Spatially coded wavelength-scanning lensless on-chip microscopy for pixel-super-resolved quantitative phase imaging.

We propose a lensfree on-chip microscopy approach for wide-field quantitative phase imaging (QPI) based on wavelength scanning. Unlike previous methods, we found that a relatively large-range wavelength diversity not only provides information to overcome spatial aliasing of the image sensor but also creates sufficient diffraction variations that can be used to achieve motion-free, pixel-super-resolved phase recovery. Based on an iterative phase retrieval and pixel-super-resolution technique, the proposed wavelength-scanning approach uses only eight undersampled holograms to achieve a half-pitch lateral resolution of 691 nm across a large field-of-view of 29.85mm2, surpassing 2.41 times the theoretical Nyquist-Shannon sampling resolution limit imposed by the pixel size of the sensor (1.67 µm). We confirmed the effectiveness of this technique in QPI and resolution enhancement by measuring the benchmark quantitative phase microscopy target. We also showed that this method can track HeLa cell growth within an incubator, revealing cellular morphologies and subcellular dynamics of a large cell population over an extended period of time.

Dielectric metasurfaces have recently attracted much attention due to their ability to efficiently control light propagation, that is, its amplitude, phase and polarization, on micro- and macro- levels. Such metasurfaces also naturally allow for integration in compact optical setups due to their small sizes. An important issue of energy losses is also addressed by employing all-dielectric platform. Advancements in nanofabrication have enabled realization of metasurface-based high-resolution wavefront engineering devices, which have been employed in different imaging applications, for example, as metalenses, polarization filters, metaholograms, etc. Quantitative phase imaging is a powerful tool for the optical inspection of transparent samples in connection with biological and technical applications. By measuring thickness and/or refractive index profiles, phase imaging facilitates, for example, the observation of dynamic events in unstained cells. As such, it has become indispensable in biological imaging, wavefront correction and metrology. However, conventional cameras and photodetectors are inherently not sensitive to the phase of an incident lightwave. As a consequence, direct phase detection is challenging. Only by multiple intensity measurements or application of specialized interferometric schemes, the phase profile of an object can be in principle reconstructed. In this paper, we report on the ability of metasurfaces to contribute to quantitative phase imaging by independent control of the phase profiles in two orthogonal polarization states of an incident beam.

Fourier Ptychographic Microscopy (FPM) and Differential Phase Contrast (DPC) are quantitative phase imaging (QPI) methods that recover the complex transmittance function of a sample through coded illumination measurements and phase retrieval optimization. The successes of these methods rely upon acquiring several or possibly hundreds of illumination-encoded measurements. The multi-shot nature of such methods limits their temporal resolution. Similar to motion-induced blur during a long photographic exposure, motion occurring during these acquisitions causes spatial distortion and errors in the reconstructed phase, which inhibits these methods' ability to image fast moving live samples. Here we present a novel approach to correct for motion during QPI capture that relies on motion navigation to register measurements together prior to phase retrieval. The different illumination patterns required for QPI cause the measurements to have a different contrasts. This makes it difficult to use standard registration approaches to estimate complex sample motion directly from the measurements. Instead, we use a color-multiplexed navigator signal (red) that is comprised of a constant illumination pattern and leverage a color camera to separate it from the primary QPI information (green). The reliable motion estimate allows measurements to be shared across time points through image registration. This enables a full set of measurements for a phase retrieval problem to be solved at each time point. We demonstrate proof-of-concept experimental results in which blurring due to live sample motion (swimming Zebra fish, cell motion, and organelle movement) is reduced.

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.

Terahertz lensless phase retrieval imaging is a promising technique for non-destructive inspection applications. In the conventional multiple-plane phase retrieval method, the convergence speed due to wave propagations and measures with equal interval distance is slow and leads to stagnation. To address this drawback, we propose a nonlinear unequal spaced measurement scheme in which the interval space between adjacent measurement planes is gradually increasing, it can significantly increase the diversity of the intensity with a smaller number of required images. Both the simulation and experimental results demonstrate that our method enables quantitative phase and amplitude imaging with a faster speed and better image quality, while also being computationally efficient and robust to noise.

Quantitative phase imaging (QPI) through multi-core fibers (MCFs) has been an emerging in vivo label-free endoscopic imaging modality with minimal invasiveness. However, the computational demands of conventional iterative phase retrieval algorithms have limited their real-time imaging potential. We demonstrate a learning-based MCF phase imaging method that significantly reduced the phase reconstruction time to 5.5 ms, enabling video-rate imaging at 181 fps. Moreover, we introduce an innovative optical system that automatically generated the first, to the best of our knowledge, open-source dataset tailored for MCF phase imaging, comprising 50,176 paired speckles and phase images. Our trained deep neural network (DNN) demonstrates a robust phase reconstruction performance in experiments with a mean fidelity of up to 99.8%. Such an efficient fiber phase imaging approach can broaden the applications of QPI in hard-to-reach areas.

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.

Microscopy combined with the transport of intensity equation is capable of retrieving both intensity and phase distributions of samples from both in-focus and defocus intensities. However, during measurements, the focal plane is often decided artificially and the improper choice may induce errors in quantitative intensity and phase retrieval. In order to obtain accurate in-focus information, quantitative intensity and phase imaging with the numerical focusing transport of intensity equation method combined with cellular duty ratio criterion and numerical wavefront propagation is introduced in this paper. Both numerical simulations and experimental measurements are provided proving this designed method can increase both retrieved in-focus intensity and phase accuracy and reduce dependence of focal plane determination in transport of intensity equation measurements. It is believed that the proposed method can be potentially applied in various fields as in-focus compensation for quantitative phase imaging and automatic focal plane determination, etc.

Quantitative differential phase-contrast (DPC) imaging is one of the commonly used methods for phase retrieval. However, quantitative DPC imaging requires several pairwise intensity measurements, which makes it difficult to monitor living cells in real-time. In this study, we present a single-shot quantitative DPC imaging method based on the combination of deep learning (DL) and color-encoded illumination. Our goal is to train a model that can generate an isotropic quantitative phase image (i.e., target) directly from a single-shot intensity measurement (i.e., input). The target phase image was reconstructed using a linear-gradient pupil with two-axis measurements, and the model input was the measured color intensities obtained from a radially asymmetric color-encoded illumination pattern. The DL-based model was trained, validated, and tested using thirteen different cell lines. The total number of training, validation, and testing images was 264 (10 cells), 10 (1 cell), and 40 (2 cells), respectively. Our results show that the DL-based phase images are visually similar to the ground-truth phase images and have a high structural similarity index (>0.98). Moreover, the phase difference between the ground-truth and DL-based phase images was smaller than 13%. Our study shows the feasibility of using DL to generate quantitative phase imaging from a single-shot intensity measurement.

Quantitative phase imaging (QPI) provides enhanced contrast for weakly absorbing specimens such as biological tissues under optical light and soft materials under X-ray. In this work, we develop a model-based phase retrieval framework by integrating the physics principles of phase imaging with the deep learning-based approach. Both measurements and the forward model are used as the inputs for a model-based neural network. The features of the object and the regularization weight of the established priors are learned by minimizing the difference between the network output to the ground truth during the training process. This method is tested on phase imaging of handwriting digital patterns and biological cells in a simulation of propagation-based TIE (transport of intensity equation) phase retrieval. We achieve enhanced accuracy for the phase retrieval compared to non-model based end-to-end neural networks and reduce the computation cost compared to traditional model-based iterative reconstruction algorithms.

The following article describes a method for 3D reconstruction of multi-material objects based on propagation-based X-ray phase-contrast tomography (PB-CT) with phase retrieval using the homogeneous form of the transport of intensity equation (TIE-Hom). Unlike conventional PB-CT algorithms that perform phase retrieval of individual projections, the described post-reconstruction phase-retrieval method is applied in 3D to a localized region of the CT-reconstructed volume. This work demonstrates, via numerical simulations, the accuracy and noise characteristics of the method under a variety of experimental conditions, comparing it with both conventional absorption tomography and 2D TIE-Hom phase retrieval applied to projection images. The results indicate that the 3D post-reconstruction method generally achieves a modest improvement in noise suppression over existing PB-CT methods. It is also shown that potentially large computational gains over projection-based phase retrieval for multi-material samples are possible. In particular, constraining phase retrieval to a localized 3D region of interest reduces the overall computational cost and eliminates the need for multiple CT reconstructions and global 2D phase retrieval operations for each material within the sample.

Phase-contrast x-ray computed tomography (PCCT) is currently investigated as an interesting extension of conventional CT, providing high soft-tissue contrast even if examining weakly absorbing specimen. Until now, the potential for dose reduction was thought to be limited compared to attenuation CT, since meaningful phase retrieval fails for scans with very low photon counts when using the conventional phase retrieval method via phase stepping. In this work, we examine the statistical behaviour of the reverse projection method, an alternative phase retrieval approach and compare the results to the conventional phase retrieval technique. We investigate the noise levels in the projections as well as the image quality and quantitative accuracy of the reconstructed tomographic volumes. The results of our study show that this method performs better in a low-dose scenario than the conventional phase retrieval approach, resulting in lower noise levels, enhanced image quality and more accurate quantitative values. Overall, we demonstrate that the lower statistical limit of the phase stepping procedure as proposed by recent literature does not apply to this alternative phase retrieval technique. However, further development is necessary to overcome experimental challenges posed by this method which would enable mainstream or even clinical application of PCCT.

Wedge prism assisted quantitative phase imaging on standard microscopes

Existing quantitative phase imaging (QPI) techniques are faced with an inherent trade-off between phase imaging fidelity and temporal resolution. Here, we propose a general algorithmic framework for QPI reconstruction that enables frame-rate-limited holographic imaging. It takes an inverse problem approach by formulating phase retrieval as a nonsmooth nonconvex optimization problem. Efficient solvers for the problem are derived whose algorithmic behaviors have been studied from both theoretical and experimental perspectives. The proposed framework is applicable to various existing holographic imaging configurations, and makes it possible to incorporate advanced image priors for quality enhancement.

Computational approaches in 3D quantitative phase Imaging: Current and future trends in cellular imaging.