Reconstruction of nonlinear wave propagation

Abstract

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.

1 . (canceled) 
     
     
         2 . A physical system, comprising:
 a medium configured to receive a first waveform and yield a second waveform; and   a processor configured to obtain information about two of a nonlinear response of the medium, said first waveform, and said second waveform and generate a characterization of the remaining one of said nonlinear response of the medium, first waveform, and second waveform, said generated characterization determined by numerical propagation of one of said first and second waveforms.   
     
     
         3 . The system of  claim 2 , wherein one of said waveforms is optical 
     
     
         4 . The system of  claim 2 , wherein one of said waveforms is acoustic. 
     
     
         5 . The system of  claim 2 , wherein one of said waveforms is ultrasonic. 
     
     
         6 . The system of  claim 2 , wherein at least one of the first and second waveforms is spatially separable. 
     
     
         7 . The system of  claim 2 , wherein at least one of the first and second waveforms is spatially non-separable. 
     
     
         8 . The system of  claim 2 , wherein the medium is transmissive. 
     
     
         9 . The system of  claim 2 , wherein the medium is reflective. 
     
     
         10 . The system of  claim 2 , wherein the medium is diffractive. 
     
     
         11 . The system of  claim 2 , wherein the medium is a spatial light modulator. 
     
     
         12 . The system of  claim 2 , wherein the medium comprises a filter. 
     
     
         13 . The system of  claim 2 , wherein the medium is a computer-controlled display. 
     
     
         14 . The system of  claim 2 , wherein at least one of the first or second waveform undergoes a change in the intensity due to the non-linear response of the medium. 
     
     
         15 . The system of  claim 2 , wherein at least one of the first or second waveform undergoes an intensity-dependent phase change due to the non-linear response of the medium. 
     
     
         16 . The system of  claim 2 , wherein the nonlinear response is from a transducer. 
     
     
         17 . The system of  claim 2 , wherein the nonlinear response results from noise. 
     
     
         18 . The system of  claim 2 , wherein the numerical propagation comprises statistical correlation.