Monte Carlo model and single-scattering approximation of the propagation of polarized light in turbid media containing glucose

Optical parameters estimation in inhomogeneous turbid media using backscattered light: for transcutaneous scattering measurement of intravascular blood

In our earlier research, a technique was developed to estimate the effective attenuation coefficient of subcutaneous blood vessels from the skin surface using the spatial distribution of backscattered near-infrared (NIR) light. The scattering effect in surrounding tissues was suppressed through the application of a differential principle, provided that the in vivo structure is known. In this study, a new method is proposed enabling the separate estimation of both scattering and absorption coefficients using NIR light of different wavelengths. The differential technique is newly innovated to make it applicable to the subcutaneous structure without requiring explicit geometrical information. Suppression of the scattering effect from surrounding tissue can be incorporated into the process of estimating the scattering and absorption coefficients. The validity of the proposed technique can be demonstrated through Monte Carlo simulations using both homogeneous and inhomogeneous tissue-simulating models. The estimated results exhibit good coherence with theoretical values (r2 = 0.988-0.999). Moreover, the vulnerability and robustness of the proposed technique against different measurement errors are verified. Optimal conditions for practical measurement are specified under various light-detection conditions. Separate estimation of scattering and absorption coefficients improves the accuracy of turbidity measurements and spectroscopy in biomedical applications considerably, particularly for noninvasive measurements and analysis of blood, lipids, and other components in subcutaneous blood vessels.

Scattering direction sampling methods for polarized Monte Carlo simulation of oceanic lidar

Monte Carlo techniques have been widely applied in polarized light simulation. Based on different preconditions, there are two main types of sampling strategies for scattering direction: one is the scalar sampling method; the others are polarized sampling approaches, including the one- and two-point rejection methods. The polarized simulation of oceanic lidar involves a variety of mediums, and an efficient scattering sampling method is the basis for the coupling simulation of the atmosphere and ocean. To determine the optimal scattering sampling method for oceanic lidar simulation, we developed a polarized Monte Carlo model and simulated Mie scattering, Rayleigh scattering, and Petzold average-particle scattering experiments. This simulation model has been validated by comparison with Ramella-Roman's program [Opt. Express13, 4420 (2005)OPEXFF1094-408710.1364/OPEX.13.004420], with differences in reflectance and transmittance Stokes less than 1% in Mie scattering. The simulation results show these scattering sampling methods differ in runtime, scattering angle distributions, and reflectance and transmittance Stokes. Considering the current simulation accuracy of oceanic lidar, the differences in reflectance and transmittance Stokes are acceptable; thus, the runtime becomes the main evaluation factor. The one-point rejection method and scalar sampling method are preferable for the oceanic lidar polarized simulation. Under complex atmosphere-ocean coupling systems, scalar sampling methods may be a better choice since the calculation process of the sampling is independent of the incident Stokes vector.

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.

Measuring glucose concentration in a solution based on the indices of polarimetric purity

Polarization imaging is a powerful tool, which can be applied in biomedical diagnosis and many research fields. Here, we propose a new application of the indices of polarimetric purity (IPPs) composed of P1, P2, P3, to describe the glucose concentrations (GC) changes in the scattering system. The results suggest that P1 of the IPPs is a better indicator to GC in the solution than the degree of polarization (DoP) for the forward scattering detection. Meanwhile, the fitting relation among radius of scattering particle, GCs and P1 parameter has also been calculated, in which the error of inversion is no more than 4.73%. In the backscattering detection, the fitted frequency statistical histogram of the IPPs is used to measure the GCs, and their modes can represent changing trend of GCs.

Development of a technique to measure local scattering in turbid media using backscattered light at the surface for noninvasive turbidity evaluation of blood in subcutaneous blood vessels

For noninvasive skin-surface evaluation of turbidity in subcutaneous blood vessels we have developed a technique to estimate the reduced scattering coefficient from spatially resolved backscattered light. The solution of the diffusion approximation was used to derive an analytical solution for the effective attenuation coefficient as a function of the spatially resolved reflectance with respect to the source–detector distance. The reduced scattering coefficient can be calculated from the effective attenuation coefficient. This represents the blood turbidity or serum triglyceride concentration. An exact solution for the reduced scattering coefficient was newly obtained as a function of the effective attenuation coefficient using the special diffusion coefficient, which expands the applicability of the diffusion approximation to the case of human blood. To eliminate the effects of strong scattering in the surrounding tissue we introduced a differential principle using spatially resolved reflectance measured at positions on and off the blood vessel. The results of Monte Carlo simulation demonstrate the validity of the proposed technique even in the case of blood, which does not necessarily satisfy the conditions of the diffusion approximation. The small dependence on absorption variation in the practical range and robustness against the measurement error were verified. With the differential principle we can estimate blood turbidity by suppressing the effect of the surrounding tissue. With this technique, one can expect more than 50 times higher sensitivity for blood turbidity than that obtained without using this principle. The validity of the simulation and the applicability of the proposed technique were verified with measurements using a model phantom of subcutaneous blood vessels in a tissue-simulating turbid medium.

The depolarization performances of scattering systems based on the Indices of Polarimetric Purity (IPPs)

In this paper, the Indices of Polarimetric Purity (IPPs) [1-3] have been proposed to analyze the depolarization performances of mono-dispersion and poly-dispersion scattering systems. Here, we mainly investigate the influences of the particles' density, Refractive Index (RI) of the medium, incident wavelengths, the mixing ratio of bi-dispersion scattering particles and particle-size distributions of poly-dispersion scattering system on the depolarization performances for the backscattering detection. For the mono-dispersion scattering system under same incident wavelength, if the relative RI ratios (m) increase linearly, the depolarization performances of the system will first weaken and then strengthen, and of course, the incident wavelength and density of scattering particles will also influence the depolarization performances of the scattering system. For the bi-dispersion scattering system, the proportion of small particles will be negatively correlated with the depolarization property of the dispersion system, and meanwhile, the particle-size distributions will also affect the depolarization performances greatly in the poly-dispersion scattering system. The results demonstrate that the IPPs can be used to describe the depolarization performances of dispersion systems effectively.

Multiple scattering of polarized light in uniaxial turbid media with arbitrarily oriented linear birefringence

The effective scattering Mueller matrices obtained by the simulation were simplified to the reduced matrices and factorized using the Lu–Chipman polar decomposition, which afforded the polarization parameters in two dimensions. In general, the scalar retardance around the illumination point of a pencil beam shows a broad azimuthal dependence with an offset. Photons may behave quite differently under the birefringence according to their polarization state. In contrast, when the birefringence is oriented along the y -axis in the plane parallel to the surface ( x ? y ) plane, for example, the azimuthal dependence of the scalar retardance shows clear maxima along the x - and y -axes and sharp valleys between the maxima. Photons propagating in the medium probably experience the retardance in nearly the same way when they are polarized linearly and circularly. Moreover, the polarization parameters generally become nonsymmetric with respect to the plane perpendicular to both the x - y plane and the plane containing the birefringence axis, which suggests that the pathway of the lateral propagation of photons from the illumination point to the surrounding is slightly oblique upward relative to the x - y plane. These results were also compared with the case in which the birefringence axis is perpendicular to the x - y plane.

Forward scattering of polarized light from a turbid slab: theory and Monte Carlo simulations

It is proved that if reciprocity and mirror symmetry hold for single scattering by a particle, they also hold for multiple scattering in turbid slab media. Monte Carlo simulations generate a reduced effective Mueller matrix for forward scattering, which satisfies reciprocity and mirror symmetry, but satisfies only reciprocity if the medium contains chiral components. The scattering matrix was factorized by using the Lu-Chipman polar decomposition, which affords the polarization parameters as a function of the radial distance from the center. The depolarization coefficients decrease with increasing distance, whereas the scattering-induced linear diattenuation and retardance become larger in the middle-distance range. The optical rotation for a chiral medium increases with increasing distance.

Multiple scattering of polarized light in turbid birefringent media: a Monte Carlo simulation

Multiple scattering of polarized light in a birefringent turbid plane medium was studied using a Monte Carlo simulation. The reduced effective scattering Mueller matrix obtained in the simulation was factorized in two dimensions using the Lu-Chipman decomposition, yielding polarization parameters that exhibited dependences on the azimuth and the radial distance around the illumination point. We propose a double-scattering model for the propagation of polarized photons in turbid infinite plane media. When the birefringence slow axis is along the azimuth of 90° on the plane surface, the retardance becomes the largest negative along the azimuth of 0° and the largest positive along the azimuth of 90° and increases with increasing the azimuth from 0° to 90°. This azimuthal dependence may result from the overlap of the contributions from the light propagations vertical to, and lateral along, the plane surface. Thus, the dependences on the azimuth and the radial distance of the polarization parameters, such as the retardance, its orientation, optical rotation, and the depolarization coefficients, are correctly predicted.

Multiple scattering of polarized light in turbid infinite planes: Monte Carlo simulations

Monte Carlo simulations were performed for infinite plane media containing spherical particles of different sizes. Most of the features of the surface plots for the elements of the effective scattering Mueller matrices are explained by the azimuthal dependence of the matrix predicted according to the theory of Raković et al. [Appl. Opt.38, 3399 (1999)10.1364/AO.38.003399APOPAI1559-128X]. The reduced effective scattering Mueller matrices calculated according to the theory have eight nonzero elements, which are only dependent on the distance from the illumination point. The reduced matrices are factorized approximately into products of a depolarizer and retarding diattenuators. The turbid infinite plane media nearly behave as a pure depolarizer at long distances and become more diattenuating and birefringent with decreasing distance.

Jones-matrix mapping of complex degree of mutual anisotropy of birefringent protein networks during the differentiation of myocardium necrotic changes

The azimuthally stable method of Jones-matrix mapping of histological sections of myocardium tissue biopsy using spatial-frequency selection of the mechanisms of linear and circular birefringence is proposed. Correlation parameter-the complex degree of mutual anisotropy-and its diagnostic application are analytically substantiated. The method of measuring the complex degree of mutual-anisotropy coordinate distributions using spatial filtration of their high- and low-frequency components is developed. The interconnections between such distributions and parameters of linear and circular birefringence of myocardium tissue histological sections are defined. The comparative investigations of coordinate distributions of the complex degree of mutual anisotropy formed by fibrillar networks of myocardium tissues of different necrotic states (dead due to coronary heart disease and acute coronary insufficiency) are performed. The values and ranges of change of the statistical (moments of the first-fourth order) parameters of coordinate distributions of the complex degree of mutual anisotropy are defined. The objective criteria of cause of death differentiation are determined.

A new approach for optical assessment of directional anisotropy in turbid media

A study of polarized light transport in scattering media exhibiting directional anisotropy or linear birefringence is presented in this paper. Novel theoretical and experimental methodologies for the quantification of birefringent alignment based on out-of-plane polarized light transport are presented here. A polarized Monte Carlo model and a polarimetric imaging system were devised to predict and measure the impact of birefringence on an impinging linearly polarized light beam. Ex-vivo experiments conducted on bovine tendon, a biological sample consisting of highly packed type I collagen fibers with birefringent property, showed good agreement with the analytical results.

Equivalence relations and symmetries for laboratory, LIDAR, and planetary Müeller matrix scattering geometries

Symmetry relationships for optical observations of matter generally fall into several common scattering geometries. The "planetary" configuration is preferred by observers of extraterrestrial planets, "laboratory" observations are performed in the biomedical research field, and the LIDAR configuration is preferred by those using lasers to probe optical properties of horizontal surfaces with mirror or axial symmetry. This paper begins with the Stokes matrix formalism and uses symmetries of Müller matrix scattering to establish links among the mathematical symmetries of each geometric configuration. We finish the paper by identifying and correcting an influential misapplication of rotational scattering matrices in the literature. The corrected equation should find wide application in models of the LIDAR scattering process.

Continuous noninvasive monitoring of changes in human skin optical properties during oral intake of different sugars with optical coherence tomography

The objective of this study was to evaluate the effects of blood glucose concentration (BGC) on in vivo human skin optical properties after oral intake of different sugars. In vivo optical properties of human skin were measured with a spectral domain optical coherence tomography (SD-OCT). Experimental results show that increase of BGC causes a decrease in the skin attenuation coefficient. And the maximum decrements in mean attenuation coefficient of skin tissue after drinking glucose, sucrose and fructose solution are 47.0%, 36.4% and 16.5% compared with that after drinking water, respectively (p < 0.05). The results also show that blood glucose levels of the forearm skin tissue are delayed compared with finger-stick blood glucose, and there are significant differences in the time delays after oral intake of different sugars. The time delay between mean attenuation coefficient and BGC after drinking glucose solution is evidently larger than that after drinking sucrose solution, and that after drinking sucrose solution is larger than that after drinking fructose solution. Our pilot studies indicate that OCT technique is capable of non-invasive, real-time, and sensitive monitoring of skin optical properties in human subjects during oral intake of different sugars.

Fourier-domain Jones-matrix mapping of a complex degree of mutual anisotropy in differentiation of biological tissues' pathological states

This article presents the theoretical background of an azimuthally stable method of Jones-matrix mapping of histological sections of a uterine wall biopsy on the basis of spatial-frequency selection of the mechanisms of linear and circular birefringence. The diagnostic application of a new correlation parameter--a complex degree of mutual anisotropy--is analytically substantiated. The method of measuring coordinate distributions of a complex degree of mutual anisotropy with further spatial filtration of their high- and low-frequency components is developed. The interconnections of such distributions with linear and circular birefringence parameters of the uterine-wall-endometrium histological sections are found. The comparative results of measuring the coordinate distributions of a complex degree of mutual anisotropy formed by fibrillar networks of myosin and collagen fibrils of uterus wall tissue of different pathological states--pre-cancer (dysplasia) and cancer (adenocarcinoma)--are shown. The values and ranges of change of the statistical (moments of the first to fourth orders) parameters of complex degree of mutual-anisotropy coordinate distributions are studied. The objective criteria of diagnosing the pathology and differentiation of its severity degree are determined.

Photopolymerizable hydrogels for implants: Monte-Carlo modeling and experimental in vitro validation

Photopolymerization is commonly used in a broad range of bioapplications, such as drug delivery, tissue engineering, and surgical implants, where liquid materials are injected and then hardened by means of illumination to create a solid polymer network. However, photopolymerization using a probe, e.g., needle guiding both the liquid and the curing illumination, has not been thoroughly investigated. We present a Monte Carlo model that takes into account the dynamic absorption and scattering parameters as well as solid-liquid boundaries of the photopolymer to yield the shape and volume of minimally invasively injected, photopolymerized hydrogels. In the first part of the article, our model is validated using a set of well-known poly(ethylene glycol) dimethacrylate hydrogels showing an excellent agreement between simulated and experimental volume-growth-rates. In the second part, in situ experimental results and simulations for photopolymerization in tissue cavities are presented. It was found that a cavity with a volume of 152  mm3 can be photopolymerized from the output of a 0.28-mm2 fiber by adding scattering lipid particles while only a volume of 38  mm3 (25%) was achieved without particles. The proposed model provides a simple and robust method to solve complex photopolymerization problems, where the dimension of the light source is much smaller than the volume of the photopolymerizable hydrogel.

Extraction of anisotropic parameters of turbid media using hybrid model comprising differential- and decomposition-based Mueller matrices

A hybrid model comprising the differential Mueller matrix formalism and the Mueller matrix decomposition method is proposed for extracting the linear birefringence (LB), linear dichroism (LD), circular birefringence (CB), circular dichroism (CD), and depolarization properties (Dep) of turbid optical samples. In contrast to the differential-based Mueller matrix method, the proposed hybrid model provides full-range measurements of all the anisotropic properties of the optical sample. Furthermore, compared to the decomposition-based Mueller matrix method, the proposed model is insensitive to the multiplication order of the constituent basis matrices. The validity of the proposed method is confirmed by extracting the anisotropic properties of a compound chitosan-glucose-microsphere sample with LB/CB/Dep properties and two ferrofluidic samples with CB/CD/Dep and LB/LD/Dep properties, respectively. It is shown that the proposed hybrid model not only yields full-range measurements of all the anisotropic parameters, but is also more accurate and more stable than the decomposition method. Moreover, compared to the decomposition method, the proposed model more accurately reflects the dependency of the phase retardation angle and linear dichroism angle on the direction of the external magnetic field for ferrofluidic samples. Overall, the results presented in this study confirm that the proposed model has significant potential for extracting the optical parameters of real-world samples characterized by either single or multiple anisotropic properties.

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.

Spatial pattern characterization of linear polarization-sensitive backscattering Mueller matrix elements of human serum albumin sphere suspension

Human serum albumin (HSA) nanometer or micron particles represent promising drug-carrier systems. The azimuthal and radial variations of a linear polarization-sensitive backscattering Mueller matrix were experimentally studied in two cases: the scattering particle was smaller or larger in size to the probing wavelength of 780 nm. The results show that the twofold and fourfold structures are characteristic of small particle size suspension, whereas the eightfold structure is characteristic of large particle size suspension. Moreover, for both particle size suspensions, the element patterns have strong radial dependence when the suspension concentration and the incident power of laser change. In addition, for both particle size suspensions, the rotational symmetry of each element is lost in the case of oblique incidence but the multifold structure is maintained. Some suggestions for applications of Mueller matrix imaging in biomedical optics are provided.

Wavelet analysis of Fourier polarized images of the human bile

The model of generalized optical anisotropy of human bile is suggested, and the method of the polarimetric phase Fourier transform of the image of the laser radiation field that is generated by the mechanisms of linear and circular birefringence of polycrystalline networks with a wavelet-diagnosis of cholelithiasis is analytically substantiated.

Depolarization of light in turbid media: a scattering event resolved Monte Carlo study

Details of light depolarization in turbid media were investigated using polarization-sensitive Monte Carlo simulations. The surviving linear and circular polarization fractions of photons undergoing a particular number of scattering events were studied for different optical properties of the turbid media. It was found that the threshold number of photon scattering interactions that fully randomize the incident polarization (defined here as <1% surviving polarization fraction) is not a constant, but varies with the photon detection angle. Larger detection angles, close to backscattering direction, show lower full depolarization threshold number for a given set of sample's optical properties. The Monte Carlo simulations also confirm that depolarization is not only controlled by the number of scattering events and detection geometry, but is also strongly influenced by other factors such as anisotropy g, medium linear birefringence, and the polarization state of the incident light.

Polarization-sensitive reflectance imaging in skeletal muscle

We acquired polarization-sensitive reflectance images in freshly excised skeletal muscle samples. The obtained raw images varied depending on the incident and detection polarization states. The Stokes vectors were measured for incident light of four different polarization states, and the whole Mueller matrix images were also calculated. We found that the images obtained in skeletal muscles exhibited different features from those obtained in a typical polystyrene sphere solution. The back-reflected light in muscle maintained a higher degree of polarization along the axis perpendicular to muscle fiber orientation. Our analysis indicates that the unique muscle sarcomere structure plays an important role in modulating the propagation of polarized light in whole muscle.

Polarization-based diffuse reflectance imaging for noninvasive measurement of glucose

BACKGROUND

The ability to measure glucose concentration through noninvasive approaches would impact the treatment of diabetes significantly. Polarization-based optical approaches have received considerable interest because of their potential medical applications. Glucose, a chiral molecule, has the ability to rotate the plane of linearly polarized light, commonly referred to as optical activity, as well as changing the refractive index of the media, which therefore affects the overall scattering coefficient in a given media. The magnitude of each effect is related to the concentration of glucose. Although most previous studies have reported on the use of polarimetry in the aqueous humor of the eye because of its nonscattering nature, one would also expect that glucose concentration could be measured in more turbid media such as tissue through a similar approach. This study investigated how each of these effects is correlated to glucose concentration in a physiological range for highly scattering biological media.

METHODS

A custom-designed imaging polarimeter was used to image highly scattering Intralipid-based media containing different concentrations of glucose. Model formation and glucose prediction were performed through the use of partial least squares (PLS) regression. Further insight into the differences between polarization-based image measurements and encoding of glucose information was provided through the use of principal component analysis (PCA).

RESULTS

When coupled with PLS regression, in vitro polarization measurements yielded highly correlated glucose predictions in both calibration and independent validation, 0.999 and 0.998, respectively. Through the use of PCA, it appears that the majority of the image-based signal yielding the most significant glucose information is attributable to changes in the overall scattering coefficient due to glucose concentration and, to a lesser degree, effects of optical activity.

CONCLUSIONS

This study showed how polarimetric-based imaging coupled with PLS regression can be used to quantify glucose concentration in highly scattering media. Such methods may potentially be able to extend the use of noninvasive in vivo polarimetric measurements, normally acquired in the anterior chamber of the eye, to other preferred sensing sites such as the skin.

Stokes polarimetry in multiply scattering chiral media: effects of experimental geometry

The spatial distribution of optical rotation alpha and surviving linear polarization fraction beta(L) of light scattered from cylindrical turbid chiral (glucose-containing) and achiral samples is studied using a linear Stokes polarimeter. alpha and beta(L) are measured in and off the incident plane as the detection angle changes from the forward to the backward direction. The experimental results exhibit a complex dependence on the detection geometry: alpha is more sensitive to glucose presence off the incident plane, whereas beta(L) exhibits larger effects in-plane, as validated by polarization sensitive Monte Carlo simulations. A rigorous methodology is presented for optimizing the experimental geometry in the polarimetric examinations of complex random systems.

Targeting spectral signatures of progressively dysplastic stratified epithelia using angularly variable fiber geometry in reflectance Monte Carlo simulations

A key component of accurate spectroscopic-based cancer diagnostics is the ability to differentiate spectral variations resulting from epithelial tissue dysplasia. Such measurement may be enhanced by discretely probing the optical properties of the epithelial tissue where the morphological and biochemical features vary according to tissue depths. More precisely, layer-specific changes in tissue optical properties correlated to cellular dysplasia can be determined by conventional reflectance spectroscopy when it is coupled with angularly variable fiber geometry. Thus, this study addresses how angularly variable fiber geometry can resolve spatially specific spectral signatures of tissue pathology by interpreting and analyzing the reflectance spectra of increasingly dysplastic epithelial tissue in reflectance-mode Monte Carlo simulation. Specifically, by increasing the obliquity of the collection fibers from 0 to 40 deg in the direction facing toward the illumination fiber, the spectral sensitivity to tissue abnormalities in the epithelial layer is thereby improved, whereas orthogonal fibers are more sensitive to the changes in the stromal layer.

Polarized light propagation in multiply scattering media exhibiting both linear birefringence and optical activity: Monte Carlo model and experimental methodology

A Monte Carlo model for polarized light propagation in birefringent, optically active, multiply scattering media is developed in an effort to accurately represent the propagation of polarized light in biological tissue. The model employs the Jones N-matrix formalism to combine both linear birefringence and optical activity into a single effect that can be applied to photons as they propagate between scattering events. Polyacrylamide phantoms with strain-induced birefringence, sucrose-induced optical activity, and polystyrene microspheres as scattering particles are used for experimental validation. Measurements are made using a Stokes polarimeter that detects scattered light in different geometries, and compared to the results of Monte Carlo simulations run with similar parameters. The results show close agreement between the experimental measurements and Monte Carlo calculations for phantoms exhibiting turbidity and birefringence, as well as for phantoms exhibiting turbidity, birefringence, and optical activity. Other scattering-independent polarization properties can be incorporated into the developed Jones N-matrix formalism, enabling quantification of the polarization effects via an accurate polarization-sensitive Monte Carlo model.

Consideration of a spread-out source in problems of near-infrared optical tomography

When the light propagates in media where absorption is not negligible and/or scattering is weak, a contribution to the energy density coming from ballistic photons cannot be neglected. A point source effectively spreads out over a scattering volume and its spatial distribution is described by the source function. We consider a boundary value problem of light propagation in half-space for such a source on the basis of the telegraph equation. A solution is found by convolution of Green's function with the source function. The final result shows a significant difference in the behavior of the radiant energy density between the solution obtained for a distributed source and the diffusion approximation. Our results agree well with the Monte Carlo simulations over a broad range of scattering and/or absorption conditions. The obtained results are of practical importance in luminescence optical tomography because an erroneous shape of the energy density function may lead to an incorrect estimate of the light source depth after image reconstruction. The range of applications of the diffusion approximation is also discussed.

Depth-sensitive reflectance measurements using obliquely oriented fiber probes

Computer simulation is used to facilitate the design of fiber-probe geometries that enable enhanced detection of optical signals arising from specific tissue depths. Obtaining understanding of the relationship between fiber-probe design and tissue interrogation is critical when developing strategies for optical detection of epithelial precancers that originate at known depths from the tissue surface. The accuracy of spectroscopic diagnostics may be enhanced by discretely probing the optical properties of epithelium and underlying stroma, within which the morphological and biochemical features vary as a function of depth. While previous studies have investigated controlling tissue-probing depth for fluorescence-based modalities, in this study we focus on the detection of reflected light scattered by tissue. We investigate how the depth of optical interrogation may be controlled through combinations of collection angles, source-detector separations, and numerical apertures. We find that increasing the obliquity of collection fibers at a given source-detector separation can effectively enhance the detection of superficially scattered signals. Fiber numerical aperture provides additional depth selectivity; however, the perturbations in sampling depth achieved through this means are modest relative to the changes generated by modifying the angle of collection and source-detection separation.

Polarization visualization and selection of biotissue image two-layer scattering medium

We analyze and experimentally test the concept of laser polarization biotissue probing. The methods of increasing the SNR in coherent images of the optically anisotropic architectonics of the morphological biotissue structure are considered. The possibilities of polarization selection and contrasting of such images screened by other biotissues are examined. The influence of the depolarization degree of the scattered background on the SNR is investigated. The possibilities of polarization correction of the probing beam for contrasting biotissue images are analyzed.

Balanced detection for low-noise precision polarimetric measurements of optically active, multiply scattering tissue phantoms

The use and advantages of balanced detection for making low-noise polarimetric measurements in turbid materials are demonstrated. The technique reduces the intensity noise originating from the laser and, in addition, makes possible a direct measurement of a component of the Stokes vector. When phase-locked detection is used with either amplitude or polarization modulation for polarimetric measurements in turbid media, one can obtain elements of the scattering matrix of very small magnitude. This methodology is used to measure optical activity and surviving linear polarization fractions in clear and turbid media containing glucose at physiologically relevant concentrations. The results are in agreement with Monte Carlo simulations of polarized light propagation in turbid media.

Optical rotation and linear and circular depolarization rates in diffusively scattered light from chiral, racemic, and achiral turbid media

The polarization properties of light scattered in a lateral direction from turbid media were studied. Polarization modulation and synchronous detection were used to measure, and Mueller calculus to model and derive, the degrees of surviving linear and circular polarization and the optical rotation induced by turbid samples. Polystyrene microspheres were used as scatterers in water solutions containing dissolved chiral, racemic, and achiral molecules. The preservation of circular polarization was found to exceed the linear polarization preservation for all samples examined. The optical rotation induced increased with the chiral molecule concentration only, whereas both linear and circular polarizations increased with an increase in the concentrations of chiral, racemic, and achiral molecules. This latter effect was shown to stem solely from the refractive index matching mechanism induced by the solute molecules, independent of their chiral nature.