Phase is a fundamental concept widely accepted in physics and informalogy, which has been used as an important indicator of the overall state evolution for many-body system. Therefore, famous physicist Chen-Ning Yang has attributed phase as one of the three main themes of development in physics in the 20th century, together with symmetry and quantum. Phase-locking technology originated from the invention of "coherent communication" in 1932, and later became an important "phase-locked loop" method for maintaining synchronization, which worked in time dimension without function of amplitude detection. Expanding from the time dimension to the signal strength dimension, based on phase-sensitive detection, the higher frequency alternating amplitude signal is down-converted to a lower frequency signal. As a result, with the ability of suppressing noise, lock-in amplifiers is usually indispensable in weak signal measurement. The lock-in amplifiers are essentially an ultra-narrowband filter with unique advantage to extract the amplitude and phase of the AC signal buried in the noise even if it is faint to nanovolts. It has extremely high frequency domain resolution and has been widely used for a long time. Industrial enterprises and scientific research fields such as physical property measurement, scanning probe microscope, laser spectroscopy, non-destructive testing, spectrum-based medical imaging, seismic measurement, etc. Lock-in amplifiers can also be found in emerging industry application scenarios, such as quantum computers, precision IoT sensing, high-precision component grading testing, third-generation biological gene sequencing, space gravitational wave detection, etc. To a certain extent, the level of application of the lock-in amplifier as a precision measurement tool for the underlying signal reflects the scientific research capability and industrialization level.

In the research on the basic principle of phase-locking, Dr. LU Jun from Institute of Physics, Chinese Academy of Sciences noticed that the measurement result of the traditional method is a complex number corresponding to the frequency of the reference signal. The real alternating frequency of the measured complex number is used as a hidden variable, which is usually regarded as exactly the same as the reference frequency. The frequency of the measured signal and the frequency of the reference signal will deviate during the transmission channel or system strain process. Some signals such as passively observed signals cannot be controlled in advance. The inconsistency between the preset frequency and the real frequency will eventually lead to inaccurate phase difference and amplitude measurement. The idea to solve this problem is actually discarding the assumption that the frequency of the measured signal is consistent with the frequency of the fixed reference signal. After improving the frequency functional analysis through the phase-locked algorithm, the researcher has simultaneously solved the anti-noise frequency measurement and accurate phase lock of the measured signal. The new developed method is hence called lock-in amplifier with frequency measurement or lock-in frequency meter (LIF). After theoretically deducing the local function form of the phase-locked spectrum of the single-period signal near the estimated frequency point, and using three-point fitting for frequency measurement, the new method can avoid the deviation problem of the parabolic function.  As a result, the accuracy reaches the limit of statistical theory, and the efficiency has been greatly enhanced. Based on simulation result, the complexity of the algorithm has reduced from O(N*logN) of the fast Fourier transform FFT to O(N) dependence. In addition to the theoretical lower limit Cramers-Raw Lower Bound, the researcher found the measurement uncertainty of the phase-lock frequency meter also has an upper limit Lock-in Upper Bound due to the limited sampling window. Therefore, the new method quantitatively gives the relationship formula of the theoretical lowest measurable signal-to-noise ratio for lock-in amplifiers.

The new method simultaneously solves the problems that the usual frequency meter cannot measure low signal-to-noise ratio signals and the phase-locked reference frequency must be preset. Because the preset parameters are reduced, it is easy to increase the intelligence of the lock-in amplifier and possess the potential to be embedded in a multimeter. After designing the new phase-locking algorithm for frequency measurement, LU Jun realized a cross-platform solution from circuit design, FPGA programming, ARM embedded and host computer programs through the collaborative enterprise Yanchuangda, and finally integrated analog and digital circuit technology to form a new domestically-made phase lock prototype. The noise floor measured by the new phase lock at 1 kHz frequency point with 1 second integration time is 1nV/√Hz; the frequency measurement accuracy can reach 1 ppb (one-billionth) at 10 kHz. Through the system test of signal and different types of noise premixing and extraction, the results show that the frequency measurement accuracy under noise is close to the theoretical limit.

This study entitled “Lock-in frequency measurement with high precision and efficiency” was published on Review of Scientific Instruments.

This work is under supports from National Natural Science Foundation of China (No. 51327806 and 61575209), Fujian Institute of Innovation (Grant No. FJCXY18040302) and Youth Innovation Promotion Association of Chinese Academy of Sciences (No.2018009 and No.2018024).