Recursive calculation of time-dependent multiple forward scattering: comparison between small-angle approximation and exact model

1990 ◽  
Author(s):  
Konrad Altmann
Keyword(s):  
Small Angle ◽  
Forward Scattering ◽  
Time Dependent ◽  
Small Angle Approximation ◽  
Exact Model ◽  
Recursive Calculation

scholarly journals An Improved Small-Angle Approximation for Forward Scattering and Its Use in a Fast Two-Component Radiative Transfer Method

2017 ◽  
Vol 74 (6) ◽  
pp. 1959-1987 ◽  
Author(s):  
Bingqiang Sun ◽  
George W. Kattawar ◽  
Ping Yang ◽  
Eli Mlawer
Keyword(s):  
Radiative Transfer ◽  
Small Angle ◽  
Delta Function ◽  
Computational Effort ◽  
Forward Scattering ◽  
Scattering Method ◽  
Diffuse Component ◽  
Dirac Delta ◽  
Small Angle Approximation ◽  
Two Component

Abstract The vector radiative transfer equation is decomposed into two components: a forward component and a diffuse component. The forward component is analytically solved with a small-angle approximation. The solution of the forward component becomes the source for the diffuse component. In the present study, the diffuse component is solved using the successive order of scattering method. The strong anisotropy of the scattering of radiation by a medium is confined to the forward component for which a semianalytical solution is given; consequently, the diffuse component slowly varies as a function of scattering angle once the forward-scattering peak is removed. Moreover, the effect on the diffuse component induced by the forward component can be interpreted by including the low orders of the generalized spherical function expansion of the forward component or even replaced by the Dirac delta function. As a result, the computational effort can be significantly reduced. The present two-component method is validated using the benchmarks related to predefined aerosol and cloud layers with a totally absorbing underlying surface. As a canonical application, the optical properties of water clouds and ice clouds used for the Moderate Resolution Imaging Spectroradiometer (MODIS) Collection 6 cloud-property retrieval products are used for radiative transfer simulations under cloudy conditions.

A small-angle approximation for bistatic polarimetry

2016 ◽  
Author(s):  
Thomas Dallmann ◽  
Matthias Roding ◽  
Dirk Heberling ◽  
Reiner S. Thoma
Keyword(s):  
Small Angle ◽  
Small Angle Approximation

Effect of finite spatial coherence length on small-angle scattering

2015 ◽  
Vol 48 (6) ◽  
pp. 1660-1664 ◽  
Author(s):  
Yuya Shinohara ◽  
Yoshiyuki Amemiya
Keyword(s):  
Small Angle ◽  
Coherence Length ◽  
Spatial Coherence ◽  
Small Angle Scattering ◽  
Forward Scattering ◽  
X Ray Diffraction ◽  
X Ray ◽  
X Ray Imaging ◽  
Angle Scattering ◽  
Diffraction Imaging

This study shows that forward scattering at the origin of reciprocal space contributes to the scattering intensity profiles of ultra-small-angle scattering. The forward scattering corresponds to a Fourier transform of the X-ray coherent volume on a sample. This contribution is usually ignored in the study of small-angle scattering, while it is fully considered in the fields of X-ray imaging, such as coherent X-ray diffraction imaging and X-ray ptychography. This effect is explicitly illustrated in the context of small-angle scattering, and the effect of a finite spatial coherence length on small-angle scattering is discussed.

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