The goal of this research is to determine fundamental bounds on estimating the shape and acoustic properties of a given medium by using acoustic sensors. This research has applications in the imaging of biological tissue and nondestructive evaluation and robotics. Included in the research is the development of a 3-d model, a study of the dominant effects of diagnostic transducer arrays on paramenter estimates, and the application of 2-d transducer arrays. This research renews previous research conducted under grant no. ECS-8307782.