Fourier Ptychography Research Articles

200mm Optical synthetic aperture imaging over 120 meters distance via Macroscopic Fourier ptychography

200mm Optical synthetic aperture imaging over 120 meters distance via Macroscopic Fourier ptychography

Fourier Ptychographic Coherent Anti-Stokes Raman Scattering Microscopy with Point-Scanning for Super-Resolution Imaging.

Fourier ptychography (FP) is a high resolution wide-field imaging method based on the extended aperture in the Fourier space, which is synthesized from raw images with varying illumination angles. If FP is extended to coherent nonlinear optical imaging, the resolution could be further improved due to the increase of the cutoff frequency of the synthesized coherent optical transfer function (C-OTF) with respect to the order of nonlinear optical processes. However, there is a fundamental conflict between wide-field FP and nonlinear optical imaging, whereby the nonlinear optical imaging typically requires a focused excitation laser beam with high power density. To tackle the problem, in this work, a unique point-scanning FP (PS-FP) method is presented for super-resolution nonlinear optical imaging, in which the nonlinear optical signal is obtained by using focused laser beam, while the conventional FP algorithm can still be used to retrieve the super-resolution image. PS-FP coherent anti-Stokes Raman scattering (PS-FP-CARS) imaging on a variety of samples, where a 1.8-fold expansion of the OTF is achieved experimentally for enhancing vibrational imaging. Further theoretical calculation shows that the C-OTF of PS-FP higher-order CARS (PS-FP-HO-CARS) can be expanded up to ≈4.9-fold, thereby improving the spatial resolution by ≈3-fold in comparison with conventional point-scanning CARS with under tightly focused beams. The generality of PS-FP method developed in this work can be adapted to other coherent nonlinear optical imaging modalities for super-resolution imaging in tissue and cells.

Space-time Fourier ptychography for in vivo quantitative phase imaging

Quantitative phase imaging of living biological specimens is challenging due to their continuous movement and complex behavior. Here, we introduce space-time Fourier ptychography (ST-FP), which combines a fast Fourier ptychography (FP) model based on compressive sensing with space-time motion priors for joint reconstruction of quantitative phase, intensity, and motion fields across consecutive frames. Using the same input data as compressive sensing FP, ST-FP increases the space-bandwidth-time product of the reconstructed complex image sequence while leveraging redundant temporal information to achieve robust reconstruction performance. The efficacy of this approach is demonstrated across various applications, particularly in observing living microorganisms undergoing rapid morphological changes and reconstructing amplitude and phase targets in motion. The improved phase retrieval capability of ST-FP enables digital refocusing, facilitating comprehensive three-dimensional analysis of microorganisms. This advancement paves the way for enhanced visualization of cellular processes, developmental biology studies, and investigations into life mechanics at the microscopic level.

Deep-ultraviolet Fourier ptychography (DUV-FP) for label-free biochemical imaging via feature-domain optimization

We present deep-ultraviolet Fourier ptychography (DUV-FP) for high-resolution chemical imaging of biological specimens in their native state without exogenous stains. This approach uses a customized 265-nm DUV LED array for angle-varied illumination, leveraging the unique DUV absorption properties of biomolecules at this wavelength region. We implemented a robust feature-domain optimization framework to overcome common challenges in Fourier ptychographic reconstruction, including vignetting, pupil aberrations, stray light problems, intensity variations, and other systematic errors. By using a 0.12 numerical aperture low-resolution objective lens, our DUV-FP prototype can resolve the 345-nm linewidth on a resolution target, demonstrating at least a four-fold resolution gain compared to the captured raw images. Testing on various biospecimens demonstrates that DUV-FP significantly enhances absorption-based chemical contrast and reveals detailed structural and molecular information. To further address the limitations of conventional FP in quantitative phase imaging, we developed a spatially coded DUV-FP system. This platform enables true quantitative phase imaging of biospecimens with DUV light, overcoming the non-uniform phase response inherent in traditional microscopy techniques. The demonstrated advancements in high-resolution, label-free chemical imaging may accelerate developments in digital pathology, potentially enabling rapid, on-site analysis of biopsy samples in clinical settings.

Development and Assessment of Multiple Illumination Color Fourier Ptychographic Microscopy for High Throughput Sample Digitization.

In this study, we proposed a multiplexed color illumination strategy to improve the data acquisition efficiency of Fourier ptychography microscopy (FPM). Instead of sequentially lighting up one single channel LED, our method turns on multiple white light LEDs for each image acquisition via a color camera. Thus, each raw image contains multiplexed spectral information. An FPM prototype was developed, which was equipped with a 4×/0.13 NA objective lens to achieve a spatial resolution equivalent to that of a 20×/0.4 NA objective lens. Both two- and four-LED illumination patterns were designed and applied during the experiments. A USAF 1951 resolution target was first imaged under these illumination conditions, based on which MTF curves were generated to assess the corresponding imaging performance. Next, H&E tissue samples and analyzable metaphase chromosome cells were used to evaluate the clinical utility of our strategy. The results show that the single and multiplexed (two- or four-LED) illumination results achieved comparable imaging performance on all the three channels of the MTF curves. Meanwhile, the reconstructed tissue or cell images successfully retain the definition of cell nuclei and cytoplasm and can better preserve the cell edges as compared to the results from the conventional microscopes. This study initially validates the feasibility of multiplexed color illumination for the future development of high-throughput FPM scanning systems.

Anisotropic regularization for sparsely sampled and noise-robust Fourier ptychography.

Fourier ptychography (FP) is a powerful computational imaging technique that provides super-resolution and quantitative phase imaging capabilities by scanning samples in Fourier space with angle-varying illuminations. However, the image reconstruction in FP is inherently ill-posed, particularly when the measurements are noisy and have insufficient data redundancy in the Fourier space. To improve FP reconstruction in high-throughput imaging scenarios, we propose a regularized FP reconstruction algorithm utilizing anisotropic total variation (TV) and Tikhonov regularizations for the object and pupil functions, respectively. To solve this regularized FP problem, we formulate a reconstruction algorithm using the alternating direction method of multipliers and show that our approach successfully recovers high-quality images with sparsely sampled and/or noisy measurements. The results are quantitatively and qualitatively compared against various FP reconstruction algorithms to analyze the effect of regularization under harsh imaging conditions. In particular, we demonstrate the effectiveness of our method on the real experimental FP microscopy images, where the TV regularizer effectively suppresses the measurement noise while maintaining the edge information in the biological specimen and helps retrieve the correct amplitude and phase images even under insufficient sampling.

Can deep neural networks work with amplitude and phase input of defocused images?

Deep neural network (DNN) models, particularly convolutional neural networks (CNNs), have demonstrated remarkable performance in biomedical image classification due to their ability to automatically learn features from large datasets. One common challenge in the preparation of large, microscopic datasets for DNN tasks is sample defocusing, potentially impairing the model performance. To handle defocusing, computational imaging, or specifically quantitative phase imaging (QPI), performs digital refocusing by using both the phase and the amplitude of the complex optical field. This leads us to investigate whether feeding the complex field into DNN would potentially address the defocusing problem as in-focus information is implicitly encoded in the complex field. In this paper, we assess the feasibility of employing neural networks to directly process full amplitude and phase data from a defocus plane without digital refocusing. Our specific focus lies in understanding the tolerance for defocus in image classification neural networks when amplitude and phase are taken as inputs. To accomplish this, we used Fourier ptychography microscopy (FPM) to acquire in-focus phase and amplitude images of two distinct object types - normal red blood cells and echinocytes. We then digitally propagate the complex field to generate progressively defocused images of the samples to serve as training and testing datasets for image classification neural networks. While the digitally defocused images contain sufficient information to recover the original in-focus images, we observed that current standard implementations of deep learning models are unable to effectively utilize the defocused field to distinguish between the two cell types. We conclude that the physical-model-based digital refocusing capability of QPI remains indispensable for overcoming defocusing issues in current standard DNN models.

Toward robust super-resolution imaging: A low-rank approximation approach for pattern-illuminated Fourier ptychography

Pattern-illuminated Fourier ptychography (piFP) is an elegant combination of structured illumination imaging and a Fourier ptychographic algorithm with the ability to image beyond the diffraction limit of the employed optics. Artifact-free piFP super-resolution reconstruction requires a high level of stability in the illumination pattern. However, unpredictable pattern variation occurs in the presence of environment perturbation, intensity fluctuation, and pointing instability at the source, leading to declines in image reconstruction quality. To address this issue, we present an efficient and robust piFP algorithm based on low-rank approximation (LRA-piFP), which relaxes the requirement for the stability of illumination patterns. This LRA-piFP method can model frame-wise pattern variation during a full scan, thus improve the reconstruction quality significantly. We take numerical simulations and proof-of-principle experiments with both long-range imaging and microscopy for demonstrations. Results show that the LRA-piFP method can handle different kinds of pattern variation and outperforms other state-of-the-art techniques in terms of reconstruction quality and resolution improvement. Our method provides effective experimental robustness to piFP with a natural algorithmic extension, paving the way for its application in both macroscopic and microscopic imaging.

Analytical linear model for Fourier ptychography: insights into image uniqueness and reconstruction factors

Analytical linear model for Fourier ptychography: insights into image uniqueness and reconstruction factors

Classifying breast cancer and fibroadenoma tissue biopsies from paraffined stain-free slides by fractal biomarkers in Fourier Ptychographic Microscopy

Breast cancer is one of the most spread and monitored pathologies in high-income countries. After breast biopsy, histological tissue is stored in paraffin, sectioned and mounted. Conventional inspection of tissue slides under benchtop light microscopes involves paraffin removal and staining, typically with H&E. Then, expert pathologists are called to judge the stained slides. However, paraffin removal and staining are operator-dependent, time and resources consuming processes that can generate ambiguities due to non-uniform staining. Here we propose a novel method that can work directly on paraffined stain-free slides. We use Fourier Ptychography as a quantitative phase-contrast microscopy method, which allows accessing a very wide field of view (i.e., mm2) in one single image while guaranteeing high lateral resolution (i.e., 0.5 µm). This imaging method is multi-scale, since it enables looking at the big picture, i.e. the complex tissue structure and connections, with the possibility to zoom-in up to the single-cell level. To handle this informative image content, we introduce elements of fractal geometry as multi-scale analysis method. We show the effectiveness of fractal features in describing and classifying fibroadenoma and breast cancer tissue slides from ten patients with very high accuracy. We reach 94.0 ± 4.2% test accuracy in classifying single images. Above all, we show that combining the decisions of the single images, each patient’s slide can be classified with no error. Besides, fractal geometry returns a guide map to help pathologist to judge the different tissue portions based on the likelihood these can be associated to a breast cancer or fibroadenoma biomarker. The proposed automatic method could significantly simplify the steps of tissue analysis and make it independent from the sample preparation, the skills of the lab operator and the pathologist.

Multi-Aperture Joint-Encoding Fourier Ptychography for a Distributed System

High-resolution infrared remote sensing imaging is critical in planetary exploration, especially under demanding engineering conditions. However, due to diffraction, the spatial resolution of conventional methods is relatively low, and the spatial bandwidth product limits imaging systems’ design. Extensive research has been conducted with the aim of enhancing spatial resolution in remote sensing using a multi-aperture structure, but obtaining high-precision co-phase results using a sub-aperture remains challenging. A new high-resolution imaging method utilizing multi-aperture joint-encoding Fourier ptychography (JEFP) is proposed as a practical means to achieve super-resolution infrared imaging using distributed platforms. We demonstrated that the JEFP approach achieves pixel super-resolution with high efficiency, without requiring subsystems to perform mechanical scanning in space or to have high position accuracy. Our JEFP approach extends the application scope of Fourier ptychographic imaging, especially in distributed platforms for planetary exploration applications.

Tensorial tomographic Fourier ptychography with applications to muscle tissue imaging

Tensorial tomographic Fourier ptychography with applications to muscle tissue imaging

High-resolution display screen as programmable illumination for Fourier ptychography

We introduce a new programmable illumination strategy for Fourier ptychographic microscopy (FPM), utilizing a high-resolution organic light-emitting diode (OLED) display screen at the vicinity of the sample to achieve super-resolution and quantitative phase imaging of biological samples. High-density pixels in the OLED screen allow for the angle-scanning illumination required for FP by placing the sample slide directly on the screen, where multiple images of the sample are captured while scanning the pixels on the screen. We discuss the design of the OLED-FP illumination and the corresponding image reconstruction strategies and experimentally validate the super-resolution and phase imaging capabilities of FP using a smartphone screen as illumination. Further, we extend our method to patterned illumination strategies, which multiplexes multiple illumination pixels to achieve full-field FP imaging with a reduced number of measurements, where we identify an optimal illumination pattern and density to maximize the imaging speed without sacrificing the image quality. Our approach offers a simple and compact programmable illuminator that can effectively transform any microscope into a compact FPM with resolution improvement and phase imaging capabilities.

Computational label-free microscope through a custom-built high-throughput objective lens and Fourier ptychography

Label-free microscopy directly images live samples without fluorescent markers, providing a panoramic view of biological structures and functions. However, pursuing high-throughput and high-content live cell imaging requires both higher spatial resolution and larger field of view, which are limited by the optical system. In this study, we custom-built a 5▪/0.35 objective with a field number of 28 mm, providing a space-bandwidth product of 34 megapixels, which is four times greater than that of commercial high-throughput objectives such as the Nikon Lambda series (4▪/0.2, 10▪/0.45, 20▪/0.75). Furthermore, we incorporated Fourier ptychography microscopy (FPM) into the system, achieving a synthetic numerical aperture of 0.72, suitable for digital pathology and long-term live cell observation. To improve the FPM performance, we proposed a phantom-based calibration method for quantitative correction of illumination angle errors. Additionally, this method can also serve as an initial step for the on-line calibration. The remarkable capabilities of our 5▪/0.35 objective have been demonstrated, as well as the effectiveness of computational label-free microscopy. Furthermore, by combining our original FPM with more advanced hardware and algorithms, our FPM can achieve higher performance.

Optical voice encryption based on speckle-illuminated fourier ptychography and plaintext-related chaotic random phase mask

In this paper, we propose an optical voice encryption scheme based on speckle-illuminated Fourier ptychography (FP) and plaintext-related chaotic random phase mask (CRPM). In this proposed encryption scheme, the plaintext-related CRPMs are generated by chaotic Lozi map and secure hash algorithm (SHA-256). During the encryption process, the voice signal to be encrypted is first converted into a two-dimensional (2D) voice map. Then, with the help of CRPMs and speckle-illuminated FP, the voice map is encrypted into a series of noise-like low-resolution images. During the decryption process, the original voice signal can be recovered from the series of noise-like low-resolution images via Fourier ptychographic phase retrieval algorithm and the CRPMs. To the best of our knowledge, it is the first time to use the Fourier ptychography and chaotic random phase mask to implement the optical encryption of the voice signal. In addition, in this proposed encryption scheme, the chaotic parameters can replace the whole random phase masks as the secret keys, which makes the management and transmission of the secret keys become more convenient. Moreover, since the plaintext-related chaotic parameter keys can be updated dynamically, the security of the proposed encryption scheme can be further improved. The feasibility, security and robustness of the proposed encryption scheme are further analyzed by numerical simulations.

Spatially-coded Fourier ptychography: flexible and detachable coded thin films for quantitative phase imaging with uniform phase transfer characteristics.

Fourier ptychography (FP) is an enabling imaging technique that produces high-resolution complex-valued images with extended field coverages. However, when FP images a phase object with any specific spatial frequency, the captured images contain only constant values, rendering the recovery of the corresponding linear phase ramp impossible. This challenge is not unique to FP but also affects other common microscopy techniques -- a rather counterintuitive outcome given their widespread use in phase imaging. The underlying issue originates from the non-uniform phase transfer characteristic inherent in microscope systems, which impedes the conversion of object wavefields into discernible intensity variations. To address this challenge, we present spatially-coded Fourier ptychography (scFP), a new method that synergizes FP with spatial-domain coded detection for true quantitative phase imaging. In scFP, a flexible and detachable coded thin film is attached atop the image sensor in a regular FP setup. The spatial modulation of this thin film ensures a uniform phase response across the entire synthetic bandwidth. It improves reconstruction quality and corrects refractive index underestimation issues prevalent in conventional FP and related tomographic implementations. The inclusion of the coded thin film further adds a new dimension of measurement diversity in the spatial domain. The development of scFP is expected to catalyse new research directions and applications for phase imaging, emphasizing the need for true quantitative accuracy with uniform frequency response.

QPI assay of fibroblasts resilience to adverse effects of nanoGO clusters by multimodal and multiscale microscopy

Graphene is considered a possible drug deliver in nanomedicine for its mechanical, physical and chemical characteristics. Thus, studying graphene biocompatibility is pivotal to contribute to the modern nano-therapy science. The coexistence between cells and graphene should be analysed using non-invasive technologies and thus quantitative phase imaging (QPI) modalities are suitable to investigate the morphometric evolution of cells under nanomaterial exposure. Here, we show how a multimodal QPI approach can furnish a noninvasive analysis for probing the dose-dependent effect of nanoGO clusters on adherent NIH 3T3 fibroblast cells. We rely on both digital holography and Fourier ptychography (FP) in transmission microscopy mode. The former allows accurate time-lapse experiments at the single cell level. The latter provides a wide field of view characterization at the cells network level, thus assuring a significant statistical measurement by exploiting the intrinsic large space-bandwidth product of FP. The combination of these two techniques allows one to extract multimodal information about the cell resilience to adverse effects of nanoGO in the surrounding buffer, namely through quantitative, multi-scale, and time-resolved characterization.

Computational polarized colorful Fourier ptychography imaging: a novel information reuse technique of polarization of scattering light field

<sec>Fourier ptychography for high-resolution imaging has been a revolutionizing technical, since it can provide abundant information about target scene by changing illumination or pupil scanning. However, many objects are covered by dynamic scattering media, such as biological tissues and mist, that disrupts the light paths and forms the scattering wall, let alone high-resolution imaging. It is worth noting that the scatting effect caused by the scattering media will reduce the correlation of scattered light field, which makes the information aliasing difficult to extract. The situation becomes worse if the image scene is in color. Typically, the wavefront shaping, optical transmission matrix, and speckle correlation technique can successfully recover hidden targets form the scattered light field. Notably, the physical model of conventional method is limited by the difficultly in extracting target information from the strong scattering environment, especially in broadband light illumination imaging. Thus, it is limited to achieve super-resolution color imaging through scattering media by utilizing the current techniques.</sec><sec>In this work, we present a computational polarized colorful Fourier ptychography imaging approach for super-resolution perspective in broadband dynamic scattering media. In order to address the challenge of current imaging methods that is limited by the width of the light spectrum, the polarization characteristics of the scattered-light-field are explored. After retrieving a series of sub-polarized images, which bring the information about different frequencies caused by the motion of scattering media and are processed by the common-mode rejection of polarization characteristic, our computational approach utilizes the iterative optimization algorithm to recover the scene. Notably, owning to the difference between the target scattering information and background scattering information of scattered light fields with different polarization rotation angles, we can obtain two images in which the target information and the background information are dominant in the scattered field. Afterwards, a series of images containing target information and background information is used to iterate the Fourier ptychographyprogram to update the target image based on the obtained image sequence until the estimation converges. During the updating procedure, the scattering effect can be removed, and the spatial-resolution is improved.</sec><sec>Compared with traditional scattering imaging model, the proposed method can perform super-resolution color imaging and descattering under various conditions, and solve the problem of color cases. Furthermore, the proposed method is easy to incorporate into a traditional Fourier Ptychography imaging system to obtain high-fidelity images with better quality and effective detail information. Therefore, the proposed method has the potential to help super-resolution imaging to obtain more practical applications.</sec>

Snapshot macroscopic Fourier ptychography: far-field synthetic aperture imaging via illumination multiplexing and camera array acquisition

Snapshot macroscopic Fourier ptychography: far-field synthetic aperture imaging via illumination multiplexing and camera array acquisition

Structured illumination and image enhancement of three-dimensional and moving objects at a distance via incoherent Fourier ptychography.

We experimentally apply incoherent Fourier ptychography to enhance the resolution of recorded images by projecting known, uncorrelated, random patterns at high speed onto 3D moving and distant objects. We find that the resolution enhancement factor can be greater than 2, depending on the projection and camera optics.