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While characterization of coherent wavefields is essential to laser, x-ray and electron imaging, sensors measure the squared magnitude of the field, rather than the field itself. Holography or phase retrieval must be used to characterize the field. The need for a reference severely restricts the utility of holography. Phase retrieval, in contrast, is theoretically consistent with sensors that directly measure coherent or partially coherent fields with no prior assumptions. Unfortunately, phase retrieval has not yet been successfully implemented for large-scale fields. Here we show that both holography and phase retrieval are capable of quantum-limited coherent signal estimation and we describe phase retrieval strategies that approach the quantum limit for >1 megapixel fields. These strategies rely on group testing using networks of interferometers, such as might be constructed using emerging integrated photonic, plasmonic and/or metamaterial devices. Phase-sensitive sensor planes using such devices could eliminate the need both for lenses and reference signals, creating a path to large aperture diffraction limited laser imaging.
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Phase retrieval approaches based on DL provide a framework to obtain phase information from an intensity hologram or diffraction pattern in a robust manner and in real time. However, current DL architectures applied to the phase problem rely i) on paired datasets, i.e., they are only applicable when a satisfactory solution of the phase problem has been found, and ii) on the fact that most of them ignore the physics of the imaging process. Here, we present PhaseGAN, a new DL approach based on Generative Adversarial Networks, which allows the use of unpaired datasets and includes the physics of image formation. Performance of our approach is enhanced by including the image formation physics and provides phase reconstructions when conventional phase retrieval algorithms fail, such as ultra-fast experiments. Thus, PhaseGAN offers the opportunity to address the phase problem when no phase reconstructions are available, but good simulations of the object or data from other experiments are available, enabling us to obtain results not possible before.
In order to increase signal-to-noise ratio in measurement, most imaging detectors sacrifice resolution to increase pixel size in confined area. Although the pixel super-resolution technique (PSR) enables resolution enhancement in such as digital holographic imaging, it suffers from unsatisfied reconstruction quality. In this work, we report a high-fidelity plug-and-play optimization method for PSR phase retrieval, termed as PNP-PSR. It decomposes PSR reconstruction into independent sub-problems based on the generalized alternating projection framework. An alternating projection operator and an enhancing neural network are derived to tackle the measurement fidelity and statistical prior regularization, respectively. In this way, PNP-PSR incorporates the advantages of individual operators, achieving both high efficiency and noise robustness. We compare PNP-PSR with the existing PSR phase retrieval algorithms with a series of simulations and experiments, and PNP-PSR outperforms the existing algorithms with as much as 11dB on PSNR. The enhanced imaging fidelity enables one-order-of-magnitude higher cell counting precision.
We present a parameter retrieval method which combines ptychography and additional prior knowledge about the object. The proposed method is applied to two applications: (1) parameter retrieval of small particles from Fourier ptychographic dark field measurements; (2) parameter retrieval of retangule with real-space ptychography. The influence of Poisson noise is discussed in the second part of the paper. The Cram{e}r Rao Lower Bound in both two applications is computed and Monte Carlo analysis is used to verify the calculated lower bound. With the computation results we report the lower bound for various noise levels and the correlation of particles in Application 1. For Application 2 the correlation of parameters of the rectangule is discussed.
Fourier phase retrieval is a classical problem that deals with the recovery of an image from the amplitude measurements of its Fourier coefficients. Conventional methods solve this problem via iterative (alternating) minimization by leveraging some prior knowledge about the structure of the unknown image. The inherent ambiguities about shift and flip in the Fourier measurements make this problem especially difficult; and most of the existing methods use several random restarts with different permutations. In this paper, we assume that a known (learned) reference is added to the signal before capturing the Fourier amplitude measurements. Our method is inspired by the principle of adding a reference signal in holography. To recover the signal, we implement an iterative phase retrieval method as an unrolled network. Then we use back propagation to learn the reference that provides us the best reconstruction for a fixed number of phase retrieval iterations. We performed a number of simulations on a variety of datasets under different conditions and found that our proposed method for phase retrieval via unrolled network and learned reference provides near-perfect recovery at fixed (small) computational cost. We compared our method with standard Fourier phase retrieval methods and observed significant performance enhancement using the learned reference.
Signal recovery from nonlinear measurements involves solving an iterative optimization problem. In this paper, we present a framework to optimize the sensing parameters to improve the quality of the signal recovered by the given iterative method. In particular, we learn illumination patterns to recover signals from coded diffraction patterns using a fixed-cost alternating minimization-based phase retrieval method. Coded diffraction phase retrieval is a physically realistic system in which the signal is first modulated by a sequence of codes before the sensor records its Fourier amplitude. We represent the phase retrieval method as an unrolled network with a fixed number of layers and minimize the recovery error by optimizing over the measurement parameters. Since the number of iterations/layers are fixed, the recovery incurs a fixed cost. We present extensive simulation results on a variety of datasets under different conditions and a comparison with existing methods. Our results demonstrate that the proposed method provides near-perfect reconstruction using patterns learned with a small number of training images. Our proposed method provides significant improvements over existing methods both in terms of accuracy and speed.
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