Tracking moving masses in several degrees of freedom with high precision and large dynamic range is a central aspect in many current and future gravitational physics experiments. Laser interferometers have been established as one of the tools of choice for such measurement schemes. Using sinusoidal phase modulation homodyne interferometry allows a drastic reduction of the complexity of the optical setup, a key limitation of multi-channel interferometry. By shifting the complexity of the setup to the signal processing stage, these methods enable devices with a size and weight not feasible using conventional techniques. In this paper we present the design of a novel sensor topology based on deep frequency modulation interferometry: the self-referenced single-element dual-interferometer (SEDI) inertial sensor, which takes simplification one step further by accommodating two interferometers in one optic. Using a combination of computer models and analytical methods we show that an inertial sensor with sub-picometer precision for frequencies above 10 mHz, in a package of a few cubic inches, seems feasible with our approach. Moreover we show that by combining two of these devices it is possible to reach sub-picometer precision down to 2 mHz. In combination with the given compactness, this makes the SEDI sensor a promising approach for applications in high precision inertial sensing for both next-generation space-based gravity missions employing drag-free control, and ground-based experiments employing inertial isolation systems with optical readout.

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.

To achieve subpicometer sensitivities in the millihertz band, laser interferometric inertial sensors rely on some form of reduction of the laser-frequency noise, typically by locking the laser to a stable frequency reference, such as the narrow-line-width resonance of an ultrastable optical cavity or an atomic or molecular transition. In this paper, we report on a compact laser-frequency stabilization technique based on an unequal-arm Mach-Zehnder interferometer that is subnanometer stable at $10\text{μ}\mathrm{Hz}$, subpicometer at $0.5$ mHz, and reaches a noise floor of $7\mathrm{fm}/\sqrt{\mathrm{Hz}}$ at 1 Hz. The interferometer is used in conjunction with a dc servo to stabilize the frequency of a laser down to a fractional instability below $4\times {10}^{-13}$ at averaging times from 0.1 to 100 s. The technique offers a wide operating range, does not rely on complex lock-acquisition procedures, and can be readily integrated as part of the optical bench in future gravity missions.

Future GRACE-like geodesy missions could benefit from adopting accelerometer technology akin to that of the LISA Pathfinder, which employed laser interferometric readout at the sub-picometer level in addition to the conventional capacitive sensing, which is at best at the level of 100 pm. Improving accelerometer performance holds great potential to enhance the scientific output of forthcoming missions, carrying invaluable implications for research in climate, water resource management, and disaster risk reduction. To reach sub-picometer displacement sensing precision in the millihertz range, laser interferometers rely on suppression of laser-frequency noise by several orders of magnitude. Many optical frequency stabilization methods are available with varying levels of complexity, size, and performance. In this paper, we describe the performance of a Mach–Zehnder interferometer based on a compact monolithic optic. The setup consists of a commercial fiber injector, a custom-designed pentaprism used to split and recombine the laser beam, and two photoreceivers placed at the complementary output ports of the interferometer. The structural stability of the prism is transferred to the laser frequency via amplification, integration, and feedback of the balanced-detection signal, achieving a fractional frequency instability better than 6 parts in ${10}^{13}$, corresponding to an interferometer pathlength stability better than $1\mathrm{pm}/\sqrt{\mathrm{Hz}}$. The prism was designed to host a second interferometer to interrogate the position of a test mass. This optical scheme has been dubbed “single-element dual-interferometer” or SEDI.

Tracking moving masses in several degrees of freedom with high precision and large dynamic range is a central aspect in many current and future gravitational physics experiments. Laser interferometers have been established as one of the tools of choice for such measurement schemes. Using sinusoidal phase modulation homodyne interferometry allows a drastic reduction of the complexity of the optical setup, a key limitation of multi-channel interferometry. By shifting the complexity of the setup to the signal processing stage, these methods enable devices with a size and weight not feasible using conventional techniques. In this paper we present the design of a novel sensor topology based on deep frequency modulation interferometry: the self-referenced single-element dual-interferometer (SEDI) inertial sensor, which takes simplification one step further by accommodating two interferometers in one optic. Using a combination of computer models and analytical methods we show that an inertial sensor with sub-picometer precision for frequencies above 10 mHz, in a package of a few cubic inches, seems feasible with our approach. Moreover we show that by combining two of these devices it is possible to reach sub-picometer precision down to 2 mHz. In combination with the given compactness, this makes the SEDI sensor a promising approach for applications in high precision inertial sensing for both next-generation space-based gravity missions employing drag-free control, and ground-based experiments employing inertial isolation systems with optical readout.

To reach sub-picometer sensitivity in the millihertz range, displacement sensors based on laser interferometry require suppression of laser-frequency noise by several orders of magnitude. Many optical frequency stabilization methods exist with varying levels of complexity, size, and performance. In this paper, we describe the performance of a compact Mach-Zehnder interferometer based on a monolithic optic. The setup consists of a commercial fiber injector, a custom-designed pentaprism used to split and recombine the laser beam, and two photoreceivers placed at the complementary output ports of the interferometer. The structural stability of the prism is transferred to the laser frequency via amplification, integration, and feedback of the balanced-detection signal, achieving a fractional frequency instability better than 6 parts in $10^{13}$, corresponding to an interferometer pathlength stability better than $10^{-12}$ m$/\sqrt{\mathrm{Hz}}$.