Inertial sensor and inertial measurement unit

Abstract

Inertial sensors and inertial measurement units are provided. In one example, the inertial sensor comprises one or more microresonators, each microresonator supporting a corresponding optical resonance. The inertial sensor further comprises a microelectromechanical inertial proof mass adjacent to and suspended discontinuously from the one or more microresonators. The proof mass is deflectable under application of an inertial force. The inertial sensor further comprises one or more electrodes for countering deflection of the proof mass with an electrostatic force. The inertial sensor further comprises one or more optical couplers for coupling light entering and exiting a corresponding microresonator. The inertial sensor further comprises one or more detectors for detecting light received by the one or more optical couplers from the one or more microresonators. A change in the spacing between the proof mass and at least one microresonator changes an optical resonance characteristic of that microresonator.

Description

[Technical Field]

[0001] This disclosure relates in general to inertial sensors and inertial measurement units. [Background technology]

[0002] As the functionality and performance of mobile devices continue to improve, they increasingly include at least one micro-electro-mechanical system (MEMS) inertial sensor for determining the mobile device's position. [Overview of the Initiative]

[0003] MEMS inertial sensors, such as accelerometers and gyroscopes, operate by determining the presence and magnitude of an inertial force from the displacement of a test mass that moves in response to the inertial force. This displacement changes the gap between the movable test mass and the fixed electrode, causing a change in capacitance. This change in capacitance is detected to determine the inertial force. However, these sensors are prone to excessive noise and drift due to factors such as manufacturing imperfections, nonlinearity in the response of the test mass, parasitic capacitance, and patch potential. To counteract the physical causes of noise and drift, electrostatic force may be used to restrict the movement of the test mass. However, the electrostatic force itself generates noise, including parasitic and stray capacitance in the sensor's electrical circuitry and on the surface of the test mass. Noise caused by electrostatic force can interfere with capacitive readout and add further noise to the output signal. However, the noise contribution from electrostatic operation (electrostatic drive) is generally lower than that from capacitive readout. Furthermore, capacitive readout interferes with operation using electrostatic force. Noise contributions from both electrostatic force and capacitance readout reduce the accuracy and sensitivity of inertial sensors as described above.

[0004] An object of embodiments of the present invention is to mitigate at least one or more problems known in the art.

[0005] According to one aspect of the present invention, an inertial sensor is provided. The inertial sensor comprises one or more microresonators, each microresonator supporting a corresponding optical resonance. The inertial sensor further comprises a microelectromechanical inertial test mass adjacent to and discontinuously suspended from one or more microresonators. The test mass is deflectable when an inertial force is applied. The inertial sensor further comprises one or more electrodes for counteracting the deflection of the test mass with an electrostatic force. The inertial sensor further comprises one or more optical couplers for coupling light entering and exiting a corresponding microresonator. The inertial sensor further comprises one or more detectors for detecting light received by the optical couplers from one or more microresonators. A change in the distance between the test mass and at least one microresonator results in a change in the optical resonance characteristics of the microresonator.

[0006] It is a common view that manufacturing devices integrating electronics, mechanical engineering, and optics is difficult and time-consuming, and that the devices can become large, especially when multiple connections are required between electronic and optical components. Designing and manufacturing such devices requires a considerable number of complex processes. For these reasons, and due to other considerations (such as the size incompatibility between photonic and electromechanical structures, and the already complex manufacturing required to create integrated photonic and electromechanical structures), current inertial sensors are either purely electromechanical or purely optical. Replacing a purely electromechanical inertial sensor (where both readout and actuation are performed using electrodes) with a purely optical inertial sensor (where both readout and actuation are performed using optical means) can eliminate the aforementioned drawbacks of capacitive readout. Furthermore, using optical actuation allows for the control of the movement of the test mass.

[0007] For the reasons stated above, there is a prejudice against combining components of optical sensors and electromechanical sensors. However, the inventors have utilized their inventive technology to provide an inertial sensor that combines a cavity-enhanced optic-mechanical readout mechanism with electrostatic actuation. The inventors have also come to the surprising realization that the combination of a cavity-enhanced optic-mechanical readout mechanism and electrostatic actuation of a test mass offers significant advantages over purely electromechanical or purely optical inertial sensors. In particular, by using voltage only for the actuation of the test mass and not for detection, noise can be greatly reduced, and as a result, the sensitivity of the sensor can be improved.

[0008] Furthermore, using voltage allows for the effective and efficient operation of large test masses. By using voltage for operation, it becomes possible to use large test masses without requiring high optical output. This is impossible when using inertial sensors with optical means for operation, because the test mass needs to be small and thin in order to operate it using optical means. Large test masses, especially thick test masses, have high mechanical sensitivity, which is advantageous because it allows for a larger and more sensitive mechanical response to inertial forces. Moreover, using resonant light in the optical-mechanical readout mechanism shifts the resonance conditions due to the motion of the test mass, amplifying the signal without amplifying noise, thus further improving sensitivity.

[0009] In inertial sensors, combining the optical-mechanical detection of the displacement of a test mass (using one or more micro-resonators and one or more optical couplers) with the electrostatic actuation of the test mass (using one or more electrodes) yields a hybrid optic-electromechanical sensor with increased sensitivity and improved signal-to-noise ratio compared to capacitive sensing-based inertial sensors, without compromising the size of the test mass. Such sensors retain the ability to actuate large test masses for large mechanical responses to inertial forces.

[0010] The hybrid nature of inertial sensors allows for both improved sensitivity and responsiveness, which is impossible with all optical sensors. Such improved responsiveness is crucial for effectively adjusting or calibrating sensor sensitivity. In fact, by fully operating the test mass, closed-loop operation can be effectively achieved, allowing for better control of the test mass's drift (e.g., thermally induced drift) and nonlinear response. Consequently, positioning errors in the sensor become less likely. The inertial sensors described herein can produce extremely low-noise measurements and track even minute positional changes.

[0011] The combination of an optical readout mechanism and closed-loop operation achieves an optimal balance of sensitivity, control, and long-term stability, providing a highly sensitive and stable inertial sensor that can be precisely controlled to achieve the required measurements.

[0012] The test mass may have an average thickness of 1 micron or more.

[0013] The test mass may have an average thickness on the order of tens or hundreds of microns.

[0014] The test mass may be larger than the micro-resonator, for example, it may be thicker. The test mass may have an average thickness of 10 microns or more. The test mass may have an average thickness of less than 500 microns. The test mass may have an average thickness between 20 and 30 microns. The test mass may be considerably larger than the micro-resonator. The test mass may be significantly thicker than the micro-resonator, for example, 100 times thicker. The test mass may have a larger surface area than the micro-resonator. The surface area of ​​the test mass may be less than 1 millimeter × 1 millimeter. The surface area of ​​the test mass may be approximately 250 microns × 250 microns. The diameter of the micro-resonator may be approximately 100 microns. A larger test mass size improves the responsiveness of the sensor to acceleration and rotational speed.

[0015] The distance between the test mass and one or more micro-resonators may be less than 1 micron. This distance may also be the distance when the inertial sensor is stationary, i.e., when there is no deflection of the test mass. If the test mass is placed within a short distance of one or more micro-resonators, the scale factor of the response will increase, and the change in the output optical signal will be larger for the same amount of detected inertial force.

[0016] The inertial sensor may comprise at least two micro-resonators, at least two optical couplers, and at least two detectors. A differential change in the optical resonance characteristics of the two micro-resonators can be caused by a change in a first distance between the test mass and the first of the two micro-resonators, and by a change in a second distance between the test mass and the second of the two micro-resonators.

[0017] The test mass may be suspended between the first micro-resonator and the second micro-resonator.

[0018] The test mass may have a protrusion located between the first microresonator and the second microresonator. The protrusion may function as an optical channel that guides photons that have escaped from the first and / or second microresonator. This improves the sensitivity of the sensor because the photons are absorbed or transmitted by the protrusion.

[0019] The test mass may further include one or more additional protrusions, each of which is located between two micro-resonators.

[0020] At least two electrodes may each include a finger portion that is stationary relative to the sensor. The test mass may include a finger portion that is movable relative to the inertial sensor. The movable finger portion of the test mass is located between the stationary finger portions of at least two electrodes, and the finger portion of the test mass and the finger portions of at least two electrodes may be interdigitally arranged (interlocking with each other).

[0021] The movement of the finger portion of the proof mass is strongly coupled with the movement of the proof mass, and the movement of the finger portion leads to the movement of the entire proof mass. Therefore, the stationary finger portion of the electrode is used to control the movement of the finger portion of the proof mass, and consequently controls the movement of the proof mass. The finger portion of the proof mass may be integrated with the proof mass, or may be rigidly fixed to the proof mass, so as to be stationary relative to the proof mass. Alternatively, the finger portion of the proof mass may have its own mechanical degrees of freedom, for example in a cantilever mode. The finger portion of the proof mass may be arranged so as to be used only for moving or maintaining the position of the entire proof mass.

[0022] The one or more microresonators may be radially spaced apart from the proof mass.

[0023] The one or more electrodes and / or the one or more microresonators may be fixed relatively to the inertial sensor.

[0024] The inertial sensor may be for detecting acceleration or rotational velocity.

[0025] The one or more microresonators may be whispering gallery mode resonators.

[0026] Each of the one or more microresonators may, in use, have an evanescent field that extends beyond an edge of the microresonator. The distance that the evanescent field extends beyond the edge of the microresonator may be based on the magnitude of the wavelength of light coupled into an optical coupler. The evanescent field may, in use, extend at least 1 micron beyond the edge of the microresonator. This provides a particularly effective sensor when the wavelength of light coupled into the optical coupler is 1550 nm.

[0027] The proof mass may be larger than each of the one or more microresonators.

[0028] One or more electrodes may be used to control the long-term stability of the inertial sensor.

[0029] The inertial sensor may further include a light source for transmitting light to each of the one or more optical couplers.

[0030] The light transmitted to each of the one or more optical couplers may be broadband light.

[0031] The light transmitted to each of the one or more optical couplers may be coherent single-frequency light.

[0032] The change in optical resonance characteristics may be a shift in the optical resonance and / or a broadening of the optical resonance.

[0033] One or more micro-resonators may each have a different optical resonance.

[0034] According to another aspect of the present invention, an inertial measurement unit is provided. The inertial measurement unit comprises one or more inertial sensors described herein and a processor. The processor is configured to receive electrical signals from one or more detectors for each inertial sensor. The processor is further configured for each inertial sensor to detect changes in the optical resonance characteristics of one or more microresonators in response to changes in the distance between a test mass and one or more microresonators. The processor is further configured for each inertial sensor to determine the acceleration and / or rotational speed of the inertial sensor based on the changes in the optical resonance characteristics of one or more microresonators. The processor is further configured for each inertial sensor to control the electrostatic force of one or more electrodes based on the changes in the optical resonance characteristics of one or more microresonators.

[0035] The inertial measurement unit may comprise six inertial sensors as described herein. The six inertial sensors comprise a first inertial sensor for detecting acceleration in a first axis; a second inertial sensor for detecting acceleration in a second axis perpendicular to the first axis; a third inertial sensor for detecting acceleration in a third axis perpendicular to the first and second axes; a fourth inertial sensor for detecting rotational velocity around the first axis; a fifth inertial sensor for detecting rotational velocity around the second axis; and a sixth inertial sensor for detecting rotational velocity around the third axis. The processor may further be configured to calculate the total acceleration and / or total rotational velocity of the inertial measurement unit based on the acceleration and / or rotational velocity of each inertial sensor.

[0036] The electrostatic force of one of the one or more electrodes may be controlled based on the change in the optical resonant properties of the corresponding micro-resonator.

[0037] For each inertial sensor used to detect rotational speed, the processor may be configured to control the electrostatic force of one or more electrodes to vibrate the test mass at a constant frequency (fixed frequency) in a first direction. Detection of changes in the optical resonance characteristics of one or more micro-resonators may be performed in response to changes in the distance between the test mass and one or more micro-resonators in a second direction perpendicular to the first direction at a fixed frequency.

[0038] The processor may be further configured to calibrate each inertial sensor by changing the electrostatic force of each electrode and detecting the change in the optical resonance characteristics of each micro-resonator.

[0039] Those skilled in the art will likely come up with numerous modifications and other embodiments of these inventions in light of the teachings presented herein. Therefore, it will be understood that the disclosure herein is not limited to the specific embodiments disclosed herein. Furthermore, while the descriptions provided herein provide exemplary embodiments in the context of specific combinations of elements, steps and / or functions may be provided by alternative embodiments without departing from the scope of the invention. [Brief explanation of the drawing]

[0040] Hereinafter, embodiments of the present invention will be described only illustratively with reference to the accompanying drawings. [Figure 1] This is a diagram illustrating an inertial sensor. [Figure 2] This figure shows an example of an optical-mechanical element and output of an inertial sensor. [Figure 3] This graph shows an example of characteristic changes in an exemplary inertial sensor. [Figure 4] This is a diagram showing an example of a flowchart. [Figure 5] This figure shows exemplary optical-mechanical elements and output examples of an inertial sensor before and during acceleration. [Figure 6] This figure shows an exemplary inertial sensor for measuring acceleration. [Figure 7] This diagram shows a control loop feedback system used when the inertial sensor detects acceleration. [Figure 8] This figure shows exemplary optical-mechanical elements and output examples of an inertial sensor before and during rotation. [Figure 9] This figure shows an exemplary inertial sensor for measuring the rate of rotation. [Figure 10] This figure shows another example of an inertial sensor for measuring rotational speed. [Figure 11]This diagram shows a control loop feedback system used when an inertial sensor detects rotational speed. [Figure 12] This is a block diagram of an example inertial measurement unit.

[0041] Throughout the description and drawings, similar reference numbers refer to similar parts. [Modes for carrying out the invention]

[0042] Various embodiments are described below, but the present invention is not limited to these embodiments, and variations of these embodiments may naturally fall within the scope of the present invention, which is limited only by the claims.

[0043] Inertial sensors are described below. While accelerometers and gyroscopes are given as examples, the inertial sensors described herein are more broadly applicable, as will be understood by those skilled in the art.

[0044] As can be understood from reading the detailed explanation, a micro-resonator is a closed circuit that supports optical resonance. A micro-resonator supporting optical resonance means that light incident on the closed circuit of the micro-resonator is amplified at at least one resonant frequency due to constructive interference and total internal reflection within the micro-resonator. Examples of micro-resonator materials include silicon, silica, silicon nitride, and crystalline fluorides. Examples of micro-resonator diameters range from a few microns to several hundred microns.

[0045] As can be understood from reading the detailed explanation, a test mass refers to a mechanical structure used in MEMS sensors. Examples of test mass materials include silicon and quartz.

[0046] As can be understood from reading the detailed explanation, an optical coupler is a means of coupling light entering a microresonator and light exiting the microresonator. The optical coupler may be a waveguide. The optical coupler may be attached to a waveguide. The optical coupler may guide light from a light source into the microresonator. The optical coupler may guide light from the microresonator to a detector. The optical coupler may be a buried waveguide, a ridge waveguide, or a rib waveguide. The optical coupler may be fabricated at the same time as the microresonator.

[0047] As can be understood by reading the detailed explanation, a change in optical resonance characteristics refers to any change in the characteristics of the optical resonance. A change in optical resonance characteristics may be a linear change in the optical resonance characteristics, such as a reduction in the peak amplitude. A change in optical resonance characteristics may also be a change in the position of the optical resonance.

[0048] Figure 1 shows an exemplary inertial sensor 100. The inertial sensor 100 includes a micro-resonator 102 that supports optical resonance. The inertial sensor 100 further includes a micro-electro-mechanical inertial test mass 104. The test mass 104 is suspended adjacent to the micro-resonator 102 and discontinuous with the micro-resonator 102. That is, the test mass 104 is positioned within the inertial sensor so as to be close to the micro-resonator 102 but separated from it by a distance / spacing "d" (shown as 112 in Figure 1). The test mass 104 is deflectable when an inertial force is applied. That is, under the influence of the inertial force, the spacing 112 between the test mass 104 and the micro-resonator 102 can change temporarily. The inertial sensor 100 further includes electrodes 106 for counteracting the deflection of the test mass 104 with electrostatic force. The inertial sensor 100 further comprises an optical coupler 108 for coupling light entering and exiting the micro-resonator 102. The inertial sensor further comprises a detector 110 for detecting the light received by the optical coupler 108 from the micro-resonator 102. A change in the distance "d" 112 between the test mass 104 and the micro-resonator 102 causes a change in the optical resonance characteristics of the micro-resonator 102.

[0049] The inertial sensor 100 detects inertial forces, for example, caused by acceleration or rotation, based on the displacement of the test mass 104, which moves in response to the inertial force. More specifically, the inertial sensor 100 in Figure 1 operates as follows: When the inertial sensor 100 is moved, for example, as part of a device, the inertial sensor accelerates to a specific speed or rotates to a specific angle. The test mass is suspended by a suspension means 114 (a spring in this example) connected to an anchor 116. The test mass 104 responds to inertial forces caused by acceleration or rotational speed and displaces based on the magnitude and direction of the inertial force. The displacement of the test mass 104 may be proportional to the inertial force caused by the acceleration or rotational speed. This displacement changes the gap "d" 112 between the test mass 104 and the micro-resonator 102, and changes the optical resonance characteristics of the micro-resonator 102. The optical coupler 108 receives light, couples it to the micro-resonator 104, and couples light from the micro-resonator 104. One or more properties of the light coupled from the micro-resonator 104 change based on the change in the optical resonance properties of the micro-resonator 104, and such changes are detected by the detector 110. Such changes in the transmission output at the detector 110 are related to the displacement of the test mass and can be used to calculate the inertial force experienced by the inertial sensor 100. In this way, the micro-resonator 104, optical coupler 108, detector 110, test mass 104, spring 114, and anchor 116 form an optical-mechanical readout mechanism for the sensor, making it possible to determine the inertial force based on the change in optical transmission detected by the detector 110.

[0050] An electrode 106 is provided to control the movement of the test mass 104. A voltage may be applied to the electrode 106. The electrode 106 is configured to output an electrostatic force due to the applied voltage in order to actuate the test mass 104. The magnitude of the electrostatic force is based on the magnitude of the applied voltage. Since the magnitude of the actuation is based on the magnitude of the electrostatic force, the magnitude of the actuation is also based on the applied voltage and can be controlled by changing the voltage applied to the electrode 106. Therefore, the electrode 106 can change the position of the test mass 104 relative to the micro-resonator by moving the test mass 104 using the electrostatic force due to the applied voltage. Such actuation is sometimes called capacitive actuation. The electrode 106 may be fixed to the sensor 100. The electrode may move the test mass in the X and / or Y directions. The electrode may also move the test mass in the Z direction (not shown).

[0051] Inertial sensors operating in an open-loop configuration without acting on the test mass are prone to drift over time due to temperature fluctuations, bias, and nonlinearity in large test mass displacements. Therefore, the inertial sensor implements a closed-loop system using a feedback mechanism in which electrode 106 acts on the test mass. The acting force of electrode 106 can be used to actively return the test mass to equilibrium, expanding linearity and detection range, and reducing or canceling drift. The acting force from electrode 106 is adjustable using feedback, allowing the test mass 104 to be positioned to provide optimal sensor measurement. Thus, electrode 106 improves the long-term stability of the inertial sensor. Electrode 106 may also be used to dampen vibrations of the test mass 104. Combining optomechanical reading with electromechanical control provides a highly sensitive inertial sensor.

[0052] Although Figure 1 shows only one of each component of the inertial sensor 100, the inertial sensor 100 may comprise multiple components. The inertial sensor 100 may comprise multiple micro-resonators 102, multiple electrodes 106, multiple springs 114, multiple anchors 116, and multiple optical couplers 108. The micro-resonators may be fixed to the sensor. In Figure 1, the test mass 104 is positioned radially from the micro-resonator 102, but the test mass 104 may be positioned at other locations relative to the micro-resonator 102.

[0053] The optical resonance characteristics change with the displacement of the test mass. The change in optical resonance characteristics may be a shift in the resonant wavelength and / or broadening or deepening of the optical resonance curve, in response to the movement of the test mass relative to the microresonator. The shift may occur in either direction, progressing towards either red detuning or blue detuning. Broadening or deepening is due to changes in optical loss, such as dissipative or scattering optomechanical coupling, as described below in relation to Figure 2.

[0054] As shown in Figure 1, the test mass may be suspended using a suspension means 114 in the form of a spring. One end of the spring is fixed to the sensor by being connected to an anchor 116, and the other end of the spring is connected to the test mass to suspend it. The spring 114 allows for the displacement of the test mass 104. Although the spring 114 and anchor 116 are shown throughout this figure and specification, those skilled in the art will understand that other types of suspension means may be used instead of the spring 114 and anchor 116 for the inertial sensor 100 and any of the inertial sensors described herein.

[0055] The micro-resonator 102 is positioned close to the test mass 104 such that the deflection of the test mass 104 changes the optical resonance characteristics of the micro-resonator 102.

[0056] The electrostatic drive provided by electrode 106 may be controlled by a controller (not shown in Figure 1), as will be further described in relation to Figure 4. The inertial sensor may include such a controller, or the controller may be located outside the inertial sensor 100.

[0057] As shown in the power supply diagram in Figure 1, a voltage is applied to electrode 106. The anchor may be grounded so that the applied voltage equals the potential difference between electrode 106 and anchor 116. The applied voltage may vary based on the electrostatic force required to counteract the deflection of the test mass 104. Therefore, although a power supply is illustrated in Figure 1, the voltage may instead be applied by the controller described above (not shown in Figure 1).

[0058] The detector 110 may be any device that converts optical signals into electrical signals. The detector 110 may be a photodetector. The detector 110 may include a processor that processes the optical signal to calculate the inertial force detected by the sensor. The detector 110 may receive optical signals from the optical coupler 108 and the micro-resonator 102 as input and output an inertial force measurement. Alternatively, the inertial force may be calculated based on the optical signal detected by the detector 110 using the controller described above (not shown in Figure 1).

[0059] The optical coupler 108 may be coupled to a waveguide. The optical coupler 108 may be a waveguide positioned close to the micro-resonator 102 such that light is coupled from the waveguide to the micro-resonator 102 and from the micro-resonator 102 to the waveguide. Light from a light source (not shown in Figure 1) may be input to the optical coupler 108, sent to the micro-resonator 102, and sent from the micro-resonator 102 to the detector 110. The light source may be inside the sensor or not be part of the sensor. For example, the light source may be connected to multiple inertial sensors and supply light to multiple inertial sensors. The light input to the optical coupler 108 may be broadband light or coherent single-frequency light.

[0060] The test mass 104 is displaced, for example, along the Y-axis toward or away from the micro-resonator. The X-axis and Y-axis are illustrated in Figure 1. The test mass 104 may also be additionally or alternatively displaced laterally relative to the micro-resonator, for example along the X-axis. The test mass may be made of silicon.

[0061] The micro-resonator 102 shown in Figure 1 is a ring resonator, but this micro-resonator can be replaced with other types of micro-resonators 102, such as a disk-type micro-resonator or a racetrack-type micro-resonator.

[0062] The micro-resonator 102 shown in Figure 1 has at least a portion of the evanescent field extending beyond the edge of the micro-resonator 102 when the sensor is in use. The evanescent field may extend only 1 micron from the edge of the micro-resonator 102. The evanescent field substantially extending from the edge of the micro-resonator 102 increases the sensitivity of the sensor as the interaction between the evanescent field and the test mass 104 increases.

[0063] The micro-resonator 102 may be a whispering gallery mode micro-resonator. When the micro-resonator is a whispering gallery mode micro-resonator, it has an evanescent field that captures light as a whispering gallery mode optical resonance and extends beyond its edges. When the test mass 104 is displaced, it interacts with the evanescent field, and the properties of the micro-resonator change as a result of this interaction with the evanescent field, changing the effective refractive index of the micro-resonator. This change causes the whispering gallery mode optical resonance of the micro-resonator to shift. Thus, when the test mass 104 moves within the evanescent field of the whispering gallery mode micro-resonator, the optical resonance of the micro-resonator is perturbed, and the properties of the optical resonance change.

[0064] The device may include an inertial sensor 100 for detecting acceleration and an inertial sensor 100 for detecting rotational speed. Such a device can be used for position tracking.

[0065] Figure 2 shows the optic-mechanical element 200 and the exemplary output 250 of an exemplary inertial sensor 100. The diagram in Figure 2 is intended to help understand the operation of the optic-mechanical element of the inertial sensor 100 and therefore does not show all the components of the inertial sensor in Figure 1. The following description assumes that the micro-resonator 102 is a whispering gallery mode (WGM) micro-resonator, but it should be understood that the micro-resonator 102 in Figure 1 may be a different type of micro-resonator. A WGM micro-resonator has an evanescent field. The figure shows the coupling ratio k which can be used to model the velocity of photons. i , k e , k a , and k s This indicates.

[0066] Light enters and exits the micro-resonator 102, as indicated by the arrows, with an external coupling ratio k e At a speed defined by the external coupling ratio, light is sent from the optical coupler 108 to the micro-resonator 102 and then returned from the micro-resonator 102 to the optical coupler 108. The external coupling ratio defines, for example, the change in the normalized electromagnetic field inside the resonator (the slowly changing portion) per second in Hertz. When light enters the micro-resonator 102, the intrinsic loss ratio k i Light leaks out due to internal losses defined by . The test mass can be displaced by inertial forces generated by the acceleration or rotation of the sensor. The displacement of the test mass is based on the magnitude and direction of the inertial force. When the test mass 104 approaches the edge of the micro-resonator 102 at a distance "d", the test mass 104 is displaced in the evanescent field and interacts with the evanescent field. This causes a change in the effective refractive index of the WGM micro-resonator, which shifts the resonant frequency of the micro-resonator 102. When the test mass is physically present, scattering losses (k s The scattering effect (represented by k) and the coupling of light to the test mass by absorption or induction (coupling loss k in Figure 2) asome photons leak out of the microresonator 102 due to both (indicated by ). For example, photons may be absorbed and / or scattered by interaction with the test mass surface due to surface roughness. The displacement of the test mass 104 causes the scattering loss k s to change. This is because k s has an exponential dependence on the distance "d" between the test mass 104 and the microresonator 102, as shown by the following formula. In the following formula, alpha is the effective decay length of the evanescent field, and k s0 is a constant. TIFF0007927254000001.tif1361

[0067] The displacement of the test mass 104 also changes the coupling loss k a for the same reason. The displacement of the test mass 104, and thus the change in the distance "d" between the test mass 104 and the microresonator 102, changes the refractive index, and consequently changes the detuning degree Δ. The detuning degree Δ refers to the detuning degree of light from the initial WGM resonance frequency ω0, and can be defined as follows. Δ=ω-ω0 Therefore, when the optical resonance of the microresonator shifts, the detuning degree changes.

[0068] Therefore, changes in the effective refractive index and coupling rate of the WGM microresonator 102 cause a shift and broadening of the WGM resonance frequency. In particular, the WGM optical resonance is broadened by the scattering coupling rate k s and / or absorption or transmission coupling rate k a and shifted by a change in effective refractive index that causes a change in detuning degree Δ.

[0069] The transmitted light intensity T at the output of the optical coupler 108 changes based on the position of the test mass 104 due to the change of the WGM optical resonance. As shown in the following formula, in this model, T depends on the coupling rate and the detuning degree, and is normalized to 1. TIFF0007927254000002.tif2684

[0070] The transmission intensity measurement obtained by detector 110 may be compared with a previous value or a reference value to determine the change in transmittance. This allows for the detection of changes in optical resonance. Changes in optical resonance indicate the displacement of the test mass. As a result, the inertial force acting on the test mass can be calculated from the detection of changes in optical resonance.

[0071] In summary, inertial forces can cause displacement of the test mass. The displacement of the test mass is based on the magnitude and direction of the inertial force. The displacement of the test mass 104 and the resulting change in the distance between the test mass 104 and the micro-resonator 102 change the coupling ratio and refractive index of the micro-resonator 102, which in turn changes the detuning. The change in detuning alters the electromagnetic field and light intensity within the resonator at the output of the waveguide coupler. As a result, the change in the optical resonant frequency of the micro-resonator 102 becomes detectable by the detector 110. Graph 250 in Figure 2 illustrates such changes.

[0072] When no inertial force is applied to the inertial sensor 100, the initial position of the inertial sensor 100 is such that the test mass 104 is at a distance d from the micro-resonator 102. The detection signal when the test mass 104 is at a distance d from the micro-resonator 102 is shown by a solid line in graph 250 of Figure 2. For example, if there is an inertial force due to the acceleration or rotation of the sensor, the test mass 104 may be located at a distance Δy away from the micro-resonator 102, at a distance of d+Δy from the micro-resonator 102. The detection signal when the test mass 104 is at a distance of d+Δy from the micro-resonator 102 is shown by a dotted line in graph 250 of Figure 2. As shown in graph 250, between the solid line (corresponding to the initial distance between the test mass 104 and the micro-resonator 102) and the dotted line (corresponding to the distance of the test mass 104 from the micro-resonator 102 after it has been deflected by the inertial force), a change in the resonant frequency Δf caused by the change in the effective refractive index of the micro-resonator 102 can be seen. Also, scattering (coefficient k s (related to) and / or absorption or transmission (coefficient k) a (Related to this) a change in the resonant linewidth Δdf caused by light emitted from the micro-resonator can also be observed.

[0073] Figure 3 is a graph showing an example of characteristic changes of an inertial sensor. These graphs are intended to illustrate the method of detecting inertial force. To detect inertial force from the displacement of the test mass 104 using the transmitted output detected by the optical coupler 108, a scale factor may be defined, for example, the change in transmittance per nanometer of displacement. The relationship between transmittance and displacement is explained above in relation to Figure 2, showing that transmittance (and therefore scale factor) is based on coupling rate and detuning. Graph A 310 shows the change in optomechanical dispersive coupling rate with respect to separation distance "d". The optomechanical dispersive coupling rate is the change in resonant frequency per meter of movement, and its unit is Hz / m. Graph B 320 shows the change in optomechanical dissipative coupling rate with respect to separation distance "d". The optomechanical dissipative coupling rate is the change in linewidth per meter of movement, and its unit is the change in loss per meter of movement, and its unit is Hz / m. The photomechanical dispersive coupling ratio has an exponential dependence with respect to the separation distance "d". This is because the optical resonance shift has an exponential dependence due to the exponential nature of the evanescent field. The photomechanical dissipative coupling ratio has an exponential dependence with respect to the separation distance "d". Scattering loss k s and the combined loss k a This is because the magnitude of the evanescent field has an exponential dependence on the separation distance "d" due to the exponential nature of the evanescent field. Therefore, the scale factor is based on these photomechanical coupling rates. As shown in Graph A 310 and Graph B 320, since both coupling rates depend exponentially on the separation distance "d", the response to the displacement of the test mass is nonlinear.

[0074] To measure the inertial force, an equilibrium position may be determined. This may be the distance between the test mass 104 and the micro-resonator 102 when the test mass 104 is in its initial position, or it may be a corresponding isolation distance. Small movements near the equilibrium position can then be detected. Since such small movements are detected near the equilibrium position, the response is substantially linear with respect to these movements.

[0075] However, the initial position of the test mass 104 may change over time, which in turn changes the equilibrium position. Different equilibrium positions result in different photomechanical coupling rates due to the exponential intensity distribution of the evanescent field around the resonator. Therefore, a change in the initial position of the test mass changes the equilibrium position, and consequently, the scale factor of the sensor 100 changes. Closed-loop operation maintains the initial position and, consequently, the scale factor. This ensures linearity and accurate measurements. Specifically, the movement of the test mass is controlled by electrostatic drive, and in particular, the optics-mechanical response is adjusted by adjusting the separation gap.

[0076] Therefore, in closed-loop operation, it is possible to keep the gap between the micro-resonator and the test mass small (e.g., smaller than a micron). This small gap is advantageous because, when the test mass is positioned close to the micro-resonator, the scale factor of the response increases, and the change in the output optical signal becomes larger even if the detected inertial force is the same. Furthermore, when the test mass is positioned close to the micro-resonator, the evanescent field around the micro-resonator spreads over only a small distance (on the order of the wavelength of light), allowing for more reliable optical readout.

[0077] Inertial sensors can be used to measure acceleration. Graphs C330 and D340 show the change in applied acceleration based on the deflection (runout) of the test mass.

[0078] To obtain acceleration measurements, an equilibrium position is determined as either d1 or d2. d1 and d2 are different separation distances "d", as shown in graphs A 310 and B 320. The selection of the equilibrium position as d1 is shown in graph C 330. The selection of the equilibrium position as d2 is shown in graph D 340. The selection of the equilibrium position, for example, between d1 and d2, defines the scale factor described above. This is because, due to the exponential intensity distribution of the evanescent field around the resonator, the photomechanical dispersive coupling rate and the photomechanical dissipative coupling rate differ at each equilibrium position, as shown in graphs A 310 and B 320, and the scale factor is based on these coupling rates.

[0079] Small movements of the test mass 104 are detected near equilibrium, such as a movement of + / - 50 nm from the equilibrium position, where the graph is still substantially linear. Thus, to operate the sensor 100, the equilibrium position may be selected and small movements detected.

[0080] By using closed-loop feedback, the electrostatic force generated by the feedback mechanism cancels out the deflection, allowing for the detection of higher acceleration with smaller movements. For example, an acceleration of 100g would result in a deflection of 50nm without closed-loop feedback, while using closed-loop feedback could result in a deflection of 10nm. As explained above, closed-loop operation stabilizes the sensor 100 in an equilibrium position, preventing unwanted offsets from occurring in the sensor 100 and allowing it to be maintained over a long period.

[0081] Figure 4 shows an example of flowchart 400. This flowchart illustrates a closed-loop feedback system used for the inertial sensor 100. The closed-loop feedback system is implemented by the sensor 100 and an internal or external controller of the sensor 100, as previously described in relation to Figure 1. When the test mass 104 is displaced multiple times by an inertial force, the test mass begins to respond nonlinearly and may drift over time. The drift may be due to thermal changes in the test mass or thermal induction due to temperature changes in the inertial sensor. The drift may also be due to asymmetric machining or damping. A closed-loop feedback system is suitable for reducing the drift of the test mass, maintaining the linearity of the test mass's response over a wide range of force magnitudes, actively stabilizing the test mass, and reducing errors in the sensor output. Specifically, the feedback continuously cancels out the drift-related responses of the test mass, particularly to reduce long-term drift. This means that closed-loop operation is particularly important when inertial sensors are used for position tracking (in which case inertial sensing continuously tracks measurements over time rather than providing single, isolated measurements). A closed-loop feedback system can also protect the test mass from impact.

[0082] In the flowchart 400 of Figure 4, the inertial sensor 100 is subjected to an inertial force that may result from the acceleration or rotation of the sensor itself (402). As described above, the test mass 104 flexes due to the inertial force (404). This is detected by an in-resonator photomechanical readout mechanism (in the form of a micro-resonator 102, an optical coupler 108, and a detector 110) (406). The photomechanical readout mechanism receives a change in the output optical signal indicating a change in the optical resonance characteristics of the micro-resonator 102 due to the flexing of the test mass 104. Based on the change in optical resonance characteristics, acceleration or rotational velocity is calculated and output (410). This calculation is performed by the detector 110 or a processing means in the controller. The controller then applies closed-loop feedback. The controller receives the change in the output optical signal (408) and acts on the test mass using electrostatic drive (electrostatic actuation) via the electrode 106 (406) to reduce the drift of the test mass 104. In this way, by applying a voltage to the electrode 106 to generate an electrostatic force and moving the test mass 104, the distance between the test mass 104 and the micro-resonator 102 is changed, thereby applying closed-loop feedback to the test mass 104.

[0083] The controller controls the voltage applied to the electrodes, and the electrostatic force is based on the applied voltage. The test mass may be grounded so that the voltage difference between the electrodes and the test mass can be determined. The electrostatic force moves the test mass to perform closed-loop operation, which provides fine positioning relative to the micro-resonator, protection from shocks, and reduces nonlinearity and drift. This closed-loop operation is advantageous for the long-term stability of the sensor because it maintains the accuracy of the sensor during longer periods of continuous operation.

[0084] The controller may employ proportional-integral-derivative (PID) control to determine the required feedback. The feedback bandwidth may be DC up to the fundamental mechanical frequency or exceed the fundamental mechanical frequency. If the inertial sensor 100 is an accelerometer, the feedback bandwidth may be considerably larger than the detection bandwidth. If the inertial sensor is a gyroscope, the closed-loop feedback may operate at the drive frequency. Signal processing may be required before the controller processes the signal to determine the feedback and / or the measurement of acceleration or rotational speed. Examples of signal processing techniques are detailed in Figures 7 and 11. In addition to performing closed-loop feedback, the controller may perform in-situ calibration of the optical readout by performing a “self-test” procedure of the sensor 100 by operating the test mass 104 for a predetermined distance using electrodes 106.

[0085] The inertial sensor 100 may be used to detect acceleration. If the test mass is suspended using a spring 114, the acceleration can be determined using Hooke's law, which states that the magnitude of the spring's expansion and contraction is directly proportional to the force applied to the spring. When the inertial sensor 100 is accelerated, an inertial force is applied to the inertial sensor, causing the test mass 104 to deflect and disrupting the resonance of the micro-resonator 102. After determining the amount of deflection from the resonance, the force is determined using Hooke's law, and as a result, the acceleration of the sensor 100 is determined.

[0086] Figure 5 shows an example of the optic-mechanical element and output of an exemplary inertial sensor before and during acceleration. In the following figures, upward is used to mean moving along the Y-axis so that the value of Y increases, and downward is used to mean moving along the Y-axis so that the value of Y decreases. The Y-axis is shown in the figures. In Image Figure B 520, acceleration is shown downward from the test mass towards the micro-resonator, but the inertial sensor 100 is not limited to detecting only downward acceleration. The inertial sensor 100 can detect upward and downward acceleration. The inertial sensor 100 may detect acceleration in the X and Y planes, or it may detect acceleration in the X, Y and Z planes.

[0087] Figure A 510 shows the optical-mechanical element when no acceleration is applied, i.e., when the sensor is stationary or moving at a constant velocity. Figure B 520 shows the optical-mechanical element when the test mass 104 is accelerating downward toward the micro-resonator 102 (downward acceleration is applied), as indicated by arrow 522. As shown in Figure B 520, when accelerating downward toward the micro-resonator 102, the test mass is displaced upward by Δy away from the micro-resonator. This displacement occurs because an upward inertial force is acting on the test mass as a result of the downward acceleration. Therefore, the difference in distance between the micro-resonator and the test mass when the sensor 100 is not accelerating and when the sensor 100 is accelerating downward is Δy.

[0088] In graphs C 530 and D 540, the solid line represents the case when the inertial sensor 100 is not accelerating, and the dashed line represents the case when the inertial sensor 100 is accelerating downwards. When the inertial sensor 100 is accelerating downwards, the displacement Δy of the test mass causes a shift Δλ in the resonant wavelength of the micro-resonator. Graph C 530 shows the signal intensity at different wavelengths at the output of the optical coupler. This graph shows that the minimum value of the signal intensity shifts from the solid line (when the sensor is not accelerating) to the dashed line (when the sensor is accelerating downwards). This shift is due to the shift Δλ in the resonant wavelength of the micro-resonator from when the sensor is not accelerating to when it is accelerating downwards. The shift in the resonant wavelength of the micro-resonator is also shown by the difference in the intensity of the signal supplied from the sensor at a given wavelength when the sensor is not accelerating and when it is accelerating downwards. The difference in signal intensity at a given wavelength is shown at points 532 and 534 in graph C 530. At this wavelength, a shift ΔI occurs in the signal intensity from when the sensor is not accelerating to when it is accelerating downwards. This shift ΔI is the shift from point 532 when sensor 100 is not accelerating to point 534 when sensor 100 is accelerating downwards. This is because when sensor 100 is not accelerating, the given wavelength is not the resonant wavelength, so the signal intensity is not minimized. However, when sensor 100 is accelerating downwards, the given wavelength is the resonant wavelength, so the signal intensity is minimized. Graph C also shows the broadening (broadbanding) of the line that can occur when the sensor is accelerated. Due to this broadening, the minimum signal intensity may increase, as shown in Graph C.

[0089] Graph D 540 shows the signal intensity over time at the same predetermined wavelength as Graph C, with point 542 corresponding to point 532 and point 544 corresponding to point 534. Graph D shows the decrease in signal intensity at the predetermined wavelength (indicated as shift ΔI) from the point when sensor 100 is not accelerating to the point when sensor 100 is accelerating downwards. As explained in relation to Graph C 530, this decrease in signal intensity is due to the fact that the predetermined wavelength is not the resonant wavelength when sensor 100 is not accelerating, but when sensor 100 is accelerating downwards, the predetermined wavelength becomes the resonant wavelength due to the displacement of the test mass away from the micro-resonator.

[0090] Figure 6 shows an exemplary inertial sensor 600 for measuring acceleration. The inertial sensor 600 is sometimes also called an acceleration sensor. The inertial sensor 600 is an embodiment of the inertial sensor 100 in Figure 1. This sensor operates using Hooke's Law, as described in relation to Figure 5. As shown in Figure 6, the inertial sensor 600 comprises a micro-electromechanical inertial test mass 604. The test mass 604 is suspended by two suspension means 614 (flexible parts of the test mass 604 in this example) connected to their respective anchors 616. These flexible parts of the test mass may function as springs. The test mass 604 is flexible (bendable) under the application of inertial force due to the acceleration of the inertial sensor 600. The anchors 616 are fixed to the sensor 600. The inertial sensor 600 also comprises four micro-resonators 602. The test mass 604 is adjacent to and discontinuously suspended from the four micro-resonators 602. The test mass has two protrusions 618, each located between the two micro-resonators 602. Each protrusion 618 can act as an optical channel guiding photons that escape from the micro-resonators 602 on either side of the protrusion 618.

[0091] The inertial sensor 600 further comprises four electrodes 606 for counteracting the deflection of the test mass 604 with an electrostatic force. The electrodes 606 are positioned on both sides of the test mass 604, thereby allowing precise control of the movement or maintenance of the position of the test mass 604 by adding an electrostatic force to either side of the test mass 604. Each of the four electrodes 606 comprises two finger portions. The finger portions are protrusions, and these terms are used interchangeably throughout this specification. Both the electrodes 606 and the finger portions are fixed and stationary relative to the sensor 600. The test mass 604 also comprises finger portions. The finger portions of the test mass 604 are located between the finger portions of the fixed electrodes. The finger portions of the test mass 604 are movable, as they also deflect when an inertial force is applied. The finger portions of the movable test mass are interdigitally arranged (interlocking) between the finger portions of the fixed electrodes (stationary electrodes). Since the movement of each finger portion of the movable test mass is strongly coupled to the motion of the test mass, the movement of the finger portion generates the movement of the entire test mass. Therefore, the finger portions of the fixed electrodes counteract the deflection of the finger portions of the movable test mass, thereby canceling out the deflection of the test mass 604 by electrostatic force. This allows each finger portion of the electrode 606 to apply a small force to each finger portion of the test mass, enabling precise control of the test mass 604 and fine positioning of the test mass 604 relative to the micro-resonator 602. The finger portions of the fixed electrodes can cancel out the deflection of the test mass in the X and / or Y directions. The finger portions of the fixed electrodes can also cancel out the deflection of the test mass in the Z direction (not shown).

[0092] The inertial sensor 600 further comprises four optical couplers 608 for coupling light entering and exiting the corresponding micro-resonators 602. The inertial sensor 600 further comprises one or more detectors (not shown in Figure 6). Light enters each optical coupler 608 at the positions indicated by the arrows, as shown in Figure 6, is input to the corresponding micro-resonator 602, output from the micro-resonator 602, and then output from the optical coupler 608 to the detector.

[0093] When the test mass 604 moves up and down along the Y-axis, a change occurs in the distance between the test mass 604 and each micro-resonator 602. Depending on the installation position of the micro-resonators 602, the movement of the test mass 604 causes a differential change in the distance between the test mass 604 and the four micro-resonators 602. This change in the distance between the test mass 604 and each micro-resonator 602 causes a change in the optical resonance characteristics of that micro-resonator 602. Because the changes in the distance of each micro-resonator 602 are different, differential changes occur in the optical output from each optical coupler 608. By comparing the different changes in the optical output from each optical coupler 608, the differential output is determined. With such a differential output, since we are focusing on the difference, errors occurring in all micro-resonators are eliminated. Therefore, by arranging the inertial sensor 600 in Figure 6, differential operation becomes possible, and with differential operation, readout is greatly improved by reducing drift and temperature offset.

[0094] The inertial sensor 600 comprises a specific number of components arranged in a particular manner, but other numbers of components and arrangements also provide an effective inertial sensor. Differential measurements can be performed, providing the above advantages, as long as there is at least one micro-resonator on each side of the test mass. The micro-resonators 602 may all have substantially the same optical resonance, or each of the micro-resonators 602 may have a different optical resonance.

[0095] Figure 6 shows electrostatic driving performed by interdigital electrodes placed at specific positions around the test mass, but electrostatic driving can be set up in any way that applies force to the test mass in the X and / or Y directions.

[0096] Figure 7 shows a control loop feedback system 700 used when the inertial sensor 100 or inertial sensor 600 detects acceleration. This control loop feedback system 700 is an example of the feedback system 400 in Figure 4. The closed-loop feedback system 700 is implemented by the sensor 100 or sensor 600 and an internal or external controller of the sensor, as previously described in relation to Figure 1.

[0097] Acceleration applies a force to the sensor, causing it to output an output voltage V (710). The voltage output from the sensor is input to the controller. This voltage is converted into a digital signal by an analog-to-digital converter (ADC) 712 and filtered by a digital signal processor (DSP) 714 within the controller. The filtering may be high-pass or low-pass filtering. Subsequently, the closed-loop control unit 716 within the controller may determine the acceleration using the filtered signal and provide it as the sensor output 722. The closed-loop control unit 716 within the controller also provides feedback to the sensor. To this end, the closed-loop control unit 716 determines nonlinearity, drift, and noise and outputs a voltage signal to the electrodes to reduce these effects. The voltage signal is generated by a digital-to-analog converter (DAC) 718 and supplied to the sensor electrodes. The electrodes output an electrostatic force based on the magnitude of the voltage signal that acts on the test mass. The actuation of the test mass by the electrodes is essentially negative feedback, as it is intended to eliminate the contribution of noise and drift to the sensor's measurement. The control loop feedback system 700 is a continuous system that continuously reduces sensor drift and noise, providing accurate and precise acceleration output measurement.

[0098] An inertial sensor may be used to detect rotational speed. The rotational speed is detected using the Coriolis effect on a vibrating gyroscope structure. To measure the rotational speed, the test mass is driven in a first direction (e.g., along the X-axis) at frequency Ω. Due to the Coriolis effect, rotation around the Z-axis causes a displacement along the Y-axis at frequency Ω. The rotational speed can then be determined by finding the change in the amplitude of the Y-axis vibration at frequency Ω.

[0099] Figure 8 shows an example of the optics-mechanical elements and output of an inertial sensor 100 before and during rotation. As described above, when the inertial sensor 100 measures rotational speed, the test mass is driven in the X direction and vibrates at frequency Ω. Image A 810 shows the optics-mechanical elements when the sensor 100 is not rotating, for example, when the sensor 100 is at rest, and Image B 820 shows the optics-mechanical elements when the sensor 100 is rotating around the Z axis. The X, Y, and Z directions are given for illustrative purposes, and it should be understood that the sensor is not limited to being used only for measuring rotational speed around the Z axis.

[0100] As shown in Figures A 810 and B 820, the inertial sensor for detecting rotational speed comprises two suspension means (springs in this example). The two suspension means are positioned substantially perpendicular to each other, thereby enabling two vertical movements. This will be further explained in relation to Figure 9. As shown in Figure B 820, when rotating about the Z-axis, the test mass is displaced by Δy along the Y-axis at frequency Ω. Therefore, the difference in distance "d" between when the sensor 100 is not rotating and when the sensor 100 is rotating about the Z-axis is Δy.

[0101] In graphs C830 and D840, the solid line represents the case when the inertial sensor 100 is not rotating, and the dashed line represents the case when the inertial sensor 100 is rotating around the Z-axis. Graph C830 shows the fast Fourier transform (FFT) of the signal at the output of the optical coupler, showing that the amplitude is maximum at frequency Ω when the test mass 104 is driven along the X-axis at frequency Ω. Graph C830 also shows the change in the amplitude of the signal ΔI at frequency Ω from when the sensor is not rotating to when the sensor is rotating around the Z-axis.

[0102] When the sensor rotates, the Coriolis force generates vibrations that are amplitude-modulated along the Y-axis at frequency Ω. This is shown in graph C830 by the increase in the signal amplitude ΔI at frequency Ω from when the sensor is stationary to when it is rotating. By determining the change in signal amplitude ΔI, the Coriolis force can be calculated using known equations, and from there the rotation speed can be determined.

[0103] Graph D 840 shows the signal intensity of the output from the optical coupler 108 over time. When the test mass 104 is driven along the X-axis at frequency Ω, a small portion of the signal with frequency Ω is detected along the Y-axis, as shown in Graph D 840. Graph D 840 also shows the increase in frequency amplitude, as described above in relation to Graph C 830. Graph D 840 also shows, in particular, the difference in peak amplitude ΔI between the non-rotating sensor and the rotating sensor. pk This is clearly shown.

[0104] A change in the distance between the micro-resonator and the test mass alters the resonant frequency characteristics of the micro-resonator, which in turn changes the transmitted output from the optical coupler in the detector. As explained in relation to Figure 2, the change in transmittance in the detector allows for the detection of a change in the resonant frequency. Since the change in resonant frequency is based on the displacement of the test mass, the change in the signal amplitude at frequency Ω can be determined, the Coriolis force can be determined, and consequently the rotational speed can be measured.

[0105] Figure 9 shows an exemplary inertial sensor 900 for measuring rotational speed. The inertial sensor 900 is sometimes called a gyroscope. The inertial sensor 900 is a type of vibrating gyroscope. The inertial sensor 900 is one embodiment of the inertial sensor 100 in Figure 1. As shown in Figure 9, the inertial sensor 900 comprises a micro-electromechanical inertial test mass 904. The test mass 904 is suspended by two suspension means. The suspension means (springs 914 in this example) are connected to their respective anchors 916. The anchors 916 are fixed to the sensor. The springs 914 are positioned substantially perpendicular to each other, thereby enabling two vertical movements. This allows the test mass to move with two degrees of freedom perpendicular to each other. These two degrees of freedom are necessary to enable the sensor to operate in sense mode and drive mode, as will be described below. The sensor operates as described in relation to Figure 8 and also detects rotation around the Z axis. However, please understand that the X, Y, and Z directions are provided for illustrative purposes only, and the sensor is not limited to being used solely for measuring rotational speed around the Z axis.

[0106] The test mass 904 is flexible along the X and Y axes. The inertial sensor 900 also comprises two micro-resonators 902. The test mass 904 is adjacent to the two micro-resonators 902 and suspended discontinuously from them. The inertial sensor 900 further comprises two optical couplers 908 for coupling light entering and exiting the corresponding micro-resonators 902. The inertial sensor 900 further comprises one or more detectors (not shown in Figure 9). Light is input to the optical couplers, and from the optical couplers, light is input to the corresponding micro-resonators 902. The light is then output from the micro-resonators 902 and returned to the optical couplers 908. The optical couplers 908 output light to the detectors.

[0107] The inertial sensor 900 further comprises two electrodes 906 for counteracting the deflection of the test mass 904 with electrostatic force. The electrodes 906 are positioned on two mutually perpendicular sides of the test mass 904, thereby allowing the test mass to be controlled along both the X and Y axes. The inertial sensor 900 has a sense mode and a drive mode that are performed simultaneously. Conceptually, the inertial sensor 900 may be the same as the two inertial sensors 100 in Figure 1, which are orthogonal to each other and have a common test mass. The primary purpose of the inertial sensor moving along the X axis is driving, and the primary purpose of the other inertial sensor moving along the Y axis is sensing.

[0108] Each of the first anchor 916, first spring 914, first electrode 906, first micro-resonator 902, and first optical coupler 908 is used in the drive mode, while each of the second anchor 916, second spring 914, second electrode 906, second micro-resonator 902, and second optical coupler 908 is used in the sense mode. As shown in Figure 9, the drive mode is a mode along the X axis, and the electrode 906 on the right side of the test mass is used to drive the test mass to vibrate at frequency Ω. The spring 914 and anchor 916 on the right side of the test mass in the figure allow the test mass 904 to move freely in the X direction to enable such vibration. The optical coupler 908 and micro-resonator 902 on the left side of the test mass are used to detect that the test mass is being driven at the correct frequency. The electrode 906 on the right side of the test mass is also used to reduce noise and drift, as described in relation to Figure 4.

[0109] The sense mode is a Y-axis mode with springs 914 and anchors 916 above the test mass. Springs 914 and anchors 916 allow the test mass 904 to move freely in the Y direction. As described in relation to Figure 8, when the test mass is driven in the X direction at frequency Ω, the test mass is displaced along the Y axis by rotation around the Z axis due to the Coriolis effect. When the test mass is displaced by Δy along the Y axis, electrodes 906 on the top of the test mass actuate the test mass along the Y axis to reduce drift and noise, as described in relation to Figure 4.

[0110] The displacement of the test mass along the Y-axis changes the distance between the test mass 904 and the micro-resonator 902 below it. This changes the optical resonance characteristics of the micro-resonator 902 below the test mass 904, and consequently, the transmitted output detected by the detector (not shown in Figure 9) from the optical coupler 908 below the micro-resonator changes. As explained in relation to Figure 8, the rotational speed can be calculated using the transmitted output from the optical coupler.

[0111] The inertial sensor 900 comprises a specific number of components arranged in a particular manner, but other numbers of components and arrangements also provide an effective inertial sensor for measuring rotational speed. The sensor may be for measuring rotational speed around the Y-axis or the X-axis. The sensor may be for measuring rotational speed around multiple axes.

[0112] Figure 10 shows another example of an inertial sensor 1000 for measuring rotational speed, also known as a gyro sensor. The inertial sensor 1000 is a type of vibrating gyroscope. The inertial sensor 1000 is one embodiment of the inertial sensor 900 in Figure 9. As shown in Figure 10, the inertial sensor 1000 comprises an outer micro-electromechanical inertial test mass body that functions like a frame 1004 and an inner micro-electromechanical inertial test mass body 1054. The outer test mass body frame 1004 is suspended by four suspension means 1034. The suspension means 1034 (which are the flexible parts of the outer test mass body frame 1004 in this example) are connected to their respective anchors 1016. The anchors 1016 are fixed to the sensor. These flexible parts of the outer test mass body frame 1004 may act as springs. The suspension means 1034 has high rigidity in the X direction but is flexible (bendable) in the Y direction. Therefore, the outer test mass frame 1004 is constrained to move in the Y direction. The inner test mass 1054 is suspended by two suspension means 1044. The suspension means 1044 (which in this example are the flexible parts of the inner test mass 1054) are connected from the outside of the inner test mass 1054 to the inside of the outer test mass frame 1004. These flexible parts of the inner test mass 1054 may act as springs. The suspension means 1044 has high rigidity in the Y direction but is flexible in the X direction. Therefore, the inner test mass 1054 is constrained to move in the Y direction relative to the outer test mass frame 1004 and moves in the Y direction together with the outer test mass frame 1004. The inner test mass 1054 can move in the X direction relative to the outer test mass frame 1004. Thus, due to the rigidity of the suspension means 1034 of the outer test mass frame 1004 in the X direction, only the inner test mass 1054 is subjected to the Coriolis force in the X axis that occurs when rotation is applied.

[0113] The inertial sensor 1000 also comprises four micro-resonators 1002. The inner test mass 1054 is adjacent to two of the micro-resonators 1002 and is suspended discontinuously from these two micro-resonators 1002. The outer test mass frame 1004 is adjacent to the other two micro-resonators 1002 and is suspended discontinuously from these other two micro-resonators 1002. The inertial sensor 1000 further comprises four optical couplers 1008 for coupling light entering the corresponding micro-resonator 1002 and light exiting the micro-resonator 1002. The inertial sensor 1000 may further comprise one or more detectors (not shown in Figure 10). As indicated by the arrows in Figure 10, light enters the optical coupler, is input to the corresponding micro-resonator, is output from that micro-resonator, and is then output to the detector.

[0114] The inertial sensor 1000 further comprises four electrodes 1006 for counteracting the Y-direction deflection of the outer test mass frame 1004 with electrostatic force. Since there are two electrodes 1006 above the outer test mass frame 1004 and two electrodes 1006 below the outer test mass frame 1004, electrostatic force can be applied to both sides of the outer test mass frame 1004 to precisely control its movement or position. The inertial sensor 1000 further comprises two electrodes 1046 for counteracting the X-direction deflection of the inner test mass 1054 with electrostatic force. Each of the six electrodes 1006, 1046 has two finger portions and is of an interdigit type, as will be described in more detail in relation to Figure 6.

[0115] The inertial sensor 1000 has a sense mode and a drive mode that are performed simultaneously, as described above in relation to Figure 9. As shown in Figure 10, the drive mode is along the Y-axis and the sense mode is along the X-axis. The orientation of the suspension means 1044, 1034 constrains the direction of movement of the inner test mass 1054 and the outer test mass frame 1004, as described above, so that the drive mode does not cross-couple with the sense mode, and similarly the Coriolis effect does not couple with the drive mode.

[0116] Regarding the drive mode, the four electrodes 1006 located on the upper and lower parts of the outer test mass frame 1004 are for driving the frame 1004 to vibrate at frequency Ω. The suspension means 1044 connecting the outer test mass frame 1004 and the inner test mass 1054 is rigid in the Y direction and therefore transmits vibrations from the outer test mass frame 1004 to the inner test mass 1054. Thus, vibration energy is transmitted from the outer test mass frame 1004 to the inner test mass 1054, causing the inner test mass to be subjected to the Coriolis effect. The micro-resonators 1002 and corresponding optical couplers 1008 located on each side of the upper and lower protrusions of the outer test mass frame 1004 are for detecting that the test mass frame 1004 is being driven at the correct frequency.

[0117] In sense mode, the inner test mass 1054 can move freely in the X direction by suspension means 1044 located on the right and left sides of the inner test mass 1054. The inner test mass 1054 is displaced in the X direction by rotation around the Z axis. When the test mass 1054 is displaced by Δx in the X direction, the electrodes 1046 inside the test mass 1054 actuate the inner test mass 1054 along the X axis, as described in relation to Figure 4, reducing drift and noise.

[0118] When the outer test mass frame 1004 is driven in the Y direction at frequency Ω, vibration energy is transmitted to the inner test mass 1054, which is constrained to move in the X-axis direction by the suspension geometry. As the sensor 1000 rotates, the inner test mass 1054 flexes along the X-axis at frequency Ω due to the Coriolis effect. The rotational speed can be detected using the micro-resonators 1002 located on either side of the central column of the inner test mass, in the same manner as described in relation to Figures 8 and 9.

[0119] Figure 10 shows electrostatic driving performed by interdigit electrodes placed at specific positions around the test mass. The electrostatic driving can be configured in any way that applies force to the test mass in the X and Y directions.

[0120] The configuration shown in Figure 10 uses two frames that can be adjusted so that the spring is very stiff in either the drive direction or the sense direction, which has the advantage of reducing cross-axis coupling between sense and drive direction vibrations.

[0121] Figure 10 shows a sensor 1000 having an inner test mass 1054 and an outer test mass frame 1004, but the sensor can have a single test mass and can be designed in other ways, such as a disk-type hemispherical system or a tuning fork structure.

[0122] Figure 10 shows a sensor with a specific number of components, but the sensor can have any number of optical couplers, micro-resonators, test masses, and electrodes, and can measure acceleration and rotational speed of any single or multiple axes.

[0123] Figure 11 shows a control loop feedback system 1100 used when the inertial sensor 900 in Figure 9 or the inertial sensor 1000 in Figure 10 detects rotational speed. This control loop feedback system 1100 is an example of the feedback system 400 in Figure 4. The closed-loop feedback system 1100 is implemented by the inertial sensor and an internal or external controller of the sensor.

[0124] When the sensor is rotating around the Z-axis (1120), the sensor is in both sense mode 1114 and drive mode 1113. The controller performing closed-loop feedback has separate closed-loop controls for drive mode and sense mode. The closed-loop control unit 1116 for drive mode uses closed-loop feedback to keep the amplitude stable and adjusts the electrostatic force by comparing the drive mode vibration amplitude to a predetermined reference setpoint and regulating it (1122). The closed-loop control unit 1118 for sense mode monitors the sensor output, examines changes in amplitude at frequency Ω, and uses the electrostatic drive unit (electrostatic actuation unit) 1146 to cancel out such changes.

[0125] In drive mode 1113, the test mass is driven in the X direction at frequency Ω using the electrostatic drive unit 1122. A driving force is applied to the sensor in the X direction, and the sensor outputs an output voltage V. The output voltage of the sensor is input to the controller for closed-loop control for drive mode. The output voltage is input to the ADC 1128 in the controller to convert the voltage into a digital signal, and is filtered using the DSP 1130. The signal is then demodulated (1132) to obtain a drive mode vibration amplitude that can be compared to a predetermined reference point. In particular, the demodulated signal is used to extract information about the vibration amplitude and vibration frequency offset, which can then be corrected by feedback from the closed-loop control. The closed-loop control unit 1134 compares the drive mode vibration amplitude to a predetermined reference setpoint and determines the sensor operation required to maintain stability. The closed-loop control unit 1134 sends the drive signal to the appropriate electrode of the sensor via the modulator 1126 and DAC 1124 for the electrostatic drive unit 1122 in the X-axis direction. Furthermore, a phase-locked loop (PLL) 1106 is provided, connected to the digital control oscillator 1108. The PLL 1106 maintains the frequency locked and generates a frequency reference used by other parts of the system. To increase the sensor's sensitivity to rotational speed, it is important to generate vibrations with very accurate and stable peak amplitude and frequency.

[0126] In sense mode 1114, a force is applied to the test mass along the Y axis by the rotation of the sensor around the Z axis (1120). The sensor outputs an output voltage V. The sensor's output voltage is input to a controller for closed-loop control for sense mode. The output voltage is input to the ADC 1136 to convert the voltage into a digital signal and is filtered using the DSP 1138. The signal is then demodulated (1140) to obtain a common-mode rate that is proportional to the rotation speed and represents the Coriolis amplitude that occurs in response to the rotation speed. The demodulator 1140 also outputs a quadrature signal that represents errors related to frequency mismatch. The closed-loop control unit 1142 then determines and outputs the rotation speed using the common-mode rate (1152). The closed-loop control unit 1142 also outputs a correction signal to suppress the quadrature signal and the common-mode rate. The correction signal is modulated (1150) and converted into a voltage signal via the DAC 1148 and sent to the appropriate electrode of the sensor for electrostatic driving in the Y axis direction (1146).

[0127] Figure 12 is a block diagram of an exemplary inertial measurement unit (IMU) 1200. The IMU 1200 comprises at least one inertial sensor 100 and a processor 1202. Figure 12 illustrates six inertial sensors 100. Five of the inertial sensors 100 are indicated by dashed lines to show they are optional. Although six sensors 100 are shown for the IMU 1200, the inertial measurement unit 1200 may comprise more or fewer inertial sensors. The processor can perform the operation of any controller described herein. Although the inertial sensor 100 in Figure 1 is shown as being included in the IMU, the IMU may comprise any inertial sensors described herein. The IMU may comprise the inertial sensor 600 in Figure 6, the inertial sensor 900 in Figure 9, and / or the inertial sensor 1000 in Figure 10.

[0128] The processor 1202 is configured to receive electrical signals from one or more detectors 110 for each inertial sensor 100, detect changes in the optical resonance characteristics of one or more micro-resonators 102 in response to changes in the distance between the test mass 104 and the micro-resonators 102, determine the acceleration and / or rotational speed of the inertial sensor 100 based on the changes in the optical resonance characteristics of one or more micro-resonators 102, and control the electrostatic force of one or more electrodes 106 based on the changes in the optical resonance characteristics of one or more micro-resonators 102. The electrostatic force of one or more electrodes 106 may be controlled based on the changes in the optical resonance characteristics of the corresponding micro-resonators 102. The processor 1202 may further be configured to calibrate each inertial sensor 100 by changing the electrostatic force of each electrode 106 and detecting changes in the optical resonance characteristics of each micro-resonator 102.

[0129] The IMU1200 may be equipped with six inertial sensors, as shown in Figure 12. The six inertial sensors include three inertial sensors 100 for acceleration detection and three inertial sensors 100 for rotational velocity detection. The three inertial sensors 100 for acceleration detection are arranged to detect different axes, and the three inertial sensors 100 for rotational velocity detection are arranged to detect different axes. For example, the three acceleration detection inertial sensors 100 may include a sensor 100 for detecting acceleration in the X-axis direction, a sensor 100 for detecting acceleration in the Y-axis direction, and a sensor 100 for detecting acceleration in the Z-axis direction. Similarly, the three rotational velocity detection inertial sensors 100 may include a sensor 100 for detecting rotational velocity around the X-axis, a sensor 100 for detecting rotational velocity around the Y-axis, and a sensor 100 for detecting rotational velocity around the Z-axis. This makes it possible to provide six degrees of freedom for tracking a three-dimensional trajectory. The processor 1202 calculates the total acceleration and / or total rotational speed of the inertial measurement unit 1200 based on the acceleration and / or rotational speed of each inertial sensor 100.

[0130] The IMU in this example includes three inertial sensors 100 for acceleration detection and three inertial sensors 100 for rotational speed detection, but the IMU 1200 can include any number of inertial sensors 100 for acceleration detection and any number of inertial sensors 100 for rotational speed detection.

[0131] Many variations of the methods described herein will be obvious to those skilled in the art.

[0132] Each feature disclosed herein (including the attached claims, abstract, and drawings) may be replaced by an alternative feature serving the same, equivalent, or similar purpose unless expressly stated otherwise. Thus, unless expressly stated otherwise, each disclosed feature is merely an example of a comprehensive series of equivalent or similar features.

[0133] The present invention is not limited to the details of the embodiments described above. The present invention extends to novel features or novel combinations of features disclosed herein (including the appended claims, abstract and drawings), or novel methods or steps of processes so disclosed herein. The claims should not be construed to cover only the embodiments described above, but should also be construed to cover any embodiments contained within the claims.

Claims

1. One or more micro-resonators, each micro-resonator supporting a corresponding optical resonance, A micro-electromechanical inertia test mass body is adjacent to one or more of the aforementioned micro-resonators and suspended discontinuously from one or more of the aforementioned micro-resonators, and is capable of bending under the application of inertial force, One or more electrodes for canceling out the deflection of the aforementioned micro-electromechanical inertia test mass with electrostatic force, One or more optical couplers for coupling light entering a corresponding micro-resonator and light exiting the corresponding micro-resonator, An inertial sensor comprising one or more optical couplers and one or more detectors for detecting light received from one or more micro-resonators, A change in the distance between the aforementioned micro-electromechanical inertia test mass and at least one micro-resonator causes a change in the optical resonance characteristics of the micro-resonator. The system comprises at least two electrodes, each of which includes a finger portion stationary relative to the inertial sensor. The aforementioned micro-electromechanical inertia test mass includes a finger portion that is movable relative to the inertia sensor, An inertial sensor in which the movable finger portion of the micro-electromechanical inertial test mass is positioned between the stationary finger portions of at least two electrodes such that the finger portions of the micro-electromechanical inertial test mass and the finger portions of at least two electrodes form an interdigit shape.

2. The inertial sensor according to claim 1, wherein the micro-electromechanical inertial test mass is thicker than each micro-resonator.

3. The inertial sensor according to claim 1 or 2, wherein the micro-electromechanical inertia test mass has an average thickness of 1 micron or more.

4. The inertial sensor according to any one of claims 1 to 3, wherein the micro-electromechanical inertial test mass has an average thickness on the order of tens or hundreds of microns.

5. The inertial sensor according to any one of claims 1 to 4, wherein the distance between the micro-electromechanical inertial test mass and each of the one or more micro-resonators is 1 micron or less.

6. The inertial sensor comprises at least two micro-resonators, at least two optical couplers, and at least two detectors. An inertial sensor according to any one of claims 1 to 5, wherein a change in the first distance between the micro-electromechanical inertial test mass and the first micro-resonator of the two micro-resonators, and a change in the second distance between the micro-electromechanical inertial test mass and the second micro-resonator of the two micro-resonators, cause a differential change in the optical resonance characteristics of the two micro-resonators.

7. The inertial sensor according to any one of claims 1 to 6, wherein the micro-electromechanical inertial test mass is suspended between a first micro-resonator and a second micro-resonator.

8. The inertial sensor according to any one of claims 1 to 7, wherein the micro-electromechanical inertial test mass has a protrusion located between a first micro-resonator and a second micro-resonator.

9. The inertial sensor according to claim 8, wherein the micro-electromechanical inertial test mass further includes one or more additional protrusions, each of which is located between two micro-resonators.

10. The inertial sensor according to any one of claims 1 to 9, wherein one or more of the micro-resonators are radially separated from the micro-electromechanical inertial test mass.

11. The inertial sensor according to any one of claims 1 to 10, wherein one or more electrodes and / or one or more micro-resonators are fixed relative to the inertial sensor.

12. The inertial sensor according to any one of claims 1 to 11, wherein the inertial sensor is for detecting acceleration or rotational speed.

13. The inertial sensor according to any one of claims 1 to 12, wherein one or more of the micro-resonators are whispering gallery mode resonators.

14. The inertial sensor according to any one of claims 1 to 13, wherein the micro-electromechanical inertial test mass is larger than each of the one or more micro-resonators.

15. The inertial sensor according to any one of claims 1 to 14, wherein one or more of the electrodes are used to control the long-term stability of the inertial sensor.

16. The inertial sensor according to any one of claims 1 to 15, further comprising a light source for transmitting light to each of the one or more optical couplers.

17. The inertial sensor according to any one of claims 1 to 16, wherein the light transmitted to each of the one or more optical couplers is broadband light.

18. The inertial sensor according to any one of claims 1 to 16, wherein the light transmitted to each of the one or more optical couplers is coherent single-frequency light.

19. The inertial sensor according to any one of claims 1 to 18, wherein the change in optical resonance characteristics is a shift in the optical resonance and / or a broadening of the optical resonance.

20. The inertial sensor according to any one of claims 1 to 19, wherein one or more of the micro-resonators each have different optical resonances.

21. An inertial measuring unit comprising one or more inertial sensors according to any one of claims 1 to 20, and a processor, The aforementioned processor, for each inertial sensor, Receiving an electrical signal from one or more of the detectors, The change in the optical resonance characteristics of one or more micro-resonators in response to a change in the distance between the micro-electromechanical inertia test mass and one or more of the micro-resonators is detected. Based on the change in the optical resonance characteristics of one or more of the micro-resonators, the acceleration and / or rotational speed of the inertial sensor is determined, and An inertia measurement unit configured to control the electrostatic force of one or more electrodes based on changes in the optical resonance characteristics of one or more of the micro-resonators.

22. The device comprises six inertial sensors as described in any one of claims 1 to 20, The six inertial sensors mentioned above are: A first inertial sensor for detecting acceleration in the first axis, A second inertial sensor for detecting acceleration in a second axis perpendicular to the first axis, A third inertial sensor for detecting acceleration in a third axis orthogonal to the first and second axes, A fourth inertial sensor for detecting the rotational speed around the first axis, A fifth inertial sensor for detecting the rotational speed around the second axis, The system includes a sixth inertial sensor for detecting the rotational speed around the third axis, The inertial measuring unit according to claim 21, wherein the processor is further configured to calculate the total acceleration and / or total rotational speed of the inertial measuring unit based on the acceleration and / or rotational speed of each inertial sensor.

23. The inertial measuring unit according to claim 21 or 22, wherein the electrostatic force of one of the one or more electrodes is controlled based on a change in the optical resonance characteristics of the corresponding micro-resonator.

24. For each inertial sensor used to detect rotational speed, the processor is configured to control the electrostatic force of one or more electrodes to cause the micro-electromechanical inertial test mass to vibrate in a first direction at a fixed frequency. The inertial measurement unit according to any one of claims 21 to 23, wherein the detection of a change in the optical resonance characteristics of one or more of the micro-resonators is performed in response to a change in the distance between the micro-electromechanical inertial test mass and one or more of the micro-resonators in a second direction perpendicular to the first direction at the fixed frequency.

25. The inertial measurement unit according to any one of claims 21 to 24, wherein the processor is further configured to calibrate each inertial sensor by changing the electrostatic force of each electrode and detecting changes in the optical resonance characteristics of each micro-resonator.

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