A method of determining residual intensity noise (RIN) of a sensor may comprise determining a first amplitude of a first harmonic of the sensor while a signal propagating through the sensor is modulated at a modulating frequency corresponding to twice an eigenfrequency of the sensor. The method may further comprise determining a second amplitude of a second harmonic of the sensor while the signal propagating through the sensor is modulated the modulating frequency, and determining the RIN of the sensor as a ratio of the first amplitude and the second amplitude.

Measurement cavities described herein include a cylindrical chamber having a first open end and a second open end; a first cap covering the first open end of the cylindrical chamber and a second cap covering the second open end of the cylindrical chamber, wherein the first and second caps hermetically seal the cylindrical chamber and wherein the first cap is rigidly coupled to the second cap; and a wafer holder positioned within and coupled to the cylindrical chamber. The measurement cavity has a mass m, a stiffness k, and a damping constant c configured such that the transmissibility $.Math.\frac{x}{F}.Math.$
of an input force at 60 Hz in the measurement cavity is reduced by a factor of at least 10 and the measurement cavity has a natural frequency of greater than 300 Hz.

The disclosed technology can be implemented in photonics integrated circuit (PIC) to provide an optical frequency detection device for measuring an optical frequency of light using two Mach-Zehnder interferometer where the delay imbalance in the first interferometer is configured to be one quarter wavelength longer than that of the second interferometer to produce an additional phase difference between the two arms. The two outputs of each interferometer are then detected by two photodetectors to produce two complementary interference signals. The difference between the two complementary interference signals of the first interferometer is a sine function of the optical frequency while the difference between the two complementary interference signals of the second interferometer is proportional to a cosine function of the optical frequency. Using the sine/cosine interpretation algorithm commonly used for the rotation encoders/decoders, any increments in optical frequency can be readily obtained.

The disclosed technology can be implemented in photonics integrated circuit (PIC) to provide an optical frequency detection device for measuring an optical frequency of light using two Mach-Zehnder interferometer where the delay imbalance in the first interferometer is configured to be one quarter wavelength longer than that of the second interferometer to produce an additional phase difference between the two arms. The two outputs of each interferometer are then detected by two photodetectors to produce two complementary interference signals. The difference between the two complementary interference signals of the first interferometer is a sine function of the optical frequency while the difference between the two complementary interference signals of the second interferometer is proportional to a cosine function of the optical frequency. Using the sine/cosine interpretation algorithm commonly used for the rotation encoders/decoders, any increments in optical frequency can be readily obtained.

Aspects of the present disclosure describe Rayleigh fading mitigation via short pulse coherent distributed acoustic sensing with multi-location beating-term combination. In illustrative configurations, systems, methods, and structures according to the present disclosure employ a two stage modulation arrangement providing short interrogator pulses resulting in a greater number of sensing data points and reduced effective sectional length. The increased number of data points are used to mitigate Rayleigh fading via a spatial combining process, multi-location-beating combining (MLBC) which uses weighted complex-valued DAS beating results from neighboring locations and aligns phase signals of each of the locations, before combining them to produce a final DAS phase measurement. Since Rayleigh scattering is a random statistic, the MLBC process allows capture of different statics from neighboring locations with correlated vibration/acoustic signal. The combined DAS results minimize a total Rayleigh fade, in both dynamic fading and static fading scenarios.

Aspects of the present disclosure describe Rayleigh fading mitigation via short pulse coherent distributed acoustic sensing with multi-location beating-term combination. In illustrative configurations, systems, methods, and structures according to the present disclosure employ a two stage modulation arrangement providing short interrogator pulses resulting in a greater number of sensing data points and reduced effective sectional length. The increased number of data points are used to mitigate Rayleigh fading via a spatial combining process, multi-location-beating combining (MLBC) which uses weighted complex-valued DAS beating results from neighboring locations and aligns phase signals of each of the locations, before combining them to produce a final DAS phase measurement. Since Rayleigh scattering is a random statistic, the MLBC process allows capture of different statics from neighboring locations with correlated vibration/acoustic signal. The combined DAS results minimize a total Rayleigh fade, in both dynamic fading and static fading scenarios.

An apparatus and method are provided. The apparatus includes an imaging device; a stage movable relative to the imaging device; an isolation plate provided between the imaging device and the stage, including a horizontal glass plate; and a plurality of interferometers in electronic communication with a processor. The plurality of interferometers include three interferometers disposed on the imaging device, configured to direct a first beam set in a first direction toward the horizontal glass plate; and three interferometers disposed on the stage, configured to direct a second beam set in a second direction toward the horizontal glass plate, the second direction being opposite to the first direction. The processor is configured to measure distances between the imaging device and the isolation plate and distances between the stage and the isolation plate based on the first beam set and the second beam set reflected from the horizontal glass plate.

An apparatus and method are provided. The apparatus includes an imaging device; a stage movable relative to the imaging device; an isolation plate provided between the imaging device and the stage, including a horizontal glass plate; and a plurality of interferometers in electronic communication with a processor. The plurality of interferometers include three interferometers disposed on the imaging device, configured to direct a first beam set in a first direction toward the horizontal glass plate; and three interferometers disposed on the stage, configured to direct a second beam set in a second direction toward the horizontal glass plate, the second direction being opposite to the first direction. The processor is configured to measure distances between the imaging device and the isolation plate and distances between the stage and the isolation plate based on the first beam set and the second beam set reflected from the horizontal glass plate.

A single-laser light source system for cold atom interferometers, comprising: a reference light module including a narrow-bandwidth laser and a frequency stabilization module and an optical frequency shift module including a first electro-optic modulator and a first narrow-bandwidth optical-fiber filter. The first electro-optic modulator is connected to the first narrow-bandwidth optical-fiber filter by an optical fiber, and the first electro-optic modulator is connected to the laser by an optical fiber. The first electro-optic modulator receives an initial light from the laser, modulates the initial light by a modulation signal with a preset frequency, and generates sidebands with the preset frequency. The first narrow-bandwidth optical-fiber filter filters the optical signal at the output of the first electro-optic modulator to obtain a frequency-shifted light as the +1-order sideband. The frequency-shifted light is used for modulation to obtain a measurement and control light of the cold atom interferometer.

A single-laser light source system for cold atom interferometers, comprising: a reference light module including a narrow-bandwidth laser and a frequency stabilization module and an optical frequency shift module including a first electro-optic modulator and a first narrow-bandwidth optical-fiber filter. The first electro-optic modulator is connected to the first narrow-bandwidth optical-fiber filter by an optical fiber, and the first electro-optic modulator is connected to the laser by an optical fiber. The first electro-optic modulator receives an initial light from the laser, modulates the initial light by a modulation signal with a preset frequency, and generates sidebands with the preset frequency. The first narrow-bandwidth optical-fiber filter filters the optical signal at the output of the first electro-optic modulator to obtain a frequency-shifted light as the +1-order sideband. The frequency-shifted light is used for modulation to obtain a measurement and control light of the cold atom interferometer.