Quantitative imaging of anisotropic material properties with vectorial ptychography

Permittivity tensor imaging: modular label-free imaging of 3D dry mass and 3D orientation at high resolution

The dry mass and the orientation of biomolecules can be imaged without a label by measuring their permittivity tensor (PT), which describes how biomolecules affect the phase and polarization of light. Three-dimensional (3D) imaging of PT has been challenging. We present a label-free computational microscopy technique, PT imaging (PTI), for the 3D measurement of PT. PTI encodes the invisible PT into images using oblique illumination, polarization-sensitive detection and volumetric sampling. PT is decoded from the data with a vectorial imaging model and a multi-channel inverse algorithm, assuming uniaxial symmetry in each voxel. We demonstrate high-resolution imaging of PT of isotropic beads, anisotropic glass targets, mouse brain tissue, infected cells and histology slides. PTI outperforms previous label-free imaging techniques such as vector tomography, ptychography and light-field imaging in resolving the 3D orientation and symmetry of organelles, cells and tissue. We provide open-source software and modular hardware to enable the adoption of the method.

Multimodal 2D and 3D microscopic mapping of growth cartilage by computational imaging techniques - a short review including new research

Being able to image the microstructure of growth cartilage is important for understanding the onset and progression of diseases such as osteochondrosis and osteoarthritis, as well as for developing new treatments and implants. Studies of cartilage using conventional optical brightfield microscopy rely heavily on histological staining, where the added chemicals provide tissue-specific colours. Other microscopy contrast mechanisms include polarization, phase- and scattering contrast, enabling non-stained or 'label-free' imaging that significantly simplifies the sample preparation, thereby also reducing the risk of artefacts. Traditional high-performance microscopes tend to be both bulky and expensive.Computational imagingdenotes a range of techniques where computers with dedicated algorithms are used as an integral part of the image formation process. Computational imaging offers many advantages like 3D measurements, aberration correction and quantitative phase contrast, often combined with comparably cheap and compact hardware. X-ray microscopy is also progressing rapidly, in certain ways trailing the development of optical microscopy. In this study, we first briefly review the structures of growth cartilage and relevant microscopy characterization techniques, with an emphasis on Fourier ptychographic microscopy (FPM) and advanced x-ray microscopies. We next demonstrate with our own results computational imaging through FPM and compare the images with hematoxylin eosin and saffron (HES)-stained histology. Zernike phase contrast, and the nonlinear optical microscopy techniques of second harmonic generation (SHG) and two-photon excitation fluorescence (TPEF) are explored. Furthermore, X-ray attenuation-, phase- and diffraction-contrast computed tomography (CT) images of the very same sample are presented for comparisons. Future perspectives on the links to artificial intelligence, dynamic studies andin vivopossibilities conclude the article.

Mixed-state ptychography for quantitative optical properties measurement of vector beam

Recent advances in ptychography have extended to anisotropic specimens, but vectorial reconstruction of probes owing to polarization aliasing remains a challenge. A polarization-sensitive ptychography that enables full optical property measurement of vector light is proposed. An optimized reconstruction strategy, first calibrating the propagation direction and then performing faithful retrieval, is established. This method avoids multiple image acquisitions with various polarizer configurations and significantly improves the measurement accuracy by correlating the intensity and position of different polarization components. The capability of the proposed method to quantify anisotropic parameters of optical materials and polarization properties of vector probe is demonstrated by experiment.

Ptychographic lens-less birefringence microscopy using a mask-modulated polarization image sensor

Birefringence, an inherent characteristic of optically anisotropic materials, is widely utilized in various imaging applications ranging from material characterizations to clinical diagnosis. Polarized light microscopy enables high-resolution, high-contrast imaging of optically anisotropic specimens, but it is associated with mechanical rotations of polarizer/analyzer and relatively complex optical designs. Here, we present a form of lens-less polarization-sensitive microscopy capable of complex and birefringence imaging of transparent objects without an optical lens and any moving parts. Our method exploits an optical mask-modulated polarization image sensor and single-input-state LED illumination design to obtain complex and birefringence images of the object via ptychographic phase retrieval. Using a camera with a pixel size of 3.45 μm, the method achieves birefringence imaging with a half-pitch resolution of 2.46 μm over a 59.74 mm2 field-of-view, which corresponds to a space-bandwidth product of 9.9 megapixels. We demonstrate the high-resolution, large-area, phase and birefringence imaging capability of our method by presenting the phase and birefringence images of various anisotropic objects, including a monosodium urate crystal, and excised mouse eye and heart tissues.

Single-shot measurement of the Jones matrix for anisotropic media using four-channel digital polarization holography

Dynamic measurement of the Jones matrix is crucial in investigating polarization light fields, which have wide applications in biophysics, chemistry, and mineralogy. However, acquiring the four elements of the Jones matrix instantly is difficult, hindering the characterization of random media and transient processes. In this study, we propose a single-shot measurement method of the Jones matrix for anisotropic media called "four-channel digital polarization holography" (FC-DPH). The FC-DPH system is created by a slightly off-axis superposition of reference light waves, which are modulated by a spatial light modulator (SLM), and signal light waves that pass through a Ronchi grating. The SLM enables flexible adjustment of the spatial carrier frequency, which can be adapted to different anisotropic media. The four elements of the Jones matrix can be obtained from the interferogram through the inverse Fourier transform. Optical experiments on anisotropic objects validate the feasibility and accuracy of the proposed method.

Extending the capabilities of vectorial ptychography to circular-polarizing materials such as cholesteric liquid crystals

The problem of imaging materials with circular-polarization properties is discussed within the framework of vectorial ptychography. We demonstrate, both theoretically and numerically, that using linear polarizations to investigate such materials compromises the unicity of the solution provided by this computational method. To overcome this limitation, an improved measurement approach is proposed, which involves specific combinations of elliptical polarizations. The effectiveness of this strategy is demonstrated by numerical simulations and experimental measurements on cholesteric liquid crystal films, which possess unique polarization properties. With the help of Pauli matrices algebra, our results highlight the technique's ability to discern between the different types of circular polarizers, uniform vs. non-uniform, and determine their handedness.

Viewing life without labels under optical microscopes

Optical microscopes today have pushed the limits of speed, quality, and observable space in biological specimens revolutionizing how we view life today. Further, specific labeling of samples for imaging has provided insight into how life functions. This enabled label-based microscopy to percolate and integrate into mainstream life science research. However, the use of labelfree microscopy has been mostly limited, resulting in testing for bio-application but not bio-integration. To enable bio-integration, such microscopes need to be evaluated for their timeliness to answer biological questions uniquely and establish a long-term growth prospect. The article presents key label-free optical microscopes and discusses their integrative potential in life science research for the unperturbed analysis of biological samples.

Jones tomographic diffractive microscopy with a polarized array sensor

Tomographic diffractive microscopy (TDM) based on scalar light-field approximation is widely implemented. Samples exhibiting anisotropic structures, however, necessitate accounting for the vectorial nature of light, leading to 3-D quantitative polarimetric imaging. In this work, we have developed a high-numerical aperture (at both illumination and detection) Jones TDM system, with detection multiplexing via a polarized array sensor (PAS), for imaging optically birefringent samples at high resolution. The method is first studied through image simulations. To validate our setup, an experiment using a sample containing both birefringent and non-birefringent objects is performed. Araneus diadematus spider silk fiber and Pinna nobilis oyster shell crystals are finally studied, allowing us to assess both birefringence and fast-axis orientation maps.

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

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

Stress and wavefront measurement of large-aperture optical components with a ptychographical iterative engine

The clamping stress of large-aperture optical elements has a significant influence on the optical quality of the system. In this study, a comprehensive measurement system combined with ptychographical iterative engine (PIE) wavefront sensors and polarization components is developed to determine the stress distribution of the optical elements and its effect on the transmitted and reflected wavefronts. This system avoids the use of multiple measuring instruments and has low cost and strong anti-interference ability. The experimental results demonstrate that the stress distributions measured at different resolutions are consistent with the finite element analysis, and the wavefront measurement accuracy is 0.1λ. This test configuration is very flexible and provides a useful means for online installation and quality control of large-aperture optical systems.

Correlative imaging of the spatio-angular dynamics of biological systems with multimodal instant polarization microscope

The spatial and angular organization of biological macromolecules is a key determinant, as well as informative readout, of their function. Correlative imaging of the dynamic spatio-angular architecture of cells and organelles is valuable, but remains challenging with current methods. Correlative imaging of spatio-angular dynamics requires fast polarization-, depth-, and wavelength-diverse measurement of intrinsic optical properties and fluorescent labels. We report a multimodal instant polarization microscope (miPolScope) that combines a broadband polarization-resolved detector, automation, and reconstruction algorithms to enable label-free imaging of phase, retardance, and orientation, multiplexed with fluorescence imaging of concentration, anisotropy, and orientation of molecules at diffraction-limited resolution and high speed. miPolScope enabled multimodal imaging of myofibril architecture and contractile activity of beating cardiomyocytes, cell and organelle architecture of live HEK293T and U2OS cells, and density and anisotropy of white and grey matter of mouse brain tissue across the visible spectrum. We anticipate these developments in joint quantitative imaging of density and anisotropy to enable new studies in tissue pathology, mechanobiology, and imaging-based screens.

Amorphous-to-crystal transition in the layer-by-layer growth of bivalve shell prisms

Biomineralization integrates complex physical and chemical processes bio-controlled by the living organisms through ionic concentration regulation and organic molecules production. It allows tuning the structural, optical and mechanical properties of hard tissues during ambient-condition crystallisation, motivating a deeper understanding of the underlying processes. By combining state-of-the-art optical and X-ray microscopy methods, we investigated early-mineralized calcareous units from two bivalve species, Pinctada margaritifera and Pinna nobilis, revealing chemical and crystallographic structural insights. In these calcite units, we observed ring-like structural features correlated with a lack of calcite and an increase of amorphous calcium carbonate and proteins contents. The rings also correspond to a larger crystalline disorder and a larger strain level. Based on these observations, we propose a temporal biomineralization cycle, initiated by the production of an amorphous precursor layer, which further crystallizes with a transition front progressing radially from the unit centre, while the organics are expelled towards the prism edge. Simultaneously, along the shell thickness, the growth occurs following a layer-by-layer mode. These findings open biomimetic perspectives for the design of refined crystalline materials. STATEMENT OF SIGNIFICANCE: Calcareous biominerals are amongst the most present forms of biominerals. They exhibit astonishing structural, optical and mechanical properties while being formed at ambient synthesis conditions from ubiquitous ions, motivating the deep understanding of biomineralization. Here, we unveil the first formation steps involved in the biomineralization cycle of prismatic units of two bivalve species by applying a new multi-modal non-destructive characterization approach, sensitive to chemical and crystalline properties. The observations of structural features in mineralized units of different ages allowed the derivation of a temporal sequence for prism biomineralization, involving an amorphous precursor, a radial crystallisation front and a layer-by-layer sequence. Beyond these chemical and physical findings, the herein introduced multi-modal approach is highly relevant to other biominerals and bio-inspired studies.

Quantitative Jones matrix imaging using vectorial Fourier ptychography

This paper presents a microscopic imaging technique that uses variable-angle illumination to recover the complex polarimetric properties of a specimen at high resolution and over a large field-of-view. The approach extends Fourier ptychography, which is a synthetic aperture-based imaging approach to improve resolution with phaseless measurements, to additionally account for the vectorial nature of light. After images are acquired using a standard microscope outfitted with an LED illumination array and two polarizers, our vectorial Fourier ptychography (vFP) algorithm solves for the complex 2x2 Jones matrix of the anisotropic specimen of interest at each resolved spatial location. We introduce a new sequential Gauss-Newton-based solver that additionally jointly estimates and removes polarization-dependent imaging system aberrations. We demonstrate effective vFP performance by generating large-area (29 mm²), high-resolution (1.24 μm full-pitch) reconstructions of sample absorption, phase, orientation, diattenuation, and retardance for a variety of calibration samples and biological specimens.

Broadband decoupling of intensity and polarization with vectorial Fourier metasurfaces

Intensity and polarization are two fundamental components of light. Independent control of them is of tremendous interest in many applications. In this paper, we propose a general vectorial encryption method, which enables arbitrary far-field light distribution with the local polarization, including orientations and ellipticities, decoupling intensity from polarization across a broad bandwidth using geometric phase metasurfaces. By revamping the well-known iterative Fourier transform algorithm, we propose "à la carte" design of far-field intensity and polarization distribution with vectorial Fourier metasurfaces. A series of non-conventional vectorial field distribution, mimicking cylindrical vector beams in the sense that they share the same intensity profile but with different polarization distribution and a speckled phase distribution, is demonstrated. Vectorial Fourier optical metasurfaces may enable important applications in the area of complex light beam generation, secure optical data storage, steganography and optical communications.

Nanoscale crystal grain characterization via linear polarization X-ray ptychography

X-ray linear dichroism and X-ray birefringence microscopy are yet to be fully utilized as instruments in the microstructural characterization of crystalline materials. Here, we demonstrate analyser-free X-ray linear dichroism microscopy using spectroscopic hard X-ray ptychography. First experiments enabled a spectroscopic and microstructural characterisation of polycrystalline vanadium pentoxide on the nanoscale, outside of diffraction-contrast based methods.

X-ray linear dichroic ptychography

Biominerals such as seashells, coral skeletons, bone, and tooth enamel are optically anisotropic crystalline materials with unique nanoscale and microscale organization that translates into exceptional macroscopic mechanical properties, providing inspiration for engineering new and superior biomimetic structures. Using Seriatopora aculeata coral skeleton as a model, here, we experimentally demonstrate X-ray linear dichroic ptychography and map the c-axis orientations of the aragonite (CaCO₃) crystals. Linear dichroic phase imaging at the oxygen K-edge energy shows strong polarization-dependent contrast and reveals the presence of both narrow (<35°) and wide (>35°) c-axis angular spread in the coral samples. These X-ray ptychography results are corroborated by four-dimensional (4D) scanning transmission electron microscopy (STEM) on the same samples. Evidence of co-oriented, but disconnected, corallite subdomains indicates jagged crystal boundaries consistent with formation by amorphous nanoparticle attachment. We expect that the combination of X-ray linear dichroic ptychography and 4D STEM could be an important multimodal tool to study nano-crystallites, interfaces, nucleation, and mineral growth of optically anisotropic materials at multiple length scales.

Reference-free quantitative microscopic imaging of coherent arbitrary vectorial light beams

Precise spatial characterization of vectorial beams is crucial for many advanced optical experiments, but challenging when wavefront and polarization features are involved together. Here we propose a reference-free method aimed at extracting the map of the complex-amplitude components of any coherent beam at an optical-microscopy resolution. Our method exploits recent advances in ptychographic imaging approaches. We emphasize its versatility by reconstructing successfully various experimental vectorial beams including polarization and phase vortices, the exit field of a multicore fiber and a speckle pattern.

Real-time Jones phase microscopy for studying transparent and birefringent specimens

Tissue birefringence is an intrinsic marker of potential value for cancer diagnosis. Traditionally, birefringence properties have been studied by using intensity-based formalisms, through the Mueller matrix algebra. On the other hand, the Jones matrix description allows for a direct assessment of the sample's anisotropic response. However, because Jones algebra is based on complex fields, requiring measurements of both phase and amplitude, it is less commonly used. Here we propose a real-time imaging method for measuring Jones matrices by quantitative phase imaging. We combine a broadband phase imaging system with a polarization-sensitive detector to obtain Jones matrices at each point in a megapixel scale image, with near video rate capture speeds. To validate the utility of our approach, we measured standard targets, partially birefringent samples, dynamic specimens, and thinly sliced histopathological tissue.

Analyzer-free linear dichroic ptychography

Linear dichroism is an important tool to characterize the transmission matrix and determine the crystal or orbital orientation in a material. In order to achieve high-resolution mapping of transmission properties, the linear-dichroism scattering model in ptychographic imaging is introduced, and an efficient two-stage reconstruction algorithm is developed. Using the proposed algorithm on a uniaxial material, the dichroic transmission matrix can be recovered without an analyzer by using ptychography measurements with as few as three different polarization angles, with the help of an empty region to remove phase ambiguities.

Revealing architectural order with quantitative label-free imaging and deep learning

We report quantitative label-free imaging with phase and polarization (QLIPP) for simultaneous measurement of density, anisotropy, and orientation of structures in unlabeled live cells and tissue slices. We combine QLIPP with deep neural networks to predict fluorescence images of diverse cell and tissue structures. QLIPP images reveal anatomical regions and axon tract orientation in prenatal human brain tissue sections that are not visible using brightfield imaging. We report a variant of U-Net architecture, multi-channel 2.5D U-Net, for computationally efficient prediction of fluorescence images in three dimensions and over large fields of view. Further, we develop data normalization methods for accurate prediction of myelin distribution over large brain regions. We show that experimental defects in labeling the human tissue can be rescued with quantitative label-free imaging and neural network model. We anticipate that the proposed method will enable new studies of architectural order at spatial scales ranging from organelles to tissue.

Single-pixel, single-input-state polarization-sensitive wavefront imaging

In this Letter, we describe a single-pixel polarization-sensitive imaging technique, capable of generating the birefringence map of a thin specimen by using single-pixel detectors. Spatially modulated light is circularly polarized to illuminate the specimen. The transmitted light through the specimen is then focused via a lens and measured by position-sensitive detectors in two orthogonal polarization channels. The measurement of the irradiance and centroid position of the optical focus and subsequent computations enable the production of polarization-dependent wavefront maps, which can then be utilized to reconstruct sample birefringence information. We demonstrate the feasibility of our method by measuring distribution of optic-axis orientation and phase retardation of various birefringent samples.

Ptychography retrieval of fully polarized holograms from geometric-phase metasurfaces

Controlling light properties with diffractive planar elements requires full-polarization channels and accurate reconstruction of optical signal for real applications. Here, we present a general method that enables wavefront shaping with arbitrary output polarization by encoding both phase and polarization information into pixelated metasurfaces. We apply this concept to convert an input plane wave with linear polarization to a holographic image with arbitrary spatial output polarization. A vectorial ptychography technique is introduced for mapping the Jones matrix to monitor the reconstructed metasurface output field and to compute the full polarization properties of the vectorial far field patterns, confirming that pixelated interfaces can deflect vectorial images to desired directions for accurate targeting and wavefront shaping. Multiplexing pixelated deflectors that address different polarizations have been integrated into a shared aperture to display several arbitrary polarized images, leading to promising new applications in vector beam generation, full color display and augmented/virtual reality imaging.

Controlling light with planar elements requires full polarization channels and reconstruction of optical signals. Here, the authors have demonstrated a general method relying on pixelated metasurfaces that enables wavefront shaping with arbitrary output polarization, allowing full utilization of polarization channels.

Fourier ptychography: current applications and future promises

Traditional imaging systems exhibit a well-known trade-off between the resolution and the field of view of their captured images. Typical cameras and microscopes can either "zoom in" and image at high-resolution, or they can "zoom out" to see a larger area at lower resolution, but can rarely achieve both effects simultaneously. In this review, we present details about a relatively new procedure termed Fourier ptychography (FP), which addresses the above trade-off to produce gigapixel-scale images without requiring any moving parts. To accomplish this, FP captures multiple low-resolution, large field-of-view images and computationally combines them in the Fourier domain into a high-resolution, large field-of-view result. Here, we present details about the various implementations of FP and highlight its demonstrated advantages to date, such as aberration recovery, phase imaging, and 3D tomographic reconstruction, to name a few. After providing some basics about FP, we list important details for successful experimental implementation, discuss its relationship with other computational imaging techniques, and point to the latest advances in the field while highlighting persisting challenges.

Super-resolution near-field ptychography

Compared to far-field ptychography, near-field ptychography can reduce the requirement on the detector dynamic range, while it is able to cover a larger field of view with a fewer number of sample scans. However, its spatial resolution is limited by the detector pixel size. Here, we utilize a pixel-super-resolved approach to overcome this limitation. The method has been applied to four types of experiment configurations using planar and divergent illuminations together with two different cameras with highly contrast specifications. The proposed method works effectively for up-sampling up to 6 times. Meanwhile, it can achieve ∼5.9-fold and ∼3.1-fold resolution improvement over the 6.5-μm and 2.4-μm detector pixel size. We also demonstrate the precisely quantitative phase imaging capability of the method by using a phase resolution target. The presented method is believed to have great potential in X-ray tomography and on-chip flow cytometry.

Joint estimation of object and probes in vectorial ptychography

Vectorial ptychography has been recently introduced to reconstruct the Jones matrix of an anisotropic object by means of series of ptychographic measurements performed using a set of polarized illumination probes in conjugation with various analyzers. So far, the probes were assumed to be completely known (amplitude, wavefront, state of polarization), which is rarely the case in practice. Here we address the issue of the joint estimating of the set of polarized illumination probes together with the Jones matrix of an anisotropic object in vectorial ptychography. We propose an algorithm based on a conjugate gradient strategy. Experimental results are reported, showing an improvement on the object estimate, in addition to a precise reconstruction of the probes.

Multiplexed single-shot ptychography

We demonstrate experimentally multiplexed single-shot ptychography. Specifically, we present a polarization-resolved single-shot ptychographic microscope, where the orthogonally polarized amplitudes and phases of a polarization-sensitive object are reconstructed from ptychographic data recorded in a single camera exposure. Moreover, the amplitudes, phases, and polarization states of the probe beams are also recovered. That is, altogether we decipher eight images from single-shot ptychographic data. This work is an important step towards experimental demonstration of time-resolved imaging by multiplexed ptychography.

Reference-free polarization-sensitive quantitative phase imaging using single-point optical phase conjugation

We propose and experimentally demonstrate a method of polarization-sensitive quantitative phase imaging using two photodetectors and a digital micromirror device. Instead of recording wide-field interference patterns, finding the modulation patterns maximizing focused intensities in terms of the polarization states enables polarization-dependent quantitative phase imaging without the need for a reference beam and an image sensor. The feasibility of the present method is experimentally validated by reconstructing Jones matrices of several samples including a polystyrene microsphere, a maize starch granule, and a mouse retinal nerve fiber layer. Since the present method is simple and sufficiently general, we expect that it may offer solutions for quantitative phase imaging of birefringent materials.

Near-field ptychographic microscope for quantitative phase imaging

Quantitative phase imaging (QPI) is the name given to a set of microscopy techniques that map out variations in optical path lengths across a sample. These maps are a useful source of contrast for transparent samples such as biological cells, and because they are quantitative they can be used to measure refractive index and thickness variations. Here we detail the setup and operation of a new form of QPI microscope based on near-field ptychography. We test our system using a range of phase objects, and analyse the phase images it produces. Our results show that accurate, high quality images can be obtained from a ptychographical dataset containing as few as four near-field diffraction patterns. We also assess how our system copes with optically thick samples and samples with a wide range of spatial frequencies - two areas where conventional and Fourier ptychography struggle.