Adaptive background interference removal for Fourier ptychographic microscopy.

Fourier ptychographic microscopy (FPM) imaging is a computational imaging technology that can reconstruct wide-field high-resolution (HR) images. It uses a series of low-resolution images captured by a camera under different illumination angles. The images are stitched in the Fourier domain to expand their spectral range. Under high-angle illumination, a dark-field image is noisy with a low signal-to-noise ratio, which significantly reduces the reconstruction quality of FPM. Conventional reconstruction algorithms often have low FPM imaging performance and efficiency due to optimization strategies. In response to these problems, this paper proposes an FPM imaging method based on an improved phase recovery strategy to optimize the alternating iterative algorithm. The technique uses an improved threshold method to reduce noise in the image preprocessing stage to maximize the retention of high-frequency sample information. Moreover, an adaptive control factor is added in the subsequent iterative update process to balance the sample spectrum function. This study verifies the effectiveness of the proposed method on both simulation and experimental images. The results show that the proposed method can effectively suppress image background noise and has a faster convergence speed and higher robustness. In addition, it can be used to reconstruct HR complex amplitude images of objects under wide field-of-view conditions.

Adaptive denoising method for Fourier ptychographic microscopy

Fourier ptychographic microscopy (FPM) is a newly developed microscopic technique for large field of view, high-resolution and quantitative phase imaging by combining the techniques from ptychographic imaging, aperture synthesizing and phase retrieval. In FPM, an LED array is utilized to illuminate the specimen from different angles and the corresponding intensity images are synthesized to reconstruct a high-resolution complex field. As a flexible and low-cost approach to achieve high-resolution, wide-field and quantitative phase imaging, FPM is of enormous potential in biomedical applications such as hematology and pathology. Conventionally, the FPM reconstruction problem is solved by using a phase retrieval method, termed Alternate Projection. By iteratively updating the Fourier spectrum with low-resolution-intensity images, the result converges to a high-resolution complex field. Here we propose a new FPM reconstruction framework with deep learning methods and design a multiscale, deep residual neural network for FPM reconstruction. We employ the widely used open-source deep learning library PyTorch to train and test our model and carefully choose the hyperparameters of our model. To train and analyze our model, we build a large-scale simulation dataset with an FPM imaging model and an actual dataset captured with an FPM system. The simulation dataset and actual dataset are separated as training datasets and test datasets, respectively. Our model is trained with the simulation training dataset and fine tuned with the fine-tune dataset, which contains actual training data. Both our model and the conventional method are tested on the simulation test dataset and the actual test dataset to evaluate the performances. We also show the reconstruction result of another neural network-based method for comparison. The experiments demonstrate that our model achieves better reconstruction results and consumes much less time than conventional methods. The results also point out that our model is more robust under system aberrations such as noise and blurring (fewer intensity images) compared with conventional methods.

The integration of neural network and physical reconstruction model for Fourier ptychographic microscopy

White blood cells (WBC) play a significant role in human immune system, so WBC detection is a meaningful work. In this paper, we propose a novel framework which combines Fourier ptychographic microscopy (FPM) and SO-you only look once (YOLO) for WCB detection. FPM is a recently developed microscope technology which can achieve high-resolution, wide-field, and quantitative phase imaging at the same time without mechanical moving and phase measurement. With the FPM, we can get high resolution, wide field-of-view blood cell images at one time. After obtaining high-resolution images, we propose SO-YOLO as our detection method. As a convolutional neural network, the SO-YOLO outperforms the state-of-the-art detection methods both in accuracy and speed. The proposed framework in this paper can be used in clinical diagnose, because the experiment setup is flexible and the detection is fast. The data set in this paper is made with FPM by ourselves. Our data set contains 1000 color high resolution images and all the WBC has been detected and counted by a human expert. The detection results by the experts are regarded as the ground truth. The experiment results show that the SO-YOLO performs well in detecting small objects compared with other methods.

Fourier ptychography microscopy (FPM) has made significant progress since its invention in 2013, thanks to its adaptable nature, high resolution, and vast field-of-view capabilities. FPM is used in various medical applications across multiple optical wavelengths, from automated digital pathology to radiology and ultraviolet label-free imaging. This review explores the fundamental physical and computational concepts that have driven advancements in digital pathology using FPM. A crucial part of the progress has been the development of computational algorithms, which have directly contributed to the improvements in FPM. We evaluate early-stage algorithms like the Gerchberg-Saxton and highlight how phase-retrieval and deep-learning advancements have propelled FPM forward. Additionally, we discuss the impact of these algorithms on digital pathology for potential automated diagnosis, providing a comprehensive explanation of their influence on medical imaging and offering insights into future researchdirections.

Phase retrieval is an important tool to unveil wavefront of light, especially in high performance microscopy such as Fourier ptychographic microscopy (FPM). In general phase-retrieval methods, the resolution and the number of measurements are in a trade-off relationship. Inspired by FPM, we devise what we believe is a novel microscopic phase-retrieval method, termed single-shot FPM (SSFPM). In our approach, the imaging performance exceeds the trade-off relationship in that it enables phase retrieval for high resolution with a single measurement. By placing the lens array at the Fourier plane of the objective lens, multiple intensity profiles required for the FPM algorithm are collected in a single shot. To achieve enough redundancy of data for satisfying convergence condition of FPM, the specimen is simultaneously illuminated by multiple light-emitting diodes. SSFPM reconstructs quantitative phase profile and enhances the resolution sacrificed by applying lens-array imaging. We demonstrate the performance of SSFPM with numerical simulation and experiments. The prototype achieves lateral resolution of 3.10 μm over a field of view of 0.34 mm2. Without an interferometer or scanning devices, SSFPM can reconstruct high resolution of a complex profile with a single shot.

Fourier ptychographic microscopy (FPM) is an attractive method to extend the resolution beyond the conventional limit defined by a microscope optics, sharing properties with ptychographic, synthetic aperture imaging and phase retrieval. The algorithm uses a sequence of low-resolution (LR) images acquired under angularly varying illumination to reconstruct a high-resolution (HR) image. However, traditional FPM may trap to the sub-optimal solution, since brute-force replacement in the Fourier domain is applied. To address this problem, we propose here a weighted replacement for Fourier ptychographic microscopy (WFPM). We employ the weighted average of spectrums corresponding to different illumination angle to replace the overlapped regions in the Fourier domain. A series of experimental results demonstrate that the reconstructed image using the proposed WFPM shows a better quality and a faster convergence compared with the results obtained by FPM.

Fourier ptychographic microscopy (FPM) is a powerful computational imaging technique that enables the reconstruction of high-resolution, wide field-of-view complex images by fusing multiple low-resolution intensity measurements obtained under varying illumination angles. In practice, FPM remains sensitive to calibration and, in particular, to the initialization of the pupil function in the non-convex joint recovery of object and pupil. We introduce pupil-initialized FPM (PI-FPM), a physically informed pupil-phase initialization computed directly from standard FPM measurements prior to reconstruction. PI-FPM exploits the relationship between lateral shifts in brightfield images and local pupil-phase gradients, and estimates low-order aberrations via a Zernike least-squares fit. The method is hardware-agnostic, algorithm-independent, and requires no additional calibration or specialized acquisition, enabling retroactive use on existing datasets. Across synthetic and real experiments, PI-FPM improves convergence stability and reconstruction fidelity, with gains up to 8 dB PSNR and robust performance under strong aberrations (up to 2 π radians root mean square (RMS) wavefront error), particularly in outer field regions. As a result, PI-FPM reduces the reliance on expert calibration and significantly enhances the practical applicability of FPM for routine use in real-world imaging scenarios, including large-field whole-slide imaging where outer-field robustness is critical.

Fourier ptychographic microscopy (FPM) is a computational imaging technique that achieves high-resolution complex amplitude reconstruction across a large field of view. However, conventional FPM is fundamentally limited to regions near the optical axis due to violations of the shift-invariance assumption in off-axis areas, resulting in challenging edge-of-field-of-view reconstructions. We propose neural pupil engineering FPM, termed NePE-FPM, a physical model that dynamically shifts the pupil function position during reconstruction instead of fixing the pupil function in the center of the pupil plane. NePE-FPM engineers the pupil function using an implicit neural representation with multi-resolution hash encoding, enabling continuous, smooth shifting of the pupil function without introducing additional physical parameters. By optimizing a feature-domain loss function, NePE-FPM adaptively filters Fourier-space information from low-resolution measurements, achieving accurate off-axis reconstruction without modeling off-axis propagation. Experimental results demonstrate isotropic resolution of 1149 lp/mm across an 11mm2 FOV using a 4×/0.1NA objective. The NePE-FPM bridges the gap between theoretical FPM capabilities and practical whole-slide imaging demands.

Fourier ptychographic microscopy (FPM) is a computational imaging technique developed in recent years. The validity of the final reconstruction results is closely related to many systematic errors, among which the pupil aberration is a key one. Although the traditional FPM can recover the pupil function in the iterative process, it increases the dependence on data redundancy invisibly, and cannot satisfy the high-speed and low redundancy FPM reconstruction with few images. In this paper, a pupil function recovering method based on annular illumination is proposed, which only uses a small number of LEDs matching the NAobj for illumination. In addition, the Zernike polynomial is used to constrain the freedom degree of aberration, to ensure that the object and pupil can be recovered correctly with fewer data. The simulation results show that the proposed method can recover and correct the pupil function within 6 annular bright-field images, which greatly reduces the requirement of data redundancy and provides the possibility for high-speed aberration recovery based on FPM.

Fourier ptychographic microscopy (FPM) is a computational imaging method that gives a significantly increased space-bandwidth product, in practice high resolution combined with a wide field of view. In this article, we propose an improved Fourier Ptychography algorithm based on Fresnel wave propagation integral for wide field-of-view coherent imaging while correcting for the misalignment of the illuminating LED board and calibration of system parameters. In addition, the wave emanating from the LEDs is taken to be parabolic instead of plane wave as done by others. The advantage of this scheme is that it enables to simulate the transition regions between bright and dark field in wide image patches, and hence this feature can be used to estimate the LED misalignment as well as the distortion of the imaging lens. Experimental results are presented for a USAF resolution target and a biological sample for on-axis and off-axis image patches over a wide sample area showing excellent performance of this scheme when compared to the traditional Fraunhofer-model based Fourier Ptychography algorithm. The article summarizes with high technical detail our experiences with developing and implementing improved FPM methods and will hopefully assist other scientists entering this scientific field.

As a typical computational method, Fourier ptychographic microscopy (FPM) can realize high spatial resolution and quantitative phase imaging while preserving the large field of view with a low numerical aperture (NA) objective. A programmable light-emitting diode (LED) array is used as a typical illuminator in an FPM system, and the illumination parameters of each LED element are crucial to the success of the FPM reconstruction algorithm. Compared with LED arrays arranged in rectangular arrays, LED arrays with special structures such as domes or rings can effectively improve FPM imaging results and imaging efficiency. As a trade-off, their calibration difficulty is greatly increased due to the lack of geometric constraints of rectangular arrays. In this paper, we propose an effective hybrid full-pose parameter calibration method for freeform LED array illuminators, combining stereoscopic 3D imaging techniques and the geometric constraints of the microscopic platform. First, a stereovision system is used to obtain the accurate 3D position of each LED element of the freeform illuminator and to construct a rigid 3D coordinate LED array system. Then, calibration between the coordinate system of the LED array and that of the optical imaging component is realized according to the geometric features of the brightfield-to-darkfield edges. Finally, we verify the feasibility and effectiveness of the proposed method through full-pose parameter calibration of LED arrays with different arrangement rules.

Fourier ptychographic microscopy (FPM) is used to achieve high resolution and a large field of view. However, traditional FPM image reconstruction methods often yield poor image quality when encountering out-of-focus issues during reconstruction. Therefore, this study proposes a defocus-distance regression network based on convolutional neural networks. In an experimental validation, the root-mean-square error calculated from 1000 sets of predicted and true values was approximately 6.2 µm. The experimental results suggest that the proposed method has good generalization, maintains high accuracy in predicting defocus distances even for different biological samples, and extends the imaging depth-of-field of the FPM system by a factor of more than 3.

Optical diffraction tomography (ODT) is a promising label-free imaging method capable of quantitatively measuring the three-dimensional (3D) refractive index distribution of transparent samples. In recent years, partially coherent ODT (PC-ODT) has attracted increasing attention due to its system simplicity and absence of laser speckle noise. Quantitative phase imaging (QPI) technologies represented by Fourier ptychographic microscopy (FPM), differential phase contrast (DPC) imaging and intensity diffraction tomography (IDT) need to collect several or hundreds of intensity images, which usually introduce motion artifacts when shooting fast-moving targets, leading to a decrease in image quality. Hence, a quantitative real-time phase microscopy (qRPM) for extended depth of field (DOF) imaging based on 3D single-shot differential phase contrast (ssDPC) imaging method is proposed in this research study. qRPM incorporates a microlens array (MLA) to simultaneously collect spatial information and angular information. In subsequent optical information processing, a deconvolution method is used to obtain intensity stacks under different illumination angles in a raw light field image. Importing the obtained intensity stack into the 3D DPC imaging model is able to finally obtain the 3D refractive index distribution. The captured four-dimensional light field information enables the reconstruction of 3D information in a single snapshot and extending the DOF of qRPM. The imaging capability of the proposed qRPM system is experimental verified on different samples, achieve single-exposure 3D label-free imaging with an extended DOF for 160 µm which is nearly 30 times higher than the traditional microscope system.