Wide-field Fourier ptychographic microscopy using laser illumination source

Aberration Estimation for Synthetic Aperture Digital Holographic Microscope Using Deep Neural Network

Digital holographic microscopy (DHM) is a valuable technique for investigating the optical properties of samples through the measurement of intensity and phase of diffracted beams. However, DHMs are constrained by Lagrange invariance, compromising the spatial bandwidth product (SBP) which relates resolution and field of view. Synthetic aperture DHM (SA-DHM) was introduced to overcome this limitation, but it faces significant challenges such as aberrations in synthesizing the optical information corresponding to the steering angle of incident wave. This paper proposes a novel approach utilizing deep neural networks (DNNs) for compensating aberrations in SA-DHM, extending the compensation scope beyond the numerical aperture (NA) of the objective lens. The method involves training a DNN from diffraction patterns and Zernike coefficients through a circular aperture, enabling effective aberration compensation in the illumination beam. This method makes it possible to estimate aberration coefficients from the only part of the diffracted beam cutoff by the circular aperture mask. With the proposed technique, the simulation results present improved resolution and quality of sample images. The integration of deep neural networks with SA-DHM holds promise for advancing microscopy capabilities and overcoming existing limitations.

Non-interferometric stand-alone single-shot holographic camera using reciprocal diffractive imaging

An ideal holographic camera measures the amplitude and phase of the light field so that the focus can be numerically adjusted after the acquisition, and depth information about an imaged object can be deduced. The performance of holographic cameras based on reference-assisted holography is significantly limited owing to their vulnerability to vibration and complex optical configurations. Non-interferometric holographic cameras can resolve these issues. However, existing methods require constraints on an object or measurement of multiple-intensity images. In this paper, we present a holographic image sensor that reconstructs the complex amplitude of scattered light from a single-intensity image using reciprocal diffractive imaging. We experimentally demonstrate holographic imaging of three-dimensional diffusive objects and suggest its potential applications by imaging a variety of samples under both static and dynamic conditions.

Fourier ptychographic topography

Topography measurement is essential for surface characterization, semiconductor metrology, and inspection applications. To date, performing high-throughput and accurate topography remains challenging due to the trade-off between field-of-view (FOV) and spatial resolution. Here we demonstrate a novel topography technique based on the reflection-mode Fourier ptychographic microscopy, termed Fourier ptychograhpic topography (FPT). We show that FPT provides both a wide FOV and high resolution, and achieves nanoscale height reconstruction accuracy. Our FPT prototype is based on a custom-built computational microscope consisting of programmable brightfield and darkfield LED arrays. The topography reconstruction is performed by a sequential Gauss-Newton-based Fourier ptychographic phase retrieval algorithm augmented with total variation regularization. We achieve a synthetic numerical aperture (NA) of 0.84 and a diffraction-limited resolution of 750 nm, increasing the native objective NA (0.28) by 3×, across a 1.2 × 1.2 mm² FOV. We experimentally demonstrate the FPT on a variety of reflective samples with different patterned structures. The reconstructed resolution is validated on both amplitude and phase resolution test features. The accuracy of the reconstructed surface profile is benchmarked against high-resolution optical profilometry measurements. In addition, we show that the FPT provides robust surface profile reconstructions even on complex patterns with fine features that cannot be reliably measured by the standard optical profilometer. The spatial and temporal noise of our FPT system is characterized to be 0.529 nm and 0.027 nm, respectively.

Depth-multiplexed ptychographic microscopy for high-throughput imaging of stacked bio-specimens on a chip

Imaging a large number of bio-specimens at high speed is essential for many biomedical applications. The common strategy is to place specimens at different lateral positions and image them sequentially. Here we report a new on-chip imaging strategy, termed depth-multiplexed ptychographic microscopy (DPM), for parallel imaging and sensing at high speed. Different from the common strategy, DPM stacks multiple specimens in the axial direction and images the entire z-stack all at once. In our prototype platform, we modify a low-cost car mirror for programmable steering of the incident laser beam. A blood-coated image sensor is then placed underneath the stacked sample for acquiring the resulting diffraction patterns. With the captured images, we perform blind recovery of the incident beam angle and model different layers of the stacked sample as different coded surfaces for object reconstruction. For in vitro experiment, we demonstrate time-lapse cell culture monitoring by imaging 3 stacked microfluidic channels on the coded sensor. For high-throughput cytometric analysis, we image 5 stacked brain sections with a 205-mm² field of view in ∼50 s. Cytometric analysis is also performed to quantify the cellular proliferation biomarkers on the slides. The DPM approach adds a new degree of freedom for data multiplexing in microscopy, enabling parallel imaging of multiple specimens using a single detector. The demonstrated 6-mm depth of field is among the longest ones in microscopy imaging. The novel depth-multiplexed configuration also complements the miniaturization provided by microfluidics devices, offering a solution for on-chip sensing and imaging with efficient sample handling.

Optical ptychography for biomedical imaging: recent progress and future directions [Invited]

Ptychography is an enabling microscopy technique for both fundamental and applied sciences. In the past decade, it has become an indispensable imaging tool in most X-ray synchrotrons and national laboratories worldwide. However, ptychography's limited resolution and throughput in the visible light regime have prevented its wide adoption in biomedical research. Recent developments in this technique have resolved these issues and offer turnkey solutions for high-throughput optical imaging with minimum hardware modifications. The demonstrated imaging throughput is now greater than that of a high-end whole slide scanner. In this review, we discuss the basic principle of ptychography and summarize the main milestones of its development. Different ptychographic implementations are categorized into four groups based on their lensless/lens-based configurations and coded-illumination/coded-detection operations. We also highlight the related biomedical applications, including digital pathology, drug screening, urinalysis, blood analysis, cytometric analysis, rare cell screening, cell culture monitoring, cell and tissue imaging in 2D and 3D, polarimetric analysis, among others. Ptychography for high-throughput optical imaging, currently in its early stages, will continue to improve in performance and expand in its applications. We conclude this review article by pointing out several directions for its future development.

High-speed Fourier ptychographic microscopy for quantitative phase imaging

Fourier ptychographic microscopy (FPM), as an emerging computational imaging method, has been applied to quantitative phase imaging with resolution bypassing the physical limit of the detection objective. Due to the weak illumination intensity and long image acquisition time, the achieved imaging speed in current FPM methods is still low, making them unsuitable for real-time imaging applications. We propose and demonstrate a high-speed FPM method based on using laser illumination and digital micro-mirror devices for illumination angle scanning. In this new, to the best of our knowledge, FPM method, we realized quantitative phase imaging and intensity imaging at over 42 frames per second (fps) with around 1 µm lateral resolution. The quantitative phase images have revealed membrane height fluctuations of red blood cells with nanometer-scale sensitivity, while the intensity images have resolved subcellular features in stained cancer tissue slices.

Dither removing Fourier ptychographic microscope based on a two-axis rotation stage

SIGNIFICANCE

Large space-bandwidth product is highly desirable in many biomedical imaging. Fourier ptychographic microscopy (FPM) is a computational imaging technique that can significantly increase the space-bandwidth product of a standard microscope. The illuminator of a Fourier ptychographic microscope is not flexible at present, and it is inconvenient to meet different imaging needs.

AIM

An illuminator based on a two-axis motorized rotation stage was presented to provide a more flexible illuminating way with the goal of meeting different imaging needs.

APPROACH

The illuminator adopts a concentric illuminating method to provide coherent illumination in any direction on the sample plane. The sampling pattern can be freely designed and changed according to the parameters of the imaging system. A dither removing algorithm was proposed to remove the potential dither influence introduced in the image acquisition process.

RESULTS

The illuminator could be conveniently integrated into different imaging systems. The feasibility and flexibility were demonstrated by applying it to imaging systems with numerical aperture of 0.045 and 0.01. The resolution gain is about 4- and 13-fold, respectively. The effectiveness of the dither removing algorithm was validated in both simulation and experiment.

CONCLUSIONS

A more flexible illuminator for FPM was presented to meet different imaging needs. A dither removing algorithm was proposed to remove dither influence.

Optical scanning Fourier ptychographic microscopy

We propose a lower-cost and practical active scanning optical scanning Fourier ptychographic microscopy (OSFPM). Featured is a simple setup of Galvo mirrors capable of scanning large-sized objects. The active scanning laser beam is projected onto the sample in a circular pattern to form multiple lower-resolution images. With multiple lower-resolution images, a higher-resolution image is subsequently reconstructed. The OSFPM is able to more precisely control the overlap of the incident light illumination as compared to that in conventional LED-based or other laser-based scanning FPM systems. The proposed microscope is also suitable for applications where a larger size of the object needs to be imaged with efficient illumination.

Coherent synthetic aperture imaging for visible remote sensing via reflective Fourier ptychography

Synthetic aperture radar can measure the phase of a microwave with an antenna, which cannot be directly extended to visible light imaging due to phase lost. In this Letter, we report an active remote sensing with visible light via reflective Fourier ptychography, termed coherent synthetic aperture imaging (CSAI), achieving high resolution, a wide field-of-view (FOV), and phase recovery. A proof-of-concept experiment is reported with laser scanning and a collimator for the infinite object. Both smooth and rough objects are tested, and the spatial resolution increased from 15.6 to 3.48 µm with a factor of 4.5. The speckle noise can be suppressed obviously, which is important for coherent imaging. Meanwhile, the CSAI method can tackle the aberration induced from the optical system by one-step deconvolution and shows the potential to replace the adaptive optics for aberration removal of atmospheric turbulence.

Single full-FOV reconstruction Fourier ptychographic microscopy

Fourier ptychographic microscopy (FPM) is a recently developed computational imaging technique that has high-resolution and wide field-of-view (FOV). FPM bypasses the NA limit of the system by stitching a number of variable-illuminated measured images in Fourier space. On the basis of the wide FOV of the low NA objective, the high-resolution image with a wide FOV can be reconstructed through the phase recovery algorithm. However, the high-resolution reconstruction images are affected by the LED array point light source. The results are: (1) the intensities collected by the sample are severely declined when edge LEDs illuminate the sample; (2) the multiple reconstructions are caused by wavevectors inconsistency for the full FOV images. Here, we propose a new lighting scheme termed full FOV Fourier ptychographic microscopy (F³PM). By combining the LED array and telecentric lens, the method can provide plane waves with different angles while maintaining uniform intensity. Benefiting from the telecentric performance and f‒θ property of the telecentric lens, the system stability is improved and the relationship between the position of LED and its illumination angle is simplified. The excellent plane wave provided by the telecentric lens guarantees the same wavevector in the full FOV, and we use this wavevector to reconstruct the full FOV during one time. The area and diameter of the single reconstruction FOV reached 14.6mm ² and 5.4 mm, respectively, and the diameter is very close to the field number (5.5 mm) of the 4× objective. Compared with the traditional FPM, we have increased the diameter of FOV in a single reconstruction by ∼ 10 times, eliminating the complicated steps of computational redundancy and image stitching.

Laser digital patterning of conductive electrodes using metal oxide nanomaterials

As an alternative approach to the conventional deposition and photolithographic processes, the laser digital patterning (LDP) process, which is also known as the laser direct writing process, has attracted considerable attention because it is a non-photolithographic, non-vacuum, on-demand, and cost-effective electrode fabrication route that can be applied to various substrates, including heat-sensitive flexible substrates. The LDP process was initially developed using noble metal nanoparticles (NPs) such as Au and Ag because such materials are free from oxidation even in a nanosize configuration. Thus, the NPs must be fused together to form continuous conductive structures upon laser irradiation. However, common metals are easily oxidized at the nanoscale and exist in oxidized forms owing to the extremely large surface-to-volume ratio of NPs. Therefore, to fabricate conductive electrodes using common metal NPs via the LDP process, laser irradiation should be used to sinter the NPs and simultaneously induce additional photochemical reactions, such as reduction, and defect structure modification to increase the conductivity of the electrodes. This review summarizes recent studies on the LDP process in which metal oxide NPs, such as ITO, ZnO, CuO, and NiO, were exclusively utilized for fabricating conductive electrodes. The outlook of the LDP process for these materials is also discussed as a method that can be used together with or as a replacement for conventional ones to produce next-generation transparent conductors, sensors, and electronics.

Long-Distance Sub-Diffraction High-Resolution Imaging Using Sparse Sampling

How to perform imaging beyond the diffraction limit has always been an essential subject for the research of optical systems. One effective way to achieve this purpose is Fourier ptychography, which has been widely used in microscopic imaging. However, microscopic imaging measurement technology cannot be directly extended to imaging macro objects at long distances. In this paper, a reconstruction algorithm is proposed to solve the need for oversampling low-resolution images, and it is successfully applied to macroscopic imaging. Compared with the traditional FP technology, the proposed sub-sampling method can significantly reduce the number of iterations in reconstruction. Experiments prove that the proposed method can reconstruct low-resolution images captured by the camera and achieve high-resolution imaging of long-range macroscopic objects.

Fourier ptychography: current applications and future promises

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.

Computational aberration correction of VIS-NIR multispectral imaging microscopy based on Fourier ptychography

Due to the chromatic dispersion properties inherent in all optical materials, even the best-designed multispectral objective will exhibit residual chromatic aberration. Here, we demonstrate a multispectral microscope with a computational scheme based on the Fourier ptychographic microscopy (FPM) to correct these effects in order to render undistorted, in-focus images. The microscope consists of 4 spectral channels ranging from 405 nm to 1552 nm. After the computational aberration correction, it can achieve isotropic resolution enhancement as verified with the Siemens star sample. We image a flip-chip to show the promise of our system to conduct fault detection on silicon chips. This computational approach provides a cost-efficient strategy for high quality multispectral imaging over a broad spectral range.

Coherent anti-Stokes Raman Fourier ptychography

We present a theoretical and numerical study of coherent anti-Stokes Raman scattering Fourier ptychography microscopy (CARS-FPM), a scheme that has not been considered so far in the previously reported CARS wide-field imaging schemes. In this approach, the distribution of the Raman scatterer density of the sample is reconstructed numerically from CARS images obtained under various angles of incidences of the pump or Stokes beam. Our inversion procedure is based on an accurate vectorial model linking the CARS image to the sample and yields both the real and imaginary parts of the susceptibility, the latter giving access to the Raman information, with an improved resolution.

Apodized coherent transfer function constraint for partially coherent Fourier ptychographic microscopy

Fourier ptychographic microscopy (FPM) is a recently developed computational microscopy approach that produces both wide field-of-view (FOV) and high resolution (HR) intensity and a phase image of the sample. Inspired by the ideas of synthetic aperture and phase retrieval, FPM iteratively stitches multiple low-resolution (LR) images with variable illumination angles in Fourier space to reconstruct an HR complex image. Typically, FPM illuminating the sample with an LED array is approximated as a coherent imaging process, and the coherent transfer function (CTF) is imposed as a support constraint in Fourier space. However, a millimeter-scale LED is inapposite to be treated as a coherent light source. As a result, the quality of reconstructed image is degraded by the inappropriate approximation. In this paper, we analyze the coherence of an FPM system and propose a novel constraint approach termed Apodized CTF (AC) constraint in Fourier space. Results on both simulated data and actual captured data show that this new constraint is more stable and robust than CTF. This approach can also relax the coherence requirement of illumination. In addition, it is simple, does not require additional computations, and is easy to be embedded in almost all the reconstruction algorithms proposed so far.

Computational aberration compensation by coded-aperture-based correction of aberration obtained from optical Fourier coding and blur estimation

We report a novel generalized optical measurement system and computational approach to determine and correct aberrations in optical systems. The system consists of a computational imaging method capable of reconstructing an optical system's pupil function by adapting overlapped Fourier coding to an incoherent imaging modality. It recovers the high-resolution image latent in an aberrated image via deconvolution. The deconvolution is made robust to noise by using coded apertures to capture images. We term this method coded-aperture-based correction of aberration obtained from overlapped Fourier coding and blur estimation (CACAO-FB). It is well-suited for various imaging scenarios where aberration is present and where providing a spatially coherent illumination is very challenging or impossible. We report the demonstration of CACAO-FB with a variety of samples including an in vivo imaging experiment on the eye of a rhesus macaque to correct for its inherent aberration in the rendered retinal images. CACAO-FB ultimately allows for an aberrated imaging system to achieve diffraction-limited performance over a wide field of view by casting optical design complexity to computational algorithms in post-processing.

Near-field Fourier ptychography: super-resolution phase retrieval via speckle illumination

High spatial resolution is the goal of many imaging systems. While designing a high-resolution lens with diffraction-limited performance over a large field of view remains a difficult task, creating a complex speckle pattern with wavelength-limited spatial features is easily accomplished with a simple random diffuser. With this observation and the concept of near-field ptychography, we report a new imaging modality, termed near-field Fourier ptychography, to address high-resolution imaging challenges in both microscopic and macroscopic imaging settings. 'Near-field' refers to placing the object at a short defocus distance with a large Fresnel number. We project a speckle pattern with fine spatial features on the object instead of directly resolving the spatial features via a high-resolution lens. We then translate the object (or speckle) to different positions and acquire the corresponding images by using a low-resolution lens. A ptychographic phase retrieval process is used to recover the complex object, the unknown speckle pattern, and the coherent transfer function at the same time. In a microscopic imaging setup, we use a 0.12 numerical aperture (NA) lens to achieve an NA of 0.85 in the reconstruction process. In a macroscale photographic imaging setup, we achieve ~7-fold resolution gain by using a photographic lens. The collection optics do not determine the final achievable resolution; rather, the speckle pattern's feature size does. This is similar to our recent demonstration in fluorescence imaging settings (Guo et al., Biomed. Opt. Express, 9(1), 2018). The reported imaging modality can be employed in light, coherent X-ray, and transmission electron imaging systems to increase resolution and provide quantitative absorption and object phase contrast.

Single-shot aperture-scanning Fourier ptychography

Aperture-scanning Fourier ptychography [Opt. Express22, 13586 (2014)] is a promising non-interferometric wavefront measurement technique. It eliminates the thin-sample requirement in typical Fourier ptychography employing angle-varying illumination. However, as aperture-scanning Fourier ptychography is based on step-by-step scanning, it requires long data acquisition time and a high-stability optical system. In this paper, we propose a single-shot aperture-scanning Fourier ptychography method. In our method, multiple low-resolution images are collected in a single shot by inserting a Dammann grating at a certain distance before the aperture, and the images are subsequently converted to a high-resolution complex wavefront. Compared with scanning-based aperture-scanning Fourier ptychography, the total acquisition time of the proposed method is dramatically reduced. The feasibility of our proposed method is demonstrated by proof-of-concept experiments.

Single-shot lensless imaging via simultaneous multi-angle LED illumination

Lensless imaging is a technique that records diffraction patterns without using lenses and recovers the complex field of object via phase retrieval. Robust lensless phase retrieval process usually requires multiple measurements with defocus variation, transverse translation or angle-varied illumination. However, making such diverse measurements is time-consuming and limits the application of lensless setup for dynamic samples. In this paper, we propose a single-shot lensless imaging scheme via simultaneous multi-angle LED illumination. Diffraction patterns under multi-angle lights are recorded by different areas of the sensor within a single shot. An optimization algorithm is applied to utilize the single-shot measurement and retrieve the aliasing information for reconstruction. We first use numerical simulations to evaluate the proposed scheme quantitatively by comparisons with the multi-acquisition case. Then a proof-of-concept lensless setup is built to validate the method by imaging a resolution chart and biological samples, achieving ∼ 4.92 μm half-pitch resolution and ∼ 1.20²mm² field of view (FOV). We also discuss different design tradeoffs and present a 4-frame acquisition scheme (with ∼ 3.48 μm half-pitch resolution and ∼ 2.35 × 2.55 mm² FOV) to show the flexibility of performance enhancement by capturing more measurements.

Efficient illumination angle self-calibration in Fourier ptychography

Fourier ptychography captures intensity images with varying source patterns (illumination angles) in order to computationally reconstruct large space-bandwidth-product images. Accurate knowledge of the illumination angles is necessary for good image quality; hence, calibration methods are crucial, despite often being impractical or slow. Here, we propose a fast, robust, and accurate self-calibration algorithm that uses only experimentally collected data and general knowledge of the illumination setup. First, our algorithm makes a fast direct estimate of the brightfield illumination angles based on image processing. Then, a more computationally intensive spectral correlation method is used inside the iterative solver to further refine the angle estimates of both brightfield and darkfield images. We demonstrate our method for correcting large and small misalignment artifacts in 2D and 3D Fourier ptychography with different source types: an LED array, a galvo-steered laser, and a high-NA quasi-dome LED illuminator.

Single-shot Fourier ptychography based on diffractive beam splitting

An optical setup and corresponding reconstruction algorithm are proposed to realize single-shot Fourier ptychography (FP). Multiple angle-varied object waves are generated by placing a Dammann grating at a certain distance behind the object, and the generated image array of low resolution corresponding to different diffraction orders formed on the detector plane is recorded simultaneously in a single exposure. The amplitude, as well as the phase information of the object, can be properly reconstructed with a common FP algorithm from the recorded image array. This method eliminates the requirement for the angular scanning of common FP, and the total acquisition time is dramatically reduced. The feasibility of this proposed method was demonstrated both numerically and experimentally. The proposed method has the advantages of fast data acquisition and corresponding high temporal resolution, making it very suitable for applications in which high imaging speed is required.

Motion-corrected Fourier ptychography

Fourier ptychography (FP) is a recently proposed computational imaging technique for high space-bandwidth product imaging. In real setups such as endoscope and transmission electron microscope, the common sample motion largely degrades the FP reconstruction and limits its practicability. In this paper, we propose a novel FP reconstruction method to efficiently correct for unknown sample motion. Specifically, we adaptively update the sample's Fourier spectrum from low spatial-frequency regions towards high spatial-frequency ones, with an additional motion recovery and phase-offset compensation procedure for each sub-spectrum. Benefiting from the phase retrieval redundancy theory, the required large overlap between adjacent sub-spectra offers an accurate guide for successful motion recovery. Experimental results on both simulated data and real captured data show that the proposed method can correct for unknown sample motion with its standard deviation being up to 10% of the field-of-view scale. We have released our source code for non-commercial use, and it may find wide applications in related FP platforms such as endoscopy and transmission electron microscopy.

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.

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.