offset) we managed to implement the full automatic alignment system, having all ten degrees of freedom controlled with full bandwidth. We decided to globally control the beam splitter instead of the west cavity input mirror, mainly because of different performances of the local control servos.

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Error signal [µrad/√Hz]

AA error signal LC error signal 10

-1

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-2

10-3

10-4

10-1

101 Frequency [Hz]

1

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Figure 8. Comparison between the in-loop error signals from local control and automatic alignment for the input mirror of the north cavity (recycled configuration). In an intermediate frequency range the two signals are comparable, assuring a correct cross calibration. 25

Power [W]

24

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21 PRC power Input power (rescaled) 20 0

5

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Time [h]

Figure 9. Trend of the power stored in the power recycling cavity (PRC) during 30 h of lock with the full AA system active, compared with the power transmitted by the input mode cleaner.

This system has proven to be stable and reliable, allowing the interferometer to remain locked for long times, up to 30 h (figure 9). The residual fluctuations of the power stored inside the recycling cavity are once again mainly due to the input beam power fluctuations. 5. Conclusions The implementation of the automatic alignment system for the recombined configuration has been the first successful experimental proof of the Anderson–Giordano technique in a large scale interferometer. It has proven to be very stable and reliable and it is now used every day as a pre-alignment phase in the lock acquisition sequence. The residual fluctuations of the power stored in the cavities are reduced almost to those of the input beam.


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We also implemented a low-bandwidth system to control the slow drifts of the mirrors, which were limiting the long term stability of the detector. This system substantially improved the overall alignment (allowing the interferometer to remain locked and well aligned for more than 39 h) and has been an important step for the development of the full bandwidth servos. The full automatic alignment system has been successfully implemented and tested before and during the last commissionig run, thus proving the feasibility of the Anderson–Giordano technique for the alignment of an interferometer with power recycling. The longest period of stable operation achieved with AA active lasted about 30 h. The on-going commissioning of the AA focuses on two tasks. The first concerns the analysis and reduction of the AA control noises, through optimization of the servos and better diagonalization of the control matrix. The second task is to implement control of the beam axes by acting on the input beam and the west cavity input mirror, both low-bandwidth servos. The input beam will be aligned using as reference the spot position of the beam transmitted through the north cavity, while the west input mirror will be aligned using the spot position at the end of the west arm. These servo systems will ensure that potential slow drifts of the input beam axis are corrected allowing for even longer stable operation. References [1] Acernese F et al (Virgo Collaboration) 2004 A local control system for the test masses of the VIRGO gravitational wave detector Astropart. Phys. 20 617 [2] Acernese F et al (Virgo Collaboration) 2004 Automatic mirror alignment for Virgo: first experimental demonstration of the Anderson technique on a large-scale interferometer Preprint gr-qc/0411116 [3] Acernese F et al (Virgo Collaboration) 2005 Measurement of the seismic attenuation performance of the Virgo superattenuator Astropart. Phys. 23 557–65 [4] Acernese F et al (Virgo Collaboration) 2006 Status of Virgo Class. Quantum Grav. 23 S63 [5] Acernese F et al (Virgo Collaboration) 2006 The variable finesse locking technique Class. Quantum Grav. 23 S85 [6] Anderson D Z 1984 Alignment of resonant optical cavities Appl. Opt. 23 2944–9 [7] Ando M et al (TAMA Collaboration) 2001 Stable operation of a 300-m laser interferometer with sufficient sensitivity to detect gravitational-wave events within our galaxy Phys. Rev. Lett. 86 3950 [8] Babusci D, Fang H, Giordano G, Matone G, Matone L and Sannibale V 1997 Alignment procedure for the Virgo interferometer: experimental results from the Frascati prototype Phys. Lett. A 226 31 (Preprint gr-qc/9611027) [9] Babusci D, Fang H, Giordano G, Matone G, Matone L and Sannibale V 1995 Mode analysis of laser interferometric gravitational wave detectors, LNF-95-063-IR [10] Freise A, Heinzel G, Lück H, Schilling R, Willke B and Danzmann K 2004 Frequency domain interferometer simulation with higher-order spatial modes Class. Quantum Grav. 21 S1067 (Preprint gr-qc/0309012) [11] Fritschel P et al 2001 Readout and control of a power-recycled interferometric gravitational-wave antenna Appl. Opt. 40 4988 [12] Grote H et al 2004 Alignment control of GEO 600 Class. Quantum Grav. 21 S441 [13] Morrison E, Meers B J, Robertson D I and Ward H 1994 Automatic alignment of optical interferometer Appl. Opt. 33 5041 [14] Morrison E, Meers B J, Robertson D I and Ward H 1994 Experimental demonstration of an automatic alignment system for optical interferometers Appl. Opt. 33 5037