Quantitative phase imaging and complex field reconstruction by pupil modulation differential phase contrast.

Differential phase contrast (DPC) is a non-interferometric quantitative phase imaging method achieved by using an asymmetric imaging procedure. We report a pupil modulation differential phase contrast (PMDPC) imaging method by filtering a sample's Fourier domain with half-circle pupils. A phase gradient image is captured with each half-circle pupil, and a quantitative high resolution phase image is obtained after a deconvolution process with a minimum of two phase gradient images. Here, we introduce PMDPC quantitative phase image reconstruction algorithm and realize it experimentally in a 4f system with an SLM placed at the pupil plane. In our current experimental setup with the numerical aperture of 0.36, we obtain a quantitative phase image with a resolution of 1.73µm after computationally removing system aberrations and refocusing. We also extend the depth of field digitally by 20 times to ±50µm with a resolution of 1.76µm.

Wide-field Fourier ptychographic microscopy using laser illumination source.

Fourier ptychographic (FP) microscopy is a coherent imaging method that can synthesize an image with a higher bandwidth using multiple low-bandwidth images captured at different spatial frequency regions. The method's demand for multiple images drives the need for a brighter illumination scheme and a high-frame-rate camera for a faster acquisition. We report the use of a guided laser beam as an illumination source for an FP microscope. It uses a mirror array and a 2-dimensional scanning Galvo mirror system to provide a sample with plane-wave illuminations at diverse incidence angles. The use of a laser presents speckles in the image capturing process due to reflections between glass surfaces in the system. They appear as slowly varying background fluctuations in the final reconstructed image. We are able to mitigate these artifacts by including a phase image obtained by differential phase contrast (DPC) deconvolution in the FP algorithm. We use a 1-Watt laser configured to provide a collimated beam with 150 mW of power and beam diameter of 1 cm to allow for the total capturing time of 0.96 seconds for 96 raw FPM input images in our system, with the camera sensor's frame rate being the bottleneck for speed. We demonstrate a factor of 4 resolution improvement using a 0.1 NA objective lens over the full camera field-of-view of 2.7 mm by 1.5 mm.

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.

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 effective error removal. Results on both simulated data and real data captured using our laser-illuminated 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.

Wide field-of-view fluorescence image deconvolution with aberration-estimation from Fourier ptychography.

This paper presents a method to simultaneously acquire an aberration-corrected, wide field-of-view fluorescence image and a high-resolution coherent bright-field image using a computational microscopy method. First, the procedure applies Fourier ptychographic microscopy (FPM) to retrieve the amplitude and phase of a sample, at a resolution that significantly exceeds the cutoff spatial frequency of the microscope objective lens. At the same time, redundancy within the set of acquired FPM bright-field images offers a means to estimate microscope aberrations. Second, the procedure acquires an aberrated fluorescence image, and computationally improves its resolution through deconvolution with the estimated aberration map. An experimental demonstration successfully improves the bright-field resolution of fixed, stained and fluorescently tagged HeLa cells by a factor of 4.9, and reduces the error caused by aberrations in a fluorescence image by up to 31%, over a field of view of 6.2 mm by 9.3 mm. For optimal deconvolution, we show the fluorescence image needs to have a signal-to-noise ratio of at least ~18.

Erratum: 0.5 gigapixel microscopy using a flatbed scanner: erratum.

When one uses USAF target to calibrate the resolution of an imaging system, the periodicity of the smallest resolvable line should be used to define the limit. However, in the original paper, the line width of the resolution target was used to characterize the resolution of our microscope system, resulting in an overestimation of the performance of the imaging system. In this erratum, we correct the parts that state incorrect resolution and also re-evaluate the performance of our micoscope.[This corrects the article on p. 1 in vol. 5, PMID: 24466471.].

Diffraction tomography with Fourier ptychography.

This paper presents a technique to image the complex index of refraction of a sample across three dimensions. The only required hardware is a standard microscope and an array of LEDs. The method, termed Fourier ptychographic tomography (FPT), first captures a sequence of intensity-only images of a sample under angularly varying illumination. Then, using principles from ptychography and diffraction tomography, it computationally solves for the sample structure in three dimensions. The experimental microscope demonstrates a lateral spatial resolution of 0.39 µm and an axial resolution of 3.7 µm at the Nyquist-Shannon sampling limit (0.54 and 5.0 µm at the Sparrow limit, respectively) across a total imaging depth of 110 µm. Unlike competing methods, this technique quantitatively measures the volumetric refractive index of primarily transparent and contiguous sample features without the need for interferometry or any moving parts. Wide field-of-view reconstructions of thick biological specimens suggest potential applications in pathology and developmental biology.

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 currently 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 ptychographic reconstruction algorithm that is currently in widespread 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 mm2 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.

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.

Embedded pupil function recovery for Fourier ptychographic microscopy: erratum.

In the original paper, the line width of the resolution target (which corresponds to half-pitch resolution) was used to characterize the resolution of our microscope system. However, we think that full-pitch resolution offers a better definition of the imaging system's resolution limit. In this erratum, we list specific sections from the manuscript that used half-pitch resolution and correct them accordingly.

Digital pathology with Fourier ptychography.

Fourier ptychographic microscopy (FPM) is a recently introduced method of acquiring high-resolution, wide field of view (FOV) giga-pixel histology images. The FPM procedure first acquires a sequence of low-resolution images of a sample under variable-angle illumination. It then combines these images using a novel phase retrieval algorithm to improve the employed microscope's resolution beyond its conventional limit. Here, we first describe how FPM's resolution improvement can enhance wide FOV histology imaging. Second, we show that FPM also records a thin sample's optical phase, which can help pathologists digitally extract as much information as possible from a given histology slide.

Overlapped Fourier coding for optical aberration removal.

We present an imaging procedure that simultaneously optimizes a camera's resolution and retrieves a sample's phase over a sequence of snapshots. The technique, termed overlapped Fourier coding (OFC), first digitally pans a small aperture across a camera's pupil plane with a spatial light modulator. At each aperture location, a unique image is acquired. The OFC algorithm then fuses these low-resolution images into a full-resolution estimate of the complex optical field incident upon the detector. Simultaneously, the algorithm utilizes redundancies within the acquired dataset to computationally estimate and remove unknown optical aberrations and system misalignments via simulated annealing. The result is an imaging system that can computationally overcome its optical imperfections to offer enhanced resolution, at the expense of taking multiple snapshots over time.

Fourier ptychographic microscopy for filtration-based circulating tumor cell enumeration and analysis.

Circulating tumor cells (CTCs) are recognized as a candidate biomarker with strong prognostic and predictive potential in metastatic disease. Filtration-based enrichment technologies have been used for CTC characterization, and our group has previously developed a membrane microfilter device that demonstrates efficacy in model systems and clinical blood samples. However, uneven filtration surfaces make the use of standard microscopic techniques a difficult task, limiting the performance of automated imaging using commercially available technologies. Here, we report the use of Fourier ptychographic microscopy (FPM) to tackle this challenge. Employing this method, we were able to obtain high-resolution color images, including amplitude and phase, of the microfilter samples over large areas. FPM's ability to perform digital refocusing on complex images is particularly useful in this setting as, in contrast to other imaging platforms, we can focus samples on multiple focal planes within the same frame despite surface unevenness. In model systems, FPM demonstrates high image quality, efficiency, and consistency in detection of tumor cells when comparing corresponding microfilter samples to standard microscopy with high correlation (R² = 0.99932). Based on these results, we believe that FPM will have important implications for improved, high throughput, filtration-based CTC analysis, and, more generally, image analysis of uneven surfaces.

Aperture-scanning Fourier ptychography for 3D refocusing and super-resolution macroscopic imaging.

We report an imaging scheme, termed aperture-scanning Fourier ptychography, for 3D refocusing and super-resolution macroscopic imaging. The reported scheme scans an aperture at the Fourier plane of an optical system and acquires the corresponding intensity images of the object. The acquired images are then synthesized in the frequency domain to recover a high-resolution complex sample wavefront; no phase information is needed in the recovery process. We demonstrate two applications of the reported scheme. In the first example, we use an aperture-scanning Fourier ptychography platform to recover the complex hologram of extended objects. The recovered hologram is then digitally propagated into different planes along the optical axis to examine the 3D structure of the object. We also demonstrate a reconstruction resolution better than the detector pixel limit (i.e., pixel super-resolution). In the second example, we develop a camera-scanning Fourier ptychography platform for super-resolution macroscopic imaging. By simply scanning the camera over different positions, we bypass the diffraction limit of the photographic lens and recover a super-resolution image of an object placed at the far field. This platform's maximum achievable resolution is ultimately determined by the camera's traveling range, not the aperture size of the lens. The FP scheme reported in this work may find applications in 3D object tracking, synthetic aperture imaging, remote sensing, and optical/electron/X-ray microscopy.

Imaging and identification of waterborne parasites using a chip-scale microscope.

We demonstrate a compact portable imaging system for the detection of waterborne parasites in resource-limited settings. The previously demonstrated sub-pixel sweeping microscopy (SPSM) technique is a lens-less imaging scheme that can achieve high-resolution (<1 µm) bright-field imaging over a large field-of-view (5.7 mm×4.3 mm). A chip-scale microscope system, based on the SPSM technique, can be used for automated and high-throughput imaging of protozoan parasite cysts for the effective diagnosis of waterborne enteric parasite infection. We successfully imaged and identified three major types of enteric parasite cysts, Giardia, Cryptosporidium, and Entamoeba, which can be found in fecal samples from infected patients. We believe that this compact imaging system can serve well as a diagnostic device in challenging environments, such as rural settings or emergency outbreaks.

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.

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.