Mean Doppler Shift Research Articles

Synthetic aperture radar interferometry applied to ship‐generated internal waves in the 1989 Loch Linnhe experiment

Interferometer synthetic aperture radar images collected during the 1989 Loch Linnhe experiment showed mean Doppler variations across the phase of ship‐generated internal waves that corresponded to “velocity” variations of the order of 50 to 100 cm/s. The in situ current data, however, showed surface currents associated with the internal wave features of the order of 5 to 10 cm/s and virtually ruled out the existence of surface currents as large as the interferometer‐inferred values. In this paper we show how the pixel‐to‐pixel phase difference measured by the Jet Propulsion Laboratory interferometer is related to the mean Doppler frequency of the backscattered field. Model calculations are used to show how this frequency can sometimes change by a large amount, even when rather small surface currents are present. In particular, for winds blowing roughly across the internal wave features, as was the case for the interferometer runs in Loch Linnhe, computations based on our wave‐current interaction and time dependent scattering models show that changes in the mean Doppler frequency corresponding to large velocities can, in fact, be produced from the much smaller measured surface currents. We show that the larger interferometer velocity estimates are essentially due to the different modulation strengths of the surface Bragg waves advancing toward and receding from the radar. Thus for these crosswind conditions, care must be taken in converting the phase differences measured by the interferometer to a surface current image. When the wind is aligned more nearly along the internal wave propagation direction, the mean Doppler shifts (and the phase differences) are dominated mostly by advection, and interferometer current estimates are more accurate. C band computations predict that if the antenna spacing is small enough so that the fields from the two antennas remain correlated, then the C band interferometer current estimates will be better than those at L band.

The altitude of type 3 auroral irregularities: Radar interferometer observations and implications

VHF coherent scatter radars at auroral latitudes have observed scatterers with narrow power spectra at sub‐ion acoustic mean Doppler shifts. These spectra have been designated “type 3.” The mean Doppler shift of these waves is often near the atomic (O+) or, less frequently, the molecular (O2+ and NO+) gyro frequencies. These type 3 echoes have been attributed to an electrostatic ion‐cyclotron (EIC) instability in the upper E region (h > 140 km), where the ion collision frequency becomes low enough to permit ion gyromotion. Interferometric analysis of recent coherent radar observations with the CUPRI (Cornell University portable radar interferometer) shows that type 3 events occur at typical electrojet altitudes (100–120 km), however. At these altitudes the ion collision frequency is greater than the ion gyrofrequency, and there can be no cyclotron motion. The cause of the observed type 3 echoes hence remains a mystery.

Method of color coding two dimensional ultrasonic doppler velocity images of blood flow on a display

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Spectral correlation of atmospheric lidar returns with range-dependent backscatter

Expressions are derived for the spectrum of atmospheric backscatter coherent lidar returns in the presence of arbitrary line-of-sight backscatter nonuniformities. It is shown that, in contrast to microwave weather radar, sample measurement spectra are smoothed, although mean spectra and therefore the first-order coherence of the return are unaffected. Simulated data are used to demonstrate that estimates of return power are degraded by sample smoothing, but some estimates of mean Doppler shift are improved.

Are type III radio aurorae directly excited by electrostatic ion cyclotron waves?

In 1981, a network of three 50‐MHz radar transmitters and two receivers was operated in the CW mode on the Canadian prairies. The echoes obtained from coherent ionospheric backscatter were divided into segments of 205 ms such that their FFT spectra yielded a frequency resolution of 4.9 Hz. The spectra were subsequently averaged over 10 s. Type III spectra (narrow spectra with sub ion‐acoustic Doppler shifts) were observed (often simultaneously) on radar links whose wave vector components perpendicular to the geomagnetic field were almost identical while their components parallel to the field were significantly different. From a statistical analysis of more than 300 type III spectra it is inferred that these are in general unlikely to arise from electrostatic ion cyclotron waves directly excited by an essentially linear process. Doppler shifts around 55 Hz were much more frequently observed than around 30 Hz, the occurrence of type III spectra increased with increasing magnetic aspect angle (deviation of the scatter wave vector from perpendicular to the geomagnetic field), and the mean Doppler shifts of type III spectra observed simultaneously on different radar links went through a minimum for aspect angles between 4° and 7° (depending on the assumed backscatter height). These three results disagree with theoretical expectations. The spectral width of the type III echoes decreased linearly with magnetic aspect by about 2 Hz/deg.

Distribution of mean Doppler shift, spectral width, and skewness of coherent 50‐MHz auroral radar backscatter

Some 7700 radio aurora spectra obtained from a six link 50‐MHz CW radar network set up on the Canadian prairies were analyzed with respect to the distributions of mean Doppler shift, spectral width and skewness. A comparison with recently published SABRE results obtained at 153 MHz (Schlegel et al., 1986) shows substantial differences in the distributions which are probably due to different experimental and geophysical conditions. Our spectra are mostly broad with mean Doppler shifts close to zero (type II spectra). The typical groupings of type I and type III spectra are clearly identified. All types appear to be in general much more symmetric than those recorded with SABRE, and the skewness is only weakly dependent on the sign of the mean Doppler shift. Its distribution peaks near zero and shows a weak positive correlation with the type II Doppler shifts while the mostly positive type I Doppler shifts are slightly negatively correlated with the skewness.

The relationship between time averaged intensity weighted mean velocity, and time averaged maximum velocity in neonatal cerebral arteries

It is usual practice to calculate the mean velocity of blood flow in neonatal cerebral vessels from the intensity weighted mean (IWM) Doppler shift signal. Theoretically however the maximum frequency envelope could be used for similar purposes, and indeed may have certain advantages. The purpose of this study was to confirm the suitability of the maximum frequency method. Good quality Doppler recordings from the anterior cerebral and middle cerebral arteries of both term and very low birth weight babies were analyzed by both methods and compared. A small number of recordings were then deliberately degraded, either by the addition of noise or by the use of inappropriate filters, and reanalyzed. The results of these comparisons suggest that the maximum frequency follower should be the follower of choice for neonatal cerebral blood flow studies.

Spline function approximation for velocimeter Doppler frequency measurement

A spline function approximation approach for measuring the Doppler spectral peak frequency in a laser Doppler velocimeter system is presented. The processor is designed for signal bursts with mean Doppler shift frequencies up to 100 MHz, input turbulence up to 20%, and photon counts as low as 300. The frequency-domain processor uses a bank of digital bandpass filters for the capture of the energy spectrum of each signal burst. The average values of the filter output energies, as a function of normalized frequency, are modeled as deterministic spline functions which are linearly weighted to evaluate the spectral peak location associated with the Doppler shift. The weighting coefficients are chosen to minimize the mean square error. Performance evaluation by simulation yields average errors in estimating mean Doppler frequencies within 0.5% for poor signal-to-noise conditions associated with a low photon count of 300 photons/burst. >

Time-domain estimation of the center frequency and spread of Doppler spectra in diagnostic ultrasound

Two sets of estimators of the centre frequency and mean-square bandwidth of a Doppler spectrum are analyzed. The first set is based on a linear combination of the complex autocorrelation of the Doppler signal for different lags. It is then shown that the argument (phase angle) of the complex autocorrelation function at unit sample lag is a close approximation to the mean Doppler shift, whereas its modulus (magnitude) gives information about the mean-square bandwidth of the spectrum. Approximate expressions for the bias and variance of the estimators are derived, valid for long averaging times. The performances of the estimators are compared for signals with rectangular spectra and different signal-to-noise ratios.

Time-domain estimation of the center frequency and spread of Doppler spectra in diagnostic ultrasound

Two sets of estimators of the center frequency and mean square bandwidth of a Doppler spectrum are analyzed. The first set is based on a linear combination of the complex autocorrelation of the Doppler signal for different lags. It is shown that the argument (phase angle) of the complex autocorrelation function at unit sample lag is a close approximation to the mean Doppler shift, whereas its modulus (magnitude) gives information about the mean square bandwidth of the spectrum. Approximate expressions for the bias and variance of the estimators are derived, valid for long averaging times. The performances of the estimators are compared for signals with rectangular spectra and different signal-to-noise ratios.

Airborne microwave Doppler measurements of ocean wave directional spectra

Abstract A technique is presented for measuring ocean wave directional spectra from aircraft using microwave Dopper radar. The technique involves backscattering coherent microwave radiation from a patch of sea surface which is small compared to dominant ocean wavelengths in the antenna look direction, and large compared to these lengths in the perpendicular (azimuthal) direction. The mean Doppler shift of the return signal measured over short time intervals is proportional to the mean sea surface velocity of the illuminated patch. Variable sea surface velocities induced by wave motion therefore produce time-varying Doppler shifts in the received signal. The large azimuthal dimension of the patch implies that these variations must be produced by surface waves travelling near the horizontal antenna look direction thus allowing determination of the direction of wave travel. Linear wave theory is used to convert the measured velocities into ocean wave spectral densities. Spectra measured simultaneously with this technique and two laser profilometers, and nearly simultaneously with a surface buoy, are presented. Applications and limitations of this airborne Doppler technique are discussed.

Three‐body scattering produces precipitation signature of special diagnostic value

Examples are given of three‐body scatter signatures produced by high reflectivity cores in thunderstorms. The process consists of (1) scattering by the hydrometeors, (2) backscattering by the ground to the hydrometeors and (3) scattering by the hydrometeors to the radar. When viewed on radar displays, the signatures have an elongated shape, radially aligned behind strong (60 dBZ) reflectivity cores. A radar equation for echo power is developed and predicted r−3 dependence of the echo power on the range between the center of scattering volume and a reflecting ground ring is confirmed by a least squares fit to actual data. It is shown theoretically that mean Doppler shifts associated with three‐body scatter signatures are caused by the vertical and radial components of hydrometeor velocities; this is also verified from least square fits of range profiles of measured Doppler velocities to theoretical curves based on geometrical considerations.

Auroral E region plasma waves and elevated electron temperatures

We have observed 3‐m auroral E region plasma waves with a high‐resolution 50‐MHz radar interferometer at Ithaca. During postmidnight periods of very strong magnetic activity at Ottawa (L = 3.5), the backscattered power and Doppler spectra vary rapidly with time and range and may have both mean Doppler shifts and half power widths in excess of 200 Hz (600 m/s). In addition, when the radar and magnetometer data imply that the current is approximately parallel to the radar line of sight, sharp spectral peaks corresponding to phase velocities approaching 1 km/s sometimes appear suddenly. These persist for at most several tens of seconds at any particular range and their amplitude seems to be more strongly dependent on the drift velocity than is the strength of the wide spectral component, which generally broadens substantially before the high‐velocity peak appears. The shape of the peaks and their time evolution lead us to believe that they represent a true two‐stream instability, implying an ion acoustic velocity in the medium of about 900 m/s in extreme cases, which, in turn, means an E region electron temperature of as much as 2000 K or more at latitudes as low as L = 3.5. This interpretation of the data is consistent with recent E region incoherent scatter measurements and helps to resolve some questions raised in connection with earlier coherent radar studies.

On the dependence of the phase velocity of equatorial irregularities on the polarization electric field and theoretical implications

We have studied the mean Doppler shift of equatorial irregularities in the E region, using data from a coherent radar situated in Ethiopia between 1976 and 1980. We found that even though the primary two‐stream (or type I) waves are drifting at a speed close to the expected ion acoustic speed, there is a small but nonnegligible increase in the phase velocity with increasing electron drift in the electrojet. We attribute this increase to a heating of the electron gas by the large‐amplitude, low‐frequency waves that are present in the region when conditions are favorable to the production of large‐scale gradient drift instabilities. On the other hand, for the single day when the production of large‐scale gradient drift instabilities was inhibited, the behavior of the irregularities was quite different. Namely, the Doppler shift of 10‐m waves (type O waves) was usually below the linear threshold value while the spectra remained narrow and type I‐like rather than type II‐like. On the other hand, the Doppler shift followed a dependence similar to that expected from type II waves. We have tentatively attributed this type O behavior to weak mode coupling, following similar inferences from recent Condor observations made near the top of the electrojet.

Noninvasive blood flow measurement in expanded polytetrafluoroethylene grafts for hemodialysis access

Volume flow rates were measured in 31 expanded polytetrafluoroethylene grafts (6 mm) of 26 patients undergoing hemodialysis. Flow was calculated from the known access graft diameter and by measurement of the mean Doppler shift frequency waveform. Overall flow rates were 750 ± 383 ml/min (range, 0 to 1921 ml/min). There was no difference in flow between grafts anastomosed to either antecubital or upper arm veins but there was a significant difference in flow rate between straight and loop grafts (652 and 914 ml/min) and between grafts anastomosed to the radial, distal brachial, and proximal brachial arteries (648, 876, and 1169 ml/min, respectively). Flow rates measured during a preocclusive 14-day period in five grafts were significantly lower than flow rates in grafts that remained patent for at least 2 weeks following examination (307 ± 172 vs. 849 ± 346 ml/min). This is a safe, repeatable noninvasive measure of access graft hemodynamics, which may be useful as a functional monitor and a warning of impending failure.

A model for Doppler peak spectral shift for low grazing angle sea scatter

A model is formulated for Doppler spectral characteristics of radar sea scatter for low grazing angles, and is compared with previous radar measurements reported in the literature. The Doppler model is based upon the two-scale model for radar scatter, with scatterer motions hypothesized as due to the orbital wave velocity of the large-scale waves, Stokes and wind drift currents, and the phase velocity of the small-scale Bragg scatterers. Expressions for Doppler shifts due to these motions are derived, and are given as a function of wave height, wave period, and wind speed. Although this model appears to account for the peak Doppler shift of the sea-scatter Doppler spectrum for vertical polarization, it is insufficient to describe horizontally and cross-polarized data, which have larger mean Doppler shifts. However, these two cases are found to scale very closely with the nearly simultaneous vertically polarized data for the variety of environmental conditions reported. Implications of the extension of these results to higher-angle remote-sensing applications are discussed.

Some characteristics of laminar flow velocity spectra detected by a 20 MHz pulsed ultrasound Doppler

For the purpose of improving accuracy of noninvasive flow measurements in small (1–2 mm diameter) blood vessels, an existing 20 MHz pulsed ultrasound Doppler velocimeter (PUDVM) has been augmented to allow fast Fourier transformation (FFT) of its Doppler shift signal. The modified instrument was used to collect velocity spectra for a benchtop test section delivering precise Poiseuille flows at velocities in the range of physiological interest. The velocity spectra demonstrated a substantial degree of broadening, much of which was attributable to the geometry of the finite sample volume size. Several spectral indices were studied as a function of flow field variables. Results showed that the intensity-weighted mean Doppler shift frequency, when converted to its corresponding velocity v M , agreed very closely with the theoretically predicted local fluid velocity. Measurement linearity and repeatability were evaluated for a number of system variables, indicating that FFT performance was essentially unaffected by several parameters capable of causing major degradation of (phasic) Doppler shift signals produced by conventional zero-crossing-counter circuitry. As presently configured, the augmented PUDVM instrument is fully capable of detailed flow field mapping in small subcutaneous vessels such as human digital arteries.

STARE doppler spectral studies of westward electrojet radar aurora

This paper presents crossed-beam Doppler spectral measurements of radar aurora during westward electrojet conditions made with the STARE system in northern Scandinavia. The averaged spectral characteristics (e.g. spectral shape, relative power, spectrum width, spectrum asymmetry) are examined relative to the electron drift velocity estimated by combining the mean Doppler shifts from both radars. The type of spectrum was found to depend on the flow angle θ defined as the angle between drift velocity and radar wavevector. Typically, narrow spectra, similar to equatorial type I spectra, are observed for angles θ up to 60° while for larger angles the spectra become much broader and less stable in space and time. The observed spectral types are closely identified with primary and secondary irregularities. On average, a power law relationship was found to exist between the relative backscatter power and the drift velocity magnitude. A weak trend was found for the narrow spectra to become narrower for larger drifts contrary to broad spectrum width which increases linearly with drift magnitude. The spectra are often asymmetric with elongated tails toward zero Doppler shifts but this asymmetry is of a different nature for the narrow and broad spectra. The averaged spectral properties presented in this paper are similar to those reported by Nielsen et al. (1984) for eastward electrojet radar aurora.

A theory of coherent radar spectra in the auroral E region

We have developed a theory of auroral radar spectra for conditions under which Farley‐Buneman waves should be strongly excited in the high‐latitude E region. The theory assumes that the unstable waves spend the larger part of their lifetime in a linear growth phase. It also uses a previously unexplored property of the waves, namely, that waves with different wave vector components along the magnetic field have markedly different phase velocities. We have constructed synthetic auroral radar spectra for 1‐m size irregularities. We have calculated the width of the spectra, their mean Doppler shift, and anisotropy. We have studied how the properties of spectra produced by Farley‐Buneman waves are affected by the presence of ion drifts and neutral winds, by the electron temperatures and densities, by the neutral atmospheric profile, and by the strength of the dc electric fields. The results seem to be in good qualitative agreement with existing observations.

Performance characterization of a remote acoustic Doppler current profiling sonar

Monostatic acoustic Doppler technology is being evaluated for application to NOAA's mission requirements for the measurement of upper ocean current profiles. As part of that evaluation, a shipboard current profiling sonar, developed in 1978 under contract to NOAA by Thomson-CSF, was tested on the Blake Plateau. The system includes a four-beam 300-kHz “Janus geometry” hull-mounted transducer, and associated microprocessor-based electronics. The system estimates vertical current profiles in the upper 100 m by detecting the mean Doppler shift in volume-backscattered pulses at multiple ranges. Although no “sea truth” was available, agreement between mean ship' speed inferred from the acoustic Doppler measurements and Loran-C was good. The variance in time series of orthogonal components of current at specified depths is discussed as a function of transmission characteristics and ship's speed. The variance reduction with averaging indicates a random noise-type dependence when averaging of up to 10–20 observations. As more observations are averaged, the decrease in variance is limited, suggesting that an optimum averaging window can be tailored to the operating environment.