Free Path Length Research Articles

Torque expression of superelastic NiTi V-Slot and conventional stainless steel orthodontic bracket-archwire combinations - A finite element analysis

BackgroundTo investigate the torque expression of conventional stainless steel (SS) brackets in combination with rectangular SS archwires and nickel-titanium (NiTi) V-slot brackets in combination with V-shaped NiTi archwires using finite element analysis (FEA). MethodsCAD models were created for a conventional bracket and rectangular archwires with dimensions of 0.018″x0.025″ and 0.019″x0.025″, and for a V-slot bracket and V-shaped archwires with heights of 0.55 mm, 0.60 mm and 0.70 mm. FEA was performed using Ansys 2022R2 software to assess the forces and moments during simulated torsion of the archwires in the brackets between 0° and 25° with varying interbracket distances and free path lengths. ResultsThe V-slot bracket-archwire combination exhibited force transmission and moment generation within 1° of torsion. The transmissible force increased with the torsion angle, but showed an upper limit of about 13–14 Nmm. The SS bracket-archwire combination showed negligible forces and moments for simulated torsion between 0° and 15°. At torsions of 25°, moments of 12 Nmm and 14 Nmm occurred for the 0.018″x0.025″ and 0.019″x0.025″ archwire dimensions, respectively. ConclusionsThe V-slot bracket-archwire combination is effective in expressing torque and preventing both over- and under-activation. Conventional bracket-archwire combinations showed torsional losses due to play between 10 and 15°, depending on the dimensions of the respective archwire, and no upper torsional moment limit.

Investigation of physicochemical characteristics of Dy3+ modified ZnO nanoparticles

In this report, pristine and Dy3+ modified ZnO nanoparticles [Zn(1-x)DyxO NPs, where x = 0, 0.05, and 0.10] were synthesized using the sol–gel route, and their physicochemical characteristics were investigated. x-ray diffractograms of all the compositions possess P63mc space group depicting hexagonal crystallinity with wurtzite-type crystal structure with no signature of impurities as confirmed using the Rietveld refinement technique. The granular microstructure displayed grain growth with Dy3+ incorporation in the ZnO crystal framework and an increment in average grain size was found to be 22.83 nm for x = 0 to 36.34 nm. The optical energy band gap also increased from 3.35 eV to 3.88 eV with Dy3+ doping in the host ZnO. Dy3+ substitution inhibits the conduction in ZnO and improves the resistivity (36 Ωcm–79 Ωcm) as carrier concentration diminishes from 7.36 × 1016 cm−3 to 4.23 × 1016 cm−3. Similarly, the mean free path length for ZnO and Dy3+ doped ZnO NPs declines from 0.0301 nm to 0.0198 nm. Dielectric properties of all the compositions were investigated using an LCR impedance analyzer and it was observed that Dy3+ substitution enhances the value of the dielectric constant from 32 to 91 with a low tangent loss at 50 Hz.

Simulation of the Diffusion of Copper Atom on Graphene by Molecular Dynamics

The results of studying the effect of geometric and thermodynamic parameters of thermal evaporation and copper deposition on graphene lying on the Cu(111) surface on the adsorption of copper atoms, as well as their surface diffusion, are presented. The simulation was carried out by classical molecular dynamics using chains of Nose–Hoover thermostats. Interatomic interactions were determined by the Tersoff–Brenner, Rosato–Gillop–Legrand, and modified Morse potentials. A simple criterion for the thermalization of adatoms on graphene lying on a Cu(111) surface was formulated and tested. The average length and mean time of free path of a copper atom before and after thermalization at low (7 K) and room temperatures were studied for two evaporation temperatures. The probability of adsorption of a copper atom was found. The distributions along the directions of motion of adatoms during equilibrium diffusion were constructed. The distributions of the free path length and time were shown to have an exponential form. The influence of the Cu(111) substrate on the diffusion of the Cu atom on graphene was studied. The results obtained can be used to simulate the growth of copper nanoclusters on graphene by the kinetic Monte Carlo method.

Electron Energy-Loss Spectroscopy Method for Thin-Film Thickness Calculations with a Low Incident Energy Electron Beam

In this study, the thickness of a thin film (tc) at a low primary electron energy of less than or equal to 10 keV was calculated using electron energy-loss spectroscopy. This method uses the ratio of the intensity of the transmitted background spectrum to the intensity of the transmission electrons with zero-loss energy (elastic) in the presence of an accurate average inelastic free path length (λ). The Monte Carlo model was used to simulate the interaction between the electron beam and the tested thin films. The total background of the transmitted electrons is considered to be the electron transmitting the film with an energy above 50 eV to eliminate the effect of the secondary electrons. The method was used at low primary electron energy to measure the thickness (t) of C, Si, Cr, Cu, Ag, and Au films below 12 nm. For the C and Si films, the accuracy of the thickness calculation increased as the energy of the primary electrons and thickness of the film increased. However, for heavy elements, the accuracy of the film thickness calculations increased as the primary electron energy increased and the film thickness decreased. High accuracy (with 2% uncertainty) in the measurement of C and Si thin films was observed at large thicknesses and 10 keV, where tλ≈1. However, in the case of heavy-element films, the highest accuracy (with an uncertainty below 8%) was found for thin thicknesses and 10 keV, where tλ≤0.29. The present results show that an accurate film thickness measurement can be obtained at primary electron energy equal to or less than 10 keV and a ratio of tλ≤2. This method demonstrates the potential of low-loss electron energy-loss spectroscopy in transmission electron microscopy as a fast and straightforward method for determining the thin-film thickness of the material under investigation at low primary electron energies.

Poissonian pair correlation for directions in multi-dimensional affine lattices and escape of mass estimates for embedded horospheres

Abstract We prove the convergence of moments of the number of directions of affine lattice vectors that fall into a small disc, under natural Diophantine conditions on the shift. Furthermore, we show that the pair correlation function is Poissonian for any irrational shift in dimension 3 and higher, including well-approximable vectors. Convergence in distribution was already proved in the work of Strömbergsson and the second author [The distribution of free path lengths in the periodic Lorentz gas and related lattice point problems. Ann. of Math. (2)172 (2010), 1949–2033], and the principal step in the extension to convergence of moments is an escape of mass estimate for averages over embedded $\operatorname {SL}(d,\mathbb {R})$ -horospheres in the space of affine lattices.

Wide-field illumination diffuse optical tomography within a framework of single-pixel time-domain spatial frequency domain imaging.

We present a wide-field illumination time-domain (TD) diffusion optical tomography (DOT) for three-dimensional (3-D) reconstruction within a shallow region under the illuminated surface of the turbid medium. The methodological foundation is laid on the single-pixel spatial frequency domain (SFD) imaging that facilitates the adoption of the well-established time-correlated single-photon counting (TCSPC)-based TD detection and generalized pulse spectrum techniques (GPST)-based reconstruction. To ameliorate the defects of the conventional diffusion equation (DE) in the forward modeling of TD-SFD-DOT, mainly the low accuracy in the near-field region and in profiling early-photon migration, we propose a modified model employing the time-dependent δ-P1 approximation and verify its improved accuracy in comparison with both the Monte Carlo and DE-based ones. For a simplified inversion process, a modified GPST approach is extended to TD-SFD-DOT that enables the effective separation of the absorption and scattering coefficients using a steady-state equivalent strategy. Furthermore, we set up a single-pixel TD-SFD-DOT system that employs the TCSPC-based TD detection in the SFD imaging framework. For assessments of the reconstruction approach and the system performance, phantom experiments are performed for a series of scenarios. The results show the effectiveness of the proposed methodology for rapid 3-D reconstruction of the absorption and scattering coefficients within a depth range of about 5 mean free pathlengths.

Molecular Interaction Study in the Binary Liquid Mixture of PEO and DMF by Ultrasonic Technique

The non‐destructive ultrasonic technique is a great employ for knowing the solute–solvent interaction in the polymer blend. By the ultrasonic velocity and attenuation evaluation, the visco‐elastic behaviors of the polymer solution have been assessed and compared with the results of conventional dynamic mechanical analysis. In the present research work, a comprehensive ultrasonic investigation of molecular interaction in a polymeric mixture of Poly (ethylene oxide) PEO and dimethyformamide (DMF) at 333 K has been executed by using the information provided by the literature. For this purpose, ultrasonic waves of two different frequencies such as 2 and 5 MHz have been implemented. Several acoustical parameters such as adiabatic compressibility, acoustic impedance, relaxation time, and ultrasonic attenuation coefficient (𝛼/𝑓2) are explored. Thermodynamic parameters like relative association and intermolecular free path length are also estimated. The evaluated values have been associated with the previous experimental results. The non‐ideal approach of the solution is analyzed and discussed in detail.

New Polarimetric Data for the Galilean Satellites: Io and Ganymede Observations and Modeling

New high-precision disk-integrated measurements of the polarization of Io and Ganymede in the UBVRI bands are presented. The observations were obtained using polarimeters mounted on the Crimean Astrophysical Observatory and the Peak Terskol Observatory in 2019–2023. For Io, the negative polarization branch (NPB) reaches a minimum of P min ≈ −0.25 ± 0.02% in the V band at a phase angle of α min = 2.°1 ± 0.°5. The inversion angle is α inv = 26° ± 6° in the V and R bands. The NPB for Ganymede is an asymmetric curve, with P min = −0.34 ± 0.01% at α min = 0.°52 ± 0.°06 and α inv = 8.°5 ± 0.°2 in the V band. Although Io and Europa have similar geometric albedos (0.63 and 0.67, respectively), their NPB shapes differ. The NPB of Ganymede (albedo of 0.43) is morphologically similar to that of Europa, although it is described by different parameter values (P min, α min, and α inv). This discrepancy is likely due to the compositions of their surfaces: Europa’s with H2O ice, Io’s with sulfuric/silicate composition, and Ganymede’s with H2O ice and silicates. Numerical computations using the radiative transfer coherent backscattering method demonstrated a match to the polarimetric observations and to the geometric albedos for Ganymede with the single-scattering albedo ≈ 0.943 and mean free path length kl = 2πl/λ eff ≈ 150, where λ eff is the wavelength. For Io’s regolith, the single-scattering albedo was found to be ≈ 0.979 and kl ≈ 40.

In English

When metal nanoparticles (MNPs) are illuminated with a monochromatic laser wave, the frequency of which is far from the plasmon frequency (the frequency of plasmon resonances), under certain conditions (depending on the frequency of the wave, its polarization, the size and shape of the MNPs), absorption of light by MNPs can be dominated by magnetic absorption (absorption caused by the magnetic component of the electromagnetic field of the light (laser) wave). This work is focused on studying the features of absorption caused by the influence of the magnetic component of laser radiation. This issue is rather poorly studied for MNPs of non-spherical shape. Therefore, how the shape of the particle manifests itself in its absorption of laser radiation (laser pulses) is one of the goals of our research. In this work, we will study the features of magnetic absorption of light (laser radiation) depending on the shape of the particles. In this paper, we will investigate the influence of spheroidal MNPs on this process. Calculations will be carried out using the kinetic equation method, because we will consider the case when the size of the MNP is smaller than the length of free path of the electron in the MNP. Note that the kinetic approach makes it possible to obtain correct results for the case when the size of the particle is greater than the length of the free path. For non-spherical MNPs, we have developed a theory that makes it possible to calculate the energy of magnetic absorption by a particle when it is irradiated with laser pulses. The dependence of magnetic absorption on the ratio of the radii of curvature of spheroidal MNPs and the vector of the magnetic field of an electromagnetic (laser) wave was constructed and theoretically investigated. An interesting result is the absorption of energy by a spheroidal MNP as its disco similarity increases. We now use to estimate the relative contributions of electric We and magnetic Wm absorption to the total absorption. For example, let us take a gold MNP’s, then ωp ≈ 5·1015 s–1, ν ≈ 1013 s–1, R = 3·10–6 sm, ω ≈ 2·1014 s–1 (carbon dioxide laser), ε' ≈ –600, ε'' ≈ 30 we received the next ratio We/Wm ≈ 2. We can see that for the given set of parameters magnetic absorption is twice as large as electric. Obviously, for different parameters of the particle and a different frequency range electric absorption can be either larger or smaller than magnetic absorption. Hence, when studying the dependence of optical absorption by MNP’s on particle form, we must allow for both electric and magnetic absorption. For an asymmetric MNP’s (for example ellipsoidal particles), apart from everything else, the ratio of the electric and magnetic contributions to absorption (as fixed frequency) is strongly dependent on the degree of particle asymmetric and wave polarization.

Assessment of modal density and free path distribution in central-planned halls.

Central-planned halls are highly widespread in the historical architectures of the Western world, such as rotundae, Christian baptisteries, and Roman tombs. In such halls, whispering galleries, flutter echoes, and sound focusing are the acoustic phenomena mainly investigated by scholars. Instead, modal behaviour and free path distribution are generally less treated in literature. The present study explores the modal density at low frequencies and the relationship with the most recurrent free path lengths in three historical nearly circular spaces, here assessed as case studies. Acoustic measurements allowed the collection of objective experimental data, i.e., room impulse responses and the resulting room acoustics criteria. Wave-based numerical models allowed for the investigation of the eigenfrequencies distribution, while the free paths trend has been experienced through ray-based models. The main outcomes of both analyses show the prominence of the circular modes, rather than the diametral and the elevation ones. Moreover, the mean free path calculated using ray-tracing proves to be higher than the theoretical value commonly assumed for any kind of shape. The consequent longer reverberations compared to halls with other shapes and the same volume justify the significant support historically provided to sound signals by circular halls.

Analysis of Sound Field Distribution in Architecturally Diverse Temples

The results of the research, which aimed to analyze the acoustic properties of selected sacred buildings located in the city of Czestochowa, Poland are presented in the paper. Three architecturally unusual and completely different from each other churches were selected for the study. The churches differed in shape of their buildings, cubic volume, years of construction, interior furnishings, etc. Nine different objective parameters were used to describe the physical properties of acoustical field in the studied churches. Various factors characterizing the acoustic properties of each building were determined, such as the distribution of sound pressure level (SPL), reverberation time T30, definition D50. Next, they were thoroughly analyzed, so as to ultimately obtain distributions of individual acoustic parameters in the space of the tested building. It allowed to evaluate the quality of the received verbal or musical message depending on the place where the listener was. Further research on speech intelligibility and the musical quality of churches was performed by determining the averaged values of next four objective acoustic parameters: centre time Ts, speech clarity C50, music clarity C80, and speech transmission index (STI). A new approach to analyzing the objective physical parameters describing the sound field was presented in Sec. 4. Mean free path length and critical distance were determined for the investigated acoustic fields in each church and they were associated with a general geometric factor characterizing the complexity of the room shape. The final part of the work presents a comparative analysis of the obtained results of acoustic quality tests of the temples, and thus their usefulness in terms achieving a maximum intelligibility of speech and music. The interesting similarities were found in the spatial distribution of individual acoustic parameters characterizing the distribution of the acoustic field in temples with completely different architecture.

The uncertainty of estimation of doses to the bone marrow from <sup>89,90</sup>Sr due to the variability of the chemical composition and bone density

Dosimetric modeling of radiation transport in skeletal bone tissues using computational phantoms provides the doses of internal exposure to active marrow. Computational phantoms of ICRP are created for reference people with anatomical and physiological characteristics typical of an average individual. The doses calculated with such phantoms will correspond to certain population-average values. Individual variability will introduce a stochastic component of uncertainty into the dose estimation. The objective of this study is to assess the influence of variability of chemical composition and bone density on the results of dosimetric modeling. The phantoms are represented by simple geometry figures filled with trabecular structures and bone marrow and covered with a cortical layer. Radiation transport was simulated using the Monte Carlo method. The dose factors to convert the radionuclide activity concentration to absorbed dose rates in active marrow were calculated assuming uniform radionuclide distribution in the volume of the trabecular and cortical bone. As a result of the numerical experiments, it has been shown that variations in chemical composition do not introduce an error of more than ± 4% into dosimetric modeling. The effect of bone density on active marrow dose formation depends on the size of a phantom. For computational phantoms with linear dimensions exceeding two electron free path lengths (~ 0.44 cm), variability of bone density within ± 3% leads to a similar relative uncertainty of the dose conversion factor. However, for smaller phantoms, bone density variability leads to uncertainties of 6% or 13% for a source deposited in the trabecular or cortical bone, respectively. The results obtained will be used to assess the uncertainty of bone marrow dosimetry, taking into account the uncertainty of all parameters including the variability of morphometric characteristics of bones, the variability of the active marrow distribution in skeletal sites, as well as the uncertainties introduced by model approximations.

On the probable interpretation of anticorrelation between the proton temperature and density in the solar wind

The anticorrelated distributions of temperature and density of protons are a well-known property of the solar wind. Nevertheless, it is unclear till now if they are formed by some kind of the universal physical mechanism? Unfortunately, a straightforward comparison of the characteristic relaxation times for the temperature and density, on the one hand, and pressure, on the other hand, encounters the problem of inapplicability of the hydrodynamical approach in the situation when the free-path length of the protons is considerably greater than the spatial scale of the structures under consideration. To resolve this problem, some kinds of the MHD turbulence—reducing the effective free paths—are usually assumed. In the present paper, we use an alternative approach based on the electrostatic (Langmuir) turbulence, described by the mathematical formalism of the spin-type Hamiltonians, which was actively discussed in the recent time in the literature on statistical physics. As follows from the corresponding calculations, formation of the anticorrelated distributions of temperature and density is a universal property of the strongly nonequilibrium plasmas governed by the spintype Hamiltonians when they gradually approach the thermodynamic equilibrium. So, just this phenomenon could be responsible for the anticorrelations observed in the solar wind.

Information transport and limits of optical imaging in the highly diffusive regime

Noninvasive imaging through the human body or dense fog at optical wavelengths requires the collection of highly scattered photons, which corrupt imaging information and restrict most diffuse imaging techniques to $<$ 10 transport mean free path (TMFP) lengths. An information theoretical analysis of numerical simulations including practical considerations shows imaging information exists at the single-photon detection limit beyond 200 TMFP lengths. Information can be enhanced through increasing the collection of light, optimizing detector placement, and resolving measurements in the space-time domain.

Research on propagation characteristic of Laguerre–Gaussian vortex beams with Far-field scattering Electric Monte Carlo method

A Far-field Scattering Electric field Monte Carlo (FSEMC) method is proposed to investigate the propagation and imaging characteristics of Laguerre–Gaussian Beams (LGB) with different Orbital Angular Momentum (OAM) in long-distance (relative to wavelength) scattering environment. As an extension of the Electric field Monte Carlo (EMC) method, the electric field transport mode is simulated to properly analyze the fading effect of scattering. The mean free path and total transmission length in the simulation are equivalent to the environment parameters of experiment. The beam transmission modes, intensity attenuation and effects on imaging quality through different turbidity media are analyzed. It is observed that vortex beams with different topological charges play a subtle role in transmission through turbid media, showing strong correlations with total transmission intensity, retention of ballistic light, and penetration depth. The experimental results fitting well with the FSEMC simulation results, validating the proposed method for far-field propagation characteristic of vortex beams in turbid media.

A practical approach to modelling railway vehicle interior acoustics

The aim of the current work is to propose a practical approach for modelling the interior acoustics of railway vehicles by investigating the spatial decay of sound within the vehicle and its relation to the reverberation time and absorption. Measurements are presented of the longitudinal distribution of sound level inside five railway vehicles as well as the corresponding reverberation times. Both quantities are determined using an omnidirectional sound source located near one end of the vehicle. The measured sound pressure level follows a roughly linear dependence with longitudinal distance and the rate of decay is found to follow a consistent trend over all five datasets when plotted against reverberation time. To interpret these results, three different modelling approaches are considered: ray tracing, Statistical Energy Analysis, and an analytical corridor model. Ray tracing models with a simple geometry resembling the interior of a railway carriage are used to explore the dependence of the spatial decay and reverberation time on the absorption and scattering coefficients of the surfaces. For high values of scattering coefficient, the reverberation time approaches the Sabine estimate but for low values of scattering coefficient it can be up to a factor of 2.5 greater than this estimate. This implies difficulties in deducing the average absorption coefficients from the measured reverberation times. The spatial decay rates obtained from the ray tracing model do not have the same consistent dependence on reverberation time as the measured results, although the results for low values of scattering coefficient are closer to the measured trend than those for higher values. Investigation of the Statistical Energy Analysis approach shows that it predicts a spatial decay rate that depends explicitly on length of the subsystems used in the model; consequently, the results do not converge as the model is refined. It is possible to use modified coupling loss factors based on an analytical corridor model to give a better approximation to the spatial decay. This corridor model is shown to give results that are consistent with the measurements if the average absorption is obtained from the reverberation time using a modified formula for the mean free path length, and if the cross-section area is reduced to allow for the blocking effect of the seats. This provides a practical way forward for using SEA for the interior sound in railway vehicles.

Superballistic boundary conductance and hydrodynamic transport in microstructures

It is shown that the ideal boundary between a perfectly conducting electrode and electron liquid state acts as a contact whose conductance per unit area is higher than the fundamental Sharvin conductance by a numerical coefficient $2\ensuremath{\alpha}$, where $\ensuremath{\alpha}$ is slightly smaller than unity and depends on the dimensionality of the system. If the boundary has a finite curvature, an additional correction to the boundary conductance appears, which is parametrically small as a product of the curvature by the electron-electron mean free path length. The relation of the normal current density to the voltage between the electrode and electron liquid represents itself a hydrodynamic boundary condition for current-penetrable boundary. Calculations of the conductance and potential distribution in microstructures by means of numerical solution of the Boltzmann equation show that the concept of boundary conductance works very good when the hydrodynamic transport regime is reached. The superballistic transport, when the device conductance is higher than the Sharvin conductance, can be realized in Corbino disk devices not only in the hydrodynamic regime, although requires that the electron-electron scattering rate must be higher than the momentum-relaxing scattering rate. The theoretical results for Corbino disks are consistent with recent experimental findings.

Combined Raman Spectroscopy and Magneto-Transport Measurements in Disordered Graphene: Correlating Raman D Band and Weak Localization Features

Although previous studies have reported the Raman and weak localization properties of graphene separately, very few studies have examined the correlation between the Raman and weak localization characterizations of graphene. Here, we report a Raman spectroscopy and low-magnetic-field electronic transport study of graphene devices with a controlled amount of defects introduced into the graphene by exposure to electron-beam irradiation and oxygen plasma etching. The relationship between the defect correlation length (LD), calculated from the Raman “D” peak, and the characteristic scattering lengths, Lϕ, Li and L*, computed from the weak localization effects measured in magneto-transport was investigated. Furthermore, the effect on the mean free path length due to the increasing amounts of irradiation incident on the graphene device was examined. Both parameters—including LD and Lϕ—decreased with the increase of irradiation, which was shown to be related to the increase of disorder through the concomitant decrease in the mean free path length, l. Although these are similar trends that have been observed separately in previous reports, this work revealed a novel nonlinear relationship between LD and Lϕ, particularly at lower levels of disorder. These findings are valuable for understanding the correlation between disorder in graphene and the phase coherence and scattering lengths of its charge carriers.

Particle sizing in non-dilute dispersions using diffusing wave spectroscopy with multiple optical path lengths

Non-dilute dispersed phase systems, such as foams, emulsions, and suspensions, are an important class of final formulations and chemical process intermediates in a variety of industries. The utility of these systems hinges on their stability over the lifetime of use, and therefore an accurate assessment of chemical and physical dynamics, asformulated, is required. We describe a unified treatment of diffusing wave spectroscopy (DWS) data using a range of optical path length with a goniometric instrument. DWS correlation data from multiple angles and robust Monte Carlo simulations are used to determine accurate values of the photon transport mean free path length. The variance on each correlation function is used to determine the physical time range that the mean squared displacement can be analyzed. Using standard solid particle suspensions of polystyrene and SiO2, we determine the average particle size with accuracy comparable to dynamic light scattering.

New Polarimetric Data for the Galilean Satellites: Europa Observations and Modeling

This paper is dedicated to a long-standing problem of the shape of the negative branch of polarization (NBP) for Jupiter's moon Europa, determination of which is crucial for the characterization of the icy regolith on this satellite and similar objects, as well as for further progress in understanding light scattering by particulate surfaces. To establish the shape of Europa's NBP, in 2018–2021 we accomplished high-precision disk-integrated polarimetry of Europa in the UBVR I bands using the identical two-channel photoelectric polarimeters mounted on the 2.6 m Shajn reflector of the Crimean Astrophysical Observatory and the 2 m telescope of the Peak Terskol Observatory. We found that the polarization dependence on the phase angle in each filter is an asymmetric curve with a sharp polarization minimum at phase angle , after which the polarization degree gradually increases to positive values, passing the inversion angle at α inv ≈ 6° − 7°. Within the error limits, the parameters P min, , and α inv of the NPB are independent of the wavelength in the visible spectrum. The polarization curve clearly demonstrates the so-called polarization opposition effect (POE). Our analysis of the previous and new polarimetric observations of Europa allows us to conclude that the POE is caused by coherent backscattering of sunlight on microscopic icy grains covering Europa’s surface. Computer modeling with the numerical radiative transfer coherent backscattering method demonstrates that the best fit to the polarimetric observations and geometric albedo of Europa is provided by a regolith layer of elementary single-scattering albedo ∼0.985 and extinction mean free path length 2π l/λ eff ≈ 150, λ eff representing the effective wavelength in the UBVR I spectral bands.