High-precision Frequency Measurement Research Articles

High-precision frequency measurement approach of diminishing multi-source errors for UAV-based aeromagnetic survey

Compared with crewed aircraft, the optically pumped sensor on the aeromagnetic UAV is closer to the electromagnetic interference sources, significantly affecting the frequency measurement of the sensor. A high-precision frequency measurement approach of diminishing multi-source errors for UAV aeromagnetic surveys is proposed to address this unique issue. The quantization error from counting the reference signal is significantly mitigated using multiple phase-shifted clocks, and the negative effect of trigger error is weakened using Tukey robust regression-based frequency estimation method. We also developed a dedicated aeromagnetic acquisition instrument and a test platform. The results indicate that the frequency resolution of the proposed method can reach 0.001 Hz at 70–350 kHz (10-Hz sampling rate) and the magnetic sensitivity is as low as 0.56 pT/Hz@1 Hz. The fourth-order difference magnetic noise on the UAV helicopter is significantly reduced from 0.0321 nT for the existing multi-channel method to 0.0045 nT for the proposed method.

A high-precision frequency measurement method combining π-type delay chain and different frequency phase coincidence detection

A high-precision frequency measurement method combining π-type delay chain and different frequency phase coincidence detection

Research on a method of high precision frequency measurement based on coordinate rotation digital computer algorithm and Kalman filter.

Frequency measurement is one of the key techniques in high-precision data acquisition technology of broadband signals. Generally, frequency measurement not only needs to deal with a large amount of data processing but also requires a high precision, but these two aspects are sometimes difficult to reconcile. Some algorithms are overly dependent on the accuracy of the to-be-measured data, which might not be the desired option for real projects since it is almost impossible to get ideal error-free data. This article adopts a frequency measurement method based on the coordinate rotation digital computer algorithm, differential algorithm, and Kalman filter. The use of these algorithms for the frequency measurement process would not only simplify the calculation but also reduce the effect of the measurement error. This method can measure all signals that satisfy the sampling theorem and can also measure multi-channel parallel signals. The experimental results of data simulation and actual measurement on the hardware platform show that the accurate frequency measurement algorithm has a strong data processing ability, stable measurement, and steady improvement in the accuracy of measurement results, which can meet the needs of most instruments for accurate frequency measurement. The measurement error could be reduced to the percentile by the Kalman filter and could be reduced to below the thousandth by the combining the algorithms.

Frequency-Modulated Signal Measurement Using Closed-Loop Methodology.

Frequency-modulated (FM) signals are widely used in sensing, measurement, and signal detection due to their strong anti-interference and easy transmission characteristics. Although the high-precision measurement methods for static signals are quite complete, the high-precision measurement methods for dynamic FM signals still need to be studied, and the measurement accuracy in the high-sampling system still has room for improvement. Traditionally, the equal-precision measurement method is widely applied in most scenarios. However, its accuracy is limited by the quantization error of ±1 word and the sampling gate time, making it difficult to improve the frequency measurement accuracy while ensuring a high sampling rate at the same time. In this paper, a high-precision feedback frequency measurement system with the capability to eliminate the quantization error of ±1 word is proposed. The proposed system consists of two stages, the rough measurement stage based on the equal-precision measurement method and the precise measurement stage based on the negative feedback tracking architecture using the phase–frequency detector (PFD) and direct digital synthesizer (DDS). The effectiveness and feasibility of the system are verified by both simulation and experiment. At the sampling rate of 2 kHz, the frequency measurement accuracy is improved by more than 30 dB.

Data augmentation using a generative adversarial network for a high-precision instantaneous microwave frequency measurement system.

In this Letter, an unsupervised-learning platform-generative adversarial network (GAN)-is proposed for experimental data augmentation in a deep-learning assisted photonic-based instantaneous microwave frequency measurement (IFM) system. Only 75 sets of experimental data are required and the GAN can augment the small amount of data into 5000 sets of data for training the deep learning model. Furthermore, frequency measurement error of the estimated frequency has improved by an order of magnitude from 50 MHz to 5 MHz. The proposed use of GAN effectively reduces the amount of experimental data needed by 98.75% and reduces measurement error by 10 times.

Fast frequency relocking for synchronization enhanced resonant accelerometer

Synchronization, as a unique phenomenon, has been extensively studied in biology, chaotic systems, nonlinear dynamics, quantum information, and other fields. Benefiting from the characteristics of frequency amplification, noise suppression, and stability improvement, synchronization has been gradually applied in sensing, communication, time keeping, and other applications. In the sensing field, synchronization provides a new strategy to improve the performance of sensors. However, the performance improvement is only effective within the synchronization range, and the narrow synchronization range has become a great challenge for the wide application of synchronization-enhanced sensing mechanism. Here, we propose a frequency automatic tracking system (FATS) to widen the synchronization range and track the periodic acceleration signals by adjusting the frequency of the readout oscillator in real time. In addition, a high-precision frequency measurement system and fast response control system based on FPGA (Field Programmable Gate Array) are built, and the tracking performance of the FATS for static and dynamic external signals is analyzed to obtain the optimal control parameters. Experimental results show that the proposed automatic tracking system is capable of static acceleration measurement, the synchronization range can be expanded to 975 Hz, and the relocking time is shortened to 93.4 ms at best. By selecting the optimal PID parameters, we achieve a faster relocking time to meet the requirements of low-frequency vibration measurements, such as seismic detection and tidal monitoring.

Weakness of weak values: Incompatibility of anomalous pulse-spectrum amplification and optical frequency combs

We probe the use of optical frequency combs to place lower bounds on anomalous amplification of a weak-value-measured pulse delay, potentially reaching a theoretical temporal resolution of better than ${10}^{\ensuremath{-}34}$ s. Owing to the interferometric behavior of weak values, we show that anomalous weak value amplification of a time delay is not equivalent to a temporal linear phase ramp. We show that the anomalous weak value is a rearrangement of amplitudes that generates an apparent shift that can be measured in direct detection, but does not change the actual frequency offset of a spectral distribution measurable in coherent detection. This implies that high-precision heterodyne beatnote frequency measurements of an optical frequency comb cannot be used in combination with the weak value amplification, at least in its currently conceived form. This unfortunate feature sheds light on the nature of anomalous weak values in shifting the pointer in a conjugate basis.

High-precision Microwave Frequency Measurement Based on Stimulated Brillouin Scattering With Simple Configuration

We propose and implement a microwave frequency measurement (MFM) scheme based on stimulated Brillouin scattering (SBS) and an apodized fiber Bragg grating (AFBG), achieving high accuracy in a wide range of measurement with a highly simplified configuration. By sweeping a reference frequency during SBS process, a frequency-to-power mapping between the reference frequency and the monitored output optical power of the MFM system is established. Unknown frequencies can be identified through a specific numerical relationship among the unknown frequency, reference frequency, and Brillouin frequency shift (BFS). The transmission and reflection properties of the AFBG are exploited to offer pump light and probe light simultaneously for SBS process, thereby reducing complexity of the MFM system. It can be derived theoretically that all frequencies larger than one BFS can be measured except for 3/2 BFS. This measurement blind spot can be eliminated by utilizing two segments of single-mode fibers with different BFSs. A measurement error of less than ±1 MHz within 10.68 GHz to 20 GHz is achieved in a proof-of-concept experiment of the proposed MFM approach. This method has also been proved to be applied to dual microwave frequency measurements.

Viterbi decoding of CRES signals in Project 8

Cyclotron radiation emission spectroscopy (CRES) is a modern approach for determining charged particle energies via high-precision frequency measurements of the emitted cyclotron radiation. For CRES experiments with gas within the fiducial volume, signal and noise dynamics can be modelled by a hidden Markov model. We introduce a novel application of the Viterbi algorithm in order to derive informational limits on the optimal detection of cyclotron radiation signals in this class of gas-filled CRES experiments, thereby providing concrete limits from which future reconstruction algorithms, as well as detector designs, can be constrained. The validity of the resultant decision rules is confirmed using both Monte Carlo and Project 8 data.

Resonant Optical Gyroscope Based on All-Optical Frequency Locking

A novel resonant optical gyroscope (ROG) is proposed based on all-optical frequency locking method, which requires a small-size, low-power and low-cost distributed feedback (DFB) semiconductor laser to simplify the locking mechanism. The frequency splitting caused by Saganc effect can be measured with higher precision than the traditional intensity measurement method for ROG as the optical noise would cause less error for frequency. Besides, a high precision frequency measurement method with time-to-digital converter (TDC) chip is also designed for miniaturization and high precision of ROG. After the theoretical and experimental demonstration, all-optical frequency locking method used in ROG has the feasibility and potential to be realized as a high precision and integration angular velocity sensor. This work is meaningful for the development of high-precision, low-power and low-cost micro-optic gyroscope.

A High-Precision and Wideband Fundamental Frequency Measurement Method for Synchronous Sampling Used in the Power Analyzer

In the dedicated high-precision power quality analyzer, synchronous sampling is required to reduce the effect of spectrum leakage produced by the discrete Fourier transform process. Thus, accurate fundamental frequency measurement is urgently needed. However, due to the harmonics and noise in the power signal, it is difficult to achieve the accurate fundamental frequency measurement. Moreover, with the wide application of high-frequency programmable power supply, the fundamental frequency is gradually increasing, which requires power analyzers to have the abilities of both high precision and a wide range of the fundamental frequency measurement. To solve these issues, a new fundamental frequency measurement architecture used in synchronous sampling is proposed. This architecture consists of a small-point fast Fourier transform module, spectrum refinement algorithm, and a multimodal optimization method to calculate the accurate fundamental frequency under large harmonic conditions. In the practical hardware platform results, this architecture has a large fundamental frequency measurement range from 20 Hz to 200 kHz with a relative error which is <0.004%. The wideband fundamental frequency measurement structure proposed in this article achieves high measurement accuracy.

A new high-precision Fourier frequency measurement algorithm based on modified sampling sequence

Aiming at the accuracy of frequency measurement algorithms in power systems, this paper proposes a new high-precision Fourier frequency measurement algorithm based on modified sampling sequence. Through the improvement of the traditional Fourier algorithm, the theoretical error of the traditional algorithm is eliminated and the speed of the algorithm is improved. By modifying the sampling sequence and iterative methods, the original sampling sequence is as close to the ideal sequence as possible, so that the sampling frequency and the fundamental frequency of the system tend to be synchronized, thereby reducing the problem of spectrum leakage and the fence effect. Through simulation analysis, the algorithm effectively improves the frequency measurement accuracy.

High-precision frequency measurement for microresonant sensors based on improved modified multi-phase clock method.

Microelectromechanical system resonant sensors are widely used in high precision applications. Frequency measurement plays an important role in such frequency readout sensors. This paper proposed an improved modified frequency measurement method based on the multi-phase clock (MPC), which can effectively improve the measurement accuracy but does not reduce the output rate. Innovative claims include (1) building a model of measurement error for MPC in which the probability of triggering error under different conditions is calculated, (2) improving the accuracy of the MPC measurement by phase reverse, and (3) proposing an algorithm to eliminate jitters of the measured signal. We compared the measurement results of this optimized MPC realized by the field programmable gate array (FPGA) device with those of the conventional MPC, spectral measurement, and equal precision measurement implemented with the National Instruments acquisition equipment PXI-4461 and USB-6366, respectively. The results show that the bias instability of the adopted method is ∼10 µHz obtained by Allan variance analysis, which is better than that of the other three methods. It can meet the accuracy requirements for the resonant frequency measurement of state-of-the-art resonant accelerometers. In addition, an algorithm running in FPGA is proposed to eliminate jitters caused by the noise of the measured signal for enhancing the robust of optimized MPC. The results demonstrate that the optimized MPC has features of high accuracy and anti-interference capability and can be easily transferred to the application specific integrated circuit in the future due to its full digital circuit version.

A Microwave Frequency Measurement System Based on Si3N4 Ring-Assisted Mach-Zehnder Interferometer

A microwave frequency measurement system based on a ring assisted Mach-Zehnder interferometer (RAMZI) with a large measurement range and high accuracy is proposed and experimentally demonstrated. By using single-sideband modulation, the microwave signal with unknown frequency is converted to an optical sideband signal, which is used to probe the two complementary output optical powers of the ring-assisted Mach-Zehnder interferometer, then a fixed frequency-to-power mapping is established by obtaining a highly linear amplitude comparison function (ACF). High-precision frequency measurement with a root mean square error (RMSE) of less than 30 MHz was achieved in a frequency range of 5.2 GHz, and relative low-precision frequency measurement with a RMSE of less than 102 MHz was achieved in a frequency range of 11 GHz. Besides, in order to break the trade-off between measurement range and measurement accuracy, a multi-band measurement method was implemented and frequency measurement range of 5∼39 GHz with RMSE lower than 37 MHz was achieved.

Distributed multi‐satellite measurement scheme oriented towards microsatellite formations

Existing high-precision inter-satellite radio frequency (RF) measurement systems were mostly based on two-satellite formations, and there lacks further research on measurement schemes for multi-satellite formations. The frequency division multiple access (FDMA) and the code division multiple access based schemes are widely used, but not applicable for distributed applications due to their poor scalability. The time division multiple access (TDMA) based scheme can overcome this weakness, and has been applied in the global positioning system (GPS) IIR/IIF inter-satellite link. However, the atomic clock used in GPS is not suitable for microsatellites. If a miniaturised frequency source instead of the atomic clock is utilised, the two way ranging (TWR) method adopted in this system would encounter a sharp decrease of measurement accuracy. To this end, this Letter aims to propose a novel TDMA based distributed RF measurement scheme for multi-microsatellite formations. A TDMA based distributed broadcast protocol is employed in the media access control layer, closely integrated with the asymmetric double-sided two-way ranging method adopted in the physical layer. Numerical and simulation results demonstrate the superiority of the proposed scheme over the conventional TDMA scheme. The proposed scheme can be recommended for future multi-microsatellite formation missions.

Absolute frequency measurements for emission transitions of molecular iodine in the range of 1053 – 1068 nm

Results of high-precision frequency measurements are presented for certain components of the 127I2 hyperfine structure, which correspond to emission transitions of the B – X band in the range of 1053 – 1068 nm. The frequencies are measured by using a femtosecond optical frequency synthesiser based on a Ti:sapphire laser. The hyperfine structure is resolved by the method of three-level laser spectroscopy. The frequency-doubled cw Nd : YAG laser is used as an excitation radiation source, and the probe radiation in the range of 1050 – 1070 nm is generated by an external-cavity diode laser. The frequencies of both lasers are simultaneously locked to those of two adjacent hyperfine structure components of iodine lines, which have a common upper level. Correspondingly, the frequency of the Nd : YAG laser is locked to the frequency of the absorption transition component, and the diode laser frequency – to the frequency of the emission transition component. The radiation frequency of the diode laser ‘locked’ in this way is measured. Frequencies of 18 hyperfine structure components for six emission lines corresponding to the bands (32 – 54) and (32 – 53) are measured. The relative uncertainty of the measurement is 8 × 10–10.

High precision frequency measurement of terahertz waves using optical combs from a Mach-Zehnder-modulator-based flat comb generator.

Using a frequency-tunable optical comb generated from a Mach-Zehnder-modulator-based flat comb generator (MZ-FCG) and a nonlinear optical fiber, we demonstrated a frequency measurement of continuous terahertz wave sources with the frequency of 0.1 and 0.6THz by an electro-optic sampling method. We clearly observed beat signals between the terahertz source and the optical two-tone extracted from the optical comb, allowing us to determine the absolute frequency. Owing to the wide comb spacing of the MZ-FCG, this method has a high potential for the high-speed measurement of the frequency of terahertz wave sources.

Room-Temperature Continuous-Wave Frequency-Referenced Spectrometer up to 7.5 THz

The lack of coherent room-temperature sources in the whole terahertz spectral window (0.3-10 THz) has significantly hampered the growth of scientific and technological applications in this range. Among them, high-precision frequency measurements of molecular transitions play a central role but remain an open challenge. Here, room-temperature generation and detection of continuous-wave, broadly tunable, narrow-linewidth THz radiation are presented, and their application to high-resolution spectroscopy in the broad 1-7.5 THz spectral range is demonstrated. This result has been achieved by implementing a Cherenkov phase-matching scheme into a channel waveguide in a nonlinear crystal. This simple approach, entirely based on robust telecom technology, unprecedently merges in a single source an ultra-broad continuous-wave spectral coverage and a state-of-the-art accuracy (approximately 10-9) in molecular-transition-center determination.

A high-precision and fast-sampling frequency measurement method based on FPGA carry chain for airborne optically pumped cesium magnetometer.

Improving the precision and sampling rate of the resonance frequency of cesium atoms is the key to enhancing the same factors of an airborne optically pumped cesium magnetometer (AOPCM). Aiming at the existed problems of AOPCM and characteristics of resonance signal, this paper proposes a high-precision and fast-sampling frequency measurement method based on carry chains of Field-Programmable Gate Array (FPGA). In order to achieve a fast-sampling rate, an improved equal precision frequency measurement method is proposed to measure the standard signal and the resonance signal continuously. Besides, by using the serial full adder to connect FPGA carry chains to a delay line, the delay line is used to compensate the unsynchronized clock edge, so the counting error can be reduced, and the precision of frequency measurement can be improved greatly. Experiments show that the frequency resolution is 0.014 nT and the relative error is lower than 2 × 10-6 when the sampling rate is 500 Hz. The experimental result indicates that the proposed method improves the precision and sampling rate of resonance frequency measurement greatly. Consequently, the precision and sampling rate of AOPCM can be improved.

High-precision frequency measurement system based on different frequency quantization phase comparison

Aiming at the requirements of phase comparison without frequency normalization, a high-precision frequency measurement system is proposed based on different frequency quantization phase comparison. Using group phase difference pulse in the least common multiple period, the period of frequency standard signal, the period of the measured signal and the pulse width of group phase difference can be respectively counted with the aid of FPGA technology. The obtained counter value is saved and sent to host computer. The measured frequency can be obtained by the data processing of the host computer. Experimental results show that the short-term frequency stability of the system better than E−12/s is achieved. Compared to the traditional frequency measurement system, the system have the advantages of wide measurement range, high frequency stability, low phase noise and low development cost. The system not only plays an important role in precise measurement physics fields such as high-precision transmission and comparison of time and frequency, measurement and suppression of phase noise, but also has a wider application in localization of spatial motion radiation source, satellite navigation equipment, precise time frequency measurement, communication, radar and other high-tech fields.