Optical measurement of ultrasonic Poynting and velocity vector fields

Abstract

This report describes a method for estimating several wide bandwidth ultrasonic field parameters from optical measurements of the local, acoustically induced, refractive index perturbation in water. These parameters include Poynting and particle velocity vector fields as well as pressure and density fields at any temporal delay under mild (forward-propagating) assumptions on the angular plane-wave spectrum of the ultrasound field. A sampling theorem is derived stating that two complete measurements of the three-dimensional pressure field separated in time by ∆t allow release of the forward-propagating assumption for every acoustic wave number k satisfying k 6 = n =(c∆t), where c is the acoustic wave speed in the medium and n an integer greater than zero. The approach provides detailed measurements of very general ultrasound fields.Two optical measurement methods that acquire the Radon transform of the three-dimensional refractive index perturbation are briefly reviewed. It is shown that the Radon transform of the field itself satisfies a twodimensional wave equation and may be propagated independently forward or backward in time under a source-free model. Conversely, the Radon transform of the ultrasound field measurement at several known time delays provides a means of applying a filter to the data based on known ultrasound propagation models. Each two-dimensional distribution may be propagated to a common time point and the ensemble averaged, thus incorporating the propagation model into the measurement. We support the presented theory with several experiments.

Progress in medical ultrasound exposimetry

“…The light intensity in the scattered beam is a function of v, and this relationship has been used for rapid 2-D mapping and visualization of the ultrasonic field pattern using a charge-coupled device (CCD) camera [63]- [67]. Pulsed fields can be measured by proper synchronizing of the light and ultrasound beams.…”

“…The optical system in [63] uses schlieren imaging (with the zeroth diffraction order suppressed), and reconstruction yields the 3-D pressure amplitude distribution, from which I SPTA and ultrasonic power can be derived. In [64], [66], [67] the instantaneous perturbation of n [and pressure per (2)] is found via optical processing in which an iterative algorithm recovers the integrated phase change at instant t i from measurements of optical intensity in two planes beyond the sound field and normal to the direction of optical wave propagation. After reconstruction, the result is p(x, y, z) at t i , and the complete field p(x, y, z, t) is obtained by varying t i .…”

Lorentz-force hydrophone characterization

“…In principle it allows quantitative measurements [13], however the linearity of the refractive index with pressure can only be assumed at low pressure [14]. Furthermore difficulties have been reported with the parameterization of such systems and with their maintenance over time [15], [16].…”