Quantitative Jones matrix imaging using vectorial Fourier ptychography

Reconstructing Three-Dimensional Optical Anisotropy with Tomographic Müller-Polarimetric Microscopy

Most visible light imaging methods using polarization to obtain ultrastructure information are limited to 2D analysis or require demanding phase measurements to be extended to 3D. A novel 3D polarized light imaging technique based on Müller-matrix formulations is introduced which numerically reconstructs 3D optical birefringence, that is anisotropic refractive indices and optical axis orientation, in each volumetric unit of sample. The new method is demonstrated, tomographic Müller-polarimetric microscopy, in simulation and using experimental data of 3D macroscopic sample of human trabecular bone sample, where the local main orientation of nanoscale collagen fibers is extracted with a resolution of ≈ 20 µm. Tomographic Müller-polarimetric microscopy offers a low-cost and experimentally simple imaging approach to access the ultrastructure which is not directly resolvable, in a wide range of biological and composite materials.

Ptychographic Mueller matrix imaging (PMMI): principle and proof-of-concept demonstration

Quantitative characterization of optical anisotropies is extremely important for wide fields and applications. The Mueller matrix, providing all the polarization-related properties of a medium, is a powerful tool for the comprehensive evaluation of optical anisotropies. Here, we propose a ptychographic Mueller matrix imaging (PMMI) technique, which features the Mueller matrix polarization modulation being introduced into the ptychography. The ptychographic reconstruction is performed for each polarization state, and the Mueller matrix can be determined from the reconstructed polarization-modulated amplitude images. A proof-of-concept of the proposed PMMI is implemented, and both simulations and experiments are conducted to demonstrate the validity of the method. Results indicate that the imaging resolution of the home-built PMMI apparatus achieves 1.550 µm at the wavelength of 633 nm, which is of the highest level for the Mueller matrix imaging to the best of our knowledge. A customized birefringent specimen is characterized, and both retardance and axis azimuth are quantitatively evaluated.

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.

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.

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.

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.

Jones-matrix imaging based on two-photon interference

Two-photon interference is an important effect that is tightly related to the quantum nature of light. Recently, it has been shown that the photon bunching from the Hong-Ou-Mandel (HOM) effect can be used for quantum imaging in which sample properties (reflection/transmission amplitude, phase delay, or polarization) can be characterized at the pixel-by-pixel level. In this work, we perform Jones matrix imaging for an unknown object based on two-photon interference. By using a reference metasurface with panels of known polarization responses in pairwise coincidence measurements, the object's polarization responses at each pixel can be retrieved from the dependence of the coincidence visibility as a function of the reference polarization. The post-selection of coincidence images with specific reference polarization in our approach eliminates the need in switching the incident polarization and thus parallelized optical measurements for Jones matrix characterization. The parallelization in preparing input states, prevalent in any quantum algorithms, is an advantage of adopting two-photon interference in Jones matrix imaging. We believe our work points to the usage of metasurfaces in biological and medical imaging in the quantum optical regime.

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.

High-resolution polarization-sensitive Fourier ptychography microscopy using a high numerical aperture dome illuminator

Polarization-sensitive Fourier-ptychography microscopy (pFPM) allows for high resolution imaging while maintaining a large field of view, and without mechanical movements of optical-setup components. In contrast to ordinary light microscopes, pFPM provides quantitative absorption and phase information, for complex and birefringent specimens, with high resolution across a wide field of view. Using a semi-spherical home-built LED illumination array, a single polarizer, and a 10x /0.28NA objective, we experimentally demonstrate high performance pFPM with a synthesized NA of 1.1. Applying the standard quantitative method, a measured half-pitch resolution of 244 nm is achieved for the 1951 USAF resolution test target. As application examples, the polarimetric properties of a herbaceous flowering plant and the metastatic carcinoma of human liver cells are analyzed and quantitatively imaged.

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.