Traditional imaging systems exhibit a well-known trade-off between the resolution and the field of view of their captured images. Typical cameras and microscopes can either “zoom in” and image at high-resolution, or they can “zoom out” to see a larger area at lower resolution, but can rarely achieve both effects simultaneously. In this review, we present details about a relatively new procedure termed Fourier ptychography (FP), which addresses the above trade-off to produce gigapixel-scale images without requiring any moving parts. To accomplish this, FP captures multiple low-resolution, large field-of-view images and computationally combines them in the Fourier domain into a high-resolution, large field-of-view result. Here, we present details about the various implementations of FP and highlight its demonstrated advantages to date, such as aberration recovery, phase imaging, and 3D tomographic reconstruction, to name a few. After providing some basics about FP, we list important details for successful experimental implementation, discuss its relationship with other computational imaging techniques, and point to the latest advances in the field while highlighting persisting challenges.

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Fourier ptychography: current applications and future promises

The competition between resolution and the imaging field of view is a long-standing problem in traditional imaging systems — they can produce either an image of a small area with fine details or an image of a large area with coarse details. Fourier ptychography (FP) is an approach for tackling this intrinsic trade-off in imaging systems. It takes the challenge of high-throughput and high-resolution imaging from the domain of improving the physical limitations of optics to the domain of computation. It also enables post-measurement computational correction of optical aberrations. We present the basic concept of FP, compare it to related imaging modalities and then discuss experimental implementations, such as aperture-scanning FP, macroscopic camera-scanning FP, reflection mode, single-shot set-up, X-ray FP, speckle-scanning scheme and deep-learning-related implementations. Various applications of FP are discussed, including quantitative phase imaging in 2D and 3D, digital pathology, high-throughput cytometry, aberration metrology, long-range imaging and coherent X-ray nanoscopy. A collection of datasets and reconstruction codes is provided for readers interested in implementing FP themselves. Fourier ptychography is an imaging approach that addresses the intrinsic trade-off between resolution and field of view in optical systems and provides computational correction of optical aberrations. This Technical Review surveys its implementations and applications.

Concept, implementations and applications of Fourier ptychography

In response to a perceived need in the vision community, an OSA taskforce was formed at the 1999 topical meeting on vision science and its applications (VSIA-99) and charged with developing consensus recommendations on definitions, conventions, and standards for reporting of optical aberrations of human eyes. Progress reports were presented at the 1999 OSA annual meeting and at VSIA-2000 by the chairs of three taskforce subcommittees on (1) reference axes, (2) describing functions, and (3) model eyes.

Standards for reporting the optical aberrations of eyes

Physics-guided Neural Networks (PGNNs) represent an emerging class of neural networks that are trained using physics-guided (PG) loss functions (capturing violations in network outputs with known physics), along with the supervision contained in data. Existing work in PGNNs have demonstrated the efficacy of adding single PG loss functions in the neural network objectives, using constant trade-off parameters, to ensure better generalizability. However, in the presence of multiple physics loss functions with competing gradient directions, there is a need to adaptively tune the contribution of competing PG loss functions during the course of training to arrive at generalizable solutions. We demonstrate the presence of competing PG losses in the generic neural network problem of solving for the lowest (or highest) eigenvector of a physics-based eigenvalue equation, common to many scientific problems. We present a novel approach to handle competing PG losses and demonstrate its efficacy in learning generalizable solutions in two motivating applications of quantum mechanics and electromagnetic propagation. All the code and data used in this work is available at this https URL.

CoPhy-PGNN: Learning Physics-guided Neural Networks with Competing Loss Functions for Solving Eigenvalue Problems

Fourier ptychography microscopy(FPM) is a recently developed computational imaging approach for microscopic super-resolution imaging. By turning on each light-emitting-diode (LED) located on different position on the LED array sequentially and acquiring the corresponding images that contain different spatial frequency components, high spatial resolution and quantitative phase imaging can be achieved in the case of large field-of-view. Nevertheless, FPM has high requirements for the system construction and data acquisition processes, such as precise LEDs position, accurate focusing and appropriate exposure time, which brings many limitations to its practical applications. In this paper, inspired by artificial neural network, we propose a Fourier ptychography multi-parameter neural network (FPMN) with composite physical prior optimization. A hybrid parameter determination strategy combining physical imaging model and data-driven network training is proposed to recover the multi layers of the network corresponding to different physical parameters, including sample complex function, system pupil function, defocus distance, LED array position deviation and illumination intensity fluctuation, etc. Among these parameters, LED array position deviation is recovered based on the features of brightfield to darkfield transition low-resolution images while the others are recovered in the process of training of the neural network. The feasibility and effectiveness of FPMN are verified through simulations and actual experiments. Therefore FPMN can evidently reduce the requirement for practical applications of FPM.

Fourier ptychography multi-parameunter neural network with composite physical priori optimization.

Significance: Fourier ptychography (FP) is a computational imaging approach that achieves high-resolution reconstruction. Inspired by neural networks, many deep-learning-based methods are proposed to solve FP problems. However, the performance of FP still suffers from optical aberration, which needs to be considered.
Aim: We present a neural network model for FP reconstructions that can make proper estimation toward aberration and achieve artifact-free reconstruction.
Approach: Inspired by the iterative reconstruction of FP, we design a neural network model that mimics the forward imaging process of FP via TensorFlow. The sample and aberration are considered as learnable weights and optimized through back-propagation. Especially, we employ the Zernike terms instead of aberration to decrease the optimization freedom of pupil recovery and perform a high-accuracy estimation. Owing to the auto-differentiation capabilities of the neural network, we additionally utilize total variation regularization to improve the visual quality.
Results: We validate the performance of the reported method via both simulation and experiment. Our method exhibits higher robustness against sophisticated optical aberrations and achieves better image quality by reducing artifacts.
Conclusions: The forward neural network model can jointly recover the high-resolution sample and optical aberration in iterative FP reconstruction. We hope our method that can provide a neural-network perspective to solve iterative-based coherent or incoherent imaging problems.

https://www.spiedigitallibrary.org/journals/journal-of-biomedical-optics/volume-26/issue-3/036502/Neural-network-model-assisted-Fourier-ptychography-with-Zernike-aberration-recovery/10.1117/1.JBO.26.3.036502.pdf

Neural network model assisted Fourier ptychography with Zernike aberration recovery and total variation constraint.

Fourier ptychography (FP) is a newly developed computational imaging approach that achieves both high resolution and wide field of view by stitching a series of low-resolution images captured under angle-varied illumination. So far, many supervised data-driven models have been applied to solve inverse imaging problems. These models need massive amounts of data to train, and are limited by the dataset characteristics. In FP problems, generic datasets are always scarce, and the optical aberration varies greatly under different acquisition conditions. To address these dilemmas, we model the forward physical imaging process as an interpretable physics-guided neural network (PgNN), where the reconstructed image in the complex domain is considered as the learnable parameters of the neural network. Since the optimal parameters of the PgNN can be derived by minimizing the difference between the model-generated images and real captured angle-varied images corresponding to the same scene, the proposed PgNN can get rid of the problem of massive training data as in traditional supervised methods. Applying the alternate updating mechanism and the total variation regularization, PgNN can flexibly reconstruct images with improved performance. In addition, the Zernike mode is incorporated to compensate for optical aberrations to enhance the robustness of FP reconstructions. As a demonstration, we show our method can reconstruct images with smooth performance and detailed information in both simulated and experimental datasets. In particular, when validated in an extension of a high-defocus, high-exposure tissue section dataset, PgNN outperforms traditional FP methods with fewer artifacts and distinguishable structures.

Xinfeng Zhang

Papers

Neural network model assisted Fourier ptychography with Zernike aberration recovery and total variation constraint.

PgNN: Physics-guided Neural Network for Fourier Ptychographic Microscopy.