Extinction Length Research Articles

The average transmitted wave in random particulate materials

Microwave remote sensing is significantly altered when passing through clouds or dense ice. This phenomenon is not unique to microwaves; for instance, ultrasound is also disrupted when traversing through heterogeneous tissues. Understanding the average transmission in particle-filled environments is central to improve data extraction or even to create materials that can selectively block or absorb certain wave frequencies. Most methods that calculate the average transmitted field assume that it satisfies a wave equation with a complex effective wavenumber. However, recent theoretical work has predicted more than one effective wave propagating even in a material which is statistically isotropic and for scalar waves. In this work we provide the first clear evidence of these predicted multiple effective waves by using high-fidelity Monte-Carlo simulations that do not make any statistical assumptions. To achieve this, it was necessary to fill in a missing link in the theory for particulate materials: we prove that the incident wave does not propagate within the material, which is usually taken as an assumption called the Ewald–Oseen extinction theorem. By proving this we conclude that the extinction length—the distance it takes for the incident wave to be extinct—is equal to the correlation length between the particles.

The respective and dependent effects of scattering and bone matrix absorption on ultrasound attenuation in cortical bone

Cortical bone is characterized by a dense solid matrix permeated by fluid-filled pores. Ultrasound scattering has potential for the non-invasive evaluation of changes in bone porosity. However, there is an incomplete understanding of the impact of ultrasonic absorption in the solid matrix on ultrasound scattering. In this study, maps were derived from scanning acoustic microscopy images of human femur cross-sections. Finite-difference time domain ultrasound scatter simulations were conducted on these maps. Pore density, diameter distribution of the pores, and nominal absorption values in the solid and fluid matrices were controlled. Ultrasound pulses with a central frequency of 8.2 MHz were propagated, both in through-transmission and backscattering configurations. From these data, the scattering, bone matrix absorption, and attenuation extinction lengths were calculated. The results demonstrated that as absorption in the solid matrix was varied, the scattering, absorption, and attenuation extinction lengths were significantly impacted. It was shown that for lower values of absorption in the solid matrix (less than 2 dB mm−1), attenuation due to scattering dominates, whereas at higher values of absorption (more than 2 dB mm−1), attenuation due to absorption dominates. This will impact how ultrasound attenuation and scattering parameters can be used to extract quantitative information on bone microstructure.

Competing effects of ultrasound absorption and scattering in porous bone

The mechanisms and effects of ultrasonic attenuation in porous cortical bone are poorly understood, and it is necessary to better understand them to evaluate bone porosity noninvasively using ultrasound. A finite-difference time domain numerical study was conducted in which ultrasound propagation was simulated in human femur cross-sections obtained via scanning acoustic microscopy. The effect of absorption on overall attenuation was studied by varying the nominal absorption level attributed to the solid matrix. Ultrasound pulses were emitted with a central frequency of 8 MHz in through-transmission and backscattering configurations. From these data, the respective extinctions lengths due to overall attenuation, scattering, and absorption were obtained. Two regimes seem to exist depending on the nominal absorption value. At low absorption values, scattering dominates overall attenuation, scattering and absorption appear to have a synergistic effect on overall attenuation, and the diffusion constant decreases with increasing average pore diameter. At high absorption values, absorption dominates overall attenuation, the extinction length for scattering increases with pore diameter, and the diffusion constant increases with increasing average pore diameter. These regimes affect how ultrasound parameters, such as the extinction lengths due to scattering, absorption, and overall attenuation, should be used to evaluate the porosity of cortical bone.

Dynamical and kinematical X-ray diffraction in a bent crystal

Numerical modeling of kinematical and dynamical X-ray diffraction in a bent crystal was performed on the basis of two approaches to integrating the Takagi–Taupin equations, and using two-dimensional recurrence relations. Within the framework of kinematical diffraction, a new equation is obtained that describes the distribution of diffracted intensity inside a bent crystal. The time taken for numerical calculations based on this equation is significantly reduced in comparison with the use of algorithms of the dynamical diffraction theory. The simulation shows for the first time that, for strongly bent crystals, the maximum value of the diffraction intensity is formed inside the deformed structure and not on its surface. In the case of strong bending of the crystal structure, the deviation of the X-ray beam from the Bragg angle does not change the diffraction pattern but shifts it along the lateral direction. The results of calculations of diffraction in a strongly bent crystal based on the equations of dynamical and kinematical diffraction coincide, while the computations for weakly bent crystals differ. The possibility of estimating the primary extinction length of a bent crystal as a function of the bending radius is shown. In the case of kinematical diffraction in bent crystalline microsystems, a new method has been developed to calculate X-ray reciprocal-space mapping.

Investigation of ultrasound propagation through dense glass bead packings immersed in water

Conventional ultrasound imaging generally relies on a single scattering assumption and a constant sound hypothesis. However, in dense granular sediments where the glass beads diameter is comparable to the wavelength (typically 500 μm), both hypothesizes are no longer valid, resulting in a loss of resolution and contrast, up to the situation where a target to image could totally vanish in the fog. To better characterize this strongly scattering medium, we have conducted several ultrasonic experiments in reflection and in transmission, either on the diffused wave or on the coherent one. Both the transport and scattering mean free paths are estimated in the imaging bandwidth (1–5 MHz), alongside with the phase velocity and extinction length of the coherent wave. These results are compared with an analytical model, i.e. Generalized Coherent Potential Approximation*, which considers a coated sphere buried in an effective medium. Finally, we show a dispersive beamformer which takes into account the measured phase and group velocity. This allows us to obtain a more resolved and contrasted image in such a scattering medium. * Jing X, Sheng P, Zhou M. Phys Rev Lett. 1991

The effects of nominal absorption in bone on the extinction lengths for scattering, absorption, and overall attenuation

In cortical bone, the effect of absorption in the solid matrix on ultrasound scattering and propagation is not well understood, and for absorption, it is not easily incorporated into simulations and is difficult to measure independently from scattering attenuation. In this study, finite-difference time-domain simulations were conducted in maps derived from scanning acoustic microscopy images of human femur cross-sections. These maps were modified by controlling pore density (fixed at 10 pores/mm2) and diameter distribution (ranging between 30 and 100 μm). Eight nominal absorption values, ranging from 0 to 100 dB/cm, were attributed to the solid matrix. Absorption in the pores was set to 0.01 dB/cm. Propagation of ultrasound pulses centered at 8 MHz was simulated in both backscattering and through-transmission configurations. The scattering, absorption, and overall attenuation extinction lengths were obtained. T-tests demonstrated that varying the absorption significantly impacts the extinction lengths for scattering, overall attenuation, and absorption. The differences in values for the scattering, attenuation, and absorption extinction lengths when absorption varied from 20 to 40 dB/cm are statistically significant (respective p-values: 9.1 × 10−14, 3.3 × 10−5, and 8.8 × 10−5). It was also demonstrated that attenuation due to scattering dominates overall attenuation at low-nominal absorption values, whereas the converse is true at higher absorption values.

X-ray third-order nonlinear asymmetric diffraction in the transmission geometry

For high intensity x-ray sources, the investigations of the nonlinear x-ray effects become essential. The x-ray third-order nonlinear asymmetric transmission case dynamical diffraction is investigated theoretically in perfect crystals. The three essential input parameters are taken into account: the deviation from the Bragg exact orientation, the asymmetry angle of reflecting atomic planes and the intensity of incident wave. The third-order nonlinear equations for the asymmetrical dynamical diffraction and two integrals of motion are presented. The exact solutions for the wave amplitudes, presented via Jacobi elliptic functions, have been found. The solutions are periodic functions of the depth. It is shown that the behavior of the waves inside the crystal is determined by the sign of a combined parameter, which includes the three input parameters, mentioned above. The regions, where this parameter is positive, negative or zero, are found. For positive values, the energy is concentrated both in the transmitted and diffracted waves while for the negative values, the energy is concentrated mainly in the transmitted beam. It is found that when this combined parameter is zero, the amplitudes are elementary periodic or non-periodic functions. For the periodic solutions, the nonlinear Pendellösung effect takes place, i.e. the transmitted and diffracted waves periodically exchange with their energies. For the period, called an extinction length, an exact expression is found. It is shown that for large values of the asymmetry factor, the observation of the nonlinear diffraction effects can be realized for sufficiently low intensities of the incident wave. The obtained results can be used for experimental investigation of the nonlinear Bragg diffraction and for preparation of high intensity x-ray beams with given parameters. The expression for the nonlinear extinction length allows to estimate the third-order nonlinear susceptibilities of crystals by measuring the extinction length in experiments.

Fast Near-Surface Changes in the Defect Structure in Lithium Tetraborate Crystals in an External Electric Field

The changes in the defect structure in the near-surface layers of lithium tetraborate (Li2B4O7) single crystals under the influence of an external electric field applied along the polar direction [001] have been studied. Using the X-ray diffractometry with 2 ms time resolution the dynamics of the 004 and 008 diffraction peak parameters (the angular position and the integral intensity) variation was determined. Two types of processes caused by the redistribution of the charge localized at the surface of the polar dielectric and by the migration of lithium ions have been observed with different velocity and response time to the external field switching. The measurements are carried out at voltages at which the induced effects have reversible characters. The use of two orders of diffraction with different X-ray extinction lengths made it possible to visualize space charge layers near the anode and cathode by the intensity variation of the diffraction peaks. The estimation of the effective thickness of the charged near-surface layer gives the value of 25 μm for lithium ions at the cathode and about 45 μm for lithium vacancies at the anode.

Multi-Parameter Optimization of an InP Electro-Optic Modulator

In this article, a method for indium phosphide (InP) electro-optic modulator (EOM) optimization is introduced. The method can be used for the design and analysis of an EOM based on the Mach-Zehnder interferometer (MZI) design. This design is based on the division of the input optical signal into two optical paths and then, after processing, it combines the light into a single waveguide. The symmetry of the structure can provide state-of-the-art EOM characteristics with a push-pull control signal. Using a traveling wave electrode (TWE) design as a starting point, the authors varied the heterostructure design and optical waveguide parameters to obtain the optimal values of initial optical loss, evenness of the initial optical loss in the operating wavelength range, and the extinction ratio and length of the modulator arm. The key features of the proposed optimization method include the following: all independent input parameters are linked into a single system, where the relationship between the electrical and optical parameters of the modulator is realized; all physically realizable combinations of the input parameters are available for analysis; and EOM optimization is possible for one target parameter or for a group of target parameters. The results of the EOM optimization using the described method are presented.

Diffracted Transitive Radiation as a Means for Indicating the Divergence of an Ultrarelativistic Electron Beam

Diffracted transition radiation (DTR) emitted by a beam of relativistic electrons traversing a thin single-crystal plate in the Laue scattering geometry is considered. An expression has been obtained describing the angular DTR density when the electron path length in a target is far less than the extinction length of x-rays in the crystal. It is shown that in this case, the DTR process has a clearly pronounced kinematic character. Numerical calculations of the DTR photon yield in the direction of Bragg’s scattering performed for different solid angles of recording show that it is significantly affected by the electron beam divergence. We have concluded that the DTR photon yield measured for a given solid angle can be used for indicating the electron beam divergence. Results of model calculations of the electron beam divergence parameters for a given yield of DTR photons traversing the slit collimator have shown that the formula proposed in this work can be successfully used as a basis for the development of methods for measuring the divergence of ultrahigh-energy relativistic electron beams based on the angular DTR distribution.

A study on the limit of application of kinematical theory of X-ray diffraction

Abstract In this work, the limit of application of the kinematical theory of X-ray diffraction was calculate integrated intensities was evaluated as a function of perfect crystal thickness, when compared with the Ewald–Laue dynamical theory. The percentual difference between the dynamical and kinematical integrated intensities was calculated as a function of unit cell volume, Bragg angle, wavelength, module, and phase of structure factor and linear absorption coefficient. A critical thickness was defined to be the value for which the intensities differ 5%. We show that this critical thickness is 13.7% of the extinction length, which a specific combination of the parameters mentioned before. Also, we find a general expression, for any percentage of the difference between both theories, to determine the validity of the application of the kinematical theory. Finally, we also showed that the linear absorption decreases this critical thickness.

Penetration depth of an electric field in a semi-infinite classical plasma

It is shown that the penetration of an oscillating electric field in a semi-infinite classical plasma obeys the standard exponential attenuation law e−x/λe (besides oscillations), where x is the distance from the wall and λe is the extinction length (penetration depth, attenuation length). This solves the problem of various approximations and semi-empirical models of the surface sheath. The penetration depth λe is computed here explicitly; it is shown that it is of the order λe≃[∣ε∣/(1−ε)]1/3vth/ω, where ε is the dielectric function, ω is the frequency of the field and vth=T/m is the thermal velocity (T being the temperature and m the particle (electron) mass). The result is obtained by including explicitly the contribution of the surface term in the (linearized) Boltzmann (Vlasov) equation for the semi-infinite plasma. A key point in solving the problem is the observation that there exists a uniform (oscillating in time) component of the response electric field, besides the spatially decaying and oscillating component.

A Sample of Edge-on H i-rich Low Surface Brightness Galaxy Candidates in the 40% ALFALFA Catalog

Low-surface-brightness galaxies(LSBGs) are defined as galaxies that are fainter than dark night sky and are important for studying our universe. Particularly, edge-on galaxies are useful for the study of rotational velocity and dynamical properties of galaxies. Hence here we focus on searching for edge-on LSBGs. In order to find these edge-on dim galaxies, a series of effects caused by inclination, including the surface brightness profile, internal extinction, and scale length, have been corrected. In this work, we present a catalog of 281 edge-on LSBG candidates, which are selected from the cross-match between SDSS DR7 and the 40% ALFALFA catalog. We also present the properties of these edge-on LSBG candidates including absolute magnitude, central surface brightness, B-V color, scale length, and relative thickness. Our result suggests that the correction of inclination effects is very important for obtaining a complete sample of LSBGs.

On the problem of application of diffracted transition radiation for indication of relativistic electron beam parameters

The diffracted transition radiation (DTR) produced by a beam of relativistic electrons traversing a thin single-crystal plate in the Laue scattering geometry is considered. We have obtained the expression describing the angular density of the DTR for the case when the path length of the electron in the target is far less than the extinction length of X-rays in the crystal. It is shown that in this case the considered DTR process has the explicit kinematic character. The numerical calculations of the yield of DTR photons in the direction of Bragg scattering performed for various values of the registration solid angle show a significant influence of the electron beam divergence on the photon yield. We have arrived at a conclusion that the measured photon output of DTR radiation emitted in a given solid angle can be used for indication of the electron beam divergence. The model calculations of the electron beam divergence parameters on the base of “measured” yield of DTR photons traversing through a slit collimator are carried out. The results of the calculation show that the proposed in this work formula can be successfully used as a base for the development of methods for measuring the divergence of beams of relativistic ultrahigh-energy electrons based on DTR angular distribution.

Intrinsic and scattering seismic wave attenuation in the Central Apennines (Italy)

Recently, an earthquake sequence formed by a series of subsequences characterized by large earthquakes (three events M ≥ 6.0 and five events M ≥ 5.0) occurred in the Central Apennines in 6–7 months during 2016–2017. Several studies interpreted this cascading type of earthquake occurrence as associated with fluid movements through an interconnected network of cracks around the active faults that triggered the subsequences in different time and location.In the present study we aim to verify if the presence of fluids is confirmed by the pattern of seismic wave attenuation. To do so we separately estimate the space-averaged parameters intrinsic Qi−1 and scattering Qs−1, proportional to the correspondent attenuation parameters, by applying a modified Multiple Lapse Time Window Analysis (MLTWA), in order to establish reference background values for the study region. MLTWA measures the decay of S-wave energy with distance and lapse time and fit it to the Energy Transport Equation solution for scattering, yielding the seismic albedo, B0 = Qs−1/Qt−1 and the extinction Length, Le,∝Qt−1 parameters as a function of frequency. The knowledge of the separated attenuation parameters allows determining which process of seismic energy dissipation dominates in the region.In the present study B0 results to be around0.6 (at 1.5 Hz) and decreases with increasing frequency down to 0.2 indicating that the attenuation of the seismic energy carried by S-wave is controlled by intrinsic dissipation rather than by scattering. Moreover, the intrinsic attenuation is frequency dependent (f−0.9 for the uniform model and f−0.4 for the crust/Moho model). This behavior well matches with the presence of fluids in the faults and fracture zones in the central Apennines, in agreement with results from other independent studies in the region.Finally, a comparison among the attenuation parameters estimated for this area and those measured in several areas of Italy and other parts of the world is presented together with a discussion on the comparison between the present MLTWA attenuation estimates and homologous results obtained for the same area with different approaches.

X-ray diffraction from strongly bent crystals and spectroscopy of X-ray free-electron laser pulses.

The use of strongly bent crystals in spectrometers for pulses of a hard X-ray free-electron laser is explored theoretically. Diffraction is calculated in both dynamical and kinematical theories. It is shown that diffraction can be treated kinematically when the bending radius is small compared with the critical radius given by the ratio of the Bragg-case extinction length for the actual reflection to the Darwin width of this reflection. As a result, the spectral resolution is limited by the crystal thickness, rather than the extinction length, and can become better than the resolution of a planar dynamically diffracting crystal. As an example, it is demonstrated that spectra of the 12 keV pulses can be resolved in the 440 reflection from a 20 µm-thick diamond crystal bent to a radius of 10 cm.

Быстрые приповерхностные изменения дефектной структуры в кристаллах тетрабората лития во внешнем электрическом поле

The results of study of the defect structure variation process in the near-surface layers of lithium tetraborate (Li2B4O7) single crystals under the influence of an external electric field applied along the [001] polar direction are presented. Using the X-ray diffractometry with 2 ms time resolution the dynamics of the 004 and 008 diffraction peak parameters (angular position and integral intensity) variation was determined. Two types of processes caused by redistribution of the charge localized at the surface of the polar dielectric and the migration of lithium ions were revealed with different velocity and response time to the external field switching. The measurements were carried out at voltages providing a reversible character of induced effects. The use of two orders of diffraction with different X-ray extinction length made it possible to visualize space charge layers near the anode and cathode by the intensity variation of the diffraction peaks. Estimation of the effective thickness of the charged surface layer gives a value of 25 μm for lithium ions at the cathode and about 45 μm for lithium vacancies at the anode.

Modeling of full-field optical coherence tomography in scattering media.

We develop a model of full-field optical coherence tomography (FF-OCT) that includes a description of partial temporal and spatial coherence, together with a mean-field scattering theory going beyond the Born approximation. Based on explicit expressions of the FF-OCT signal, we discuss essential features of FF-OCT imaging, such as the influence of partial coherence on the optical transfer function, and on the decay of the signal with depth. We derive the conditions under which the spatially averaged signal exhibits a pure exponential decay, providing a clear frame for the use of the Beer-Lambert law for quantitative measurements of the extinction length in scattering media.

Output coupling from x-ray free-electron laser cavities with intracavity beam splitters

Permeable mirrors are typically used for coupling photons out of laser cavities. A similar approach was proposed for output coupling photons from the cavities of x-ray free-electron laser (XFEL) oscillators. One of the Bragg-reflecting crystal mirrors is thin, just a few extinction length, and is used as a permeable mirror. However, this method is very often limited to extractions of only a few tenths of the intracavity power. Other cavity-based XFELs, such as the high-gain regenerative amplifier XFEL, require much higher outcoupling efficiency. Here, alternative schemes are proposed and analyzed for coupling x-ray photons out of XFEL cavities using intracavity Bragg-reflecting, x-ray-transparent diamond crystal beam splitters. The intracavity beam splitters are efficient and flexible in terms of the amount of the power they are capable of coupling out of the cavity, an amount that can be varied promptly from zero to close to 100%. The schemes can be readily extended to multi-beam outcoupling.

Dust concentration estimation of underground working face based on dark channel prior

In this paper, combined with video monitoring system for each working face under the mine, distance measurement system under the mine and Matlab software, real-time monitoring, analysis and calculation of dust concentration under the mine are carried out. Firstly, the image of dust degradation was obtained according to the video monitoring system in the underground dust environment, and the transmission chart with block effect was obtained. Secondly, the obtained transmission figure is processed by Matlab to obtain the corresponding transmission of each pixel in the dust image. Then according to the dust dispersion measurement system to calculate the extinction coefficient, according to the distance measurement system measured the length of the radiation channel distance;Finally, according to the established dust image degradation model, the dust concentration change process and dust mass concentration at each moment and point can be obtained from the extinction coefficient, transmission rate and length of radiation channel. The research method in this paper is rapid and can be used for real-time and online continuous detection, so as to obtain the dust mass concentration and dust distribution in the dust environment.