Depolarization of multiply scattered waves by spherical diffusers: Influence of the size parameter

Full transmission of vectorial waves through 3D multiple-scattering media

A striking prediction from the random matrix theory (RMT) in mesoscopic physics is the existence of "open channels": waves that use multipath interference to achieve perfect transmission across an opaque disordered medium even in the multiple-scattering regime. Realization of such open channels requires a coherent control of the complete incident wavefront and has only been achieved for scalar waves in two dimensions (2D) so far. Here, we utilize a recently proposed "augmented partial factorization" full-wave simulation method to compute the polarization-resolved scattering matrix from 3D vectorial Maxwell's equations and demonstrate the existence of open channels in 3D disordered media. We examine the spatial profile of such open channels, demonstrate the existence of a bimodal transmission eigenvalue distribution, and study the effects of incomplete polarization control and finite-area illumination. The simulations provide full access to all spatiotemporal properties of the complex wave transport in 3D disordered systems, filling the gap left by experimental capabilities.

Phase preservation of orbital angular momentum of light in multiple scattering environment

Recent advancements in wavefront shaping techniques have facilitated the study of complex structured light's propagation with orbital angular momentum (OAM) within various media. The introduction of spiral phase modulation to the Laguerre-Gaussian (LG) beam during its paraxial propagation is facilitated by the negative gradient of the medium's refractive index change over time, leading to a notable increase in the rate of phase twist, effectively observed as phase retardation of the OAM. This approach attains remarkable sensitivity to even the slightest variations in the medium's refractive index (∼10-6). The phase memory of OAM is revealed as the ability of twisted light to preserve the initial helical phase even propagating through the turbid tissue-like multiple scattering medium. The results confirm fascinating opportunities for exploiting OAM light in biomedical applications, e.g. such as non-invasive trans-cutaneous glucose diagnosis and optical communication through biological tissues and other optically dense media.

Depolarization diagrams for circularly polarized light scattering for biological particle monitoring

Significance

The depolarization of circularly polarized light (CPL) caused by scattering in turbid media reveals structural information about the dispersed particles, such as their size, density, and distribution, which is useful for investigating the state of biological tissue. However, the correlation between depolarization strength and tissue parameters is unclear.

Aim

We aimed to examine the generalized correlations of depolarization strength with the particle size and wavelength, yielding depolarization diagrams.

Approach

The correlation between depolarization intensity and size parameter was examined for single and multiple scattering using the Monte Carlo simulation method. Expanding the wavelength width allows us to obtain depolarization distribution diagrams as functions of wavelength and particle diameter for reflection and transparent geometries.

Results

CPL suffers intensive depolarization in a single scattering against particles of various specific sizes for its wavelength, which becomes more noticeable in the multiple scattering regime.

Conclusions

The depolarization diagrams with particle size and wavelength as independent variables were obtained, which are particularly helpful for investigating the feasibility of various particle-monitoring methods. Based on the obtained diagrams, several applications have been proposed, including blood cell monitoring, early embryogenesis, and antigen-antibody interactions.

Exploring the evolution of circular polarized light backscattered from turbid tissue-like disperse medium utilizing generalized Monte Carlo modeling approach with a combined use of Jones and Stokes-Mueller formalisms

SIGNIFICANCE

Phase retardation of circularly polarized light (CPL), backscattered by biological tissue, is used extensively for quantitative evaluation of cervical intraepithelial neoplasia, presence of senile Alzheimer's plaques, and characterization of biotissues with optical anisotropy. The Stokes polarimetry and Mueller matrix approaches demonstrate high potential in definitive non-invasive cancer diagnosis and tissue characterization. The ultimate understanding of CPL interaction with tissues is essential for advancing medical diagnostics, optical imaging, therapeutic applications, and the development of optical instruments and devices.

AIM

We investigate propagation of CPL within turbid tissue-like scattering medium utilizing a combination of Jones and Stokes-Mueller formalisms in a Monte Carlo (MC) modeling approach. We explore the fundamentals of CPL memory effect and depolarization formation.

APPROACH

The generalized MC computational approach developed for polarization tracking within turbid tissue-like scattering medium is based on the iterative solution of the Bethe-Salpeter equation. The approach handles helicity response of CPL scattered in turbid medium and provides explicit expressions for assessment of its polarization state.

RESULTS

Evolution of CPL backscattered by tissue-like medium at different conditions of observation in terms of source-detector configuration is assessed quantitatively. The depolarization of light is presented in terms of the coherence matrix and Stokes-Mueller formalism. The obtained results reveal the origins of the helicity flip of CPL depending on the source-detector configuration and the properties of the medium and are in a good agreement with the experiment.

CONCLUSIONS

By integrating Jones and Stokes-Mueller formalisms, the combined MC approach allows for a more complete representation of polarization effects in complex optical systems. The developed model is suitable to imitate propagation of the light beams of different shape and profile, including Gaussian, Bessel, Hermite-Gaussian, and Laguerre-Gaussian beams, within tissue-like medium. Diverse configuration of the experimental conditions, coherent properties of light, and peculiarities of polarization can be also taken into account.

Single-shot decoherence polarization gated imaging through turbid media

We propose a method for imaging through a turbid medium by using a single-shot decoherence polarization gate (DPG). The DPG is made up of a polarizer, an analyzer, and a weakly scattering medium. Contrary to intuition, we discover that the preferential utilization of sparsely scattered photons by introducing weakly scattering mediums can lead to better image quality. The experimental results show that the visibilities of the images acquired from the DPG imaging method are obviously improved. The contrast of the bar can be increased by 50% by the DPG imaging technique. Furthermore, we study the effect of the volume concentration of the weakly scattering medium on the speckle suppression and the enhancement of the visibilities of the images. The variances of the contrasts of the image show that there exists an optimum optical depth (∼0.8) of the weakly scattering medium for DPG imaging through a specific turbid medium.

Synthesizing the degree of polarization uniformity from non-polarization-sensitive optical coherence tomography signals using a neural network

Degree of polarization uniformity (DOPU) imaging obtained by polarization-sensitive optical coherence tomography (PS-OCT) has the potential to provide biomarkers for retinal diseases. It highlights abnormalities in the retinal pigment epithelium that are not always clear in the OCT intensity images. However, a PS-OCT system is more complicated than conventional OCT. We present a neural-network-based approach to estimate the DOPU from standard OCT images. DOPU images were used to train a neural network to synthesize the DOPU from single-polarization-component OCT intensity images. DOPU images were then synthesized by the neural network, and the clinical findings from ground truth DOPU and synthesized DOPU were compared. There is a good agreement in the findings for RPE abnormalities: recall was 0.869 and precision was 0.920 for 20 cases with retinal diseases. In five cases of healthy volunteers, no abnormalities were found in either the synthesized or ground truth DOPU images. The proposed neural-network-based DOPU synthesis method demonstrates the potential of extending the features of retinal non-PS OCT.

Spatial helicity response metric to quantify particle size and turbidity of heterogeneous media through circular polarization imaging

Backscattered circularly polarized light from turbid media consists of helicity-flipped and helicity-preserved photon sub-populations (i.e., photons of perpendicular and parallel circular handedness). Their intensities and spatial distributions are found to be acutely sensitive to average scatterer size and modestly sensitive to the scattering coefficient (medium turbidity) through an interplay of single and multiple scattering effects. Using a highly sensitive intensified-CCD camera, helicity-based images of backscattered light are captured, which, with the aid of corroborating Monte Carlo simulation images and statistics, enable (1) investigation of subsurface photonic pathways and (2) development of the novel 'spatial helicity response' metric to quantify average scatterer size and turbidity of tissue-like samples. An exciting potential application of this work is noninvasive early cancer detection since malignant tissues exhibit alterations in scatterer size (larger nuclei) and turbidity (increased cell density).

Optical birefringence changes in myelinated and unmyelinated nerves: A comparative study

The measurement of birefringence variations related to nerve activity is a promising label-free technique for sensing compound neural action potentials (CNAPs). While widely applied in crustaceans, little is known about its efficiency on mammal peripheral nerves. In this work, birefringence recordings to detect CNAPs, and Stokes parameters measurements were performed in rat and lobster nerves. While single-trial detection of nerve activity in crustaceans was achieved successfully, no optical signal was detected in rats, even after extensive signal filtering and averaging. The Stokes parameters showed that a high degree of polarization of light is maintained in lobster sample, whereas an almost complete light depolarization occurs in rat nerve. Our results indicate that depolarization itself is not sufficient to explain the absence of birefringence signals in rats. We hypothesize that this absence comes from the myelin sheets, which constraint the birefringence changes to only take place at the nodes of Ranvier.

Depth estimation of tumor invasion in early gastric cancer using scattering of circularly polarized light: Monte Carlo Simulation study

Quantitative depth estimation of tumor invasion in early gastric cancer by scattering of circularly polarized light is computationally investigated using the Monte Carlo method. Using the optical parameters of the human stomach wall and its carcinoma, the intensity and circular polarization of light scattered from pseudo-healthy and cancerous tissues were calculated over a wide spectral range. Large differences in the circular polarization with opposite signs, together with the large intensity, are obtained at wavelengths 600 nm and 950 nm. At these two wavelengths, the sampling depth of the biological tissues can be modulated by tuning the detection angle. In bi-layered pseudo-tissues with a cancerous layer on a healthy layer and vice versa, the degree of circular polarization of scattered light shows systematic changes depending on the thickness and depth of the cancerous layer, which indicates the feasibility of in vivo quantitative estimation of cancer progression in early gastric cancer.

Polarization and intensity analysis of lateral scattering light from nanoparticles

The characteristics of laterally scattered light from nanoparticles can be experimentally studied by polarization imaging technology. This paper compares and analyzes the differences in polarization between nanoparticles and microparticles. Then, the influence of the incident light intensity on scattered light and the degree of polarization is studied. It is found that, when the concentration of nanoparticles is constant, the degree of polarization of scattered light is not affected compared with the scattered light intensity. Finally, the variation law of nanoparticle concentration and polarization is studied. It is found that, with the increase of particle concentration, the polarization of lateral scattered light increases and then decreases.

Analyzing the Influence of Imaging Resolution on Polarization Properties of Scattering Media Obtained From Mueller Matrix

The Mueller matrix contains abundant micro- and even nanostructural information of media. Especially, it can be used as a powerful tool to characterize anisotropic structures quantitatively, such as the particle size, density, and orientation information of fibers in the sample. Compared with unpolarized microscopic imaging techniques, Mueller matrix microscopy can also obtain some essential structural information about the sample from the derived parameters images at low resolution. Here, to analyze the comprehensive effects of imaging resolution on polarization properties obtained from the Mueller matrix, we, first, measure the microscopic Mueller matrices of unstained rat dorsal skin tissue slices rich in collagen fibers using a series of magnifications or numerical aperture (NA) values of objectives. Then, the first-order moments and image texture parameters are quantified and analyzed in conjunction with the polarization parameter images. The results show that the Mueller matrix polar decomposition parameters diattenuation D, linear retardance δ, and depolarization Δ images obtained using low NA objective retain most of the structural information of the sample and can provide fast imaging speed. In addition, the scattering phase function analysis and Monte Carlo simulation based on the cylindrical scatterers reveal that the diattenuation parameter D images with different imaging resolutions are expected to be used to distinguish among the fibrous scatterers in the medium with different particle sizes. This study provides a criterion to decide which structural information can be accurately and rapidly obtained using a transmission Mueller matrix microscope with low NA objectives to assist pathological diagnosis and other applications.

Underwater image restoration via Stokes decomposition

In this Letter, we present a Stokes imaging-based method to restore objects and enhance image contrast in turbid water. In the system, a light source illuminates the objects with two orthometric polarization states; based on a new Stokes decomposition model, the recorded images are converted to Stokes maps and subsequently restored to a clear image, free of reflections and scattered lights. A mathematical model has been developed to explain the Stokes decomposition and how the undesired reflections and scattered lights are rejected. Imaging experiments have been devised and performed on different objects, e.g., metals and plastics, under different turbidities. The results demonstrate enhanced image quality and capability to distinguish polarization differences. This new, to the best of our knowledge, method can be readily applied to practical underwater object detection and potentially realize clear vision in other scattering media.

Image-restoration algorithm based on an underwater polarization imaging visualization model

The polarization bidirectional reflection distribution function theory of a target is combined with microfacet theory, and the Monte Carlo method is used to establish an underwater laser active-polarization imaging model based on Mie scattering theory. The model presented herein can simulate imaging of an underwater target with a high degree of polarization, and the effects of optical thickness and target surface roughness on active underwater laser imaging results are demonstrated by the simulation image. Combined with histogram equalization and the traditional polarization differential imaging algorithm, an algorithm is presented herein that globally estimates the mutual information value between the target polarization degree and the correction factor of backscattered light polarization degree. The images received from the simulation test can be restored, and results show that the algorithm can restore the target image with a high degree of polarization to some extent. Finally, the correctness of the active underwater laser polarization imaging model and the feasibility of global estimation based on the polarization differential restoration algorithm are verified experimentally.

Stretchable PPG sensor with light polarization for physical activity-permissible monitoring

Skin-attachable sensors, which represent the ultimate form of wearable electronic devices that ensure conformal contact with skin, suffer from motion artifact limitations owing to relative changes in position between the sensor and skin during physical activities. In this study, a polarization-selective structure of a skin-conformable photoplethysmographic (PPG) sensor was developed to decrease the amount of scattered light from the epidermis, which is the main cause of motion artifacts. The motion artifacts were suppressed more than 10-fold in comparison with those of rigid sensors. The developed sensor-with two orthogonal polarizers-facilitated successful PPG signal monitoring during wrist angle movements corresponding to high levels of physical activity, enabling continuous monitoring of daily activities, even while exercising for personal health care.

Polarization memory rate as a metric to differentiate benign and malignant tissues

Non-invasive optical methods for cancer diagnostics, such as microscopy, spectroscopy, and polarimetry, are rapidly advancing. In this respect, finding new and powerful optical metrics is an indispensable task. Here we introduce polarization memory rate (PMR) as a sensitive metric for optical cancer diagnostics. PMR characterizes the preservation of circularly polarized light relative to linearly polarized light as light propagates in a medium. We hypothesize that because of well-known indicators associated with the morphological changes of cancer cells, like an enlarged nucleus size and higher chromatin density, PMR should be greater for cancerous than for the non-cancerous tissues. A thorough literature review reveals how this difference arises from the anomalous depolarization behaviour of many biological tissues. In physical terms, though most biological tissue primarily exhibits Mie scattering, it typically exhibits Rayleigh depolarization. However, in cancerous tissue the Mie depolarization regime becomes more prominent than Rayleigh. Experimental evidence of this metric is found in a preliminary clinical study using a novel Stokes polarimetry probe. We conducted in vivo measurements of 20 benign, 28 malignant and 59 normal skin sites with a 660 nm laser diode. The median PMR values for cancer vs non-cancer are significantly higher for cancer which supports our hypothesis. The reported fundamental differences in depolarization may persist for other types of cancer and create a conceptual basis for further developments in polarimetry applications for cancer detection.

Discriminating turbid media by scatterer size and scattering coefficient using backscattered linearly and circularly polarized light

The effects of scatterer size and scattering coefficient on backscattered linearly and circularly polarized light are investigated through Stokes polarimetry. High-SNR polarization modulation/synchronous detection measurements are corroborated by polarization-sensitive Monte Carlo simulations. Circular degree of polarization (DOP) is found to be sensitive to scatterer size, but is equivocal at times due to helicity flipping effects; linear DOP appears to be mostly dependent on the medium scattering coefficient. We exploit these trends to generate a DOP_C - DOP_L response surface which clusters turbid samples based on these medium properties. This work may prove useful in biomedicine, for example in noninvasive assessment of epithelial precancer progression.

Controlling the optical pathlength in continuous-wave reflectance spectroscopy using polarization

We investigate potential improvements of continuous-wave diffuse reflectance spectroscopy within highly scattering media by employing polarization gating. Simulations are used to show the extent at which the effective optical pathlength varies in a typical scattering medium as a function of the optical wavelength, the total level of absorption, and the selected polarization channels, including elliptical and circular polarization channels. Experiments then demonstrate that a wavelength dependent polarization gating scheme may reduce the prior knowledge required to solve the problem of chromophore quantification. This is achieved by finding combinations of polarization channels which have similar effective optical pathlengths through the medium at each wavelength.

Lateral-Type Spin-Photonics Devices: Development and Applications

Spin-photonic devices, represented by spin-polarized light emitting diodes and spin-polarized photodiodes, have great potential for practical use in circularly polarized light (CPL) applications. Focusing on the lateral-type spin-photonic devices that can exchange CPL through their side facets, this review describes their functions in practical CPL applications in terms of: (1) Compactness and integrability, (2) stand-alone (monolithic) nature, (3) room temperature operation, (4) emission with high circular polarization, (5) polarization controllability, and (6) CPL detection. Furthermore, it introduces proposed CPL applications in a wide variety of fields and describes the application of these devices in biological diagnosis using CPL scattering. Finally, it discusses the current state of spin-photonic devices and their applications and future prospects.

Angular optimization for cancer identification with circularly polarized light

Depolarization of circularly polarized light scattered from biological tissues depends on structural changes in cell nuclei, which can provide valuable information for differentiating cancer tissues concealed in healthy tissues. In this study, we experimentally verified the possibility of cancer identification using scattering of circularly polarized light. We investigated the polarization of light scattered from a sliced biological tissue with various optical configurations. A significant difference between circular polarizations of light scattered from cancerous and healthy tissues is observed, which is sufficient to distinguish a cancerous region. The line-scanning experiments along a region incorporating healthy and cancerous parts indicate step-like behaviors in the degree of circular polarization corresponding to the state of tissues, whether cancerous or normal. An oblique and perpendicular incidence induces different resolutions for identifying cancerous tissues, which indicates that the optical arrangement can be selected according to the priority of resolution.

Polarimetric LiDAR backscattering contrast of linearly and circularly polarized pulses for ideal depolarizing targets in generic water fogs

In this paper, we investigate the backscattering depolarization of linearly and circularly polarized laser sources propagating in dense water fogs. We limit our investigation to a simple case where an active LiDAR system is pointed toward a white depolarizing Lambertian solid target. The receiver captures the reflected signal in the orthogonal channel so as to remove most of the backscattering from the water fog. It is shown that in the studied cases, a circularly polarized signal is depolarized faster than a linearly polarized signal and thus produces less contrast. We show that in the cases that can be described by the small angle approximation, the Rubenson degree of polarization (DoP) of a circularly polarized beam can be predicted by the DoP of a linearly polarized beam as DoP_cir=2DoP_lin-1, even for low-order multiple scattering events. In these conditions, since the linear DoP is always stronger, the contrast is expected to be better in linear polarization for ideal depolarizing targets.

Evolution of transmitted depolarization in diffusely scattering media

We performed Mueller matrix Monte Carlo simulations of the propagation of optical radiation in diffusely scattering media for collimated incidence and report the results as a function of thickness and the angle subtended by the detector. For sufficiently small thickness, a fraction of the radiation does not undergo any scattering events and is emitted at zero angle. Thus, for a very small detector angle, the measured signal will indicate mostly the attenuation of the coherent contribution, while for larger angles, the diffuse scattering radiation will contribute significantly more. The degree to which the radiation is depolarized thus depends on the angle subtended by the detector. A three-stream model-where the coherent radiation, the forward diffusely scattered radiation, and the backward scattered radiation are propagated according to the differential Mueller matrix formalism-is introduced and describes the results from the Monte Carlo simulations and the results of measurements well. This scatter-based model for depolarization in diffusely scattering media is an alternative to that based upon elementary fluctuation theory applied to a single propagation stream. Results for average photon path length, determined from the Monte Carlo simulations, suggest that applying fluctuation theory to photon path length may unify the two approaches.

Observation of elliptically polarized light from total internal reflection in bubbles

Bubbles are ubiquitous in the natural environment, where different substances and phases of the same substance forms globules due to differences in pressure and surface tension. Total internal reflection occurs at the interface of a bubble, where light travels from the higher refractive index material outside a bubble to the lower index material inside a bubble at appropriate angles of incidence, which can lead to a phase shift in the reflected light. Linearly polarized skylight can be converted to elliptically polarized light with efficiency up to 53% by single scattering from the water-air interface. Total internal reflection from air bubble in water is one of the few sources of elliptical polarization in the natural world. Stationary and dynamic scenes of air bubbles in water in both indoor and outdoor settings are studied using an imaging polarimeter. Our results are important for studies in fluid dynamics, remote sensing, and polarimetry.

Role of scattering and birefringence in phase retardation revealed by locus of Stokes vector on Poincaré sphere

SIGNIFICANCE

Biological tissues are typically characterized by high anisotropic scattering and may also exhibit linear form birefringence. Both scattering and birefringence bias the phase shift between transverse electric field components of polarized light. These phase alterations are associated with particular structural malformations in the tissue. In fact, the majority of polarization-based techniques are unable to distinguish the nature of the phase shift induced by birefringence or scattering of light.

AIM

We explore the distinct contributions of scattering and birefringence in the phase retardation of circularly polarized light propagated in turbid tissue-like scattering medium.

APPROACH

The circularly polarized light in frame of Stokes polarimetry approach is used for the screening of biotissue phantoms and chicken skin samples. The change of optical properties in chicken skin is accomplished by optical clearing, which reduces scattering, and mechanical stretch, which induces birefringence. The change of optical properties of skin tissue is confirmed by spectrophotometric measurements and second-harmonic generation imaging.

RESULTS

The contributions of scattering and birefringence in the phase retardation of circularly polarized light propagated in biological tissues are distinguished by the locus of the Stokes vector mapped on the Poincaré sphere. The phase retardation of circularly polarized light due to scattering alterations is assessed. The value of birefringence in chicken skin is estimated as 0.3  ×  10-3, which agrees with alternative studies. The change of birefringence of skin tissue due to mechanical stretch in the order of 10-6 is detected.

CONCLUSIONS

While the polarimetric parameters on their own do not allow distinguishing the contributions of scattering and birefringence, the resultant Stokes vector trajectory on the Poincaré sphere reveals the role of scattering and birefringence in the total phase retardation. The described approach, applied independently or in combination with Mueller polarimetry, can be beneficial for the advanced characterization of various types of malformations within biological tissues.

Study of polarization memory's impact on detection range in natural water fogs

The influence of the initial polarization state of a source on the detection range of a system probing through natural dense water fog is analyzed. Information about the source is conveyed by ballistic, snake, and highly scattered photons. During propagation, the polarization state of ballistic and snake photons is not altered. It is shown that though circular polarization is not altered by simple direction changes during scattering, and has thus a tendency to be preserved longer in the highly scattered photons, it does not necessarily convey more useful information about the source than linear polarization or even an unpolarized beam. It is also shown that in any forward propagating system that can be described by the small-angle approximation the impact of polarization memory can be neglected.

Forward transmission characteristics in polystyrene solution with different concentrations by use of circularly and linearly polarized light

Polarized light forward propagation in scattering environments is important basic research. Polystyrene microspheres in water are common scattering environments that can be helpful to investigate in existing literature research. In this paper, we investigated the polarization state persistence of both linearly and circularly polarized light. We used a single active source with a wavelength of 532 nm to illuminate 1 μm diameter polystyrene spheres immersed in water. To evaluate the polarization state persistence of linearly and circularly polarized light, a parameter change of polarization state was used to replace the Stokes parameters. In the setting environments of different concentrations, circularly polarized light has superior polarization state persistence to that of linearly polarized light.

Characterizing the depolarization of circularly polarized light in turbid scattering media

We investigate the effectiveness of various bulk optical parameters in characterizing the degree of circular polarization (DOCP) of light diffusely reflected from scattering media. It is demonstrated that the traditional set of bulk optical parameters (namely, the scattering and absorption coefficients and the scattering asymmetry parameter) fail to characterize the observed depolarization. However, we find that there exists an additional parameter connected to the circular polarization memory phenomenon that consistently relates to observations, even in media with widely varying refractive indices and particle size distributions. This relationship is demonstrated using both Monte Carlo simulations and a new method for designing microsphere-based phantom media, which contain carefully controlled particle size distributions and depolarization characteristics.

Superior signal persistence of circularly polarized light in polydisperse, real-world fog environments

We present simulation results quantitatively showing that circularly polarized light persists in transmission through several real-world and model fog environments better than linearly polarized light over broad wavelength ranges from the visible through the infrared. We present results for polydisperse particle distributions from realistic and measured fog environments, comparing the polarization persistence of linear and circular polarization. Using a polarization-tracking Monte Carlo program, we simulate polarized light propagation through four MODTRAN fog models (moderate and heavy radiation fog and moderate and heavy advection fog) and four real-world measured fog particle distributions (Garland measured radiation and advection fogs, Kunkel measured advection fog, and Sandia National Laboratories' Fog Facility's fog). Simulations were performed for each fog environment with wavelengths ranging from 0.4 to 12 µm for increasing optical thicknesses of 5, 10, and 15 (increasing fog density or sensing range). Circular polarization persists superiorly for all optical wavelength bands from the visible to the long-wave infrared in nearly all fog types for all optical thicknesses. Throughout our analysis, we show that if even a small percentage of a fog's particle size distribution is made up of large particles, those particles dominate the scattering process. In nearly all real-world fog situations, these large particles and their dominant scattering characteristics are present. Larger particles are predominantly forward-scattering and contribute to circular polarization's persistence superiority over broad wavelength ranges and optical thicknesses/range. Circularly polarized light can transmit over 30% more signal in its intended state compared to linearly polarized light through real-world fog environments. This work broadens the understanding of how circular polarization persists through natural fog particle distributions with natural variations in mode particle radius and single or bimodal characteristics.

Extended polar decomposition method of Mueller matrices for turbid media in reflection geometry

The polar decomposition method for Mueller matrices proposed by Lu-Chipman has been demonstrated and validated for many applications. However, in some situations, e.g., when analyzing the Mueller matrix of birefringent turbid media with Mie-sized scatterers acquired in reflection geometry, the method may suffer from limitations due to the assumptions required by this method. Here we extend the Lu-Chipman method and show that it can provide more reasonable results for these situations. The method has been validated experimentally with turbid phantoms. Thus, this Letter may prove useful in tissue polarimetry.

Polarization recovery through scattering media

The control and use of light polarization in optical sciences and engineering are widespread. Despite remarkable developments in polarization-resolved imaging for life sciences, their transposition to strongly scattering media is currently not possible, because of the inherent depolarization effects arising from multiple scattering. We show an unprecedented phenomenon that opens new possibilities for polarization-resolved microscopy in strongly scattering media: polarization recovery via broadband wavefront shaping. We demonstrate focusing and recovery of the original injected polarization state without using any polarizing optics at the detection. To enable molecular-level structural imaging, an arbitrary rotation of the input polarization does not degrade the quality of the focus. We further exploit the robustness of polarization recovery for structural imaging of biological tissues through scattering media. We retrieve molecular-level organization information of collagen fibers by polarization-resolved second harmonic generation, a topic of wide interest for diagnosis in biomedical optics. Ultimately, the observation of this new phenomenon paves the way for extending current polarization-based methods to strongly scattering environments.

Asymptotic theory of circular polarization memory

We establish a quantitative theory of circular polarization memory, which is the unexpected persistence of the incident circular polarization state in a strongly scattering medium. Using an asymptotic analysis of the three-dimensional vector radiative transfer equation (VRTE) in the limit of strong scattering, we find that circular polarization memory must occur in a boundary layer near the portion of the boundary on which polarized light is incident. The boundary layer solution satisfies a one-dimensional conservative scattering VRTE. Through a spectral analysis of this boundary layer problem, we introduce the dominant mode, which is the slowest-decaying mode in the boundary layer. To observe circular polarization memory for a particular set of optical parameters, we find that this dominant mode must pass three tests: (1) this dominant mode is given by the largest, discrete eigenvalue of a reduced problem that corresponds to Fourier mode k=0 in the azimuthal angle, and depends only on Stokes parameters U and V; (2) the polarization state of this dominant mode is largely circular polarized so that |V|≫|U|; and (3) the circular polarization of this dominant mode is maintained for all directions so that V is sign-definite. By applying these three tests to numerical calculations for monodisperse distributions of Mie scatterers, we determine the values of the size and relative refractive index when circular polarization memory occurs. In addition, we identify a reduced, scalar-like problem that provides an accurate approximation for the dominant mode when circular polarization memory occurs.

Mueller polarimetric imaging for surgical and diagnostic applications: a review

Polarization is a fundamental property of light and a powerful sensing tool that has been applied to many areas. A Mueller matrix is a complete mathematical description of the polarization characteristics of objects that interact with light, and is known as a transfer function of Stokes vectors which characterise the state of polarization of light. Mueller polarimetric imaging measures Mueller matrices over a field of view and thus allows for visualising the polarization characteristics of the objects. It has emerged as a promising technique in recent years for tissue imaging, improving image contrast and providing a unique perspective to reveal additional information that cannot be resolved by other optical imaging modalities. This review introduces the basis of the Stokes-Mueller formulism, interpretation methods of Mueller matrices into fundamental polarization properties, polarization properties of biological tissues, and considerations in the construction of Mueller polarimetric imaging devices for surgical and diagnostic applications, including primary configurations, optimization procedures, calibration methods as well as the instrument polarization properties of several widely-used biomedical optical devices. The paper also reviews recent progress in Mueller polarimetric endoscopes and fibre Mueller polarimeters, followed by the future outlook in applying the technique to surgery and diagnostics. Tissue polarization properties convey morphological, micro-structural and compositional information of tissue with great potential for label free characterization of tissue pathological changes. Recent progress in tissue polarimetric imaging and polarization resolved endoscopy paved the way for translation of polarimetric imaging to surgery and tissue diagnosis.

Backscattering of linearly polarized light from turbid tissue-like scattering medium with rough surface

In the framework of further development of a unified computational tool for the needs of biomedical optics, we introduce an electric field Monte Carlo (MC) model for simulation of backscattering of coherent linearly polarized light from a turbid tissue-like scattering medium with a rough surface. We consider the laser speckle patterns formation and the role of surface roughness in the depolarization of linearly polarized light backscattered from the medium. The mutual phase shifts due to the photons’ pathlength difference within the medium and due to reflection/refraction on the rough surface of the medium are taken into account. The validation of the model includes the creation of the phantoms of various roughness and optical properties, measurements of co- and cross-polarized components of the backscattered/reflected light, its analysis and extensive computer modeling accelerated by parallel computing on the NVIDIA graphics processing units using compute unified device architecture (CUDA). The analysis of the spatial intensity distribution is based on second-order statistics that shows a strong correlation with the surface roughness, both with the results of modeling and experiment. The results of modeling show a good agreement with the results of experimental measurements on phantoms mimicking human skin. The developed MC approach can be used for the direct simulation of light scattered by the turbid scattering medium with various roughness of the surface.

Polarized light interaction with tissues

This tutorial-review introduces the fundamentals of polarized light interaction with biological tissues and presents some of the recent key polarization optical methods that have made possible the quantitative studies essential for biomedical diagnostics. Tissue structures and the corresponding models showing linear and circular birefringence, dichroism, and chirality are analyzed. As the basis for a quantitative description of the interaction of polarized light with tissues, the theory of polarization transfer in a random medium is used. This theory employs the modified transfer equation for Stokes parameters to predict the polarization properties of single- and multiple-scattered optical fields. The near-order of scatterers in tissues is accounted for to provide an adequate description of tissue polarization properties. Biomedical diagnostic techniques based on polarized light detection, including polarization imaging and spectroscopy, amplitude and intensity light scattering matrix measurements, and polarization-sensitive optical coherence tomography are described. Examples of biomedical applications of these techniques for early diagnostics of cataracts, detection of precancer, and prediction of skin disease are presented. The substantial reduction of light scattering multiplicity at tissue optical clearing that leads to a lesser influence of scattering on the measured intrinsic polarization properties of the tissue and allows for more precise quantification of these properties is demonstrated.

A high definition Mueller polarimetric endoscope for tissue characterisation

The contrast mechanism of medical endoscopy is mainly based on metrics of optical intensity and wavelength. As another fundamental property of light, polarization can not only reveal tissue scattering and absorption information from a different perspective, but can also provide insight into directional tissue birefringence properties to monitor pathological changes in collagen and elastin. Here we demonstrate a low cost wide field high definition Mueller polarimetric endoscope with minimal alterations to a rigid endoscope. We show that this novel endoscopic imaging modality is able to provide a number of image contrast mechanisms besides traditional unpolarized radiation intensity, including linear depolarization, circular depolarization, cross-polarization, directional birefringence and dichroism. This enhances tissue features of interest, and additionally reveals tissue micro-structure and composition, which is of central importance for tissue diagnosis and image guidance for surgery. The potential applications of the Mueller polarimetric endoscope include wide field early epithelial cancer diagnosis, surgical margin detection and energy-based tissue fusion monitoring, and could further benefit a wide range of endoscopic investigations through intra-operative guidance.

Impact of wave polarization on long-range intensity correlations in a disordered medium

We present a theory of long-range intensity correlations in phase-coherent transport of polarized light through a disordered medium. Diagrammatic calculations of the intensity correlation function are performed beyond the scalar wave approximation. The correlations between the cross-polarized fields are shown to result in the dependence of mesoscopic intensity fluctuations on the polarization of the incident light. The intensity correlation function is represented as a sum of the contributions from the scalar mode and the basic modes of circular and linear polarization. The calculations, as applied to media with large scattering inhomogeneities, are carried out for diffusive transport and for small-angle multiple scattering of light. Each polarization contribution to the variance of relative transmission fluctuations is shown not to be a self-averaging quantity and tends to a nonvanishing value as the sample thickness increases. This value is proportional to the length of polarization decay in the medium and can be measured by varying the initial polarization of light.

Evolution of circular and linear polarization in scattering environments

This work quantifies the polarization persistence and memory of circularly polarized light in forward-scattering and isotropic (Rayleigh regime) environments; and for the first time, details the evolution of both circularly and linearly polarized states through scattering environments. Circularly polarized light persists through a larger number of scattering events longer than linearly polarized light for all forward-scattering environments; but not for scattering in the Rayleigh regime. Circular polarization's increased persistence occurs for both forward and backscattered light. The simulated environments model polystyrene microspheres in water with particle diameters of 0.1 μm, 2.0 μm, and 3.0 μm. The evolution of the polarization states as they scatter throughout the various environments are illustrated on the Poincaré sphere after one, two, and ten scattering events.

Quantitative analysis of light scattering in polarization-resolved nonlinear microscopy

Polarization resolved nonlinear microscopy (PRNM) is a powerful technique to gain microscopic structural information in biological media. However, deep imaging in a variety of biological specimens is hindered by light scattering phenomena, which not only degrades the image quality but also affects the polarization state purity. In order to quantify this phenomenon and give a framework for polarization resolved microscopy in thick scattering tissues, we develop a characterization methodology based on four wave mixing (FWM) process. More specifically, we take advantage of two unique features of FWM, meaning its ability to produce an intrinsic in-depth local coherent source and its capacity to quantify the presence of light depolarization in isotropic regions inside a sample. By exploring diverse experimental layouts in phantoms with different scattering properties, we study systematically the influence of scattering on the nonlinear excitation and emission processes. The results show that depolarization mechanisms for the nonlinearly generated photons are highly dependent on the scattering center size, the geometry used (epi/forward) and, most importantly, on the thickness of the sample. We show that the use of an un-analyzed detection makes the polarization-dependence read-out highly robust to scattering effects, even in regimes where imaging might be degraded. The effects are illustrated in polarization resolved imaging of myelin lipid organization in mouse spinal cords.

Application of circularly polarized light for non-invasive diagnosis of cancerous tissues and turbid tissue-like scattering media

Polarization-based optical techniques have become increasingly popular in the field of biomedical diagnosis. In the current report we exploit the directional awareness of circularly and/or elliptically polarized light backscattered from turbid tissue-like scattering media. We apply circularly and elliptically polarized laser light which illuminates the samples of interest, and a standard optical polarimeter is used to observe the polarization state of light backscattered a few millimeters away from the point of incidence. We demonstrate that the Stokes vector of backscattered light depicted on a Poincaré sphere can be used to assess a turbid tissue-like scattering medium. By tracking the Stokes vector of the detected light on the Poincaré sphere, we investigate the utility of this approach for characterization of cancerous and non-cancerous tissue samples in vitro. The obtained results are discussed in the framework of a phenomenological model and the results of a polarization tracking Monte Carlo model, developed in house. Schematic illustration of the experimental approach utilizing circularly and elliptically polarized light for probing turbid tissue-like scattering media.

Isotropically polarized speckle patterns

The polarization of the light scattered by an optically dense and random solution of dielectric nanoparticles shows peculiar properties when the scatterers exhibit strong electric and magnetic polarizabilities. While the distribution of the scattering intensity in these systems shows the typical irregular speckle patterns, the helicity of the incident light can be fully conserved when the electric and magnetic polarizabilities of the scatterers are equal. We show that the multiple scattering of helical beams by a random dispersion of "dual" dipolar nanospheres leads to a speckle pattern exhibiting a perfect isotropic constant polarization, a situation that could be useful in coherent control of light as well as in lasing in random media.

Detection range enhancement using circularly polarized light in scattering environments for infrared wavelengths

We find for infrared wavelengths that there are broad ranges of particle sizes and refractive indices that represent fog and rain, where circular polarization can persist to longer ranges than linear polarization. Using polarization tracking Monte Carlo simulations for varying particle size, wavelength, and refractive index, we show that, for specific scene parameters, circular polarization outperforms linear polarization in maintaining the illuminating polarization state for large optical depths. This enhancement with circular polarization can be exploited to improve range and target detection in obscurant environments that are important in many critical sensing applications. Initially, researchers employed polarization-discriminating schemes, often using linearly polarized active illumination, to further distinguish target signals from the background noise. More recently, researchers have investigated circular polarization as a means to separate signal from noise even more. Specifically, we quantify both linearly and circularly polarized active illumination and show here that circular polarization persists better than linear for radiation fog in the short-wave infrared, for advection fog in the short-wave and long-wave infrared, and large particle sizes of Sahara dust around the 4 μm wavelength. Conversely, we quantify where linear polarization persists better than circular polarization for some limited particle sizes of radiation fog in the long-wave infrared, small particle sizes of Sahara dust for wavelengths of 9-10.5 μm, and large particle sizes of Sahara dust through the 8-11 μm wavelength range in the long-wave infrared.

Circular polarization memory in polydisperse scattering media

We investigate the survival of circularly polarized light in random scattering media. The surprising persistence of this form of polarization has a known dependence on the size and refractive index of scattering particles, however a general description regarding polydisperse media is lacking. Through analysis of Mie theory, we present a means of calculating the magnitude of circular polarization memory in complex media, with total generality in the distribution of particle sizes and refractive indices. Quantification of this memory effect enables an alternate pathway toward recovering particle size distribution, based on measurements of diffusing circularly polarized light.

Forward-peaked scattering of polarized light

Polarized light propagation in a multiple scattering medium is governed by the vector radiative transfer equation. We analyze the vector radiative transfer equation in asymptotic limit of forward-peaked scattering and derive an approximate system of equations for the Stokes parameters, which we call the vector Fokker-Planck approximation. The vector Fokker-Planck approximation provides valuable insight into several outstanding issues regarding the forward-peaked scattering of polarized light such as the polarization memory phenomenon.

Monte Carlo modeling of polarized light propagation: Stokes vs. Jones. Part II

In this second part of our comparative study inspecting the (dis)similarities between "Stokes" and "Jones," we present simulation results yielded by two independent Monte Carlo programs: (i) one developed in Bern with the Jones formalism and (ii) the other implemented in Ulm with the Stokes notation. The simulated polarimetric experiments involve suspensions of polystyrene spheres with varying size. Reflection and refraction at the sample/air interfaces are also considered. Both programs yield identical results when propagating pure polarization states, yet, with unpolarized illumination, second order statistical differences appear, thereby highlighting the pre-averaged nature of the Stokes parameters. This study serves as a validation for both programs and clarifies the misleading belief according to which "Jones cannot treat depolarizing effects."

Depolarization coefficients of light in multiply scattering media

The depolarization coefficients are calculated for multiply scattered linearly and circularly polarized light. For a number of media (aqueous suspension of polystyrene particles, water droplets in air), the calculations are carried out both numerically, with solving the vector radiative transfer equation and analytically, within the polarization mode approximation. In the latter case the depolarization coefficients are expressed explicitly in terms of the scattering and absorption coefficients, and the scattering matrix elements of the medium. The range of applicability of the polarization mode approximation is established. For most practically important cases, this method is shown to provide a satisfactory degree of accuracy. We also find the fundamental values of the depolarization coefficients for a Rayleigh medium.

Long-range polarimetric imaging through fog

We report an experimental implementation of long-range polarimetric imaging through fog over kilometric distance in real field atmospheric conditions. An incoherent polarized light source settled on a telecommunication tower is imaged at a distance of 1.3 km with a snapshot polarimetric camera including a birefringent Wollaston prism, allowing simultaneous acquisition of two images along orthogonal polarization directions. From a large number of acquisitions datasets and under various environmental conditions (clear sky/fog/haze, day/night), we compare the efficiency of using polarized light for source contrast increase with different signal representations (intensity, polarimetric difference, polarimetric contrast, etc.). With the limited-dynamics detector used, a maximum fourfold increase in contrast was demonstrated under bright background illumination using polarimetric difference image.

Prediction of electric field frequency correlations for randomly scattering slabs in the nondiffusive regime with the scalar Bethe-Salpeter equation

We show that a scalar Bethe-Salpeter equation model captures the measured copolarized electric field frequency correlation magnitude for randomly scattering slabs in the weakly scattering, nondiffusive regime. Consequently, the model could be used to form images of tissue on the millimeter and submillimeter length scale, and for environmental sensing with comparable scatter, as dictated by the optical scattering length in relation to the scattering domain size.

Linearly polarized emission from random lasers with anisotropically amplifying media

Simulations on three-dimensional random lasers were performed by finite-difference time-domain integration of Maxwell's equations combined with rate-equations providing gain. We investigated the frequency-dependent emission polarization of random lasers in the far-field of the sample and characterized the influence of anisotropic pumping in orthogonal polarizations. Under weak scattering, the polarization states of random lasing modes were random for isotropic pumping and linear under anisotropic pumping. These findings are in accordance with recent experimental observations. A crossover was observed towards very strong scattering, in which the scattering destroys the pump-induced polarization-anisotropy of the random lasing modes and randomizes (scrambles) the mode-polarization.