Embedded pupil function recovery for Fourier ptychographic microscopy

We develop and test a pupil function determination algorithm, termed embedded pupil function recovery (EPRY), which can be incorporated into the Fourier ptychographic microscopy (FPM) algorithm and recover both the Fourier spectrum of sample and the pupil function of imaging system simultaneously. This EPRY-FPM algorithm eliminates the requirement of the previous FPM algorithm for a priori knowledge of the aberration in the imaging system to reconstruct a high quality image. We experimentally demonstrate the effectiveness of this algorithm by reconstructing high resolution, large field-of-view images of biological samples. We also illustrate that the pupil function we retrieve can be used to study the spatially varying aberration of a large field-of-view imaging system. We believe that this algorithm adds more flexibility to FPM and can be a powerful tool for the characterization of an imaging system’s aberration

0.5 gigapixel microscopy using a flatbed scanner

The capability to perform high-resolution, wide field-of-view (FOV) microscopy imaging is highly sought after in biomedical applications. In this paper, we report a wide FOV microscopy system that uses a closed-circuit-television (CCTV) lens for image relay and a flatbed scanner for data acquisition. We show that such an imaging system is capable of capturing a 10 mm × 7.5 mm FOV image with 0.78 µm resolution, resulting in more than 0.5 billion pixels across the entire image. The resolution and field curve of the proposed system were characterized by imaging a USAF resolution target and a hole-array target. To demonstrate its application, 0.5 gigapixel images of histology slides were acquired using this system

Aperture scanning Fourier ptychographic microscopy

Fourier ptychographic microscopy (FPM) is implemented through aperture scanning by an LCOS spatial light modulator at the back focal plane of the objective lens. This FPM configuration enables the capturing of the complex scattered field for a 3D sample both in the transmissive mode and the reflective mode. We further show that by combining with the compressive sensing theory, the reconstructed 2D complex scattered field can be used to recover the 3D sample scattering density. This implementation expands the scope of application for FPM and can be beneficial for areas such as tissue imaging and wafer inspection

Quantitative phase imaging via Fourier ptychographic microscopy

Fourier ptychographic microscopy (FPM) is a recently developed imaging modality that uses angularly varying illumination to extend a system’s performance beyond the limit defined by its optical components. The FPM technique applies a novel phase-retrieval procedure to achieve resolution enhancement and complex image recovery. In this Letter, we compare FPM data to theoretical prediction and phase-shifting digital holography measurement to show that its acquired phase maps are quantitative and artifact-free. We additionally explore the relationship between the achievable spatial and optical thickness resolution offered by a reconstructed FPM phase image. We conclude by demonstrating enhanced visualization and the collection of otherwise unobservable sample information using FPM’s quantitative phase

Characterization of spatially varying aberrations for wide field-of-view microscopy

We describe a simple and robust approach for characterizing the spatially varying pupil aberrations of microscopy systems. In our demonstration with a standard microscope, we derive the location-dependent pupil transfer functions by first capturing multiple intensity images at different defocus settings. Next, a generalized pattern search algorithm is applied to recover the complex pupil functions at ~350 different spatial locations over the entire field-of-view. Parameter fitting transforms these pupil functions into accurate 2D aberration maps. We further demonstrate how these aberration maps can be applied in a phase-retrieval based microscopy setup to compensate for spatially varying aberrations and to achieve diffraction-limited performance over the entire field-of-view. We believe that this easy-to-use spatially-varying pupil characterization method may facilitate new optical imaging strategies for a variety of wide field-of-view imaging platforms

High numerical aperture Fourier ptychography: principle, implementation and characterization

Fourier ptychography (FP) utilizes illumination control and computational post-processing to increase the resolution of bright-field microscopes. In effect, FP extends the fixed numerical aperture (NA) of an objective lens to form a larger synthetic system NA. Here, we build an FP microscope (FPM) using a 40X 0.75NA objective lens to synthesize a system NA of 1.45. This system achieved a two-slit resolution of 335 nm at a wavelength of 632 nm. This resolution closely adheres to theoretical prediction and is comparable to the measured resolution (315 nm) associated with a standard, commercially available 1.25 NA oil immersion microscope. Our work indicates that Fourier ptychography is an attractive method to improve the resolution-versus-NA performance, increase the working distance, and enlarge the field-of-view of high-resolution bright-field microscopes by employing lower NA objectives

Solving ptychography with a convex relaxation

Ptychography is a powerful computational imaging technique that transforms a collection of low-resolution images into a high-resolution sample reconstruction. Unfortunately, algorithms that are currently used to solve this reconstruction problem lack stability, robustness, and theoretical guarantees. Recently, convex optimization algorithms have improved the accuracy and reliability of several related reconstruction efforts. This paper proposes a convex formulation of the ptychography problem. This formulation has no local minima, it can be solved using a wide range of algorithms, it can incorporate appropriate noise models, and it can include multiple a priori constraints. The paper considers a specific algorithm, based on low-rank factorization, whose runtime and memory usage are near-linear in the size of the output image. Experiments demonstrate that this approach offers a 25% lower background variance on average than alternating projections, the current standard algorithm for ptychographic reconstruction.Comment: 8 pages, 8 figure

Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient

Fourier ptychographic microscopy (FPM) is a novel computational coherent imaging technique for high space-bandwidth product imaging. Mathematically, Fourier ptychographic (FP) reconstruction can be implemented as a phase retrieval optimization process, in which we only obtain low resolution intensity images corresponding to the sub-bands of the sample's high resolution (HR) spatial spectrum, and aim to retrieve the complex HR spectrum. In real setups, the measurements always suffer from various degenerations such as Gaussian noise, Poisson noise, speckle noise and pupil location error, which would largely degrade the reconstruction. To efficiently address these degenerations, we propose a novel FP reconstruction method under a gradient descent optimization framework in this paper. The technique utilizes Poisson maximum likelihood for better signal modeling, and truncated Wirtinger gradient for error removal. Results on both simulated data and real data captured using our laser FPM setup show that the proposed method outperforms other state-of-the-art algorithms. Also, we have released our source code for non-commercial use

Counting White Blood Cells from a Blood Smear Using Fourier Ptychographic Microscopy

White blood cell (WBC) count is a valuable metric for assisting with diagnosis or prognosis of various diseases such as coronary heart disease, type 2 diabetes, or infection. Counting WBCs can be done either manually or automatically. Automatic methods are capable of counting a large number of cells to give a statistically more accurate reading of the WBC count of a sample, but the specialized equipment tends to be expensive. Manual methods are inexpensive since they only involve a conventional light microscope setup. However, it is more laborious and error-prone because the small field-of-view (FOV) of the microscope necessitates mechanical scanning of a specimen for counting an adequate number of WBCs. Here, we investigate the use of Fourier ptychographic microscopy (FPM) to bypass these issues of the manual methods. With a 2x objective, FPM can provide a FOV of 120 mm^2 with enhanced resolution comparable to that of a 20x objective, which is adequate for non-differentially counting WBCs in just one FOV. A specialist was able to count the WBCs in FPM images with 100% accuracy compared to the count as determined from conventional microscope images. An automatic counting algorithm was also developed to identify WBCs from FPM’s captured images with 95% accuracy, paving the way for a cost-effective WBC counting setup with the advantages of both the automatic and manual counting methods