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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$7.5\text{pm}/\sqrt{\text{Hz}}$at 1 Hz 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 compact heterodyne laser interferometer developed for high-sensitivity displacement sensing applications. This interferometer consists of customized prisms and wave plates 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$11\mathrm{p}\mathrm{m}/\sqrt{\mathrm{H}\mathrm{z}}$at$100\mathrm{m}\mathrm{H}\mathrm{z}$and as low as$0.6\mathrm{p}\mathrm{m}/\sqrt{\mathrm{H}\mathrm{z}}$above$1\mathrm{p}\mathrm{m}$. The prototype unit is$20\mathrm{m}\mathrm{m}\times <\#comment/>20\mathrm{m}\mathrm{m}\times <\#comment/>10\mathrm{m}\mathrm{m}$in size and weighs$4.5\mathrm{g}$, allowing subsequent integration in compact systems.

 

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 3.31×10−11m/Hz at 100 mHz is achieved after applying our noise subtraction algorithm to a benchtop prototype interferometer that showed a noise level of 2.76×10−10m/Hz at 100 mHz when tested in vacuum at levels of 3×10−5 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 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 on the order of$1\times <\#comment/>{10}^{-<\#comment/>11}\mathrm{m}/{\mathrm{s}}^2\sqrt{\mathrm{H}\mathrm{z}}$. Furthermore, from our performance models, we devised an optimization approach for our sensor designs, sensitivity, and bandwidth trade space. We conducted characterization measurements of these compact mechanical resonators, demonstrating$\mathit{\text{mQ}}$-products at levels of 250 kg, which highlight their exquisite acceleration sensitivity.

 

We discuss the design of quantum hybrid inertial sensor that combines an optomechanical inertial sensor with the retroreflector 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.