Phase imaging of nanostructures

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.

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.

Quantitative phase imaging (QPI) has advanced by accurately quantifying phase shifts caused by weakly absorbing biological and artificial structures. Despite extensive research, the diffraction limits of QPI have not been established and examined. Hence, it remains unclear whether diffraction-affected QPI provides reliable quantification or merely visualizes phase objects, similar to phase contrast methods. Here, we develop a general diffraction phase imaging theory and show that it is intrinsically connected with Rayleigh’s resolution theory. Our approach reveals the entanglement of phases under restoration, imposing diffraction bounds on spatial phase resolution and, unexpectedly, on phase accuracy. We prove that the phase accuracy depends on the size, shape, and absorption of objects forming the sample and significantly declines if the object size approaches the Rayleigh limit (a relative phase error of −16% for an Airy disk-sized object with low phase shift). We show that the phase accuracy limits can be enhanced at the cost of deteriorated phase resolution by attenuating the sample background light. The QPI diffraction limits are thoroughly examined in experiments with certified phase targets and biological cells. The study’s relevance is underscored by results showing that the phase accuracy of some structures is lost (a relative phase error of −40%) even though they are spatially resolved (a phase visibility of 0.5). A reliable procedure is used to estimate phase errors in given experimental conditions, opening the way to mitigate errors’ impact through data post-processing. Finally, the phase accuracy enhancement in super-resolution QPI is discovered, which has not been previously reported.

Quantitative phase microscopy (QPM) is a label-free imaging technique often employed for long-term, high-contrast imaging of live bio-samples. Yet, QPM is not specific to a certain subcellular organelle. As a remedy, fluorescence microscopy can visualize specific subcellular organelles once being labeled with fluorescent markers. In this paper, a high-resolution phase/fluorescence dual-modality microscopic imaging method based on structured light illumination is proposed. In a dual-modality microscopic system, periodic stripes are generated by a digital micromirror array (DMD), and are used as the common illumination for both modalities. For QPM imaging, the holograms of the sample under structured light illuminations from different directions and phase shifts are recorded, from which a quantitative phase image with resolution enhancement can be reconstructed via a synthetic aperture procedure. Furthermore, a numerical approach is proposed to compensate for the environmental disturbances that often challenge aperture synthesis of phase imaging. This method determines each time the phase distortions caused by environmental disturbances through using the spectrum of the 0th order of the structured light illumination, and the phase distortions are removed from the phase distributions of the waves along the 0th and the ±1st diffraction orders. Resolution enhancement of QPM imaging is realized by synthesizing the spectra of all the waves along different diffraction orders of the structured light illuminations of different orientations. With phase images, three-dimensional shapes, inner structures, or refractive index distributions of transparent and translucent samples can be obtained. For fluorescence imaging, intensity images (morie patterns) of the sample under different structured light illuminations are recorded. The spectra along different diffraction orders are separated by using a phase shifting reconstruction algorithm, and are shifted to their original positions, forming a synthesized spectrum that is much broader than the spectra of raw intensity images (NA-limited spectra). An inverse Fourier transform on the synthesized spectrum yields a super-resolution fluorescence image of the sample. With the reconstructed fluorescence images, specific subcellular organelles labeled with fluorescent markers can be visualized. The combination of quantitative phase microscopy and fluorescence microscopy can obtain multidimensional information about the sample. In this dual-mode imaging system, the spatial resolution of quantitative phase imaging and fluorescence imaging are 840 nm and 440 nm, respectively. The proposed dual-mode microscopy imaging technique has been demonstrated for imaging fluorescent beads, fly wings, spring/rice leaves, mouse tail transection, and fluorescence-stained SiHa cells. We envisage that this method can be further applied to many fields, such as biomedicine, industry, and chemistry.

This dissertation has mainly aimed at developing novel techniques, methodologies for measuring the optical field, specifically both the amplitude and phase distribution. Furthermore, we have attempted to extend their applications in the scope of optical imaging, including lensless/holographic imaging, quantitative phase imaging and the calibration for light-sheet microscopes.

Inflammatory bowel diseases (IBD) are inflammatory disorders of the gastrointestinal tract characterized by a chronic relapsing disease course. As uncontrolled intestinal inflammation can result in severe disease complications, recent treatment targets of IBD evolved toward seeking the absence of mucosal and histological inflammation. However, this approach requires adequate histological evaluation of IBD disease activity. The diagnostic challenge of histological examination of intestinal inflammation is documented by the multitude of proposed histological scoring systems. In this context, we review quantitative phase imaging (QPI) techniques such as digital holographic microscopy (DHM) for characterizing intestinal inflammation. DHM determines optical path-length delays in a stain-free manner, thereby providing the tissue refractive index as a biophysical marker that directly correlates to tissue density. Recently, DHM has been successfully applied in cell biology, cancer cell research and infectious-induced cellular alterations. We summarized the capabilities of DHM and related QPI techniques to assess the severity of intestinal inflammation in experimental colitis as well as in colonic samples from human IBD patients. Moreover, we illustrate major advantages of DHM facilitated multimodal evaluation of epithelial wound healing processes as assessed by physical parameters like cell volume, density, thickness and dry mass in vitro. Furthermore, potential limitations of DHM and future utilities of QPI are discussed. In conclusion, DHM represents a promising, easy-to-use quantitative tool to provide accurate and objective assessment of intestinal inflammation and may pave the way towards automated label-free digital pathology and related in vitro cell culture analysis in future.

Quantitative phase measurements at multiple wavelengths has created an opportunity for exploring new avenues in phase microscopy such as enhancing imaging-depth (1), measuring hemoglobin concentrations in erythrocytes (2), and more recently in tomographic mapping of the refractive index of live cells (3). To this end, quantitative phase imaging has been demonstrated both at few selected spectral points as well as with high spectral resolution (4,5). However, most of these developed techniques compromise imaging speed, field of view, or the spectral resolution to perform interferometric measurements at multiple colors. In the specific application of quantitative phase in studying blood diseases and red blood cells, current techniques lack the required sensitivity to quantify biological properties of interest at individual cell level. Recently, we have set out to develop a stable quantitative interferometric microscope allowing for measurements of such properties for red cells without compromising field of view or speed of the measurements. The feasibility of the approach will be initially demonstrated in measuring dispersion curves of known solutions, followed by measuring biological properties of red cells in sickle cell anemia.

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.

A well-known speckle which comes from the coherent property of laser source has limited the laser imaging application. Quantitative Phase Imaging (QPI) also suffers from this speckle noise when illuminate with coherent source. A rotational diffuser is a considerable method to minimize the speckle by averaging the speckle contrast in time. Here, we employ the dual optical diffuser-static and moving diffusers — to suppress speckle noise in QPI. Continuous-wave laser is used to illuminate polystyrene micro-bead as a sample. Due to the averaging independent speckle pattern, speckle noise in phase image is reduced by maintaining the quality of fringe. The ability of moving diffuser in speckle noise suppression is presented in Fourier domain via Fast Fourier Transform (FFT) technique and topographic phase map. This work proposes a valuable technique for efficient suppression of the coherent speckle in QPI.

Increasing field of view and signal to noise ratio in the quantitative phase imaging with phase shifting holography based on the Hanbury Brown-Twiss approach

It is well known that the quantitative phase information which is vital in the biomedical study is hard to be directly obtained with bright-field microscopy under incoherent illumination. In addition, it is impossible to maintain the living sample in focus over long-term observation. Therefore, both the autofocusing and quantitative phase imaging techniques have to be solved in microscopy simultaneously. Here, we propose a lightweight deep learning-based framework, which is constructed by residual structure and is constrained by a novel loss function model, to realize both autofocusing and quantitative phase imaging. It outputs the corresponding in-focus amplitude and phase information at high speed (10fps) from a single-shot out-of-focus bright-field image. The training data were captured with a designed system under a hybrid incoherent and coherent illumination system. The experimental results verify that the focused and quantitative phase images of non-biological samples and biological samples can be reconstructed by using the framework. It provides a versatile quantitative technique for continuous monitoring of living cells in long-term and label-free imaging by using a traditional incoherent illumination microscopy system.

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.

Digital holographic microscopy (DHM) is an important technique that may be used for quantitative phase imaging of unstained biological cell samples. Since the DHM technology is not commonly used in clinics or bioscience research labs, at present there is no well-accepted focusing criterion for unstained samples that users can follow while recording image plane digital holograms of cells. The usual sharpness metrics that are useful for auto-focusing of stained cells do not work well for unstained cells as there is no amplitude contrast. In this work, we report a practical method for estimating the best focus plane for unstained cells in the digital hologram domain. The method is based on an interesting observation that for the best focus plane the fringe pattern associated with individual unstained cells predominantly shows phase modulation effect in the form of bending of fringes and minimal amplitude modulation. This criterion when applied to unstained red blood cells shows that the central dip in the doughnut-like phase profile of cells is maximal in this plane. The proposed methodology is helpful for standardizing the usage of DHM technology across different users and application developmentefforts. LAY DESCRIPTION: Digital holographic microscopy (DHM) is slowly but steadily becoming an important microscopy modality and gaining acceptability for basic bio-science research as well as clinical usage. One of the important features of DHM is that it allows users to perform quantitative imaging of unstained transparent cells. Instead of using dyes or fluorescent labelling, DHM systems use quantitative phase as a contrast mechanism which depends on the natural refractive index variation within the cell samples. Since minimal wet lab processing is required in order to image cell samples with a DHM, cells can be imaged in their natural state. While DHM is gaining popularity among users, the imaging protocols across the labs or users need to be standardized in order to make sure that the same quantitative phase parameters are used for tasks such as quantitative phased based cellclassification. One of the important operational tasks for any microscopy work is to focus the sample under study. While focusing comes naturally to users of brightfield microscopes based on image contrast, the focusing is not straightforward when samples are unstained so that they do not offer any amplitude contrast. When performing quantitative phase imaging, defocus can actually change the phase profile of the cell due to near-zone (Fresnel) diffraction effects. So unless a standardized focusing methodology is used, it will be difficult for multiple DHM users (potentially at different sites) to agree on quantitative results out of their phase images. DHM literature has prior works which perform numerical focusing of recovered complex wave-field in the hologram plane to find the best focus plane. However such methods are not user friendly and do not allow user the same focusing experience as in a brightfield microscope. The numerical focusing is therefore a reasonably good method for an optics researcher but not necessarily so for a microscopy technician looking at cell samples with a DHM system in a clinicalsetting. The present work provides a simple focusing criterion for unstained samples that works directly in the hologram domain. The technique is based on an interesting observation that the when an unstained cell sample is in the best-focus plane, its corresponding hologram (or fringe pattern) predominantly shows phase modulation manifested by bending of fringes at the location of the cell. This criterion can be converted into a simple numerical method as we have used to find the best-focus plane using a stack of through focus holograms. We believe that the technique can be used manually by visually observing the holograms or can be converted to an auto-focus algorithm for a motorized DHMsystem.

Hybrid Random Walk-Linear Discriminant Analysis Method for Unwrapping Quantitative Phase Images of Biological Samples

Wedge prism assisted quantitative phase imaging on standard microscopes