Optical measurement of ultrasonic Poynting and velocity vectorfields

摘要

This report describes a method for estimating several widenbandwidth ultrasonic field parameters from optical measurements of thenlocal, acoustically induced, refractive index perturbation in water.nThese parameters include Poynting and particle velocity vector fields asnwell as pressure and density fields at any temporal delay under mildn(forward-propagating) assumptions on the angular plane-wave spectrum ofnthe ultrasound field. A sampling theorem is derived stating that twoncomplete measurements of the three-dimensional pressure field separatednin time by Δt allow release of the forward-propagating assumptionnfor every acoustic wave number k satisfying k ≠ nΠ/(cΔt),nwhere c is the acoustic wave speed in the medium and n an integerngreater than zero. The approach provides detailed measurements of veryngeneral ultrasound fields. Two optical measurement methods that acquirenthe Radon transform of the three-dimensional refractive indexnperturbation are briefly reviewed. It is shown that the Radon transformnof the field itself satisfies a two-dimensional wave equation and may benpropagated independently forward or backward in time under a source-freenmodel. Conversely, the Radon transform of the ultrasound fieldnmeasurement at several known time delays provides a means of applying anfilter to the data based on known ultrasound propagation models. Eachntwo-dimensional distribution may be propagated to a common time pointnand the ensemble averaged, thus incorporating the propagation model intonthe measurement. We support the presented theory with severalnexperiments