Spatio-temporal deconvolution of pulsed ultrasonic fields received by a transducer of linear aperture : a simulation study

Abstract

In ultrasonic field measurements, the signal delivered by the receiving transducer is affected by the receiver spatiotemporal transmission properties. The pressure is spatially averaged over its finite-size aperture. Furthermore, frequency variations of its transfer function may distort the output signal. The efficiency of the deconvolution of these effects is shown by means of numerical simulations. The pulsed pressure field radiated by a wideband 10.3mm-radius planar transducer, with a central frequency f c = 2.25 MHz ( λ c : corresponding ultrasonic wavelength in water) is considered. The receiver is a linear aperture 25 µm-thick PVDF membrane hydrophone. The study shows that the quality of the reconstructed signal depends strongly upon the signal-to-noise ratio (SNR), the aperture dimensions and the distance from the source. For an aperture of length L = 2.6 mm ≈ 3.9λ c , placed on axis at z = 3 mm, correlation coefficients between the reconstructed pressure and the original one, p p rˆ, of 0.999, 0.988 and 0.655 have been obtained, for SNRs of 60, 40 and 20 dB respectively. For a greater aperture (L = 4.6 mm ≈ 6.9λ c ) and SNR = 40 dB, no satisfactory results could be obtained at this distance ( p p rˆ = 0.912). At a greater axial distance (z = 20 mm), better deconvolution results could be achieved ( p p rˆ = 0.928).

Application of Inverse Methods for Spatial Deconvolution of Pulsed Ultrasound Fields Radiated in Solids

“…The Advanced Materials Forum V study has been achieved for the field of a circular planar transducer and a receiver of rectangular aperture. It could, however, be generalized to other aperture geometry [4] and any kind of ultrasound field.…”

“…(2) the power spectral equalization method that is based on equalization between the spatial power spectral densities of the field to be reconstructed and on its estimated value; (3) the maximum a posteriori method, where the maximum a posteriori probability density function for the reconstructed field is searched. The possibility of deconvolving the spatial effects has been shown for harmonic and pulsed ultrasound fields radiated in fluids [3,4]. The present contribution is a generalization of the study of pulsed ultrasound fields radiated in isotropic solids.…”

“…The spatial frequencies bandwidth of the investigated ultrasound field decreases, for a given time-frequency with the axial distance to the source [4].When studying the direct problem, it has been shown that the effect of spatial averaging decreases while moving the receiver away from the source [3,4]. That suggests studying the influence of the axial distance on the quality of reconstructed field.…”

“…This characterizes the ill-posedness of this inverse problem. Even if the zeros are numerically avoided, the problem remains ill-conditioned [3,4] because of the drastic amplification of the noise level in the deconvolved signals. Therefore, it is necessary to use a regularization procedure such as Wiener's method, the PSE method and the MAP method.…”

“…The PSE filter [4] is based on the equalization between the spatial PDSs, of the field to be reconstructed,    vv and its estimated value…”