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.