Interferometric Signal Research Articles

Equilibrium reconstruction method for self-organized plasmas on reversed field pinches with polarimeter-interferometer

In the reversed field pinch (RFP), plasmas exhibit various self-organized states. Among these, the three-dimensional (3D) helical state known as the “quasi-single-helical” (QSH) state enhances RFP confinement. However, accurately describing the equilibrium is challenging due to the presence of 3D structures, magnetic islands, and chaotic regions. It is difficult to obtain a balance between the available diagnostic and the real equilibrium structure. To address this issue, we introduce KTX3DFit, a new 3D equilibrium reconstruction code specifically designed for the Keda Torus eXperiment (KTX) RFP. KTX3DFit utilizes the stepped-pressure equilibrium code (SPEC) to compute 3D equilibria and uses polarimetric interferometer signals from experiments. KTX3DFit is able to reconstruct equilibria in various states, including axisymmetric, double-axis helical (DAx), and single-helical-axis (SHAx) states. Notably, this study marks the first integration of the SPEC code with internal magnetic field data for equilibrium reconstruction and could be used for other 3D configurations.

Measuring Black Hole Light Echoes with Very Long Baseline Interferometry

Light passing near a black hole can follow multiple paths from an emission source to an observer due to strong gravitational lensing. Photons following different paths take different amounts of time to reach the observer, which produces an echo signature in the image. The characteristic echo delay is determined primarily by the mass of the black hole, but it is also influenced by the black hole spin and inclination to the observer. In the Kerr geometry, echo images are demagnified, rotated, and sheared copies of the direct image and lie within a restricted region of the image. Echo images have exponentially suppressed flux, and temporal correlations within the flow make it challenging to directly detect light echoes from the total light curve. In this Letter, we propose a novel method to search for light echoes by correlating the total light curve with the interferometric signal at high spatial frequencies, which is a proxy for indirect emission. We explore the viability of our method using numerical general relativistic magnetohydrodynamic simulations of a near-face-on accretion system scaled to M87-like parameters. We demonstrate that our method can be used to directly infer the echo delay period in simulated data. An echo detection would be clear evidence that we have captured photons that have circled the black hole, and a high-fidelity echo measurement would provide an independent measure of fundamental black hole parameters. Our results suggest that detecting echoes may be achievable through interferometric observations with a modest space-based very long baseline interferometry mission.

Fiber Fabry-Perot accelerometer with extended dynamic range and low noise floor

Optical interferometric accelerometers are widely used in seismic monitoring, petroleum resources exploration, and structural health monitoring due to their low noise floor and resistance to electromagnetic interference (EMI). However, their small working range limits further applications. To broaden the working range of the sensor while ensuring the inherent anti-electromagnetic interference capability of the optical sensor, this paper proposes an orthogonal optical path (OP) range broadening scheme (OORBS). The linear working range is widened by splicing the linear intervals in the two interferometric signals. Subsequently, a platform based on a nano-displacement unit was built to validate the feasibility of the OORBS under static and AC cavity length variations. The experimental results show that the OORBS can recover the cavity length completely. Finally, the OORBS was combined with an accelerometer to realize the range broadening. The OORBS extends the accelerometer’s working range from 0.42 mg to 68 mg while maintaining the high sensitivity, which is about a 162-time improvement. The accelerometer’s noise floor reaches 4.8 ng/Hz1/2 at 15 Hz and accordingly, the dynamic range of the accelerometer increases from 98.8 dB to 143 dB. The proposed method is general to address the Fabry-Perot-based dynamic range limitation and can be adapted for various interferometric sensors, such as Fabry-Perot, grating, and Mach–Zehnder.

An analytic, efficient and optimal readout algorithm for compact interferometers based on deep frequency modulation

Compact laser interferometers with large dynamic range are one of the core emerging tools to improve low frequency performance in gravitational wave detectors by providing local displacement sensing with sub 1 pmHz-0.5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {pm Hz}^{-0.5}$$\\end{document} precision. Strong sinusoidal frequency modulations are used in such laser interferometers to create heterodyne-like photodetector signals from which the phase and other parameters, such as the absolute distance, can be extracted. The nested sinusoidal function in such signals is a challenge for the real-time parameter estimation in low-noise applications. In this article, we present an algorithm to calculate exact signal parameters in a non-iterative way from such interferometric signals. The algorithm makes use of a recurrence relation between Bessel functions to enable a direct extraction of modulation parameters from the signal. Additionally, the algorithm is capable of dealing with high phase dynamics where the Doppler-shift of the signal becomes relevant and can limit the range and precision of the parameter estimation, if not accounted for. Simulations show that the algorithm is computationally efficient, can be well parallelised and the phase estimation is close to optimal precision given by the Cramer–Rao lower bound of the signal parameters.

Line-field confocal optical coherence tomography based on tandem interferometry with a focus-tunable lens.

This article introduces an innovative line-field confocal optical coherence tomography (LC-OCT) system based on tandem interferometry, featuring a focus-tunable lens for dynamic focusing. The principle of tandem interferometry is first recalled, and an analytical expression of the interferometric signal detected is established in order to identify the influence of key experimental parameters. The LC-OCT system is based on a Linnik-type imaging interferometer with a focus-tunable lens for focus scanning, coupled to a Michelson-type compensating interferometer using a piezoelectric linear translation stage for coherence plane scanning. The system achieves axial and lateral image resolutions of approximately 1 µm over the entire imaging depth (400 µm), in line with conventional LC-OCT. Vertical section images (B-scans) of skin acquired at 14.3 fps reveal distinguishable structures within the epidermis and dermis. Using refocusing and stitching, images of a tissue phantom were obtained with an imaging depth superior to 1.4 mm. The system holds promise for LC-OCT miniaturization, along with enhanced imaging speed and extended imaging depth.

Signal generation in dynamic interferometric displacement detection.

Laser interferometry is a well-established and widely used technique for precise displacement measurements. In a non-contact atomic force microscope (NC-AFM), it facilitates the force measurement by recording the periodic displacement of an oscillating microcantilever. To understand signal generation in a NC-AFM-based Michelson-type interferometer, we evaluate the non-linear response of the interferometer to the harmonic displacement of the cantilever in the time domain. As the interferometer signal is limited in amplitude because of the spatial periodicity of the interferometer light field, an increasing cantilever oscillation amplitude creates an output signal with an increasingly complex temporal structure. By the fit of a model to the measured time-domain signal, all parameters governing the interferometric displacement signal can precisely be determined. It is demonstrated, that such an analysis specifically allows for the calibration of the cantilever oscillation amplitude with 2% accuracy.

A Mach-Zehnder interferometric acoustic sensor using incomplete symmetry 3×3 coupler-based phase shifting demodulator

A Mach-Zehnder interferometric (MZI) acoustic sensor and an incomplete symmetry 3×3 coupler-based phase shifting demodulator are presented. The demodulator is used to recover the acoustic signal detected by the proposed sensor. To eliminate interfering signals loaded on the transmission path, all couplers and interference arms constituting the sensing MZI are packaged into the sensor. Therefore, a path-matched interferometer (PMI) is used to separate the sensor from the demodulator and to compensate for the optical path difference in order to generate interference. The 3×3 coupler of the PMI is used to introduce phase differences of interferometric signals. Two constant large-amplitude carrier signals with a phase difference of π are loaded on the PMI to ensure normalization of the interferometric signals. By normalizing interferometric signals, fluctuations in both fringe visibility and received power are eliminated. The measurement errors caused by the incomplete symmetry of the 3×3 coupler are reduced through phase compensation. The sensor and PMI are designed to be insensitive to environmental disturbances. The phase shifting demodulation technique is then performed to recover the measurand. The proposed sensor is experimentally demonstrated to be able to detect acoustic signals with frequencies between 200 Hz and 20 kHz. This sensor exhibits a linear response to the sound pressure with a sensitivity of 9.101 nm/mPa. The minimum detectable pressure is 9.74 μPa/Hz1/2 at 20 kHz. The proposed sensor has high sensitivity, high robustness, low cost and anti-interference properties.

A nonparametric point-by-point method to measure time-dependent frequency in wavelength modulation spectroscopy

A nonparametric point-by-point (NPP) method is presented for high-accuracy measurement of the time-dependent frequency (laser frequency) in tunable laser absorption spectroscopy, crucial for ensuring ultimate measurement accuracy. In wavelength modulation spectroscopy in particular, the parametric methods in current use for time-dependent frequency measurement are insufficiently accurate and are difficult to apply to complex modulation scenarios. Based on a multi-scale viewpoint, point-by-point measurement of the frequency is realized by linear superposition of the frequency information mapped from the interferometric signal on a unit scale and on a local scale. Validation experiments indicate that the measurement accuracy of the proposed NPP method is three times that of the existing parametric methods, while effectively immunizing against non-ideal tuning effects. Additionally, the NPP method is suitable for use with arbitrarily complex modulations such as square wave modulation, for which parametric methods are inapplicable.

Frequency planning for LISA

The Laser Interferometer Space Antenna (LISA) is poised to revolutionize astrophysics and cosmology in the late 2030s by unlocking unprecedented insights into the most energetic and elusive astrophysical phenomena. The mission envisages three spacecraft, each equipped with two lasers, on a triangular constellation with 2.5 million-kilometer arm-lengths. Six interspacecraft laser links are established on a laser-transponder configuration, where five of the six lasers are offset phase locked to another. The need to determine a suitable set of transponder offset frequencies precisely, given the constraints imposed by the onboard metrology instrument and the orbital dynamics, poses an interesting technical challenge. In this paper we describe an algorithm that solves this problem via quadratic programming. The algorithm can produce concrete frequency plans for a given orbit and transponder configuration, ensuring that all of the critical interferometric signals stay within the desired frequency range throughout the mission lifetime, and enabling LISA to operate in science mode uninterruptedly. Published by the American Physical Society 2024

Probing pair correlations in Fermi gases with Ramsey-Bragg interferometry

We propose an interferometric method to probe pair correlations in a gas of spin-1/21/2 fermions. The method consists of a Ramsey sequence where both spin states of the Fermi gas are set in a superposition of a state at rest and a state with a large recoil velocity. The two-body density matrix is extracted via the fluctuations of the transferred fraction to the recoiled state. In the pair-condensed phase, the off-diagonal long-range order is directly reflected in the asymptotic behavior of the interferometric signal for long interrogation times. The method also allows to probe the spatial structure of the condensed pairs: the interferometric signal is an oscillating function of the interrogation time in the Bardeen-Cooper-Schrieffer regime; it becomes an overdamped function in the molecular Bose-Einstein condensate regime.

Bending classification from interference signals of a fiber optic sensor using shallow learning and convolutional neural networks

Bending monitoring is critical in engineering applications, as it helps determine any structural deformation caused by load action or fatigue effect. While strain gauges and accelerometers were previously used to measure bending magnitude, optical fiber sensors have emerged as a reliable alternative. In this work, a machine-learning-based model is proposed to analyze the interference signal of an interferometric fiber sensor system and characterize the bending magnitude and direction. In particular, shallow learning-based and convolutional neural network-based (CNN) models have been implemented to perform this task. Furthermore, given the repeatability of the interference signals, a synthetic dataset was created to train the models, whereas real interferometric signals were used to evaluate the models’ performance. Experiments were conducted on a flexible rod in fixed–free and fixed–fixed ends configurations for bending monitoring. Although both models achieved mean accuracies above 91%, only the CNN-based model reached a mean accuracy above 98%. This confirms that monitoring bending movements through interference signal analysis by means of a CNN-based model is a viable approach.

Time-domain Vernier effect-based optical fiber sensor.

In this Letter, we demonstrate an easy-to-fabricate time-domain Vernier-effect-based sensor. An all-fiber variable optical delay line (VODL) is utilized to drive an OPD scan of two interferometers simultaneously, and fiber Bragg gratings are used to filter out two slightly detuned time-domain interferometric signals. Then two normalized interferograms with different spatial frequencies can be achieved and utilized to generate an envelope modulation, viz., a Vernier envelope, with enhanced sensitivity in comparison to the native state of the interferometers used. The sensitivity magnification factor of our structure can be regulated simply via altering the resonant wavelength difference of FBGs rather than optimizing the OPDs of the interferometers. The proposed sensor is independent of the precise and complicated fabrication procedures. The Vernier signal can be demodulated without a broadband light source and spectrometer. We argue that the proposed structure may inspire a new concept for constructing simple and cheap Vernier effect-based sensors that are well suited for practical applications.

Self-calibrated atom-interferometer gyroscope by modulating atomic velocities.

Atom-interferometer gyroscopes have attracted much attention for their long-term stability and extremely low drift. For such high-precision instruments, self-calibration to achieve an absolute rotation measurement is critical. In this work, we propose and demonstrate the self-calibration of an atom-interferometer gyroscope. This calibration is realized by using the detuning of the laser frequency to control the atomic velocity, thus modulating the scale factor of the gyroscope. The modulation determines the order and the initial phase of the interference stripe, thus eliminating the ambiguity caused by the periodicity of the interferometric signal. This self-calibration method is validated through a measurement of the Earth's rotation rate, and a relative uncertainty of 162 ppm is achieved. Long-term stable and self-calibrated atom-interferometer gyroscopes have important applications in the fields of fundamental physics, geophysics, and long-time navigation.

Phase demodulation method of high line density grating interferometric signal based on wavelet transform

The increasing line density of the reference grating and the accelerating miniaturization of ultra-precision displacement measurement technology necessitate more stable interferometric signal processing methods for high line density gratings, particularly in low signal-to-noise ratio scenarios. This paper presents a phase demodulation method for dynamic interferometric signals for high line density gratings. The Morlet wavelet transform is utilized to obtain the instantaneous frequency of the interferometric signal, integration of which yields the relative displacement, while adding adjacent relative displacements without gaps provides the absolute displacement during dynamic motion of the grating. In simulations with a signal-to-noise ratio ranging from 40 to 70 dB, the proposed method demonstrates greater robustness compared to the traditional method. By establishing a platform for repeated experiments and comparing it with traditional methods, it was found that the maximum deviation between calculation results obtained using this method and traditional methods is 0.8 nm, further confirming its potential application.

Extracting electromagnetic signatures of spacetime fluctuations

We present a formalism to discern the effects of fluctuations of the spacetime metric on electromagnetic radiation. The formalism works via the measurement of electromagnetic field correlations, while allowing a clear assessment of the assumptions involved. As an application of the formalism, we present a model of spacetime fluctuations that appear as random fluctuations of the refractive index of the vacuum in single, and two co-located Michelson interferometers. We compare an interferometric signal predicted using this model to experimental data from the Holometer and aLIGO. We show that if the signal manifests at a frequency at which the interferometers are sensitive, the strength and scale of possible spacetime fluctuations can be constrained. The bounds, thus obtained, on the strength and scale of the spacetime fluctuations, are also shown to be more stringent than the bounds obtained previously using astronomical observation at optical frequencies. The formalism enables us to evaluate proposed experiments such as QUEST for constraining quantum spacetime fluctuations and to design new ones.

Research on a Multi-Channel High-Speed Interferometric Signal Acquisition System

In order to capture the large-scale interferometric signal generated by the space-borne interferometric infrared Fourier spectrometer (IRIFS) in real time, and overcome the limitations of insufficient sampling rate, transmission rate, and significant signal noise in current equipment, a multi-channel high-speed acquisition system for large-scale interferometric signals is designed. A high-performance analog-to-digital converter (ADC) oversampling scheme is designed, which can realize up to 8 synchronous acquisition channels and has a maximum sampling rate of 125 Msps/Ch to ensure the acquisition of interferometric signals. The scheme of jesd204b inter-board transmission and optical fiber terminal transmission is designed. The inter-board transmission rate is 12.5 Gbps, and the terminal transmission rate is 10 GB/s to ensure high-speed data transmission. A hardware filter is designed to realize spatial noise processing of interference signals and ensure the accuracy of acquisition results. The dynamic performance of the data acquisition (DAQ) card is analyzed using discrete Fourier transform in the frequency domain. The spurious free dynamic range (SFDR) is 84 dB, the signal-to-noise ratio (SNR) is 72.7 dB, and the cross-talk is −81.6 dB, which verifies the dynamic stability of the DAQ card. Finally, the infrared radiation in real space is measured. The average ΔNESR of long wave reaches 48 mW∗m−2∗sr−1, and the average ΔNESR of medium wave reaches 12.3 mW∗m−2∗sr−1, which verifies the reliability of the system performance. The system is of great significance for large-scale infrared interferometric signal acquisition, and has strong practical application value in multi-channel synchronization, real-time high-speed acquisition, and high-speed data transmission.

SAL vibration estimation and compensation based on triangular interferometric signals.

Synthetic aperture Ladar (SAL) is an extension of synthetic aperture technology in the optical frequency band. Owing to the short wavelength of lasers, the system has high-resolution, high-data-rate, and refined imaging capabilities, which has potential in high-resolution observation fields such as ground observation and space target observation. However, the short wavelength of lasers also makes SAL severely sensitive to vibrations even on the micron order which cause azimuth defocusing and range cell migration. To address this problem, we establish a de-chirp signal model under vibration environment, and propose a vibration error estimation and compensation method using triangular interferometric signals. According to the symmetrical characteristics of triangular frequency modulated continuous wave (T-FMCW) and the time-frequency information introduced by the azimuthal vibration phase, we use a two-stage interferometry method to estimate instantaneous frequency introduced by the vibration errors that cause range cell migration. For the scenarios without obvious range cell migration, we use a one-stage interferometry method to estimate the instantaneous frequency. Subsequently, we establish a vibration compensation filter using the estimated instantaneous frequency to compensate for the vibration errors. We use two experiments to verify the effectiveness and superiority of the proposed method. The results show that the proposed method effectively eliminates range cell migration and azimuthal phase errors introduced by vibration errors, producing SAL imaging results with higher resolution than the conventional spectral correlation method.

A Real-Time Determination Method for Homodyne Grating Interferometer Signal Nonlinear Error Based on Duty Cycle Measurement of States

A Real-Time Determination Method for Homodyne Grating Interferometer Signal Nonlinear Error Based on Duty Cycle Measurement of States

Hilbert transform for modulation of interference fringes of liquid substances

The demodulation of interferometric signals presents a challenge in the study of object, especially when working in environments with disturbances, instability or noise. This document presents a procedure to demodulate a pair of highly noisy interferograms obtained with a fiber optic Mach Zehnder interferometer, the procedure is based on using the reconfiguration of the interference fringes as a result of Hilbert Transform. The method shown is fast, it does not present susceptibilities at high frequencies, it avoids demodulating interference patterns of closed fringes and with little carrier signal, in addition, it allows to verify the mathematical equivalence of the spectral analysis using Fourier Transform. As an application model, samples of liquid substances were used, where it was possible to know changes between substances according to their density

Study of interferometric signal correction methods in ultra-precision displacement measurement

The measurement of critical dimensions in the field of integrated circuits has moved from 7 nm to 5 nm. The existing chromium atomic lithography grating has a pitch period of 4700 l mm−1 and uniformity of picometer, and the interferometric signal period based on the above grating is as small as 106.4 nm, which brings new problems and challenges to the accurate processing of the signal. This paper investigates the error characteristics of ultra-high precision grating interferometric signals, establishes a Heydemann correction mathematical model for high inscribed line density grating interferometric signals, corrects the grating interferometer signals based on the random sample consensus (RANSAC), and verifies the effectiveness of the algorithm through simulation. By comparing the repeatability and linearity of the original algorithm and the self-traceable grating interferometric displacement measurement data processed by RANSAC, the conclusion that the standard deviation of the self-traceable grating interferometer repeat measurement after RANSAC is 1.60 nm in a 10 000 nm travel is obtained, and the purpose of improving the stability and uniformity of the signal solution with the algorithm of this paper is achieved, which is important for the study of laser interferometer and grating interferometer The results show that the stability and uniformity of the signal solution can be improved by the algorithm of this paper, which is of great significance for the study of the displacement solution of laser and grating interferometers.