Abstract
High precision measurement of all six degrees of freedom of freely floating test masses is necessary for future gravitational space missions as the sensing noise is frequently a limiting factor in the overall performance of the instrument. Femto-meter sensitivity has been demonstrated with LISA Pathfinder which used a complex laser interferometric setup. However, these measurements where restricted to the length changes in one degree of freedom only. When aiming for sensing multiple degrees of freedom, typically capacitive sensing is used, which facilitates a compact setup but does not provide competitive precision. An alternative approach to improve the sensitivity beyond capacitance readout systems and to reduce the complexity of the setup, is to use optical levers. Here, we report on the realization of a test mass sensing system by means of a modulation/demodulation technique in combination with four optical levers detected by quadrant photodiodes. The results of our table-top experiment show that this configuration allows us to extract information on five degrees of freedom of a cubic test mass. With basic off-the-shelf laser diodes we demonstrate an angular resolution of below 600 nrad at frequencies between 10 mHz and 1 Hz (which is better than a conventional autocollimator) while simultaneously measuring the linear motion of the test mass with a precision of better than 300 nm in the same frequency band. Extension of the geometry will enable optical sensing of all six degrees of freedom of the test mass.
Highlights
Determining and tracking the position of, or the distance between freely floating, macroscopic reference objects, typically test masses (TMs), is the underlying concept for gravity related satellite missions such as LISA (Laser Interferometer Space Antenna) [1] which is planned to be launched around the year 2030 in order to detect gravitational waves
We have presented an optical test mass readout system based on the combination of four optical levers and quadrant photodiodes
Our systems allows for an independent measurement of the five degrees of freedom xTM, yTM, θTM, ψTM, and φTM of a cubic test mass
Summary
Determining and tracking the position of, or the distance between freely floating, macroscopic reference objects, typically test masses (TMs), is the underlying concept for gravity related satellite missions such as LISA (Laser Interferometer Space Antenna) [1] which is planned to be launched around the year 2030 in order to detect gravitational waves. The interferometric system implemented therein was limited to sensing one translational and two rotational degrees of freedom (DOFs) and simple upscaling of this technology to achieve readout in 6-DoFs would be challenging in terms of optical complexity and payload dimensions This has triggered the investigation of novel, more compact concepts such as deep phase modulation interferometry [7] and its variant deep frequency modulation interferometry [8] which both are promising candidates to facilitate high-precision interferometric measurements with a compact optical setup. The analysis presented here focuses on the two translational DoFs (TM motion along x and y -axis) and the rotational DoF around the z-axis (θ) To first order, these DoFs contain the information of a TM suspended from a fiber as can be realized in a laboratory setup, for example in a torsion pendulum. By measuring the two angular DoFs, θ and φ with a commercial autocollimator when a sinusoidal motion is applied to the hexapod, we show that the optical lever performs with a better sensitivity than the commercially available device
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