Systems and methods are disclosed for improving the resolution and quality of an image formed by signals from an array of receivers. Multiple receivers introduce variations in arrival times that can be less than the period of an operating signal, and also less than the period associated with a sampling operation. Thus, multiple receivers allow sampling of fine features of reflected signals that would be considered beyond the resolution associated with the operating signal. Use of multiple receivers also provides an effective sampling rate that is greater than the sampling rate of an individual receiver. Similar advantages can be obtained using multiple transmitters. Such advantageous features can be used to obtain high resolution images of objects in a medium in applications such as ultrasound imaging. Sub-Nyquist sampling is discussed. Accounting for the effects of refraction on pathlengths as a signal passes between two regions of different sound speed allows improved calculation of focus distances. Extending the analysis to account for additional layers or sub-layers allows further improvement.
