Totagraphy: coherent diffractive/digital information reconstruction by iterative phase recovery using reference wave
A totagram is produced by an iterative spectral phase recovery process resulting in complete information recovery using special masks and using a reference beam. Using these special masking systems reduce computation time, number of masks, and number of iterations. Adding a reference wave to the iterative process provides better phase recovery systems and aid in the preventing of phase wrapping. The reference wave is added on-axis to provide a well-controlled amplitude. The reference wave is added after the physical or digital transformation system and subtracted before recording the initial amplitude.
1. A method for recovering phase information of an input from a coherent wave, the method comprising:
providing at least one transformation unit with an input plane and an output plane;
providing at least two masks one of which is a unity mask, each of the at least two masks configured to be disposed at the input plane;
separately applying the coherent wave at the input plane to each of the at least two masks to generate a modified input from each of the masks;
passing the modified inputs through the at least one transformation unit, wherein the at least one transformation units performs a generalized Fourier transform on each modified input to produce at its output plane a transformed modified input from each modified input;
combining a reference wave with each transformed modified input to produce a combined wave from each transformed modified input;
recording amplitude values at an array of points of each combined wave to produce phasorgrams;
associating a phase value with each point on each phasorgram to form a plurality of complex phasorgrams;
subtracting the reference wave from each of the complex phasorgrams; and
iteratively processing the plurality of complex phasorgrams after having been through subtraction, until convergence is achieved to produce a totagram constituting a reconstructed input with amplitude and phase information.
2. The method of claim 1 , wherein each mask includes an outer border that blocks an outer periphery of the coherent wave.
3. The method of claim 1 , further comprising switching from one of the at least two masks to another of the at least two masks such that the coherent wave is individually received sequentially in time by each of the at least two masks.
4. The method of claim 1 , further comprising splitting the coherent wave so that it is individually received in parallel by each of the at least two masks.
5. The method of claim 1 , wherein the at least two masks consist of the unity mask and a complex phase mask.
6. The method of claim 5 , wherein the complex phase mask comprises a bipolar binary mask.
7. The method of claim 1 , wherein the at least two masks consist of the unity mask and a pair of complementary unipolar binary masks.
8. The method of claim 1 , wherein the at least two masks are implemented in real time by optical devices including any of spatial light modulators and micromirror arrays.
9. The method of claim 1 , wherein recording is performed by an intensity sensor.
10. The method of claim 1 , further comprising, after completion, using the totagram to generate a representation of the information embedded in the reconstructed amplitude and phase.
11. The method of claim 1 , wherein the transformation unit comprises a lens system and the output plane is the focal plane of the lens system.
12. The method of claim 1 , wherein each reference wave arrives in parallel to each transformed modified input when combining.
13. A system for recovering phase information of an input from a coherent wave comprising:
a transformation unit having an input plane and an output;
at least two masks, one of which is a unity mask, each of the at least two masks being disposed at the input plane of the transformation unit for receiving the coherent wave;
wherein the at least two masks are configured to separately modify the coherent wave, and wherein the transformation unit effects a generalized Fourier transform on each of the separately modified waves to produce a transformed wave from each of the separately modified waves;
a reference wave source;
an optical beam combiner which combines the reference wave with each transformed wave to produce a combined wave from each transformed wave;
at least one sensor system configured to record amplitude values at an array of points of each combined wave to produce a phasorgram from each combined wave; and
a digital processor configured to:
associate a phase value with each point on each phasorgram to form a plurality of complex phasorgrams;
subtract the reference wave from each of the complex phasorgrams; and then 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.
14. The system of claim 13 , wherein the at least two masks consist of the unity mask and a bipolar binary mask.
15. The system of claim 13 , wherein the at least two masks consist of the unity mask and a pair of complementary unipolar binary masks.
16. The system of claim 13 , wherein each mask is surrounded by an outer border that blocks the coherent wave.
17. The system of claim 13 , wherein to iteratively process 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, adding reference wave values to corresponding points in the transformed intermediate arrays, replacing amplitude values at each point with corresponding recorded amplitude values and then subtracting reference wave values from corresponding points to generate another plurality of complex phasorgrams; and
(d) repeating step (a) for the 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.
18. The system of claim 17 , wherein convergence is determined by any of (1) when a difference between successive single estimates reach a predetermined threshold, and (2) when a given number of iterations of step (a) is completed.
19. The system of claim 13 , wherein the at least two masks are configured so as to switch from one of the at least two masks to another of the at least two masks such that the coherent wave is individually received in sequence by each of the at least two masks.
20. The system of claim 13 , further comprising a beam splitter arranged to split the coherent wave so that it is individually received in parallel by each of the at least two masks.
21. The system of claim 13 , wherein the transformation unit comprises a lens system and the output corresponds to a focal plane of the lens system.
22. The system of claim 13 , wherein each reference wave is parallel to each transformed modified input at the optical beam combiner.
23. The system of claim 13 , wherein the masks are made from a photographic film or plate.
24. The system of claim 23 , further comprising a shutter system between the object and the at least two masks.
25. The system of claim 23 , wherein the sensor system comprises two cameras, a first camera recording the amplitude values at an array of points of a combined wave passing through the unity mask and a second camera recording the amplitude values at an array of points of a combined wave passing through the other mask.