Compact integrated optical sensors and electromagnetic actuators for vibration isolation systems in the gravitational-wave detector KAGRA.

This paper reports on the design and characteristics of a compact module integrating an optical displacement sensor and an electromagnetic actuator for use with vibration-isolation systems installed in KAGRA, the 3-km baseline gravitational-wave detector in Japan. In the technical concept, the module belongs to a family tree of similar modules used in other interferometric gravitational-wave detector projects. After the initial test run of KAGRA in 2016, the sensor part, which is a type of slot sensor, was modified by increasing the spacing of the slot from 5 mm to 15 mm to avoid the risk of mechanical interference with the sensor flag. We confirm that the sensor performance is comparable to that of the previous design despite the modification. We also confirm that the sensor noise is consistent with the theoretical noise budget. The noise level is 0.5 nm/Hz1/2 at 1 Hz and 0.1 nm/Hz1/2 at 10 Hz, and the linear range of the sensor is 0.7 mm or more. We measured the response of the actuator to be 1 N/A and also measured the resistances and inductances of coils of the actuators to confirm consistency with theory. Coupling coefficients among the different degrees of freedom were also measured and shown to be negligible, varying little between designs. A potential concern about thermal noise contribution due to eddy current loss is discussed. As of 2020, 42 of the modules are in operation at the site.

Characterization of the room temperature payload prototype for the cryogenic interferometric gravitational wave detector KAGRA.

KAGRA is a cryogenic interferometric gravitational wave detector currently under construction in the Kamioka mine in Japan. Besides the cryogenic test masses, KAGRA will also rely on room temperature optics which will hang at the bottom of vibration isolation chains. The payload of each chain comprises an optic, a system to align it, and an active feedback system to damp the resonant motion of the suspension itself. This article describes the performance of a payload prototype that was assembled and tested in vacuum at the TAMA300 site at the NAOJ in Mitaka, Tokyo. We describe the mechanical components of the payload prototype and their functionality. A description of the active components of the feedback system and their capabilities is also given. The performance of the active system is illustrated by measuring the quality factors of some of the resonances of the suspension. Finally, the alignment capabilities offered by the payload are reported.

Interferometric measurement of angular motion.

This paper describes the design and realization of a homodyne polarization interferometer for measuring angular motion. The optical layout incorporates carefully designed cat's eye retroreflectors that maximize the measurable range of angular motion and facilitate initial alignment. The retroreflectors are optimized and numerically characterized in terms of defocus and spherical aberrations using Zemax software for optical design. The linearity of the measurement is then calculated in terms of the aberrations. The actual physical interferometer is realized as a compact device with optical components from stock and without relying on adjustable holders. Evaluation of its performance using a commercial autocollimator confirmed a reproducibility within 0.1%, a non-linearity of less than 1 ppm with respect to the autocollimator, an upper limit to its sensitivity of about 5 × 10(-11) rad/Hz from audioband down to 100 mHz and an angular measurement range of more than ±1°.

Mirror tilt immunity interferometry with a cat's eye retroreflector.

This paper describes the behavior of a cat's eye retroreflector, which is incorporated in a novel way in a double-pass homodyne polarization interferometer. The amount of mirror tilt immunity a cat's eye provides is calculated within the paraxial approximation using 4×4 ABCD matrices. It is found that there is a position of the target mirror in which the tilt immunity is at a maximum. A real cat's eye, which is affected by aberrations, is optimized and examined using Zemax software for optical design. The maximum amount of mirror tilt immunity is numerically calculated and written in terms of defocus and spherical aberration. Finally, for the purposes of comparison, the amplitude of the Lissajous pattern as the target mirror tilts is calculated for both an interferometer with an integrated cat's eye and an interferometer with a cube corner.

Development of a second generation torsion balance based on a spherical superconducting suspension.

This paper describes the development of a second generation superconducting torsion balance to be used for a precision measurement of the Casimir force and a short range test of the inverse square law of gravity at 4.2 K. The instrument utilizes niobium (Nb) as the superconducting element and employs passive damping of the parasitic modes of oscillation. Any contact potential difference between the torsion balance and its surroundings is nulled to within approximately 50 mV by applying known DC biases and fitting the resulting parabolic relationship between the measured torque and the applied voltage. A digital proportional-integral-derivative servo system has been developed and characterized in order to control the azimuthal position of the instrument. The angular acceleration and displacement noise are currently limited by the capacitive sensor at the level 3x10(-8) rad s(-2)/ squarerootHz and 30 nm/ squarerootHz at 100 mHz. The possibility of lossy dielectric coatings on the surface of the torsion balance test masses is also investigated. Our measurements show that the loss angles delta are (1.5+/-2.3)x10(-4) and (2.0+/-2.2)x10(-4) at frequencies of 5 and 10 mHz, respectively. These values of loss are not significant sources of error for measurements of the Casimir force using this experimental setup.