Three-dimensional optical measurement of instantaneous pressure

Local perturbations in material density induced in a material by a compressional wave give rise to local perturbations in refractive index. Accurate, high-resolution, three-dimensional, optical measurements of an instantaneous refractive index perturbation in a homogeneous, optically transparent medium may be obtained from measurements of scattered optical intensity alone. The method of generalized projections allows incorporation of optical intensity measurements into an iterative algorithm for computing the phase of the interrogating optical pulse as the solution of a fixed point equation. The complex optical field amplitude, computed in this manner, is unique up to a constant unit magnitude complex coefficient. The three-dimensional refractive index distribution may be computed via the Fourier slice reconstruction algorithm from the optical phase data under the assumption of weak optical scattering. The refractive index perturbation is related to local instantaneous pressure under a linear, small-displacement model for the mechanical wave. A numerical simulation of the measurement experiment, phase recovery, and reconstruction process for a plane piston ultrasound transducer with a semicircular aperture and center frequency of 1.5 MHz is described and corresponds very well with experiment. Experimental data obtained using an 810-nm laser source are used to reconstruct the three-dimensional pressure field from two elements of a 2.5-MHz linear array. Comparison with a measurement obtained via a 500-microm needle hydrophone shows excellent agreement.