Disclosed are systems and methods for characterizing a nonlinear propagation environment by numerically propagating a measured output waveform resulting from a known input waveform. The numerical propagation reconstructs the input waveform, and in the process, the nonlinear environment is characterized. In certain embodiments, knowledge of the characterized nonlinear environment facilitates determination of an unknown input based on a measured output. Similarly, knowledge of the characterized nonlinear environment also facilitates formation of a desired output based on a configurable input. In both situations, the input thus characterized and the output thus obtained include features that would normally be lost in linear propagations. Such features can include evanescent waves and peripheral waves, such that an image thus obtained are inherently wide-angle, farfield form of microscopy.
STATEMENT REGARDING FEDERALLY SPONSORED R&D
 This invention was made with Government support under Grant No. NSF PHY-0605976 awarded by the National Science Foundation; Grant No. AFOSR FA9550-07-1-0249 awarded by the Air Force Office of Scientific Research; Department of Defense grant awarded by the Army Research Office through a National Defense Science and Engineering Graduate Fellowship; and Grant No. DE-FG02-08ER55001 awarded by the Department of Energy. The Government has certain rights in this invention.