The Optical Properties Of Light Waves On Weak Scattering From A Medium And Its Inverse Problem

When a light wave is incident on a medium, it deviates from its origin path and is scattered in all directions, which is known as light wave scattering. There are many types of light wave scattering. For examples, the scattering medium may be determinate or random, isotropic or anisotropic, homogeneous or inhomogeneous. The response of the scattering medium may be static or dynamic, linear or non-linear. The incident light may be monochromatic or polychromatic. The scattering of light waves from various media has been investigated extensively due to the potential application in areas such as physics, astronomy, chemistry, meteorology, and biomedical. In this dissertation, we discuss the optical properties of light waves scattered from a linear, isotropic, and statistical stationary medium under the condition of first-order Born approximation. Firstly, we discuss the scattering of scalar light waves, and secondly the scattering theory is generalized from scalar light waves to vector light waves. After that, the spectral shift of light waves on scattering is studied, and then the inverse problem (i.e., the problem of finding the statistical properties of scattering media from the statistical properties of the scattered field) of light wave scattering is discussed. The detailed structure of this dissertation is arranged as follows.In Chapter1, we introduce the research background of this dissertation. Firstly, the progress of the research on light wave scattering, the spectral shift on light wave scattering, and the inverse problem on light wave scattering are introduced. After that, the motivation and the significance of this dissertation are emphasized. Finally, the content of this dissertation and the arrangement of each chapter are presented.In Chapter2, we present the basic theory of this dissertation as follows:the scattering theory of scalar light waves is introduced, and the first-order Born approximation and the far-zone approximation are discussed; the frequently mentioned scattering medium, including the deterministic medium, the random medium, and the collection of particles is introduced; the scattering theory of vector light waves is discussed.In Chapter3, the property of scalar light waves on scattering is discussed. The scattering of scalar light waves from a Gaussian-Schell model medium is studied, and the influences of the correlation function of the scattering potentials on the spectral density and the spectral degree of coherence of the far-zone scattered field are discussed. The spectral degree of coherence of scalar light waves on scattering is investigated, and the condition for the invariance of spatially coherent plane waves on scattering is presented. Moreover, the condition is illustrated by the scattering of light waves from a deterministic medium, a random medium, and a collection of particles.In Chapter4, the scattering property of vector light waves is discussed as follows. Firstly, the description of the scattering of vector light waves is discussed and the cross-spectral density matrix of the scattered field is introduced. By use of the cross-spectral density matrix, the properties of the scattered field, including the spectral density, the spectral degree of coherence, and the spectral degree of polarization are discussed. After that, we study the spectral degree of coherence of the scattered field, and discuss the polarization-induced coherence changes. Examples of light waves scattered from a deterministic medium and a quasi-homogeneous medium are discussed to illustrate the phenomenon of polarization-induced coherence changes. In addition, the Stokes parameters of the scattered field are investigated, which are applyed to study the polarization distribution of the scattered field. An example of light waves scattered from a quasi-homogeneous medium is discussed to illustrate the influence of the polarization of the incident light on the distributions of the Stokes parameters and the spectral degree of polarization of the scattered field.In Chapter5, we study the spectral shift of light waves on scattering. The spectral shift of the scattering of scalar light waves is discussed, and the influence of the scattering potential on the spectral shift is discussed for the scattering of light waves from a deterministic medium. The influence of the source correlation on the spectral shift is discussed, and the correlation-induced spectral shift and the scattering-induced spectral shift are investigated in great detail. The scattered spectrum of vector light waves on scattering is also discussed, and an example of vector light waves scattered from a deterministic medium is discussed to show the influence of the incident spectrum, the scattering angle, and the scattering potential of the medium on the spectral shift of the scattered field. In addition, the condition for the far-zone isotropy of vector light waves on scattering is also investigated.In Chapter6. we discuss the inverse problem of light wave scattering. The theory of the inverse problem is introduced. The determination of the correlation function by use of the incidence of a pair of correlated source is discussed, and an example of the determination of the correlation function of a quasi-homogeneous medium is discussed. The inverse problem of light waves scattered from a collection of particles is studied, and a method of the determination of the pair-structure factor of a collection with random distribution is discussed. In addition, the determination of the two-point density correlation function of particles collection is studied, and a method is discussed to improve the accuracy of the determination.In Chapter7, a brief conclusion is given, and some possible future works are discussed.