Mueller matrix measurements of algae with different shape and size distributions

Non-destructive latent fingerprint development and background elimination by Mueller Polarimetry

In this article we have explored the use of Mueller polarimetry for the simultaneous and non-destructive latent fingerprint development and background elimination. This proposal not only expands previously reported uses of the polarization state of light for fingerprint development, but offers some advantages. Samples of a few donors, taken on different heavily back grounded substrates, were measured and processed. Several strategies for background removal were applied. The results are very promising, since the background was successfully erased in all cases and the quality of the developed fingerprints was excellent for most substrates and donors. Considering that the method is non-destructive and that the proposed measurement instrument is inexpensive and portable the method could be tried in real cases with no risk for the evidence. In addition, the success of the procedure for background removal raises the possibility of exploring if it would work for the enhancement of fingerprints developed with other methods.

Validation of the polarized Monte Carlo model of shipborne oceanic lidar returns

The polarized Monte Carlo (PMC) model has been applied to study the backscattering measurement of oceanic lidar. This study proposes a PMC model for shipborne oceanic lidar simulation. This model is validated by the Rayleigh scattering experiment, lidar equation, and in-situ lidar LOOP (Lidar for Ocean Optics Profiler) returns [Opt. Express30, 8927 (2022)10.1364/OE.449554]. The relative errors of the simulated Rayleigh scattering results are less than 0.07%. The maximum mean relative error (MRE) of the simulated single scattering scalar signals and lidar equation results is 30.94%. The maximum MRE of simulated total scattering signals and LOOP returns in parallel and cross channels are 33.29% and 22.37%, respectively, and the maximal MRE of the depolarization ratio is 24.13%. The underwater light field of the laser beam is also simulated to illustrate the process of beam energy spreading. These results prove the validity of the model. Further analyses show that the measured signals of shipborne lidar LOOP are primarily from the particle single scatterings. This model is significant for analyzing the signal contributions from multiple scattering and single scattering.

Recognition of microplastics suspended in seawater via refractive index by Mueller matrix polarimetry

Microplastics have become the marine pollution posing a human health risk, but they are difficult to be detected and recognized for different materials, irregular shapes, and broad size distributions. Microplastics' refractive index (RI) is related to the materials and can be characterized by the Mueller matrix. In this work, the particles are suspended in water and their Mueller matrices are measured by a particulate Mueller matrix polarimetry setup. Four kinds of spherical particles including microplastics are effectively classified by their Mueller matrices. Moreover, two kinds of common microplastics with broad size distributions, irregular shapes, and random orientations are also well recognized by the Mueller matrix. These results imply that RI plays a vital role in the recognition of microplastics suspended in water. By using the Mie theory and discrete dipole approximation simulation, the discussions explain in physics origin how RI affects Mueller matrix coupling with size and structure, and give some decoupling methods. Results in this work help advance future tools to in situ recognize the microplastics in seawater.

Applications of Mueller Matrix Polarimetry to Biological and Agricultural Diagnostics: A Review

The review contains a systematization of the main approaches to the practical implementation of Mueller matrix polarimetry and the prospects for its application in biology and agriculture. The most typical optical layouts for measuring the Mueller matrix of various objects, such as disperse systems, tissues and surface structures, are discussed. Mueller matrix measurements, being integrated into standard schemes of conventional optical methods, such as scatterometry, optical coherence tomography, fluorimetry, spectrophotometry and reflectometry, can significantly expand their capabilities in the characterization of biological systems and bioorganic materials. Additionally, microwave Mueller matrix polarimetry can be used for monitoring soil conditions and crop growth. The proposed systematization is aimed at outlining the conceptual directions for the development of non-invasive diagnostic tools based on measuring the Mueller matrix, primarily with a focus on biological research and agricultural practice.

Machine Learning Powered Microalgae Classification by Use of Polarized Light Scattering Data

Microalgae are widely distributed in the ocean, which greatly affects the ocean environment. In this work, a dataset is presented, including the polarized light scattering data of 35 categories of marine microalgae. To analyze the dataset, several machine learning algorithms are applied and compared, such as linear discrimination analysis (LDA) and two types of support vector machine (SVM). Results show that non-linear SVM performs the best among these algorithms. Then, two data preparation approaches for non-linear SVM are compared. Subsequently, more than 10 categories of microalgae out of the dataset can be identified with an accuracy greater than 0.80. The basis of the dataset is shown by finding the categories independent to each other. The discussions about the performance of different incident polarization of light gives some clues to design the optimal incident polarization of light for future instrumentation. With this proposed technique and the dataset, these microalgae can be well differentiated by polarized light scattering data.

Measurements of Aquatic Particle Volume Scattering Function up to 178.5° in the East China Sea

Particulate volume scattering function (VSF), especially at angles larger than 170°, is of particular importance for interpreting ocean optical remote sensing signals and underwater imagery. In this study, a laboratory-based VSF instrument (VSFlab) adopting the periscopic optical system was developed to obtain VSF measurements from 1°–178.5°. In the VSFlab, a new prism design that simply combines a single prism and a neutral density filter was proposed to more efficiently reduce the stray light in the backward direction, while a detailed calibration procedure was given. A full validation based on standard beads of various sizes and a comparison with the results from LISST-VSF and POLVSM indicated that the VSFlab can provide reliable results from 1° to 178.5°. VSFlab measurements in the East China Sea (ECS) exhibited a moderate increase (not more than 5 times) in VSF from 170° to 178.5° rather than a sharp increase of more than one order of magnitude presented in other instrument results measured in other coastal regions. The estimates of the particulate backscattering coefficient using single angle scattering measurements near 120° or 140° and suitable χp were justified. Two types of the VSFs with different size distribution and shape parameters in the ECS can be distinguished based on the variability of χp after 155°. The measured VSF could provide a basis for the parameterization of VSF in the radiative transfer model and the variability of χp in the backward direction had the potential to be used to characterize the particles in the coastal region of the ECS.

Characterization of suspended particulate matter in contrasting coastal marine environments with angle-resolved polarized light scattering measurements

Optical proxies based on light scattering measurements have potential to improve the study and monitoring of aquatic environments. In this study, we evaluated several optical proxies for characterization of particle mass concentration, composition, and size distribution of suspended particulate matter from two contrasting coastal marine environments. We expanded upon our previous study of Southern California coastal waters, which generally contained high proportions of organic particles, by conducting angle-resolved polarized light scattering measurements in predominantly turbid and inorganic-particle dominated Arctic coastal waters near Prudhoe Bay, Alaska. We observed that the particulate backscattering coefficient b_bp was the most effective proxy for the mass concentration of suspended particulate matter (SPM) when compared with particulate scattering and attenuation coefficients b_p and c_p. Improvements were seen with b_bp as a proxy for the concentration of particulate organic carbon (POC), although only if particulate assemblages were previously classified in terms of particle composition. We found that the ratio of polarized-light scattering measurements at 110º and 18º was superior in performance as a proxy for the composition parameter POC/SPM in comparison to the particulate backscattering ratio b_bp/b_p. The maximum value of the degree of linear polarization DoLP_p,max observed within the range of scattering angles 89°-106° was found to provide a reasonably good proxy for a particle size parameter (i.e., 90th percentile of particle volume distribution) which characterizes the proportions of small- and large-sized particles. These findings can inform the development of polarized light scattering sensors to enhance the capabilities of autonomous platforms.

Probing Individual Particles in Aquatic Suspensions by Simultaneously Measuring Polarized Light Scattering and Fluorescence

Suspended particles play a significant role in aquatic systems. However, existing methods to probe suspended particles have several limitations. In this paper, we present a portable prototype to in situ probe individual particles in aquatic suspensions by simultaneously measuring polarized light scattering and fluorescence, aiming to obtain an effective classification of microplastics and microalgae. Results show that the obtained classification accuracy is significantly higher than that for either of these two methods. The setup also successfully measures submicron particles and discriminates two species of Synechococcus. Our study demonstrates the feasibility of simultaneously measuring polarized light scattering and fluorescence, and the promising capability of our method for further aquatic environmental monitoring.

Classification of marine microalgae using low-resolution Mueller matrix images and convolutional neural network

In this paper, we used a convolutional neural network to study the classification of marine microalgae by using low-resolution Mueller matrix images. Mueller matrix images of 12 species of algae from 5 families were measured by a Mueller matrix microscopy with an LED light source at 514 nm wavelength. The data sets of seven resolution levels were generated by the bicubic interpolation algorithm. We conducted two groups of classification experiments; one group classified the algae into 12 classes according to species category, and the other group classified the algae into 5 classes according to family category. In each group of classification experiments, we compared the classification results of the Mueller matrix images with those of the first element (M11) images. The classification accuracy of Mueller matrix images declines gently with the decrease of image resolution, while the accuracy of M11 images declines sharply. The classification accuracy of Mueller matrix images is higher than that of M11 images at each resolution level. At the lowest resolution level, the accuracy of 12-class classification and 5-class classification of full Mueller matrix images is 29.89% and 35.83% higher than those of M11 images, respectively. In addition, we also found that the polarization information of different species had different contributions to the classification. These results show that the polarization information can greatly improve the classification accuracy of low-resolution microalgal images.

Polarized light scattering measurements as a means to characterize particle size and composition of natural assemblages of marine particles

Polarized light scattering measurements have the potential to provide improved characterization of natural particle assemblages in terms of particle size and composition. However, few studies have investigated this possibility for natural assemblages of marine particles. In this study, seawater samples representing contrasting assemblages of particles from coastal environments have been comprehensively characterized with measurements of angle-resolved polarized light scattering, particle size distribution, and particle composition. We observed robust trends linking samples containing higher proportions of large-sized particles with lower values of the maximum degree of linear polarization and the second element of the scattering matrix at a scattering angle of 100°, p₂₂(100^∘). In contrast, lower values of p₂₂(20^∘) were found in more non-phytoplankton-or inorganic--dominated samples. We also determined that three measurements involving the combinations of linearly polarized incident and scattered beams at two scattering angles (110° and 18°) have the potential to serve as useful proxies for estimating particle size and composition parameters.

Error analysis and compensation for a discrete dual rotating retarder Mueller matrix polarimeter

In this work, the error sources that affect a dual rotating retarder polarimeter working in a discrete rotation scheme are studied. Moreover, those errors not sufficiently analyzed in the literature are addressed in detail. To this end, the equations necessary for characterizing its components, performing its calibration, and carrying out measurements are deduced. We also discuss strategies to perform the experimental implementation, correct the existing errors, and estimate the margin of uncertainty associated with those errors that cannot be corrected. The study developed in this work allows us to generate a polarimeter with an error margin of 0.2%, almost an order of magnitude below recently reported values.

Polarized lidar and ocean particles: insights from a mesoscale coccolithophore bloom

Oceanographic lidar can provide remote estimates of the vertical distribution of suspended particles in natural waters, potentially revolutionizing our ability to characterize marine ecosystems and properly represent them in models of upper ocean biogeochemistry. However, lidar signals exhibit complex dependencies on water column inherent optical properties (IOPs) and instrument characteristics, which complicate efforts to derive meaningful biogeochemical properties from lidar return signals. In this study, we used a ship-based system to measure the lidar attenuation coefficient (α) and linear depolarization ratio (δ) across a variety of optically and biogeochemically distinct water masses, including turbid coastal waters, clear oligotrophic waters, and calcite rich waters associated with a mesoscale coccolithophore bloom. Sea surface IOPs were measured continuously while underway to characterize the response of α and δ to changes in particle abundance and composition. The magnitude of α was consistent with the diffuse attenuation coefficient (K_d), though the α versus K_d relationship was nonlinear. δ was positively related to the scattering optical depth and the calcite fraction of backscattering. A statistical fit to these data suggests that the polarized scattering properties of calcified particles are distinct and contribute to measurable differences in the lidar depolarization ratio. A better understanding of the polarized scattering properties of coccolithophores and other marine particles will further our ability to interpret polarized oceanographic lidar measurements and may lead to new techniques for measuring the material properties of marine particles remotely.

Sensitivity study on the contribution of scattering by randomly oriented nonspherical hydrosols to linear polarization in clear to semi-turbid shallow waters

The influence of hydrosol nonsphericity on the polarization characteristics of light under water is investigated by combining accurate single-scattering models for randomly oriented spheroidal scatterers with a radiative transfer model that employs Stokes formalism and considers refraction of direct unpolarized solar radiation and 100% linearly polarized radiation at the air-water interface followed by single scattering. Variations in what we call the "linear polarization phase function" (the degree of linear polarization as a function of scattering angle and the angle of linear polarization as a function of scattering angle) are examined for a wide range of spheroid aspect ratios and complex refractive indices of hydrosols. Implications for polarization-sensitive marine organisms and for remote sensing of the marine environment are discussed.

Measurements of the Volume Scattering Function and the Degree of Linear Polarization of Light Scattered by Contrasting Natural Assemblages of Marine Particles

The light scattering properties of seawater play important roles in radiative transfer in the ocean and optically-based methods for characterizing marine suspended particles from in situ and remote sensing measurements. The recently commercialized LISST-VSF instrument is capable of providing in situ or laboratory measurements of the volume scattering function, β p ( ψ ) , and the degree of linear polarization, DoLP p ( ψ ) , associated with particle scattering. These optical quantities of natural particle assemblages have not been measured routinely in past studies. To fully realize the potential of LISST-VSF measurements, we evaluated instrument performance, and developed calibration correction functions from laboratory measurements and Mie scattering calculations for standard polystyrene beads suspended in water. The correction functions were validated with independent measurements. The improved LISST-VSF protocol was applied to measurements of β p ( ψ ) and DoLP p ( ψ ) taken on 17 natural seawater samples from coastal and offshore marine environments characterized by contrasting assemblages of suspended particles. Both β p ( ψ ) and DoLP p ( ψ ) exhibited significant variations related to a broad range of composition and size distribution of particulate assemblages. For example, negative relational trends were observed between the particulate backscattering ratio derived from β p ( ψ ) and increasing proportions of organic particles or phytoplankton in the particulate assemblage. Our results also suggest a potential trend between the maximum values of DoLP p ( ψ ) and particle size metrics, such that a decrease in the maximum DoLP p ( ψ ) tends to be associated with particulate assemblages exhibiting a higher proportion of large-sized particles. Such results have the potential to advance optically-based applications that rely on an understanding of relationships between light scattering and particle properties of natural particulate assemblages.

Measuring and Modeling the Polarized Upwelling Radiance Distribution in Clear and Coastal Waters

The upwelling spectral radiance distribution is polarized, and this polarization varies with the optical properties of the water body. Knowledge of the polarized, upwelling, bidirectional radiance distribution function (BRDF) is important for generating consistent, long-term data records for ocean color because the satellite sensors from which the data are derived are sensitive to polarization. In addition, various studies have indicated that measurement of the polarization of the radiance leaving the ocean can used to determine particle characteristics (Tonizzo et al., 2007; Ibrahim et al., 2016; Chami et al., 2001). Models for the unpolarized BRDF (Morel et al., 2002; Lee et al., 2011) have been validated (Voss et al., 2007; Gleason et al., 2012), but variations in the polarization of the upwelling radiance due to the sun angle, viewing geometry, dissolved material, and suspended particles have not been systematically documented. In this work, we simulated the upwelling radiance distribution using a Monte Carlo-based radiative transfer code and measured it using a set of fish-eye cameras with linear polarizing filters. The results of model-data comparisons from three field experiments in clear and turbid coastal conditions showed that the degree of linear polarization (DOLP) of the upwelling light field could be determined by the model with an absolute error of ±0.05 (or 5% when the DOLP was expressed in %). This agreement was achieved even with a fixed scattering Mueller matrix, but did require in situ measurements of the other inherent optical properties, e.g., scattering coefficient, absorption coefficient, etc. This underscores the difficulty that is likely to be encountered using the particle scattering Mueller matrix (as indicated through the remote measurement of the polarized radiance) to provide a signature relating to the properties of marine particles beyond the attenuation/absorption coefficient.

Polarimetric learning: a Siamese approach to learning distance metrics of algal Mueller matrix images

Polarimetric measurements are becoming increasingly accurate and fast to perform in modern applications. However, analysis on the polarimetric data usually suffers from its high-dimensional nature spatially, temporally, or spectrally. This paper associates polarimetric techniques with metric learning algorithms, namely, polarimetric learning, by introducing a distance metric learning method called Siamese network that aims to learn good distance metrics of algal Mueller matrix images in low-dimensional feature spaces. As an experimental example, 12,162 Mueller matrix images of eight algal species are measured via a forward Mueller matrix microscope. Eight classical metric learning algorithms, including principle component analysis, multidimensional scaling, isometric feature mapping, t-distributed stochastic neighbor embedding, Laplacian eigenmaps, locally linear embedding, linear discriminant analysis, and metric learning to rank, are considered, by which the algal Mueller matrix images are mapped to two-dimensional (2D) feature spaces with different distance metrics. Support-vector-machine-based holdout sample classification accuracies of the 2D feature vectors are provided in a supervised manner for quantitative comparisons of the low-dimensional distance metrics, including the results of the eight metric learning algorithms and 16 Siamese architectures with varying convolution, inception, and full connection modules. This study shows that the Siamese approach is an effective metric learning algorithm that can adaptively extract features exhibiting empirical correlations with the fast-axis-orientation-dependent and spatially variant algal retardance induced by the algal microstructures.

Classification of morphologically similar algae and cyanobacteria using Mueller matrix imaging and convolutional neural networks

We present the Mueller matrix imaging system to classify morphologically similar algae based on convolutional neural networks (CNNs). The algae and cyanobacteria data set contains 10,463 Mueller matrices from eight species of algae and one species of cyanobacteria, belonging to four phyla, the shapes of which are mostly randomly oriented spheres, ovals, wheels, or rods. The CNN serves as an automatic machine with learning ability to help in extracting features from the Mueller matrix, and trains a classifier to achieve a 97% classification accuracy. We compare the performance in two ways. One way is to compare the performance of five CNNs that differ in the number of convolution layers as well as the classical principle component analysis (PCA) plus the support vector machine (SVM) method; the other way is to quantify the differences of scores between full Mueller matrix and the first matrix element m11, which does not contain polarization information under the same conditions. As the results show, deeper CNNs perform better, the best of which outperforms the conventional PCA plus SVM method by 19.66% in accuracy, and using the full Mueller matrix earns 6.56% increase of accuracy than using m11. It demonstrates that the coupling of Mueller matrix imaging and CNN may be a promising and efficient solution for the automatic classification of morphologically similar algae.

Stokes-vector and Mueller-matrix polarimetry [Invited]

This paper reviews the current status of instruments for measuring the full 4×1 Stokes vector S, which describes the state of polarization (SOP) of totally or partially polarized light, and the 4×4 Mueller matrix M, which determines how the SOP is transformed as light interacts with a material sample or an optical element or system. The principle of operation of each instrument is briefly explained by using the Stokes-Mueller calculus. The development of fast, automated, imaging, and spectroscopic instruments over the last 50 years has greatly expanded the range of applications of optical polarimetry and ellipsometry in almost every branch of science and technology. Current challenges and future directions of this important branch of optics are also discussed.

Laboratory experiments for inter-comparison of three volume scattering meters to measure angular scattering properties of hydrosols

Measurements of the volume scattering function (VSF) of hydrosols is of primary importance to investigate the interaction of light with hydrosols and to further interpret in situ and remote sensing data of ocean color. In this paper, a laboratory inter-comparison experiment of three recently developed VSF meters that are able to measure the scattered light for a wide range of scattering angle at 515 nm wavelength is performed using phytoplankton cultures and mineral-like hydrosols. A rigorous measurement protocol was employed to ensure good quality data. In particular, the protocol enabled removing the influence of bacteria on the hydrosols within the sample. The differences in the VSF measurements between the instruments vary from 10 to 25% depending on the composition of the hydrosols. The analysis of the angular features of the VSF revealed a sharp increase of the VSF beyond the scattering angle of 150° for some phytoplankton species. Such behavior is observed for two of the three VSF meters, thus suggesting that it is not due to instrumental artifacts but more likely to phytoplankton optical properties themselves. Moreover, comparisons with currently used theoretical phase functions show that the models are not able to reproduce satisfactorily the directional patterns in the backscattering region. This study suggests that a better modelling of the VSF shape of phytoplankton at high scattering angles is required to correctly represent the angular shape of the VSF in the backscattering hemisphere. Tabulated values of the measured phase functions are provided for scattering angles from 0.1 to 175°.

Inherent optical properties of the coccolithophore: Emiliania huxleyi

A realistic nonspherical model for Emiliania huxleyi (EHUX) is built, based on electron micrographs of coccolithophore cells. The Inherent Optical Properties (IOP) of the EHUX are then calculated numerically by using the discrete dipole approximation. The coccolithophore model includes a near-spherical core with the refractive index of 1.04 + m(i)j, and a carbonate shell formed by smaller coccoliths with refractive index of 1.2 + m(i)j, where m(i) = 0 or 0.01 and j(2) = -1. The reported IOP are the Mueller scattering matrix, backscattering probability, and depolarization ratio. Our calculation shows that the Mueller matrices of coccolithophores show different angular dependence from those of coccoliths.