In the original paper describing the first measurements performed with LISA Pathfinder, a bulge in the acceleration noise was shown in the 200 mHz - 20 mHz frequency band. This bulge noise originated from cross-coupling of spacecraft motion into the longitudinal readout and it was shown that it is possible to subtract this cross-talk noise. We discuss here the model that was used for subtraction as well as an alternative approach to suppress the cross talk by realignment of the test masses. Such a realignment was performed after preliminary analysis of a dedicated cross-talk experiment, and we show the resulting noise suppression. Since then, further experiments have been performed to investigate the cross-coupling behaviour, however analysis of these experiments is still on-going. © Published under licence by IOP Publishing Ltd.ESA/22331/09/NL/HBESA/16238/10/NL/HBDLR/FKZ/OQ 0501DLR/FKZ/50 OQ 1601DFG/EXC/QUES

Karnesis, N.

Wanner, G.

Journal of Physics : Conference Series

MPG.PuRe

Preliminary results on the suppression of sensing cross-talk in LISA Pathfinder

1Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distributionof this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.Published under licence by IOP Publishing Ltd123456789011th International LISA Symposium  IOP PublishingIOP Conf. Series: Journal of Physics: Conf. Series 840 (2017) 012043  doi :10.1088/1742-6596/840/1/012043Preliminary results on the suppression of sensingcross-talk in LISA PathfinderGudrun Wanner and Nikolaos Karnesis on behalf of the LISAPathfinder collaborationMax Planck Institute for Gravitational Physics (Albert Einstein Institute) and Institute forGravitational Physics of the Leibniz Universitt HannoverE-mail: gudrun.wanner@aei.mpg.deAbstract. In the original paper describing the first measurements performed with LISAPathfinder, a bulge in the acceleration noise was shown in the 200 mHz - 20 mHz frequencyband. This bulge noise originated from cross-coupling of spacecraft motion into the longitudinalreadout and it was shown that it is possible to subtract this cross-talk noise. We discuss here themodel that was used for subtraction as well as an alternative approach to suppress the cross talkby realignment of the test masses. Such a realignment was performed after preliminary analysisof a dedicated cross-talk experiment, and we show the resulting noise suppression. Since then,further experiments have been performed to investigate the cross-coupling behaviour, howeveranalysis of these experiments is still on-going.1. IntroductionThe well known LISA Pathfinder differential acceleration measurement published in [1] anddisplayed for convenience in Fig. 1(a), showed a bulge in the noise curve in the 200 mHz -20 mHz frequency band. This bulge was caused by cross-coupling of spacecraft motion leakinginto the main differential acceleration measurement and it was shown in [1] that it is possibleto subtract the cross-coupling noise resulting in the blue curve in Fig. 1(a). This subtractionwas performed by fitting the following model to the measured acceleration noise, i.e. to the redtrace in Fig 1(a) yielding estimates of the coefficients Ci and δifo:∆gx-talk = C1φ̈[t] + C2η̈[t] + C3ÿ[t] + C4z̈[t] + C5y[t] + C6z[t] + δifoẍ1[t] . (1)Each term in this equation defines a cross-coupling of spacecraft motion to the differentialacceleration measurement:• All but the last summand are cross-coupling terms, because φ, η, y, z are orthogonalcoordinates to the differential readout along x. See Fig. 2(a) for a definition of the coordinatesystem.• The annotation k̄ with k ∈ {φ, η, y, z}, defines a mean motion of both test masses along k,which is a description of the spacecraft motion along −k.• The last summand, describes a residual coupling of spacecraft motion along x enteringthe differential readout. As the term ‘differential readout’ indicates, ∆g is defined as∆g = ẍ2 − ẍ1 (neglecting here corrections such as for applied or inertial forces). It should2123456789011th International LISA Symposium  IOP PublishingIOP Conf. Series: Journal of Physics: Conf. Series 840 (2017) 012043  doi :10.1088/1742-6596/840/1/012043(a) Subtraction methodLPF RequirementsLISA Requirements(b) Suppression methodFigure 1. (a): Result taken from [1], showing that the bulge at 200-20 mHz can be subtracted.(b) In this figure, no subtraction was performed. Instead the reduction was achieved by arealignment of the test masses prior to the second noise run.1therefore be insensitive to any common-mode motion, where ẍ2 = ẍ1. Since spacecraftmotion effectively shows as common test mass motion, ∆g should not sense spacecraftmotion. However, there is a residual leakage, because the interferometer readout responseis not identical to TM1 motion as to TM2 motion, such that ∆g = k2ẍ2 − k1ẍ1 withk2 ≈ k1 ≈ 1. The small difference between k1 and k2 causes the residual cross-coupling.Fitting eq. (1) to the measurement data and subtracting the resulting model works very well, asvisible in Fig. 1(a). However, this technique has several disadvantages: First of all, the modelprovides no interpretation what the coefficients physically mean, and therefore no explanationhow the cross-coupling could be suppressed. Secondly, several parameters show high correlation,such that the given model is not the only one allowing a fit and subtraction with low residuals.Instead, there is a set of models, performing comparably well. Finally, the coefficients vary overmission time, and this variation cannot be explained with the shown model.For these reasons, there is an ongoing effort, to build a physical model, which can describe thecross-coupling over the entire mission duration with a constant set of parameters, and can beused without adaptation for any set of data to subtract the bulge. Additionally, such a modelalso allows a direct suppression of the cross-talk. In fact, Fig. 1(a) shows a noise run performedin April 2016 (2016-04-08 to 2016-04-14), which was after a first realignment of the test masseshad already reduced the amount of cross-talk. This will be further discussed in the next section.2. Cross-coupling suppressionOf all terms given in eq. (1), we will focus now on the first four summands. For these four termsexists a multitude of mechanisms contributing to the parameters C1 to C4. Some of these aregeometric, others result from the interference of Gaussian beams and their phase detection (seee.g. [2, 3] for more information on some non-geometric cross-talk mechanisms). Unfortunately,the amount of cross-coupling originating from non-geometric effects needs to be regarded asunknown. The geometric effects however, are known very well and can be used to counteractany unknown effects.In Fig. 2 we illustrate two related geometrical effects. If a test mass is tilted with respect to1 Please note: the slight difference in curvature around 3 mHz in the LPF requirements in the two figures resultsfrom different notations: while in Fig. 1(a) correlated noise sources were assumed, we chose in Fig. 1(b) thenotation for uncorrelated noise sources.3123456789011th International LISA Symposium  IOP PublishingIOP Conf. Series: Journal of Physics: Conf. Series 840 (2017) 012043  doi :10.1088/1742-6596/840/1/012043(a) Coordinate systemTM1TM1(b) Lateral jitter couplingTM1TM1xCoR(c) Angular jitter couplingFigure 2. Illustration of the displacement of the laser beam reflection point on test mass 1(TM1). These are two related cases of geometrical cross-coupling.the optical bench and performs a lateral motion, the reflection point on the test mass moveslongitudinally, i.e. in x-direction. This causes a direct coupling of lateral motion into thelongitudinal readout signal, since the optical pathlength of the laser beam changes.A second geometric coupling effect occurs, if the test mass reflection point does not coincidewith the center of rotation of the test mass - as shown in Fig. 2(c). In this case, a test mass tiltcauses a longitudinal displacement of the reflection point and thereby a change in the opticalpathlength. In both cases, there was no motion of the test mass along x present, but sincethe reflection point on the test mass was displaced in x-direction, the interferometer senses anapparent test mass x-motion.In fact, these two coupling mechanisms are closely related since in both cases, the couplingoccurs due to a combination of rotation and lateral displacement, and both can be described bythe following simple equation:xrp = yϕ . (2)Here, xrp annotates the displacement of the reflection point along x, and thereby the apparentlongitudinal test mass displacement. The lateral shift between the center of rotation and thereflection point is labeled y, and ϕ is the test mass angle with respect to the optical bench. Thesame equation holds for the orthogonal plane:xrp = zη (3)where z is a vertical displacement of a reflection point with respect to the center of rotation, andη a test mass tilt around the y-axis, measured relative to the optical bench (see Fig. 2(a) for anillustration of the coordinate system). Since eq. (2) and (3) are linear in each degree of freedom,they can be used to counter act all other cross-coupling mechanisms - at least to first order.For example, assume a cross-coupling of TM1 ϕ-jitter was measured to be c1 · ϕ1 + O(ϕ21). Inthat case, a lateral displacement of TM1 by y1 = −c1 would suppress this measured cross talkto first order. This means, by a well chosen set of rotations and shifts of the test masses, theamount of cross-coupling leaking into ∆g can be reduced. In order to find the required offsets,we injected sinusoidal motion in each degree of freedom and extracted the parameters via fittinga dedicated model to the measured data. Fig. 3 shows an excerpt of the injections performed4123456789011th International LISA Symposium  IOP PublishingIOP Conf. Series: Journal of Physics: Conf. Series 840 (2017) 012043  doi :10.1088/1742-6596/840/1/012043Figure 3. Example of injections performed during the ‘engineering-day’ cross-talk experimentperformed on 2016-March-16. The labels ‘GRS z1,2’ indicate, that the shown vertical test massdisplacement (z1, z2) is taken from the ‘Gravitational Reference Sensor’ readout.on 2016-March-16: the common-mode and counter-mode injections into the vertical test massmotion. To the right-hand axis, also the measured differential acceleration ∆g is plotted, whichshows a clear correlation to the injections and thereby the cross-coupling. A preliminary dataanalysis resulted in a first estimate of the parameters which were then used to realign the testmasses. The resulting reduction of cross-coupling noise is given in Fig. 1(b). Please note, thateq. (2) and eq. (3) are not the physical model yet, which is needed to describe the cross-talk withconstant parameters over the entire mission duration. Instead, these are toy-models describingtwo geometric cross-talk effects. Furthermore, the parameters in this model are written herenot in terms of readout signals, which is necessary for applying the model to the data. The fullmodel is still work in progress, the analysis of the cross-talk behaviour is therefore still ongoingand further information will follow in a separate paper.3. AcknowledgmentsThis work has been made possible by the LISA Pathfinder mission, which is part of thespace-science program of the European Space Agency. We gratefully acknowledge support bythe European Space Agency (ESA) (22331/09/NL/HB, 16238/10/NL/HB), by the DeutschesZentrum fur Luft- und Raumfahrt (DLR) with funding of the Bundesministerium fur Wirtschaftund Energie with a decision of the Deutschen Bundestag (DLR project reference numbers FKZOQ 0501 and FKZ 50 OQ 1601), and thank the German Research Foundation for funding theCluster of Excellence QUEST (Centre for Quantum Engineering and Space-Time Research).References[1] Armano, et al, PRL 116, 231101 (2016), DOI: 10.1103/PhysRevLett.116.231101[2] Schuster, et al, Optics Express 10466 (2016) DOI: 10.1364/OE.24.01046[3] Schuster, et al, Applied Optics 54 (2015) DOI: 10.1364/AO.54.001010

English

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: 194.95.157.241This content was downloaded on 13/07/2017 at 10:13Please note that terms and conditions apply.Preliminary results on the suppression of sensing cross-talk in LISA PathfinderView the table of contents for this issue, or go to the journal homepage for more2017 J. Phys.: Conf. Ser. 840 012043(http://iopscience.iop.org/1742-6596/840/1/012043)Home Search Collections Journals About Contact us My IOPscienceYou may also be interested in:The Engineering of LISA Pathfinder – the quietest Laboratory ever flown in SpaceChristian Trenkel, Dave Wealthy, Neil Dunbar et al.LISA Pathfinder: Understanding DWS noise performance for the LISA missionLennart Wissel and LPF collaborationCalibrating LISA Pathfinder raw data into femto-g differential accelerometryDaniele Vetrugno, Nikolaos Karnesis and on behalf of the LPF collaborationLISA Pathfinder: OPD loop characterisationMichael Born and LPF collaborationGround-based self-gravity tests for LISA Pathfinder and LISAC Trenkel, C Warren and D WealthyInterferometry for LISA and LISA PathfinderA F García Marín, G Heinzel and K DanzmannLISA Pathfinder: Optical Metrology System monitoring during operationsHeather E Audley and LISA Pathfinder collaborationBayesian statistics for the calibration of the LISA Pathfinder experimentM Armano, H Audley, G Auger et al.LISA Pathfinder: First steps to observing gravitational waves from spaceLISA Pathfinder collaboration1Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distributionof this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.Published under licence by IOP Publishing Ltd123456789011th International LISA Symposium  IOP PublishingIOP Conf. Series: Journal of Physics: Conf. Series 840 (2017) 012043  doi :10.1088/1742-6596/840/1/012043Preliminary results on the suppression of sensingcross-talk in LISA PathfinderGudrun Wanner and Nikolaos Karnesis on behalf of the LISAPathfinder collaborationMax Planck Institute for Gravitational Physics (Albert Einstein Institute) and Institute forGravitational Physics of the Leibniz Universitt HannoverE-mail: gudrun.wanner@aei.mpg.deAbstract. In the original paper describing the first measurements performed with LISAPathfinder, a bulge in the acceleration noise was shown in the 200 mHz - 20 mHz frequencyband. This bulge noise originated from cross-coupling of spacecraft motion into the longitudinalreadout and it was shown that it is possible to subtract this cross-talk noise. We discuss here themodel that was used for subtraction as well as an alternative approach to suppress the cross talkby realignment of the test masses. Such a realignment was performed after preliminary analysisof a dedicated cross-talk experiment, and we show the resulting noise suppression. Since then,further experiments have been performed to investigate the cross-coupling behaviour, howeveranalysis of these experiments is still on-going.1. IntroductionThe well known LISA Pathfinder differential acceleration measurement published in [1] anddisplayed for convenience in Fig. 1(a), showed a bulge in the noise curve in the 200 mHz -20 mHz frequency band. This bulge was caused by cross-coupling of spacecraft motion leakinginto the main differential acceleration measurement and it was shown in [1] that it is possibleto subtract the cross-coupling noise resulting in the blue curve in Fig. 1(a). This subtractionwas performed by fitting the following model to the measured acceleration noise, i.e. to the redtrace in Fig 1(a) yielding estimates of the coefficients Ci and δifo:∆gx-talk = C1φ¨[t] + C2η¨[t] + C3y¨[t] + C4z¨[t] + C5y[t] + C6z[t] + δifox¨1[t] . (1)Each term in this equation defines a cross-coupling of spacecraft motion to the differentialacceleration measurement:• All but the last summand are cross-coupling terms, because φ, η, y, z are orthogonalcoordinates to the differential readout along x. See Fig. 2(a) for a definition of the coordinatesystem.• The annotation k¯ with k ∈ {φ, η, y, z}, defines a mean motion of both test masses along k,which is a description of the spacecraft motion along −k.• The last summand, describes a residual coupling of spacecraft motion along x enteringthe differential readout. As the term ‘differential readout’ indicates, ∆g is defined as∆g = x¨2 − x¨1 (neglecting here corrections such as for applied or inertial forces). It should2123456789011th International LISA Symposium  IOP PublishingIOP Conf. Series: Journal of Physics: Conf. Series 840 (2017) 012043  doi :10.1088/1742-6596/840/1/012043(a) Subtraction methodLPF RequirementsLISA Requirements(b) Suppression methodFigure 1. (a): Result taken from [1], showing that the bulge at 200-20 mHz can be subtracted.(b) In this figure, no subtraction was performed. Instead the reduction was achieved by arealignment of the test masses prior to the second noise run.1therefore be insensitive to any common-mode motion, where x¨2 = x¨1. Since spacecraftmotion effectively shows as common test mass motion, ∆g should not sense spacecraftmotion. However, there is a residual leakage, because the interferometer readout responseis not identical to TM1 motion as to TM2 motion, such that ∆g = k2x¨2 − k1x¨1 withk2 ≈ k1 ≈ 1. The small difference between k1 and k2 causes the residual cross-coupling.Fitting eq. (1) to the measurement data and subtracting the resulting model works very well, asvisible in Fig. 1(a). However, this technique has several disadvantages: First of all, the modelprovides no interpretation what the coefficients physically mean, and therefore no explanationhow the cross-coupling could be suppressed. Secondly, several parameters show high correlation,such that the given model is not the only one allowing a fit and subtraction with low residuals.Instead, there is a set of models, performing comparably well. Finally, the coefficients vary overmission time, and this variation cannot be explained with the shown model.For these reasons, there is an ongoing effort, to build a physical model, which can describe thecross-coupling over the entire mission duration with a constant set of parameters, and can beused without adaptation for any set of data to subtract the bulge. Additionally, such a modelalso allows a direct suppression of the cross-talk. In fact, Fig. 1(a) shows a noise run performedin April 2016 (2016-04-08 to 2016-04-14), which was after a first realignment of the test masseshad already reduced the amount of cross-talk. This will be further discussed in the next section.2. Cross-coupling suppressionOf all terms given in eq. (1), we will focus now on the first four summands. For these four termsexists a multitude of mechanisms contributing to the parameters C1 to C4. Some of these aregeometric, others result from the interference of Gaussian beams and their phase detection (seee.g. [2, 3] for more information on some non-geometric cross-talk mechanisms). Unfortunately,the amount of cross-coupling originating from non-geometric effects needs to be regarded asunknown. The geometric effects however, are known very well and can be used to counteractany unknown effects.In Fig. 2 we illustrate two related geometrical effects. If a test mass is tilted with respect to1 Please note: the slight difference in curvature around 3 mHz in the LPF requirements in the two figures resultsfrom different notations: while in Fig. 1(a) correlated noise sources were assumed, we chose in Fig. 1(b) thenotation for uncorrelated noise sources.3123456789011th International LISA Symposium  IOP PublishingIOP Conf. Series: Journal of Physics: Conf. Series 840 (2017) 012043  doi :10.1088/1742-6596/840/1/012043(a) Coordinate systemTM1TM1(b) Lateral jitter couplingTM1TM1xCoR(c) Angular jitter couplingFigure 2. Illustration of the displacement of the laser beam reflection point on test mass 1(TM1). These are two related cases of geometrical cross-coupling.the optical bench and performs a lateral motion, the reflection point on the test mass moveslongitudinally, i.e. in x-direction. This causes a direct coupling of lateral motion into thelongitudinal readout signal, since the optical pathlength of the laser beam changes.A second geometric coupling effect occurs, if the test mass reflection point does not coincidewith the center of rotation of the test mass - as shown in Fig. 2(c). In this case, a test mass tiltcauses a longitudinal displacement of the reflection point and thereby a change in the opticalpathlength. In both cases, there was no motion of the test mass along x present, but sincethe reflection point on the test mass was displaced in x-direction, the interferometer senses anapparent test mass x-motion.In fact, these two coupling mechanisms are closely related since in both cases, the couplingoccurs due to a combination of rotation and lateral displacement, and both can be described bythe following simple equation:xrp = yϕ . (2)Here, xrp annotates the displacement of the reflection point along x, and thereby the apparentlongitudinal test mass displacement. The lateral shift between the center of rotation and thereflection point is labeled y, and ϕ is the test mass angle with respect to the optical bench. Thesame equation holds for the orthogonal plane:xrp = zη (3)where z is a vertical displacement of a reflection point with respect to the center of rotation, andη a test mass tilt around the y-axis, measured relative to the optical bench (see Fig. 2(a) for anillustration of the coordinate system). Since eq. (2) and (3) are linear in each degree of freedom,they can be used to counter act all other cross-coupling mechanisms - at least to first order.For example, assume a cross-coupling of TM1 ϕ-jitter was measured to be c1 · ϕ1 + O(ϕ21). Inthat case, a lateral displacement of TM1 by y1 = −c1 would suppress this measured cross talkto first order. This means, by a well chosen set of rotations and shifts of the test masses, theamount of cross-coupling leaking into ∆g can be reduced. In order to find the required offsets,we injected sinusoidal motion in each degree of freedom and extracted the parameters via fittinga dedicated model to the measured data. Fig. 3 shows an excerpt of the injections performed4123456789011th International LISA Symposium  IOP PublishingIOP Conf. Series: Journal of Physics: Conf. Series 840 (2017) 012043  doi :10.1088/1742-6596/840/1/012043Figure 3. Example of injections performed during the ‘engineering-day’ cross-talk experimentperformed on 2016-March-16. The labels ‘GRS z1,2’ indicate, that the shown vertical test massdisplacement (z1, z2) is taken from the ‘Gravitational Reference Sensor’ readout.on 2016-March-16: the common-mode and counter-mode injections into the vertical test massmotion. To the right-hand axis, also the measured differential acceleration ∆g is plotted, whichshows a clear correlation to the injections and thereby the cross-coupling. A preliminary dataanalysis resulted in a first estimate of the parameters which were then used to realign the testmasses. The resulting reduction of cross-coupling noise is given in Fig. 1(b). Please note, thateq. (2) and eq. (3) are not the physical model yet, which is needed to describe the cross-talk withconstant parameters over the entire mission duration. Instead, these are toy-models describingtwo geometric cross-talk effects. Furthermore, the parameters in this model are written herenot in terms of readout signals, which is necessary for applying the model to the data. The fullmodel is still work in progress, the analysis of the cross-talk behaviour is therefore still ongoingand further information will follow in a separate paper.3. AcknowledgmentsThis work has been made possible by the LISA Pathfinder mission, which is part of thespace-science program of the European Space Agency. We gratefully acknowledge support bythe European Space Agency (ESA) (22331/09/NL/HB, 16238/10/NL/HB), by the DeutschesZentrum fur Luft- und Raumfahrt (DLR) with funding of the Bundesministerium fur Wirtschaftund Energie with a decision of the Deutschen Bundestag (DLR project reference numbers FKZOQ 0501 and FKZ 50 OQ 1601), and thank the German Research Foundation for funding theCluster of Excellence QUEST (Centre for Quantum Engineering and Space-Time Research).References[1] Armano, et al, PRL 116, 231101 (2016), DOI: 10.1103/PhysRevLett.116.231101[2] Schuster, et al, Optics Express 10466 (2016) DOI: 10.1364/OE.24.01046[3] Schuster, et al, Applied Optics 54 (2015) DOI: 10.1364/AO.54.001010

Preliminary results on the suppression of sensing cross-talk in LISA Pathfinder

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