Convergence of solutions to the rough-surface scattering problem

A new formulation of the rough-surface scattering problem is obtained that is closely linked to the Kirchhoff approximation. The governing equation is cast into a form amenable to solution by the method of successive approximations. The domain of convergence of this solution is established and is shown to apply also to the odd-ordered operator expansion, small-slope approximation and perturbation theory provided that the slope of the scattering surface is everywhere less than unity. The analysis is performed for scattering from one-dimensional pressure-release surfaces. Numerical examples are presented for sinusoidal and echelette gratings.     

Approximation of off-shell scattering operators for non-lorentzian line shape calculations

A previously derived approximation for the matrix elements of the Fano relaxation operator m(ω), which gives rise to non-Lorentzian line wings, is examined. This approximation is expressed in terms of an off-the-energy shell scattering operator. Calculation of this operator by a second-order Born expansion is unsuitable because this procedure limits the radiation frequency dependence to the same order. The main part of this paper is devoted to expressing the off-shell scattering operator in the time-ordered formalism. In this form, a scattering operator approximation suggested by Dillonet al.⁽⁶⁾ can be applied which is not restrictive to the frequency dependence.     

Convergence of solutions to the rough-surface scattering problem

Abstract

A new formulation of the rough-surface scattering problem is obtained that is closely linked to the Kirchhoff approximation. The governing equation is cast into a form amenable to solution by the method of successive approximations. The domain of convergence of this solution is established and is shown to apply also to the odd-ordered operator expansion, small-slope approximation and perturbation theory provided that the slope of the scattering surface is everywhere less than unity. The analysis is performed for scattering from one-dimensional pressure-release surfaces. Numerical examples are presented for sinusoidal and echelette gratings.     

Finite-difference approximation for inverse scattering problem

For the first time potentials are reconstructed in a finite-difference approximation using a genuine inverse scattering method instead of multiple repeated solutions of a direct problem with iterative fitting of scattering data. Up to now a fundamental difference between spectral properties of the Schrödinger operator and its discrete analog hindered from doing this.     

Wigner transform and the eikonal approximation for nonlocal potentials

The same approximation scheme which leads to the Thomas-Fermi theory in bound state problems is applied to scattering by a nonlocal potential. Based on the Wigner transform of the evolution operator, it gives in a very simple way the eikonal approximation for the scattering amplitude. As an application a generalized Fermi gas model for inclusive scattering from nuclei is derived.     

Inelastic electron scattering and the Brown-Green model for O (I). The even-partity states

A formalism for calculating matrix elements of the Coulomb operator in the first Born approximation from the Brown-Green states is developed. The form factors for inelastic electron scattering and other relevant quantities are calculated and compared with experimental results. A satisfactory agreement is found and it is concluded that especially the data from the excitation of the 2⁺ states provide strong support for the validity of the model.     

Modeling elastic wave forward propagation and reflection using the complex screen method.

Formulation for calculating forward propagation and reflection in a 3D elastic structure based on the complex-screen method is given in this paper. The calculation of reflections is formulated based on the local Born approximation. When using a small angle approximation, the backscattering operator reduces to a screen operator which is similar to the forward screen propagator. Combining the forward propagator and backscattering operator together, the new method can properly handle the multiple forward scattering and single backscattering in a 3D heterogeneous model. Using a dual-domain technique, the new method is highly efficient in CPU time and memory savings. For models where reverberation and resonance scattering can be neglected, this method provides a fast and accurate algorithm. Synthetic seismograms for two-dimensional elastic models are calculated with this method and compared with those generated by the finite-difference method. The results show that the method works well for small to medium scattering angles and medium velocity contrasts.     

Modeling of laser reflectance evolution during metalorganic vapor phase epitaxy growth of GaN using SiN treatment

We present the simulation of laser reflectance measurements performed during GaN growth by metalorganic vapor phase epitaxy (MOVPE). We used the scattering theory approximation to determine the root mean square (rms) surface roughness versus growth time. In the region of large roughness, the determined rms roughness exceeds the maximum value authorized by the Rayleigh criterion limiting the validity of the macroscopic roughness model. Another approach based on the effective medium approximation is used to simulate the entire reflectance signal evolution. An effective refractive index and growth rate profiles are determined.     

漫射近似在测量生物组织光学性质中的适用范围

漫射近似理论经常被用来作为测量生物组织光学特性参数实验和方法的理论基础,但是漫射近似理论只是一种对辐射传输理论的近似结果,在一定条件下有其特定的适用范围.为了确定漫射近似理论在活体非侵入式无损测量要求下的适用范围,本文采用Monte Carlo模拟校验的方法,对漫射近似理论和Monte Carlo模拟计算的结果进行了比较,给出了基于单散射反照率a和各向异性因子g的漫射近似理论适用范围数值标准.这一标准为漫射理论的应用提供了参考依据.     

A non-singular equation for the three-body scattering problem

This paper derives a non-singular integral equation for the three-body problem. Starting from the three-body equations obtained by Karlsson and Zeiger we introduce a set of algebraic transformations that remove all the Green function pole singularities. For scattering energies on the real axis we find a singularity-free momentum-space integral equation. This equation requires only a finite range of momentum values for its solution. In the case of well-behaved two-body interactions, such as the superposition of Yukawa interactions, we prove that the kernels of this equation have a finite Hilbert-Schmidt norm. This same norm provides a general criteria for establishing when the impulse approximation is accurate.     

Unitarity and the BFKL pomeron

High energy onium-onium scattering is calculated as a function of impact parameter in the one- and two-pomeron exchange approximation. Difficulties with using the multiple scattering series to unitarize single pomeron exchange at high energy are noted. An operator formalism which sums all numbers of pomeron exchange is given. A toy model which has a similar operator structure at high energy as QCD is presented and the S-matrix is evaluated. Estimates of the energies and impact parameters at which blackness occurs in onium-onium scattering are given. It is emphasized that the problem of unitarity in high energy onium-onium scattering can be solved in a purely perturbative context, with a non-running coupling if the onium is heavy enough.     

An extended Rytov approximation and its significance for remote sensing and inverse scattering

The Born approximation has been shown by Wolf to be particularly convenient for formulating inverse scattering problems. The Rytov approximation is known to be more widely applicable than the Born approximation. We introduce an improvement that further increases the range of validity of the Rytov approximation. It transpires that our extension of the Rytov approximation is as convenient for inverse scattering as the Born approximation.     

The curvilinear coordinate method associated with the short-coupling-range approximation for the study of scattering from one-dimensional random rough surfaces

This paper deals with the scattering of an incident plane wave from a mono-dimensional rough surface. The analysis of the scattering phenomenon is performed using the curvilinear coordinate method (C method) associated with the short-coupling-range approximation (SCRA) and the Huygens principle. The C method is based on the solving of Maxwell’s equations under their covariant form written in a nonorthogonal coordinate system which fits the scattering surface profile. This leads to eigenvalue problems. The scattered surface fields are expressed as linear combinations of eigensolutions and the combination coefficients are determined using the boundary conditions. Electromagnetic fields are obtained using the surface fields and the Huygens principle. The short-coupling-range approximation (SCRA) applied with the C method allows a significant saving in computation time. We confirm the efficiency and the validity of this new approach with respect to the C method.     

Gaussian estimation of electron scattering cross sections on the basis of a Feynman path integral

A version of Gaussian estimation of a Feynman path integral is considered and its validity for a scattering problem is investigated. Test calculations of the differential and total cross sections are performed for the scattering of a plane wave by a three-dimensional spherically symmetric Gaussian potential and for the electron impact excitation of the 1s → 2s transition in the hydrogen atom. The data on the scattering by a potential are compared with the analogous results obtained using the first Born approximation and the method of phase functions (which gives almost exact results). The excitation cross sections for the transition in the hydrogen atom are compared with those obtained by the convergent close-coupling method. The validity of this approach is demonstrated. The accuracy of the method proposed is acceptable for many cases. For total cross sections, the result obtained in terms of the density matrix formalism turned out to be more exact than that derived from differential cross sections. Among all the above approaches using path integration to solve problems of scattering of electrons by atoms, the method proposed here.     

On the Cook-Kuroda criterion in scattering theory

A new criterion of the Cook-Kuroda type for the existence of the wave operator in the two-space scattering theory is introduced. The condition is quite simple, but it generalizes not only the original Cook-Kuroda condition but also its generalization recently given by Schechter. Specialized to the one-space case, it is actually equivalent to Schechter's condition for an optimal choice of factorization. An application to potential scattering leads to a new result.This work was partially supported by NSF Grant MCS 76-04655     

On the validity of some new acoustic scattering approximations

Two new approximations for predicting the elastic scattering of plane acoustic waves by a weak scatterer are proposed. The approximations have been obtained by drawing an analogy between acoustic and light scattering problems. The validity of these approximations has been examined numerically for the exactly soluble case of scattering by a homogeneous sphere. Results show that for small angle scattering the proposed approximations have a considerably larger domain of validity in comparison to the extensively used Born approximation.     

Three dimensional analyses of scattering by pressure-release sinusoidal surfaces

Scattering by pressure-release sinusoidal surfaces in three dimensions is analyzed using the Fresnel phase approximation and realistic source and receiver directivity approximations. Geometrical shadowing and second-order scattering are explicitly included to explore the validity of the Kirchhoff approximation. No restrictions on the surface heights and slopes are made. The "goodness" of the resulting expressions is verified by requiring the pressure scattered by a sinusoidal surface to reduce to the image solution as the surface amplitude goes to zero. The first-order scattered pressure achieves a very good approximation to the image solution, and the second-order scattered pressure goes to zero, as expected, under this requirement. The theory is compared with available experimental scattering measurements, and the agreement is good. Because the slopes on the experimental surface are very steep, shadowing corrections are indispensible to achieving accurate first and second order scattering results. Shadowing has a greater impact on the scattering prediction than the second-order scattering contribution. This suggests that the Kirchhoff approximation may be more robust when incorporated into a theory including a detailed shadowing treatment as well as the Fresnel phase approximation and a good directivity approximation.     

On the validity of some new acoustic scattering approximations

Abstract

Two new approximations for predicting the elastic scattering of plane acoustic waves by a weak scatterer are proposed. The approximations have been obtained by drawing an analogy between acoustic and light scattering problems. The validity of these approximations has been examined numerically for the exactly soluble case of scattering by a homogeneous sphere. Results show that for small angle scattering the proposed approximations have a considerably larger domain of validity in comparison to the extensively used Born approximation.     

轻介质传输中辐射热传导近似成立的判别因子

 从辐射输运方程出发,通过递推的方法,推导并得到了包含高级修正的辐射能流表达式。利用这个表达式,分析了辐射在轻介质中传输时,辐射热传导近似的成立条件。热传导近似的成立条件总是要求温度空间变化尺度与自由程之比远大于某个值,该值即判别因子,它表征热传导近似条件满足的苛刻程度,其值越大,热传导近似就越难满足。讨论得出：当同时考虑轫致和散射过程时,这一判别因子的值在3~60之间。并进一步分析了密度的空间变化以及1维球坐标下的半径对判别因子的影响。     

Excitation of collective nuclear states by fast particles

The elastic and inelastic scattering of a fast particle by a vibrating nucleus is discussed in the semicalssical approximation. For elastic scattering it is shown that the effect of the vibrations can be described by an effective deformed optical potential which is axially symmetric about the incident direction. Explicit results are obtained for inelastic scattering. In an appendix, the validity of the semiclassical approximation for potential scattering is discussed and numerical tests made.