Scattering: general principles, partial waves, review of one-dimension, low-energy approximations, resonance, Born approximation.
This is the essence of the (first order) Born approximation, for which Eq. (2) becomes In order to solve this Helmholtz equation we calculate its Fourier transform with respect to r and use two basic properties of the Fourier transform, namely In Eq. (4), ↔ indicates the Fourier transformation, χ ˜ is the Fourier transform of χ, k (k = | k | ) is the conjugate variable to r, and k i = k 0 z ^ .
Considering that the tsunami has a long wavelength and the sea-bottom topography acts as a set of pointlike scatterers, we use a first-order Born approximation.
The scattering of radiation from the roughness is calculated within the distorted-wave Born approximation and is compared to experimental measurements.
Scattering theory: phase shifts, Born approximation.
Scattering theory, partial wave expansion, Born approximation.
Analytical models based on the Mindlin plate theory and Born approximation are presented to predict the A0 Lamb wave scattering at a delamination, which is modelled as an inhomogeneity, in an equivalent isotropic model of the QI composite laminate.
For weak fluorochrome concentrations the contribution of the fluorochrome to the optical parameters can be neglected, which yields the first-order Born approximation [ 23, 24].
With the Born approximation we assume the absorption and diffusion is known in the background but here we estimate chromophore concentrations and diffusion of the object of interest as well as chromophore concentration in the background.
In that paper, under the Born approximation we assumed the absorption and reduced scattering coefficient to be known in the background, and estimated chromophore concentrations and diffusion properties of a compactly supported object of interest.
The known limitations of the Born approximation and the high number of unknowns encountered in the pixel-based approach, made reconstructions sensitive to the choice of regularization parameters [ 14].
