Tomographic measurement of dielectric tensors at optical frequency

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.

Quantitative phase imaging based on holography: trends and new perspectives

In 1948, Dennis Gabor proposed the concept of holography, providing a pioneering solution to a quantitative description of the optical wavefront. After 75 years of development, holographic imaging has become a powerful tool for optical wavefront measurement and quantitative phase imaging. The emergence of this technology has given fresh energy to physics, biology, and materials science. Digital holography (DH) possesses the quantitative advantages of wide-field, non-contact, precise, and dynamic measurement capability for complex-waves. DH has unique capabilities for the propagation of optical fields by measuring light scattering with phase information. It offers quantitative visualization of the refractive index and thickness distribution of weak absorption samples, which plays a vital role in the pathophysiology of various diseases and the characterization of various materials. It provides a possibility to bridge the gap between the imaging and scattering disciplines. The propagation of wavefront is described by the complex amplitude. The complex-value in the complex-domain is reconstructed from the intensity-value measurement by camera in the real-domain. Here, we regard the process of holographic recording and reconstruction as a transformation between complex-domain and real-domain, and discuss the mathematics and physical principles of reconstruction. We review the DH in underlying principles, technical approaches, and the breadth of applications. We conclude with emerging challenges and opportunities based on combining holographic imaging with other methodologies that expand the scope and utility of holographic imaging even further. The multidisciplinary nature brings technology and application experts together in label-free cell biology, analytical chemistry, clinical sciences, wavefront sensing, and semiconductor production.

Deep-learning based 3D birefringence image generation using 2D multi-view holographic images

Refractive index stands as an inherent characteristic of a material, allowing non-invasive exploration of the three-dimensional (3D) interior of the material. Certain materials with different refractive indices produce a birefringence phenomenon in which incident light is split into two polarization components when it passes through the materials. Representative birefringent materials appear in calcite crystals, liquid crystals (LCs), biological tissues, silk fibers, polymer films, etc. If the internal 3D shape of these materials can be visually expressed through a non-invasive method, it can greatly contribute to the semiconductor, display industry, optical components and devices, and biomedical diagnosis. This paper introduces a novel approach employing deep learning to generate 3D birefringence images using multi-viewed holographic interference images. First, we acquired a set of multi-viewed holographic interference pattern images and a 3D volume image of birefringence directly from a polarizing DTT (dielectric tensor tomography)-based microscope system about each LC droplet sample. The proposed model was trained to generate the 3D volume images of birefringence using the two-dimensional (2D) interference pattern image set. Performance evaluations were conducted against the ground truth images obtained directly from the DTT microscopy. Visualization techniques were applied to describe the refractive index distribution in the generated 3D images of birefringence. The results show the proposed method's efficiency in generating the 3D refractive index distribution from multi-viewed holographic interference images, presenting a novel data-driven alternative to traditional methods from the DTT devices.

Non-steady state thermometry with optical diffraction tomography

Label-free thermometry is a pivotal tool for many disciplines. However, most current approaches are only suitable for planar heat sources in steady state, thereby restricting the range of systems that can be reliably studied. Here, we introduce pump probe-based optical diffraction tomography (ODT) as a method to map temperature precisely and accurately in three dimensions (3D) at the single-particle level. To do so, we first systematically characterize the thermal landscape in a model system consisting of gold nanorods in a microchamber and then benchmark the results against simulations and quantitative phase imaging thermometry. We then apply ODT thermometry to resolve thermal landscapes inaccessible to other label-free approaches in the form of nonplanar heat sources embedded in complex environments and freely diffusing gold nanorods in a microchamber. Last, we foresee that our approach will find many applications where routine thermal characterization of heterogeneous nanoparticles samples in 3D or in non-steady state is required.

Recent Advances and Current Trends in Transmission Tomographic Diffraction Microscopy

Optical microscopy techniques are among the most used methods in biomedical sample characterization. In their more advanced realization, optical microscopes demonstrate resolution down to the nanometric scale. These methods rely on the use of fluorescent sample labeling in order to break the diffraction limit. However, fluorescent molecules' phototoxicity or photobleaching is not always compatible with the investigated samples. To overcome this limitation, quantitative phase imaging techniques have been proposed. Among these, holographic imaging has demonstrated its ability to image living microscopic samples without staining. However, for a 3D assessment of samples, tomographic acquisitions are needed. Tomographic Diffraction Microscopy (TDM) combines holographic acquisitions with tomographic reconstructions. Relying on a 3D synthetic aperture process, TDM allows for 3D quantitative measurements of the complex refractive index of the investigated sample. Since its initial proposition by Emil Wolf in 1969, the concept of TDM has found a lot of applications and has become one of the hot topics in biomedical imaging. This review focuses on recent achievements in TDM development. Current trends and perspectives of the technique are also discussed.

High-resolution assessment of multidimensional cellular mechanics using label-free refractive-index traction force microscopy

A critical requirement for studying cell mechanics is three-dimensional assessment of cellular shapes and forces with high spatiotemporal resolution. Traction force microscopy with fluorescence imaging enables the measurement of cellular forces, but it is limited by photobleaching and a slow acquisition speed. Here, we present refractive-index traction force microscopy (RI-TFM), which simultaneously quantifies the volumetric morphology and traction force of cells using a high-speed illumination scheme with 0.5-Hz temporal resolution. Without labelling, our method enables quantitative analyses of dry-mass distributions and shear (in-plane) and normal (out-of-plane) tractions of single cells on the extracellular matrix. When combined with a constrained total variation-based deconvolution algorithm, it provides 0.55-Pa shear and 1.59-Pa normal traction sensitivity for a 1-kPa hydrogel substrate. We demonstrate its utility by assessing the effects of compromised intracellular stress and capturing the rapid dynamics of cellular junction formation in the spatiotemporal changes in non-planar traction components.

Roadmap on Label-Free Super-Resolution Imaging

Label-free super-resolution (LFSR) imaging relies on light-scattering processes in nanoscale objects without a need for fluorescent (FL) staining required in super-resolved FL microscopy. The objectives of this Roadmap are to present a comprehensive vision of the developments, the state-of-the-art in this field, and to discuss the resolution boundaries and hurdles which need to be overcome to break the classical diffraction limit of the LFSR imaging. The scope of this Roadmap spans from the advanced interference detection techniques, where the diffraction-limited lateral resolution is combined with unsurpassed axial and temporal resolution, to techniques with true lateral super-resolution capability which are based on understanding resolution as an information science problem, on using novel structured illumination, near-field scanning, and nonlinear optics approaches, and on designing superlenses based on nanoplasmonics, metamaterials, transformation optics, and microsphere-assisted approaches. To this end, this Roadmap brings under the same umbrella researchers from the physics and biomedical optics communities in which such studies have often been developing separately. The ultimate intent of this paper is to create a vision for the current and future developments of LFSR imaging based on its physical mechanisms and to create a great opening for the series of articles in this field.

Vectorial inverse scattering for dielectric tensor tomography: overcoming challenges of reconstruction of highly scattering birefringent samples

Many important microscopy samples, such as liquid crystals, biological tissue, or starches, are birefringent in nature. They scatter light differently depending on the polarization of the light and the orientation of the molecules. The complete characterization of a birefringent sample is a challenging task because its 3 × 3 dielectric tensor must be reconstructed at every three-dimensional position. Moreover, obtaining a birefringent tomogram is more arduous for thick samples, where multiple light scattering should also be considered. In this study, we developed a new dielectric tensor tomography algorithm that enables full characterization of highly scattering birefringent samples by solving the vectoral inverse scattering problem while accounting for multiple light scattering. We proposed a discrete image-processing theory to compute the error backpropagation of vectorially diffracting light. Finally, our theory was experimentally demonstrated using both synthetic and biologically birefringent samples.

Efficient and accurate intensity diffraction tomography of multiple-scattering samples

Optical Diffraction Tomography (ODT) is a label-free method to quantitatively estimate the 3D refractive index (RI) distributions of microscopic samples. Recently, significant efforts were directed towards methods to model multiple-scattering objects. The fidelity of reconstructions rely on accurately modelling light-matter interactions, but the efficient simulation of light propagation through high-RI structures over a large range of illumination angles is still challenging. Here we present a solution dealing with these problems, proposing a method that allows one to efficiently model the tomographic image formation for strongly scattering objects illuminated over a wide range of angles. Instead of propagating tilted plane waves we apply rotations on the illuminated object and optical field and formulate a new and robust multi-slice model suitable for high-RI contrast structures. We test reconstructions made by our approach against simulations and experiments, using rigorous solutions to Maxwell's equations as ground truth. We find the proposed method to produce reconstructions of higher fidelity compared to conventional multi-slice methods, especially for the challenging case of strongly scattering samples where conventional reconstruction methods fail.

Polarization-sensitive intensity diffraction tomography

Optical anisotropy, which is an intrinsic property of many materials, originates from the structural arrangement of molecular structures, and to date, various polarization-sensitive imaging (PSI) methods have been developed to investigate the nature of anisotropic materials. In particular, the recently developed tomographic PSI technologies enable the investigation of anisotropic materials through volumetric mappings of the anisotropy distribution of these materials. However, these reported methods mostly operate on a single scattering model, and are thus not suitable for three-dimensional (3D) PSI imaging of multiple scattering samples. Here, we present a novel reference-free 3D polarization-sensitive computational imaging technique-polarization-sensitive intensity diffraction tomography (PS-IDT)-that enables the reconstruction of 3D anisotropy distribution of both weakly and multiple scattering specimens from multiple intensity-only measurements. A 3D anisotropic object is illuminated by circularly polarized plane waves at various illumination angles to encode the isotropic and anisotropic structural information into 2D intensity information. These information are then recorded separately through two orthogonal analyzer states, and a 3D Jones matrix is iteratively reconstructed based on the vectorial multi-slice beam propagation model and gradient descent method. We demonstrate the 3D anisotropy imaging capabilities of PS-IDT by presenting 3D anisotropy maps of various samples, including potato starch granules and tardigrade.

Neural networks determination of material elastic constants and structures in nematic complex fluids

Supervised machine learning and artificial neural network approaches can allow for the determination of selected material parameters or structures from a measurable signal without knowing the exact mathematical relationship between them. Here, we demonstrate that material nematic elastic constants and the initial structural material configuration can be found using sequential neural networks applied to the transmmited time-dependent light intensity through the nematic liquid crystal (NLC) sample under crossed polarizers. Specifically, we simulate multiple times the relaxation of the NLC from a random (qeunched) initial state to the equilibirum for random values of elastic constants and, simultaneously, the transmittance of the sample for monochromatic polarized light. The obtained time-dependent light transmittances and the corresponding elastic constants form a training data set on which the neural network is trained, which allows for the determination of the elastic constants, as well as the initial state of the director. Finally, we demonstrate that the neural network trained on numerically generated examples can also be used to determine elastic constants from experimentally measured data, finding good agreement between experiments and neural network predictions.

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.

3D differential interference contrast microscopy using polarisation-sensitive tomographic diffraction microscopy

Tomographic diffraction microscopy (TDM) is a generalisation of digital holographic microscopy (DHM), for which the illumination angle onto the sample is fully controlled, which has become a tool of choice for 3D, high-resolution imaging of unlabelled samples. TDM makes it possible to obtain the optical field in both amplitude and phase for each illumination angle. Proper information reallocation eventually allows for 3D reconstruction of the complex refractive index map. On the other hand, polarisation array sensors (PAS) paves new way for TDM, as vectorial information assessment about the investigated sample. In this contribution, we show an alternative use of this polarisation information based on the phase sensitive nature of TDM. Here, we demonstrated that TDM coupled with PAS can lead to a 3D differential interference contrast (DIC) microscope with almost no experimental configuration modification.

Regularization of dielectric tensor tomography

Dielectric tensor tomography reconstructs the three-dimensional dielectric tensors of microscopic objects and provides information about the crystalline structure orientations and principal refractive indices. Because dielectric tensor tomography is based on transmission measurement, it suffers from the missing cone problem, which causes poor axial resolution, underestimation of the refractive index, and halo artifacts. In this study, we study the application of total variation and positive semi-definiteness regularization to three-dimensional tensor distributions. In particular, we demonstrate the reduction of artifacts when applied to dielectric tensor tomography.

Standardizing image assessment in optical diffraction tomography

Optical diffraction tomography (ODT) has gradually become a popular label-free imaging technique that offers diffraction-limited resolution by mapping an object's three-dimensional (3D) refractive index (RI) distribution. However, there is a lack of comprehensive quantitative image assessment metrics in ODT for studying how various experimental conditions influence image quality, and subsequently optimizing the experimental conditions. In this Letter, we propose to standardize the image assessment in ODT by proposing a set of metrics, including signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), and structural distinguishability (SD). To test the feasibility of the metrics, we performed experiments on angle-scanning ODT by varying the number of illumination angles, RI contrast of samples, sample feature sizes, and sample types (e.g., standard polystyrene beads and 3D printed structures) and evaluated the RI tomograms with SNR, CNR, and SD. We further quantitatively studied how image quality can be improved, and tested the image assessment metrics on subcellular structures of living cells. We envision the proposed image assessment metrics may greatly benefit end-users for assessing the RI tomograms, as well as experimentalists for optimizing ODT instruments.

Spatially multiplexed dielectric tensor tomography

Dielectric tensor tomography (DTT) enables the reconstruction of three-dimensional (3D) dielectric tensors, which provides a physical measure of 3D optical anisotropy. Herein, we present a cost-effective and robust method of DTT using spatial multiplexing. Exploiting two orthogonally polarized reference beams with different angles in an off-axis interferometer, two polarization-sensitive interferograms were multiplexed and recorded using a single camera. Then, the two interferograms were demultiplexed in the Fourier domain. By measuring the polarization-sensitive fields for various illumination angles, 3D dielectric tensor tomograms were reconstructed. The proposed method was experimentally demonstrated by reconstructing the 3D dielectric tensors of various liquid-crystal (LC) particles with radial and bipolar orientational configurations.

Angularly resolved polarization microscopy for birefringent materials with Fourier ptychography

Polarization light microscopy is a very popular approach for structural imaging in optics. So far these methods mainly probe the sample at a fixed angle of illumination. They are consequently only sensitive to the polarization properties along the microscope optical axis. This paper presents a novel method to resolve angularly the polarization properties of birefringent materials, by retrieving quantitatively the spatial variation of their index ellipsoids. Since this method is based on Fourier ptychography microscopy the latter properties are retrieved with a spatial super-resolution factor. An adequate formalism for the Fourier ptychography forward model is introduced to cope with angularly resolved polarization properties. The inverse problem is solved using an unsupervised deep neural network approach that is proven efficient thanks to its performing regularization properties together with its automatic differentiation. Simulated results are reported showing the feasibility of the methods.

Scalar approximation of Maxwell equations: derivation and accuracy

Replacing Maxwell equations by a scalar wave equation is often used in computational imaging to simulate the light-sample interaction. It significantly reduces the computational burden but provides field maps that are insensitive to the polarization of the incident field, provided the latter is constant throughout the sample. Here, we develop a scalar approximation that accounts for the polarization of the incident field. Comparisons with rigorous simulations show that this approach is more accurate than the classical scalar approximation with similar computational cost.

Multimodal image reconstruction from tomographic diffraction microscopy data

Tomographic Diffraction Microscopy (TDM) is a tool of choice for high-resolution, marker-less 3D imaging of biological samples. Based on a generalization of Digital Holographic Microscopy (DHM) with full control of the sample's illumination, TDM measures, from many illumination directions, the diffracted fields in both phase and amplitude. Photon budget associated to TDM imaging is low. Therefore, TDM is not limited by photo-toxicity issues. The recorded information makes it possible to reconstruct 3D refractive index distribution (with both refraction and absorption contributions) of the object under scrutiny, without any staining. In this contribution, we show an alternate use of this information. A tutorial for multimodal image reconstruction is proposed. Both intensity contrasts and phase contrasts are proposed, from the image formation model to the final reconstruction with both 2D and 3D rendering, turning TDM into a kind of "universal" digital microscope. This article is protected by copyright. All rights reserved.