The implementation of a mode cleaner at the output port of the GEO 600 gravitational wave detector will be part of the upcoming transition from GEO 600 to GEO-HF. Part of the transition will be the move from a heterodyne readout to a DC readout scheme. DC readout performance will be limited by higher order optical modes and control sidebands present at the output port. For optimum performance of DC readout an output mode cleaner (OMC) will clean the output beam of these contributions. Inclusion of an OMC will introduce new noise sources whose magnitudes needed to be estimated and for which new control systems will be needed. In this article we set requirements on the performance of these control systems and investigate the simulated performance of different designs.Science and Technology Facilities Council (STFC)BMBFMax Planck Society (MPG)State of Lower Saxony in GermanyEuropean Gravitational Observatory (EGO)DFG/SFB/Transregio 

Affeldt, C.

Danzmann, K.

Degallaix, J.

Freise, A.

Grote, H.

Hewitson, M.

Hild, S.

Leong, J.

Luck, H.

Marka, S.

Marka, Z.

Prijatelj, M.

Strain, K.A.

Willke, B.

Wittel, H.

Journal of Physics : Conference Series

The implementation of a mode cleaner at the output port of the GEO 600 gravitational wave detector will be part of the upcoming transition from GEO 600 to GEO-HF. Part of the transition will be the move from a heterodyne readout to a DC readout scheme. DC readout performance will be limited by higher order optical modes and control sidebands present at the output port. For optimum performance of DC readout an output mode cleaner (OMC) will clean the output beam of these contributions. Inclusion of an OMC will introduce new noise sources whose magnitudes needed to be estimated and for which new control systems will be needed. In this article we set requirements on the performance of these control systems and investigate the simulated performance of different designs

Prijatelj, M

Grote, H

Degallaix, J

Hewitson, M

Hild, S

Affeldt, C

Freise, Andreas

Leong, J

Lück, H

Strain, KA

Wittel, H

Willke, B

Danzmann, K

University of Birmingham Research Portal

Control and automatic alignment of the output mode cleaner of GEO 600

The implementation of a mode cleaner at the output port of the GEO 600 gravitational wave detector will be part of the upcoming transition from GEO 600 to GEO-HF. Part of the transition will be the move from a heterodyne readout to a DC readout scheme.DC readout performance will be limited by higher order optical modes and control sidebands present at the output port. For optimum performance of DC readout an output mode cleaner (OMC) will clean the output beam of these contributions.Inclusion of an OMC will introduce new noise sources whose magnitudes needed to be estimated and for which new control systems will be needed.In this article we set requirements on the performance of these control systems and investigate the simulated performance of different designs

Maastricht University Research Portal

M Prijatelj

H Grote

J Degallaix

M Hewitson

S Hild

C Affeldt

A Freise

J Leong

H Lück

K A Strain

H Wittel

B Willke

K Danzmann

Crossref

Journal of Physics Conference Series

The implementation of a mode cleaner at the output port of the GEO600 gravitational wave detector will be part of the upcoming transition from GEO600 to GEOHF. Part of the transition will be the move from a heterodyne readout to a DC readout scheme. DC readout performance will be limited by higher order optical modes and control sidebands present at the output port. For optimum performance of DC readout an output mode cleaner (OMC) will clean the output beam of these contributions. Inclusion of an OMC will introduce new noise sources whose magnitudes needed to be estimated and for which new control systems will be needed. In this article we set requirements on the performance of these control systems and investigate the simulated performance of different designs

Lück, H.

Strain, K.

MPG.PuRe

Grote, Hartmut

Affeldt, Christoph

Lück, Harald

Strain, Kenneth A.

Willke, Benno

Danzmann, Karsten

Institutionelles Repositorium der Leibniz Universität Hannover

This content has been downloaded from IOPscience. Please scroll down to see the full text.Download details:IP Address: 194.95.157.184This content was downloaded on 26/04/2017 at 10:36Please note that terms and conditions apply.Control and automatic alignment of the output mode cleaner of GEO 600View the table of contents for this issue, or go to the journal homepage for more2010 J. Phys.: Conf. Ser. 228 012014(http://iopscience.iop.org/1742-6596/228/1/012014)Home Search Collections Journals About Contact us My IOPscienceYou may also be interested in:Commissioning of the tuned DC readout at GEO 600J Degallaix, H Grote, M Prijatelj et al.The output mode cleaner of GEO 600M Prijatelj, J Degallaix, H Grote et al.Advanced techniques in GEO 600C Affeldt, K Danzmann, K L Dooley et al.GEO 600 and the GEO-HF upgrade program: successes and challengesK L Dooley, J R Leong, T Adams et al.DC readout experiment in Enhanced LIGOTobin T Fricke, Nicolás D Smith-Lefebvre, Richard Abbott et al.The Virgo 3 km interferometer for gravitational wave detectionF Acernese, P Amico, M Alshourbagy et al.Length sensing and control strategies for the LCGT interferometerY Aso, K Somiya and O MiyakawaAdvanced Virgo: a second-generation interferometric gravitational wave detectorF Acernese, M Agathos, K Agatsuma et al.Control and automatic alignment of the output modecleaner of GEO600M. Prijatelj1, H. Grote1, J. Degallaix1, M. Hewitson1, S. Hild2,3, C.Affeldt1, A. Freise2, J. Leong1, H. Lu¨ck 1, K. A. Strain1,3, H. Wittel1,B. Willke1 and K. Danzmann11 Max-Planck-Institut fu¨r Gravitationsphysik (Albert-Einstein-Institut) and LeibnizUniversita¨t Hannover, Callinstr. 38, 30167 Hannover, Germany2 School of Physics and Astronomy, The University of Birmingham, Edgbaston, Birmingham,B15 2TT, United Kingdom3 Institute for Gravitational Research, University of Glasgow, Glasgow, G12 8QQ, UnitedKingdom, United KingdomE-mail: mirko.prijatelj@aei.mpg.deAbstract. The implementation of a mode cleaner at the output port of the GEO600gravitational wave detector will be part of the upcoming transition from GEO600 to GEO-HF. Part of the transition will be the move from a heterodyne readout to a DC readout scheme.DC readout performance will be limited by higher order optical modes and control sidebandspresent at the output port. For optimum performance of DC readout an output mode cleaner(OMC) will clean the output beam of these contributions.Inclusion of an OMC will introduce new noise sources whose magnitudes needed to beestimated and for which new control systems will be needed.In this article we set requirements on the performance of these control systems andinvestigate the simulated performance of different designs.1. IntroductionThe upcoming GEO-HF [1] upgrade to GEO600 [2] consists among other things in the changefrom the current heterodyne readout scheme to a DC readout scheme [3]. DC readoutperformance will be limited by higher order optical modes (HOMs) and modulation sidebandspresent in the output beam of GEO600.HOMs and sidebands contribute to shot noise but no gravitation wave signal will be extractedfrom them. In combination with the planned upgrade of the laser power by a factor of 10 thepresence of HOMs and sidebands would require multiple photo diodes to accommodate for theincreased light power. To reject sidebands and HOMs from the output beam an output modecleaner (OMC) will be installed. The OMC will be located on a suspended bench. For moredetails see [3]. Transmissivity of the OMC for the TEM00 carrier will depend on the frequencymismatch ∆f between the GEO600 output beam and the OMC resonance frequency. It willalso depend on the alignment of the output beam onto the OMC.Fluctuations in ∆f and the alignment will create fluctuations in the power transmittedthrough the OMC. In DC readout these fluctuations couple directly to the GEO600 strainmeasurement. The impact of these two new noise sources are investigated and compared to other8th Edoardo Amaldi Conference on Gravitational Waves IOP PublishingJournal of Physics: Conference Series 228 (2010) 012014 doi:10.1088/1742-6596/228/1/012014c© 2010 IOP Publishing Ltd 1MPRMCNMCEMFNMFEMSRBDO2BDO1BDO3L4a L4bLaserFigure 1. Simplified optical layout of the GEO-HF gravitational wave detector. Theinterferometer is formed by the mirrors MPR, MCN, MCE, MFN, MFE and MSR. BDO1 toBDO3 steer the output beam. L4a and L4b are used to mode match the output beam to theOMC. The output mode cleaner is shown in the lower right corner inside the dashed box.noise sources in section 2. These investigations lead to requirements onto the control systemsthat minimize ∆f and misalignment. In section 3 different designs for control systems arepresented and expected performances are compared to the requirements derived in the previoussection. In section 4 the current status of the preliminary experiments with the OMC under airare layed out and a outlook is given.2. Investigations regarding noise sources introduced by the OMCThe magnitude of the noise sources introduced by the OMC are investigated. Requirements areformulated to ensure that they are below shot noise for the frequencies of interest.The frequency of the GEO600 laser is locked to the GEO600 power recycling cavity (PRC) [4].The PRC is formed by the mirrors MPR, MCE and MCN (see fig. 1). These mirrors areseismically isolated by multiple pendulum stages with a resonance frequency around 1Hz [5].If we omit frequencies below 0.3Hz their residual motion is dominated by frequencies around1Hz. This is well below the GEO-HF measurement band. The amplitude of these low frequencyfluctuations can be assumed to be ±2µm. Given the length of the PRC of 1200m this results ina frequency change of the laser of ±470 kHz. Since fluctuations in the OMC length around 1Hzare negligible due to its monolithic design this introduces a frequency mismatch ∆fLF betweenthe output beam of GEO600 and the OMC resonance frequency of the same amount. At higherfrequencies in the GEO-HF measurement band length fluctuations of the PRC can be neglecteddue to the elaborate seismic isolation system of the mirrors forming the PRC.In addition to ∆fLF there are higher frequency fluctuations ∆faudio in the frequency mismatchdominated by length changes of the OMC. The actual value of ∆fLF defines the couplingcoefficient for ∆faudio into the power transmitted through the OMC. Since fluctuations in the8th Edoardo Amaldi Conference on Gravitational Waves IOP PublishingJournal of Physics: Conference Series 228 (2010) 012014 doi:10.1088/1742-6596/228/1/0120142length of the OMC at ∆faudio happen in the measurement band of GEO-HF they contribute tonoise in the strain signal. It is therefore important to minimize the low frequency frequencymismatch to minimize the coupling coefficient. Coupling coefficients were calculated usingFINESSE software [6]. We want the fluctuations in the power transmitted through the OMC dueto ∆faudio to be less than 1/10 shot noise. The resulting requirement for ∆faudio was calculated:∆faudio ≤ 10.79Hz√Hz470 kHz∆fLF. (1)The OMC length will be 65.8 cm. The required stability in the measurement band was calculatedasOMC length stability ≤ 7.69 · 10−16 m√Hz470 kHz∆fLF. (2)The OMC will be located on a suspended bench. We assume that the OMC will achieve alength stability of 1 · 10−15m/√Hz. This requires ∆fLF to be less than 100 kHz. This requiresthe closed loop suppression at the dominant frequencies around 1Hz to be at least 5. Thisshould be achievable without great difficulty.2.1. Alignment requirementsDetermination of alignment requirements follows the same structure as the determination of thefrequency mismatch requirements. Again the margin of allowed fluctuations in the measurementband is determined by lower frequency fluctuations. Alignment fluctuations in and below themeasurement band are both caused by fluctuations in the rotation and tilt of the GEO600mirrors MPR, MCE, MCN, MSR, BDO1, BDO3 and translation of the OMC itself. Due tothe GEO600 configuration it is useful to investigate motions of the mirrors MCE and MCNas the degrees of freedom (DOFs) MCE-MCN and MCE+MCN. MCE-MCN is the differentialmisalignment. Low frequency rotations of the mirrors are assumed to be ±250 nrad. Mirrorfluctuations in the measurement band were estimated by multiplying seismometer data from theGEO site with the respective pendulum transfer functions. Pendulum transfer functions wereassumed to be of magnitude 1 up to the pendulum resonance frequency at 1Hz and f−2n with nthe number of pendulum stages for higher frequencies. The number of pendulum stages for thedifferent mirrors can be seen in table 1. The suspension points of the pendulums are isolated bystack isolators consisting of layers of metal and rubber. These stack isolators provide additionalisolation above approximately 10Hz.Coupling of alignment fluctuations in the measurement band in any DOF into the powertransmitted through the OMC is determined by the current misalignments of all other DOFs.To simulate the coupling coefficients of a DOF the other DOFs were assumed to be misalignedby discrete values in steps of 50 nrad between -250 nrad and 250 nrad. This leads to 23716possible configurations: (7DOFs times 11misalignment values times 2 axes)2. To reduce thecomputational needs only 2 DOFs at a time were evaluated yielding less than 1000 configurations.For each DOF the biggest coupling coefficient was recorded and the misalignment fluctuations inthe measurement band were multiplied by it. The resulting fluctuations in the power transmittedthrough the OMC were summed coherently. The resulting noise is shown in figure 2. It canbe seen that noise due to misalignments falls below shot noise at 300Hz (see ’all DOFs’ trace).This is for a power transmitted through the OMC of 40mW. It should be noted that this noiseestimation is very conservative. The DOFs of the MPR mirror and MCE-MCN are controlledby automatic alignment (AA) systems that reduce their misalignments. If perfect alignment forthese DOFs is assumed this results in a alignment noise as shown in trace ’w/o AA-controlledDOFs’ in figure 2. Noise introduced by the OMC will fall below shot noise above frequencies of100Hz to 300Hz. Therefore only a drift control is needed.8th Edoardo Amaldi Conference on Gravitational Waves IOP PublishingJournal of Physics: Conference Series 228 (2010) 012014 doi:10.1088/1742-6596/228/1/0120143Table 1. Number of pendulum seismic isolation stages of different GEO600 mirrors.MPR MCE MCN MSR BDO1 BDO3# of pendulum stages 2 3 3 3 1 1102 10310−1610−1410−1210−1010−810−610−4Freq, [Hz]Noise, [W/rt(Hz)]  all DOFsshot noisew/o AA−controlled DOFsFigure 2. Noise in the power transmitted through the OMC induced by misalignments.Uncalibrated spectrum at the detector behind the OMC. Transmitted power 40mW.3. Potential output mode cleaner control systems3.1. Longitudinal controlAs has been stated in the previous section the frequency mismatch between the OMC andthe PRC resonance frequencies needs to be controlled and minimized. The error signal forthis control system is generated via dither locking. The OMC length is dithered (modulated) atfdither. At zero frequency mismatch this leads to a modulation of the power transmitted throughthe OMC at 2 · fdither. With increasing frequency mismatch, a modulation at fdither appears.It is possible to either make the OMC follow the PRC or to make the PRC follow the OMC.We will first make the OMC follow the PRC. This has the benefit of avoiding adding additionalfeedback into the complex control loops controlling the suspended GEO600 mirrors. If it shouldprove necessary to extend the actuation range actuation on the PRC length will however bepossible. Tuning the length of the OMC is done with a piezo actuator (Physik InstrumenteS-303) attached to one of the OMC mirrors (see fig. 3). Actuation range of the PZT is 3µm8th Edoardo Amaldi Conference on Gravitational Waves IOP PublishingJournal of Physics: Conference Series 228 (2010) 012014 doi:10.1088/1742-6596/228/1/012014438cm16cmFigure 3. Schematic view of the output mode cleaner. Modified from [3].corresponding to a change in resonance frequency of the OMC of 1.3MHz. We do not expectlengh-to-angle coupling to be a problem.3.2. Alignment controlAll possible alignment configurations can be represented as points in a 4D parameter space.Misalignments in one plane can be represented as a transversal shift and a rotation. For twoplanes this results in a 4D parameter space. A requirement for the automatic alignment system isto have actuators available that can cover the whole 4D alignment parameter space. Promisingactuators in our case are BDO1 and BDO3. Actuators can be represented by vectors in thealignment parameter space. These vectors are the rows of the control matrix. The angle betweenthe two actuator vectors in the alignment space is a measure the controllability of the system.As a rule of thumb a bigger angle leads to a more robust control system. This separation angleis influenced by the optical configuration of the output optics. Several configurations for theoutput optics are possible: keep the existing BDO mirrors and add two lenses or change theBDOs ROCs and add either one or no lens. For simplicity we have decided to keep the existingBDOs and accept the non-optimal separation angle. Separation angles for several configurationsare compared in table 2. The benefit of keeping the existing BDO mirrors convinced us to choosethe two lens configuration.Several designs for the automatic alignment system were investigated:1. Dither lock with four frequencies. Dithering is applied to BDO1 and BDO3:Both tilt (pitch) and rotation (yaw) degrees of freedom for BDO1 and BDO3 respectively aredithered at separate frequencies f1 to f4. At perfect alignment the power transmitted throughthe OMC will be modulated at frequencies (2 · f1) to (2 · f4). Proportionally to misalignmentmodulations at f1 to f4 appear. In the current coil driver design, the maximum possible ditheramplitude is limited toDither amplitude ≤ 1.14 · 10−7 rad100Hz2fdither2(3)8th Edoardo Amaldi Conference on Gravitational Waves IOP PublishingJournal of Physics: Conference Series 228 (2010) 012014 doi:10.1088/1742-6596/228/1/0120145Table 2. Comparison of optical configurations of the output optics and resulting separationangles for the actuators BDO1 and BDO3. RBDO1 and RBDO2 are the radii of curvature ofBDO1 and BDO2. fL4a and fL4b are the focal lengths of L4a and L4b.Configuration RBDO1 [m] RBDO2 [m] fL4a [m] fL4b [m] Sep. angle [◦]Two lens 6.27 ∞ 0.25 -0.052 17.44One lens 6.27 -6.86 -0.50 ∞ 9.47Zero lens 4.12 -1.14 ∞ ∞ 64.69Table 3. Shot noise limited sensitivity of different designs for the output mode cleaner automaticalignment system in terms of BDO1 and BDO3 misalignments.Design 1 Design 2 Design 3BDO1 rotation [rad] 4.88 · 10−12 9.00 · 10−3 2.04 · 10−9BDO1 tilt [rad] 1.95 · 10−10 9.30 · 10−4 1.48 · 10−9BDO3 rotation [rad] 1.05 · 10−9 7.26 · 10−2 2.70 · 10−8BDO3 tilt [rad] 9.78 · 10−8 1.19 · 10−1 3.15 · 10−8In the simulation we assumed a dither amplitude of 1 · 10−7 rad which corresponds to a ditherfrequency of about 105Hz. A lower dither frequency can also be implemented.2. Dither lock with a common frequency. Dithering is applied to BDO1 and BDO3:Again the BDO mirrors are dithered. This time with a common frequency. The light reflectedoff of the OMC is split 50:50 and detected by two quadrant photo detectors. The Gouy phaseshift between them is pi/2. Essentially this is differential wavefront sensing [7] with sidebandscreated by dithering the BDO mirrors instead of by a electro-optic modulator. HOM-content ofthe GEO 600 output beam was assumed to be 1.4mW. Ideal mode matching was assumed.3. Dither lock with a common frequency. Dithering is applied to the OMC length:In this configuration the OMC length is dithered. The same OMC length dither can be usedfor longitudinal and alignment control. The full width at half maximum of the OMC resonanceis about 7 nm. A realistic dither amplitude can be assumed to be 1 nm. Just as in design 2 thelight reflected off of the OMC is split 50:50 and detected by two quadrant photo detectors.The shot noise limited sensitivities of designs 1 to 3 were estimated using the FINESSEsimulation software for a power of 40mW transmitted through the OMC. Their sensitivitiesare presented in table 3. Since the sensitivities of design 1 and 3 are considerably better thanthe requirements we derived on mirror movements in section 2, both designs seem promising.Sensitivities and requirements should scale proportionally for different noise levels. We intendto test designs 1 and 3 in GEO-HF.4. Preliminary tests of the output mode cleanerThe output mode cleaner has been assembled in a clean room. The frequency locking schemehas been successfully tested by locking the OMC to a laser (Innolight Mephisto 500 NE). Thefrequency mismatch has been minimized in this test setup by actuating on the laser frequency.The dithering, demodulation and the control loop filter were implemented with a real-timecomputer control system identical to the one developed for the Advanced LIGO detector. Theunity gain frequency of this control loop was 145Hz and closed loop suppression at 1Hz wasabove 30 dB.It has become obvious that the OMC can easily lock onto HOMs instead of the TEM00 mode.Since HOMs do not contain an easily usable gravitational wave signal the OMC must not lock8th Edoardo Amaldi Conference on Gravitational Waves IOP PublishingJournal of Physics: Conference Series 228 (2010) 012014 doi:10.1088/1742-6596/228/1/0120146onto HOMs when integrated into GEO600. Future investigations will show if this will pose aproblem in the GEO600 implementation.AcknowledgmentsThe authors are grateful for support from the Science and Technology Facilities Council (STFC)in the UK, the BMBF, Max Planck Society (MPG) and the state of Lower Saxony in Germanyand the European Gravitational Observatory (EGO). This work was partly supported by DFGgrant SFB/Transregio 7 ”Gravitational Wave Astronomy”. This document has been assignedLIGO Laboratory document number LIGO-P0900156-v2.References[1] Lu¨ck H, Affeldt C, Degallaix J, Freise A, Grote H, Hewitson M, Hild S, Leong J, Prijatelj M, Strain K A, WillkeB, Wittel H, Danzmann K 2009 Commissioning of the tuned DC readout at GEO600 J. Phys.: Conf. Seriespublished in this issue[2] Grote H (for the LIGO Scientic Collaboration) 2008 Class. and Quantum Grav. B 25 114043[3] Degallaix J, Grote H, Prijatelj M, Hewitson M, Hild S, Affeldt C, Freise A, Leong J, Lu¨ck H, Strain K A,Wittel H, Willke B and Danzmann K 2009 J. Phys.: Conf. Series published in this issue[4] Wilke B et al 2002 Class. and Quantum Grav. 19 1377[5] Goßler S 2004 Phd thesis http://edok01.tib.uni-hannover.de/edoks/e01dh04/389559768.pdf[6] Freise A http://www.rzg.mpg.de/adf/[7] Morrison E et al 1994 Appl. Opt. 33 5041-5049[8] Risk W P, Gosnell T R, Nurmikko A V 2003 Compact blue-green lasers (Cambridge: Cambridge UniversityPress)8th Edoardo Amaldi Conference on Gravitational Waves IOP PublishingJournal of Physics: Conference Series 228 (2010) 012014 doi:10.1088/1742-6596/228/1/0120147

Control and automatic alignment of the output modecleaner of GEO600M. Prijatelj1, H. Grote1, J. Degallaix1, M. Hewitson1, S. Hild2,3, C.Affeldt1, A. Freise2, J. Leong1, H. Lu¨ck 1, K. A. Strain1,3, H. Wittel1,B. Willke1 and K. Danzmann11 Max-Planck-Institut fu¨r Gravitationsphysik (Albert-Einstein-Institut) and LeibnizUniversita¨t Hannover, Callinstr. 38, 30167 Hannover, Germany2 School of Physics and Astronomy, The University of Birmingham, Edgbaston, Birmingham,B15 2TT, United Kingdom3 Institute for Gravitational Research, University of Glasgow, Glasgow, G12 8QQ, UnitedKingdom, United KingdomE-mail: mirko.prijatelj@aei.mpg.deAbstract. The implementation of a mode cleaner at the output port of the GEO600gravitational wave detector will be part of the upcoming transition from GEO600 to GEO-HF. Part of the transition will be the move from a heterodyne readout to a DC readout scheme.DC readout performance will be limited by higher order optical modes and control sidebandspresent at the output port. For optimum performance of DC readout an output mode cleaner(OMC) will clean the output beam of these contributions.Inclusion of an OMC will introduce new noise sources whose magnitudes needed to beestimated and for which new control systems will be needed.In this article we set requirements on the performance of these control systems andinvestigate the simulated performance of different designs.1. IntroductionThe upcoming GEO-HF [1] upgrade to GEO600 [2] consists among other things in the changefrom the current heterodyne readout scheme to a DC readout scheme [3]. DC readoutperformance will be limited by higher order optical modes (HOMs) and modulation sidebandspresent in the output beam of GEO600.HOMs and sidebands contribute to shot noise but no gravitation wave signal will be extractedfrom them. In combination with the planned upgrade of the laser power by a factor of 10 thepresence of HOMs and sidebands would require multiple photo diodes to accommodate for theincreased light power. To reject sidebands and HOMs from the output beam an output modecleaner (OMC) will be installed. The OMC will be located on a suspended bench. For moredetails see [3]. Transmissivity of the OMC for the TEM00 carrier will depend on the frequencymismatch ∆f between the GEO600 output beam and the OMC resonance frequency. It willalso depend on the alignment of the output beam onto the OMC.Fluctuations in ∆f and the alignment will create fluctuations in the power transmittedthrough the OMC. In DC readout these fluctuations couple directly to the GEO600 strainmeasurement. The impact of these two new noise sources are investigated and compared to other8th Edoardo Amaldi Conference on Gravitational Waves IOP PublishingJournal of Physics: Conference Series 228 (2010) 012014 doi:10.1088/1742-6596/228/1/012014c© 2010 IOP Publishing Ltd 1MPRMCNMCEMFNMFEMSRBDO2BDO1BDO3L4a L4bLaserFigure 1. Simplified optical layout of the GEO-HF gravitational wave detector. Theinterferometer is formed by the mirrors MPR, MCN, MCE, MFN, MFE and MSR. BDO1 toBDO3 steer the output beam. L4a and L4b are used to mode match the output beam to theOMC. The output mode cleaner is shown in the lower right corner inside the dashed box.noise sources in section 2. These investigations lead to requirements onto the control systemsthat minimize ∆f and misalignment. In section 3 different designs for control systems arepresented and expected performances are compared to the requirements derived in the previoussection. In section 4 the current status of the preliminary experiments with the OMC under airare layed out and a outlook is given.2. Investigations regarding noise sources introduced by the OMCThe magnitude of the noise sources introduced by the OMC are investigated. Requirements areformulated to ensure that they are below shot noise for the frequencies of interest.The frequency of the GEO600 laser is locked to the GEO600 power recycling cavity (PRC) [4].The PRC is formed by the mirrors MPR, MCE and MCN (see fig. 1). These mirrors areseismically isolated by multiple pendulum stages with a resonance frequency around 1Hz [5].If we omit frequencies below 0.3Hz their residual motion is dominated by frequencies around1Hz. This is well below the GEO-HF measurement band. The amplitude of these low frequencyfluctuations can be assumed to be ±2µm. Given the length of the PRC of 1200m this results ina frequency change of the laser of ±470 kHz. Since fluctuations in the OMC length around 1Hzare negligible due to its monolithic design this introduces a frequency mismatch ∆fLF betweenthe output beam of GEO600 and the OMC resonance frequency of the same amount. At higherfrequencies in the GEO-HF measurement band length fluctuations of the PRC can be neglecteddue to the elaborate seismic isolation system of the mirrors forming the PRC.In addition to ∆fLF there are higher frequency fluctuations ∆faudio in the frequency mismatchdominated by length changes of the OMC. The actual value of ∆fLF defines the couplingcoefficient for ∆faudio into the power transmitted through the OMC. Since fluctuations in the8th Edoardo Amaldi Conference on Gravitational Waves IOP PublishingJournal of Physics: Conference Series 228 (2010) 012014 doi:10.1088/1742-6596/228/1/0120142length of the OMC at ∆faudio happen in the measurement band of GEO-HF they contribute tonoise in the strain signal. It is therefore important to minimize the low frequency frequencymismatch to minimize the coupling coefficient. Coupling coefficients were calculated usingFINESSE software [6]. We want the fluctuations in the power transmitted through the OMC dueto ∆faudio to be less than 1/10 shot noise. The resulting requirement for ∆faudio was calculated:∆faudio ≤ 10.79Hz√Hz470 kHz∆fLF. (1)The OMC length will be 65.8 cm. The required stability in the measurement band was calculatedasOMC length stability ≤ 7.69 · 10−16 m√Hz470 kHz∆fLF. (2)The OMC will be located on a suspended bench. We assume that the OMC will achieve alength stability of 1 · 10−15m/√Hz. This requires ∆fLF to be less than 100 kHz. This requiresthe closed loop suppression at the dominant frequencies around 1Hz to be at least 5. Thisshould be achievable without great difficulty.2.1. Alignment requirementsDetermination of alignment requirements follows the same structure as the determination of thefrequency mismatch requirements. Again the margin of allowed fluctuations in the measurementband is determined by lower frequency fluctuations. Alignment fluctuations in and below themeasurement band are both caused by fluctuations in the rotation and tilt of the GEO600mirrors MPR, MCE, MCN, MSR, BDO1, BDO3 and translation of the OMC itself. Due tothe GEO600 configuration it is useful to investigate motions of the mirrors MCE and MCNas the degrees of freedom (DOFs) MCE-MCN and MCE+MCN. MCE-MCN is the differentialmisalignment. Low frequency rotations of the mirrors are assumed to be ±250 nrad. Mirrorfluctuations in the measurement band were estimated by multiplying seismometer data from theGEO site with the respective pendulum transfer functions. Pendulum transfer functions wereassumed to be of magnitude 1 up to the pendulum resonance frequency at 1Hz and f−2n with nthe number of pendulum stages for higher frequencies. The number of pendulum stages for thedifferent mirrors can be seen in table 1. The suspension points of the pendulums are isolated bystack isolators consisting of layers of metal and rubber. These stack isolators provide additionalisolation above approximately 10Hz.Coupling of alignment fluctuations in the measurement band in any DOF into the powertransmitted through the OMC is determined by the current misalignments of all other DOFs.To simulate the coupling coefficients of a DOF the other DOFs were assumed to be misalignedby discrete values in steps of 50 nrad between -250 nrad and 250 nrad. This leads to 23716possible configurations: (7DOFs times 11misalignment values times 2 axes)2. To reduce thecomputational needs only 2 DOFs at a time were evaluated yielding less than 1000 configurations.For each DOF the biggest coupling coefficient was recorded and the misalignment fluctuations inthe measurement band were multiplied by it. The resulting fluctuations in the power transmittedthrough the OMC were summed coherently. The resulting noise is shown in figure 2. It canbe seen that noise due to misalignments falls below shot noise at 300Hz (see ’all DOFs’ trace).This is for a power transmitted through the OMC of 40mW. It should be noted that this noiseestimation is very conservative. The DOFs of the MPR mirror and MCE-MCN are controlledby automatic alignment (AA) systems that reduce their misalignments. If perfect alignment forthese DOFs is assumed this results in a alignment noise as shown in trace ’w/o AA-controlledDOFs’ in figure 2. Noise introduced by the OMC will fall below shot noise above frequencies of100Hz to 300Hz. Therefore only a drift control is needed.8th Edoardo Amaldi Conference on Gravitational Waves IOP PublishingJournal of Physics: Conference Series 228 (2010) 012014 doi:10.1088/1742-6596/228/1/0120143Table 1. Number of pendulum seismic isolation stages of different GEO600 mirrors.MPR MCE MCN MSR BDO1 BDO3# of pendulum stages 2 3 3 3 1 1102 10310−1610−1410−1210−1010−810−610−4Freq, [Hz]Noise, [W/rt(Hz)]  all DOFsshot noisew/o AA−controlled DOFsFigure 2. Noise in the power transmitted through the OMC induced by misalignments.Uncalibrated spectrum at the detector behind the OMC. Transmitted power 40mW.3. Potential output mode cleaner control systems3.1. Longitudinal controlAs has been stated in the previous section the frequency mismatch between the OMC andthe PRC resonance frequencies needs to be controlled and minimized. The error signal forthis control system is generated via dither locking. The OMC length is dithered (modulated) atfdither. At zero frequency mismatch this leads to a modulation of the power transmitted throughthe OMC at 2 · fdither. With increasing frequency mismatch, a modulation at fdither appears.It is possible to either make the OMC follow the PRC or to make the PRC follow the OMC.We will first make the OMC follow the PRC. This has the benefit of avoiding adding additionalfeedback into the complex control loops controlling the suspended GEO600 mirrors. If it shouldprove necessary to extend the actuation range actuation on the PRC length will however bepossible. Tuning the length of the OMC is done with a piezo actuator (Physik InstrumenteS-303) attached to one of the OMC mirrors (see fig. 3). Actuation range of the PZT is 3µm8th Edoardo Amaldi Conference on Gravitational Waves IOP PublishingJournal of Physics: Conference Series 228 (2010) 012014 doi:10.1088/1742-6596/228/1/012014438cm16cmFigure 3. Schematic view of the output mode cleaner. Modified from [3].corresponding to a change in resonance frequency of the OMC of 1.3MHz. We do not expectlengh-to-angle coupling to be a problem.3.2. Alignment controlAll possible alignment configurations can be represented as points in a 4D parameter space.Misalignments in one plane can be represented as a transversal shift and a rotation. For twoplanes this results in a 4D parameter space. A requirement for the automatic alignment system isto have actuators available that can cover the whole 4D alignment parameter space. Promisingactuators in our case are BDO1 and BDO3. Actuators can be represented by vectors in thealignment parameter space. These vectors are the rows of the control matrix. The angle betweenthe two actuator vectors in the alignment space is a measure the controllability of the system.As a rule of thumb a bigger angle leads to a more robust control system. This separation angleis influenced by the optical configuration of the output optics. Several configurations for theoutput optics are possible: keep the existing BDO mirrors and add two lenses or change theBDOs ROCs and add either one or no lens. For simplicity we have decided to keep the existingBDOs and accept the non-optimal separation angle. Separation angles for several configurationsare compared in table 2. The benefit of keeping the existing BDO mirrors convinced us to choosethe two lens configuration.Several designs for the automatic alignment system were investigated:1. Dither lock with four frequencies. Dithering is applied to BDO1 and BDO3:Both tilt (pitch) and rotation (yaw) degrees of freedom for BDO1 and BDO3 respectively aredithered at separate frequencies f1 to f4. At perfect alignment the power transmitted throughthe OMC will be modulated at frequencies (2 · f1) to (2 · f4). Proportionally to misalignmentmodulations at f1 to f4 appear. In the current coil driver design, the maximum possible ditheramplitude is limited toDither amplitude ≤ 1.14 · 10−7 rad100Hz2fdither2(3)8th Edoardo Amaldi Conference on Gravitational Waves IOP PublishingJournal of Physics: Conference Series 228 (2010) 012014 doi:10.1088/1742-6596/228/1/0120145Table 2. Comparison of optical configurations of the output optics and resulting separationangles for the actuators BDO1 and BDO3. RBDO1 and RBDO2 are the radii of curvature ofBDO1 and BDO2. fL4a and fL4b are the focal lengths of L4a and L4b.Configuration RBDO1 [m] RBDO2 [m] fL4a [m] fL4b [m] Sep. angle [◦]Two lens 6.27 ∞ 0.25 -0.052 17.44One lens 6.27 -6.86 -0.50 ∞ 9.47Zero lens 4.12 -1.14 ∞ ∞ 64.69Table 3. Shot noise limited sensitivity of different designs for the output mode cleaner automaticalignment system in terms of BDO1 and BDO3 misalignments.Design 1 Design 2 Design 3BDO1 rotation [rad] 4.88 · 10−12 9.00 · 10−3 2.04 · 10−9BDO1 tilt [rad] 1.95 · 10−10 9.30 · 10−4 1.48 · 10−9BDO3 rotation [rad] 1.05 · 10−9 7.26 · 10−2 2.70 · 10−8BDO3 tilt [rad] 9.78 · 10−8 1.19 · 10−1 3.15 · 10−8In the simulation we assumed a dither amplitude of 1 · 10−7 rad which corresponds to a ditherfrequency of about 105Hz. A lower dither frequency can also be implemented.2. Dither lock with a common frequency. Dithering is applied to BDO1 and BDO3:Again the BDO mirrors are dithered. This time with a common frequency. The light reflectedoff of the OMC is split 50:50 and detected by two quadrant photo detectors. The Gouy phaseshift between them is pi/2. Essentially this is differential wavefront sensing [7] with sidebandscreated by dithering the BDO mirrors instead of by a electro-optic modulator. HOM-content ofthe GEO 600 output beam was assumed to be 1.4mW. Ideal mode matching was assumed.3. Dither lock with a common frequency. Dithering is applied to the OMC length:In this configuration the OMC length is dithered. The same OMC length dither can be usedfor longitudinal and alignment control. The full width at half maximum of the OMC resonanceis about 7 nm. A realistic dither amplitude can be assumed to be 1 nm. Just as in design 2 thelight reflected off of the OMC is split 50:50 and detected by two quadrant photo detectors.The shot noise limited sensitivities of designs 1 to 3 were estimated using the FINESSEsimulation software for a power of 40mW transmitted through the OMC. Their sensitivitiesare presented in table 3. Since the sensitivities of design 1 and 3 are considerably better thanthe requirements we derived on mirror movements in section 2, both designs seem promising.Sensitivities and requirements should scale proportionally for different noise levels. We intendto test designs 1 and 3 in GEO-HF.4. Preliminary tests of the output mode cleanerThe output mode cleaner has been assembled in a clean room. The frequency locking schemehas been successfully tested by locking the OMC to a laser (Innolight Mephisto 500 NE). Thefrequency mismatch has been minimized in this test setup by actuating on the laser frequency.The dithering, demodulation and the control loop filter were implemented with a real-timecomputer control system identical to the one developed for the Advanced LIGO detector. Theunity gain frequency of this control loop was 145Hz and closed loop suppression at 1Hz wasabove 30 dB.It has become obvious that the OMC can easily lock onto HOMs instead of the TEM00 mode.Since HOMs do not contain an easily usable gravitational wave signal the OMC must not lock8th Edoardo Amaldi Conference on Gravitational Waves IOP PublishingJournal of Physics: Conference Series 228 (2010) 012014 doi:10.1088/1742-6596/228/1/0120146onto HOMs when integrated into GEO600. Future investigations will show if this will pose aproblem in the GEO600 implementation.AcknowledgmentsThe authors are grateful for support from the Science and Technology Facilities Council (STFC)in the UK, the BMBF, Max Planck Society (MPG) and the state of Lower Saxony in Germanyand the European Gravitational Observatory (EGO). This work was partly supported by DFGgrant SFB/Transregio 7 ”Gravitational Wave Astronomy”. This document has been assignedLIGO Laboratory document number LIGO-P0900156-v2.References[1] Lu¨ck H, Affeldt C, Degallaix J, Freise A, Grote H, Hewitson M, Hild S, Leong J, Prijatelj M, Strain K A, WillkeB, Wittel H, Danzmann K 2009 Commissioning of the tuned DC readout at GEO600 J. Phys.: Conf. Seriespublished in this issue[2] Grote H (for the LIGO Scientic Collaboration) 2008 Class. and Quantum Grav. B 25 114043[3] Degallaix J, Grote H, Prijatelj M, Hewitson M, Hild S, Affeldt C, Freise A, Leong J, Lu¨ck H, Strain K A,Wittel H, Willke B and Danzmann K 2009 J. Phys.: Conf. Series published in this issue[4] Wilke B et al 2002 Class. and Quantum Grav. 19 1377[5] Goßler S 2004 Phd thesis http://edok01.tib.uni-hannover.de/edoks/e01dh04/389559768.pdf[6] Freise A http://www.rzg.mpg.de/adf/[7] Morrison E et al 1994 Appl. Opt. 33 5041-5049[8] Risk W P, Gosnell T R, Nurmikko A V 2003 Compact blue-green lasers (Cambridge: Cambridge UniversityPress)8th Edoardo Amaldi Conference on Gravitational Waves IOP PublishingJournal of Physics: Conference Series 228 (2010) 012014 doi:10.1088/1742-6596/228/1/0120147

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Control and automatic alignment of the output mode cleaner of GEO 600

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