K. V. Tokmakov

A low-noise transimpedance amplifier for the detection of "Violin-Mode" resonances in advanced Laser Interferometer Gravitational wave Observatory suspensions

This paper describes the design and performance of an extremely low-noise differential transimpedance amplifier, which takes its two inputs from separate photodiodes. The amplifier was planned to serve as the front-end electronics for a highly sensitive shadow-displacement sensing system, aimed at detecting very low-level Violin-Mode (VM) oscillations in 0.4 mm diameter by 600 mm long fused-silica suspension fibres. Four such highly tensioned fibres support the 40 kg test-masses/mirrors of the Advanced Laser Interferometer Gravitational wave Observatory interferometers. This novel design of amplifier incorporates features which prevent noise-gain peaking arising from large area photodiode (and cable) capacitances, and which also usefully separate the DC and AC photocurrents coming from the photodiodes. In consequence, the differential amplifier was able to generate straightforwardly two DC outputs, one per photodiode, as well as a single high-gain output for monitoring the VM oscillations-this output being derived from the difference of the photodiodes two, naturally anti-phase, AC photocurrents. Following a displacement calibration, the amplifiers final VM signal output was found to have an AC displacement responsivity at 500 Hz of (9.43 ± 1.20) MV(rms) m(-1)(rms), and, therefore, a shot-noise limited sensitivity to such AC shadow- (i.e., fibre-) displacements of (69 ± 13) picometres/√Hz at this frequency, over a measuring span of ±0.1 mm.

Bi-filar pendulum mode Q factor for silicate bonded pendulum

An all fused silica pendulum with record Q factor fabricated using the technique of hydroxide-catalysis bonding is described. Possible sources of loss which limited the measured Q are discussed.

An AC modulated near infrared gain calibration system for a “Violin-Mode” transimpedance amplifier, intended for advanced LIGO suspensions

The background to this work was a prototype shadow sensor, which was designed for retro-fitting to an advanced LIGO (Laser Interferometer Gravitational wave Observatory) test-mass/mirror suspension, in which a 40 kg test-mass/mirror is suspended by four approximately 600 mm long by 0.4 mm diameter fused-silica suspension fibres. The shadow sensor comprised a LED source of Near InfraRed (NIR) radiation, and a tall-thin rectangular silicon photodiode detector, which together were to bracket the fibre under test. The photodiode was positioned so as to be sensitive (primarily) to transverse Violin-Mode vibrations of such a fibre, via the oscillatory movement of the shadow cast by the fibre, as this moved across the face of the detector. In this prototype shadow sensing system the photodiode was interfaced to a purpose-built transimpedance amplifier, this having both AC and DC outputs. A quasi-static calibration was made of the sensors DC responsivity, i.e., incremental rate of change of output voltage versus fibre position, by slowly scanning a fused-silica fibre sample transversely through the illuminating beam. The work reported here concerns the determination of the sensors more important AC (Violin-Mode) responsivity. Recognition of the correspondence between direct AC modulation of the source, and actual Violin-Mode signals, and of the transformative role of the AC/DC gain ratio for the amplifier, at any modulation frequency, f, resulted in the construction of the AC/DC calibration source described here. A method for determining in practice the transimpedance AC/DC gain ratio of the photodiode and amplifier, using this source, is illustrated by a specific numerical example, and the gain ratio for the prototype sensing system is reported over the frequency range 1 Hz-300 kHz. In fact, a maximum DC responsivity of 1.26 kV.m(-1) was measured using the prototype photodiode sensor and amplifier discussed here. Therefore, the measured AC/DC transimpedance gain ratio of 922.5 for this sensor, at 500 Hz, translated into a maximum Violin-Mode (AC) responsivity of (1.16 ± 0.05) MV m(-1), at that frequency.

Load-cell based characterization system for a “Violin-Mode” shadow-sensor in advanced LIGO suspensions

The background to this work was a prototype shadow sensor, which was designed for retro-fitting to an advanced LIGO (Laser Interferometer Gravitational wave Observatory) test-mass/mirror suspension, in which 40 kg test-mass/mirrors are each suspended by four approximately 600 mm long by 0.4 mm diameter fused-silica suspension fibres. The shadow sensor comprised a LED source of Near InfraRed (NIR) radiation and a rectangular silicon photodiode detector, which, together, were to bracket the fibre under test. The aim was to detect transverse Violin-Mode resonances in the suspension fibres. Part of the testing procedure involved tensioning a silica fibre sample and translating it transversely through the illuminating NIR beam, so as to measure the DC responsivity of the detection system to fibre displacement. However, an equally important part of the procedure, reported here, was to keep the fibre under test stationary within the beam, whilst trying to detect low-level AC Violin-Mode resonances excited on the fibre, in order to confirm the primary function of the sensor. Therefore, a tensioning system, incorporating a load-cell readout, was built into the test fibres holder. The fibre then was excited by a signal generator, audio power amplifier, and distant loudspeaker, and clear resonances were detected. A theory for the expected fundamental resonant frequency as a function of fibre tension was developed and is reported here, and this theory was found to match closely with the detected resonant frequencies as they varied with tension. Consequently, the resonances seen were identified as being proper Violin-Mode fundamental resonances of the fibre, and the operation of the Violin-Mode detection system was validated.

A step-wise steerable source of illumination for low-noise "Violin-Mode" shadow sensors, intended for use in interferometric gravitational wave detectors.

A steerable low-noise source of illumination is described for shadow-sensors having a displacement sensitivity of ∼100 pm (rms)/√Hz, at 500 Hz, over a measuring span of at least ±0.5 mm. These sensors were designed to detect lateral Violin-Mode resonances in the highly tensioned fused-silica suspension fibres of the test-masses/mirrors for the Advanced Laser Interferometer Gravitational Wave Observatory gravitational wave detectors. The shadow sensors-one intended for each of the four fibres in a suspension-comprised a source of Near InfraRed (NIR) radiation (emitter) and a differential shadow-displacement sensor (detector), these bracketing the fibre under test. The suspension fibres themselves were approximately 600 mm long by 0.4 mm in diameter, and when illuminated from the side, they cast narrow, vertical, shadows onto their respective detectors-these being located at an effective distance of 50 fibre diameters behind the axes of the fibres themselves. The emitter described here was designed to compensate for a significant degree of mechanical drift or creep over time in the mean position of its suspension fibre. This was achieved by employing five adjacent columns of 8u2009 × miniature NIR LEDs (Light Emitting Diodes, λ = 890 nm), with one column being activated at a time. When used in conjunction with a reverse Galilean telescope, the LED sources allowed the collimated beam from the emitter to be steered azimuthally in fine angular increments (0.65°), causing the fibres shadow to move laterally, in a step-wise manner, across the plane of its facing detector. Each step in shadow position was approximately 0.23 mm in size, and this allowed the fibres shadow to be re-centred, so as to bridge once again both elements of its photodiode detector-even if the fibre was off-centred by as much as ±0.5 mm. Re-centring allowed Violin-Mode vibrations of the fibre to be sensed once again as differential AC photocurrents, these flowing in anti-phase in the two elements of the split-photodiode detector.

Erratum: Beating the spin-down limit on gravitational wave emission from the Crab pulsar (vol 683, pg L45, 2008)

This is an Erratum for the article 2008 ApJ 683 L45 A processing error in the signal template used in this search led to upper limits about 30% lower than we now know is warranted by the early S5 data. We have re-analyzed that data and find new upper limits on the strain parameter h(0) of 4.9 x 10(-25)/3.9 x 10(-25) for uniform/restricted prior assumptions concerning the Crab inclination and polarization angles. These results have now been superseded by upper limits of 2.6 x 10(-25)/2.0 x 10(-25) based on the full S5 data and presented in Abbott et al. (2009). The multitemplate search was not affected by the error.