Totagraphy: Coherent Diffractive/Digital Information Reconstruction by Iterative Phase Recovery Using Special Masks

A system for recovering phase information from an input wave comprising:

• an optical lens system having an input with a spectral output;
• at least two physical spatial masks including at least one pair of masks binary in amplitude, wherein the masks in a pair are complementary with each other with respect to amplitude, each of the at least two physical spatial masks being disposed at the input of the optical lens system for receiving the input wave;
• wherein the at least two physical spatial masks are configured to separately modify the input wave, and wherein the optical lens system effects a generalized Fourier transform on each of the separately modified waves to produce a transformed wave from each of the separately modified input waves;
• at least one sensor system configured to record amplitude values at an array of points of each transformed wave at the spectral plane to produce a phasorgram from each transformed wave;
• and
• a digital processor configured to:
• associate a phase value with each point on each phasorgram to form a plurality of complex phasorgrams;
• and
• iteratively process the plurality of complex phasorgrams until convergence is achieved to produce a totagram constituting a reconstructed input wave with amplitude and phase information.

A method for recovering phase information from an array of points, each point having an amplitude, the method comprising:

• providing at least one transformation unit having an input and a spectral output and at least two masks including at least one pair of masks binary in amplitude, wherein the masks in a pair are complementary with each other with respect to amplitude, each of the at least two masks configured to operate upon the input of the at least one transformation unit;
• separately applying the array of points at the input to each of the at least two masks to generate a modified input from each of the masks;
• performing, by the at least one transformation unit, a generalized Fourier transform on each modified input to produce a transformed modified input from each modified input;
• recording amplitude values at an array of points of each transformed modified input to produce phasorgrams;
• associating a phase value with each point on each phasorgram to form a plurality of complex phasorgrams;
• and
• iteratively processing the plurality of complex phasorgrams until convergence is achieved to produce a totagram constituting a reconstructed input with amplitude and phase information, wherein iteratively processing the plurality of complex phasorgrams comprises:
• (a) processing the plurality of complex phasorgrams to obtain a single estimate of the input by performing on the complex phasorgrams an inverse generalized Fourier transform and averaging complex information at each point at corresponding locations;
• (b) passing the single estimate of the input through a process replicating each of the masks to obtain a plurality of intermediate arrays;
• (c) performing a generalized fast Fourier transform on each of the intermediate arrays and replacing amplitude values at each point in the transformed intermediate arrays with corresponding recorded amplitude values, to generate another plurality of complex phasorgrams;
• and
• (d) repeating step (a) for another plurality of complex phasorgrams followed by steps (b) and (c) until convergence is achieved, wherein upon completion the single estimate of the input is the totagram.