Vibratory gyroscopes are inertial sensors, used to measure rotation rates in a number of applications. The performance of these sensors is limited by imperfections that occur during manufacture of the resonators. The effects of resonator imperfections, in piezoelectric vibratory gyroscopes, were studied. Hamilton's principle and the Rayleigh-Ritz method provided an effective approach for modeling the coupled electromechanical dynamics of piezoelectric resonators. This method produced accurate results when applied to an imperfect piezoelectric vibrating cylinder gyroscope. The effects of elastic boundary conditions, on the dynamics of rotating thin-walled cylinders, were analyzed by an exact solution of the Flügge shell theory equations of motion. A range of stiffnesses in which the cylinder dynamics was sensitive to boundary stiffness variations was established. The support structure, of a cylinder used in a vibratory gyroscope, should be designed to have stiffness outside of this range. Variations in the piezoelectric material properties were investigated. A figure-of- merit was proposed which could be used to select an existing piezoceramic material or to optimize a new composition for use in vibratory gyroscopes. The effects of displacement and velocity feedback on the resonator dynamics were analyzed. It was shown that displacement feedback could be used to eliminate the natural frequency errors, that occur during manufacture, of a typical piezoelectric vibrating cylinder gyroscope. The problem of designing the control system to reduce the effects of resonator imperfections was investigated. Averaged equations of motion, for a general resonator, were presented. These equations provided useful insight into the dynamics of the imperfect resonator and were used to motivate the control system functions. Two control schemes were investigated numerically and experimentally. It was shown that it is possible to completely suppress the first-order effects of resonator mass/stiffness imperfections. Damping imperfections, are not compensated by the control system and are believed to be the major source of residual error. Experiments performed on a piezoelectric vibrating cylinder gyroscope showed an order of magnitude improvement, in the zero-rate offset variation over a temperature range of 60°C, when the control systems were implemented. / Ph. D.

This thesis reports development of three different high performance, low g-sensitive micromachined gyroscopes having single, double, and quadruple masses. The single mass gyroscope (SMG) is developed for comparison of its performance with the double mass gyroscope (DMG) and quadruple mass gyroscope (QMG). DMG is a tuning fork gyroscope, diminishing the effects of unpredictable g-loadings during regular operation, while QMG is a twin tuning fork gyroscope, developed for a uniform and minimized g-sensitivity. DMG and QMG use novel ring spring connections for merging the masses in drive modes, providing uniform and anti-phase drive mode vibrations that minimize the cross-coupling and the effects of intrinsic and extrinsic accelerations on the scale factor and bias levels of the gyroscopes. The sense mode of each mass of the multi-mass gyroscopes is designed to have higher resonance frequencies than that of the drive mode for possible matching requirements, and these sense modes have dedicated frequency tuning electrodes for frequency matching or tuning. Detailed performance simulations are performed with a very sophisticated computer model using the ARCHITECT software. These gyroscopes are fabricated using a standard SOIMUMPs process of MEMSCAP Inc., which provides capacitive gaps of 2 &micro / m and structural layer thickness of 25 &micro / m. Die sizes of the fabricated gyroscope chips are 4.1 mm x 4.1 mm for the single mass, 4.1 mm x 8.9 mm for the double mass, and 8.9 mm x 8.9 mm for the quadruple mass gyroscope. Fabricated gyroscopes are tested with dedicated differential readout electronics constructed with discrete components. Drive mode resonance frequencies of these gyroscopes are in a range of 3.4 kHz to 5.1 kHz. Depending on the drive mode mechanics, the drive mode quality (Q) factors of the fabricated gyroscopes are about 300 at atmospheric pressure and reaches to a value of 2500 at a vacuum ambient of 50 mTorr. Resolvable rates of the fabricated gyroscopes at atmospheric pressure are measured to be 0.109 deg/sec, 0.055 deg/sec, and 1.80 deg/sec for SMG, DMG, and QMG, respectively. At vacuum, the respective resolutions of these gyroscopes improve significantly, reaching to 106 deg/hr with the SMG and 780 deg/hr with the QMG, even though discrete readout electronics are used. Acceleration sensitivity measurements at atmosphere reveal that QMG has the lowest bias g-sensitivity and the scale factor g sensitivity of 1.02deg/sec/g and 1.59(mV/(deg/sec))/g, respectively. The performance levels of these multi-mass gyroscopes can be even further improved with high performance integrated capacitive readout electronics and precise sense mode phase matching.

I used a Mach-Zehnder atom interferometer to measure the static electric-dipole polarizabilities of K, Rb, and Cs atoms with 0.11\% uncertainty. Static polarizability measurements serve as benchmark tests for 𝑎𝑏 𝑖𝑛𝑖𝑡𝑖𝑜 atomic structure calculations. Calculating atomic properties such as polarizabilities, van der Waals coefficients, state lifetimes, or oscillator strengths involves accurately calculating the valence electrons' electric-dipole transition matrix elements. Additionally, testing Cs atomic structure calculations helps interpret the results of parity non-conservation experiments, which in turn places constraints on beyond-the-standard-model physics. I discuss improvements to our experiment that allowed us to measure static polarizabilities with 0.11% uncertainty, and we present our results in the context of recent 𝑎𝑏 𝑖𝑛𝑖𝑡𝑖𝑜 and semi-empirical static polarizabilities and recent, high-precision measurements of excited state lifetimes and van der Waals C₆ coefficients. I also used our interferometer to develop a new technique for inertial sensing. High precision, portable, atom-interferometer gyroscopes and accelerometers are desirable for self-contained inertial navigation and in the future may be used for tests of General Relativity and searches for gravitational waves using satellite-mounted inertial sensors. Satellite-mounted atom interferometers are challenging to build because of size, weight, power, and reliability constraints. Atom interferometers that use nanogratings to diffract atoms are attractive for satellite-mounted inertial sensing applications because nanogratings weigh approximately nothing and require no power. We developed a new 𝑖𝑛 𝑠𝑖𝑡𝑢 measurement technique using our nanograting atom interferometer, and we used it to measure inertial forces for the benefit of our static polarizability measurements. I also review how to calculate the sensitivity of a nanograting atom interferometer, and I employed these calculations in order to design a portable, nanograting atom interferometer inertial sensor.

Intelligent devices such as smart phones, smart watches, virtual reality (VR) headsets and personal exercise devices have become integral elements of accessories used by many people. The ability of these devices to verify or identify the user could be applied for enhanced security and user experience customization among other things. Almost all these devices have built-in inertial sensors such as accelerometer and gyroscope. These inertial sensors respond to the movements made by the user while performing day to day activities like walking, getting up and sitting down. The response depends on the activity being performed and thus can be used for activity recognition. The response also captures the user's unique way of doing the activity and can be used as a behavioral biometric for verification or identification. The acceleration (accelerometer) and rate of rotation (gyroscope) are recorded in the device coordinate frame. But to determine the user's motion, these need to be converted to a coordinate frame relative to the user. In most situations the orientation of the device relative to the user can neither be controlled nor determined reliably. The solution to this problem requires methods to remove the dependence on device orientation while comparing the signals collected at different times. In a vast of majority of research to date, the performance of authentication algorithms using inertial sensors have been evaluated on small datasets with few tens of subjects, collected under controlled placement of the sensors. Very often stand alone inertial sensors have been used to collect the data. Stand alone sensors afford better calibration, while the sensors built into smart devices offer little or no means of calibration. Due to these limitations of the datasets used, it is difficult to extend the results from these research to realistic performance with a large number subjects and natural placement of off-the-shelf smart devices. This dissertation describes the Kabsch algorithm which is used to achieve orientation invariance of the recorded inertial data, enabling better authentication independent of device orientation. It also presents the Vector Cross Product (VCP) method developed to achieve orientation invariance. Details of a realistic inertial dataset (USF-PDA dataset) collected with commercial smart phones placed in natural positions and orientations using 101 subjects are given. The data includes sessions from different days on a subset of 56 subjects. This would enable realistic evaluation of authentication algorithms. This dataset has been made publicly available. The performance of five methods that address the orientation dependence of signals are compared to a baseline that performs no compensation for orientation of the device. The methods as a part of a overall gait authentication algorithm are evaluated on the USF-PDA dataset mentioned above and another large dataset with more than 400 subjects. The results show that the orientation compensation methods are able to improve the authentication performance on data with uncontrolled orientation to be close to performance on data collected with controlled orientation. The Kabsch method shows the highest improvement.

Rocking-mass gyroscope consists of an assembly of four cantilever beams with a rigid mass attached to them in the middle subjected to base rotations. Due to the gyroscope effect, the beams undergo coupled flexural-torsional vibrations. The main goal of the research is to develop an accurate model of such a system and along this line a detailed mathematical modeling of the gyroscope is developed. The equations of motion clearly show the presence of the gyroscopic couplings in all cantilever beams. A computer simulation model in its most general form has been developed, to analyze the effectiveness of this type of gyroscope. / UOIT

Integrated ring resonators have attracted a considerable interest in optical communications because of their small size and wide range of applicability. Here we consider several aspects of these devices, beginning with a tunable hybrid ring resonators consisting of a silicon over insulator (SOI) ring covered with a polymer layer in a variable electric field. Varying the field changes the polymer refractive index and consequently the resonance condition of the cavity. This device offers a large degree of optical confinement together with a high modulation speed. Subsequently, we design and present fabrication results for a Wavelength Division Multiplexing (WDM) multiplexer/demultiplexer formed from a series of ring resonators with two channels separated by 50 GHz each that is predicted to exhibit a free spectral range (FSR) of 100 GHz , signal dispersion less than 30 ps/nm and a signal cross-talk less than -23 dB. Finally, we analyze the application of the coupled ring waveguide circuit to rotation sensors based on the Sagnac phase shift. Here, however our analysis indicates that a single ring, of the same area exhibits a higher degree of sensitivity to rotational motion than a multiple ring circuit.

This thesis reports on a design and modeling of a micro-machined gyroscope. The proposed sensor is a dual mass type, electro-statically driven to primary mode oscillation and senses, capacitively, the output signal. Full decoupling between drive and sense modes minimizes the mechanical crosstalk and based on this a novel gyroscope is designed and modeled which has separate sensing and driving masses. The dual mass gyroscope is designed such that driving and sensing resonant frequency is 23101 Hz with 0% mismatch (in simulation)with quality factor of 31.6227 and bandwidth of 730.51Hz. The gyroscope when actuated in simulation with 25V ac and 10V dc showed sensing capacitance variation of 126aF for 1 rad/s with base capacitance of 244.16fF. To the design of the gyroscope a new semi automatic tool was formulated for the noise analysis and noise based optimization of the resonant MEMS structures. Design of a sensitive gyroscope needs to take into account the noise shaping induced by damping phenomena at micro scale and is critical for optimization. The analysis was further extended to the design of the gyroscope and estimation shows that there is a trade of between the S/N ratio and the sensitivity and the design could be made much better in-terms of S/N by tuning its resonant frequency to 10⁶Hz.

A ring laser gyroscope (gyro) is an active laser interferometer designed to sense rotation through the Sagnac frequency shift encountered by two beams travelling in opposite directions around a closed path. The classes of devices considered in this thesis are the large and ultra-large ring laser gyros. These instruments are designed for direct measurement of earth rotation rate and find applications in geodesy, geophysics, and tests of physical theories. The research presented in this thesis focuses on the demonstration of new techniques for operating ring laser gyros. The main goal of these techniques has been the correction for variations in the geometry of an ultra-large ring laser gyro, UG-3. This instrument is a 77 m perimeter ultra-large ring laser gyro of heterolithic construction and is the primary instrument used in the experiments presented here. UG-3 has been used to demonstrate measurement of earth strains which have been used to correct for changes in the geometry of the instrument. It has also been used to demonstrate a control technique where the co-rotating beams were alternately offset allowing the number of wavelengths around the perimeter to be counted and a Sagnac rotation signal to be obtained. Among the most important outcomes of this research of interest to the large ring laser gyro community is that we now understand most of the problems that would affect a next generation ring laser gyro. This understanding allows us to choose an operational technique best suited to the measurements being made and thus maximise the scientific potential of the instrument. Additionally, the development of a new standard for data storage and an associated suite of software to acquire, query and analyse ring laser data is expected to improve collaboration with the wider research community. Other research outcomes of more general interest include the analysis of how oscillation of a single mode is established in a high finesse laser cavity. We demonstrate that the ultimate mode of operation can be selected with a ‘seed’ beam of exceptionally low intensity. An interesting related outcome is the demonstration of Sagnac beat frequency measurement during the ring down of a ring cavity, a type of measurement immune to dispersive and flow related frequency shifts.

Integrated ring resonators have attracted a considerable interest in optical communications because of their small size and wide range of applicability. Here we consider several aspects of these devices, beginning with a tunable hybrid ring resonators consisting of a silicon over insulator (SOI) ring covered with a polymer layer in a variable electric field. Varying the field changes the polymer refractive index and consequently the resonance condition of the cavity. This device offers a large degree of optical confinement together with a high modulation speed. Subsequently, we design and present fabrication results for a Wavelength Division Multiplexing (WDM) multiplexer/demultiplexer formed from a series of ring resonators with two channels separated by 50 GHz each that is predicted to exhibit a free spectral range (FSR) of 100 GHz , signal dispersion less than 30 ps/nm and a signal cross-talk less than -23 dB. Finally, we analyze the application of the coupled ring waveguide circuit to rotation sensors based on the Sagnac phase shift. Here, however our analysis indicates that a single ring, of the same area exhibits a higher degree of sensitivity to rotational motion than a multiple ring circuit.

This thesis reports on a design and modeling of a micro-machined gyroscope. The proposed sensor is a dual mass type, electro-statically driven to primary mode oscillation and senses, capacitively, the output signal. Full decoupling between drive and sense modes minimizes the mechanical crosstalk and based on this a novel gyroscope is designed and modeled which has separate sensing and driving masses. The dual mass gyroscope is designed such that driving and sensing resonant frequency is 23101 Hz with 0% mismatch (in simulation)with quality factor of 31.6227 and bandwidth of 730.51Hz. The gyroscope when actuated in simulation with 25V ac and 10V dc showed sensing capacitance variation of 126aF for 1 rad/s with base capacitance of 244.16fF. To the design of the gyroscope a new semi automatic tool was formulated for the noise analysis and noise based optimization of the resonant MEMS structures. Design of a sensitive gyroscope needs to take into account the noise shaping induced by damping phenomena at micro scale and is critical for optimization. The analysis was further extended to the design of the gyroscope and estimation shows that there is a trade of between the S/N ratio and the sensitivity and the design could be made much better in-terms of S/N by tuning its resonant frequency to 10⁶Hz.