Optomechanical inertial sensors

Abstract

An optomechanical inertial sensor includes a monolithic mechanical resonator having a frame and a test mass coupled to the frame by two leaf spring flexures such that the test mass is displaced along a sensing direction relative to the frame when the frame accelerates along the sensing direction, the test mass including a mirror, and a heterodyne laser interferometer for measuring motion of the test mass in the sensing direction. Multiple optomechanical inertial sensors may be combined to sense in three or more directions.

Description

PATENTDocket No. UOAZ.P2150WO / 00646245OPTOMECHANICAL INERTIAL SENSORSCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of and priority to US Provisional Application Serial No.: 63 / 700,965, titled “Optomechanical Inertial Sensors,” filed September 30, 2024, which is incorporated herein by reference in it’s entirety.GOVERNMENT RIGHTS

[0002] This invention was made with U.S. government support under Grant No. 2426360 awarded by NSF; and Grant No. 80NSSC24K1097 awarded by NASA. The U.S. Government has certain rights in the invention.BACKGROUND

[0003] Acceleration measurements are a vital aspect in many precision observation systems. From inertial sensing and navigation to gravitational waves detectors and geodesy missions, accelerometers allow for the necessary sensing and subtraction of the multitude of forces acting on a system. Of particular note is the accelerometer’s role in mass change missions, such as GRACE and GRACE follow-on (GRACE-FO), where sensing in all six degrees of freedom, both linear and angular, are required.

[0004] Many of the currently available accelerometer technologies have demonstrated limitations, including large and bulky test masses, limited dynamic range, in instances limited vacuum compatibility, and electrostatic readouts that hinder ground-based testing. Current accelerometers used in space geodesy missions typically have a free-floating test mass with a capacitive readout which limits testing capabilities on Earth. Failure of an accelerometer in both the GRACE and GRACE-FO missions highlighted the need for this type of testing and potential redundancy candidates for these crucial devices.SUMMARY

[0005] An optomechanical accelerometer includes a monolithic fused silica mechanical resonator with an optical readout using a compact quasi-monolithic heterodyne laser1LEGAL\80273455\4Docket No. UOAZ.P2150WO / 00646245 interferometer. The resonator includes a test mass on the end of two leaf spring flexures that oscillates in a linear fundamental mode.

[0006] The interferometer is integrated on the frame of the resonator and may include both reference and measurement interferometers with spatially separated beams.

[0007] Further, the interferometer is a quasi-monolithic system of fused silica prisms and the frame, and the test mass are fabricated from fused silica.

[0008] The monolithic mechanical resonator has a fundamental frequency of approximately 5 Hz and outer dimensions of approximately 90 mm by 80 mm and a thickness of approximately 6.6 mm.

[0009] A triaxial optomechanical inertial sensor has a first layer having a first frame including an x-axis mechanical resonator having an x-axis test mass coupled to the first frame by two leaf spring flexures such that the x-axis test mass is displaced along an x-axis sensing direction, and an x-axis laser interferometer for measuring motion of the x-axis test mass in the x-axis sensing direction and a y-axis mechanical resonator having a y-axis test mass coupled to the first frame by two leaf spring flexures such that the y-axis test mass is displaced along a y-axis sensing direction perpendicular to the x-axis sensing direction, and a y-axis laser interferometer for measuring motion of the y-axis test mass in the y-axis sensing direction. A second layer of the triaxial optomechanical inertial sensor has a second frame coupled to the first frame by one or more spacers, the second layer comprising a z-axis mechanical resonator having a z-axis test mass coupled to the second frame by two leaf spring flexures such that the z-axis test mass is displaced along a z-axis sensing direction perpendicular to both the x-axis and y-axis sensing directions, and a z-axis heterodyne laser interferometer for measuring motion of the z-axis test mass in the z-axis sensing direction.

[0010] The x-axis, y-axis, and z-axis interferometers may be integrated on the first frame and are quasi-monolithic systems of fused silica prisms. The first layer, the second layer and the spacers are fabricated from fused silica.

[0011] Further, the x-axis, y-axis, and z-axis mechanical resonators have a fundamental frequency of approximately 5 Hz and the x-axis, y-axis, and z-axis test masses include a mirror.

[0012] The triaxial optomechanical inertial sensor may also include a housing enclosing the first and second layers and fiber injector mounts on an edge of the housing for providing input laser beams to the x-axis, y-axis, and z-axis interferometers.2LEGAL\80273455\4Docket No. UDAZ.P2150WO / 00646245

[0013] An optomechanical inertial sensor includes an array of six dual accelerometers, each dual accelerometer having a first mechanical resonator having a first test mass coupled to a frame by two leaf spring flexures such that the first test mass is displaced along a first sensing direction and a first heterodyne laser interferometer integrated on the frame for measuring motion of the first test mass in the first sensing direction and a second mechanical resonator having a second test mass coupled to the frame by two leaf spring flexures such that the second test mass is displaced along a second sensing direction at an angle less than 90° to the first sensing direction and a second heterodyne laser interferometer integrated on the frame for measuring motion of the second test mass in the second sensing direction. Each dual accelerometer is mounted in a different face of a cube housing enclosing the optomechanical inertial sensor.

[0014] Further, each dual accelerometer is mounted to a face of the cube housing such that the first sensing direction is parallel to an edge of the face and the angle between the first sensing direction and the second sensing direction is 45°.BRIEF DESCRIPTION OF THE DRAWINGS

[0015] FIG. 1 depicts a schematic diagram of a monolithic fused silica mechanical resonator, in an embodiment.

[0016] FIG. 2 depicts a perspective view of a quasi-monolithic heterodyne interferometer with a laser and fiber collimator mount, in embodiments.

[0017] FIG. 3A depicts a side schematic diagram of the interferometer of FIG. 2.

[0018] FIG. 3B depicts a top schematic diagram of the interferometer of FIG. 2.

[0019] FIG. 4 is a perspective view of a uniaxial optomechanical accelerometer, in embodiments.

[0020] FIG. 5 is a perspective view of a triaxial optomechanical sensor, in embodiments.

[0021] FIG. 6 is a cross-sectional view of the sensor of FIG. 5.

[0022] FIG. 7A is a perspective view of the triaxial optomechanical sensor of FIG. 5 in a housing, in embodiments.

[0023] FIG. 7B is a perspective view of the housing of FIG. 7A with a lid.

[0024] FIG. 8 is a perspective view of a dual accelerometer, in an embodiment.

[0025] FIG. 9 is a perspective view of an array of six dual accelerometers mounted in a cube housing, in an embodiment.3LEGAL\80273455\4Docket No. UOAZ.P2150WO / 00646245DETAILED DESCRIPTION

[0026] In the following specification and the claims, reference will be made to a number of terms, which shall be defined to have the following meanings.

[0027] The singular forms “a,” “an,” and “the” include plural references unless the context clearly dictates otherwise.

[0028] “Optional” or “optionally” means that the subsequently described event or circumstance may or may not occur, and that the description includes instances where the event occurs and instances where it does not.

[0029] Approximating language, as used herein throughout the specification and claims, may be applied to modify any quantitative representation that could permissibly vary without resulting in a change in the basic function to which it is related. Accordingly, a value modified by a term or terms, such as “about,” “approximately,” and “substantially,” are not to be limited to the precise value specified. In at least some instances, the approximating language may correspond to the precision of an instrument for measuring the value. Here and throughout the specification and claims, range limitations may be combined and / or interchanged; such ranges are identified and include all the sub-ranges contained therein unless context or language indicates otherwise.

[0030] Embodiments disclosed herein feature highly compact, portable, and cost- effective optomechanical inertial sensors with high sensitivity, vacuum compatibility, and optical readouts. The disclosed devices include a highly stable monolithic fused silica mechanical oscillator paired with a compact heterodyne displacement interferometer, enabling performances in small form factors. They are applicable across a wide range of environments, including space, air, underground, and deep water.

[0031] FIG. 1 depicts a schematic diagram of a monolithic fused silica mechanical resonator 100 for use in a uniaxial optomechanical inertial sensor. Resonator 100 includes a frame 102. Test mass 104 is attached to frame 102 by leaf spring flexures 106 and 108 so that it oscillates in a linear fundamental mode as seen in the direction of arrow 110. To avoid cross talk, higher order modes have a frequency at least one order of magnitude above the fundamental mode. This geometry is scalable to various sizes and frequencies.

[0032] Test mass motion is read out optically. A mirror 112 is mounted to one side of test mass 104 so that motion of test mass 104 may be optically read by an interferometer integrally attached to frame 102 at mounting area 114.4LEGAL\80273455\4Docket No. UOAZ.P2150WO / 00646245

[0033] These oscillations are modeled according to the equation of motion (EOM) of a damped harmonic oscillator, as given by Equation 1:

[0034] where F is an external force acting on the system, m is the mass of the test mass, x is the test mass displacement,is the gas damping rate, a>0is the fundamental angular resonant frequency of the resonator, a> is the angular frequency of observation,is the internal damping coefficient. Displacement oscillations are readout optically and converted to accelerations according to the transfer function given in Equation 2. This transfer function can be derived from the EOM in Equation 1. Here, / (m) is the test mass displacement, A(o>) is the acceleration, i is the square root of negative one, and Q is the mechanical quality factor of the resonator.

[0035] At low frequencies, thermal noise dominates, while gas damping dominates at higher frequencies in-air. At high frequencies in vacuum, shot noise or vibrations dominate. The thermal noise is therefore considered the fundamental sensitivity limit. The thermal displacement and acceleration noise floors can be found using Equations 3 and 4, respectively. These are obtained by applying the fluctuation dissipation theorem to the EOM in Equation 1. They provide the theoretical limit to a given resonator geometry’s sensitivity. In these equations, kBis the Boltzmann constant, and T is the temperature.

[0036] In Equation 4, it is clear that the noise floor of this sensitivity limit is inversely proportional to the mQ product of the resonator. To facilitate a compact sensor, the value of Q and the size of the text mass is maximized within the constraints of application. To achieve this high Q, resonator 100 is etched from monolithic fused silica, a low loss material when operating near room temperature. Additionally, geometries may be optimized to minimize loss.

[0037] In a representative example, uniaxial resonator 100 has outer dimensions of approximately 90 mm x 80 mm with a thickness of approximately 6.6 mm, although other5LEGAL\80273455\4Docket No. UOAZ.P2150WO / 00646245 dimensions may be used depending on the application. In vacuum ringdown measurements, resonator 100 indicated a measured fundamental frequency of 4.7 Hz, a mechanical quality factor of approximately Q = 4.77 X 105, and mQ products of 1200 kg.

[0038] A compact quasi-monolithic heterodyne laser interferometer made of fused silica prisms may be used to perform optical readout of the resonator. FIG. 2 depicts a perspective view of a quasi-monolithic heterodyne laser interferometer 120 with fiber collimator mount 122 which connects to a laser (not shown). FIGS. 3A-3B depict top and side view of the paths of the spatially separated beams through interferometer 120. FIGS. 2 and 3A-3B are best viewed together in the following description.

[0039] Interferometer 120 includes equilateral triangular prisms 124 and 126, a polarizing beam splitter 128, a quarter waveplate 130 and a reference mirror 132. First beam splitting surface 134 is embedded in prism 124 and second beam splitting surface 136 is embedded in prism 126, dividing them into two 30-60-90 prisms.

[0040] Spatially separated beams are generated from a common laser source, then frequency shifted to slightly different frequencies. Reference beam 138 and measurement beam 140 are split into four beams after trans versing through first beam splitting surface 134. All four beams are reflected by high-reflectivity coating on the outside surface of prism 124 and enter polarizing beam splitter 128 perpendicularly. The split beams of reference beam 138 are reflected by reference mirror 132 that serves as the global reference. Split beams 142 and 144 of measurement beam 140 exit quarter waveplate 130. One of split beams 142, 144 is incident on a mirror mounted on test mass 104 while the other is reflected by a local reference mirror (FIG. 5) that is fixed near test mass 104. The reflected beams return to polarizing beam splitter 128 and propagate towards prism 126, where beam pairs are combined by second beam splitting surface 136 to build the reference interferometer and the measurement interferometer, respectively, and are detected by corresponding photodetectors (FIG. 5).

[0041] As described herein, quasi-monolithic heterodyne interferometer 120 produces both a reference and a measurement interferometer with spatially separated beams. These spatially separated beams reduce periodic errors. With a differential phase readout between the measurement and reference interferometers, this design allows for the mitigation of common mode optical pathlength noise and, as a result, sub-picometer precision. This heterodyne6LEGAL\80273455\4Docket No. UOAZ.P2150WO / 00646245 interferometer has a large dynamic range, necessary for tracking both the millimeter scale and sub-micron scale displacements possible with the lower frequency resonator units.

[0042] FIG. 4 is a perspective view of a uniaxial optomechanical accelerometer, in embodiments. Resonator 100 of FIG. 1 is integrated with interferometer 120 of FIGS. 2 and 3A- 3B.

[0043] In another embodiment, three of the uniaxial optomechanical accelerometers of FIG. 4 may be combined into triaxial optomechanical inertial sensor 200, with acceleration sensing capabilities in all three linear directions as shown in FIG. 5. FIG. 6 is a cross-sectional view of triaxial optomechanical inertial sensor 200. FIGS. 7A and 7B show triaxial optomechanical inertial sensor 200 of FIGS. 5 and 6 mounted in housing 250. FIGS. 5-7B are best viewed together in the following description. In a representative example, triaxial optomechanical sensor 200 has dimensions of approximately 110 mm x 110 mm x 22 mm, although other dimensions may be used depending on the application.

[0044] Triaxial optomechanical inertial sensor 200 may be referred to as an XYZ system and includes two layers, separated by fused silica spacers 246. First layer 202 is the XY system. First layer 202 may also be referred to as the top layer, but this is to illustrate relative positions of various components, it does not limit the orientation of sensor 200 during use. First layer 202 is a monolithic biaxial design that holds two resonators, which are examples of resonator 100 with a fundamental frequency of approximately 6.5 Hz.

[0045] First layer 202 is a monolithic frame with an overall rectangular perimeter. It may include solid areas for mounting and / or integrating other components, and open areas that accommodate components on other layers or motion of test masses. The configuration of the frame shown in the figures is for purposes of illustration and other designs may be used that allow the movement of text masses along the x-axis, y-axis and z-axis.

[0046] First layer 202 includes x-axis test mass 206 coupled to the frame by two leaf spring flexures 208 so that x-axis test mass 206 is displaced along x-axis sensing direction 210. X-axis interferometer 212 measures motion of x-axis test mass 206 in x-axis sensing direction 210 using mirror 214 mounted on x-axis test mass 206 and local reference mirror 216. The reference interferometer and measurement interferometer beams are detected by corresponding photodetectors 218.7LEGAL\80273455\4Docket No. UOAZ.P2150WO / 00646245

[0047] First layer 202 also includes y-axis test mass 220 coupled to the frame by two leaf spring flexures 222 so that y-axis test mass 220 is displaced along y-axis sensing direction 224. Y-axis interferometer 226 measures motion of y-axis test mass 220 in y-axis sensing direction 224 using mirror 228 mounted on y-axis test mass 220 and local reference mirror 230. The reference interferometer and measurement interferometer beams are detected by corresponding photodetectors 232.

[0048] Second layer 204 also includes a monolithic frame with an overall rectangular perimeter approximately the same as that of first layer 202. The configuration of the frame shown in the figures is for purposes of illustration and other designs may be used that allow the movement of text masses along the x-axis, y-axis and z-axis.

[0049] Second layer 204 includes out-of-plane z-axis test mass 234 coupled to the frame by two rotated leaf spring flexures 236 so that z-axis test mass 234 is displaced along z-axis sensing direction, where the z-axis is perpendicular to both the x-axis and the y-axis. Z-axis interferometer 238 measures motion of z-axis test mass 234 in z-axis sensing direction using mirror (not shown) mounted on z-axis test mass 234 and local reference mirror 240. The reference interferometer and measurement interferometer beams are detected by corresponding photodetectors 242. A hole 245 in the first layer 202 allows a beam from interferometer 238 to be deflected downward toward the z-axis text mass 234. This deflection is done by a penta-prism 244 placed over the hole 245.

[0050] A plurality of spacers 246 may be positioned between first layer 202 and second layer 204 to retain the frames and components in the correct orientation. First layer 202, second layer 204, interferometers 212, 226 and 238, and spacers 246 may each be monolithically fabricated, then bonded together to make a quasi-monolithic system. All three resonators are read out with an individual quasi-monolithic heterodyne interferometer unit.

[0051] FIG. 7A shows triaxial optomechanical inertial sensor 200 of FIGS. 5 and 6 mounted in housing 250. FIG. 7B shows housing 250 together with lid 256 enclosing sensor 200. Fiber injector mounts 252 are mounted directly housing 250 at cut-outs 254 to make the system compact and portable without misalignment of the input beams of the interferometer. A similar output photodiode mount may be attached to lid 256 of housing 250 using holes 258.

[0052] As disclosed herein, an optomechanical inertial sensor for precision science-grade observations and engineering applications can be used in space, air, underground, deep water,8LEGAL\80273455\4Docket No. UOAZ.P2150WO / 00646245 and planetary environments, as well as for inertial navigation. These sensors are based on compact low-noisc optomechanical accelerometers which arc comprised of monolithically fabricated mechanical resonators that incorporate compact and highly sensitive laser interferometric displacement sensors. Current laboratory prototypes have demonstrated very low mechanical losses consistent with quality factors Q of 4.77x105, and mQ-products above 1200 kg, having a fundamental mechanical resonance of 4.7 Hz. These characteristics highlight their high sensitivity in acceleration sensing with noise floor near 10-11 m s-2 / Hz. Recent measurements on dedicated test platforms indicate that the sensors are overwhelmingly dominated by signal above 1 mHz, and exhibit noise floors in the laboratory at levels of 8 pico-g above 60 mHz.

[0053] FIG. 8 is a perspective view of a dual accelerometer 300. Dual accelerometer 300 includes two resonators having a test mass 304 mounted to frame 302 by leaf spring flexures. One of the resonators is positioned to have a first sensing direction, and the other is positioned to have a second sensing direction at an angle of less than 90° to the first sensing direction. In embodiments, the angle between the first and second sensing directions may be approximately 45°.

[0054] FIG. 9 is a perspective view of an array of six dual accelerometers 300 mounted in a cube housing 400. Each dual accelerometer is mounted in a face of the cube housing 400 so that the first sensing direction is parallel to an edge of the face. In embodiments, cube housing 400 is a CubeSat compatible unit capable of obtaining highly sensitive linear and angular accelerations with a gyro-free configuration.

[0055] Changes may be made in the above methods and systems without departing from the scope hereof. It should thus be noted that the matter contained in the above description or shown in the accompanying drawings should be interpreted as illustrative and not in a limiting sense. The following claims are intended to cover all generic and specific features described herein, as well as all statements of the scope of the present method and system, which, as a matter of language, might be said to fall therebetween.9LEGAL\80273455\4

Claims

Docket No. UOAZ.P2150WO / 00646245CLAIMS1. An optomechanical inertial sensor comprising: a monolithic mechanical resonator comprising: a frame; and a test mass coupled to the frame by two leaf spring flexures such that the test mass is displaced along a sensing direction relative to the frame when the frame accelerates along the sensing direction, the test mass including a mirror; and a heterodyne laser interferometer for measuring motion of the test mass in the sensing direction.

2. The sensor of claim 1, wherein the interferometer is integrated on the frame of the resonator.

3. The sensor of claim 1, wherein the interferometer comprises both reference and measurement interferometers with spatially separated beams.

4. The sensor of claim 1, wherein the interferometer is a quasi-monolithic system of fused silica prisms.

5. The sensor of claim 1, wherein the frame and the test mass are fabricated from fused silica.

6. The sensor of claim 1 , wherein the monolithic mechanical resonator has a fundamental frequency of approximately 5 Hz.

7. The sensor of claim 1, wherein the resonator has outer dimensions of approximately 90 mm by 80 mm and a thickness of approximately 6.6 mm.

8. A triaxial optomechanical inertial sensor comprising: a first layer having a first frame comprising: an x-axis mechanical resonator having an x-axis test mass coupled to the first frame by two leaf spring flexures such that the x-axis test mass is displaced along an x-axis sensing direction, and an x-axis laser interferometer for measuring motion of the x-axis test mass in the x-axis sensing direction; and10LEGAL\80273455\4Docket No. UOAZ.P2150WO / 00646245 a y-axis mechanical resonator having a y-axis test mass coupled to the first frame by two leaf spring flexures such that the y-axis test mass is displaced along a y-axis sensing direction perpendicular to the x-axis sensing direction, and a y-axis laser interferometer for measuring motion of the y-axis test mass in the y-axis sensing direction; and a second layer having a second frame coupled to the first frame by one or more spacers, the second layer comprising a z-axis mechanical resonator having a z-axis test mass coupled to the second frame by two leaf spring flexures such that the z-axis test mass is displaced along a z-axis sensing direction perpendicular to both the x-axis and y- axis sensing directions, and a z-axis heterodyne laser interferometer for measuring motion of the z-axis test mass in the z-axis sensing direction.

9. The triaxial optomechanical inertial sensor of claim 8, wherein the x-axis, y-axis, and z- axis interferometers are integrated on the first frame.

10. The triaxial optomechanical inertial sensor of claim 8, wherein the x-axis, y-axis, and z- axis interferometers are quasi- monolithic systems of fused silica prisms.

11. The triaxial optomechanical inertial sensor of claim 8, wherein the first layer, the second layer and the spacers are fabricated from fused silica.

12. The triaxial optomechanical inertial sensor of claim 8, wherein the x-axis, y-axis, and z- axis mechanical resonators have a fundamental frequency of approximately 5 Hz.

13. The triaxial optomechanical inertial sensor of claim 8, wherein the x-axis, y-axis, and z- axis test masses include a mirror.

14. The triaxial optomechanical inertial sensor of claim 8, further comprising: a housing enclosing the first and second layers; and fiber injector mounts on an edge of the housing for providing input laser beams to the x- axis, y-axis, and z-axis interferometers.

15. An optomechanical inertial sensor, comprising: an array of six dual accelerometers, each dual accelerometer comprising:11LEGAL\80273455\4Docket No. UOAZ.P2150WO / 00646245 a first mechanical resonator having a first test mass coupled to a frame by two leaf spring flexures such that the first test mass is displaced along a first sensing direction and a first heterodyne laser interferometer integrated on the frame for measuring motion of the first test mass in the first sensing direction; and a second mechanical resonator having a second test mass coupled to the frame by two leaf spring flexures such that the second test mass is displaced along a second sensing direction at an angle less than 90° to the first sensing direction and a second heterodyne laser interferometer integrated on the frame for measuring motion of the second test mass in the second sensing direction; and a cube housing, wherein each dual accelerometer is mounted in a different face of the cube housing.

16. The optomechanical inertial sensor of claim 15, where each dual accelerometer is mounted to a face of the cube housing such that the first sensing direction is parallel to an edge of the face.

17. The optomechanical inertial sensor of claim 15, where the angle between the first sensing direction and the second sensing direction is 45°.12LEGAL\80273455\4

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