System calibration method for Fourier ptychographic microscopy

Fourier ptychographic microscopy (FPM) is a recently proposed quantitative phase imaging technique with high resolution and wide field-of-view (FOV). In current FPM imaging platforms, systematic error sources come from the aberrations, LED intensity fluctuation, parameter imperfections and noise, which will severely corrupt the reconstruction results with artifacts. Although these problems have been researched and some special methods have been proposed respectively, there is no method to solve all of them. However, the systematic error is a mixture of various sources in the real situation. It is difficult to distinguish a kind of error source from another due to the similar artifacts. To this end, we report a system calibration procedure, termed SC-FPM, based on the simulated annealing (SA) algorithm, LED intensity correction and adaptive step-size strategy, which involves the evaluation of an error matric at each iteration step, followed by the re-estimation of accurate parameters. The great performance has been achieved both in simulation and experiments. The reported system calibration scheme improves the robustness of FPM and relaxes the experiment conditions, which makes the FPM more pragmatic.Comment: 18 pages, 9 figure

Coherence retrieval using trace regularization

The mutual intensity and its equivalent phase-space representations quantify an optical field's state of coherence and are important tools in the study of light propagation and dynamics, but they can only be estimated indirectly from measurements through a process called coherence retrieval, otherwise known as phase-space tomography. As practical considerations often rule out the availability of a complete set of measurements, coherence retrieval is usually a challenging high-dimensional ill-posed inverse problem. In this paper, we propose a trace-regularized optimization model for coherence retrieval and a provably-convergent adaptive accelerated proximal gradient algorithm for solving the resulting problem. Applying our model and algorithm to both simulated and experimental data, we demonstrate an improvement in reconstruction quality over previous models as well as an increase in convergence speed compared to existing first-order methods.Comment: 28 pages, 10 figures, accepted for publication in SIAM Journal on Imaging Science

Identification and adaptive control of a high-contrast focal plane wavefront correction system

All coronagraphic instruments for exoplanet high-contrast imaging need wavefront correction systems to reject optical aberrations and create sufficiently dark holes. Since the most efficient wavefront correction algorithms (controllers and estimators) are usually model-based, the modeling accuracy of the system influences the ultimate wavefront correction performance. Currently, wavefront correction systems are typically approximated as linear systems using Fourier optics. However, the Fourier optics model is usually biased due to inaccuracies in the layout measurements, the imperfect diagnoses of inherent optical aberrations, and a lack of knowledge of the deformable mirrors (actuator gains and influence functions). Moreover, the telescope optical system varies over time because of instrument instabilities and environmental effects. In this paper, we present an expectation-maximization (E-M) approach for identifying and real-time adapting the linear telescope model from data. By iterating between the E-step (a Kalman filter and a Rauch smoother) and the M-step (analytical or gradient-based optimization), the algorithm is able to recover the system even if the model depends on the electric fields, which are unmeasurable hidden variables. Simulations and experiments in Princeton's High Contrast Imaging Lab demonstrate that this algorithm improves the model accuracy and increases the efficiency and speed of the wavefront correction