Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Scientific Reports

Adaptive optical phase estimation for real-time sensing of fast-varying signals

Liu Wang, Fang Xi Xie, Yong Zhang, Min Xiao, Fang Liu

Published Dec 16, 2022• 4 citations
Publisher

Abstract

Abstract Optical phase tracking is an important technique for use in high-precision measurement applications, including optical frequency metrology and ground- or space-based gravitational wave observation, and coherent optical communications. When measuring fast-varying real-time signals, the response time limitations of the measurement system’s phase-locked loop cause the best operating point to be mismatched, and the measurement then becomes nonlinear. To make these measurements possible, this work proposes a time delay loop that theoretically enables optimal homodyne detection. When the time delay loop is combined with an extended Kalman filter, the estimated measurement accuracy is improved by 2.4 dB when tracking a fast-varying random signal with a velocity of 107 rad/s. This phase estimation improvement also increases as the interference angle deviates further from the optimal measurement point. The proposed method shows potential for use in real-time sensing and measurement applications.

DOI
10.1038/s41598-022-26329-1

Related papers

Fast, accurate, and robust frequency offset estimation based on modified adaptive Kalman filter in coherent optical communication system

Yanfu Yang, Qian Xiang, Qun Zhang +4 more

We propose a joint estimation scheme for fast, accurate, and robust frequency offset (FO) estimation along with phase estimation based on modified adaptive Kalman filter (MAKF). The scheme consists of three key modules: extend Kalman filter (EKF), lock detector, and FO cycle slip recovery. The EKF module estimates time-varying phase induced by both FO and laser phase noise. The lock detector module makes decision between acquisition mode and tracking mode and consequently sets the EKF tuning parameter in an adaptive manner. The third module can detect possible cycle slip in the case of large FO and make proper correction. Based on the simulation and experimental results, the proposed MAKF has shown excellent estimation performance featuring high accuracy, fast convergence, as well as the capability of cycle slip recovery.

Optical Engineering•Sep 23, 2017•13 citations

Robust Filtering for Adaptive Homodyne Estimation of Continuously Varying Optical Phase

Shibdas Roy, Ian R. Petersen, Elanor H. Huntington

Recently, it has been demonstrated experimentally that adaptive estimation of a continuously varying optical phase provides superior accuracy in the phase estimate compared to static estimation. Here, we show that the mean-square error in the adaptive phase estimate may be further reduced for the stochastic noise process considered by using an optimal Kalman filter in the feedback loop. Further, the estimation process can be made robust to fluctuations in the underlying parameters of the noise process modulating the system phase to be estimated. This has been done using a guaranteed cost robust filter.

arXiv:1211.7203•Nov 30, 2012•5 citations

Adaptive estimation of time-varying phase via weak value amplification

Chunhui Shi, Qi Song, Hongjing Li +4 more

The real-time estimation of a time-varying phase is of great importance in several fields. In order to estimate a time-varying phase with high precision and sensitivity, we propose and experimentally demonstrate an adaptive phase estimation method via weak value amplification by splitting the light into sensing path and monitoring path. In the proposed method, the phase shift can be amplified, an adjustable sensitivity and linear dynamic range can be obtained through the insertion of the reference phase, and a full-range phase estimation could be realized via an appropriate adjustment strategy. Furthermore, detectors with a higher resolution could be selected to detect weak signal by the adjustment of attenuation. Potentially, the phase estimation precision of about 10−8 rad could be achieved with the available equipment.

Applied Physics Letters•Mar 18, 2024•5 citations

Coherent state phase estimation based on digital nonlinear phase-locked loop

Xu Han, Shuxin Chen, Hao Wu +2 more

The navigation mechanism of obtaining phase parameters based on quantum theory can break through the limitation of classical physical limit to navigation accuracy. In order to achieve the accurate estimation of the coherent state phase, it is usually assumed that the local oscillator phase must be orthogonal to the coherent state phase in the method of quantum homodyne detection. However, the coherent state phase is unknown and the hypothesis cannot be guaranteed to be correct in practice. In this paper we design a nonlinear phase-locked loop to solve the problem. Firstly, in order to obtain the Wigner distribution for a coherent state, we start with the Wigner distribution for the vacuum state and analyze the noise characteristics according to Wigner distribution of coherent state, then the output of homodyne detection is derived. Secondly, in order to avoid introducing errors in theory, caused by linearization and cope with the limiting requirement between local oscillator phase and coherent state phase in the phase tracking of coherent state, we design an orthogonal simplex cubature Kalman filter (OSCKF) algorithm to achieve the function of the nonlinear phase-locked loop. The algorithm converges by updating the state of the local oscillator phase multiple times, and then, the accurate coherent phase is obtained. Finally, according to the design of the phase-locked loop, we observe the data of homodyne detection and then verify the correctness of the OSCKF algorithm. The simulation results show that the OSCKF can converge to the real phase after observing 200 sampled data and the accuracy is higher than extended Kalmn filter (EKF) and cubature Kalman filter (CKF), and the real phase can be obtained under different local oscillator phase. In conclusion, the nonlinear phase-locked loop based on OSCKF algorithm breaks the limitation of traditional way in which the initial local oscillator phase is required to be orthogonal to the coherent state phase, and effectively avoid the linearization error and improve the anti-nonlinear ability. It is very significant in theory and application .

Acta Physica Sinica•Jan 1, 2019•2 citations

Quantum theory of optical temporal phase and instantaneous frequency

Mankei Tsang, Jeffrey H. Shapiro, Seth Lloyd

We propose a general quantum theory of optical phase and instantaneous frequency in the time domain for slowly varying optical signals. Guided by classical estimation theory, we design homodyne phase-locked loops that enable quantum-limited measurements of temporal phase and instantaneous frequency. Standard and Heisenberg quantum limits to such measurements are then derived. For optical sensing applications, we propose multipass and Fabry-P\'erot position and velocity sensors that take advantage of the signal-to-noise-ratio enhancement effect of wide-band angle modulation without requiring nonclassical light. We also generalize our theory to three spatial dimensions for nonrelativistic bosons and define a Hermitian fluid velocity operator, which provides a theoretical underpinning to the current-algebra approach of quantum hydrodynamics.

arXiv:0804.0463•Physical Review A•Nov 18, 2008•31 citations

Enhanced Long-Distance Weak Signal Transmission Capabilities via Weak Measurement

Ding Wang, Qi 琦 Song 宋, Hongjing Li +3 more

Abstract Reliable detection of weak phase signals under significant channel loss and complex noise environments is a crucial step for practical applications of optical integrated communication and sensing systems. In this letter, we propose and experimentally demonstrate an enhanced long-distance weak signal transmission method assisted by weak measurement. Performing heterodyne detection and light intensity compensation on two nearly symmetric post-selected paths, the method enables real-time estimation of a time-varying phase while maintaining robustness against technical noises proportional to light intensity or photon number, detector common-mode noise, and significant attenuation over long-distance transmission. Experimental results indicate a potential phase sensitivity at the level of 10 −8 rad even with a signal light intensity attenuation of 48.1 dB. Potentially, combining the adaptive adjustment strategy, the method may provide a viable solution in remote weak signal detection and extraction, thereby contributing to optical integrated communication and sensing.

Chinese Physics Letters•Sep 19, 2025•2 citations
Abstract Optical phase tracking is an important technique for use in high-precision measurement applications, including optical frequency metrology and ground- or space-based gravitational wave observation, and coherent optical communications. When measuring fast-varying real-time signals, the response time limitations of the measurement system’s phase-locked loop cause the best operating point to be mismatched, and the measurement then becomes nonlinear. To make these measurements possible, this work proposes a time delay loop that theoretically enables optimal homodyne detection. When the time delay loop is combined with an extended Kalman filter, the estimated measurement accuracy is improved by 2.4 dB when tracking a fast-varying random signal with a velocity of 107 rad/s. This phase estimation improvement also increases as the interference angle deviates further from the optimal measurement point. The proposed method shows potential for use in real-time sensing and measurement applications.
We propose a joint estimation scheme for fast, accurate, and robust frequency offset (FO) estimation along with phase estimation based on modified adaptive Kalman filter (MAKF). The scheme consists of three key modules: extend Kalman filter (EKF), lock detector, and FO cycle slip recovery. The EKF module estimates time-varying phase induced by both FO and laser phase noise. The lock detector module makes decision between acquisition mode and tracking mode and consequently sets the EKF tuning parameter in an adaptive manner. The third module can detect possible cycle slip in the case of large FO and make proper correction. Based on the simulation and experimental results, the proposed MAKF has shown excellent estimation performance featuring high accuracy, fast convergence, as well as the capability of cycle slip recovery.
Recently, it has been demonstrated experimentally that adaptive estimation of a continuously varying optical phase provides superior accuracy in the phase estimate compared to static estimation. Here, we show that the mean-square error in the adaptive phase estimate may be further reduced for the stochastic noise process considered by using an optimal Kalman filter in the feedback loop. Further, the estimation process can be made robust to fluctuations in the underlying parameters of the noise process modulating the system phase to be estimated. This has been done using a guaranteed cost robust filter.
The real-time estimation of a time-varying phase is of great importance in several fields. In order to estimate a time-varying phase with high precision and sensitivity, we propose and experimentally demonstrate an adaptive phase estimation method via weak value amplification by splitting the light into sensing path and monitoring path. In the proposed method, the phase shift can be amplified, an adjustable sensitivity and linear dynamic range can be obtained through the insertion of the reference phase, and a full-range phase estimation could be realized via an appropriate adjustment strategy. Furthermore, detectors with a higher resolution could be selected to detect weak signal by the adjustment of attenuation. Potentially, the phase estimation precision of about 10−8 rad could be achieved with the available equipment.
The navigation mechanism of obtaining phase parameters based on quantum theory can break through the limitation of classical physical limit to navigation accuracy. In order to achieve the accurate estimation of the coherent state phase, it is usually assumed that the local oscillator phase must be orthogonal to the coherent state phase in the method of quantum homodyne detection. However, the coherent state phase is unknown and the hypothesis cannot be guaranteed to be correct in practice. In this paper we design a nonlinear phase-locked loop to solve the problem. Firstly, in order to obtain the Wigner distribution for a coherent state, we start with the Wigner distribution for the vacuum state and analyze the noise characteristics according to Wigner distribution of coherent state, then the output of homodyne detection is derived. Secondly, in order to avoid introducing errors in theory, caused by linearization and cope with the limiting requirement between local oscillator phase and coherent state phase in the phase tracking of coherent state, we design an orthogonal simplex cubature Kalman filter (OSCKF) algorithm to achieve the function of the nonlinear phase-locked loop. The algorithm converges by updating the state of the local oscillator phase multiple times, and then, the accurate coherent phase is obtained. Finally, according to the design of the phase-locked loop, we observe the data of homodyne detection and then verify the correctness of the OSCKF algorithm. The simulation results show that the OSCKF can converge to the real phase after observing 200 sampled data and the accuracy is higher than extended Kalmn filter (EKF) and cubature Kalman filter (CKF), and the real phase can be obtained under different local oscillator phase. In conclusion, the nonlinear phase-locked loop based on OSCKF algorithm breaks the limitation of traditional way in which the initial local oscillator phase is required to be orthogonal to the coherent state phase, and effectively avoid the linearization error and improve the anti-nonlinear ability. It is very significant in theory and application .
We propose a general quantum theory of optical phase and instantaneous frequency in the time domain for slowly varying optical signals. Guided by classical estimation theory, we design homodyne phase-locked loops that enable quantum-limited measurements of temporal phase and instantaneous frequency. Standard and Heisenberg quantum limits to such measurements are then derived. For optical sensing applications, we propose multipass and Fabry-P\'erot position and velocity sensors that take advantage of the signal-to-noise-ratio enhancement effect of wide-band angle modulation without requiring nonclassical light. We also generalize our theory to three spatial dimensions for nonrelativistic bosons and define a Hermitian fluid velocity operator, which provides a theoretical underpinning to the current-algebra approach of quantum hydrodynamics.
Abstract Reliable detection of weak phase signals under significant channel loss and complex noise environments is a crucial step for practical applications of optical integrated communication and sensing systems. In this letter, we propose and experimentally demonstrate an enhanced long-distance weak signal transmission method assisted by weak measurement. Performing heterodyne detection and light intensity compensation on two nearly symmetric post-selected paths, the method enables real-time estimation of a time-varying phase while maintaining robustness against technical noises proportional to light intensity or photon number, detector common-mode noise, and significant attenuation over long-distance transmission. Experimental results indicate a potential phase sensitivity at the level of 10 −8 rad even with a signal light intensity attenuation of 48.1 dB. Potentially, combining the adaptive adjustment strategy, the method may provide a viable solution in remote weak signal detection and extraction, thereby contributing to optical integrated communication and sensing.