Quasi-static displacement calibration system for a “ Violin-Mode ” shadow-sensor intended for Gravitational Wave detector suspensions

This paper describes the design of, and results from, a calibration system for optical linear displacement (shadow) sensors. The shadow sensors were designed to detect “Violin-Mode” (VM) resonances in the 0.4 mm diameter silica fibre suspensions of the test masses/mirrors of Advanced Laser Interferometer Gravitational Wave Observatory gravitational wave interferometers. Each sensor illuminated the fibre under test, so as to cast its narrow shadow onto a “synthesized split photodiode” detector, the shadow falling over adjacent edges of the paired photodiodes. The apparatus described here translated a vertically orientated silica test fibre horizontally through a collimated Near InfraRed illuminating beam, whilst simultaneously capturing the separate DC “shadow notch” outputs from each of the paired split photodiode detectors. As the ratio of AC to DC photocurrent sensitivities to displacement was known, a calibration of the DC response to quasi-static shadow displacement allowed the required AC sensitivity to vibrational displacement to be found. Special techniques are described for generating the required constant scan rate for the test fibre using a DC motor-driven stage, for removing “jitter” at such low translation rates from a linear magnetic encoder, and so for capturing the two shadownotch signals at each micrometre of the test fibre’s travel. Calibration, across the four detectors of this work, gave a vibrational responsivity in voltage terms of (9.45 ± 1.20) MV (rms)/m, yielding a VM displacement sensitivity of (69 ± 13) pm (rms)/√Hz, at 500 Hz, over the required measuring span of ±0.1 mm. © 2014 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License. [http://dx.doi.org/10.1063/1.4895640]


I. INTRODUCTION A. Background
A prototype system of four shadow sensors was designed to be retro fitted to an Advanced LIGO (Laser Interferometer Gravitational Wave Observatory) test mass/mirror suspension, in which a 40 kg test mass was suspended by four fused silica fibres.2][3][4][5] These shadow sensors-one per fibre-each comprised an emitter and a detector, which bracketed the illuminated fibre.The emitter was in the form of a collimated source of Near In-fraRed (NIR) illumination, coming from a column of miniature light emitting diodes (LEDs), 9 such that the source casts a vertical shadow of its illuminated fibre onto the facing detector.The corresponding detector was a "synthesized split photodiode," and this was optimized for its (differential) response to lateral shadow displacement. 8There is negligible optical absorption in a fused silica fibre measuring 0.4 mm in diameter, over a wavelength range for the incident light of 200 nm-2 μm.The shadow cast by such a fibre, when illuminated from its side, depends instead primarily on strong refraction, and a very small amount of reflection, at the fibre's cylindrical surface.Illuminating beams in the Near InfraRed (λ = 890 nm) were employed in the work reported here because this wavelength is well-matched to silicon photodiode-based shadow sensors.The collimated beams used were of low intensity (2.8 W m −2 ), and unmodulated, in order to avoid potential interference with the main gravitational wave interferometer (λ = 1064 nm).A schematic cut-away diagram of the shadow sensor is shown in Figure 1, and a photo of it is presented in Figure 2the shadow sensor as a whole being described in detail in Refs.8 and 9.
The primary purpose of the full detection system was to monitor any transverse "Violin-Mode" (VM) resonances that might be excited on these fibres, 10 since the frequencies of these fundamental modes and their harmonics spanned the gravitational wave detection bandwidth.However, the system of shadow sensors was capable also of detecting any "large amplitude," very low frequency, transverse pendulummode motion of the test mass and its suspension fibres (at ∼0.6 Hz). 10,11 nce detected, the oscillatory motion of the suspension fibres then could be cold damped, actively. 6,7 M resonances in the highly tensioned silica suspension fibres were found to have fundamental frequencies ∼500 Hz, and for this application the shadow sensors were required to have a fibre (i.e., a shadow) displacement sensitivity of 100 pm (rms)/ √ Hz at this frequency, over a ±0.1 mm range of fibre position.

B. The displacement calibration procedure
The displacement calibration system for the shadow sensors, which is described below, was designed and built in order to help confirm that the displacement sensitivity of the full detection system met the target value given above.Naturally, this confirmation fell into two parts: first, a  The test-fibre sample was moved at a constant rate of traverse so as to cut through the sensor's NIR beam at right angles to its optic axis (i.e., in this figure either into, or out of, the page).Please refer to the text.
determination of the raw displacement responsivity, in volts per metre of fibre displacement; and second, a determination of the intrinsic noise level at the detection amplifier's output, this being in the form of noise power spectral density, measured in volts 2 /Hz, or (more usefully) in the form of noise amplitude spectral density, measured in volts (rms)/ √ Hz-at 500 Hz (say).The work reported here addresses the first part, i.e., the calibration of the displacement responsivity.The noise performance of the shadow sensors has been described elsewhere. 8,9  order to measure their displacement responsivities, each of the four emitter-detector pairs underwent the following calibration procedure, with the relative emitter/fibre/detector distances mimicking those of a VM sensor installed in an actual test-mass suspension: a vertically orientated silica fibre test sample (diameter = 0.4 mm) was moved FIG. 2. Left: silica test-fibre holder, showing the tensioning arrangement, and tension monitoring system.In the work reported here, the tension was set to 0.55 kg wt.The holder was bolted onto the carriage of a linear translation stage.Right: photo of the silica test fibre as it was being scanned transversely through the shadow sensor's NIR beam.A dual shadow detector housing is shown at the rear, centre left, of the photo.Here, only the rightmost of the two synthesized-split-photodiode detectors (viewed from the front of the housing) was being employed.The NIR emitter is on the right of the photo.
horizontally, at a steady translation rate, so as to pass from side-to-side through the emitter under test's static, collimated, NIR beam (λ = 890 nm), as shown in Figure 1.In this way, the fibre cast a moving shadow onto the facing, fixed, detector.Simultaneously, the DC (photocurrent-derived) voltages from the two sensing elements in each detector were recorded as a function of fibre (i.e., of shadow) position-at every 1 μm incremental change in its position, in fact.The emitter-to-fibre and detector-to-fibre stand-off separations were each 20 mm.

C. "Shadow notch" measurements
The shadow sensor's detector comprised two adjacent rectangular ("tall, narrow": 29.1 mm × 0.86 mm) photodiode elements, with essentially no dead band between them.Thus, as the fibre's shadow passed over each of these elements, in turn, it caused a "shadow notch" to appear in their respective DC response-as shown in Figure 11.By differentiating these signals off-line with respect to test-fibre position (ξ ), the rate of change of differential DC voltage with fibre positioni.e., the DC displacement responsivity-was found.However, the dimensionless ratio of AC to DC photocurrent (shadow displacement) responsivity was determined in advance by the design of the transimpedance amplifier used.Nominally, this ratio had a value of 1000, mid-band. 13Therefore, a calibration of the "DC responsivity to quasi-static displacement" allowed the required "AC responsivity to vibrational displacement" to be deduced, at any vibrational frequency (500 Hz, say).
Therefore, a "bespoke" piece of apparatus was designed and constructed so that these DC displacement responsivity measurements could be made.A test-fibre holder was constructed, shown both schematically and in the photo of Figure 2, and this was attached to the carriage of a low-cost manual leadscrew-actuator stage, with a 190 mm stroke.The stage itself then was adapted to be driven at a regulated, constant, speed by a DC motor coupled to an in-line planetary gearbox.The position of the fibre was recorded with a resolution of ±1 μm by retro fitting an inexpensive commercial linear magnetic encoder to the stage.

II. THE SHADOW SENSOR
A cut-away schematic view of the shadow sensor used in this work is shown in Figure 1.The source of illumination in the emitter was a single column of 16 × OP224 NIR LEDs, arranged as two strings of 8 series-connected LEDs (for redundancy), with alternate LEDs belonging to the same string. 9Only one string was active at any time, this being powered by a constant current of 25 mA.The radiation (λ = 890 nm) from this source was collimated by the 80 mm focal length lens, and this casts a moving shadow of the illuminated fused silica fibre sample onto the detector-the shadow moving at the same speed as the fibre.The detector was a synthesized split photodiode, outlined in Sec.I C above. 8The DC output voltages derived from the detector's two sensing elements, denoted here by VDC,a and VDC,b, were captured at every 1 μm increment of fibre position, with 12-bit accuracy, typically over a measuring span of 15 mm.

III. THE TEST-FIBRE HOLDER
The holder, which was used to keep the silica test-fibre sample under tension, is shown in Figure 2. It was bolted to the carriage of the leadscrew-driven actuator stage, the stage itself being driven by a DC motor via a 1621:1 planetary reduction gearbox.The fibre was attached at its upper end to a pivoted tensioning arm, which was provided with a knurled tension adjustment knob, whilst the lower end of the fibre was attached to the free end of load cell having a 10 kg wt.Full scale (the test fibre was much shorter than the 600 mm used in aLIGO, and so a smaller tension was adequate for this calibration work-as indicated in the figure caption).This load cell, together with its signal-conditioning interface, allowed the actual tension in the fibre to be monitored, and adjusted.

IV. THE TRIPLE-OUTPUT TRANSIMPEDANCE AMPLIFIER
The transimpedance amplifier used in this work is shown schematically in Figure 3.It is described in detail elsewhere. 13he right side of Figure 3 shows in plan view an incident, collimated, NIR beam illuminating a suspension fibreilluminating it from the right.The continuation of this incident beam, together with the shadow cast by the fibre, next falls across the facing ridge of a 45 • -90 • -45 • Au/Cr mirrorcoated beam-splitting prism.The reflected (split) NIR beam then is incident, albeit differentially, onto the two photodiode detector elements labelled PDa and PDb, generating within these elements the photocurrents i PDa and i PDb , respectively, as indicated in the figure .In Figure 3, these two photocurrents form the signal inputs to the "Transimpedance Amplifiers" block, which functioned as follows: the mean, "DC," components of these photocurrents were amplified to yield the (positive) DC output voltages VDC,a and VDC,b, mentioned above in Sec.II, where both of these voltages were generated through a Only one of the two synthesized-split-photodiode detectors which were located within this housing was employed, at a time.Here, only the leftmost detector (seen from the rear of the housing) was in use.In the figure, D houses the DC motor driver (Figure 5), M is the in-line motor plus gearbox, and E houses the position encoder interface (Figures 8 and 9).Right: The emitter (LED source) is seen mounted on an adjustable Lab-jack, which was used to set its elevation to coincide with the mid plane of the silica test fibre sample (labelled fibre).The DC motor-driven leadscrew translated the test fibre in its holder slowly (over a period of 4-5 min), so that it passed laterally through the NIR beam coming from the emitter to the detector (please see Figure 1).The bold arrow in the left figure indicates the scanning sense of the fibre sample.All of the scanner's components were mounted onto the optical baseplate in the photos, this having 45 • angled corners.The-essentially-square baseplate measured 440 mm on a side.The 190 mm track of the linear stage had microswitches at its ends, to prevent over-run of the stage's driven carriage.
transimpedance gain of R = 120 k .Any AC photocurrent components, however, were amplified along separate transduction pathways, so that for these components the transimpedance gains were 10× higher (at R = 1.2 M ), yielding the intermediate AC voltages VAC,a and VAC,b in Figure 3these voltages being in natural anti-phase.These two AC voltages were differenced-thereby doubling the signal's sizebefore being amplified further by a factor of 100, as indicated in the figure, to yield the single Violin-Mode AC output voltage, VM AC.In practice, the AC pass band of this amplifier extended from 226 Hz-8.93 kHz (−3 dB points).
Therefore, the nominal AC to DC differential (shadow) displacement responsivities stood in the ratio 1000:1 (mid band).In practice, due to the amplifier's circumscribed pass band, and roll-off towards both high and low frequencies, this dimensionless ratio was found to be 976 ± 4 mid band, at 1.48 kHz, and 904 ± 4, at 500 Hz.

V. THE SCANNING SYSTEM
Figure 4 shows two views of the complete calibration apparatus.This apparatus allowed the vertically orientated, tensioned, silica test fibre to be translated at a constant rate so that it passed from side-to-side through the collimated NIR beam linking the shadow sensor's emitter and detector.For the intended brief use of this calibration system the relatively high cost of an off-the-shelf scanning unit was not justified.Therefore, a much lower-cost option was developed in-house, and this is described briefly, below.This approach proved to be adequate in resolution, and had the added benefit of being tailored to the very low, and constant speed, scanning rates that were eventually used.Parenthetically, a very constant (and low) rate of translation of the fibre through the emitter's NIR beam turned out to be essential, in order to avoid apparently variable spatial rates of change of shadow signal being measured-in particular, as the fibre's shadow passed from detector element PDa to element PDb.Such variable rates of change did arise, initially, in this work, before the discovery that they actually were artefacts of the frequency-dependent cross-over network within the Transimpedance Amplifiers block, which was used to separate, conveniently, the AC from the DC photocurrents.Generally, scanning rates in the range 50-60 μm s −1 were used, with a constancy of translation rate at the 0.1% level.This was achieved by utilizing the constantspeed DC motor controller shown in Figure 5.

A. The constant-speed DC motor controller
The constant-speed motor driver of Figure 5 [Ref.14] functioned as follows: op-amps IC3 and IC4 compensated for the DC motor's winding resistance plus connecting leads, labelled R w (=3.5 ) in the figure, by creating effectively a negative resistance of this value in series with the motor itself.As a direct result of this compensation the circuitry around these two op-amps forced the motor's back emf to be equal to the voltage applied to the non-inverting input of IC3which was itself equal, under steady state conditions, to the input voltage set at the point V in the circuit.Since the motor's back emf was necessarily directly proportional to its rotational speed, this compensation forced the motor's speed to be held constant, for a constant input voltage-irrespective of any changes in frictional torque, or load, on the motor.
Figure 6 shows how the rotational rate of the output shaft of the gearbox-used to drive the leadscrew of the translation stage-was proportional to the applied control voltage.

B. Interface for eliminating "jitter" from the magnetic linear encoder: The "dither filter"
The DC motor driven translation stage was fitted with a Renishaw LM10 magnetic linear (incremental) position encoder, the pickup head of the encoder being attached to the moving carriage, and a magnetically encoded self-adhesive ribbon track being attached to the aluminium alloy optical  4).The control voltage (point V in the circuit diagram), which governed the motor's speed of rotation, was set using one of two switch-selectable potentiometers: "speed 1" or "speed 2" (or STOP).This circuit kept the speed of rotation of the motor constant, in spite of any varying load torque due to the attached gearbox and leadscrew-driven stage.It was achieved by effectively cancelling out the winding resistance of the DC motor, and its leads (R w = 3.5 ).Please refer to the text.The motor (Maxon A-max 110119) was used to drive an Ondrives LA7-30002 leadscrew-actuator stage via a 1621:1 planetary reduction gearbox (Maxon GP 22 A 110341).
baseplate.Figure 7 shows the digital quadrature phase output signals A and B from the linear encoder, as the carriage of the translational stage-carrying the silica test fibre in its holder-was moving very slowly at a constant rate parallel to this track: here, at a translation rate of ∼0.9 μm s −1 .Besides the two quadrature phase signals shown in the figure, the encoder also provided a datum signal (denoted by Z in Figure 8), so that absolute positions of the test fibre relative to that datum point could be recorded.Figure 7 demonstrates that the switching edges of the digital A and B phase outputs from the magnetic encoder could be corrupted severely by dither noise at the very low translation rates used in this work, and such signals could not be used reliably to keep track of the moving carriage's position.The source of this dither was possibly vibration coming from the motor/gearbox/leadscrew.Even at the somewhat higher translation rates which were generally used for profiling the shadow-notches, as described in Sec.IV, these signals still could be corrupted.
Consequently, a digital interface was designed and implemented in order to overcome this problem (it is labelled E in Figure 4).Figure 8 shows how the two quadrature signals A and B from the encoder were "cleaned" using FIG.6.In the figure the "r.p.m." ordinate refers to the output shaft of the 1621:1 planetary reduction gearbox, which drove the leadscrew-actuator.The "Input voltage" abscissa refers to the voltage used to set the constant speed of the 9 V DC motor, which drove the gearbox.This voltage (at point "V" in Figure 5) therefore determined the constant traversing rate of the linear stage (please refer to the text).
This article is copyrighted as indicated in the article.Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 130.159.82.88 On: Mon, 20 Oct 2014 10:39:25 FIG. 7. The Renishaw LM10D01_07 linear magnetic encoder, with 1 μm position resolution, was intended for use primarily at higher translation rates (up to 4 m s −1 ).It was not optimised for use at very low translation rates, and the figure shows typical phase A and phase B outputs from this magnetic position sensor at a very low translation rate of ∼0.9 μm s −1 .The two phase outputs are seen to be correctly in quadrature, but with significant dither-induced noise at their transitional switching edges-possibly induced by the leadscrew drive of the mechanical translation stage.These signals were the inputs to the dither filter of Figures 8 and 9.
a microcontroller based dither-filter, which functioned as a transition-noise-eliminating interface.This interface also generated brief (1.6 μs) synchronising clock (CLK) pulses on every edge of the cleaned quadrature signals A_out and B_out, so that these pulses could be used to trigger data capture of the detector's output voltages VDC,a and VDC,b as a function of the silica test fibre's position.In this way, the detector's two DC voltages, VDC,a and VDC,b, were recorded simultaneously at every 1 μm step, and with 12-bit resolution, using a National Instruments USM-6259 DAQ device, con-trolled by a LabView data acquisition program running on a laptop PC.
Figure 9 shows the algorithm used by the microcontroller unit (MCU) to remove jitter from the LM10's quadrature phase outputs A and B. The algorithm used a system of flags to determine if phase transitions were allowable, i.e., followed a permissible pattern on the encoder's outputs A and B, or not, ignoring dither transitions (jitter) that formed no proper part of this pattern.Figure 10 3), "cleaned these up" using this algorithm, and then output digital signals A_out and B_out-with the dither noise eliminated (as shown in Figure 8).Please refer to the text for a description of the algorithm's operation.FIG.11.Shadow-notch signals VDC,a and VDC,b from adjacent photodiode elements PDa and PDb, respectively.These data were captured with 12bit resolution at every 1 μm change in position of the 0.4 mm diameter silica test-fibre sample, using the CLK signal (shown in Figure 8) as the sampling trigger.Here, the silica test fibre was scanned slowly in the positive ξ direction, so that its shadow fell first onto photodiode element PDa, and then onto element, PDb.

105003- 2 N
FIG.1.Schematic cut-away view of the shadow sensor (Emitter + Detector), which was mounted rigidly onto an optical plate, as shown in Figures2 and 4. The test-fibre sample was moved at a constant rate of traverse so as to cut through the sensor's NIR beam at right angles to its optic axis (i.e., in this figure either into, or out of, the page).Please refer to the text.
FIG.1.Schematic cut-away view of the shadow sensor (Emitter + Detector), which was mounted rigidly onto an optical plate, as shown in Figures2 and 4. The test-fibre sample was moved at a constant rate of traverse so as to cut through the sensor's NIR beam at right angles to its optic axis (i.e., in this figure either into, or out of, the page).Please refer to the text.

FIG. 3 .
FIG. 3. "Plan view" schematic of the VM shadow detector and its Transimpedance Amplifiers for an individual silica test fibre.The collimated Near InfraRed beam illuminating the suspension fibre-from the right-fell, together with the shadow of that fibre, across the facing ridge of a 45 • -90 • -45 • Au/Cr mirror-coated beam-splitting prism.The prism caused the two photodiode detector elements PDa and PDb to appear to merge, via reflection, along the ridge of the prism.The moving shadow of the fibre therefore slipped seamlessly across the detector from one element to the other.VM oscillations on the fibre therefore generated AC photocurrent components flowing in anti phase in PDa and PDb.This article is copyrighted as indicated in the article.Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 130.159.82.88 On: Mon, 20 Oct 2014 10:39:25 FIG.5.Circuit diagram of the constant-speed DC motor driver (D, in Figure4).The control voltage (point V in the circuit diagram), which governed the motor's speed of rotation, was set using one of two switch-selectable potentiometers: "speed 1" or "speed 2" (or STOP).This circuit kept the speed of rotation of the motor constant, in spite of any varying load torque due to the attached gearbox and leadscrew-driven stage.It was achieved by effectively cancelling out the winding resistance of the DC motor, and its leads (R w = 3.5 ).Please refer to the text.The motor (Maxon A-max 110119) was used to drive an Ondrives LA7-30002 leadscrew-actuator stage via a 1621:1 planetary reduction gearbox (Maxon GP 22 A 110341).
FIG. 8. Circuit diagram of the magnetic position encoder's dither filter.The digital input signals to this filter, labelled A, B, and Z, were, respectively, the two quadrature outputs, and the datum output, from a Renishaw LM10D01_07 linear magnetic encoder.At low translation rates, A and B exhibited significant jitter around their logic transitions, as shown in Figure 7.An LS084 IC generated automatically a clock pulse (CLK) on each "cleaned" quadrature edge.The CLK (trigger) pulses were 1.6 μs wide: they were used to trigger data capture (please refer to the text).The PIC16F684 MCU ran at an 8 MHz internal clock frequency.An example of the now-cleaned signals is shown in Figure 10.This article is copyrighted as indicated in the article.Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 130.159.82.88 On: Mon, 20 Oct 2014 10:39:25

Figure 11
Figure 11 shows an example of a pair of detected "shadow notch" signals, these being generated by the detector's photodiode elements PDa and PDb as the illuminated 0.4 mm diameter test-fibre sample was translated linearly across in front of them.The fibre's developing position was generated by the National Instruments DAQ device, which was configured to read the Z, A (A_out), and B (B_out) inputs from the dither filter.Simultaneously, the DAQ sampled and stored the DC voltages VDC,a and VDC,b, shown in the figure, on every CLK pulse.In reality, these "DC" responses were convolutions between the fibre's actual shadow and the width of each detector element (0.86 mm, on average).