Study Of Statistical Properties Of Stochastic Field In Interference And Scattering

The research of propagation of light beams in free space and the properties of coherence and polarization of scattered field generated by random media has gradually played its pivotal role in many applications such as free space optical communication,biomedicine,optical remote sensing,environmental monitoring,optical imaging,material testing and so on.With the establishment and application of the theory of coherence and polarization to analyze the beam propagation and scattering problems,many researchers have made remarkable achievements,and a whole new field of research focusing on the statistical properties of light fields has been established.However,the changes of the spectrum and polarization of the light field need to be further explored.At the same time,the stochastic media and the incident light field,which are relatively simple in mathematical form,are often used in the scattering problems,and more complicated media and incident light need to be studied.This thesis centers on the statistical properties of the light field generated by Young's pinholes,the properties of scattered field generated by anisotropic particulate media,the quasi-homogeneous source and the quasi-homogeneous media,the polarization properties of the scattering field and the method to modulate the polarization.Based on the theory of coherence and polarization of random electromagnetic fields,the analytical relationship between the cross-spectral density of the field transmitted from double-pinholes and the incident light field at pinholes is established.The traditional concept of cross-spectral purity is extended to cross-spectral purity of Stokes parameters,and the condition of it is derived.The relationship between cross-spectral purity of the Stokes parameter and complete coherence is also studied by the concept of statistical similarity.The concept and condition of purity of partial polarization are obtained.The relationship between purity of partial polarization and complete coherence is also studied.At last,the relationship between the two kinds of purity is obtained under a strict condition.Based on the unified theory of coherence and polarization and the theory of weak scattering,the scattering properties of stochastic light field generated by random media are studied.We focus on anisotropic particulate and quasi-homogeneous media.By considering the more complex stochastic media,the physical model of anisotropic particulate media is proposed based on the models of anisotropic continuous media and particle media.According to the scattering potential model and the theory of weak scattering,the analytical expression of cross-spectral density matrix of far-zone scattered field generated by the anisotropic particulate medium.By theoretical analysis and simulation,it is found that the polarization of incident light,the scattering potential of each particle and the distribution of particle all have an irreversible influence on the coherence of the scattering field.Then the far-fields radiated from quasi-homogeneous source and transmitted from Young's pinholes are considered as the incident fields.With the first-order Born approximation,the cross-spectral density function of far-fields are yielded.By mathematical analysis,we study the spectral density of these two kinds of scattered fields,and get the condition for far-zone spectral isotropy,namely the scaling law.The cross-spectral density matrix of the scattering field generated by the anisotropic medium is expressed in term of tensor.Then,the polarization characteristics of the three-dimensional scattered field are discussed.The three-dimensional scattered field is transformed from the Cartesian coordinate into the spherical one.In the two-dimensional plane,the distribution of polarization degree and polarization state of the scattered field is shown.By selecting different parameters of the medium,it is found that the polarization of the scattering field is effected by different parameters.Two kinds of singularities,namely singularity of polarization and singularity of the degree of polarization,are discussed.With the mathematical derivation and deduction,the transformation relationship between two kinds of singularities under certain conditions is obtained.By using the relationship yielded,the relationship between the degree of polarization and the intensity of light is obtained.An experiment to generate the singularities of the degree of polarization and the field with any desired distribution of the degree of polarization is designed.The results of the experiment are in quite satisfactory qualitative agreement with the simulation ones.