Polarization holographic microscopy for extracting spatio-temporally resolved Jones matrix

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.

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.

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.

Time-Resolved Four-Channel Jones Matrix Measurement of Birefringent Materials Using an Ultrafast Laser

A method for ultrafast time-resolved four-channel Jones matrix measurement of birefringent materials using an ultrafast laser is investigated. This facilitated the acquisition of a four-channel angular multiplexing hologram in a single shot. The Jones matrix information of a birefringent sample was retrieved from the spatial spectrum of a hologram. The feasibility of this approach was established by measuring the Jones matrix of starch granules in microfluidic chips and the complex amplitude distribution and phase delay distribution of liquid crystal cell at different voltages. Moreover, when the picosecond laser was switched to a femtosecond laser, ultrafast measurements were possible provided that the time interval between two detection pulses was larger than the pulse width.

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.

Combined Jones–Stokes Polarimetry and Its Decomposition into Associated Anisotropic Characteristics of Spatial Light Modulator

Jones–Stokes polarimetry is a robust in vitro polarimetric technique that can be used to investigate the anisotropic properties of a birefringent medium. The study of spatially resolved Jones matrix components of an object is a heuristic approach to extract its phase and polarization information. However, direct interpretation of Jones matrix elements and their decomposition into associated anisotropic properties of a sample is still a challenging research problem that needs to be investigated. In this paper, we experimentally demonstrate combined Jones–Stokes polarimetry to investigate the amplitude, phase, and polarization modulation characteristics of a twisted nematic liquid crystal spatial light modulator (TNLC-SLM). The anisotropic response of the SLM is calibrated for its entire grayscale range. We determine the inevitable anisotropic properties viz., diattenuation, retardance, isotropic absorption, birefringence, and dichroism, which are retrieved from the measured Jones matrices of the SLM using Jones polar decomposition and a novel algebraic approach for Jones matrix decomposition. The results of this study provide a complete polarimetric calibration of the SLM within the framework of its anisotropic characteristics.

Tomographic measurement of dielectric tensors at optical frequency

The dielectric tensor is a physical descriptor of fundamental light-matter interactions, characterizing anisotropic materials with principal refractive indices and optic axes. Despite its importance in scientific and industrial applications ranging from material science to soft matter physics, the direct measurement of the three-dimensional dielectric tensor has been limited by the vectorial and inhomogeneous nature of light scattering from anisotropic materials. Here, we present a dielectric tensor tomographic approach to directly measure dielectric tensors of anisotropic structures including the spatial variations of principal refractive indices and directors. The anisotropic structure is illuminated with a polarized plane wave with various angles and polarization states. Then, the scattered fields are holographically measured and converted into vectorial diffracted field components. Finally, by inversely solving a vectorial wave equation, the three-dimensional dielectric tensor is reconstructed. Using this approach, we demonstrate quantitative tomographic measurements of various nematic liquid-crystal structures and their fast three-dimensional non-equilibrium dynamics.

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.

Linear diattenuation imaging of biological samples with digital lensless holographic microscopy

A digital lensless holographic microscope (DLHM) sensitive to the linear diattenuation produced by biological samples is reported. The insertion of a linear polarization-states generator and a linear polarization-states analyzer in a typical DLHM setup allows the proper linear diattenuation imaging of microscopic samples. The proposal has been validated for simulated and experimental biological samples containing calcium oxalate crystals extracted from agave leaves and potato starch grains. The performance of the proposed method is similar to that of a traditional polarimetric microscope to obtain linear diattenuation images of microscopic samples but with the advantages of DLHM, such as numerical refocusing, cost effectiveness, and the possibility of field-portable implementation.

Retardance measurement by spatially probing the sample with optical vortices

Modern optical systems utilize various degrees of freedom, such as polarization, for shaping and controlling the light. Common representative of such a component is spatial light modulator (SLM), consisting of liquid crystal display, allowing for imposing predetermined retardation with given orientation of optical axis of anisotropy. Therefore, it is widely used for polarization coded phase shifting, polarization splitting of wavefront in digital holography etc. Narrowing tolerance in optical experiments puts higher demands on precise setting of the modulator and the parameters set. Consequently, measuring such devices and their parameters is essential for proper functionality. We present a single shot, common path method for measuring retardance map of the modulator, based on spatial probing the modulator with point images of spatially coherent light source and transforming them to optical vortices.

Single-Shot Quantitative Polarization Imaging of Complex Birefringent Structure Dynamics

Polarization light microscopes are powerful tools for probing molecular order and orientation in birefringent materials. While a number of polarization microscopy techniques are available to access steady-state properties of birefringent samples, quantitative measurements of the molecular orientation dynamics on the millisecond time scale have remained a challenge. We propose polarized shearing interference microscopy (PSIM), a single-shot quantitative polarization imaging method, for extracting the retardance and orientation angle of the laser beam transmitting through optically anisotropic specimens with complex structures. The measurement accuracy and imaging performance of PSIM are validated by imaging a birefringent resolution target and a bovine tendon specimen. We demonstrate that PSIM can quantify the dynamics of a flowing lyotropic chromonic liquid crystal in a microfluidic channel at an imaging speed of 506 frames per second (only limited by the camera frame rate), with a field-of-view of up to 350 × 350 μm² and a diffraction-limit spatial resolution of ~2 μm. We envision that PSIM will find a broad range of applications in quantitative material characterization under dynamical conditions.

Compact polarization-resolved common-path digital holography based on the Pancharatnam-Berry phase

We propose a compact polarization-resolved common-path digital holography for measuring the polarization distribution of a light field dynamically with high temporal stability. The designed experimental setup allows simultaneously recording, in a common-path manner, two holograms carrying the complex amplitude information of two orthogonal polarization components of the light field. Based on the theory of the Pancharatnam-Berry phase to retrieve the full Stokes parameters of the light field, we demonstrate the experiments with polarized optical elements, stressed glass plate, and micrometer-sized liquid crystal droplet. The measurement results verify the method's high accuracy and stability, and the capability of measuring light fields with sizes ranging from centimeters to micrometers. Owing to the stable and compact optical path structure, this method is conducive to instrumentation and is expected to find wide applications in many fields.

Silicon substrate significantly alters dipole-dipole resolution in coherent microscope

Considering a coherent microscopy setup, influences of the substrate below the sample in the imaging performances are studied, with a focus on high refractive index substrate such as silicon. Analytical expression of 3D full-wave vectorial point spread function, i.e. the dyadic Green's function is derived for the optical setup together with the substrate. Numerical analysis are performed in order to understand and compare magnification, depth of field, and resolution when using silicon substrate versus the conventional glass substrate or usually modelled condition of no substrate. Novel insights are generated about the scope of resolution improvement due to near field effect of the silicon substrate. Importantly, we show that the expected resolution varies greatly with the position of the sources and the substrate interface relative to the focal plane. Both better and worse resolution as compared to glass substrate may be expected with small changes in their positions. Therefore, our studies show that deriving a single indicative number of expected resolution is neither possible nor judicious for the case of silicon substrate.

Exploiting a holographic polarization microscope for rapid autofocusing and 3D tracking

We report a fast autofocusing and accurate 3D tracking scheme for a digital hologram (DH) that intrinsically exploits a polarization microscope setup with two off-axis illumination beams having different polarization. This configuration forms twin-object images that are recorded in a digital hologram by angular and polarization multiplexing technique. We show that the separation of the two images on the recording plane follows a linear relationship with the defocus distance and indicates the defocus direction. Thus, in the entire field of view (FOV), the best focus distance of each object can be directly retrieved by identifying the respective separation distance with a cross-correlation algorithm, at the same time, 3D tracking can be performed by calculating the transverse coordinates of the two images. Moreover, we estimate this linear relationship by utilizing the numerical propagation calculation based on a single hologram, in which the focus distance of one of the objects in the FOV is known. We proved the proposed approach in accurate 3D tracking through multiple completely different experimental cases, i.e., recovering the swimming path of a marine alga (tetraselmis) in water and fast refocusing of ovarian cancer cells under micro-vibration stimulation. The reported experimental results validate the proposed strategy's effectiveness in dynamic measurement and 3D tracking without multiple diffraction calculations and any precise knowledge about the setup. We claim that it is the first time that a holographic polarization multiplexing setup is exploited intrinsically for 3D tracking and/or fast and accurate refocusing. This means that almost any polarization DH setup, thanks to our results, can guarantee accurate focusing along the optical axis in addition to polarization analysis of the sample, thus overcoming the limitation of the poor axial resolution.

Deep Learning-Based Holographic Polarization Microscopy

Polarized light microscopy provides high contrast to birefringent specimen and is widely used as a diagnostic tool in pathology. However, polarization microscopy systems typically operate by analyzing images collected from two or more light paths in different states of polarization, which lead to relatively complex optical designs, high system costs, or experienced technicians being required. Here, we present a deep learning-based holographic polarization microscope that is capable of obtaining quantitative birefringence retardance and orientation information of specimen from a phase-recovered hologram, while only requiring the addition of one polarizer/analyzer pair to an inline lensfree holographic imaging system. Using a deep neural network, the reconstructed holographic images from a single state of polarization can be transformed into images equivalent to those captured using a single-shot computational polarized light microscope (SCPLM). Our analysis shows that a trained deep neural network can extract the birefringence information using both the sample specific morphological features as well as the holographic amplitude and phase distribution. To demonstrate the efficacy of this method, we tested it by imaging various birefringent samples including, for example, monosodium urate and triamcinolone acetonide crystals. Our method achieves similar results to SCPLM both qualitatively and quantitatively, and due to its simpler optical design and significantly larger field-of-view this method has the potential to expand the access to polarization microscopy and its use for medical diagnosis in resource limited settings.

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.

Polarization holographic microscope slide for birefringence imaging of anisotropic samples in microfluidics

Birefringence is an important optical property of anisotropic materials arising from anisotropies of tissue microstructures. Birefringence parameters have been found to be important to understand optical anisotropic architecture of many materials and polarization imaging has been applied in many researches in the field of biology and medicine. Here, we propose a scheme to miniaturize a double-channel polarization holographic interferometer optics to create a polarization holographic microscope slide (P-HMS) suitable for integrating with microfluidic lab-on-a-chip (LoC) systems. Based on the P-HMS combined with a simple reconstruction algorithm described in the paper, we can not only simultaneously realize holographic imaging of two orthogonal polarization components of dynamic samples in a microfluidic channel but also quantitative measurement of 2D birefringence information, both including the birefringence phase retardation and optic-axis orientation. This chip interferometer allows for off-axis double-channel polarization digital holographic recording using only a single illumination beam without need of any beam splitter or mirror. Its quasi-common path configuration and self-aligned design also make it tolerant to vibrations and misalignment. This work about the P-HMS could play a positive role in promoting the application of birefringence imaging in microfluidic LoC technology.

Radial polarizing phase-shifting interferometry with applications to single-shot n interferogram measurements and potential usage for white light interferogram analysis

In this research, we present an interferometric system to analyze transparent samples using interferograms generated by a phase-shifting radial shear grating interferometer for two cases: the first obtaining n simultaneous phase-shifting interferograms using a coherent light source and the second one using sequential phase steps with a white light source. For the first case, the simultaneous interferograms are generated using two optical systems: the first one generates the polarized pattern while the second one consists of a 4f system creating replicas of the output interferograms. By using a 2D sinusoidal phase grating, we have the advantage of obtaining up to nine replicated interferograms, all of them with comparable intensities and having amplitudes modulated by the 2D sinusoidal phase grating diffraction orders as zero-order Bessel's functions. To obtain the optical phase map, several phase shifts are generated by placing a polarizing filter covering each replicated interferogram. We highlight the advantage of using n simultaneous interferograms by comparing resulting optical phases processed by a conventional four-step algorithm against those obtained by an implemented n=N+1 method, reducing errors with noisy interferograms. Results for n=7 and n=9 cases are presented. In addition, we have tested the setup with white light interference techniques by employing the polarizer radial shearing interferometer; for this case, the optical phase is calculated with the four-step and the three-step algorithms. Results of testing the developed system to examine static and dynamic phase objects are also included.

Polarization-resolved dual-view holographic system for 3D inspection of scattering particles

A novel dual-view polarization-resolved pulsed holographic system for particle measurements is presented. Both dual-view configuration and polarization-resolved registration are well suited for particle holography. Dual-view registration improves the accuracy in the detection of 3D position and velocities, and polarization-resolved registration provides polarization information about individual particles. The necessary calibrations are presented, and aberrations are compensated for by mapping the positions in the two views to positions in a global coordinate system. The system is demonstrated on a sample consisting of 7 μm spherical polystyrene particles dissolved in water in a cuvette. The system is tested with different polarizations of the illumination. It is found that the dual view improves the accuracy significantly in particle tracking. It is also found that by having polarization-resolved holograms, it is possible to separate naturally occurring sub-micrometer particles from the larger, 7 μm seeding particles.

Single-shot phase-shifting image-plane digital holography with tri-focal Fibonacci-Billet split lens

Phase-shifting holography has been widely applied in the field of non-destructive testing and interference imaging. Compared to the previous single-shot phase-shifting holography, here tri-focal Fibonacci-Billet split lens was introduced into Mach-Zehnder interferometer, in which the upper half of the Fibonacci-Billet split lens can realize three phase-locking copies of the planar reference wave and the lower half is used to generate three identical copies of object. The interference pattern is recorded by a detector in one single exposure. The test object can be reconstructed by three-step phase-shifting interferometry. The corresponding experiment is carried out to verify the effectiveness of this method. With advantages of real-time reconstruction and amplitude-only diffraction lens, it is very useful for fast imaging and optical element detection.

Real-time measurement of the liquid-crystal optic-axis angle and effective refractive index distribution based on a common-path interferometer

A common-path interferometer for the real-time measurement of the liquid-crystal (LC) optic-axis angle and effective refractive index distribution is proposed. This method involves adding a polarizer and polarization camera to a general optical microscope. This requires only single-exposure imaging without changing any optical elements, and greatly simplifies the measurement process and system. In addition, the measurement results are unaffected by light-source power fluctuations or a non-uniform spatial distribution. Therefore, this method is suitable for measuring the LC optic-axis angle and effective refractive index of electrically controlled LC devices. Finally, the feasibility and validity of the proposed method are verified by simulation and experimentation.

Single-shot quantitative birefringence microscopy for imaging birefringence parameters

A method for realizing 2D single-shot measurements of birefringence parameters (including both retardation and optic axis orientation) of anisotropic materials using a simple recording setup and an efficient processing algorithm is proposed. The recording setup can be built simply by inserting a circular polarizer and a polarization beam splitter, respectively, in the object path and reference path of a conventional off-axis holographic imaging system, with no need for other adjustments. An algorithm for quantitatively retrieving the birefringence parameters from one single-shot hologram is proposed and demonstrated, in which a new quantity describing the birefringence, called complex birefringence parameter, is introduced, and a set of formulas used to extract the birefringence parameters is derived. Some experimental results are given for demonstrating the feasibility of the method that reveal that the method may provide another effective approach for investigating the birefringence properties of dynamic anisotropic materials, especially the birefringence induced by ultrafast pulse lasers.

Low-coherent optical diffraction tomography by angle-scanning illumination

Temporally low-coherent optical diffraction tomography (ODT) is proposed and demonstrated based on angle-scanning Mach-Zehnder interferometry. Using a digital micromirror device based on diffractive tilting, the full-field interference of incoherent light is successfully maintained during every angle-scanning sequences. Further, current ODT reconstruction principles for temporally incoherent illuminations are thoroughly reviewed and developed. Several limitations of incoherent illumination are also discussed, such as the nondispersive assumption, optical sectioning capacity and illumination angle limitation. Using the proposed setup and reconstruction algorithms, low-coherent ODT imaging of plastic microspheres, human red blood cells and rat pheochromocytoma cells is experimentally demonstrated.

Ultrafast polarization bio-imaging based on coherent detection and time-stretch techniques

Optical polarization imaging has played an important role in many biological and biomedical applications, as it provides a label-free and non-invasive detection scheme to reveal the polarization information of optical rotation, birefringence, and photoelasticity distribution inherent in biological samples. However, the imaging speeds of the previously demonstrated polarization imaging techniques were often limited by the slow frame rates of the arrayed imaging detectors, which usually run at frame rates of several hundred hertz. By combining the optical coherent detection of orthogonal polarizations and the optical time-stretch imaging technique, we achieved ultrafast polarization bio-imaging at an extremely fast record line scanning rate up to 100 MHz without averaging. We experimentally demonstrated the superior performance of our method by imaging three slices of different kinds of biological samples with the retrieved Jones matrix and polarization-sensitive information including birefringence and diattenuation. The proposed system in this paper may find potential applications for ultrafast polarization dynamics in living samples or some other advanced biomedical research.

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.

Single-Shot Optical Anisotropy Imaging with Quantitative Polarization Interference Microscopy

Optical anisotropy measurement is essential for material characterization and biological imaging. In order to achieve single-shot mapping of the birefringence parameters of anisotropic samples, a novel polarized light imaging concept is proposed, namely quantitative polarization interference microscopy (QPIM). QPIM can be realized through designing a compact polarization-resolved interference microscopy system that captures interferograms bearing sample's linear birefringence information. To extract the retardance and the orientation angle maps from a single-shot measurement, a mathematical model for QPIM is further developed. The QPIM system is validated by measuring a calibrated quarter-wave plate, whose fast-axis orientation angle and retardance are determined with great accuracies. The single-shot nature of QPIM further allows to measure the transient dynamics of birefringence changes in material containing anisotropic structures. This application is demonstrated by capturing transient retardance changes in a custom-designed parallel-aligned nematic liquid crystal-based device.

Label-free non-invasive quantitative measurement of lipid contents in individual microalgal cells using refractive index tomography

Microalgae are promising candidates for biofuel production due to their high lipid content. To facilitate utilization of the microalgae for biofuel, rapid quantification of the lipid contents in microalgae is necessary. However, conventional methods based on the chemical extraction of lipids require a time-consuming destructive extraction process. Here, we demonstrate label-free, non-invasive, rapid quantification of the lipid contents in individual micro-algal cells measuring the three-dimensional refractive index tomograms. We measure three-dimensional refractive index distributions within Nannochloropsis oculata cells and find that lipid droplets are identifiable in tomograms by their high refractive index. In addition, we alter N. oculata under nitrogen deficiency by measuring the volume, lipid weight, and dry cell weight of individual cells. Characterization of individual cells allows correlative analysis between the lipid content and size of individual cells.

Polarization modulation by means of tunable polarization gratings in an azobenzene side-chain liquid-crystalline polymer film

Polarization modulation was achieved by means of a new type of grating recorded with two 532 nm beams at varying polarization angles in an azobenzene side-chain liquid-crystalline polymer film through light regulation instead of voltage control. In contrast to conventional polarization holographic gratings, the polarization state of the ± first-order diffracted beams of the recorded gratings depended strongly on angles between polarization directions of two recording beams, while the polarization state of the second-order diffraction remained unchanged. With the polarization angle changing from 0 to 90 deg, the ± first-order diffraction efficiency increased from 5.15% to 10.53%. Diffraction properties of the recorded gratings were attributed to the combination of polarization holographic gratings and amplitude gratings based on the calculation of Jones matrices and polarization holographic theory.

Measurements of polarization-dependent angle-resolved light scattering from individual microscopic samples using Fourier transform light scattering

We present a method to measure the vector-field light scattering of individual microscopic objects. The polarization-dependent optical field images are measured with quantitative phase imaging at the sample plane, and then numerically propagated to the far-field plane. This approach allows the two-dimensional polarization-dependent angle-resolved light scattered patterns from individual object to be obtained with high precision and sensitivity. Using this method, we present the measurements of the polarization-dependent light scattering of a liquid crystal droplet and individual silver nanowires over scattering angles of 50°. In addition, the spectroscopic extension of the polarization-dependent angle-resolved light scattering is demonstrated using wavelength-scanning illumination.

Jones matrix microscopy from a single-shot intensity measurement

Quantitative measurement of Jones matrix elements is crucial for the study of light polarization with the wide range of applications. Here, we propose and experimentally demonstrate a novel method of Fourier space sharing to determine spatially resolved all four elements of the Jones matrix from a single-intensity frame. This is achieved by applying a holographic approach and making use of two triangular polarization Sagnac interferometers in the sample and reference arms. The proposed technique is flexible to adjust carrier frequencies in order to meet the varying demand of different anisotropic samples. A Jones matrix microscopy system is developed and applied to transparent samples. Experimental implementation of the proposed technique is demonstrated by determining the Jones matrix elements of commercially available known samples and liquid crystal droplets.

Double-channel angular-multiplexing polarization holography with common-path and off-axis configuration

We propose a double-channel angular-multiplexing polarization holographic imaging system with common-path and off-axis configurations. In the system, its input plane is spatially divided into three windows: an object window and two reference windows, and two orthogonal linear polarizers are attached, respectively, on the two reference windows; a two-dimensional cross grating is inserted between the input and output planes of the system. Thus the object beam passing through the object window and the two orthogonal polarized reference beams passing through the two reference windows can overlap each other at the output plane of the system and form a double-channel angular-multiplexing polarization hologram (DC-AM-PH). Using this system, the complex amplitude distributions of two orthogonal polarized components from an object can be recorded and reconstructed by one single-shot DC-AM-PH at the same time. Theoretical analysis and experimental results demonstrated that the system can be used to measure the Jones matrix parameters of polarization-sensitive or birefringent materials.

Holographic deep learning for rapid optical screening of anthrax spores

Establishing early warning systems for anthrax attacks is crucial in biodefense. Despite numerous studies for decades, the limited sensitivity of conventional biochemical methods essentially requires preprocessing steps and thus has limitations to be used in realistic settings of biological warfare. We present an optical method for rapid and label-free screening of Bacillus anthracis spores through the synergistic application of holographic microscopy and deep learning. A deep convolutional neural network is designed to classify holographic images of unlabeled living cells. After training, the network outperforms previous techniques in all accuracy measures, achieving single-spore sensitivity and subgenus specificity. The unique "representation learning" capability of deep learning enables direct training from raw images instead of manually extracted features. The method automatically recognizes key biological traits encoded in the images and exploits them as fingerprints. This remarkable learning ability makes the proposed method readily applicable to classifying various single cells in addition to B. anthracis, as demonstrated for the diagnosis of Listeria monocytogenes, without any modification. We believe that our strategy will make holographic microscopy more accessible to medical doctors and biomedical scientists for easy, rapid, and accurate point-of-care diagnosis of pathogens.

Holographic deep learning for rapid optical screening of anthrax spores

Establishing early warning systems for anthrax attacks is crucial in biodefense. Despite numerous studies for decades, the limited sensitivity of conventional biochemical methods essentially requires preprocessing steps and thus has limitations to be used in realistic settings of biological warfare. We present an optical method for rapid and label-free screening of Bacillus anthracis spores through the synergistic application of holographic microscopy and deep learning. A deep convolutional neural network is designed to classify holographic images of unlabeled living cells. After training, the network outperforms previous techniques in all accuracy measures, achieving single-spore sensitivity and subgenus specificity. The unique "representation learning" capability of deep learning enables direct training from raw images instead of manually extracted features. The method automatically recognizes key biological traits encoded in the images and exploits them as fingerprints. This remarkable learning ability makes the proposed method readily applicable to classifying various single cells in addition to B. anthracis, as demonstrated for the diagnosis of Listeria monocytogenes, without any modification. We believe that our strategy will make holographic microscopy more accessible to medical doctors and biomedical scientists for easy, rapid, and accurate point-of-care diagnosis of pathogens.

Fiber-based lensless polarization holography for measuring Jones matrix parameters of polarization-sensitive materials

We report a fiber-based lensless holographic imaging system to realize a single-shot measurement of two dimensional (2-D) Jones matrix parameters of polarization-sensitive materials. In this system, a multi-source lensless off-axis Fresnel holographic recording geometry is adopted, and two optical fiber splitters are used to generate the multiple reference and illumination beams required for recording a four-channel angular-multiplexing polarization hologram (AMPH). Using this system and the method described in this paper, spatially resolved Jones matrix parameters of a polarization-sensitive material can be retrieved from one single-shot AMPH. We demonstrate the feasibility of the method by extracting a 2-D Jones matrix of a composite polarizer. Applications of the method to measure the Jones matrix maps of a stressed polymethyl methacrylate sample and a mica fragment are also presented. Benefit from the fiber-based and lensless off-axis holographic design, the system possesses a quite compact configuration, which provides a feasible approach for development of an integrated and portable system to measure Jones matrix parameters of polarization-sensitive materials.

Quantifying the polarization properties of non-depolarizing optical elements with virtual distorting elements

It is well known that polarization can be potentially distorted by optical elements in optical paths, which intensively influences researches and techniques related to polarization analysis. For this, we proposed to exactly quantify the polarization properties of non-depolarizing optical elements with virtual distorting elements characterized by three parameters: orientation Θ, diattenuation Γ, and retardation Δ. Utilizing the least-squares fitting method, these three parameters can be determined by fitting the measured output polarization states from the optical element with the polarization responses of VDEs. The principle of this method is detailed, and a corresponding experimental setup is further presented. The feasibility of this method has been verified in reflective mirrors and a dichroic mirror. Based on the quantification results with our setup, we have successfully compensated the polarization distortion induced by a dichroic mirror. The precision of this method has been investigated in detail with Monte Carlo simulations. The investigation results show that this method has high precision at certain measurement conditions, and the precision can be further improved.

Single-shot digital holographic microscopy for quantifying a spatially-resolved Jones matrix of biological specimens

Field-based polarization measurements are essential for the completeness of information when exploiting the complex nature of optical responses of target objects. Here, we demonstrate digital holographic microscopy for quantifying a polarization-sensitive map of an object with a single-shot measurement. Using the image-splitting device generating four different copies of an object image and a separate reference beam of an off-axis configuration enables single-shot and multi-imaging capability. With the use of two polarization filters, four complex field images containing an object's polarization response are obtained simultaneously. With this method, we can construct a complete set of 2-by-2 Jones matrix at every single point of the object's images, and thus clearly visualize the anisotropic structures of biological tissues with low level of birefringence. This method will facilitate the high-precision measurements for fast dynamics of the polarization properties of biological specimens.

Label-free optical quantification of structural alterations in Alzheimer's disease

We present a wide-field quantitative label-free imaging of mouse brain tissue slices with sub-micrometre resolution, employing holographic microscopy and an automated scanning platform. From the measured light field images, scattering coefficients and anisotropies are quantitatively retrieved by using the modified the scattering-phase theorem, which enables access to structural information about brain tissues. As a proof of principle, we demonstrate that these scattering parameters enable us to quantitatively address structural alteration in the brain tissues of mice with Alzheimer’s disease.

White-light quantitative phase imaging unit

We introduce the white-light quantitative phase imaging unit (WQPIU) as a practical realization of quantitative phase imaging (QPI) on standard microscope platforms. The WQPIU is a compact stand-alone unit which measures sample induced phase delay under white-light illumination. It does not require any modification of the microscope or additional accessories for its use. The principle of the WQPIU based on lateral shearing interferometry and phase shifting interferometry provides a cost-effective and user-friendly use of QPI. The validity and capacity of the presented method are demonstrated by measuring quantitative phase images of polystyrene beads, human red blood cells, HeLa cells and mouse white blood cells. With speckle-free imaging capability due to the use of white-light illumination, the WQPIU is expected to expand the scope of QPI in biological sciences as a powerful but simple imaging tool.

Active illumination using a digital micromirror device for quantitative phase imaging

We present a powerful and cost-effective method for active illumination using a digital micromirror device (DMD) for quantitative phase-imaging techniques. Displaying binary illumination patterns on a DMD with appropriate spatial filtering, plane waves with various illumination angles are generated and impinged onto a sample. Complex optical fields of the sample obtained with various incident angles are then measured via Mach-Zehnder interferometry, from which a high-resolution 2D synthetic aperture phase image and a 3D refractive index tomogram of the sample are reconstructed. We demonstrate the fast and stable illumination-control capability of the proposed method by imaging colloidal spheres and biological cells. The capability of high-speed optical diffraction tomography is also demonstrated by measuring 3D Brownian motion of colloidal particles with the tomogram acquisition rate of 100 Hz.

Label-free characterization of white blood cells by measuring 3D refractive index maps

The characterization of white blood cells (WBCs) is crucial for blood analyses and disease diagnoses. However, current standard techniques rely on cell labeling, a process which imposes significant limitations. Here we present three-dimensional (3D) optical measurements and the label-free characterization of mouse WBCs using optical diffraction tomography. 3D refractive index (RI) tomograms of individual WBCs are constructed from multiple two-dimensional quantitative phase images of samples illuminated at various angles of incidence. Measurements of the 3D RI tomogram of WBCs enable the separation of heterogeneous populations of WBCs using quantitative morphological and biochemical information. Time-lapse tomographic measurements also provide the 3D trajectory of micrometer-sized beads ingested by WBCs. These results demonstrate that optical diffraction tomography can be a useful and versatile tool for the study of WBCs.

Quantitative retardance imaging of biological samples using quadriwave lateral shearing interferometry

We describe a new technique based on the use of a high-resolution quadri-wave lateral shearing interferometer to perform quantitative linear retardance and birefringence measurements on biological samples. The system combines quantitative phase images with varying polarization excitation to create retardance images. This technique is compatible with living samples and gives information about the local retardance and structure of their anisotropic components. We applied our approach to collagen fibers leading to a birefringence value of (3.4 ± 0.3) · 10(-3) and to living cells, showing that cytoskeleton can be imaged label-free.

Label-free identification of individual bacteria using Fourier transform light scattering

Rapid identification of bacterial species is crucial in medicine and food hygiene. In order to achieve rapid and label-free identification of bacterial species at the single bacterium level, we propose and experimentally demonstrate an optical method based on Fourier transform light scattering (FTLS) measurements and statistical classification. For individual rod-shaped bacteria belonging to four bacterial species (Listeria monocytogenes, Escherichia coli, Lactobacillus casei, and Bacillus subtilis), two-dimensional angle-resolved light scattering maps are precisely measured using FTLS technique. The scattering maps are then systematically analyzed, employing statistical classification in order to extract the unique fingerprint patterns for each species, so that a new unidentified bacterium can be identified by a single light scattering measurement. The single-bacterial and label-free nature of our method suggests wide applicability for rapid point-of-care bacterial diagnosis.

Polarization-controlled images based on double-exposure polarization holography in an azobenzene liquid-crystalline polymer

Polarization-controlled optical image operations were demonstrated based on the double-exposure polarization holographic method. Two images were stored in the same volume of an azobenzene liquid-crystalline polymer by recording superimposed holograms, a pair of polarization gratings with one spatial frequency, using two orthogonal circularly polarized 532 nm beams and were reconstructed with a 650 nm laser. The recorded polarization holographic gratings were investigated to show distinctive polarization selectivity, high diffraction efficiency, and good stability. The brightness and the polarization of the diffracted images were found to be dependent on the polarization of the readout beam, and two images could be reconstructed individually or simultaneously.

One-step Jones matrix polarization holography for extraction of spatially resolved Jones matrix of polarization-sensitive materials

We propose, for the first time to our knowledge, a method for realizing one-step measurement of two-dimensional Jones matrix parameters of polarization-sensitive materials. This method could be called one-step Jones matrix polarization holography (JMPH). Our theoretical analysis and the experimental results demonstrate that a double-source polarization interferometer combined with angular multiplexing holography make it possible to realize one-step holographic measurements of four spatially resolved Jones matrix parameters. Compared with the existing methods, our one-step JMPH has a simpler optical arrangement and easier measuring procedure. We believe that it will provide a new approach for development of an integrated system suitable for measuring, in real-time, a Jones matrix or transmittance matrix, as well as dynamic polarization imaging.

Profiling individual human red blood cells using common-path diffraction optical tomography

Due to its strong correlation with the pathophysiology of many diseases, information about human red blood cells (RBCs) has a crucial function in hematology. Therefore, measuring and understanding the morphological, chemical, and mechanical properties of individual RBCs is a key to understanding the pathophysiology of a number of diseases in hematology, as well as to opening up new possibilities for diagnosing diseases in their early stages. In this study, we present the simultaneous and quantitative measurement of the morphological, chemical, and mechanical parameters of individual RBCs employing optical holographic microtomography. In addition, it is demonstrated that the correlation analyses of these RBC parameters provide unique information for distinguishing and understanding diseases.

LCD panel characterization by measuring full Jones matrix of individual pixels using polarization-sensitive digital holographic microscopy

We present measurements of the full Jones matrix of individual pixels in a liquid-crystal display (LCD) panel. Employing a polarization-sensitive digital holographic microscopy based on Mach-Zehnder interferometry, the complex amplitudes of the light passing through individual LCD pixels are precisely measured with respect to orthogonal bases of polarization states, from which the full Jones matrix components of individual pixels are obtained. We also measure the changes in the Jones matrix of individual LCD pixels with respect to an applied bias. In addition, the complex optical responses of a LCD panel with respect to arbitrary polarization states of incident light were characterized from the measured Jones matrix.

Biomedical applications of holographic microspectroscopy [invited]

The identification and quantification of specific molecules are crucial for studying the pathophysiology of cells, tissues, and organs as well as diagnosis and treatment of diseases. Recent advances in holographic microspectroscopy, based on quantitative phase imaging or optical coherence tomography techniques, show promise for label-free noninvasive optical detection and quantification of specific molecules in living cells and tissues (e.g., hemoglobin protein). To provide important insight into the potential employment of holographic spectroscopy techniques in biological research and for related practical applications, we review the principles of holographic microspectroscopy techniques and highlight recent studies.

Quantitative phase imaging unit

A simple and cost-effective method is presented for quantitative phase imaging. A common-path lateral phase shifting interferometer is realized through attaching a compact filter set to the output port of an existing microscope. The working principles, design criteria, and limitations are also derived and explained. In order to demonstrate the capability and applicability of the method, the optical phase images of a microsphere and individual human red blood cells are measured with high stability.

Angle-resolved light scattering of individual rod-shaped bacteria based on Fourier transform light scattering

Two-dimensional angle-resolved light scattering maps of individual rod-shaped bacteria are measured at the single-cell level. Using quantitative phase imaging and Fourier transform light scattering techniques, the light scattering patterns of individual bacteria in four rod-shaped species (Bacillus subtilis, Lactobacillus casei, Synechococcus elongatus, and Escherichia coli) are measured with unprecedented sensitivity in a broad angular range from −70° to 70°. The measured light scattering patterns are analyzed along the two principal axes of rod-shaped bacteria in order to systematically investigate the species-specific characteristics of anisotropic light scattering. In addition, the cellular dry mass of individual bacteria is calculated and used to demonstrate that the cell-to-cell variations in light scattering within bacterial species is related to the cellular dry mass and growth.