High accuracy in measuring target motions can be realized by combined use of our previously developed lateral Gaussian envelope cosine modulation method (LGECMM) and displacement vector measurement methods that enable simultaneous axial and lateral displacement measurements, such as the multidimensional autocorrelation method (MAM). In this paper, LGECMM is improved by using parabolic functions and Hanning windows instead of Gaussian functions in the apodization function, i.e., parabolic apodization and Hanning apodization. The new modulations enable decreases in effective aperture length (i.e., channels) and yield more accurate displacement vector measurements than LGECMM due to increased echo signal-to-noise ratio and lateral spatial resolution. That is, on the basis of a priori knowledge about ultrasound propagation using the focusing scheme and shape of the apodization function, we stopped using Fraunhofer approximation. As practical applications of the modulations, for an agar phantom that is deformed in a lateral direction, stable and accurate 2-D shear modulus reconstructions are performed using our previously developed direct inversion approach together with 2-D strain tensor measurements using MAM.

Previously, we proposed to set ultrasound (US) beam-forming parameters in order to realize the required point spread function (PSF) on the basis of optimization theory. In this report, for high quality-lateral cosine modulation (LCM) US imaging and measurements of accurate displacement vector and elasticity (i.e., strain tensor, shear modulus), after briefly reviewing our trials that broke away from the use of the Fraunhofer approximation to determine the apodization function, images and measurements obtained for an agar phantom are shown. In this study, the previously reported lateral parabolic modulation (PAM) and lateral Gaussian envelope cosine modulation (LGECM) are carried out. Comparisons of the spatial resolutions of the US images obtained and the measurement accuracies of the displacement vectors and elasticity measurements obtained using our previously developed multidimensional autocorrelation and Doppler methods (i.e., MAM and MDM) are also made. The development of next-generation US imaging systems has already begun.