Random walk of polarized light in turbid media

On the bubble-bubbleless ocean continuum and its meaning for the LiDAR equation: LiDAR measurement of underwater bubble properties during storm conditions

This paper presents the NRL shipboard LiDAR and the first LiDAR dataset of underwater bubbles. The meaning of these LiDAR observations, the algorithms used and their current limitations are discussed. The derivation of the LiDAR multiple scattering regime is derived from the LiDAR observations and theory. The detection of the underwater bubble presence and their depth is straightforward to estimate from the depolarized laser return. This dataset strongly suggest that the whitecaps term in the LiDAR equation formalism needs to be revisited. The retrieval of the fraction of air volume within a given volume of water (void fraction) is possible and the algorithm is stable with a simple ocean backscatter LiDAR system. The accuracy of the void fraction retrieval will increase significantly with future developments.

Single-shot digital optical fluorescence phase conjugation through forward multiple-scattering samples

Aberrations and multiple scattering in biological tissues critically distort light beams into highly complex speckle patterns. In this regard, digital optical phase conjugation (DOPC) is a promising technique enabling in-depth focusing. However, DOPC becomes challenging when using fluorescent guide stars for four main reasons: the low photon budget available, the large spectral bandwidth of the fluorescent signal, the Stokes shift between the emission and the excitation wavelength, and the absence of reference beam preventing holographic measurement. Here, we demonstrate the possibility to focus a laser beam through multiple-scattering samples by measuring speckle fields in a single acquisition step with a reference-free, high-resolution wavefront sensor. By taking advantage of the large spectral bandwidth of forward multiply scattering samples, digital fluorescence phase conjugation is achieved to focus a laser beam at the excitation wavelength while measuring the broadband speckle field arising from a micrometer-sized fluorescent bead.

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.

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.

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.

Speckle Engineering through Singular Value Decomposition of the Transmission Matrix

Speckle patterns are ubiquitous in optics and have multiple applications for which the control of their spatial correlations is essential. Here, we report on a method to engineer speckle correlations behind a scattering medium through the singular value decomposition of the transmission matrix. We not only demonstrate control over the speckle grain size and shape but also realize patterns with nonlocal correlations. Moreover, we show that the reach of our method extends also along the axial dimension, allowing volumetric speckle engineering behind scattering layers.

Holistic Monte-Carlo optical modelling of biological imaging

The invention and advancement of biological microscopy depends critically on an ability to accurately simulate imaging of complex biological structures embedded within complex scattering media. Unfortunately no technique exists for rigorous simulation of the complete imaging process, including the source, instrument, sample and detector. Monte-Carlo modelling is the gold standard for the modelling of light propagation in tissue, but is somewhat laborious to implement and does not incorporate the rejection of scattered light by the microscope. On the other hand microscopes may be rigorously and rapidly modelled using commercial ray-tracing software, but excluding the interaction with the biological sample. We report a hybrid Monte-Carlo optical ray-tracing technique for modelling of complete imaging systems of arbitrary complexity. We make the software available to enable user-friendly and rigorous virtual prototyping of biological microscopy of arbitrary complexity involving light scattering, fluorescence, polarised light propagation, diffraction and coherence. Examples are presented for the modelling and optimisation of representative imaging of neural cells using light-sheet and micro-endoscopic fluorescence microscopy and imaging of retinal vasculature using confocal and non-confocal scanning-laser ophthalmoscopes.

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.

Numerical investigation of polarization filtering for direct optical imaging within scattering media

We investigate the ability of polarization filtering to improve direct imaging of absorbing objects which are buried within scattering environments. We extend on previous empirical investigations by exploiting an efficient perturbation-based formalism, which is applicable to arbitrarily arranged sources and detectors with arbitrary polarizations. From this approach, we are able in some cases to find certain non-trivial linear combinations of polarization measurement channels that maximize the object resolution and visibility.

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.

Propagation of polarized waves through bounded composite materials

We describe a numerical model, based on a Monte Carlo algorithm, to calculate the propagation of polarized waves through highly scattering microstructured materials, and to properly account for the effect of both loss and boundaries. As an example, we investigate the impact of a strongly scattering object of air-polymer composite material on a broadband collimated source. We also calculate the depolarization of linearly polarized and circularly polarized waves escaping from the sample boundaries, especially at large scattering angles, and we show how boundaries can modify the distribution and the polarization of the scattered waves propagating out of the sample.

Diagnosis of the phase function of random media from light reflectance

Light reflectance has been widely used to diagnose random media in both in situ and in vivo applications. The quantification of the phase function of the medium from reflectance measurements, however, remains elusive due to the lack of an explicit connection between the light reflectance profile and the phase function. Here we first present an analytical model for reflectance of scattered light at an arbitrary source-detector separation by forward-peaked scattering media such as biological tissue and cells. The model incorporates the improved small-angle scattering approximation (SAA) to radiative transfer for sub-diffusive light reflectance and expresses the dependence of the light reflectance on the phase function of the scattering medium in a closed form. A spreading length scale, l_Θ, is found to characterise subdiffusive light reflectance at the high spatial frequency (close separation) limit. After validation by Monte Carlo simulations, we then demonstrate the application of the model in accurate determination of the complete set of optical properties and the phase function of a turbid medium from the profile of subdiffusive and diffusive light reflectance.

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.

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.

Tissue multifractality and Born approximation in analysis of light scattering: a novel approach for precancers detection

Multifractal, a special class of complex self-affine processes, are under recent intensive investigations because of their fundamental nature and potential applications in diverse physical systems. Here, we report on a novel light scattering-based inverse method for extraction/quantification of multifractality in the spatial distribution of refractive index of biological tissues. The method is based on Fourier domain pre-processing via the Born approximation, followed by the Multifractal Detrended Fluctuation Analysis. The approach is experimentally validated in synthetic multifractal scattering phantoms, and tested on biopsy tissue slices. The derived multifractal properties appear sensitive in detecting cervical precancerous alterations through an increase of multifractality with pathology progression, demonstrating the potential of the developed methodology for novel precancer biomarker identification and tissue diagnostic tool. The novel ability to delineate the multifractal optical properties from light scattering signals may also prove useful for characterizing a wide variety of complex scattering media of non-biological origin.

Photon transport in cylindrically-shaped disordered meso-macroporous materials

We theoretically and experimentally investigate light diffusion in disordered meso-macroporous materials with a cylindrical shape. High Internal Phase Emulsion (HIPE)-based silica foam samples, exhibiting a polydisperse pore-size distribution centered around 19 μm to resemble certain biological tissues, are realized. To quantify the effect of a finite lateral size on measurable quantities, an analytical model for diffusion in finite cylinders is developed and validated by Monte Carlo random walk simulations. Steady-state and time-resolved transmission experiments are performed and the transport parameters (transport mean free path and material absorption length) are successfully retrieved from fits of the experimental curves with the proposed model. This study reveals that scattering losses on the lateral sides of the samples are responsible for a lowering of the transmission signal and a shortening of the photon lifetime, similar in experimental observables to the effect of material absorption. The recognition of this geometrical effect is essential since its wrong attribution to material absorption could be detrimental in various applications, such as biological tissue diagnosis or conversion efficiency in dye-sensitized solar cells.

Monte Carlo model of the depolarization of backscattered linearly polarized light in the sub-diffusion regime

We present a predictive model of the depolarization ratio of backscattered linearly polarized light from spatially continuous refractive index media that is applicable to the sub-diffusion regime of light scattering. Using Monte Carlo simulations, we derived a simple relationship between the depolarization ratio and both the sample optical properties and illumination-collection geometry. Our model was validated on tissue simulating phantoms and found to be in good agreement. We further show the utility of this model by demonstrating its use for measuring the depolarization length from biological tissue in vivo. We expect our results to aid in the interpretation of the depolarization ratio from sub-diffusive reflectance measurements.

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.

Polarization sensitive optical low-coherence reflectometry for blood glucose monitoring in human subjects

A device based on polarization sensitive optical low-coherence reflectometry is developed to monitor blood glucose levels in human subjects. The device was initially tested with tissue phantom. The measurements with human subjects for various glucose concentration levels are found to be linearly dependent on the ellipticity obtainable from the home-made phase-sensitive optical low-coherence reflectometry device. The linearity obtained between glucose concentration and ellipticity are explained with theoretical calculations using Mie theory. A comparison of results with standard clinical methods establishes the utility of the present device for non-invasive glucose monitoring.

Determination of optical coefficients and fractal dimensional parameters of cancerous and normal prostate tissues

Optical extinction and diffuse reflection spectra of cancerous and normal prostate tissues in the 750 to 860 nm spectral range were measured. Optical extinction measurements using thin ex vivo prostate tissue samples were used to determine the scattering coefficient (μ(s)), while diffuse reflection measurements using thick prostate tissue samples were used to extract the absorption coefficient (μ(a)) and the reduced scattering coefficient (μ'(s)). The anisotropy factor (g) was obtained using the extracted values of μ(s) and μ'(s). The values of fractal dimension (D(f)) of cancerous and normal prostate tissues were obtained by fitting to the wavelength dependence of μ'(s). The number of scattering particles contributing to μ(s) as a function of particle size and the cutoff diameter d(max) as a function of g were investigated using the fractal soft tissue model and Mie theory. Results show that d(max) of the normal tissue is larger than that of the cancerous tissue. The cutoff diameter d(max) is observed to agree with the nuclear size for the normal tissues and the nucleolar size for the cancerous tissues. Transmission spectral polarization imaging measurements were performed that could distinguish the cancerous prostate tissue samples from the normal tissue samples based on the differences between their absorption and scattering parameters.

Tissue polarimetry: concepts, challenges, applications, and outlook

Polarimetry has a long and successful history in various forms of clear media. Driven by their biomedical potential, the use of the polarimetric approaches for biological tissue assessment has also recently received considerable attention. Specifically, polarization can be used as an effective tool to discriminate against multiply scattered light (acting as a gating mechanism) in order to enhance contrast and to improve tissue imaging resolution. Moreover, the intrinsic tissue polarimetry characteristics contain a wealth of morphological and functional information of potential biomedical importance. However, in a complex random medium-like tissue, numerous complexities due to multiple scattering and simultaneous occurrences of many scattering and polarization events present formidable challenges both in terms of accurate measurements and in terms of analysis of the tissue polarimetry signal. In order to realize the potential of the polarimetric approaches for tissue imaging and characterization/diagnosis, a number of researchers are thus pursuing innovative solutions to these challenges. In this review paper, we summarize these and other issues pertinent to the polarized light methodologies in tissues. Specifically, we discuss polarized light basics, Stokes-Muller formalism, methods of polarization measurements, polarized light modeling in turbid media, applications to tissue imaging, inverse analysis for polarimetric results quantification, applications to quantitative tissue assessment, etc.

Laser speckle reduction via colloidal-dispersion-filled projection screens

We use projection screens filled with colloidal dispersions to reduce laser speckle in laser projection systems. Laser light is multiply scattered at the globules of the colloidal dispersion's internal phase, which do Brownian movement. The integration time of the human eye causes a perception of a reduced laser speckle contrast because of temporal averaging. As a counteracting effect, blurring of projected images occurs in the colloidal dispersion, which degrades image quality. We measure and compare speckle reduction and blurring of three different colloidal dispersions filled into transmission screens of different thicknesses. We realized a high speckle contrast reduction at simultaneously low blurring with a thin screen filled with a highly scattering colloidal dispersion with forward-peaked scattering. We realize speckle contrast values below 3% at acceptable blurring.

Mueller matrix decomposition for polarized light assessment of biological tissues

The Mueller matrix represents the transfer function of an optical system in its interactions with polarized light and its elements relate to specific biologically or clinically relevant properties. However, when many optical polarization effects occur simultaneously, the resulting matrix elements represent several "lumped" effects, thus hindering their unique interpretation. Currently, no methods exist to extract these individual properties in turbid media. Here, we present a novel application of a Mueller matrix decomposition methodology that achieves this objective. The methodology is validated theoretically via a novel polarized-light propagation model, and experimentally in tissue simulating phantoms. The potential of the approach is explored for two specific biomedical applications: monitoring of changes in myocardial tissues following regenerative stem cell therapy, through birefringence-induced retardation of the light's linear and circular polarizations, and non-invasive blood glucose measurements through chirality-induced rotation of the light's linear polarization. Results demonstrate potential for both applications.

Polarization-sensitive optoacoustic tomography of optically diffuse tissues

Polarization is indicative of material anisotropy, a property that reveals structural orientation information of molecules inside the material. Herein we investigate whether polarization can be detected optoacoustically in scattering and absorbing tissues. Using a laboratory prototype of polarization-sensitive optoacoustic tomography, we demonstrate high-resolution reconstructions of dichroism contrast deep in optically diffusive tissue-mimicking phantoms. The technique is expected to enable highly accurate imaging of polarization contrast in tissues, far beyond the current capabilities of pure optical polarization-imaging approaches.

Detection of multiple scattering in optical coherence tomography using the spatial distribution of Stokes vectors

Multiple scattering is one of the main degrading influences in optical coherence tomography, but to date its presence in an image can only be indirectly inferred. We present a polarization-sensitive method that shows the potential to detect it more directly, based on the degree to which the detected polarization state at any given image point is correlated with the mean state over the surrounding region. We report the validation of the method in microsphere suspensions, showing a strong dependence of the degree of correlation upon the extent to which multiply scattered light is coherently detected. We demonstrate the method's utility in various tissues, including chicken breast ex vivo and human skin and nailfold in vivo.

Coherence loss in light backscattering by random media with nanoscale nonuniformities

An experimental technique for measuring time-resolved coherence loss and destruction of backscattered wave packets in random media is described. The results of such measurements, performed with a modified Michelson interferometer, contain rich information about the characteristics of media nonuniformities. Experimental data for model nanosuspensions are compared with theoretical expressions developed in the paper which include the effects of Mie-type resonant scattering. We attribute one such observed effect to enhanced ineleastic optical transitions near the surface of nonmetallic nanoparticles. The inverse problem of characterization of multiscattering random media by backscattering is also considered.

Light scattering regimes along the optical axis in turbid media

We inject an angularly collimated laser beam into a scattering medium of a nondairy creamer-water solution and examine the distribution of the scattered light along the optical axis as a function of the source-detector spacing. The experimental and simulated data obtained from a Monte Carlo simulation suggest four regimes characterizing the transition from unscattered to diffusive light. We compare the data also with theoretical predictions based on a first-order scattering theory for regions close to the source, and with diffusionlike theories for larger source-detector spacings. We demonstrate the impact of the measurement process and the effect of the unavoidable absorption of photons by the detection fiber on the light distribution inside the medium. We show that the range of validity of these theories can depend on the experimental parameters such as the diameter and acceptance angle of the detection fiber.

Analytical cumulant solution of the vector radiative transfer equation investigates backscattering of circularly polarized light from turbid media

The backscattering of circularly polarized light pulses from an infinite uniform scattering medium is studied as a function of helicity of the incident light and size of scatterers in the medium. The approach considers a polarized short pulse of light incident on the scattering medium, and uses an analytical cumulant solution of the vector radiative transfer equation with the phase matrix obtained from the Mie theory to calculate the temporal profile of scattered polarized photons for any position and any angle of detection. The general expression for the scattered photon distribution function is an expansion in spatial cumulants up to an arbitrary high order. Truncating the expansion at the second-order cumulant, a Gaussian analytical approximate expression for the temporal profile of scattered polarized photons is obtained, whose average center position and half width are always exact. The components of scattered light copolarized and cross polarized with that of the incident light can be calculated and used for determining the degree of polarization of the scattered light. The results show that circularly polarized light of the same helicity dominates the backscattered signal when scatterer size is larger than the wavelength of light. For the scatterers smaller than the wavelength, the light of opposite helicity makes the dominant contribution to the backscattered signal. The theoretical estimates are in good agreement with our experimental results.

Circular polarization memory of light

Circular polarization memory of light multiply scattered by Mie particles is investigated. The mechanism of randomization of helicity is found, in general, to dominate light circular depolarization by particles of large size or a high refractive index while the mechanism of randomization of direction dominates for small particles of a lower refractive index. The characteristic length for circular polarized light to lose its helicity is determined for Mie scatterers of arbitrary size and refractive index and is used successfully to analyze circular depolarization of light transmission through a slab. Circular polarization memory of light is found to be most pronounced for not only large soft particles but also particles of smaller size and a high refractive index.