Quantitative optical phase microscopy

Label-Free Single Nanoparticle Identification and Characterization in Demanding Environment, Including Infectious Emergent Virus

Unknown particle screening-including virus and nanoparticles-are keys in medicine, industry, and also in water pollutant determination. Here, RYtov MIcroscopy for Nanoparticles Identification (RYMINI) is introduced, a staining-free, non-invasive, and non-destructive optical approach that is merging holographic label-free 3D tracking with high-sensitivity quantitative phase imaging into a compact optical setup. Dedicated to the identification and then characterization of single nano-object in solution, it is compatible with highly demanding environments, such as level 3 biological laboratories, with high resilience to external source of mechanical and optical noise. Metrological characterization is performed at the level of each single particle on both absorbing and transparent particles as well as on immature and infectious HIV, SARS-CoV-2 and extracellular vesicles in solution. The capability of RYMINI to determine the nature, concentration, size, complex refractive index and mass of each single particle without knowledge or model of the particles' response is demonstrated. The system surpasses 90% accuracy for automatic identification between dielectric/metallic/biological nanoparticles and ≈80% for intraclass chemical determination of metallic and dielectric. It falls down to 50-70% for type determination inside the biological nanoparticle's class.

Toward cell nuclei precision between OCT and H&E images translation using signal-to-noise ratio cycle-consistency

Medical image-to-image translation is often difficult and of limited effectiveness due to the differences in image acquisition mechanisms and the diverse structure of biological tissues. This work presents an unpaired image translation model between in-vivo optical coherence tomography (OCT) and ex-vivo Hematoxylin and eosin (H&E) stained images without the need for image stacking, registration, post-processing, and annotation. The model can generate high-quality and highly accurate virtual medical images, and is robust and bidirectional. Our framework introduces random noise to (1) blur redundant features, (2) defend against self-adversarial attacks, (3) stabilize inverse conversion, and (4) mitigate the impact of OCT speckles. We also demonstrate that our model can be pre-trained and then fine-tuned using images from different OCT systems in just a few epochs. Qualitative and quantitative comparisons with traditional image-to-image translation models show the robustness of our proposed signal-to-noise ratio (SNR) cycle-consistency method.

Structured illumination contrast transfer function for high resolution quantitative phase imaging

We report a sub-diffraction resolution imaging of non-fluorescent samples through quantitative phase imaging. This is achieved through a novel application of structured illumination microscopy (SIM), a super-resolution imaging technique established primarily for fluorescence microscopy. Utilizing our contrast transfer function formalism with SIM, we extract the high spatial frequency components of the phase profile from the defocused intensity images, enabling the reconstruction of a quantitative phase image with a frequency spectrum that surpasses the diffraction limit imposed by the imaging system. Our approach offers several advantages including a deterministic, phase-unwrapping-free algorithm and an easily implementable, non-interferometric setup. We validate the proposed technique for high-resolution phase imaging through both simulation and experimental results, demonstrating a two-fold enhancement in resolution. A lateral resolution of 0.814 µm is achieved for the phase imaging of human cheek cells using a 0.42 NA objective lens and an illumination wavelength of 660 nm, highlighting the efficacy of our approach for high-resolution quantitative phase imaging.

Untrained deep learning-based differential phase-contrast microscopy

Quantitative differential phase-contrast (DPC) microscopy produces phase images of transparent objects based on a number of intensity images. To reconstruct the phase, in DPC microscopy, a linearized model for weakly scattering objects is considered; this limits the range of objects to be imaged, and requires additional measurements and complicated algorithms to correct for system aberrations. Here, we present a self-calibrated DPC microscope using an untrained neural network (UNN), which incorporates the nonlinear image formation model. Our method alleviates the restrictions on the object to be imaged and simultaneously reconstructs the complex object information and aberrations, without any training dataset. We demonstrate the viability of UNN-DPC microscopy through both numerical simulations and LED microscope-based experiments.

Quantitative phase gradient metrology using diffraction phase microscopy and deep learning

In quantitative phase microscopy, measurement of the phase gradient is an important problem for biological cell morphological studies. In this paper, we propose a method based on a deep learning approach that is capable of direct estimation of the phase gradient without the requirement of phase unwrapping and numerical differentiation operations. We show the robustness of the proposed method using numerical simulations under severe noise conditions. Further, we demonstrate the method's utility for imaging different biological cells using diffraction phase microscopy setup.

Hilbert phase microscopy based on pseudo thermal illumination in the Linnik configuration

Quantitative phase microscopy (QPM) is often based on recording an object-reference interference pattern and its further phase demodulation. We propose pseudo Hilbert phase microscopy (PHPM) where we combine pseudo thermal light source illumination and Hilbert spiral transform (HST) phase demodulation to achieve hybrid hardware-software-driven noise robustness and an increase in resolution of single-shot coherent QPM. Those advantageous features stem from physically altering the laser spatial coherence and numerically restoring spectrally overlapped object spatial frequencies. The capabilities of PHPM are demonstrated by analyzing calibrated phase targets and live HeLa cells in comparison with laser illumination and phase demodulation via temporal phase shifting (TPS) and Fourier transform (FT) techniques. The performed studies verified the unique ability of PHPM to combine single-shot imaging, noise minimization, and preservation of phase details.

Force Estimation during Cell Migration Using Mathematical Modelling

Cell migration is essential for physiological, pathological and biomedical processes such as, in embryogenesis, wound healing, immune response, cancer metastasis, tumour invasion and inflammation. In light of this, quantifying mechanical properties during the process of cell migration is of great interest in experimental sciences, yet few theoretical approaches in this direction have been studied. In this work, we propose a theoretical and computational approach based on the optimal control of geometric partial differential equations to estimate cell membrane forces associated with cell polarisation during migration. Specifically, cell membrane forces are inferred or estimated by fitting a mathematical model to a sequence of images, allowing us to capture dynamics of the cell migration. Our approach offers a robust and accurate framework to compute geometric mechanical membrane forces associated with cell polarisation during migration and also yields geometric information of independent interest, we illustrate one such example that involves quantifying cell proliferation levels which are associated with cell division, cell fusion or cell death.

Quantitative phase and refractive index imaging of 3D objects via optical transfer function reshaping

Deconvolution phase microscopy enables high-contrast visualization of transparent samples through reconstructions of their transmitted phases or refractive indexes. Herein, we propose a method to extend 2D deconvolution phase microscopy to thick 3D samples. The refractive index distribution of a sample can be obtained at a specific axial plane by measuring only four intensity images obtained under optimized illumination patterns. Also, the optical phase delay of a sample can be measured using different illumination patterns.

Intermixed Time-Dependent Self-Focusing and Defocusing Nonlinearities in Polymer Solutions

Low-power visible light can lead to spectacular nonlinear effects in soft-matter systems. The propagation of visible light through transparent solutions of certain polymers can experience either self-focusing or defocusing nonlinearity, depending on the solvent. We show how the self-focusing and defocusing responses can be captured by a nonlinear propagation model using local spatial and time-integrating responses. We realize a remarkable pattern formation in ternary solutions and model it assuming a linear combination of the self-focusing and defocusing nonlinearities in the constituent solvents. This versatile response of solutions to light irradiation may introduce a new approach for self-written waveguides and patterns.

Stability of Intracellular Protein Concentration under Extreme Osmotic Challenge

Cell volume (CV) regulation is typically studied in short-term experiments to avoid complications resulting from cell growth and division. By combining quantitative phase imaging (by transport-of-intensity equation) with CV measurements (by the exclusion of an external absorbing dye), we were able to monitor the intracellular protein concentration (PC) in HeLa and 3T3 cells for up to 48 h. Long-term PC remained stable in solutions with osmolarities ranging from one-third to almost twice the normal. When cells were subjected to extreme hypoosmolarity (one-quarter of normal), their PC did not decrease as one might expect, but increased; a similar dehydration response was observed at high concentrations of ionophore gramicidin. Highly dilute media, or even moderately dilute in the presence of cytochalasin, caused segregation of water into large protein-free vacuoles, while the surrounding cytoplasm remained at normal density. These results suggest that: (1) dehydration is a standard cellular response to severe stress; (2) the cytoplasm resists prolonged dilution. In an attempt to investigate the mechanism behind the homeostasis of PC, we tested the inhibitors of the protein kinase complex mTOR and the volume-regulated anion channels (VRAC). The initial results did not fully elucidate whether these elements are directly involved in PC maintenance.

Optical module for single-shot quantitative phase imaging based on the transport of intensity equation with field of view multiplexing

We present a cost-effective, simple, and robust method that enables single-shot quantitative phase imaging (QPI) based on the transport of intensity equation (TIE) using an add-on optical module that can be assembled into the exit port of any regular microscope. The module integrates a beamsplitter (BS) cube (placed in a non-conventional way) for duplicating the output image onto the digital sensor (field of view - FOV - multiplexing), a Stokes lens (SL) for astigmatism compensation (introduced by the BS cube), and an optical quality glass plate over one of the FOV halves for defocusing generation (needed for single-shot TIE algorithm). Altogether, the system provides two laterally separated intensity images that are simultaneously recorded and slightly defocused one to each other, thus enabling accurate QPI by conventional TIE-based algorithms in a single snapshot. The proposed optical module is first calibrated for defining the configuration providing best QPI performance and, second, experimentally validated by using different phase samples (static and dynamic ones). The proposed configuration might be integrated in a compact three-dimensional (3D) printed module and coupled to any conventional microscope for QPI of dynamic transparent samples.

Nanophotonics enhanced coverslip for phase imaging in biology

The ability to visualise transparent objects such as live cells is central to understanding biological processes. Here we experimentally demonstrate a novel nanostructured coverslip that converts phase information to high-contrast intensity images. This compact device enables real-time, all-optical generation of pseudo three-dimensional images of phase objects on transmission. We show that by placing unstained human cancer cells on the device, the internal structure within the cells can be clearly seen. Our research demonstrates the significant potential of nanophotonic devices for integration into compact imaging and medical diagnostic devices. The nanophotonics enhanced coverslip (NEC) enables ultra-compact phase imaging of samples placed directly on top of the device. Visualisation of artificial phase objects and unstained biological cells is demonstrated.

Accurate quantitative phase imaging by the transport of intensity equation: a mixed-transfer-function approach

As a well-established deterministic phase retrieval approach, the transport of intensity equation (TIE) is able to recover the quantitative phase of a sample under coherent or partially coherent illumination with its through-focus intensity measurements. Nevertheless, the inherent paraxial approximation limits its validity to low-numerical-aperture imaging and slowly varying objects, precluding its application to high-resolution quantitative phase imaging (QPI). Alternatively, QPI can be achieved by phase deconvolution approaches based on the coherent contrast transfer function or partially coherent weak object transfer function (WOTF) without invoking paraxial approximation. But these methods are generally appropriate for "weakly scattering" samples in which the total phase delay induced by the object should be small. Consequently, high-resolution high-accuracy QPI of "nonweak" phase objects with fine details and large phase excursions remains a great challenge. In this Letter, we propose a mixed-transfer-function (MTF) approach to address the dilemma between measurement accuracy and imaging resolution. By effectively merging the phases reconstructed by TIE and WOTF in the frequency domain, the high-accuracy low-frequency phase "global" profile can be secured, and high-resolution high-frequency features can be well preserved simultaneously. Simulations and experimental results on a microlens array and unstained biological cells demonstrate the effectiveness of MTF.

Deep learning for label-free nuclei detection from implicit phase information of mesenchymal stem cells

Monitoring of adherent cells in culture is routinely performed in biological and clinical laboratories, and it is crucial for large-scale manufacturing of cells needed in cell-based clinical trials and therapies. However, the lack of reliable and easily implementable label-free techniques makes this task laborious and prone to human subjectivity. We present a deep-learning-based processing pipeline that locates and characterizes mesenchymal stem cell nuclei from a few bright-field images captured at various levels of defocus under collimated illumination. Our approach builds upon phase-from-defocus methods in the optics literature and is easily applicable without the need for special microscopy hardware, for example, phase contrast objectives, or explicit phase reconstruction methods that rely on potentially bias-inducing priors. Experiments show that this label-free method can produce accurate cell counts as well as nuclei shape statistics without the need for invasive staining or ultraviolet radiation. We also provide detailed information on how the deep-learning pipeline was designed, built and validated, making it straightforward to adapt our methodology to different types of cells. Finally, we discuss the limitations of our technique and potential future avenues for exploration.

Experimental test of the geometric model of image formation in bright-field microscopy

In the geometric optics approximation, an image formed by an objective lens replicates the distribution of intensity at the front focal plane of the objective. Although this fact represents a fundamental optical principle, its application to analysis of bright-field microscopic images was developed only recently and has not been tested experimentally. In this paper, we applied simple ray tracing to compute an image of a glass cylinder at various positions of the objective and to compare it to the experiment. We obtained a close match between theory and observation, except for a slight underestimation of the intensity in the middle part of the cylinder. The likely reason for this minor difference was constructive interference due to lens-like properties of a cylinder, which could not be accounted for by geometric approximation. We expect that such artefacts would be negligible in imaging of live cells, and the geometric approach would successfully complement the existing quantitative phase methods.

3D imaging using scanning diffractometry

Imaging of cells is a challenging problem as they do not appreciably change the intensity of the illuminating light. Interferometry-based methods to do this task suffer from high sensitivity to environmental vibrations. We introduce scanning diffractometry as a simple non-contact and vibration-immune methodology for quantitative phase imaging. Fresnel diffractometry by a phase step has led to several applications such as high-precision measurements of displacement. Additional scanning may lead to 3D imaging straightforwardly. We apply the technique to acquire 3D images of holographic grating, red blood cell, neuron, and sperm cell. Either visibility of the diffraction fringes or the positions of extrema may be used for phase change detection. The theoretical analysis through the Fresnel diffraction from one-dimensional phase step is presented and the experimental results are validated with digital holographic microscopy. The presented technique can be suggested to serve as a robust device for 3D phase imaging and biomedical measurements.

Biophysical phenotyping of mesenchymal stem cells along the osteogenic differentiation pathway

Mesenchymal stem cells represent an important resource, for bone regenerative medicine and therapeutic applications. This review focuses on new advancements and biophysical tools which exploit different physical and chemical markers of mesenchymal stem cell populations, to finely characterize phenotype changes along their osteogenic differentiation process. Special attention is paid to recently developed label-free methods, which allow monitoring cell populations with minimal invasiveness. Among them, quantitative phase imaging, suitable for single-cell morphometric analysis, and nanoindentation, functional to cellular biomechanics investigation. Moreover, the pool of ion channels expressed in cells during differentiation is discussed, with particular interest for calcium homoeostasis.Altogether, a biophysical perspective of osteogenesis is proposed, offering a valuable tool for the assessment of the cell stage, but also suggesting potential physiological links between apparently independent phenomena.

Acoustofluidic phase microscopy in a tilted segmentation-free configuration

A low-cost device for registration-free quantitative phase microscopy (QPM) based on the transport of intensity equation of cells in continuous flow is presented. The method uses acoustic focusing to align cells into a single plane where all cells move at a constant speed. The acoustic focusing plane is tilted with respect to the microscope's focal plane in order to obtain cell images at multiple focal positions. As the cells are displaced at constant speed, phase maps can be generated without the need to segment and register individual objects. The proposed inclined geometry allows for the acquisition of a vertical stack without the need for any moving part, and it enables a cost-effective and robust implementation of QPM. The suitability of the solution for biological imaging is tested on blood samples, demonstrating the ability to recover the phase map of single red blood cells flowing through the microchip.

Modified inverted selective plane illumination microscopy for sub-micrometer imaging resolution in polydimethylsiloxane soft lithography devices

Moldable, transparent polydimethylsiloxane (PDMS) elastomer microdevices enable a broad range of complex studies of three-dimensional cellular networks in their microenvironment in vitro. However, the uneven distribution of refractive index change, external to PDMS devices and internally in the sample chamber, creates a significant optical path difference (OPD) that distorts the light sheet beam and so restricts diffraction limited performance. We experimentally showed that an OPD of 120 μm results in the broadening of the lateral point spread function by over 4-fold. In this paper, we demonstrate steps to adapt a commercial inverted selective plane illumination microscope (iSPIM) and remove the OPD so as to achieve sub-micrometer imaging ranging from 0.6 ± 0.04 μm to 0.91 ± 0.03 μm of a fluorescence biological sample suspended in regular saline (RI ≈1.34) enclosed in 1.2 to 2 mm thick micromolded PDMS microdevices. We have proven that the removal of the OPD from the external PDMS layer by refractive index (RI) matching with a readily accessible, inexpensive sucrose solution is critical to achieve a >3-fold imaging resolution improvement. To monitor the RI matching process, a single-mode fiber (SMF) illuminator was integrated into the iSPIM. To remove the OPD inside the PDMS channel, we used an electrically tunable lens (ETL) that par-focuses the light sheet beam with the detection objective lens and so minimised axial distortions to attain sub-micrometer imaging resolution. We termed this new light sheet imaging protocol as modified inverted selective plane illumination microscopy (m-iSPIM). Using the high spatial-temporal 3D imaging of m-iSPIM, we experimentally captured single platelet (≈2 μm) recruitment to a platelet aggregate (22.5 μm × 22.5 μm × 6 μm) under flow at a 150 μm depth within a microfluidic channel. m-iSPIM paves the way for the application of light sheet imaging to a wide range of 3D biological models in microfluidic devices which recapitulate features of the physiological microenvironment and elucidate subcellular responses.

On a universal solution to the transport-of-intensity equation

The transport-of-intensity equation (TIE) is one of the most well-known approaches for phase retrieval and quantitative phase imaging. It directly recovers the quantitative phase distribution of an optical field by through-focus intensity measurements in a non-interferometric, deterministic manner. Nevertheless, the accuracy and validity of state-of-the-art TIE solvers depend on restrictive pre-knowledge or assumptions, including appropriate boundary conditions, a well-defined closed region, and quasi-uniform in-focus intensity distribution, which, however, cannot be strictly satisfied simultaneously under practical experimental conditions. In this Letter, we propose a universal solution to TIE with the advantages of high accuracy, convergence guarantee, applicability to arbitrarily shaped regions, and simplified implementation and computation. With the "maximum intensity assumption," we first simplify TIE as a standard Poisson equation to get an initial guess of the solution. Then the initial solution is further refined iteratively by solving the same Poisson equation, and thus the instability associated with the division by zero/small intensity values and large intensity variations can be effectively bypassed. Simulations and experiments with arbitrary phase, arbitrary aperture shapes, and nonuniform intensity distributions verify the effectiveness and universality of the proposed method.

Single-shot sequential projection phase retrieval and 3D localization from chromatic aberration

A phase retrieval method based on sequential projection and chromatic aberration is reported. Construction of this method includes a red, green and blue (RGB) LED, an objective and a color camera. Owing to the chromatic aberration characteristics of the objective, three color images obtained by the color camera correspond to three equivalent propagation planes. Equivalent relative distances among these planes can be obtained by defining and iteratively minimizing the convergence index. Then, sequential projection strategy is used for phase retrieval in each image plane. Based on the recovered phase information and angular spectrum propagation principle, digital refocusing and 3D localization can be achieved for each subregion of the sample. Finally, the feasibility of our method is demonstrated by simulations and experiments.

Comparative phase imaging of live cells by digital holographic microscopy and transport of intensity equation methods

We describe a microscopic setup implementing phase imaging by digital holographic microscopy (DHM) and transport of intensity equation (TIE) methods, which allows the results of both measurements to be quantitatively compared for either live cell or static samples. Digital holographic microscopy is a well-established method that provides robust phase reconstructions, but requires a sophisticated interferometric imaging system. TIE, on the other hand, is directly compatible with bright-field microscopy, but is more susceptible to noise artifacts. We present results comparing DHM and TIE on a custom-built microscope system that allows both techniques to be used on the same cells in rapid succession, thus permitting the comparison of the accuracy of both methods.

PhUn-Net: ready-to-use neural network for unwrapping quantitative phase images of biological cells

We present a deep-learning approach for solving the problem of 2π phase ambiguities in two-dimensional quantitative phase maps of biological cells, using a multi-layer encoder-decoder residual convolutional neural network. We test the trained network, PhUn-Net, on various types of biological cells, captured with various interferometric setups, as well as on simulated phantoms. These tests demonstrate the robustness and generality of the network, even for cells of different morphologies or different illumination conditions than PhUn-Net has been trained on. In this paper, for the first time, we make the trained network publicly available in a global format, such that it can be easily deployed on every platform, to yield fast and robust phase unwrapping, not requiring prior knowledge or complex implementation. By this, we expect our phase unwrapping approach to be widely used, substituting conventional and more time-consuming phase unwrapping algorithms.

X-ray Fokker-Planck equation for paraxial imaging

The Fokker-Planck equation can be used in a partially-coherent imaging context to model the evolution of the intensity of a paraxial x-ray wave field with propagation. This forms a natural generalisation of the transport-of-intensity equation. The x-ray Fokker-Planck equation can simultaneously account for both propagation-based phase contrast, and the diffusive effects of sample-induced small-angle x-ray scattering, when forming an x-ray image of a thin sample. Two derivations are given for the Fokker-Planck equation associated with x-ray imaging, together with a Kramers-Moyal generalisation thereof. Both equations are underpinned by the concept of unresolved speckle due to unresolved sample micro-structure. These equations may be applied to the forward problem of modelling image formation in the presence of both coherent and diffusive energy transport. They may also be used to formulate associated inverse problems of retrieving the phase shifts due to a sample placed in an x-ray beam, together with the diffusive properties of the sample. The domain of applicability for the Fokker-Planck and Kramers-Moyal equations for paraxial imaging is at least as broad as that of the transport-of-intensity equation which they generalise, hence the technique is also expected to be useful for paraxial imaging using visible light, electrons and neutrons.

Phase-retrieval method for measuring small contact angles of pentane on water

Pentane drops on a water surface are predicted to have contact angles of the order of 1 degree or less in the phase of frustrated complete wetting. We have developed an optical method of measuring such small contact angles, applicable to cases where the refractive indices of the substrate and adsorbate are very similar and the fluid dynamics do not allow delay between image acquisitions, by using phase retrieval to map the surface profile of the drops. It is empirically shown that, with our method, a difference of nanometer order can be achieved for the phase-retrieved dimensions relative to their expected value. Results agree with numerical predictions by Weiss and Widom [Physica A292, 137 (2001)PHYADX0378-437110.1016/S0378-4371(00)00619-1].

Digital holography free of 2π ambiguity, using coherence modulation

In this Letter, a quantitative measurement method with an extended axial range in low-coherence light digital holography is presented. Based on the characteristics of the light source, the degree of coherence and phase values are obtained. Because the degree of coherence is modulated with respect to the optical path difference, it can be used to remove the 2π ambiguity of the phase, without the use of numerical or dual-wavelength methods. The mathematical procedures from three phase-shifting holograms are numerically described. From experimental results, the accurate measurements of a sample with high step are presented to confirm the effectiveness.

Simple adaptive mobile phone screen illumination for dual phone differential phase contrast (DPDPC) microscopy

Phase contrast imaging is widely employed in the physical, biological, and medical sciences. However, typical implementations involve complex imaging systems that amount to in-line interferometers. We adapt differential phase contrast (DPC) to a dual-phone illumination-imaging system to obtain phase contrast images on a portable mobile phone platform. In this dual phone differential phase contrast (dpDPC) microscope, semicircles are projected sequentially on the display of one phone, and images are captured using a low-cost, short focal length lens attached to the second phone. By numerically combining images obtained using these semicircle patterns, high quality DPC images with ≈ 2 micrometer resolution can be easily acquired with no specialized hardware, circuitry, or instrument control programs.

One-step robust deep learning phase unwrapping

Phase unwrapping is an important but challenging issue in phase measurement. Even with the research efforts of a few decades, unfortunately, the problem remains not well solved, especially when heavy noise and aliasing (undersampling) are present. We propose a database generation method for phase-type objects and a one-step deep learning phase unwrapping method. With a trained deep neural network, the unseen phase fields of living mouse osteoblasts and dynamic candle flame are successfully unwrapped, demonstrating that the complicated nonlinear phase unwrapping task can be directly fulfilled in one step by a single deep neural network. Excellent anti-noise and anti-aliasing performances outperforming classical methods are highlighted in this paper.

Label-free color staining of quantitative phase images of biological cells by simulated Rheinberg illumination

Modern microscopes are designed with functionalities that are tailored to enhance image contrast. Dark-field imaging, phase contrast, differential interference contrast, and other optical techniques enable biological cells and other phase-only objects to be visualized. Quantitative phase imaging refers to an emerging set of techniques that allow for the complex transmission function of the sample to be measured. With this quantitative phase image available, any optical technique can then be simulated; it is trivial to generate a phase contrast image or a differential interference contrast image. Rheinberg illumination, proposed almost a century ago, is an optical technique that applies color contrast to images of phase-only objects by introducing a type of optical staining via an amplitude filter placed in the illumination path that consists of two or more colors. In this paper, the complete theory of Rheinberg illumination is derived, from which an algorithm is proposed that can digitally simulate the technique. Results are shown for a number of quantitative phase images of diatom cells obtained via digital holographic microscopy. The results clearly demonstrate the potential of the technique for label-free color staining of subcellular features.

Stress-induced optical waveguides written by an ultrafast laser in Nd3+, Y3+ co-doped SrF2 crystals

In this paper, we report on the ultrafast laser-induced birefringence, refractive index changes, and enhanced photoluminescence properties in the volume of neodymium (Nd), yttrium (Y) co-doped strontium fluoride (SrF₂) and Nd, Y co-doped calcium fluoride (CaF₂) crystals. The optical waveguides written with 500 kHz repetition rate provided lowest propagation loss of 1.63±0.21  dB cm^-1 for transverse magnetic (TM) polarization at 632.8 nm in Nd,Y:SrF₂ crystal. The measured retardance can be interpreted by stress-induced birefringence related to the permanent volume expansion, photo induced by a non-spherical irradiated zone. The absorption, steady-state, and time-resolved photoluminescence properties are also carried out in and out of the laser irradiated zone, enabling the local changes of the Nd and Y network in Nd,Y:SrF₂, as well as well-preserved Nd fluorescence in the written optical waveguides.

Is multiplexed off-axis holography for quantitative phase imaging more spatial bandwidth-efficient than on-axis holography? [Invited]

Digital holographic microcopy is a thriving imaging modality that attracts considerable research interest due to its ability not only to create excellent label-free contrast but also to supply valuable physical information regarding the density and dimensions of the sample with nanometer-scale axial sensitivity. Three basic holographic recording geometries currently exist, including on-axis, off-axis, and slightly off-axis holography, each of which enables a variety of architectures in terms of bandwidth use and compression capacity. Specifically, off-axis holography and slightly off-axis holography allow spatial hologram multiplexing, enabling one to compress more information into the same digital hologram. In this paper, we define an efficiency score to analyze the various possible architectures and compare the signal-to-noise ratio and the mean squared error obtained using each of them, thus determining the optimal holographic method.

Simultaneous measurement and reconstruction tailoring for quantitative phase imaging

We propose simultaneous measurement and reconstruction tailoring (SMaRT) for quantitative phase imaging; it is a joint optimization approach to inverse problems wherein minimizing the expected end-to-end error yields optimal design parameters for both the measurement and reconstruction processes. Using simulated and experimentally-collected data for a specific scenario, we demonstrate that optimizing the design of the two processes together reduces phase reconstruction error over past techniques that consider these two design problems separately. Our results suggest at times surprising design principles, and our approach can potentially inspire improved solution methods for other inverse problems in optics as well as the natural sciences.

Motion-resolved quantitative phase imaging

The temporal resolution of quantitative phase imaging with Differential Phase Contrast (DPC) is limited by the requirement for multiple illumination-encoded measurements. This inhibits imaging of fast-moving samples. We present a computational approach to model and correct for non-rigid sample motion during the DPC acquisition in order to improve temporal resolution to that of a single-shot method and enable imaging of motion dynamics at the framerate of the sensor. Our method relies on the addition of a simultaneously-acquired color-multiplexed reference signal to enable non-rigid registration of measurements prior to phase retrieval. We show experimental results where we reduce motion blur from fast-moving live biological samples.

3D Imaging Based on Depth Measurement Technologies

Three-dimensional (3D) imaging has attracted more and more interest because of its widespread applications, especially in information and life science. These techniques can be broadly divided into two types: ray-based and wavefront-based 3D imaging. Issues such as imaging quality and system complexity of these techniques limit the applications significantly, and therefore many investigations have focused on 3D imaging from depth measurements. This paper presents an overview of 3D imaging from depth measurements, and provides a summary of the connection between the ray-based and wavefront-based 3D imaging techniques.

Wide-field anti-aliased quantitative differential phase contrast microscopy

Differential phase contrast (DPC) microscopy is a popular methodology to recover quantitative phase information of thin transparent samples under multi-axis asymmetric illumination patterns. Based on spatially partially coherent illuminations, DPC provides high-quality, speckle-free 3D reconstructions with lateral resolution up to twice the coherent diffraction limit, under the precondition that the pixel size of the imaging sensor is small enough to prevent spatial aliasing/undersampling. However, microscope cameras are in general designed to have a large pixel size so that the intensity information transmitted by the optical system cannot be adequately sampled or digitized. On the other hand, using an image sensor with a smaller pixel size or adding a magnification camera adapter to the camera can resolve the undersampling at the expense of a reduced field of view (FOV). To solve this tradeoff, we introduce a new variation of quantitative DPC approach, termed anti-aliased DPC (AADPC), which uses several aliased intensity images under asymmetric illuminations to recover wide-field aliasing-free phase images. Besides, phase transfer functions under different illumination patterns in DPC are analyzed to design an illumination scheme with better phase transfer characteristics. AADPC starts from an initial phase estimate obtained by a DPC-like deconvolution based on the system's weak phase transfer function under discrete half-annular illumination. Then the obtained initial phase map is further refined by the iterative de-multiplexing algorithm to overcome pixel-aliasing and improve the imaging resolution. The data redundancy requirement as well as the optimal illumination scheme of AADPC are analyzed and discussed based on several simulations, suggesting that the spatial undersampling can be mitigated through the iterative algorithm that uses only 4 images, yielding a nearly 4-fold increase in the space-bandwidth product (SBP) compared to the conventional DPC approach. We experimentally verify that AADPC can achieve a half-pitch imaging resolution of 345 nm, corresponding to 1.88× of the theoretical Nyquist-Shannon sampling resolution limit imposed by the sensor pixel size. The high-speed, high-throughput quantitative phase imaging capabilities of AADPC are also demonstrated by imaging HeLa cells mitosis in vitro, achieving a full-pitch lateral resolution of 665 nm across a wide FOV of 1.77mm² at 25 fps.

Adaptive dual-exposure fusion-based transport of intensity phase microscopy

Via the transport of intensity phase microscopy, quantitative phase can be retrieved directly from captured multi-focal intensities. The accuracy of the retrieved phases depends highly on the quality of the recorded images; therefore, the exposure time should be carefully chosen for high-quality intensity captures. However, it is difficult to record well-exposure intensities to maintain rather a high signal to noise ratio and to avoid over-exposure due to the complex samples. In order to simplify the exposure determination, here the adaptive dual-exposure fusion-based transport of intensity phase microscopy is proposed: with captured short- and long-exposure images, the well-exposure multi-focal images can be numerically reconstructed, and then high-accurate phase can be computed from these reconstructed intensities. With both simulations and experiments provided in this paper, it is proved that the adaptive dual-exposure fusion-based transport of intensity phase microscopy not only provides numerically reconstructed well-exposure image with simple operation and fast speed but also extracts highly accurate retrieved phase. Moreover, the exposure time selection scope of the proposed method is much wider than that based on single exposure, and even though there is an over-exposure region in the long-exposure image, a well-exposure image can still be reconstructed with high precision. Considering its advantages of high accuracy, fast speed, simple operation, and wide application scope, the proposed technique can be adopted as quantitative phase microscopy for high-quality observations and measurements.

Lensfree dynamic super-resolved phase imaging based on active micro-scanning

In this Letter, we present a new active micro-scanning-based imaging platform and associated super-resolution (SR) phase retrieval method in lensfree microscopy to achieve SR dynamic phase imaging. The samples are illuminated by a nearly coherent illumination system, where two orthogonal parallel plates are inserted into the light path and rotate to achieve controllable source micro-scanning, permitting sub-pixel shifts of the holograms on x- and y-axis directions independently. Then sequential low-resolution sub-pixel-shifted holograms are processed to enhance spatial resolution and reconstruct quantitative phase images of the sample simultaneously. The reconstruction result of the benchmark quantitative phase microscopy target (QPT^TM) demonstrates a half-pitch lateral resolution of 775 nm across a large field-of-view of ∼29.84  mm², surpassing 2.15 times that of the theoretical Nyquist-Shannon sampling resolution limit imposed by the pixel size of the imaging sensor (1.67 μm). The proposed approach is also evaluated by imaging unstained HeLa cells, suggesting it is a promising toolset for high-throughput monitoring and quantitative analysis of unlabeled biological samples.

Single-shot quantitative phase microscopy based on color-multiplexed Fourier ptychography

We present a single-shot quantitative phase imaging (QPI) method based on color-multiplexed Fourier ptychographic microscopy (FPM). Three light-emitting diode (LED) elements with respective R/G/B channels in a programmable LED array illuminate the specimen simultaneously, providing triangle oblique illuminations matching the numerical aperture of the objective precisely. A color image sensor records the light transmitted through the specimen, and three monochromatic intensity images at each color channel are then separated and utilized to recover the phase of the specimen. After one-step deconvolution based on the phase contrast transfer function, the obtained initial phase map is further refined by the FPM-based iterative recovery algorithm to overcome pixel-aliasing and improve the phase recovery accuracy. The high-speed, high-throughput QPI capabilities of the proposed approach are demonstrated by imaging HeLa cells mitosis in vitro, achieving a half-pitch resolution of 388 nm across a wide field of view of 1.33  mm² at camera-limited frame rates (50 fps).

Solvent-Dependent Light-Induced Structures in Gem-Dichlorocyclopropanated Polybutadiene Solutions

The formation of permanent structures upon mild red laser illumination in transparent polydiene solutions is examined in the case of gem-dichlorocyclopropanated polybutadiene (gDCC-PB) polymers bearing 15% functional units of the dichlorocyclopropane groups. The response was found to be distinct from the precursor PB. Whereas fiber-like patterns were clearly observed in both precursor and gDCC-PB solutions in cyclohexane, these were absent in the case of gDCC-PB/chloroform but were present in the precursor PB/chloroform solutions. The involved mechanical stresses were not sufficient for the gDCC activation to be detected by NMR spectroscopy. Remarkably, addition of even 10 wt % gDCC-PB into the latter solution sufficed to suppress the light-induced patterning. The importance of the chemical environment on the response to light irradiation was further checked and confirmed by use of other PB copolymers. Different diameter patterns and kinetics were observed. The strong solvent and comonomer mediated effect was reflected neither in solvency nor in optical polarizability differences of the polymers solvent couples.

Comparative study of quantitative phase imaging techniques for refractometry of optical waveguides

A comparative study of quantitative phase imaging techniques for refractometry of optical waveguides is presented. Three techniques were examined: a method based on the transport-of-intensity equation, quadri-wave lateral shearing interferometry and digital holographic microscopy. The refractive index profile of a SMF-28 optical fiber was thoroughly characterized and served as a gold standard to assess the accuracy and precision of the phase imaging methods. Optical waveguides were inscribed in an Eagle2000 glass chip using a femtosecond laser and used to evaluate the sensitivity limit of these phase imaging approaches. It is shown that all three techniques provide accurate, repeatable and sensitive refractive index measurements. Using these phase imaging methods, we report a comprehensive map of the photosensitivity to femtosecond pulses of Eagle2000 glass. Finally, the reported data suggests that the phase imaging techniques are suited to be used as precise and non-destructive refractive index shift measuring tools to study and control the inscription process of optical waveguides.

High-speed Fourier ptychographic microscopy based on programmable annular illuminations

High-throughput quantitative phase imaging (QPI) is essential to cellular phenotypes characterization as it allows high-content cell analysis and avoids adverse effects of staining reagents on cellular viability and cell signaling. Among different approaches, Fourier ptychographic microscopy (FPM) is probably the most promising technique to realize high-throughput QPI by synthesizing a wide-field, high-resolution complex image from multiple angle-variably illuminated, low-resolution images. However, the large dataset requirement in conventional FPM significantly limits its imaging speed, resulting in low temporal throughput. Moreover, the underlying theoretical mechanism as well as optimum illumination scheme for high-accuracy phase imaging in FPM remains unclear. Herein, we report a high-speed FPM technique based on programmable annular illuminations (AIFPM). The optical-transfer-function (OTF) analysis of FPM reveals that the low-frequency phase information can only be correctly recovered if the LEDs are precisely located at the edge of the objective numerical aperture (NA) in the frequency space. By using only 4 low-resolution images corresponding to 4 tilted illuminations matching a 10×, 0.4 NA objective, we present the high-speed imaging results of in vitro Hela cells mitosis and apoptosis at a frame rate of 25 Hz with a full-pitch resolution of 655 nm at a wavelength of 525 nm (effective NA = 0.8) across a wide field-of-view (FOV) of 1.77 mm², corresponding to a space-bandwidth-time product of 411 megapixels per second. Our work reveals an important capability of FPM towards high-speed high-throughput imaging of in vitro live cells, achieving video-rate QPI performance across a wide range of scales, both spatial and temporal.

Quantitative phase microscopy for cellular dynamics based on transport of intensity equation

We demonstrate a simple method for quantitative phase imaging of tiny transparent objects such as living cells based on the transport of intensity equation. The experiments are performed using an inverted bright field microscope upgraded with a flipping imaging module, which enables to simultaneously create two laterally separated images with unequal defocus distances. This add-on module does not include any lenses or gratings and is cost-effective and easy-to-alignment. The validity of this method is confirmed by the measurement of microlens array and human osteoblastic cells in culture, indicating its potential in the applications of dynamically measuring living cells and other transparent specimens in a quantitative, non-invasive and label-free manner.

Optical convolution for quantitative phase retrieval using the transport of intensity equation

Propagation-based phase imaging using the transport of intensity equation (TIE) allows rapid, deterministic phase retrieval from defocused images. However, computational solutions to the TIE suffer from significant low-frequency noise artifacts and are unique up to the application of boundary conditions on the phase. We demonstrate that quantitative phase can be imaged directly at the detector for a class of pure-phase samples by appropriately patterning the illumination to solve the TIE through an optical convolution with the source. This can reduce noise artifacts, obviates the need for user-supplied boundary conditions and is demonstrated via simulation and experiment.

Chitosan nanoparticles’ functionality as redox active drugs through cytotoxicity, radical scavenging and cellular behaviour

The goal of the present study is to explore the mechanism of the ROS mediated effect of chitosan nanoparticles on acute T cell leukemia as redox active drug.

Optofluidic time-stretch quantitative phase microscopy

Innovations in optical microscopy have opened new windows onto scientific research, industrial quality control, and medical practice over the last few decades. One of such innovations is optofluidic time-stretch quantitative phase microscopy - an emerging method for high-throughput quantitative phase imaging that builds on the interference between temporally stretched signal and reference pulses by using dispersive properties of light in both spatial and temporal domains in an interferometric configuration on a microfluidic platform. It achieves the continuous acquisition of both intensity and phase images with a high throughput of more than 10,000 particles or cells per second by overcoming speed limitations that exist in conventional quantitative phase imaging methods. Applications enabled by such capabilities are versatile and include characterization of cancer cells and microalgal cultures. In this paper, we review the principles and applications of optofluidic time-stretch quantitative phase microscopy and discuss its future perspective.

Label-free nanoscale characterization of red blood cell structure and dynamics using single-shot transport of intensity equation

We report the results of characterization of red blood cell (RBC) structure and its dynamics with nanometric sensitivity using transport of intensity equation microscopy (TIEM). Conventional transport of intensity technique requires three intensity images and hence is not suitable for studying real-time dynamics of live biological samples. However, assuming the sample to be homogeneous, phase retrieval using transport of intensity equation has been demonstrated with single defocused measurement with x-rays. We adopt this technique for quantitative phase light microscopy of homogenous cells like RBCs. The main merits of this technique are its simplicity, cost-effectiveness, and ease of implementation on a conventional microscope. The phase information can be easily merged with regular bright-field and fluorescence images to provide multidimensional (three-dimensional spatial and temporal) information without any extra complexity in the setup. The phase measurement from the TIEM has been characterized using polymeric microbeads and the noise stability of the system has been analyzed. We explore the structure and real-time dynamics of RBCs and the subdomain membrane fluctuations using this technique.