1. An acoustic imaging device for providing an image of at least a portion of a medium comprising: A) an acoustic broadcasting means for broadcasting into said medium acoustic signals from at least seven broadcast locations on a circle at least partially surrounding said medium, one location at a time said acoustic signals being at least one discrete frequency and continuous for a period of time equal to at least the travel time of said acoustic signal across said medium, B) an acoustic signal detection means for detecting, at a plurality of detection locations on said circle at least partially surrounding said medium, acoustic signals broadcast by said broadcasting means, C) a data collection and comparison means for comparing signals received to said signals broadcast in order to provide with respect to each of said plurality of locations a set of data representing the phases and amplitudes of acoustic signals received at said plurality of locations relative to the phase and amplitude of said signals broadcast from said at least seven locations, and D) a computing means for mathematically constructing at least one image of at least a portion of said medium utilizing said phase and amplitude data said computing means being programmed to accomplish the following steps: 1) transform said phase and amplitude data into a set of data defining an azimuthal data set in an azimuthal mode space said set of data representing azimuthal modes at the location of said broadcasting means and said detection means, 2) modify said azimuthal data set to account for transducer antenna patterns to produce an antenna independent azimuthal data set, and 3) multiply said antenna independent azimuthal data set by weighting function calculated at a large number of locations in said medium and sum over said azimuthal modes to produce a convolved image of said medium, and 4) deconvolved said convolved image of said medium to produce said image of said medium.