Two improved defocus quantitative phase imaging methods: discussion.

Digital holographic microscopy (DHM), which provides quantitative phase imaging (QPI), has been widely applied in material and biological applications. The performance of DHM technologies relies heavily on computational reconstruction methods to provide accurate phase measurements. For example, non-telecentric DHM systems should compensate for the spherical wavefront associated with a non-telecentric configuration. The size of the ±1 diffraction orders in the hologram spectrum depends inversely on the radius of the curvature of the spherical wavefront introduced by the non-telecentric DHM system. Therefore, one can estimate the radius of curvature of the spherical wavefront by analyzing the hologram spectrum. Here, we outline the steps for the automatic reconstruction of phase images without distortions and with minimum user input from a hologram recorded in a non-telecentric DHM system. The proposed reconstruction approach can be divided into six main steps. The first step automatically selects the +1 diffraction order in the hologram spectrum. Secondly, the spherical wavefront parameters and the interference angle are estimated by analyzing the size and position of the selected +1 order. The third and fourth steps are the spatial filtering of the +1 order and the compensation of the interference angle, respectively. The next step involves the estimation of the center of the spherical wavefront. Finally, there is a fine-tuning step to optimize the estimated parameters and provide a phase image with minimum phase distortions. We have identified the relevant metrics in each step, compared multiple approaches, and selected the one with the higher performance for all our experimental holograms.

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.

Blood testing has been used as an essential tool to diagnose diseases for decades. Recently, there has been a rapid developing trend in using Quantitative Phase Imaging (QPI) methods for blood cell screening. Compared to traditional blood testing techniques, QPI has the advantage of avoiding dyeing or staining the specimen, which may cause damage to the cells. However, most existing systems are bulky and costly, requiring experienced personnel to operate. This work demonstrates the integration of one QPI method onto a smartphone platform and the application of imaging red blood cells. The adopted QPI method is based on solving the Intensity Transport Equation (ITE) from two de-focused pupil images taken in one shot by the smartphone camera. The device demonstrates a system resolution of about 1 μm, and is ready to be used for 3D morphological study of red blood cells.

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.

A computational phase retrieval method is presented that utilizes the transport of intensity equation (TIE) and its solution as a physics-based prior in an iterative reconstruction process. TIE is a non-interferometric quantitative phase imaging (QPI) method that is experimentally simple to implement, needing a minimum of two through focus intensity measurements. However, the accuracy of TIE is severely affected by certain theoretical and practical limitations such as the requirement of uniform intensity, prior knowledge of boundary conditions. Moreover, the finite-difference approximation for intensity derivatives produces blurring for large defocus distances. We propose an iterative phase recovery algorithm that updates the required phase by minimizing the difference of axial intensity derivatives obtained using experiments and expected from angular spectrum propagation theory while integrating a TIE phase-compensation solution in the iterative steps for a fast and accurate phase recovery. We show the validity of the proposed algorithm with simulations for different cases of non-uniform intensity, noise, boundary conditions, and defocus distance. We experimentally verify the working of the proposed method for large defocus distances and compare the results with standard TIE solutions and algorithms to verify its robustness.

Tomographic deconvolution phase microscopy (TDPM) is a three-dimensional (3D) quantitative phase imaging (QPI) method using partially coherent light that can be implemented on a commercial microscope platform. However, the measurement procedure is relatively time-consuming because it requires many illumination angles. In the present work, an edge-preserving iterative optimization algorithm is presented and applied to TDPM, so that the required number of illumination angles is reduced from 15 to 3, while the measurement accuracy remains high. In addition, the iterative algorithm does not require matrix representation of operators, so the memory requirement is correspondingly reduced.

A Michelson interferometer is commonly used for evaluating the morphology of a cell. However, the interference imaging with reference and object beams is easily affected by external vibrations and environmental disturbances, leading to unstable interference patterns. In this paper, the three-dimensional surface morphology of the biological cell is evaluated by a new quantitative phase imaging method, which couples Michelson-like lateral shear interferometric microscopy with self-referencing numerical phase calibration. The Michelson-like lateral shear interferometric microscopy is constructed by replacing the two plane mirrors of the traditional Michelson interferometer with two common right-angle prisms and generates interference fringe patterns. The lateral shear is created and freely adjustable by simply translating/or rotating one right-angle prism. To calculate the phase information of the biological cells quantitatively, the classical Fourier transform method is used to process the recorded interferogram, and then the self-referencing numerical phase calibration method is utilized for acquiring accurate phase information. Successfully achieving quantitative phase imaging of a cell verifies the feasibility and practicability of the proposed method.

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.

Diffraction Phase Microscopy (DPM) is a widely used quantitative phase imaging method, whose common-path nature endows it with low noise and high sensitivity. Current applications of DPM include biological topography as well as biological dynamics for its nondestructive feature. Many different forms of DPM based on the original idea have appeared according to the different demands. In this paper, both the principle and the DPM classification will be given a comprehensive description. Furthermore, the future trend of DPM development is also discussed.

Quantitative phase imaging (QPI) has emerged as a powerful tool in label-free bioimaging, in situ microstructure characterization for advanced manufacturing, and high-speed imaging of material property changes. Among various QPI methods, quadri-wave lateral shearing interferometry (QWLSI) stands out for its unique advantages in compactness, robustness, and high temporal resolution, making it an ideal choice for a wide range of applications. The compact design of QWLSI allows for easy integration with existing microscopy systems, while its robustness is manifested in the ability to maintain precise interferometric sensitivity even in high-vibration environments. Moreover, QWLSI also enables single-shot measurements that facilitate the capture of fast dynamic processes. This paper provides an in-depth exploration of the technical aspects of QWLSI, focusing on the evolution of its optical system and the primary algorithms used in wavefront reconstruction. The review also showcases significant applications of QWLSI, with a particular emphasis on its contributions to biomedical imaging. By discussing the advantages, limitations, and potential future developments of QWLSI, this paper aims to provide a comprehensive overview of this powerful QPI technique and its impact on various research fields.

White light diffraction phase microscopy with slightly off-axis blind two-step phase-shifting

Quantitative phase imaging provides a way to image transparent objects, such as biological cells, and measure their thickness. We report on a phase-imaging method that achieves twice the phase shift and approximately 1.7 times the spatial resolution of an equivalent spatially and temporally coherent classical quantitative phase-imaging system by using quantum interference between successive spontaneous parametric downconversion events in a nonlinear crystal. Furthermore, our method is approximately 1000 times faster than imaging the parametric downconversion photons in coincidence, which requires measurement times on the order of tens of hours. Our method may be useful for imaging sensitive transparent objects that require low illumination intensities at near-infrared and longer illumination wavelengths, such as photosensitive biological samples.

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.

Objective Task-Based Evaluation of Quantitative Medical Imaging Methods: Emerging Frameworks and Future Directions.

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.