Revisiting the normalized Born approximation: effects of scattering

The normalized Born approximation has been suggested as a ratiometric method in fluorescence molecular tomography (FMT) applications, to account for heterogeneity variations. The method enabled practical inversions, as it offered fluorescence reconstruction accuracy over a wide range of absorption heterogeneity, while also accounting for unknown experimental factors, such as the various system gains and losses. Yet it was noted that scattering variations affect the robustness and accuracy. Herein we decompose the effects of absorption and scattering and capitalize on the recent development of hybrid FMT/x-ray computed tomography imaging methods to proposed amendments to the method, which improve the overall accuracy of the approach.     

Nonlinear scatterers in nonlinear media: Born approximation and local perturbation method

Wave scattering by inhomogeneous nonlinear particles placed in a nonlinear host medium is studied. In the case of weak scattering the scattering indicatrix is calculated in the first Born approximation. Scattering from small nonlinear particles loaded in a medium with saturation of permittivity is studied by the local perturbation method. A small perturbation method is developed for nonlinear equations of rather general type with a random, intensity-dependent, scattering potential.     

Nonlinear scatterers in nonlinear media: Born approximation and local perturbation method

Abstract

Wave scattering by inhomogeneous nonlinear particles placed in a nonlinear host medium is studied. In the case of weak scattering the scattering indicatrix is calculated in the first Born approximation. Scattering from small nonlinear particles loaded in a medium with saturation of permittivity is studied by the local perturbation method. A small perturbation method is developed for nonlinear equations of rather general type with a random, intensity-dependent, scattering potential.     

Estimating optical properties in layered tissues by use of the Born approximation of the radiative transport equation

We use the Born approximation of the radiative transport equation to recover simultaneously the absorption and scattering coefficients in a single layer of a two-layer tissue sample from reflectance data. This method reduces the estimation of both optical properties to a single linear, least-squares problem. It is valid over length scales smaller than a transport mean free path and hence is useful for epithelial tissue layers. We demonstrate the accuracy of this method by using spatially resolved reflectance data computed with Monte Carlo simulations.     

On the unitarization of the Born approximation

A new approximation for the elastic scattering transition matrix is suggested. This approximation satisfies the unitarity condition. A modified Born series is introduced which has this unitarized Born approximation as the leading term. The series is applied to the solvable case of scattering by a separable potential and is found to converge in a wider region of energies than that of the conventional Born series.     

Multielectron ionization of atoms by fast ions: An approximation by normalized exponentials

Multielectron ionization of neutral atoms by fast positive ions is considered in terms of the independent particle model. A relatively simple technique for calculating the multielectron ionization probabilities and cross sections through the impact parameter is suggested in which one-electron ionization probabilities are represented as normalized exponentials p _nl(b) = p _nl(b) = p _nl(0)exp(?α_nl b), where b is the impact parameter and n and l are quantum numbers of the target atomic shell. Exponent α_nl is determined from the Born one-electron ionization cross section for target atoms, and preexponential p _nl(0) (the ionization probability at a zero impact parameter) is found from a geometrical model. This technique provides the normalization condition p _nl(b) ≤ 1 irrespective of the velocity and charge of striking ions and makes it possible to calculate the one-, two-, and three-electron ionization cross sections, which, when added up, make a major contribution to the total cross section, up to a factor of 2. The results of our computations are compared with experimental data and analytical results of other authors.     

Experimental validation for time-domain fluorescence diffuse optical tomography of linear scheme

We present a full three-dimensional, featured-data algorithm for time-domain fluorescence diffuse optical tomography that inverts the Laplace-transformed time-domain coupled diffusion equations and employs a pair of appropriate transform-factors to effectively separate the fluorescent yield and lifetime parameters. By use of a time-correlation single-photon counting system and the normalized Born formulation, we ex-perimentally validate that the proposed scheme can achieve simultaneous reconstruction of the fluorescent yield and lifetime distributions with a reasonable accuracy.     

Polynomial approximation method for tomographic reconstruction of three-dimensional refractive index fields with limited data

We propose a polynomial approximation method (PAM) for reconstruction of three-dimensional refractive index fields by interferometric tomography using limited data. Based on the assumption that the fields to be reconstructed are usually smooth and can be decomposed into a finite order of (orthogonal) polynomials, a set of linear equations can be constructed using both the measured projection data and the Radon transform of the basis functions. By solving these equations, the least-squares solutions of expansion coefficients can be obtained and then substituted back to yield the desired fields. Numerical results have demonstrated that the proposed method is fast, robust to noise and can achieve satisfactory results for refractive index fields with limited projection views and large opaque objects.     

Experimental reconstruction of nonlocal response of thermal nonlinear optical media

We study experimentally and theoretically the nonlocal response of a medium with thermal nonlinearity and show that despite its inherently infinite range it can be accurately characterized by a well-defined nonlocal response function. We retrieve the shape of this function and analyze its transformation with the change of boundaries.     

Quantification of fluorescent molecules in heterogeneous media by use of the fluorescence decay amplitude analysis

In heterogeneous media, including biological objects, fluorescent molecules of one kind often exist as a mixture of species with different fluorescence parameters. Fractional concentrations of these species can be measured by analyzing their fluorescence decay amplitudes. The amplitudes are linear functions of concentrations of actually fluorescent molecules, i.e., molecules whose fluorescence decay can be measured. Other (quenched) molecules do not influence these amplitudes. The other parameter that has to be measured to calculate these concentrations is the radiative rate constant. The parameter can be excluded by comparison of decay amplitudes of the sample studied and a standard. The comparison should be made taking into account the dependence of the radiation rates on emision wavelength. The method has been tested in experiments with the fluorescent probe 3-methoxybenzanthrone (MBA) bound with phosphatidylcholine bilayer membranes. The probe has a complex fluorescence decay in these membranes. The decay can be described as two exponentials, with decay times of 2 and 12 ns and a blue-shifted fluorescence spectrum of the short-life component as compared with long-life one. The shift was used to correct calculated radiative rate values. After this, about 100% of the MBA molecules were found to be fluorescent in these membranes. Thus, this approach can be used to measure absolute concentrations of subpopulations of fluorescent molecules in heterogeneous biological objects.     

Inversion of synthetic and experimental acoustical scattering data for the comparison of two reconstruction methods employing the Born approximation

This work is concerned with the reconstruction, from measured (synthetic or real) data, of a 2D penetrable fluid-like object of arbitrary cross-section embedded in a fluid of infinite extent and insonified by a plane acoustic wave. Green's theorem is used to provide a domain integral representation of the scattered field. The introduction therein of the Born approximation gives rise to a linearized form of the inverse problem. The actual inversion is carried out by two methods. The first diffraction tomography (DT), exhibits the contrast function very conveniently and explicitly in the form of a wave number/incident angle Fourier transform of the far backscattered field and thus requires measurements of this field for incident waves all around the object and at all frequencies. The second discretized domain integral equation with Born approximation method, is numerically more intensive, but enables a wider choice of configurations and requires less measurements (one or several frequencies, one or several incident waves, choice of measurement points) than the DT method. A comparison of the two methods is carried out by inversion of both simulated and experimental scattered field data.     

Dynamics of Rabi model under second-order Born Oppenheimer approximation

We apply the second-order Born–Oppenheimer(BO)approximation to investigate the dynamics of the Rabi model,which describes the interaction between a two-level system and a single bosonic mode beyond the rotating wave approximation.By comparing with the numerical results,we find that our approach works well when the frequency of the two-level system is much smaller than that of the bosonic mode.     

The second Born approximation in electron-helium scattering in a Nd-YAG laser field

The dynamics of laser-assisted elastic collisions in helium is studied using the second-order Born approximation. Detailed calculations of the scattering amplitudes are performed by using the Sturmian basis expansion. Differential cross sections for elastic scattering with the net absorption/emission of up to two photons are calculated for collision energies of 5 eV, 10 eV, and 20 eV. We discuss the influence of the low-energy electrons on the differential cross section (DCS) as a function of the scattering angle for selected choices of the laser frequency and the number of photons exchanged between the external field and electron-helium system.     

Elastic scattering of electrons by helium atoms in high energy higher order Born approximation

The differential cross-sections forē-helium elastic scattering are calculated by using Yateshigh-energy higher order Born approximations, through 0 (K _i ^{Emphasis>−2} ) of the incident electron momentum, and comparisons have been made with the recent theoretical and experimental results.     

共面双对称条件下电子碰撞Ar原子单电离的一阶扭曲波Born近似

在共面双对称几何条件下,利用一阶扭曲波Born近似计算了中低能电子碰撞Ar原子(3p壳层电子)单电离的三重微分截面,并与最近的实验数据做了比较.结果表明,对于Ar原子,当入射电子能量比电离阈高40 eV以上,随着入射能量的增加,binary和recoil碰撞机理逐渐占据支配地位;在近阈能量范围,上述碰撞机理不再处于支配地位,扭曲效应明显.要完备地描述中低能入射条件下Ar原子的电子碰撞电离过程,理论模型必须同时考虑多种散射机理.     

The second Born approximation of electron–argon elastic scattering in a bichromatic laser field

We study the elastic scattering of atomic argon by electron in the presence of a bichromatic laser field in the second Born approximation. The target atom is approximated by a simple screening potential and the continuum states of the impinging and emitting electrons are described as Volkov states. We evaluate the S-matrix elements numerically. The dependence of differential cross-section on the relative phase between the two laser components is presented. The results obtained in the first and second Born approximations are compared and analysed.     

Higher-order modified Born approximation for potential scattering in the presence of a strong magnetic field

Summary The total cross-section for potential scattering in the presence of a strong magnetic field presents singularities and exhibits giant growth (cyclotron resonances) at values of the incident particle energy exactly matching the differences between the initial-and final-state Landau levels. In this paper (in cylindrical coordinates) a higher-order modified Born series has been derived that can be summed at all orders giving a nondivergent total cross-section at the Landau thresholds.     

A rigorous criterion to identify the validity of the Born approximation

This paper intends to identify the validity of the orn approximation by a new universal criterion, which is ultimately reduced to the calculation of an operator norm. With the purpose of enabling the criterion to be applicable to general scattering problems, a method is proposed to estimate the norm of the operator concerned. Compared with the conventional criterion, this method excels in its ability to acquire a quantificational upper bound of the relative error by Born approximation as well as to extend its valid frequency to a wider range. Two canonical scattering examples are given as evidence for the validity of the criterion.     

Breakup of light nuclei within the modified distorted wave Born approximation

Reactions of the elastic breakup of loosely bound light nuclei are investigated in the scope of the distorted wave Born approximation, with deuterium breakup reactions used as an example. Some drawbacks of this approximation in calculating the breakup amplitude in the prior form are shown and their causes analyzed. We propose eliminating the drawbacks by employing a modified nucleus-nucleus potential in calculating the distorted wave functions of scattering in the exit reaction channel. The calculations are compared to the experimental data.     

Effect of distortion in electron impact excitation in Coulomb-projected Born approximation

We have calculated total and differential cross-sections for 1s →ns (n = 2, 3, 4) electron impact excitation of hydrogen and hydrogenic ions at various energies in Coulomb-projected Born approximation. Distortion due to static interactions, target polarization and exchange effects has been incorporated in the initial channel. The present calculations have been compared with other theoretical and experimental results.