Scattering Anisotropy Parameter Research Articles

Exact analytical solution of the one-dimensional time-dependent radiative transfer equation with linear scattering

The radiative transfer equation (RTE) is a cornerstone for describing the propagation of electromagnetic radiation in a medium, with applications spanning atmospheric science, astrophysics, remote sensing, and biomedical optics. Despite its importance, an exact analytical solution to the RTE has remained elusive, necessitating the use of numerical approximations such as Monte Carlo, discrete ordinate, and spherical harmonics methods. In this paper, we present an exact solution to the one-dimensional time-dependent RTE. We delve into the moments of the photon distribution, providing a clear view of the transition to the diffusion regime. This analysis offers a deeper understanding of light propagation in the medium. Furthermore, we demonstrate that the one-dimensional RTE is equivalent to the Klein-Gordon equation with an imaginary mass term determined by the inverse reduced scattering length. Contrary to naive expectations of superluminal solutions, we find that our solution is strictly causal under appropriate boundary conditions, determined by the light transport problem. We validate the found solution using Monte Carlo simulations and benchmark the performance of the latter. Our analysis reveals that even for highly forward scattering, dozens of random light scatterings are required for an accurate estimate, underscoring the complexity of the problem. Moreover, we propose a method for faster convergence by adjusting the parameters of Monte Carlo sampling. We show that a Monte Carlo method sampling photon scatterings with input parameters (μs,g), where μs is the inverse scattering length and g is the scattering anisotropy parameter, is equivalent to that with (μs(1−g)/2,−1). This equivalence leads to a significantly faster convergence to the exact solution, offering a substantial improvement of the Monte Carlo method for the one-dimensional RTE. Our findings not only contribute to the theoretical understanding of the RTE but also have potential implications for improving the numerical methods used to approximate it.

Anisotropy of Light Scattering by Foamed Liquids

Optical transport parameters (transport propagation length of radiation and scattering length) have been experimentally studied in samples of a foamed liquid for a wavelength range of 500–900 nm. On the basis of the obtained experimental data, the values of the anisotropy parameter of light scattering in a foamed liquid are found as a function of the aging time. It is concluded that the values of the scattering anisotropy parameter close to zero in the early stages of aging are due to a strong correlation of the spatial positions of the scattering centers (gas bubbles in the liquid-phase matrix). The increase in the scattering anisotropy parameter with aging of the foam is due to “optical” inversion (a transition from the regime of light scattering by gas bubbles in a liquid to scattering by regions of intersections of the foam cell boundaries in a gas matrix medium).

The effect of scattering-medium parameters on signal magnitude under acousto-optic tomography

We have experimentally studied the influence of scattering anisotropy parameter g of a medium on the magnitude of signal S (visualization parameter) at an ultrasonic frequency that is registered upon acoustooptic tomography. Aqueous solutions of mixtures of cream and skimmed milk with different ratios between them were used as scattering media. The optical properties of media (absorption coefficient μa and reduced scattering coefficient μ′S) have been measured on a spectrophotometer (Perkin-Elmer Lambda 950 UV-VIS-NIR) using the inverse adding-doubling technique. As a result of the investigation, we have found that there is a certain correlation between the value of the scattering anisotropy parameter g of aqueous solutions of investigated mixtures and the percentage of the mixture in the aqueous solution, which ensures the required small value of extinction coefficient μ of the scattering medium. An increase in signal S has been revealed with increasing anisotropy parameter g of the medium at a invariable value of extinction coefficient μ. We have concluded that, to solve an inverse problem on the acousto-optic tomography, it is necessary to take into account possible changes in the g factor in scattering media, including biological ones.

Determination of the scattering anisotropy with optical coherence tomography

In this work we demonstrate measurements with optical coherence tomography (OCT) of the scattering phase function in the backward direction and the scattering anisotropy parameter g. Measurements of the OCT attenuation coefficient and the backscattering amplitude are performed on calibrated polystyrene microspheres with a time-domain OCT system. From these measurements the phase function in the backward direction is determined. The measurements are described by the single scattering model and match Mie calculations very well. Measurements on Intralipid demonstrate the ability to determine the g of polydisperse samples and, for Intralipid, g = 0.35 ± 0.03 is measured, which is well in agreement with g from literature. These measurements are validated using the Intralipid particle size distribution determined from TEM measurements. Measurements of g and the scattering phase function in the backward direction can be used to monitor changes in backscattering, which can indicate morphological changes of the sample or act as contrast enhancement mechanism.

In Vitro Assessment of Optical Properties of Blood by Applying the Extended Huygens-Fresnel Principle to Time-Domain Optical Coherence Tomography Signal at 1300 nm

A direct method for the measurement of the optical attenuation coefficient and the scattering anisotropy parameter based on applying the extended Huygens-Fresnel principle to optical coherence tomography images of blood is demonstrated. The images are acquired with a low-power probing beam at the wavelength of 1300 nm. Values of 12.15 mm−1 and 0.95 are found for the total attenuation coefficient and the scattering anisotropy factor, respectively. Also, as a preliminary step, the optical refraction index is determined with a precision of two decimal numbers directly from optical coherence images. The total attenuation coefficient and the scattering anisotropy factor are determined with precisions within experimental error margins of 5% and 2%, respectively. Readable OCT signal is obtained for a maximum propagation of light into blood of 0.25 mm. At the maximum probed depth, the measured signal is almost 103 smaller than its initial intensity when entering the sample.

The influence of the scattering anisotropy parameter on diffuse reflection of light

We discuss the impact of the scattering anisotropy parameter on the path length distribution of multiply scattered light. A quantitative treatment based on the radiative transfer equation is compared to an extended photon diffusion formalism. We compare both models with diffusing-wave spectroscopy measurements using randomly polarized light.

Application of neural networks for determining optical parameters of strongly scattering media from the intensity profile of backscattered radiation

We analyse the possibilities of simultaneous measuring three optical parameters of scattering media, namely, the scattering and absorption coefficients and the scattering anisotropy parameter by the intensity profile of backscattered radiation by using the neural network inversion method and the method of adaptive-network-based fuzzy inference system. The measurement errors of the absorption and scattering coefficients and the scattering anisotropy parameter are 20%, 5%, and 10%, respectively.

Depolarization of backscattered linearly polarized light.

We formulate a quantitative description of backscattered linearly polarized light with an extended photon diffusion formalism taking explicitly into account the scattering anisotropy parameter g of the medium. From diffusing wave spectroscopy measurements, the characteristic depolarization length for linearly polarized light, lp , is deduced. We investigate the dependence of this length on the scattering anisotropy parameter g spanning an extended range from -1 (backscattering) to 1 (forward scattering). Good agreement is found with Monte Carlo simulations of multiply scattered light.

Photonic properties of strongly correlated colloidal liquids.

The optical and structural properties of dense colloidal suspensions in the presence of long-range electrostatic repulsion are determined from both light and small-angle neutron scattering experiments. Short-range structural order induces an enhancement of the scattering strength while at the same time the total transmission shows strong wavelength dependence, reminiscent of a photonic crystal. Interestingly, the interplay between diffusive scattering and local order leads to negative values of the scattering anisotropy parameter. The tunable optical properties of these liquids furthermore suggest potential applications such as transparency switches or filters.

Determination of optical parameters of a medium by the profile of backscattered radiation

The possibilities of determining the scattering coefficient, the absorption coefficient, and the scattering anisotropy parameter of strongly scattering media are analyzed on the basis of comparison of experimentally obtained profiles of backscattered radiation with the profiles calculated with help of the numerical Monte Carlo method.

Interfacial properties of Fe/Cr multilayers in the current-perpendicular-to-plane geometry

Recent arguments that the Current-Perpendicular-to-Plane (CPP) Magnetoresistance of Fe/Cr multilayers is sensitive to interfacial roughness stimulated us to try to repeat the experiments on which the claims were made. While our CPP specific-resistances are comparable to those previously reported, their detailed behaviors are different. Our data are consistent with a simple two-current series-resistor model with a single enhanced interface resistance 2AR Fe/Cr *=1.6±0.15 fΩ m 2, in reasonable agreement with recent calculations. However, our best estimate of the interfacial scattering anisotropy parameter, γ Fe/Cr=−(0.7±0.15), is larger in magnitude than predicted by the same calculations. We discuss possible reasons for the differences between our results and previous data.

The decay dynamics of photoexcited rare gas cluster ions

The kinetic energies of fast neutrals ejected from photoexcited rare gas cluster ions have been measured for the following systems: Arn+, Krn+, Xen+ at two photon wavelengths: 355 and 532 nm, and for n in the range 2–19. New data are presented for xenon at both wavelengths, and for argon and krypton cluster ions at 355 nm. For argon and krypton cluster ions at 532 nm, new data have been recorded which are more accurate than those presented previously. A Monte Carlo model of the experiment has been used to simulate the kinetic energy releases and also to investigate variations in the scattering anisotropy parameter (β) as a function of photon energy and cluster composition and size. Significant fluctuations in β are observed, and these are attributed to a combination of structural variation and changes to the nature of the central chromophore. For small cluster ions the kinetic energy release data show evidence of being influenced by the final spin-orbit state of the atomic ion. Overall, there is a gradual decline in kinetic energy release as a function of increasing cluster size; however, there are marked variations within this trend. For all three rare gas systems the results show that the primary response to photoexcitation is the ejection of a single atom with a high kinetic energy on a time scale that is short compared with the rotational period of a cluster.

Why is d-wave pairing in HTS robust in the presence of impurities?

In the recent theory of strong correlations by [1] – [3] it was shown that by lowering doping concentration a forward peak is developed in the charge scattering channel. Physically, this means that short-range impurity scattering potential is transformed into long-range one. Accordingly, near the optimal doping the nonmagnetic scattering is pronounced in the d-channel and d-wave pairing is robust against defects and impurities. It is reflected in a decrease of the slope of the critical temperature T c ( Γ s ) at Γ s → 0 by factor (1 − β), where β is the scattering anisotropy parameter and Γ s is an average scattering rate. For large doping, β is small [1], [2] and d-wave pairing loses its robustness. The theory is generally formulated for the bi-layer model by including: (1) intra- and inter-plane pairing; (2) intra- and inter-plane impurities.