Quantitative retardance imaging of biological samples using quadriwave lateral shearing interferometry

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.

Common-path intrinsically achromatic optical diffraction tomography

In this work we propose an open-top like common-path intrinsically achromatic optical diffraction tomography system. It operates as a total-shear interferometer and employs Ronchi-type amplitude diffraction grating, positioned in between the camera and the tube lens without an additional 4f system, generating three-beam interferograms with achromatic second harmonic. Such configuration makes the proposed system low cost, compact and immune to vibrations. We present the results of the measurements of 3D-printed cell phantom using laser diode (coherent) and superluminescent diode (partially coherent) light sources. Broadband light sources can be naturally employed without the need for any cumbersome compensation because of the intrinsic achromaticity of the interferometric recording (holograms generated by -1st and +1st conjugated diffraction orders are not affected by the illumination wavelength). The results show that the decreased coherence offers much reduced coherent noise and higher fidelity tomographic reconstruction especially when applied nonnegativity constraint regularization procedure.

Quantitative phase microscopy for non-invasive live cell population monitoring

We present here a label-free development based on preexisting Quantitative Phase Imaging (QPI) that allows non-invasive live monitoring of both individual cells and cell populations. Growth, death, effect of toxic compounds are quantified under visible light with a standard inverted microscope. We show that considering the global biomass of a cell population is a more robust and accurate method to assess its growth parameters in comparison to compiling individually segmented cells. This is especially true for confluent conditions. This method expands the use of light microscopy in answering biological questions concerning live cell populations even at high density. In contrast to labeling or lysis of cells this method does not alter the cells and could be useful in high-throughput screening and toxicity studies.

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.

Advantages of Fresnel biprism-based digital holographic microscopy in quantitative phase imaging

SIGNIFICANCE

The hallmarks of digital holographic microscopy (DHM) compared with other quantitative phase imaging (QPI) methods are high speed, accuracy, spatial resolution, temporal stability, and polarization-sensitivity (PS) capability. The above features make DHM suitable for real-time quantitative PS phase imaging in a broad number of biological applications aimed at understanding cell growth and dynamic changes occurring during physiological processes and/or in response to pharmaceutical agents.

AIM

The insertion of a Fresnel biprism (FB) in the image space of a light microscope potentially turns any commercial system into a DHM system enabling QPI with the five desired features in QPI simultaneously: high temporal sensitivity, high speed, high accuracy, high spatial resolution, and PS. To the best of our knowledge, this is the first FB-based DHM system providing these five features all together.

APPROACH

The performance of the proposed system was calibrated with a benchmark phase object. The PS capability has been verified by imaging human U87 glioblastoma cells.

RESULTS

The proposed FB-based DHM system provides accurate phase images with high spatial resolution. The temporal stability of our system is in the order of a few nanometers, enabling live-cell studies. Finally, the distinctive behavior of the cells at different polarization angles (e.g., PS capability) can be observed with our system.

CONCLUSIONS

We have presented a method to turn any commercial light microscope with monochromatic illumination into a PS QPI system. The proposed system provides accurate quantitative PS phase images in a new, simple, compact, and cost-effective format, thanks to the low cost (a few hundred dollars) involved in implementing this simple architecture, enabling the use of this QPI technique accessible to most laboratories with standard light microscopes.

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.

Phase Imbalance Optimization in Interference Linear Displacement Sensor with Surface Gratings

In interferential linear displacement sensors, accurate information about the position of the reading head is calculated out of a pair of quadrature (sine and cosine) signals. In double grating interference schemes, diffraction gratings combine the function of beam splitters and phase retardation devices. Specifically, the reference diffraction grating is located in the reading head and regulates the phase shifts in diffraction orders. Measurement diffraction grating moves along with the object and provides correspondence to the displacement coordinate. To stabilize the phase imbalance in the output quadrature signals of the sensor, we propose to calculate and optimize the parameters of these gratings, based not only on the energetic analysis, but along with phase relationships in diffraction orders. The optimization method is based on rigorous coupled-wave analysis simulation of the phase shifts of light in diffraction orders in the optical system. The phase properties of the reference diffraction grating in the interferential sensor are studied. It is confirmed that the possibility of quadrature modulation depends on parameters of static reference scale. The implemented optimization criteria are formulated in accordance with the signal generation process in the optical branch. Phase imbalance and amplification coefficients are derived from Heydemann elliptic correction and expressed through the diffraction efficiencies and phase retardations of the reference scale. The phase imbalance of the obtained quadrature signals is estimated in ellipticity correction terms depending on the uncertainties of influencing parameters.

Two improved defocus quantitative phase imaging methods: discussion

Multifilter phase imaging with partially coherent light (MFPI-PC) and phase optical transfer function recovery (POTFR) are two viable defocus-based, two-dimensional quantitative phase imaging (QPI) methods. While both methods use transfer function inversion, MFPI-PC is based on the in-focus intensity derivative, while POTFR is based on the intensity difference between symmetrically defocused images. This paper compares and contrasts MFPI-PC and POTFR. Six disadvantages (five in MFPI-PC and one in POTFR) are identified. Improvement strategies to overcome each of the six shortcomings are identified and implemented, and both methods are shown to be clearly improved. The revised MFPI-PC is shown to be more accurate than the original MFPI-PC and generally more accurate than the revised POTFR. The revised POTFR is shown to be inherently faster than the original POTFR and also slightly faster than the revised MFPI-PC.

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.

Multi-wavelength quantitative polarization and phase microscope

We introduce a snapshot multi-wavelength quantitative polarization and phase microscope (MQPPM) for measuring spectral dependent quantitative polarization and phase information. The system uniquely integrates a polarized light microscope and a snap-shot quantitative phase microscope in a single system, utilizing a novel full-Stokes camera operating in the red, green, and blue (RGB) spectrum. The linear retardance and fast axis orientation of a birefringent sample can be measured simultaneously in the visible spectra. Both theoretical analysis and experiments have been performed to demonstrate the capability of the proposed microscope. Data from liquid crystal and different biological samples are presented. We believe that MQPPM will be a useful tool in measuring quantitative polarization and phase information of live cells.

Geometric-Phase Microscopy for Quantitative Phase Imaging of Isotropic, Birefringent and Space-Variant Polarization Samples

We present geometric-phase microscopy allowing a multipurpose quantitative phase imaging in which the ground-truth phase is restored by quantifying the phase retardance. The method uses broadband spatially incoherent light that is polarization sensitively controlled through the geometric (Pancharatnam-Berry) phase. The assessed retardance possibly originates either in dynamic or geometric phase and measurements are customized for quantitative mapping of isotropic and birefringent samples or multi-functional geometric-phase elements. The phase restoration is based on the self-interference of polarization distinguished waves carrying sample information and providing pure reference phase, while passing through an inherently stable common-path setup. The experimental configuration allows an instantaneous (single-shot) phase restoration with guaranteed subnanometer precision and excellent ground-truth accuracy (well below 5 nm). The optical performance is demonstrated in advanced yet routinely feasible noninvasive biophotonic imaging executed in the automated manner and predestined for supervised machine learning. The experiments demonstrate measurement of cell dry mass density, cell classification based on the morphological parameters and visualization of dynamic dry mass changes. The multipurpose use of the method was demonstrated by restoring variations in the dynamic phase originating from the electrically induced birefringence of liquid crystals and by mapping the geometric phase of a space-variant polarization directed lens.

Weighted-least-squares multi-filter phase imaging with partially coherent light: characteristics of annular illumination

Multi-filter phase imaging with partially coherent light (MFPI-PC) is a promising microscopic quantitative phase imaging (QPI) method that measures the phase of a transparent object. In the present work, a weighted-least-squares version is developed and applied to the important case of annular illumination. The resulting improved algorithms have largely solved the noise magnification problem associated with the original MFPI-PC in annular illumination. Simulation and microlens experiments are used to validate the new QPI method for the case of annular illumination.

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.

Structure and collagen crimp patterns of functionally distinct equine tendons, revealed by quantitative polarised light microscopy (qPLM)

Structure-function relationships in tendons are directly influenced by the arrangement of collagen fibres. However, the details of such arrangements in functionally distinct tendons remain obscure. This study demonstrates the use of quantitative polarised light microscopy (qPLM) to identify structural differences in two major tendon compartments at the mesoscale: fascicles and interfascicular matrix (IFM). It contrasts functionally distinct positional and energy storing tendons, and considers changes with age. Of particular note, the technique facilitates the analysis of crimp parameters, in which cutting direction artefact can be accounted for and eliminated, enabling the first detailed analysis of crimp parameters across functionally distinct tendons.

IFM shows lower birefringence (0.0013 ± 0.0001 [−]), as compared to fascicles (0.0044 ± 0.0005 [−]), indicating that the volume fraction of fibres must be substantially lower in the IFM. Interestingly, no evidence of distinct fibre directional dispersions between equine energy storing superficial digital flexor tendons (SDFTs) and positional common digital extensor tendons (CDETs) were noted, suggesting either more subtle structural differences between tendon types or changes focused in the non-collagenous components.

By contrast, collagen crimp characteristics are strongly tendon type specific, indicating crimp specialisation is crucial in the respective mechanical function. SDFTs showed much finer crimp (21.1 ± 5.5 µm) than positional CDETs (135.4 ± 20.1 µm). Further, tendon crimp was finer in injured tendon, as compared to its healthy equivalents. Crimp angle differed strongly between tendon types as well, with average of 6.5 ± 1.4° in SDFTs and 13.1 ± 2.0° in CDETs, highlighting a substantially tighter crimp in the SDFT, likely contributing to its effective recoil capacity.

Statement of Significance

This is the first study to quantify birefringence in fascicles and interfascicular matrix of functionally distinct energy storing and positional tendons. It adopts a novel method – quantitative polarised light microscopy (qPLM) to measure collagen crimp angle, avoiding artefacts related to the direction of histological sectioning, and provides the first direct comparison of crimp characteristics of functionally distinct tendons of various ages.

A comparison of matched picrosirius red stained and unstained tendons sections identified non-homogenous staining effects, and leads us to recommend that only unstained sections are analysed in the quantitative manner.

qPLM is successfully used to assess birefringence in soft tissue sections, offering a promising tool for investigating the structural arrangements of fibres in (soft) tissues and other composite materials.

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.

Laser-induced birefringence measurements by quantitative polarized-phase microscopy

A technique that provides quantitative and spatially resolved retardance measurement is studied for application to laser-induced modification in transparent materials. The method is based on the measurement of optical path differences between two wavefronts carrying different polarizations, measured by a wavefront sensor placed in the image plane of a microscope. We have applied the technique to the investigation of stress distribution induced by CO₂ laser processing of fused silica samples. By comparing experiments to the results of thermomechanical simulations we demonstrate quantitative agreement between measurements and simulations of optical retardance. The technique provides an efficient and simple way to measure retardance of less than 1 nm with a diffraction-limited spatial resolution in transparent samples, and coupled to thermomechanical simulations it gives access to birefringence distribution in the sample.

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.

Quantitative phase imaging method based on an analytical nonparaxial partially coherent phase optical transfer function

Multifilter phase imaging with partially coherent light (MFPI-PC) is a promising new quantitative phase imaging method. However, the existing MFPI-PC method is based on the paraxial approximation. In the present work, an analytical nonparaxial partially coherent phase optical transfer function is derived. This enables the MFPI-PC to be extended to the realistic nonparaxial case. Simulations over a wide range of test phase objects as well as experimental measurements on a microlens array verify higher levels of imaging accuracy compared to the paraxial method. Unlike the paraxial version, the nonparaxial MFPI-PC with obliquity factor correction exhibits no systematic error. In addition, due to its analytical expression, the increase in computation time compared to the paraxial version is negligible.

Integrated quantitative phase and birefringence microscopy for imaging malaria-infected red blood cells

A dual-modality birefringence/phase imaging system is presented. The system features a crystal retarder that provides polarization mixing and generates two interferometric carrier waves in a single signal spectrum. The retardation and orientation of sample birefringence can then be measured simultaneously based on spectral multiplexing interferometry. Further, with the addition of a Nomarski prism, the same setup can be used for quantitative differential interference contrast (DIC) imaging. Sample phase can then be obtained with two-dimensional integration. In addition, birefringence-induced phase error can be corrected using the birefringence data. This dual-modality approach is analyzed theoretically with Jones calculus and validated experimentally with malaria-infected red blood cells. The system generates not only corrected DIC and phase images, but a birefringence map that highlights the distribution of hemozoin crystals.

Quantitative phase imaging of weakly scattering objects using partially coherent illumination

In this paper, we extend our recent work on partially coherent quantitative phase imaging (pcQPI) from two-dimensional (2D) to three-dimensional (3D) imaging of weakly scattering samples. Due to the mathematical complexity, most theoretical modeling of quantitative phase image formation under partial coherence has focused on thin, well-focused samples. It is unclear how these abberations are affected by defocusing. Also, as 3D QPI techniques continue to develop, a better model needs to be developed to understand and quantify these aberrations when imaging thicker samples. Here, using the first order Born's approximation, we derived a mathematical framework that provides an intuitive model of image formation under varying degrees of coherence. Our description provides a clear connection between the halo effect and phase underestimation, defocusing and the 3D structure of the sample under investigation. Our results agree very well with the experiments and show that the microscope objective defines the sectioning ability of the imaging system while the condenser lens is responsible for the halo effect.

Living cell dry mass measurement using quantitative phase imaging with quadriwave lateral shearing interferometry: an accuracy and sensitivity discussion

Single-cell dry mass measurement is used in biology to follow cell cycle, to address effects of drugs, or to investigate cell metabolism. Quantitative phase imaging technique with quadriwave lateral shearing interferometry (QWLSI) allows measuring cell dry mass. The technique is very simple to set up, as it is integrated in a camera-like instrument. It simply plugs onto a standard microscope and uses a white light illumination source. Its working principle is first explained, from image acquisition to automated segmentation algorithm and dry mass quantification. Metrology of the whole process, including its sensitivity, repeatability, reliability, sources of error, over different kinds of samples and under different experimental conditions, is developed. We show that there is no influence of magnification or spatial light coherence on dry mass measurement; effect of defocus is more critical but can be calibrated. As a consequence, QWLSI is a well-suited technique for fast, simple, and reliable cell dry mass study, especially for live cells.