Wave space resolution in ultrasonic scattering measurements.

The spatial-frequency spectra of the spatial properties of a scattering medium can be determined from measurements of scattering over a number of angles or frequencies. In such measurements, the spatial localization associated with transducer beam patterns and time gates causes an uncertainty in the measured spatial-frequency domain properties of the scatterer. This uncertainty is analyzed using an analytic and computational model in which system effects are represented by a spatial-frequency domain function. Wave space resolution in a particular direction is shown to be inversely proportional to the spatial-frequency spread of the system function in that direction. In the backscatter case, wave space resolution is limited in the direction of the scattering vector by a convolution of the emitted pulse and the detector time gate, and resolution in the lateral direction depends mainly on the transducer aperture, increasing approximately in proportion to the aperture diameter. In the case of backscatter measurements, smooth aperture apodization improves lateral resolution somewhat but has little effect on resolution in the direction of the scattering vector. For angular scattering measurements, resolution in all directions depends on both the aperture size and (for sufficiently short time gates) on the time gates employed. Illustration of the practical importance of wave space resolution is provided using analysis of two previously published tissue characterization experiments.