Doppler tomography for vector fields

Abstract

The problem considered is to reconstruct a vector eld in the case when for each line the distribution of the vector eld components along the line is known. Such data are obtained from spectral analysis of signals, a ected by Doppler shifts, caused by re ections on moving particles (\velocity spectra"). In the general setting, the problem is unsolved. Using only integrated data along lines, one encounters the same problem as when reconstructing vector elds by means of time-of-ight measurements. Reconstruction formulas are given in this case, establishing the known fact that only the curl of the vector eld can be reconstructed without additional information. Inspired by the application to which the paper is most devoted, ultrasound Doppler measurements on blood ows, the case where the ow takes place in narrow channels is investigated in simulations and experiments.

Design and Development of an Electronic Sensor to Detect and Measure Curvature of Spaces Using Curvature Energy

“…The curvature perception in the space is associated increasingly with their interpretation as a distortion of the e reflected signals [15] (Figure 8(b)). Abbreviations SOIC-Small-outline integrated circuit; mV-Micro-volts; EDMC-Electromagnetic device to measure curvature; ASIC-Application-specific integrated circuit; QFT-Quantum field theory; SUSY-Super-symmetry theory; FRW-cohomology-Friedman-Robertson-Walker metrics.…”

Attenuated Vector Tomography -- An Approach to Image Flow Vector Fields with Doppler Ultrasonic Imaging

“…The Doppler flow measurements obtained using a directional beam of a continuous ultrasound wave can be formulated as a directional projection of a flow vector field [1,2,3]. The continuous wave reflects from points at different distances from the ultrasound detector.…”

3D reconstruction of tensors and vectors

“…History of Vector Field Tomography Tensor tomography builds on much of the work already accomplished in vector field tomography [2,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35]. Applications have involved acoustic flow imaging using time-of-flight measurements in medicine [7], non-destructive evaluation [11], and ocean tomography [9,14].…”

“…Other Works Vector field tomography has been applied in other applications: optics, to measure flow [16,17,21]; deflection optical tomography, to determine densities in supersonic expansions and flames [15]; optical polarization tomography, to measure electric fields in a Kerr material by measuring polarization of the transmitted light [12,13,25]; acoustic tomography, to determine temperature distributions and velocity vector fields in furnaces [26]; polarimetric tomography of the magnetic field in TOKOMAK [8,27]; and velocity vector fields of heavy particles in plasma [32,28]. It has also been shown that continuous doppler data can be analyzed in the framework of vector field tomography [2,21,24,22,33,32,28,29].…”

“…It has also been shown that continuous doppler data can be analyzed in the framework of vector field tomography [2,21,24,22,33,32,28,29].…”