According to elementary theory, the resolution of an ultrasonic imaging system increases with the ultrasonic frequency. However, frequency is limited by frequency-dependent attenuation. For imaging at any required depth, resolution improvement beyond the limit imposed by ultrasonic frequency can be obtained by increasing the ultrasonic intensity. This is itself, however, dependent on safety considerations and the effects of nonlinearity. In homogeneous media, image resolution increases with decreasing f-number. Particularly at low f-numbers, however, tissue inhomogeneity leads to a deterioration in image quality. Inhomogeneity may also be considered in terms of phase aberration. It has been found that for a given aperture, image degradation due to phase aberration is worse at higher frequencies. Schemes have been proposed for correction of this problem, but so far model systems do not lend themselves to clinical application. Deconvolution is unsatisfactory, speed correction is impracticable and synthetic aperture scanning and holography are virtually useless in biological tissues. Ultrasound-computed tomography has had only limited success. Speckle reduction can improve target detectability, but at the expense of resolution. Time-frequency control provides a useful partial solution to the problem of resolution reduction resulting from attenuation. It is clear that improved resolution would result in significant clinical benefits. An optimisation system for aperture size and ultrasonic frequency is proposed with signal averaging for resolution enhancement of a defined object area. This would have a compact ultrasonic beam and would allow frame rate to be traded for resolution, by means of signal averaging.