Heterodyne Frequency Research Articles

Measuring the impact of laser relative intensity noise on heterodyne interferometers using differential wavefront sensing

Laser-intensity fluctuations cause undesired phase noise even in balanced heterodyne interferometers. However, in space missions in particular, such as LISA Pathfinder or LISA, direct measurements of these fluctuations at the relevant frequencies are often not available. Hence, it can be challenging to estimate their impact on the interference phase. To address this, we propose a new method for characterizing laser relative intensity noise (RIN) using differential wavefront sensing (DWS), with the latter being a well-established technique typically used for angular sensing and control. Unlike other methods, this approach does not require an additional reference interferometer and instead takes advantage of the inherent phase subtraction of DWS. This allows us to estimate the RIN value at the heterodyne frequency and its harmonic, relative to the sensor noise floor of the total measurement system. Moreover, it provides a strategy to identify the ideal set point for minimizing RIN couplings in DWS. Published by the American Physical Society 2024

Multi-Perspective Heterodyne Digital Holography For High-Speed Imaging Of Density Fluctuations In Supersonic Flow

Density fluctuation measurements with high spatio-temporal resolution provide meaningful insights into the dynamics of turbulent structures in shear layers, boundary layers, and disturbances that influence the transition to turbulence. The current contribution presents a new multiple perspective digital holographic imaging technique that aims to resolve high-frequency density fluctuations with spatial discrimination along the line of sight. A key element of the proposed method is the generation of a beamlet array of varying view angles that is spatially overlapped within the measurement zone. We present the first experimental realization of this approach using a 7-element hexagonally packed fly’s eye lens array and analyze results for a pair of mutually perpendicular and axially offset sonic jets. The experimental apparatus also incorporates heterodyne detection with a heterodyne frequency set to 1/4 of the imaging frame rate. The optical system performance is evaluated for a crossing jet flow and key design considerations for the multi-perspective optical system are discussed.

Low-Power Wireless Sensor Module for Machine Learning-Based Continuous Monitoring of Nuclear Power Plants.

This paper introduces the novel design and implementation of a low-power wireless monitoring system designed for nuclear power plants, aiming to enhance safety and operational efficiency. By utilizing advanced signal-processing techniques and energy-efficient technologies, the system supports real-time, continuous monitoring without the need for frequent battery replacements. This addresses the high costs and risks associated with traditional wired monitoring methods. The system focuses on acoustic and ultrasonic analysis, capturing sound using microphones and processing these signals through heterodyne frequency conversion for effective signal management, accommodating low-power consumption through down-conversion. Integrated with edge computing, the system processes data locally at the sensor level, optimizing response times to anomalies and reducing network load. Practical implementation shows significant reductions in maintenance overheads and environmental impact, thereby enhancing the reliability and safety of nuclear power plant operations. The study also sets the groundwork for future integration of sophisticated machine learning algorithms to advance predictive maintenance capabilities in nuclear energy management.

Dual-heterodyne Kelvin probe force microscopy.

We present a new open-loop implementation of Kelvin probe force microscopy (KPFM) that provides access to the Fourier spectrum of the time-periodic surface electrostatic potential generated under optical (or electrical) pumping with an atomic force microscope. The modulus and phase coefficients are probed by exploiting a double heterodyne frequency mixing effect between the mechanical oscillation of the cantilever, modulated components of the time-periodic electrostatic potential at harmonic frequencies of the pump, and an ac bias modulation signal. Each harmonic can be selectively transferred to the second cantilever eigenmode. We show how phase coherent sideband generation and signal demodulation at the second eigenmode can be achieved by using two numerical lock-in amplifiers configured in cascade. Dual-heterodyne KPFM (DHe-KPFM) can be used to map any harmonic (amplitude/phase) of the time-periodic surface potential at a standard scanning speed. The Fourier spectrum (series of harmonics) can also be recorded in spectroscopic mode (DHe-KPFM spectroscopy), and 2D dynamic images can be acquired in data cube mode. The capabilities of DHe-KPFM in terms of time-resolved measurements, surface photovoltage (SPV) imaging, and detection of weak SPV signals are demonstrated through a series of experiments on difference surfaces: a reference substrate, a bulk organic photovoltaic heterojunction thin film, and an optoelectronic interface obtained by depositing caesium lead bromide perovskite nanosheets on a graphite surface. The conclusion provides perspectives for future improvements and applications.

Continuous dynamic measurement of frequency scanning interferometry based on motion phase synchronization compensation and calibration.

We present a continuous dynamic frequency scanning interferometry (DFSI) measurement method based on motion phase synchronization compensation and calibration. By introducing heterodyne interferometry (HI) synchronization measurement and frequency scanning interferometry (FSI) motion phase compensation, dynamic continuous measurement is achieved and effectively suppresses the distance error introduced by the Doppler effect (DE). Based on this, the influence of the initial optical frequency deviation (OFD) of the tunable laser and the OFD of the HI laser on the dynamic absolute distance measurement (DADM) is analyzed; the relationships between the error of DADM with the variation of the OFD and the target motion parameters are investigated; and the residual DE introduced by the OFD is shown as the fundamental cause of the degradation of the accuracy of DFSI. We propose an online optical frequency measurement method based on HI combined with H13C14N gas absorption cells to resolve this problem. High-precision motion phase compensation is achieved by calibrating the optical frequency (fixed frequency) of the measured HI laser and the initial frequency of the tunable laser online during measurement and then performing motion phase calibration. To verify the effectiveness of our method, an optical frequency calibration experiment, a continuous DADM experiment, and a precision evaluation experiment were conducted, and a highly accurate continuous DADM was achieved.

On measurements of spurious components of heterodyne signal in radiometric receivers

With a heterodyne frequency conversion, a significant contribution to the intrinsic noise of the radiometric receiver is made by a heterodyne. The spectral components generated by the heterodyne will be present in the processed signal at the output of the radiometric receiver and may manifest themselves when analyzing the received signal in spectral lines when high frequency resolution is required for processing. The purpose of the work is to analyze various types of modulation of the heterodyne signal, including modulation with an arbitrary phase shift between the components in the lower and upper side bands of the heterodyne signal. In this article, the methods of frequency transfer used in determining the spectral composition of the signal received by a radiometric receiver are considered. For heterodyne frequency conversion, in addition to the classical types of parasitic modulation of the heterodyne signal described in the literature – amplitude, phase (frequency) and single-band modulation, modulation with an arbitrary phase shift between the components in the lower and upper side bands of the heterodyne signal is considered. It is shown that with a small deviation of the frequencies of the modulating signal, ambiguity is possible in determining the level of components when using signal analyzers to measure the characteristics of heterodynes of radiometric receivers. The results of the analysis performed in the article can be used in the design of heterodynes with multiple output frequencies, taking into account the spectral comtent of the synthesized signal. The study was carried out at the expense of the grant of the Russian Science Foundation No. 22-19-00063 dated 13.05.2022. https://rscf.ru/project/22-19-00063.

Microwave emissions from the cold atmospheric helium plasma jet

One of the recently observed effects of plasma in medical applications is the physical effect, suggesting that the electromagnetic (EM) emission of cold atmospheric plasmas can lead to cell membrane oscillations and sensitization to the chemical active ingredient of treatments such as cancer drugs. This is a new aspect that must be considered along with the plasma chemical effects for the future dose definition which is the most urgent research topic of plasma medicine. However, unlike the reactive oxygen and nitrogen species generated from plasma chemistry which is well-known as playing a key role in apoptosis cancer cells, the EM emission power spectrum and emission mechanism are still unquantified. This makes the uncertainty of the physical dosage of the therapy and thus impedes the further understanding and optimization of the plasma therapy. In this paper, we compute the 3D spatial distribution of the power density spectrum of EM emission from a cold atmospheric helium plasma jet. The simulations indicate that the plasma oscillations following the plasma streamer propagation are the main source of EM emission, while the emissions of the bulk current caused by net charge movements and the bremsstrahlung due to charge collisions are negligible. The results are also verified by a microwave power measurement using a heterodyne frequency sweep. These findings will thus fill out the last missing piece of the jigsaw before the plasma medicine community can define the dose in the future.

Femtosecond-laser-based full-field three-dimensional imaging with phase compensation.

Coherence scanning interferometer (CSI) enables 3D imaging with nanoscale precision. However, the efficiency of such a system is limited because of the restriction imposed by the acquisition system. Herein, we propose a phase compensation method that reduces the interferometric fringe period of femtosecond-laser-based CSI, resulting in larger sampling intervals. We realize this method by synchronizing the heterodyne frequency with the repetition frequency of the femtosecond laser. The experimental results show that our method can keep the root-mean-square axial error down to 2 nm at a high scanning speed of 6.44 µm per frame, which enables fast nanoscale profilometry over a wide area.

Glucose Concentration Measurement by All-Grating-Based System.

An accurate, easy setup, low-cost, and time-saving method for measuring glucose concentration was proposed. An all-grating-based glucose concentration measurement system contained moving-grating-based heterodyne interferometry and a grating-based self-align sensor. By combining the first-order diffraction lights from two separated moving gratings by a polarization beam splitter and creating S- and P-polarized light interference by an analyzer, the interference signal could be a heterodyne light source with a heterodyne frequency depending on the relative velocities of the two moving gratings. Next, a grating-based self-align sensor was used to make the optical configuration setup easy and accurate. Moreover, the sensor was deposited on GOx film to improve the measurement sensitivity and specificity for glucose. Finally, the phase change induced by the reaction of the sensor and glucose solutions was detected. The validity of this method was proved, and the measurement resolution can reach 2 mg/dL.

Dual-bias modulation heterodyne Kelvin probe force microscopy in FM mode

The use of a heterodyne detection scheme in Kelvin probe force microscopy (KPFM) is an effective way for enhancing the performance of KPFM. However, this detection scheme generally has difficulty in detecting the first- and second-harmonic electrostatic forces simultaneously. To overcome this problem, we propose dual-bias modulation heterodyne frequency modulation KPFM (DM-hetero-FM KPFM), in which dual AC biases at 2f1±fm are applied between the tip and the sample. DM-hetero-FM KPFM enables us to measure the contact potential difference and capacitance gradient simultaneously at high frequencies (in the MHz range) beyond the bandwidth of phase-lock loop. Moreover, the present method allows us to perform it in the open-loop mode, which is highly desired for performing KPFM on semiconductors or in liquids at high frequencies.

Modulation leakage-free continuous-variable quantum key distribution

Distributing cryptographic keys over public channels in a way that can provide information-theoretic security is the holy grail for secure communication. This can be achieved by exploiting quantum mechanical principles in so-called quantum key distribution (QKD). Continuous-variable (CV) QKD based on coherent states, in particular, is an attractive scheme for secure communication since it requires only standard telecommunication technology that can operate at room temperature. However, a recently discovered side-channel created in the process of state preparation leads to a leakage of information about the transmitted quantum state, opening a security loophole for eavesdroppers to compromise the security of the CVQKD system. Here, we present a CVQKD system without this modulation leakage vulnerability. Our implementation is based on a baseband modulation approach and uses an in-phase and quadrature (IQ) modulator for state preparation and radio frequency heterodyne detection together with carefully designed digital signal processing for state measurement. We consider practical aspects in the implementation and demonstrate the generation of a composable secret key secure against collective attacks. This work is a step towards protecting CVQKD systems against practical imperfections of physical devices and operational limitations without performance degradation.

All-fiber heterodyne velocity and displacement interferometer based on DPLL Doppler tracking with sub-nanometer per second and picometer sensitivity.

Velocity and displacement measurements play an important role not only in the process of industrial production and metrology on the ground but also in satellite gravity measurement in space. A high-precision all-fiber heterodyne velocity and displacement interferometer based on digital phase-locked loop (DPLL) Doppler tracking is proposed in this paper. The target velocity is measured by tracking the heterodyne frequency changes of the beat-note signal, and the displacement is obtained by the integrated phase of the Doppler frequency change. A dual-signal differential optical-path scheme combined with DPLL signal tracking technology enables high-precision and high-linearity measurement of velocity and displacement simultaneously. For integration and compactness, the interferometer uses all-fiber optics that are packaged in a small box with dimensions of 150×150×70m m 3, except for an externally fiber-connected collimator as the sensor head. The experimental results show a velocity sensitivity below 30p m/s/H z 1/2 in the 0.03-2Hz band and a displacement sensitivity below 10p m/H z 1/2 above 0.4Hz.

Differential Frequency Heterodyne Time-of-Flight Imaging for Instantaneous Depth and Velocity Estimation

In this study, we discuss the imaging of depth and velocity using heterodyne-mode time-of-flight (ToF) cameras. In particular, Doppler ToF (D-ToF) imaging utilizes heterodyne modulation to measure the velocity from the Doppler frequency shift, which uniquely facilitates the instantaneous radial velocity estimation. However, theoretical discussion on D-ToF is limited to orthogonal frequency and sinusoidal waveform modulation. This study extends the formulation of the D-ToF imaging, and proposes an arbitrary-frequency, arbitrary-waveform framework considering a phase-compensated, symmetrical two-dimensional correlation map. With the proposed framework, the optimal heterodyne frequency for frequency decoding is found. A differential frequency sampling and decoding method is then proposed, which computes the frequency and phase from as few as four simultaneously captured images. With an experiment platform we built, it is confirmed that the minimum velocity sensing error is half that of the orthogonal frequency method, and the sensible phase range is approximately 2.5 times larger. The conclusions in this study allow the ToF velocity imaging to be applied at the optimal sample frequencies for a wide range of ToF sensors. This pushes one step further to the practical use of ToF velocity imaging.

APPLICATION OF THREE-WAVE HETERODINE INTERFEROMETRY FOR NANORIZED LAYERS THICKNESS MEASUREMENT IN THE PROCESS OF THEIR DEPOSITION

The paper proposes a new method of current measurement of the layer thickness of optical films in the process of their forming, in particular, by the method of vacuum deposition. Such films, among other things, are used to create a variety of optoelectronic devices and optical nanosensors for laboratory research in the chemical and pharmaceutical industries, for environmental monitoring.
 We propose a method for measuring the phase of a laser beam, which is based on heterodyne interferometry. The method of heterodyne interferometry in comparison with ordinary interference methods provides better S/N ration results due to the transfer of the investigated signal from the low frequency domain to heterodyne frequency. Our proposed approach is the three-wave heterodyne interferometry (TGI), otherwise - TWI (three waves interference). The TGI method is designed to critically increase the sensitivity to small amplitudes of laser Doppler vibrometers and increase their noise resistance. In interference gauges of optical film thickness, in refractometers, and in many other film thickness gauges as well as in laser Doppler vibrometers the investigated parameter is the phase shift of probing optical radiation. Therefore, the developments of TGI in laser Doppler vibrometers can be used to measure the phase shift.
 The analysis of the new method on mathematical model of TGI was provided. We have got the relations of the output signal of a three-wave heterodyne interferometer dependence on the phase shift , as well as on the thickness of optical films and on their refractive index. The simulation results show that for the optoelectronic equipment that provides with an error of up to 10 %, the absolute error of phase shift measurement, compared to the classical heterodyne interferometer, can be reduced to 103 times. The same results applies to the thickness of the optical coating layer.
 The paper also analyzes the results of experiments on the use of TGI in laser vibrometers and shows that they indicate the possibility of measuring the phase of optical radiation up to 10-5. The disadvantage of the proposed method is its non-linearity and, as a result, a limited linear range. Ways of extending the linear range are discussed.

Expanded North Pacific Subtropical Gyre and Heterodyne Expression During the Mid‐Pleistocene

AbstractThe Kuroshio Current (KC) and Kuroshio Current Extension (KCE) form a western boundary current as part of the North Pacific Subtropical Gyre. This current plays an important role in regulating weather and climate dynamics in the Northern Hemisphere in part by controlling the delivery of moisture to the lower atmosphere. Previous studies indicate the KCE responded dynamically across glacial and interglacial periods throughout the Pliocene‐Pleistocene. However, the response of the KCE during Pleistocene super‐interglacials has not been examined in detail. We present a ∼2.2 Ma record of X‐ray fluorescence elemental data from Ocean Drilling Program Hole 1207A and employ hierarchical clustering techniques to demonstrate paleoenvironmental changes around the KCE. Time‐frequency analysis identifies significant heterodyne frequencies, which suggests there were nonlinear interactions between high‐latitude and low‐latitude climate regulating expansion and contraction of the North Pacific Subtropical Gyre prior to the onset of the Mid‐Pleistocene Climate Transition (MPT). We observe two periods of elevated ln Ca/Ti, which may represent sustained warmth with northward migrations of the KCE in the northwestern Pacific. These intervals correspond to Marine Isotope Stages 29‐25, 15, and 11‐9 and occur around recent climatic transitions, the MPT and Mid‐Brunhes Event. Northward expansion of the subtropical gyre during these exceptionally warm interglacials would have delivered more heat and moisture to the high latitudes of the northwest Pacific. Furthermore, enhanced evaporation from the warm KCE vented to the lower atmosphere may have preconditioned the Northern Hemisphere for ice volume growth during two of the most recent periods of climate transition.

A quantitative analysis method based on collision broadening for trace gas using terahertz heterodyne spectrometer

Quantitative analysis of trace gases is an important research field in analytical chemistry. The terahertz electronic spectrometer is one of the most powerful tools for detecting trace gas. Here, a terahertz spectrometer based on frequency multiplier chain and heterodyne detection was presented. The rotational spectra of acetonitrile (CH3CN) gas were measured in the 290–370 GHz frequency band with 100 kHz spectral resolution. The spectrometer demonstrated excellent spectral specificity and the extrapolated limit of detection for CH3CN gas of 1.4 ppm. Furthermore, a novel quantification method of trace gas was proposed based on broadening mechanisms. The CH3CN self- and nitrogen (N2)- collisional broadening coefficients were obtained experimentally for verifying the method. The CH3CN concentration of the validation group was calculated, and the relative error was 0.1%. The error analysis of the different number of measurements of the method was carried out. The method could provide a new perspective for trace gas quantitative analysis.

Relative-Intensity-Noise Coupling in Heterodyne Interferometers

Laser interferometers are the core measurement tool in gravitational wave observatories. An important factor that can limit the performance is the relative power instability of the laser, a problem often called relative intensity noise (RIN). But exactly how this influences the interferometer performance is not completely understood. Therefore in this paper we analyze laser RIN coupling into the phase readout in balanced and unbalanced heterodyne interferometers. We describe the coupling theoretically, then simulate and finally measure it. Our results reveal a combination of RIN contributions from the heterodyne frequency and twice the heterodyne frequency in the interferometric phase readout. We also show that when an additional, correlated reference measurement is subtracted the combined coupling factor depends on the differential phase between the two measurements and thus can be minimized. Our results have implications for noise models in future space-based gravitational wave observatories like Laser Interferometer Space Antenna, where RIN-to-phase coupling arises directly and is modulated via spacecraft jitter, testmass position and orientation.

The influence of fluid–structure interaction on cloud cavitation about a rigid and a flexible hydrofoil. Part 3

Experimental studies of the influence of fluid–structure interaction on cloud cavitation about a stiff stainless steel (SS) and a flexible composite (CF) hydrofoil have been presented in Parts I (Smithet al.,J. Fluid Mech., vol. 896, 2020a, p. A1) and II (Smithet al.,J. Fluid Mech., vol. 897, 2020b, p. A28). This work further analyses the data and complements the measurements with reduced-order model predictions to explain the complex response. A two degrees-of-freedom steady-state model is used to explain why the tip bending and twisting deformations are much higher for the CF hydrofoil, while the hydrodynamic load coefficients are very similar. A one degree-of-freedom dynamic model, which considers the spanwise bending deflection only, is used to capture the dynamic response of both hydrofoils. Peaks in the frequency response spectrum are observed at the re-entrant jet-driven and shock-wave-driven cavity shedding frequencies, system bending frequency and heterodyne frequencies caused by the mixing of the two cavity shedding frequencies. The predictions capture the increase of the mean system bending frequency and wider bandwidth of frequency modulation with decreasing cavitation number. The results show that, in general, the amplitude of the deformation fluctuation is higher, but the amplitude of the load fluctuation is lower for the CF hydrofoil compared with the SS hydrofoil. Significant dynamic load amplification is observed at subharmonic lock-in when the shock-wave-driven cavity shedding frequency matches with the nearest subharmonic of the system bending frequency of the CF hydrofoil. Both measurements and predictions show an absence of dynamic load amplification at primary lock-in because of the low intensity of cavity load fluctuations with high cavitation number.

Study of high–low KPFM on a pn-patterned Si surface

Comparative measurements between frequency modulation Kelvin probe force microscopy (FM-KPFM) using low frequency bias voltage and heterodyne FM-KPFM using high frequency bias voltage were performed on the surface potential measurement. A silicon substrate patterned with p- and n-type impurities was used as a quantitative sample. The multi-pass scanning method in the measurements of FM-KPFM and heterodyne FM-KPFM was used to eliminate the effect of the tip–sample distance dependence. The measured surface potentials become lower in the order of the p-type region, n-type region and n+-type region by both FM-KPFM and heterodyne FM-KPFM, which are in good agreement with the order of the work functions of the pn-patterned Si sample. We observed the difference in the surface potentials due to the surface band bending measured by FM-KPFM and heterodyne FM-KPFM. The difference is due to the fact that the charge transfer between the surface and bulk levels may or may not respond to AC bias voltage.

Phase unwrapping method combining dual-frequency heterodyne with dual complementary phase encoding

Phase encoding and phase-shift profilometry are two commonly used 3D measurement techniques. However, the acquired phases in the techniques are subject to jump errors due to phase ambiguity and phase errors caused by multiple heterodyne. The phase-shifting profilometry also makes the selection of fringe period difficult. To overcome this problem and achieve high-precision measurement, a phase unwrapping method that combines dual-frequency heterodyne with double complementary phase encoding is proposed. First, two wrapped phases are obtained by two groups of sinusoidal fringes; the heterodyne phase is obtained after heterodyne processing, and the high-frequency phase is expanded by heterodyne phase. Second, the fringe levels are obtained using the complementary phase encoding fringes that are shifted by half an order, and then the absolute phase is obtained by selecting different phase coding levels according to different regions for the first phase unwrapping; Finally, the phase noise is removed by exploiting the difference between the phase slopes of adjacent pixels. Experimental results show that a system with the proposed method achieves an RMS error of 0.015 mm. In addition, the period of dual-frequency heterodyne synthesis does not need to cover the whole field of view, which breaks the limitation of frequency selection of the traditional dual-frequency heterodyne method and triple frequency heterodyne method, enabling high-precision measurement with higher frequency fringes. This method overcomes the limitations of the phase principal value error when using higher frequency fringes for high-precision measurement, improves the measurement effect of reflective objects, and effectively avoids the error caused by phase jump.