Resolution of the Ultrasound Doppler System Using Coherent Plane-Wave Compounding Technique

Abstract

In this work, in the process of plane-wave ultrasound probing from different angles the attainable spatial resolution was estimated on the basis of the previously developed theory of the Doppler response formation. In the theoretical calculations coherent compounding of the Doppler response signals was conducted over the period of changing the steering angles of probing. For this case an analytical expression for the ultrasound system sensitivity function over the field, which corresponds to the point spread function, is obtained. In the case of a rectangular weighting window for the response signals, the resolution is determined by the well-known sinc-function. The magnitude of the lateral resolution is inversely proportional to the range of the steering angles. It is shown that the theoretically estimated magnitude of the Doppler system lateral resolution, when using the technique of coherent plane-wave compounding, is in good agreement with the experimental data presented in literature.

Spectra of Ultrasound Doppler Response Using Plane-Wave Compounding Technique

“…Using (5), it is possible to obtain a sensitivity function with completely suppressed side lobes, unlike in [35]:…”

“…Note that the results presented here are based on a linear approximation of the time dependence of the deviation of the wave vector ∆𝑘 ⃗ (𝑡) = 𝑘 ⃗ (𝑡) − 𝑘 ⃗ . This means that only the projection of the vector ∆𝑘 ⃗ (𝑡) onto the 𝑦 -axis was taken into account [35], which is small due to the small values of the angles Φ(𝑡). At the same time, this vector also has a projection on the 𝑥 axis, which depends on the square of time.…”

“…The time dependence is caused by small deviations of the wave vector from the wave vector of plane waves without inclination. Earlier [35], in this approximation, the Fourier image of the function 𝐺 𝑟 ⃗, 𝑡 was found with a linear dependence on time of the wave vector deflection angle Φ 𝑡 Ω𝑡. Most conventional pulse systems use sequential emission of pulses characterized by the same spatial geometry and configuration of wavefronts.…”

“…THEORETICAL MODEL Within the framework of the continuum model of the biological medium, the low-frequency Doppler signal 𝑒 𝑡 under the pulsed mode of ultrasound wave emission [34,35] depends on the motion of the density inhomogeneities 𝜌 𝑟 ⃗, 𝑡 and compressibility 𝛽 𝑟 ⃗, 𝑡 . It also depends on the complex sensitivity function 𝐺 𝑟 ⃗, 𝑡 over the emission-receiving field.…”

“…Within the framework of the model described in [35][36][37], it follows from (4) that in this case the sensitivity function is independent of frequency similar to (2).…”