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The optical truss interferometer (OTI) is a contingent subsystem proposed for the LISA telescopes to aid in the verification of a $1 \frac{\mathrm{pm}}{\sqrt{\mathrm{Hz}}}$ optical path length stability. Each telescope would be equipped with three pairs of compact fiber-coupled units, each forming an optical cavity with a baseline proportional to the telescope length at different points around the aperture. Employing a Pound-Drever-Hall approach to maintain a modulated laser field on resonance with each cavity, the dimensional stability of the telescope can be measured and verified. We have designed and developed prototype OTI units to demonstrate the capability of measuring stable structures, such as the LISA telescope, with a $1 \frac{\mathrm{pm}}{\sqrt{\mathrm{Hz}}}$ sensitivity using a set of freely mountable fiber-injected cavities. Aside from its initial motivation for the telescope, the OTI can also be readily integrated with other systems to aid in ground testing experiments. In this paper, we outline our experimental setup, measurement results, and analyses of the noise limitations., Comment: 10 pages, 10 figures

The LISA telescopes must exhibit an optical path length stability of $\frac{\mathrm{pm}}{\sqrt{\mathrm{Hz}}}$ in the mHz observation band to meet mission requirements. The optical truss interferometer is a proposed method to aid in the ground testing of the telescopes, as well as a risk-mitigation plan for the flight units. This consists of three Fabry-Perot cavities mounted to the telescope which are used to monitor structural displacements. We have designed and developed a fiber-based cavity injection system that integrates fiber components, mode-matching optics, and a cavity input mirror into a compact input stage. The input stages, paired with return mirror stages, can be mounted to the telescope to form the optical truss cavities. We performed a thorough sensitivity analysis using various simulation methods to support the fabrication and assembly of three first-generation prototype cavities, each of which exhibited a satisfactory performance based on our models., Comment: 9 pages, 9 figures, 13 pdf figures attached

An inertial sensor design is proposed in this paper to achieve high sensitivity and large dynamic range in the sub-Hz frequency regime. High acceleration sensitivity is obtained by combining optical cavity readout systems with monolithically fabricated mechanical resonators. A high-sensitivity heterodyne interferometer simultaneously monitors the test mass with an extensive dynamic range for low-stiffness resonators. The bandwidth is tuned by optical feedback cooling to the test mass via radiation pressure interaction using an intensity-modulated laser. The transfer gain of the feedback system is analyzed to optimize system parameters towards the minimum cooling temperature that can be achieved. To practically implement the inertial sensor, we propose a cascaded cooling mechanism to improve cooling efficiency while operating at low optical power levels. The overall system layout presents an integrated design that is compact and lightweight.

We present a method to characterize the noise in ground-based gravitational-wave observatories such as the Laser Gravitational-Wave Observatory (LIGO). This method uses linear regression algorithms such as the least absolute shrinkage and selection operator (LASSO) to identify noise sources and analyzes the detector output versus noise witness sensors to quantify the coupling of such noise. Our method can be implemented with currently available resources at LIGO, which avoids extra coding or direct experimentation at the LIGO sites. We present two examples to validate and estimate the coupling of elevated ground motion at frequencies below 10 Hz with noise in the detector output.

We present a noise estimation and subtraction algorithm capable of increasing the sensitivity of heterodyne laser interferometers by one order of magnitude. The heterodyne interferometer is specially designed for dynamic measurements of a test mass in the application of sub-Hz inertial sensing. A noise floor of 3.31E-11 m/rtHz at 100mHz is achieved after applying our noise subtraction algorithm to a benchtop prototype interferometer that showed a noise level of 2.76E-10 m/rtHz at 100mHz when tested in vacuum at levels of 3E-5 Torr. Based on the previous results, we investigated noise estimation and subtraction techniques of non-linear optical pathlength noise, laser frequency noise, and temperature fluctuations in heterodyne laser interferometers. For each noise source, we identified its contribution and removed it from the measurement by linear fitting or a spectral analysis algorithm. The noise correction algorithm we present in this article can be generally applied to heterodyne laser interferometers.

We present a compact heterodyne laser interferometer developed for high-sensitivity displacement sensing applications. This interferometer consists of customized prisms and waveplates assembled as a quasi-monolithic unit to realize a miniaturized system. The interferometer design adopts a common-mode rejection scheme to provide a high rejection ratio to common environmental noise. Experimental tests in vacuum show a displacement sensitivity level of 11 pm/rtHz at 100mHz, and as low as 0.6pm/rtHz above 1Hz. The prototype unit has a size of 20mm X 20mm X 10mm and weighs 4.5 grams, which allows subsequent integration into compact systems.

Displacement measuring interferometry is a crucial component in metrology applications. In this paper, we propose a fiber-based two-wavelength heterodyne interferometer as a compact and highly sensitive displacement sensor that can be used in inertial sensing applications. In the proposed design, two individual heterodyne interferometers are constructed using two different wavelengths, 1064 nm and 1055 nm; one of which measures the target displacement and the other monitors the common-mode noise in the fiber system. A narrow-bandwidth spectral filter separates the beam paths of the two interferometers, which are highly common and provide a high rejection ratio to the environmental noise. The preliminary test shows a sensitivity floor of 7.5pm/rtHz at 1Hz when tested in an enclosed chamber. We also investigated the effects of periodic errors due to imperfect spectral separation on the displacement measurement and propose algorithms to mitigate these effects.

We present a novel optomechanical inertial sensor for low frequency applications and corresponding acceleration measurements. This sensor has a resonant frequency of 4.7Hz, a mechanical quality factor of 476k, a test mass of 2.6 gram, and a projected noise floor of approximately 5E-11 m s-2. per root-Hz at 1Hz. Such performance, together with its small size, low weight, reduced power consumption, and low susceptibility to environmental variables such as magnetic field or drag conditions makes it an attractive technology for future geodesy missions. In this paper, we present an experimental demonstration of low-frequency ground seismic noise detection by direct comparison with a commercial seismometer, anda data analysis algorithms for the identification, characterization, and correction of several noise sources.

We have developed an inertially sensitive optomechanical laser by combining a Vertical-External-Cavity Surface-Emitting Laser with a monolithic fused silica resonator. By placing the external cavity mirror of the VECSEL onto the optomechanical resonator test mass, we create a sensor where external accelerations are directly transcribed onto the lasing frequency. We developed a proof-of-principle laboratory prototype and observe test mass oscillations at the resonance frequency of the sensor through the VECSEL lasing frequency, 4.18 +/- .03 Hz. In addition, we set up an ancillary heterodyne interferometer to track the motion of the mechanical oscillator's test mass, observing a resonance of 4.194 +/- 0.004 Hz. The interferometer measurements validate the VECSEL results, confirming the feasibility of using optomechanical lasers for inertial sensing.

We discuss the design of quantum hybrid inertial sensor that combines an optomechanical inertial sensor with the retro-reflector of a cold atom interferometer. This sensor fusion approach provides absolute and high accuracy measurements with cold atom interferometers, while utilizing the optomechanical inertial sensor at frequencies above the repetition rate of the atom interferometer. This improves the overall measurement bandwidth as well as the robustness and field deployment capabilities of these systems. We evaluate which parameters yield an optimal acceleration sensitivity, from which we anticipate a noise floor at nano-g levels from DC to 1 kHz.

We present a performance analysis of compact monolithic optomechanical inertial sensors that describes their key fundamental limits and overall acceleration noise floor. Performance simulations for low frequency gravity-sensitive inertial sensors show attainable acceleration noise floors of the order of 10^-11 ms^-2/rtHz. Furthermore, from our performance models, we determine the optimization criteria in our sensor designs, sensitivity, and bandwidth trade space. We conducted characterization measurements of these compact mechanical resonators, demonstrating mQ-products at levels of 250kg, which highlight their exquisite acceleration sensitivity.

We present the design, bench-top setup, and experimental results of a compact heterodyne interferometer that achieves picometer-level displacement sensitivities in air over frequencies above 100 mHz. The optical configuration with spatially separated beams prevents frequency and polarization mixing, and therefore eliminates periodic errors. The interferometer is designed to maximize common-mode optical laser beam paths to obtain high rejection of environmental disturbances, such as temperature fluctuations and acoustics. The results of our experiments demonstrate the short- and long-term stabilities of the system during stationary and dynamic measurements. In addition, we provide measurements that compare our interferometer prototype with a commercial system, verifying our higher sensitivity of 3\,pm, higher thermal stability by a factor of two, and periodic-error-free performance.

We present a highly compact and fully monolithic optomechanical accelerometer fabricated of a single wafer of fused-silica with a total volume of less than 2cc and a total mass of approximately 4 grams. This sensor demonstrates an unprecedented mQ-product of 50kg, highlighting its unique capabilities for reaching high sensitivity in acceleration sensing. The sensor includes a monolithically co-fabricated Fabry-Perot interferometer that uses the accelerometer test mass as a mirror to measure its displacement in orders of 10-12 m/rtHz, reaching acceleration sensitivities to the order of 100 ng/rtHz - 1 ug/rtHz above 1 Hz.

During the On-Station Thermal Test campaign of the LISA Pathfinder the data and diagnostics subsystem was tested in nearly space conditions for the first time after integration in the satellite. The results showed the compliance of the temperature measurement system, obtaining temperature noise around $10^{-4}\,{\rm K}\, {\rm Hz}^{-1/2}$ in the frequency band of $1-30\;{\rm mHz}$. In addition, controlled injection of heat signals to the suspension struts anchoring the LISA Technology Package (LTP) Core Assembly to the satellite structure allowed to experimentally estimate for the first time the phase noise contribution through thermo-elastic distortion of the LTP interferometer, the satellite's main instrument. Such contribution was found to be at $10^{-12}\,{\rm m}\, {\rm Hz}^{-1/2}$, a factor of 30 below the measured noise at the lower end of the measurement bandwidth ($1\,{\rm mHz}$)., Comment: Submitted to CQG