Аннотация:In medical ultrasound, it is important to accurately measure the acoustic fields to which patients are
exposed. Especially for focused fields used for therapy, direct hydrophone measurements at high pressures and
throughout the relevant 3D volume may be challenging or impossible. Acoustic holography is a known method for
characterizing continuous-wave (CW) sound fields with measurements in two dimensions. In conjunction with
numerical projection methods, a measured hologram is capable of fully characterizing the 3D ultrasound field.
However, errors implicit in this approach have not been quantified. Such errors are analyzed here to develop
holography as a practical tool in ultrasound metrology.
Hologram accuracy was investigated for linear CW ultrasound fields, for which a hologram comprises a
set of pressure magnitude and phase values measured at a finite number of points. To evaluate error, numerical
simulations were conducted to compare a reference field and holographic representations of the same field. Two
idealized sources with uniform surface vibration velocities were considered: a flat source and a spherically focused
source (10 cm radius of curvature), both with apertures of 10 cm and operating frequencies of 1 MHz. All calculations
to simulate holography measurements were made in a transverse plane located 5 cm from the center of the source,
using half-wavelength spacing between measurements. The accuracy of reconstructed fields was evaluated with
consideration of the following parameters: hologram aperture, hydrophone directivity, uncertainty in the alignment of
measurement coordinates, and uncertainty in the temperature of the acoustic medium. Experiments were conducted
using several focused sources. Holographic reconstructions from experimental measurements were then compared to
independent hydrophone measurements. To provide quantitative comparisons of reference fields and reconstructed
fields, normalized error metrics were defined in terms of the maximum pressure discrepancy over a collection of field
points, the RMS pressure discrepancy over a collection of field points, and the relative change in the dimensions of
the focal region.
For idealized sources analyzed numerically, errors associated with the representation of linear fields by
holograms remained less than about 1% for parameters corresponding to conditions expected in practice. For the
experimental cases, errors were higher but remained less than 10%. As depicted in Fig. 1 for a C5-2 imaging probe,
the experimentally measured holograms accurately capture many details of the 3D field.
This study provides detailed practical recommendations for accurate implementation of acoustic
holography and demonstrates its potential as a metrological tool in medical ultrasound. Work supported by NIH
R21EB016118, R01EB007643, P01DK43881; RFBR 14-02-00426; and NSBRI through NASA NCC 9-58.