Phase retrieval from speckle patterns of ordering systems.
The time dependence of the Fourier transform phase of coherently scattered radiation from a system undergoing ordering is studied. Specifically, we derive a simple model that takes into account the known scaling laws for ordering dynamics to predict the statistical behavior of the Fourier transform phase. We consider a two-dimensional system of domains undergoing ordering for both the nonconserved and conserved order-parameter cases (models A and B, respectively). Predictions from our model are compared with numerical experiments, where a time-dependant Ginzburg-Landau equation is integrated to compute the dynamics of the real-space system; then a simple numerical (discrete) Fourier transform is applied to compute the Fourier phase as well as the amplitude (directly related to scattering intensity). An average phase-decorrelation time (the average time it takes for the phase to change by a specific amount) is obtained using both our theoretical model and the numerical results. This quantity is then used to implement a phase-retrieval strategy that consists of measuring scattering intensities of the same nonequilibrium system at different times and then applying an iterative phase-retrieval algorithm (like Fienup's hybrid input-output) recursively with improved initial estimates for faster convergence and higher convergence rates.
Montiel
David
D
Physics Department and Centre for the Physics of Materials, McGill University, Rutherford Building, 3600 Rue University, Montréal, Québec, Canada.
Sutton
Mark
M
Grant
Martin
M