A vertical inertial sensor with interferometric readout

Abstract High precision interferometers such as gravitational-wave detectors require complex seismic isolation systems in order to decouple the experiment from unwanted ground motion. Improved inertial sensors for active isolation potentially enhance the sensitivity of existing and future gravitational-wave detectors, especially below 30 Hz, and thereby increase the range of detectable astrophysical signals. This paper presents a vertical inertial sensor which senses the relative motion between an inertial test mass suspended by a blade spring and a seismically isolated platform. An interferometric readout was used which introduces low sensing noise, and preserves a large dynamic range due to fringe-counting. The expected sensitivity is comparable to other state-of-the-art interferometric inertial sensors and reaches values of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>10</mml:mn> </mml:mrow> </mml:msup> <mml:mrow> <mml:mi mathvariant="normal">m</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">H</mml:mi> <mml:mi mathvariant="normal">z</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mrow> <mml:msup> <mml:mo stretchy="false">)</mml:mo> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> at 100 mHz and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>12</mml:mn> </mml:mrow> </mml:msup> <mml:mrow> <mml:mi mathvariant="normal">m</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">H</mml:mi> <mml:mi mathvariant="normal">z</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mrow> <mml:msup> <mml:mo stretchy="false">)</mml:mo> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> at 1 Hz. The potential sensitivity improvement compared to commercial L-4C geophones is shown to be about two orders of magnitude at 10 mHz and 100 mHz and one order of magnitude at 1 Hz. The noise performance is expected to be limited by thermal noise of the inertial test mass suspension below 10 Hz. Further performance limitations of the sensor, such as tilt-to-vertical coupling from a non-perfect levelling of the test mass and nonlinearities in the interferometric readout, are also quantified and discussed.