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Phase retrieval from speckle patterns of ordering systems.

David Montiel¹, Mark Sutton, Martin Grant

¹Physics Department and Centre for the Physics of Materials, McGill University, Rutherford Building, 3600 Rue University, Montréal, Québec, Canada.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|November 13, 2009

Summary

We developed a model to predict the statistical behavior of Fourier transform phase in ordering systems. This model aids in phase retrieval by analyzing scattering intensities over time for improved convergence.

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Area of Science:

Condensed Matter Physics
Materials Science
Statistical Mechanics

Background:

Ordering dynamics in systems are crucial for understanding phase transitions.
Fourier transform phase provides insights into system structure and evolution.
Phase retrieval is essential for reconstructing real-space images from scattering data.

Purpose of the Study:

To model the time dependence of the Fourier transform phase in ordering systems.
To predict the statistical behavior of the Fourier transform phase using scaling laws.
To implement an efficient phase-retrieval strategy for nonequilibrium systems.

Main Methods:

Derivation of a theoretical model incorporating ordering dynamics scaling laws.
Numerical integration of the time-dependent Ginzburg-Landau equation for real-space dynamics.
Application of discrete Fourier transform to compute Fourier phase and amplitude.
Calculation of average phase-decorrelation time from theoretical and numerical results.

Main Results:

A model predicting Fourier transform phase behavior in 2D ordering systems (models A and B) was developed.
Numerical experiments validated the model's predictions for phase and amplitude dynamics.
Average phase-decorrelation time was accurately determined using both theoretical and numerical approaches.

Conclusions:

The derived model effectively captures the statistical behavior of Fourier transform phase during ordering.
The calculated phase-decorrelation time enables an improved phase-retrieval strategy.
Recursive application of iterative algorithms with enhanced initial estimates accelerates convergence and improves accuracy in phase retrieval.