The information about the distance of separation between two-point targets that is contained in scattering data is explored in the context of the scalar Helmholtz operator via the Fisher information and associated Cramér-Rao bound (CRB) relevant to unbiased target separation estimation. The CRB results are obtained for the exact multiple scattering model and, for reference, also for the single scattering or Born approximation model applicable to weak scatterers. The effects of the sensing configuration and the scattering parameters in target separation estimation are analyzed. Conditions under which the targets' separation cannot be estimated are discussed for both models. Conditions for multiple scattering to be useful or detrimental to target separation estimation are discussed and illustrated.
Microstructural parameters of high-purity alumina powder are determined quantitatively throughout the bulk of the material using small-angle neutron scattering techniques. A unified theoretical and experimental approach for analyzing multiple scattering data is developed to obtain values for particle size, volume fraction and surface area. It is shown how particle size and volume fraction can be measured in a practical way from SANS data totally dominated by incoherent multiple scattering (`beam broadening'). The general phase-shift dependence of single-particle scattering is incorporated into the multiple scattering formalism, and it is also shown that the diffractive limit (small phase shift) applies even for phase shifts as large as unity (particle radii of order 1 μm). The stability of the Porod law against multiple scattering and the phase-shift scale are described, a useful empirical formula for analysis of beam broadening data is exhibited, and the applicability of the formulations to polydispersed systems is discussed.
Abstract
In this paper, we try to answer the question: how the multiple scattering, the sun elevation, shape and orientation of ice crystals in the cirrus clouds affect a halo pattern. To study the radiation transfer in optically anisotropic clouds, we have developed the software based on Monte Carlo method and ray tracing. In addition to halos, this software enables one to simulate “anti-halos”, which above the cloud layer can be seen by observers. We present the visualization of halos and anti-halos generated by the cirrus clouds for different shapes and orientations of ice crystals.
Cramér-Rao Bound Study of Multiple Scattering Effects in Target Separation Estimation