A micro-electromechanical device includes a semiconductor substrate, in which a first microstructure and a second microstructure of reference are integrated. The first microstructure and the second microstructure are arranged in the substrate so as to undergo equal strains as a result of thermal expansions of the substrate. Furthermore, the first microstructure is provided with movable parts and fixed parts with respect to the substrate, while the second microstructure has a shape that is substantially symmetrical to the first microstructure but is fixed with respect to the substrate. By subtracting the changes in electrical characteristics of the second microstructure from those of the first, variations in electrical characteristics of the first microstructure caused by changes in thermal expansion or contraction can be compensated for.

An example accelerometer includes a first excitation ring comprising a first material having a first coefficient of thermal expansion (CTE), a second excitation ring comprising the first material having the first CTE; and a proof mass assembly disposed between and in contact with the first excitation ring and the second excitation ring. The proof mass assembly comprises a second material having a second CTE, wherein a difference between the first CTE and the second CTE is equal to or less than 0.5 parts per million per degree Celsius (ppm/ C.).

An optical sensor having one or more sensing interference elements is disclosed. A first detector function generates a coarse optical path difference signal for example using a discrete Fourier transform of a detected interference spectrum, and a second detector function generates a refined optical path difference signal using the coarse optical path difference signal and for example a cross correlation of the interference spectrum with one or more sets of periodic transfer functions.

The method and system for determining position with improved calibration allows a device to initiate activity at the proper location, such as navigating a drill bit through a rock formation. A pair of position sensors in opposite orientations generates position data signals. A temperature sensor detects temperature and duration of the temperature. An adjusted plastic bias value is determined by a processor module based on the temperature data signal, the duration of the temperature, and the position data signals so as to account for bias and hysteresis errors and error correction based on the opposing orientations of the pair of position sensors. A position value is set according to the adjusted plastic bias value so that the position value is more accurate. The activity of the terminal device is initiated or maintained according to the position value calibrated by the adjusted plastic bias value.

Systems and methods are disclosed for generating temperature compensated acceleration data in both analog and digital format from a torque balance accelerometer (TBA). During manufacture of the TBA, a calibration process is used consisting of cooling and heating the TBA to discrete temperatures within a range and at each discrete temperature measuring the TBA scale factor and offset. After collecting scale and offset data, said data is loaded into the memory of the TBA.

During field operation, sensing a current temperature, retrieving the closest scale and offset correction factors from memory of the TBA, and performing linear interpolation to generate a temperature-compensated output for the TBA.

Methods of forming micro-electromechanical device include a semiconductor substrate, in which a first microstructure and a second microstructure of reference are integrated. The first microstructure and the second microstructure are arranged in the substrate so as to undergo equal strains as a result of thermal expansions of the substrate. Furthermore, the first microstructure is provided with movable parts and fixed parts with respect to the substrate, while the second microstructure has a shape that is substantially symmetrical to the first microstructure but is fixed with respect to the substrate. By subtracting the changes in electrical characteristics of the second microstructure from those of the first, variations in electrical characteristics of the first microstructure caused by changes in thermal expansion or contraction can be compensated for.

An inertial measurement unit includes a spherical gimbal system and a heat exchanger system that cool components of the spherical gimbal system without affecting the operations of the spherical gimbal system. The heat exchanger system can be configured to flow chilled air to the components of the spherical gimbal system by using the spherical gimbals as transport pathways for the chilled air and the returned heated air.

A downhole measurement system includes a data logger. The data logger includes a containment vessel containing a processor, an accelerometer, and memory. The containment vessel is characterized by a radial dimension less the diameter of a hole to be measured. The processor is operative to execute processor-readable instructions. The accelerometer is in data communication with the processor, and is operative to measure acceleration along three mutually orthogonal axes. The accelerometer is operative to output, to the processor, data characterizing the measured acceleration. The memory, in data communication with the processor, is operative to store processor-readable instructions. The stored instructions include processor-readable instructions, that when executed by the processor, cause the processor to receive the outputted acceleration data and write the received acceleration data to the memory.

An inertial sensor apparatus includes: a base substrate; and a stacked body bonded to the base substrate by a first junction. The stacked body includes: a first inertial sensor that outputs a first detection signal in accordance with an inertial force; a processing circuit that drives the first inertial sensor and that processes the first detection signal; and a second junction that is positioned between the first inertial sensor and the processing circuit and that bonds the first inertial sensor to the processing circuit. A thermal conductivity of the second junction is higher than a thermal conductivity of the first junction.

An apparatus for measuring acceleration includes: a reference cavity having a first fixed reflecting surface and a second fixed reflecting surface; a sense cavity having a fixed reflecting surface and a non-fixed reflecting surface, the non-fixed reflecting surface being configured to be displaced when subject to an acceleration force; a light source to illuminate the reference and sense cavities; a controller to vary a wavelength of light emitted by the light source and/or an index of refraction of an optical medium of the cavities; a photodetector to detect light emitted by the reference and sense cavities; an interferometer sensor to measure using the detected light, for each variation of the wavelength of light and/or the index of refraction a reference displacement of the reference cavity and a sense displacement of the sense cavity; and a processor to calculate the acceleration using each of the reference displacements and the sense displacements.