Auswahl der wissenschaftlichen Literatur zum Thema „Frequency drift interferometry“

The technique utilizing single-frequency laser interferometry has very high measurement accuracy, but it has rigorous requirements for optical design which is affected by many factors. In order to achieve single-frequency laser interferometry with large stroke and high precision, the integral layout, the polarization phase shifting technique and the common mode rejection method are adopted to design the length interferometry system. This paper analyzes factors and design requirements which affect measurement accuracy with large stroke. Based on polarization phase shifting technique, the system employs the four-beam-signal detection technique and the common mode rejection method, to make a differential processing of four mutually orthogonal signals. Thus, the influences of zero-drift of intensity and environmental change on system are reduced. Combined with a 200 phase subdivision, the system achieves the resolution with 0.8 nm. Under the VC++ environment, the displacement measurement results are compensated and corrected according to the environmental parameters. Compared with the Renishaw XL-80 laser interferometer, the system has better stability in short term. In the measuring range of 60 mm, the effectiveness of the system is verified.

Using polarization-maintaining fiber (PMF) in dual-frequency heterodyne interferometry has the advantages of reducing the laser’s own drift, obtaining high-quality light spots, and improving thermal stability. Using only one single-mode PMF to achieve the transmission of dual-frequency orthogonal, linearly polarized beam requires angular alignment only once to realize the transmission of dual-frequency orthogonal, linearly polarized light, avoiding coupling inconsistency errors, so that it has the advantages of high efficiency and low cost. However, there are still many nonlinear influencing factors in this method, such as the ellipticity and non-orthogonality of the dual-frequency laser, the angular misalignment error of the PMF, and the influence of temperature on the output beam of the PMF. This paper uses the Jones matrix to innovatively construct an error analysis model for the heterodyne interferometry using one single-mode PMF, to realize the quantitative analysis of various nonlinear error influencing factors, and clarify that the main error source is the angular misalignment error of the PMF. For the first time, the simulation provides a goal for the optimization of the alignment scheme of the PMF and the improvement of the accuracy to the sub-nanometer level. In actual measurement, the angular misalignment error of the PMF needs to be smaller than 2.87° to achieve sub-nanometer interference accuracy, and smaller than 0.25° to make the influence smaller than ten picometers. It provides theoretical guidance and an effective means for improving the design of heterodyne interferometry instruments based on PMF and further reducing measurement errors.

Abstract Solar radio U-bursts are generated by electron beams traveling along closed magnetic loops in the solar corona. Low-frequency (<100 MHz) U-bursts serve as powerful diagnostic tools for studying large-sized coronal loops that extend into the middle corona. However, the positive frequency drift component (descending leg) of U-bursts has received less attention in previous studies, as the descending radio flux is weak. In this study, we utilized LOFAR interferometric solar imaging data from a U-burst that has a significant descending leg component, observed between 10 and 90 MHz on 2020 June 5th. By analyzing the radio source centroid positions, we determined the beam velocities and physical parameters of a large coronal magnetic loop that reached just about 1.3 R ⊙ in altitude. At this altitude, we found the plasma temperature to be around 1.1 MK, the plasma pressure around 0.20 mdyn, cm−2, and the minimum magnetic field strength around 0.07 G. The similarity in physical properties determined from the image suggests a symmetric loop. The average electron beam velocity on the ascending leg was found to be 0.21c, while it was 0.14c on the descending leg. This apparent deceleration is attributed to a decrease in the range of electron energies that resonate with Langmuir waves, likely due to the positive background plasma density gradient along the downward loop leg.

Abstract. During summer months at solar cycle minimum, F-region lacuna and slant-Es conditions (SEC) are common features of daytime ionograms recorded around local magnetic noon at Casey, Antarctica. Digisonde measurements of drift velocity height profiles show that the occurrence of lacuna prevents the determination of F-region drift velocities and also affects E-region drift velocity measurements. Unique E-region spectral features revealed as intervals of Bragg scatter superimposed on typical background E-region reflection were observed in Digisonde Doppler spectra during intense lacuna conditions. Daytime E-region Doppler spectra recorded at carrier frequencies from 1.5 to 2.7MHz, below the E-region critical frequency foE, have two side-peaks corresponding to Bragg scatter at approximately ±1-2Hz symmetrically located on each side of a central-peak corresponding to near-zenith total reflections. Angle-of-arrival information and ray-tracing simulations show that echo returns are coming from oblique directions most likely resulting from direct backscatter from just below the total reflection height for each sounding frequency. The Bragg backscatter events are shown to manifest during polar lacuna conditions, and to affect the determination of E-region background drift velocities, and as such must be considered when using standard Doppler-sorted interferometry (DSI) techniques to estimate ionospheric drift velocities. Given the Doppler and spatial separation of the echoes determined from high-resolution Doppler measurements, we are able to estimate the Bragg scatter phase velocity independently from the bulk E-region motion. The phase velocity coincides with the ExB direction derived from in situ fluxgate magnetometer records. When ionospheric refraction is considered, the phase velocity amplitudes deduced from DSI are comparable to the ion-acoustic speed expected in the E-region. We briefly consider the plausibility that these previously unreported polar cap E-region Bragg scatter Doppler spectral signatures, observed at Casey in December 1996 during SEC/lacuna conditions may be linked to ionosphere irregularities. These irregularities may possibly be generated by primary plasma waves triggered by current-driven instabilities, that is to say, a hybrid of the "modified two-stream" and "gradient drift" instability mechanisms.

AirSWOT is an airborne Ka-band synthetic aperture radar, capable of mapping water surface elevation (WSE) and water surface slope (WSS) using single-pass interferometry. AirSWOT was designed as a calibration and validation instrument for the forthcoming Surface Water and Ocean Topography (SWOT) mission, an international spaceborne synthetic aperture radar mission planned for launch in 2022 which will enable global mapping of WSE and WSS. As an airborne instrument, capable of quickly repeating overflights, AirSWOT enables measurement of high frequency and fine scale hydrological processes encountered in coastal regions. In this paper, we use data collected by AirSWOT in the Mississippi River Delta and surrounding wetlands of coastal Louisiana, USA, to investigate the capabilities of Ka-band interferometry for mapping WSE and WSS in coastal marsh environments. We introduce a data-driven method to estimate the time-varying interferometric phase drift resulting from radar hardware response to environmental conditions. A system of linear equations based on AirSWOT measurements is solved for elevation bias and time-varying phase calibration parameters using weighted least squares. We observed AirSWOT WSE uncertainty of 12 cm RMS compared to in situ water level measurements when averaged over an area of 0.5 km 2 at incidence angles below 15 ∘ . At higher incidence angles, the observed AirSWOT elevation bias is possibly due to residual phase calibration errors or radar backscatter from vegetation. Elevation profiles along the Wax Lake Outlet river channel indicate AirSWOT can measure WSS over a 24 km distance with uncertainty below 0.3 cm/km, 8% of the true water surface slope as measured by in situ data. The data analysis and results presented in this paper demonstrate the potential of AirSWOT to measure water surface elevation and slope within highly dynamic and spatially complex coastal environments.

The low-frequency fluctuations of the atomic density within the cell can induce the longterm drift of the K-Rb-21Ne spin-exchange relaxation-free (SERF) co-magnetometer output, such that the accurate measurement of in situ atomic density is of great significance for improving the performance of co-magnetometer. In this paper, the complex refractive index model of the spin ensembles under the hybrid optical pumping condition is established first, according to which the relation between atomic density and its complex refractive index is revealed and an optical heterodyne-based scheme for atomic density detection is proposed. The dependence of the atomic density on the demodulated phase signal from the optical heterodyne-based scheme is provided by numerical simulations. After that, a dual acousto-optics frequency shifter (AOFS)-based optical heterodyne interferometry is constructed with a noise level below 1 mrad/Hz for frequencies > 1 Hz, and a compact SERF co-magnetometer is implemented as the testing medium, by which the atomic density detection with resolution of 0.40 K @ 473 K is reached and the experimental results agree well with theoretical simulations. Moreover, the detection scheme proposed in this paper has the properties of high detection sensitivity and immunity to laser power fluctuation, which are also proved experimentally.

Abstract. During the Sporadic E Experiment over Kyushu 2 (SEEK-2) campaign, field-aligned irregularities (FAIs) associated with midlatitude sporadic-E (Es) layers were observed with two backscatter radars, the Lower Thermosphere Profiler Radar (LTPR) and the Frequency Agile Radar (FAR), which were located 40 km apart in Tanegashima, Japan. We conducted observations of FAI echoes from 31 July to 24 August 2002, and the radar data were used to determine launch timing of two sounding rockets on 3 August 2002. Our comparison of echoes obtained by the LTPR and the FAR revealed that echoes often appeared at the FAR about 10min earlier than they did at the LTPR and were well correlated. This indicates that echoing regions drift with a southward velocity component that maintains the spatial shape. Interferometry observations that were conducted with the LTPR from 3 to 8 August 2002, revealed that the quasi-periodic (QP) striations in the Range-Time-Intensity (RTI) plots were due to the apparent motion of echoing regions across the radar beam including both main and side lobes. In most cases, the echo moved to the east-southeast at an almost constant altitude of 100–110 km, which was along the locus of perpendicularity of the radar line-of-sight to the geomagnetic field line. We found that the QP pattern on the RTI plot reflects the horizontal structure and motion of the (Es layer, and that echoing regions seemed to be in one-dimensionally elongated shapes or in chains of patches. Neutral wind velocities from 75 to 105 km altitude were simultaneously derived with meteor echoes from the LTPR. This is the first time-continuous simultaneous observation FAIs and neutral wind with interferometry measurements. Assuming that the echoing regions were drifting with an ambient neutral wind, we found that the echoing region was aligned east-northeast-west-southwest in eight out of ten QP echo events during the SEEK-2 campaign. A range rate was negative (positive), when a frontal structure of echoing regions elongated east-northeast-west-southwest drifts with southward (northward) neutral wind. Keywords. Ionosphere-atmosphere interactions; Ionospheric irregularities; Plasma waves and instabilities

Abstract Probing the solar corona is crucial to study the coronal heating and solar wind acceleration. However, the transient and inhomogeneous solar wind flows carry large-amplitude inherent Alfvén waves and turbulence, which make detection more difficult. We report the oscillation and propagation of the solar wind at 2.6 solar radii (Rs) by observation of China’s Tianwen and ESA’s Mars Express with radio telescopes. The observations were carried out on 2021 October 9, when one coronal mass ejection (CME) passed across the ray paths of the telescope beams. We obtain the frequency fluctuations (FFs) of the spacecraft signals from each individual telescope. First, we visually identify the drift of the frequency spikes at a high spatial resolution of thousands of kilometers along the projected baselines. They are used as traces to estimate the solar wind velocity. Then we perform the cross-correlation analysis on the time series of FF from different telescopes. The velocity variations of solar wind structure along radial and tangential directions during the CME passage are obtained. The oscillation of tangential velocity confirms the detection of a streamer wave. Moreover, at the tail of the CME, we detect the propagation of an accelerating fast field-aligned density structure indicating the presence of magnetohydrodynamic waves. This study confirms that the ground-station pairs are able to form particular spatial projection baselines with high resolution and sensitivity to study the detailed propagation of the nascent dynamic solar wind structure.

LISA (Laser Interferometer Space Antenna) est un interféromètre spatial dédié à la détection des ondes gravitationnelles dans la gamme de fréquence [20 µHz-1 Hz], actuellement en développement (phase B). Ce projet international géré par l'ESA sera composé d'une constellation de trois satellites en formation triangulaire, chacun d'entre eux émettant deux faisceaux laser vers les deux autres satellites. Il y a donc au total 6 liens laser, et 6 unités, appelées MOSA (Moving Optical Sub-Assembly) chargées d'émettre et de recevoir les faisceaux, et de réaliser la mesure des variations de distance inter-satellites. Chaque MOSA contient trois interféromètres hétérodynes, et comme dans tout dispositif optique la lumière parasite peut compromettre l'exactitude, la résolution ou encore la dynamique des mesures.Il est donc nécessaire d'élaborer une instrumentation (appelé le SL-OGSE, Stray Light-Optical Ground Support Equipment) pouvant détecter et identifier les contributions de lumière parasite cohérente interférant avec les faisceaux nominaux du dispositif. Il devra répondre notamment à deux exigences : déterminer le chemin optique de la lumière parasite avec une résolution meilleure que 2 mm, donnant une précision de 1 mm sur la position du composant défectueux, et atteindre un plancher de mesure en amplitude optique fractionnaire de 1,1.10-6 (ou 2,2.10-6 en amplitude fractionnaire électrique) dans la gamme de chemins optiques à couvrir.La méthode qui a été retenue est l'interférométrie à dérive de fréquence (FMCW, Frequency Modulated Continuous Wave) en injectant un laser à balayage de fréquence dans le système sous test. Les signaux optiques et électriques sortants sont capturés pendant le balayage de fréquence optique, et toute modulation de ces signaux sera attribuée à l'existence d'une amplitude de lumière parasite, qui interfère avec l'amplitude de lumière nominale. La différence de chemin optique (DCO) entre la lumière parasite et le faisceau nominal est déduite de la fréquence de ces franges d'interférence. C'est en exploitant la valeur de la DCO qu'on peut identifier le trajet suivi par la lumière parasite, et remonter au composant fautif.La thèse vise donc à développer un prototype de cette instrumentation comprenant essentiellement une diode laser balayable sur 2 nm (pour atteindre la résolution désirée en DCO), une boucle d'asservissement en phase du laser, une mesure précise de la rampe en fréquence, un calibrateur temps réel de la rampe et un système d’acquisition et de traitement de données.Ce prototype, testé d'abord sur un montage simplifié où nous contrôlons la présence de lumière parasite puis sur un système complexe proche du MOSA, aura permis entre autres de vérifier que la méthode fonctionne pour la détection de tout type de lumière parasite, qu'elle soit de type faisceau parasite ou de type lumière diffusée. La résolution permet d'enregistrer séparément les réflexions sur la face avant et arrière d'une lame de verre de 1 mm d'épaisseur et d'atteindre un plancher de détection meilleur que 10-6 en amplitude optique fractionnaire (10-12 en puissance optique fractionnaire) dans une gamme de valeurs de DCO allant de 15 mm à plus de 10 m, qui couvre les trajets typiques de la lumière parasite dans le MOSA. Le prototype a finalement été utilisé pour mesurer la lumière parasite dans un démonstrateur interférométrique dont la complexité est voisine de la complexité d'un MOSA. Ce test a notamment permis d'identifier certaines perturbations, telles que la modification, du fait du balayage en fréquence, de la polarisation du faisceau injecté, ou les imperfections du balayage en fréquence, qui affectent les signaux optiques enregistrés. Des stratégies sont proposées afin de réduire ces perturbations, ou encore d'en tenir compte au moment du traitement des signaux enregistrés
LISA (Laser Interferometer Space Antenna) is a space interferometer dedicated to the detection of gravitational waves in the frequency range [20 µHz-1 Hz], currently under development (phase B). This international project, managed by ESA, will comprise a constellation of three satellites in a triangular formation, each emitting two laser beams towards the other two. There are therefore a total of 6 laser links, and 6 units, called MOSA (Moving Optical Sub-Assembly) responsible for transmitting and receiving the beams, and for measuring inter-satellite distance variations. Each MOSA contains three heterodyne interferometers, and as with any optical device, stray light can compromise measurement accuracy, resolution and dynamics. It is therefore necessary to develop an instrumentation (called the SL-OGSE, Stray Light-Optical Ground Support Equipment) capable of detecting and identifying the contributions of coherent stray light interfering with the device's nominal beams. It will have to meet two requirements in particular: determine the optical path length of the stray light with a resolution better than 2 mm, giving an accuracy of 1 mm on the position of the faulty component, and achieve a measurement floor in fractional optical amplitude of 1,1.10-6 (or 2,2.10-6 in electrical fractional amplitude) in the range of optical paths to be covered.The chosen method is frequency-drift interferometry (FMCW, Frequency Modulated Continuous Wave) by injecting a frequency-swept laser beam into the system under test. The outgoing optical and electrical signals are captured during the optical frequency sweep, and any modulation of these signals will be attributed to the existence of a stray light amplitude, which interferes with the nominal light amplitude. The optical path difference (OPD) between stray and nominal light is deduced from the frequency of these interference fringes. It is by exploiting the OPD value that we can identify the path followed by the stray light, and trace it back to the offending component.The aim of this thesis is to develop a prototype of this instrumentation, comprising a laser diode that can be scanned over 2 nm (to achieve the desired OPD resolution), a laser phase-locked loop, a precise frequency ramp measurement, a real-time ramp calibrator and a data acquisition and processing system.This prototype, tested first on a simplified set-up where we control the presence of stray light, then on a complex system close to the MOSA, has enabled various verifications. The method works for the detection of any type of stray light (stray beam or scattered light type), effectively resolving the contributions from the two sides of a 1mm glass plate and achieving a detection floor below 10-6 in fractional optical amplitude (below 10-12 in fractionnal optical power) in a range of OPD values from 15 mm to over 10 m, covering typical stray light paths in the MOSA. The prototype was finally used to measure stray light in an interferometric demonstrator whose complexity is close to that of a MOSA. This test enabled us to identify certain disturbances, such as changes in the polarization of the injected beam due to the frequency scanning, or imperfections in the frequency scanning, which affect the optical signals recorded. Strategies are proposed to reduce these disturbances, or to take them into account when processing the recorded signals

Doppler Global Velocimeters (DGV) requires a narrow bandwidth laser beam which can be accurately tuned to a desired frequency. One laser used for this application is an ND-YAG which is seeded using a laser diode. By adjusting the laser diode output, the frequency of the ND-YAG laser beam can be modified. This technique also narrows the bandwidth of the laser frequency to below 100 MHz. Monitoring this output is difficult due to the 9 ns pulse duration which makes normal interferometry techniques ineffective for the 10 to 20 MHz frequency resolution required. This paper will describe a system constructed to monitor the frequency in real time which can be used in conjunction with a DGV system to correct for laser frequency drift. The particular ND-YAG system response and stability will be presented and discussed in relationship to DGV system accuracy.

Stable single-frequency, narrow-linewidth, tunable lasers are required in applications such as coherent optical communications, optical fiber sensoring and spectroscopy. One can reduce the frequency drift of semiconductor lasers by locking to a Fabry-Perot interferometer using an automatic-frequency-control loop with feedback to the injection current [1] or temperature [2]. More recently very fast electronic feedback systems have achieved laser linewidth reduction as well as center frequency stabilization [3]. In addition, a variety of methods have been developed to reduce semiconductor laser linewidths by using optical techniques, including direct single-mirror optical feedback, optical injection locking and even optical feedback from fiber reference cavities [4].

Wind speed is useful from a meteorological standpoint, in atmospheric modeling, and assessment of trace gas dispersal. A continuing effort is involved in improving the sensitivity of such measurements, and is exemplified by the literature.[1-10] The Mobile Atmospheric Research Laboratory (MARL) at Lawrence Livermore National Laboratory (LLNL) is currently developing a method to improve the sensitivity of wind sounding in the lower through middle atmosphere using a pair of Fabry-Perot interferometers in parallel. This technique, first described by Chanin, et al.[4], for the middle atmosphere using Doppler Rayleigh lidar, can be applied to the lower atmosphere where Mie (aerosol) backscatter is strong. Elastic events, inherent in both Rayleigh and Mie backscatter, dominate the return signal throughout the atmosphere. Both are susceptible to local wind vectors; which will Doppler shift the laser frequency proportional to the wind velocity. A pair of Fabry-Perot interferometers, tuned to either side of the laser frequency, will provide necessary data to determine the shift in frequency of the backscattered signal. Spectral drift and jitter of the laser and a lack of data points to determine the wind vector place limits on the sensitivity of the system. A method to minimize each of these will be presented.

Very high speed modulation of guided light has been reported using directional coupler switches (ref. |1, 2|) or Mach-Zehnder interferometers (ref |3, 4, 5, 6|). In some applications base band operation is not necessary and band pass type modulators around a given frequency may be preferred. Such resonance has been predicted in ref |7| where switching diagrams of Y-fed directional couplers have been investigated. A Y-fed coupler as reported in ref |8|, appears to be the combination of a directional coupler switch and of a Y junction through which light is launched. This results in - 3 dB built-in optical bias and makes the device free of any electrical DC drift which is regarded to be a problem in most cases for long term operation. Those considerations lead to consider Y-fed directional couplers as very good candidates for very high speed and band pass operation as it will be discussed in the following.

We are investigating the problems of transferring the intrinsic stability of a thoughtfully designed and isolated stable interferometer into an equivalent frequency stability of the laser locked onto its fringe.1 Tests with two lasers independently locked to adjacent orders show locking precision below 50 mHz (1 × 10−16) for times ~1–100 s, degrading toward shorter times as t−1/2 due to finite SNR. Toward longer times performance degrades as t+1 due to changes in the systematic offsets. Locking to various orders gives an estimate that the locking accuracy is <2 Hz (4 × 10−15). Reductions in lock inaccuracy seem possible using harmonic detection.2 Experiments to measure drift of the Zerodur etalon use a 129l2-stabilized laser as a reference. Unfortunately its SNR is too low to give useful information quickly: the cavity’s 2-Hz/s drift just matches the reference laser’s random noise at ~40 s. Comparison over longer times (~days), taken with precise thermal controls operating, is consistent with the idea that the observed 75-Hz noise amplitudes near 24 h are due to remaining thermal problems, and the 1 % uncertainty in the observed drift rate is due to limitations of the iodine-stabilized reference laser. We are considering use of the powerful method of modulation transfer spectroscopy with an external l2 cell,3 in combination with five massive copper shielding walls with independent stabilization and hence thermal gradient control.

By employing the input-output theory of damped quantum systems developed by Gardiner and Collett,1 we discuss the propagation of nonclassical fields through optical systems containing frequency selective elements such as Fabry-Perot interferometers. Our results are of general applicability and are expressed in terms of the linearized drift and diffusion coefficients of the generalized Fokker-Planck equation describing the intracavity field of the nonlinear source. The two nonclassical effects of photon antibunching and squeezing are treated in detail with reference to the examples of intracavity harmonic conversion and optical bistability. Not surprisingly photon antibunching can be enhanced by the suppression of the coherent part of the spectrum of intensity fluctuations with a narrow bandwidth cavity. However the enhancement is ultimately limited and the antibunching lost altogether as the amplitude of the coherent carrier is reduced to a level comparable to that of the field fluctuations (which are set by the system size). Following the suggestion of Levenson et al., 2 we investigate the use of auxiliary cavities for the control of phase and amplitude in the propagation and detection of squeezed states of light. While for a small degree of squeezing such filter cavities operate in a straightforward fashion, a mixing of field quadratures can occur as the degree of squeezing increases leading to a loss of nonclassical behavior.