Technique for interaction of optical fields with turbulent medium containing particles

We develop a method for transmission of stochastic fields through turbulent media (atmosphere, ocean, biotissues) containing randomly distributed particles. The method is based on the angular spectrum representation of stochastic, statistically stationary, scalar fields, the Rytov perturbation series for propagation in weakly fluctuating media, and the first Born approximation for weak scattering from particulate media. The results for transmission of the deterministic (laser) field may be obtained from our general results as a limiting case.     

Improving the Born approximation for the scattering of ultrasound in elastic solids

It has recently been demonstrated that the Born approximation for predicting the scattering response of flaws can be improved through the use of simple modifications called the "doubly distorted Born approximation". In this paper the doubly distorted Born approximation itself is modified with phase and amplitude corrections that further improve the Born scattering results for isotropic elastic media. The reliability of this new modification of the Born approximation has been evaluated by comparison with the exact solution for spherical inclusions obtained with the method of separation of variables. Unlike the ordinary Born approximation which works well only for very weak scattering inclusions, our modification of the doubly distorted Born approximation gives improved scattering results for both weak and strong scattering inclusions.     

Bayesian compressive optical imaging within the Rytov approximation

Within the range of validity of the Rytov approximation (RA), an innovative Bayesian compressive sensing (BCS) inverse scattering technique is developed. Potentialities and limitations of the BCS-RA method are validated through numerical experiments and representative results are discussed.     

Beam wave propagation within the second Rytov perturbation approximation

The applicability of the classical Rytov method in statistical wave propagation problems is reconsidered and expanded by demanding results that are of second order in the permittivity fluctuations, rather than limiting them to just the first Rytov perturbation approximation, as is traditionally done. It is shown that one must augment the well-known second order statistics (e.g., log-amplitude variance), as calculated from the first Rytov approximation, with first-order statistics (e.g., the average log-amplitude), as calculated from the second Rytov approximation. Thus, a complete solution is derived for the second Rytov approximation for general beam wave propagation through turbulent media, the permittivity fluctuations of which are described by the Kolmogorov-Obukhov spectrum. This then allows a complete and consistent treatment that yields the fact that the average log-amplitude is, in the general beam wave case, not equal to the additive inverse of the log-amplitude variance. This gives results from the Rytov method that are then in exact agreement with the corresponding limiting case of strong fluctuation theory, as well as a simplified analytical expression for beam wave broadening, and the correct theoretical explanation of the well-known applicability limit for the Rytov method.     

An impact parameter representation for the off-energy-shell scattering amplitude

The unitarized Born approximation for the scattering amplitude, suggested previously, is considered in the short wavelength limit. It is found that its on-energy-shell component is equivalent to the well-known impact parameter representation developed by Glauber. An approximate expression is then derived for the off-energy-shell scattering amplitude on the basis of the unitarized Born approximation which is expected to be as accurate as the Glauber approximation.     

Modeling of Microwave Images of Buried Cylindrical Objects

Tomographic methods of image reconstruction of two-dimensional cross-sections of volumetric objects in millimeter wavelengths band are suggested and considered.It is shown that in the frequency band under consideration, the images of investigated objects may be obtained by first-order diffraction tomography method (Born, Rytov or high frequency approximation of the first-order for scattered electromagnetic field).     

Application of tomography method in millimeter wavelengths band I. Theoretical

Tomographic methods of image reconstruction of two-dimensional cross-sections of volumetric objects in millimeter wavelengths band are suggested and considered. It is shown that in the frequency band under consideration, the images of investigated objects may be obtained by first-order diffraction tomography method (Born, Rytov or high frequency approximation of the first-order for scattered electromagnetic field).     

Equivalence of the born and rytov approximations for back-scattered scalar fields

The Rytov and first Born approximations are investigated in the near field limit for waves scattering from slowly varying potentials of compact support. For the special case of measurements made at the source point of the illuminating radiation the approximations are shown to give an identical form for the back-scattered fields. The special properties of the system facilitate an exact reconstruction of the potential to be obtained.     

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.     

In vivo biomicroscopy with ultrasound 2

In the first article of this series it was shown that the use of inverse scattering theory to analyse ultrasound reflections could provide high resolution images of the acoustic impedance profile of the retina. Unlike the retina, most tissue structures of interest, like small tumours and arterial plaque deposits, are shielded from view by intervening layers of tissue of appreciable acoustic impedance and attenuation. By analysing a one-dimensional model for a plaque deposit on the wall of a carotid artery embedded in a 5 cm thick layer of tissue, we demonstrate that a relatively high quality image can be recovered when compensation for the attenuation of the intervening tissue is made. We observe that because of the dearth of low frequency power in the recovered signal of ultrasound transducers, it is important that the field of view imaged is not taken to be too large. We compare the exact iterative distorted wave Born approximation inverse scattering method with the approximate but computationally faster plane wave Born approximation method and find that they give images of comparable quality for this model.     

Magnus expansion and eikonal approximation in potential scattering

An expansion procedure due to Magnus is applied to the case of potential scattering. This technique, which is superior to the usual Born-Dyson expansion in that it preserves unitarity at each state, leads in first approximation to an expression for the scattering amplitude which contains as special cases the eikonal approximation and also the second Born approximation. In particular the first Magnus approximation provides a basis for the ad hoc addition of the real part of the second Born contribution to the eikonal scattering amplitude as was considered by Byron et al.     

双模激光场中电子-原子散射

在一阶玻恩近似的基础之上,本文首次在激光场的极化方向平行于入射电子的方向这种散射模式下,应用二阶玻恩近似理论对双模激光场中电子-氩原子散射的自由-自由跃迁过程进行了研究,并与一阶玻恩近似结果进行比较.结果表明,二阶玻恩近似理论在多模激光场中的应用也是比较成功的.     

The scattering of ultrasound by cylinders: implications for diffraction tomography

The validity of wave equations employed as system models in acoustical diffraction tomography is investigated using simulations and measurements of the scattering of plane ultrasound waves by cylinders. It is demonstrated by simulation and experiment that it can be appropriate to neglect density fluctuations and shear waves, implying that the commonly used form of the wave equation suitably describes scattering by fluctuations of acoustic speed and absorption. Diffraction tomographic reconstructions of simulated data reveal the importance of absorption, the behavior of the real and imaginary parts of the reconstructed refractive index, and the relative advantages and limitations of the Born and Rytov approximate transformations.     

Free of speckle ultrasound images of small tissue structures

By using the Born approximation deconvolved inverse scattering method instead of the traditional pulse-echo method for analyzing ultrasound pulse reflections from plastic phantoms and soft tissue specimens, improvement in image resolution is shown to be possible provided these targets are fair approximations to layered media. These images are free of speckle and are more vivid than the usual pulse-echo images.     

Reconstructing the adhesion stiffness distribution in a laminated elastic plate: Exact and approximate inverse scattering solutions

This paper formulates and solves a time harmonic inverse scattering problem to reconstruct the effective stiffness distribution of an adhesive bond in a layered elastic plate. The motivation is based on the assumption that localized adhesion flaws that diminish bond stiffness also tend to diminish bond strength. The formulation is based on the invariant imbedding method, applies to isotropic and anisotropic elastic layers, and is essentially that of identifying embedded acoustic sources in elastic layered structures. This paper presents two solutions for the inverse problem: the Born approximation and the exact solution. The example calculations compare the two solutions and show that when imperfections are too large in either magnitude or extent the accuracy of the Born approximation breaks down. The impact of noise and uncertainties in the background properties in the inversion is also investigated. A regularization strategy is introduced in the exact solution that controls solution sensitivity in regions with low signal to noise ratio.     

On Born approximation in black hole scattering

A massless field propagating on spherically symmetric black hole metrics such as the Schwarzschild, Reissner–Nordström and Reissner–Nordström–de Sitter backgrounds is considered. In particular, explicit formulae in terms of transcendental functions for the scattering of massless scalar particles off black holes are derived within a Born approximation. It is shown that the conditions on the existence of the Born integral forbid a straightforward extraction of the quasi normal modes using the Born approximation for the scattering amplitude. Such a method has been used in literature. We suggest a novel, well defined method, to extract the large imaginary part of quasinormal modes via the Coulomb-like phase shift. Furthermore, we compare the numerically evaluated exact scattering amplitude with the Born one to find that the approximation is not very useful for the scattering of massless scalar, electromagnetic as well as gravitational waves from black holes.     

On multidimensional ultrasonic scattering in an inhomogeneous elastic background.

This work is concerned with the modeling of elastic wave scattering by solid or fluid-filled objects embedded in an inhomogeneous elastic background. The medium is probed by a monochromatic force and the scattered field is computed (forward problem) or observed (inverse problem) at some known receiver locations. Based on vector integral equations for elastic scattering, a general framework is developed, independent of both the problem geometry and the transmitter-receiver characteristics. This framework encompasses both forward and inverse modeling. In the forward model, a Born approximation for an inhomogeneous background is applied to obtain a closed form expression for the scattered field. In the inverse model, this approximation is also invoked to linearize for the multiparameter characteristic of the object. Finally, an iterative inversion scheme alternating forward and inverse modeling is proposed to improve the resolution and accuracy of the reconstruction algorithm.     

Tissue self-affinity and polarized light scattering in the born approximation: a new model for precancer detection

Light scattered from biological tissues can exhibit an inverse power law spectral component. We develop a model based on the Born approximation and von Karman (self-affine) spatial correlation of submicron tissue refractive index to account for this. The model is applied to light scattering spectra obtained from excised esophagi of normal and carcinogen-treated rats. Power law exponents used to fit dysplastic tissue site spectra are significantly smaller than those from normal sites, indicating that changes in tissue self-affinity can serve as a potential biomarker for precancer.     

Numerical solution of inverse scattering for near-field optics

A novel regularized recursive linearization method is developed for a two-dimensional inverse medium scattering problem that arises in near-field optics, which reconstructs the scatterer of an inhomogeneous medium located on a substrate from data accessible through photon scanning tunneling microscopy experiments. Based on multiple frequency scattering data, the method starts from the Born approximation corresponding to weak scattering at a low frequency, and each update is obtained by continuation on the wavenumber from solutions of one forward problem and one adjoint problem of the Helmholtz equation.     

Coulomb effects in polarization transfer in elastic antiproton and proton electron scattering at low energies

The influence of Coulomb distortion on the polarization transfer in elastic proton and antiproton electron scattering at low energies is calculated in a distorted-wave Born approximation. For antiproton electron scattering Coulomb effects reduce substantially the polarization transfer cross-section compared to the plane-wave Born approximation, whereas for proton electron scattering they lead to a dramatic increase for kinetic proton lab energies below about 20keV.