Systems and methods for acoustic and/or electromagnetic imaging

A method for generating an image, including:

• receiving, at a receiver, a wave pulse having a wave pulse frequency fo, wherein the wave pulse is a single continuous wave pulse having a bandwidth B;
• sampling, at the receiver, the received wave pulse at a sampling rate fs to generate a set of received samples x(n), wherein the sampling rate fs is at least double the bandwidth B of the wave pulse;
• obtaining, by a processor, a selection of a desired angular resolution for an image to be generated from the set of received samples x(n), the desired angular resolution being finer than an angular resolution obtainable at the wave pulse frequency fo;
• determining, by the processor, a desired effective frequency fo+kfs associated with the desired angular resolution, wherein the effective frequency fo+kfs is higher than the wave pulse frequency fo, and wherein the effective frequency fo+kfs was not received at the receiver;
• forming and solving, by the processor, equations based on the set of received samples x(n) and the effective frequency fo+kfs to obtain phase and magnitude data at the effective frequency fo+kfs using the equation:
• x(n)=sin(2πfonts)=sin(2π(fo+kfs)nts)
• where x(n) is the sample n data obtained, fo is the wave pulse frequency, fs is the sampling rate,
• t
• s
• =
• 1
• f
• s
• ,
• k is an integer, and fo+kfs is the effective frequency;
• and
• generating, by the processor, the image based upon the phase and magnitude data at the effective frequency fo+kfs.