Precise Phase Measurements Research Articles

On the phase consistency of apical organ of Corti vibrations

Low-frequency hearing is critically important for speech and music perception. However, technical and anatomical limitations previously made it difficult to study the mechanics of the low-frequency parts of the cochlea, but this changed with the introduction of optical coherence tomography vibrometry. With this technique, sound-evoked vibration can be measured from the apex of a fully intact cochlea. Results of such measurements generated controversy because conventional traveling waves, the hallmark of which is longer group delay closer to the helicotrema, were absent within the apical 20% of the guinea pig cochlea (Burwood et al, Science Advances 8:eabq2773, 2022). The validity of this result was questioned, primarily because group delays were calculated from phase values averaged across many points within the organ of Corti. Here we show that variations in phase across the organ of Corti are minor and does not affect the group delay significantly. We also assess the precision of phase measurements with optical coherence tomography. An artificial target with reflectivity similar to the organ of Corti was used. These measurements revealed that a commonly used commercial optical coherence tomography system produces half-cycle errors in 1-5 % of pixels, leading to a bimodal distribution of phase values. This problem can be easily addressed by using medians when computing averages, as was done by Burwood et al (2022). Hence, neither averaging across pixels nor technical factors can explain the apparent lack of conventional traveling waves at the apex of the guinea pig cochlea at low stimulus levels. The physiological mechanisms that operate at the apex apparently differ from other cochlear regions.

Single-Photon Interference over 8.4km Urban Atmosphere: Toward Testing Quantum Effects in Curved Spacetime with Photons.

The emergence of quantum mechanics and general relativity has transformed our understanding of the natural world significantly. However, integrating these two theories presents immense challenges, and their interplay remains untested. Recent theoretical studies suggest that the single-photon interference covering huge space can effectively probe the interface between quantum mechanics and general relativity. We developed an alternative design using unbalanced Michelson interferometers to address this and validated its feasibility over an 8.4km free-space channel. Using a high-brightness single-photon source based on quantum dots, we demonstrated single-photon interference along this long-distance baseline. We achieved a phase measurement precision of 16.2mrad, which satisfied the measurement requirements for a gravitational redshift at the geosynchronous orbit by 5 times the standard deviation. Our results confirm the feasibility of the single-photon version of the Colella-Overhauser-Werner experiment for testing the quantum effects in curved spacetime.

Room-scale Location Trace Tracking via Continuous Acoustic Waves

The increasing prevalence of smart devices spurs the development of emerging indoor localization technologies for supporting diverse personalized applications at home. Given marked drawbacks of popular chirp signal-based approaches, we aim at developing a novel device-free localization system via the continuous wave of the inaudible frequency. To achieve this goal, solutions are developed for fine-grained analyses, able to precisely locate moving human traces in the room-scale environment. In particular, a smart speaker is controlled to emit continuous waves at inaudible 20kHz , with a co-located microphone array to record their Doppler reflections for localization. We first develop solutions to remove potential noises and then propose a novel idea by slicing signals into a set of narrowband signals, each of which is likely to include at most one body segment’s reflection. Different from previous studies, which take original signals themselves as the baseband, our solutions employ the Doppler frequency of a narrowband signal to estimate the velocity first and apply it to get the accurate baseband frequency, which permits a precise phase measurement after I-Q (i.e., in-phase and quadrature) decomposition. A signal model is then developed, able to formulate the phase with body segment’s velocity, range, and angle. We next develop novel solutions to estimate the motion state in each narrowband signal, cluster the motion states for different body segments corresponding to the same person, and locate the moving traces while mitigating multi-path effects. Our system is implemented with commodity devices in room environments for performance evaluation. The experimental results exhibit that our system can conduct effective localization for up to three persons in a room, with the average errors of 7.49 cm for a single person, with 24.06 cm for two persons, with 51.15 cm for three persons.

Phase Diffusion Mitigation in the Truncated Mach–Zehnder Interferometer

The presence of phase diffusion noise may lead to the loss of quantum measurement advantages, resulting in measurement results that cannot beat the standard quantum limit (SQL). Squeezing is considered an effective method for reducing the detrimental effect of phase diffusion on a measurement. Reasonable use of squeezing can make a measurement exceed the SQL. The Mach–Zehnder (MZ) interferometer has been exploited as a generic tool for precise phase measurement. Describing the reduction in quantum advantage caused by phase diffusion in an MZ interferometer that can be mitigated by squeezing is not easy to handle analytically because the input state changes from a pure state to a mixed state after experiencing the diffusion noise in the MZ interferometer. We introduce a truncated MZ interferometer, a symmetrical structure that can achieve the same potential phase sensitivity as the conventional MZ interferometer. This scheme can theoretically explain how phase diffusion reduces phase estimation and why squeezing counteracts the presence of phase diffusion. Using the Gaussian property of the input state and the characteristic of Gaussian operation in the squeezing, the two orthogonal field quantities of the quantum state are squeezed and anti-squeezed to different degrees, and the analytic results are obtained. This result can beat the SQL and provide reliable theoretical guidance for the experiment. The truncated MZ interferometer is more straightforward to build and operate than the conventional MZ interferometer. Moreover, it mitigates the phase diffusion noise via the squeezing operation, thus making it useful for applications in quantum metrology.

Interferometry analysis with fringe normalization and matrix Abel inversion for plasma diagnostics

In plasma diagnostics using interferometry, the phase shift caused by the plasma in the fringes is extracted to determine the plasma density. The common method to extract the phase shift from the fringes is the fast-Fourier-Transform (FFT), but this technique encounters challenges when dealing with insufficient fringe numbers, spatially varying fringe frequencies, or extremely sharp phase changes. These challenges result in errors and hinder the acquisition of precise phase measurements. To tackle this issue, we introduced the fringe normalization (FN) method. The simulations demonstrated that the FN method extracts accurate phase information, surpassing the capabilities of the FFT method. As a result, this advancement enables more precise plasma diagnostics by mitigating errors that arise during the phase data processing. Furthermore, we improved the code for the inverse matrix Abel inversion to convert phase information into density. The simulation employing this code showed that the developed code provides more accurate values in the analysis of plasmas with a sharp density profile, assisting in electron beam manipulation in laser-plasma acceleration.

Precise Phase Measurement for Fringe Reflection Technique through Optimized Camera Response

The Fringe Reflection is a robust and non-contact technique for optical measurement and specular surface characterization. The periodic alternation between dark and light cycles of the fringe patterns encodes the geometric information and provides a non-contact method of spatial measurement through phase extraction. Precisely expressing the positions of the points of the fringe pattern is a fundamental requirement for an accurate fringe reflection measurement. However, the nonlinear processes, both in generating the fringe pattern on a screen and capturing it using pixel values, cause inevitable errors in the phase measurement and eventually reduce the system’s precision. Aiming at reducing these nonlinear errors, we focus on constructing a new quantity from the pixel values of the photos of the fringe patterns that could linearly respond to the ideal fringe pattern. To this end, we hypothesize that the process of displaying the fringe pattern on a screen using a control function is similar to the process of capturing the pattern and converting the illuminating information into pixel values, which can be described using the camera’s response function. This similarity allows us to build a scaled energy quantity that could have a better linear relation with the control function. We optimize the extracted camera response function using an objective to increase the precision and reduce the quoted error. Experiments designed to determine the positions of points along the quartile lines verify the effectiveness of the proposed method in improving fringe reflection measurement precision.

White Rabbit Expansion Board: Design, Architecture, and Signal Integrity Simulations

The White Rabbit protocol allows synchronization and communication via an optical link in an integrated, modular, and scalable manner. It provides a solution to those applications that have very demanding requirements in terms of synchronization. Field-programmable gate arrays are used to implement the protocol; additionally, special hardware is needed to provide the necessary clock signals used by the dual-mixer time difference for precise phase measurement. In the present work, an expansion board that allows for White Rabbit functionality is presented. The expansion board contains the oscillators required by the White Rabbit protocol, one running at 125 MHz and another at 124.922 MHZ. The architecture of this board includes two oscillator systems for tests and comparison. One is based on VCOs and another on crystal oscillators running at the desired frequencies. In addition, it incorporates a temperature sensor, from where the medium access control address is extracted, an electrically erasable programmable read-only memory, a pulse-per-second output, and a USB UART to access the White Rabbit IP core at the field-programmable gate array. Finally, to ensure the quality of the layout design and guarantee the level of synchronization desired, the results of the power and signal integrity simulations are also presented.

Phase Measurement Method Based on Digital Dual Frequency Comb for High-Precision High-Speed Heterodyne Interferometry

The heterodyne interferometer is widely used as a precise displacement sensor in ultraprecision processing. However, there is a trade-off between measurement speed and measurement precision in the existing interference signal processing methods. In this work, a novel phase measurement method based on digital dual frequency comb is proposed. The proposed method uses the intrinsic frequency comb signal and a narrowband low-pass filter to form a band-pass filter bank, which divides the broadband brought by high-speed movement into multiple narrow bands. The signal-to-noise ratio (SNR) is improved for phase calculation. In addition, two groups of intrinsic frequency comb signals are used simultaneously for phase measurement and the rotation of the output, preventing the inaccurate phase measurement of the input signal whose frequency is the average of two frequencies in the frequency comb signal. The heterodyne laser interferometer can maintain high precision at high measurement speed. The simulation results show that the precision of the proposed method is more than 50% higher than that of the phase-locked loop method. The experiment with a circuit board combined with 100 Msps sampling 16-bit A/D converter shows that the phase measurement precision of the input signal frequency in the bandwidth range of 2.5–37.5 MHz can reach 0.77 mrad, equivalent to the displacement measurement precision of the double-pass interferometer (19 pm) at a measurement speed of less than 2.77 m/s.

Probing virtual ALPs by precision phase measurements: time-varying magnetic field background

We propose an experimental scheme for detecting the effects of off-shell axion-like particles (ALPs) through optical cavities. In this proposed experiment, linearly polarized photons are pumped into an optical cavity where an external time-dependent magnetic field is present. The magnetic field mediates an interaction between the cavity photons and ALPs giving rise to a modification in the phase of the cavity photons. The time-dependent nature of the external magnetic field prompts a novel amplification effect which significantly enhances this phase modification. A detection scheme is then proposed to identify such axion-induced phase shifts. We find that the phase modification is considerably sensitive to the photon-ALPs coupling constants gaγγ for the range of ALPs mass 3.1 μeV ⩽ ma ⩽ 44.4 μeV.

Precise RF Phase Measurement by Optical Sideband Generation Using Mach–Zehnder Modulators

A novel radio frequency (RF) phase measurement method that uses optical modulation was proposed. The mathematical model of Mach–Zehnder modulator (MZM) characterization was reviewed. By measuring the output sideband power of the optical modulator, the phase difference of the electric signals fed to the modulator was experimentally measured, and picosecond-level accuracies were achieved. This technique is expected to be useful for radio-over-fiber-based antenna array systems.

A mathematical framework for nonlinear wavefront reconstruction in adaptive optics systems with Fourier-type wavefront sensing

Advanced adaptive optics (AO) instruments have applications in ophthalmic imaging, free-space optical communications and the future generation of extremely large telescopes. These AO systems are designed to perform real-time corrections of dynamic wavefront aberrations. The corrections can be performed by converting wavefront measurements into deformable mirror (DM) actuator commands. The role of the DM is to mitigate aberrations by restoring a planar wavefront. Optimal DM actuator commands therefore require precise phase measurements across the entire wavefront. Reconstructing a wavefront from wavefront sensor (WFS) data is an inverse problem that depends on the type of WFS implemented. Nonlinear Fourier-type WFSs are included in the design of many current and upcoming AO systems. Conventionally, these sensors perform AO control based on simplifications and linearisations of the underlying models. However, in nonlinear regimes, approximation errors critically degrade image quality. This study looks at overcoming nonlinear wavefront sensing regimes by introducing a nonlinear, iterative algorithm for Fourier-type wavefront reconstruction. The algorithm used is well-known in the field of inverse problems. The underlying mathematical theory for modelling Fourier-type WFSs is provided, along with how these models can be used to perform nonlinear wavefront reconstruction. A significant advantage of the analysis presented is its generalised applicability to any Fourier-type sensor. The only input required is the mathematical expression for the optical element transfer function. The generalised and full mathematical model of Fourier-type WFSs is introduced in a Sobolev space setting. Necessary inputs are derived for the nonlinear iterative algorithms, such as Fréchet derivatives and adjoints. The generalised theory is then expanded to solve the inverse problem of wavefront reconstruction for all Fourier-type WFSs. Moreover, the study concentrates on the pyramid WFS (PWFS)—one of the most well-known Fourier-type WFSs—and shows a Hilbert transform representation of the amplitude of the incoming light on its detector. The developed theory is demonstrated using a simulated PWFS to measure an example wavefront.

Application of optimized 2D S-transform in digital speckle interferometry phase pattern denoising

To address the problem of a large amount of noise in the phase pattern in digital speckle pattern interferometry, which seriously affects the phase reconstruction and measurement precision, a filtering method based on optimized 2D S-transform is proposed in this paper. The optimized 2D S-transform provides high signal-to-noise ratio denoising method by adding tilt factors and translation factors to keep the Gaussian window of the appropriate size at different frequency positions. The analysis results of different frequency fringe pattern denoising show that the criteria metrics indicator signal-to-noise ratio (SNR) of the results of the proposed method can reach at least 14.5435 dB and the criteria metrics peak signal-to-noise ratio (PSNR) can reach at least 19.4555 dB, which has better precision compared with the traditional method and solves the incongruity between the smoothness of low-density fringe and the integrity of high-density fringe.

Probing virtual axion-like particles by precision phase measurements

We propose an experiment for detecting Axion-Like Particles (ALPs) based on the axion-photon interaction in the presence of a non-uniform magnetic field. The impact of virtual ALPs on the polarization of the photons inside a cavity is studied and a detection scheme is proposed. We find that the cavity normal modes are dispersed differently owing to their coupling to the ALPs in the presence of a background magnetic field. This birefringence, in turn, can be observed as a phase difference between the cavity polarization modes. The signal is considerably enhanced for a squeezed light source. We argue that the amplified signal allows for exclusion of a range of axion mass 6 × 10-4 eV ≲ ma ≲ 6 × 10-3 eV even at very small axion-photon coupling constant with the potential to reach sensitivity to the QCD axion. Our scheme allows for the exclusion of a range of axion masses that has not yet been covered by other experimental techniques.

A Batch Algorithm for GNSS Carrier Phase Cycle Slip Correction

Signal-phase measurements from global navigation satellite systems (GNSSs) have become an important tool for various remote sensing applications, including measuring ionosphere plasma content, atmospheric radio occultation, and water and ice reflectometry. In these types of scenarios, GNSS signals often experience harsh propagation conditions, such as low signal-to-noise ratios, multipath, and semicoherent scattering. These conditions, in turn, lead to the frequent occurrence of cycle slips, which manifests as persistent discrete changes in the bias of the carrier phase measurement. In order to effectively use the precise GNSS phase measurements under such conditions, we argue that a window of high-rate measurements must be used. In addition, we suggest that enforcing sparsity in the occurrence of detected cycle slips can aid in detection. We, therefore, develop a batch cycle-slip detection and estimation method that is effective and computationally tractable under harsh signal conditions. This work focuses in particular on strong ionosphere scintillation, which is among the most difficult scenarios for estimating cycle slips. We demonstrate the effectiveness of our method on both simulated and real GNSS scintillation datasets, showing around a 90% reduction of slips.

Carrier-Aided Dual-Frequency Vectorized Tracking Architecture for NavIC Signals

A new carrier-aided dual-frequency vectorized tracking (CA-DFVT) architecture for the Navigation with Indian Constellation (NavIC) is presented. CA-DFVT tracks both NavIC L5 (1176.45 MHz) and S-band (2492.028 MHz) signals concurrently. It uses the precise carrier phase measurements from the S-band signal and the unambiguous code phase measurements from the L5 signal to form a new measurement model for the extended Kalman filter (EKF) to estimate the position, velocity, and time (PVT) solutions. The new measurement model takes advantage of the benefits of the higher frequency S-band signal, i.e., less ionospheric delay and carrier phase noise, as well as the L5 signal’s inherent noise mitigation capabilities. Compared to the single-frequency approach, the dual-frequency approach in CA-DFVT eliminates the ionospheric effect and minimizes other errors, resulting in better navigation solutions. The proposed CA-DFVT enhances the reliability and robustness of NavIC signal tracking and position estimation in interference and high dynamics environments. We used static and dynamic field tests to validate the performance and robustness of the proposed CA-DFVT receiver architecture. In comparison to single-frequency (L5/S-band) vector tracking, the CA-DFVT receiver demonstrated consistent signal tracking and position estimation with higher position accuracy. In the static case, the mean horizontal position accuracy of CA-DFVT improves by approximately 2–4 and 9–14 m compared to L5-only VT and S-only VT, respectively, while, in the dynamic case, it improves by approximately 2–5 and 25–42 m, respectively.

A high precision phase measurement system implemented in FPGA with phase interpolator.

High precision timing distribution is crucial to many large scale cosmology and particle physics experiments. Besides the space and energy information, the accurate timing provides an extra dimension for physics event reconstruction. In the timing distribution system, accurate clock phase measurement is an indispensable tool to monitor the phase drift and to achieve accurate phase adjustment. This paper introduces a novel phase measurement method implemented in the Xilinx Field Programmable Gate Array (FPGA). It uses the dedicated phase interpolator in the multi-gigabit transceiver. A design based on this method is implemented within the Kintex Ultrascale series FPGA. The preliminary test result shows that a sub-picosecond level precision is achieved. With this system, the nonlinearity of the phase adjustment in the Xilinx transceiver is measured.

High precision phase estimation with controllable sensitivity and dynamic range

High precision phase estimation is at the core of modern physics and practical applications. We investigate a method for high precision phase estimation via inserting a reference state which enables weak measurement technique to be used in wide dynamic range. A reference phase is introduced artificially to offset the time delay between preselection state and reference state. The sensitivity of measured phase and the linear dynamic range are controllable by adjusting reference phase. Moreover, an arbitrary postselection in measurement is applicable by choosing appropriate reference phase. This method has merits of controllable sensitivity and wide dynamic range, which shows great potential practical applications in high precision phase measurement.

Improving phase estimation using number-conserving operations

We propose a theoretical scheme to improve the resolution and precision of phase measurement with parity detection in the Mach-Zehnder interferometer by using a nonclassical input state which is generated by applying a number-conserving generalized superposition of products (GSP) operation, (saa^{{\dag}}+ta^{{\dag}}a)^{m} with s^2+t^2=1, on two-mode squeezed vacuum (TMSV) state. The nonclassical properties of the proposed GSP-TMSV are investigated via average photon number (APN), anti-bunching effect, and degrees of two-mode squeezing. Particularly, our results show that both higher-order m GSP operation and smaller parameter s can increase the total APN, which leads to the improvement of quantum Fisher information. In addition, we also compare the phase measurement precision with and without photon losses between our scheme and the previous photon subtraction/addition schemes. It is found that our scheme, especially for the case of s=0, has the best performance via the enhanced phase resolution and sensitivity when comparing to those previous schemes even in the presence of photon losses. Interestingly, without losses, the standard quantum-noise limit (SQL) can always be surpassed in our our scheme and the Heisenberg limit (HL) can be even achieved when s=0.5,1 with small total APNs. However, in the presence of photon losses, the HL cannot be beaten, but the SQL can still be overcome particularly in the large total APN regimes. Our results here can find important applications in quantum metrology.

A high-accuracy nonlinear phase error compensation method

In the phase measuring profilometry, the phase measuring accuracy could be heavily affected by the nonlinearity effects of the projecting and imaging devices. Therefore, it is very important to reduce the nonlinear errors fast and efficiently. An analytic model of nonlinear errors is introduced. Then we propose a phase compensation method which is based on the accurate mathematical model of the phase error. The proportion of each harmonic component is collected by using a large-step phase-shifting algorithm to measure a reference plane. Then the phase errors of the measured object could be compensated by an iterative algorithm. The experimental results show that the proposed method can realize nonlinear error compensation effectively and improve the precision of phase measurement. Meanwhile, since all the harmonic components are pre-calibrated, there is no extra fringe needed, which can meet the requirements of fast and real-time measurement.

Phase-shifting electron holography for accurate measurement of potential distributions in organic and inorganic semiconductors.

Phase-shifting electron holography (PS-EH) is an interference transmission electron microscopy technique that accurately visualizes potential distributions in functional materials, such as semiconductors. In this paper, we briefly introduce the features of the PS-EH that overcome some of the issues facing the conventional EH based on Fourier transformation. Then, we present a high-precision PS-EH technique with multiple electron biprisms and a sample preparation technique using a cryo-focused-ion-beam, which are important techniques for the accurate phase measurement of semiconductors. We present several applications of PS-EH to demonstrate the potential in organic and inorganic semiconductors and then discuss the differences by comparing them with previous reports on the conventional EH. We show that in situ biasing PS-EH was able to observe not only electric potential distribution but also electric field and charge density at a GaAs p-n junction and clarify how local band structures, depletion layer widths and space charges changed depending on the biasing conditions. Moreover, the PS-EH clearly visualized the local potential distributions of two-dimensional electron gas layers formed at AlGaN/GaN interfaces with different Al compositions. We also report the results of our PS-EH application for organic electroluminescence multilayers and point out the significant potential changes in the layers. The proposed PS-EH enables more precise phase measurement compared to the conventional EH, and our findings introduced in this paper will contribute to the future research and development of high-performance semiconductor materials and devices.