Statistics of phase quadrature components of microwave fields transmitted through a random medium

The phase quadrature components of the total microwave field transmitted through a random volume distribution of Styrofoam spheres have been measured in the laboratory. The radii (a) of the spheres were large compared to the wavelengths ( ), and their index of refraction was close to unity ( ). The statistical results lead in general to the bivariate normal distribution with correlation ( ) to describe the scattered incoherent field, rather than to the simpler Rayleigh distribution. The quadrature components of the incoherent field are Gaussian, but in general and . However, by rotating (in phase) the quadrature axes, two simpler situations arise: (a) at one orientation, but ; (b) at an orientation from case (a), but . Probability density expressions for these simpler cases exist in the literature. As the quadrature axes are rotated, the sum remains equal to a constant (the incoherent power), as it should. These departures of the incoherent field from the Rayleigh distribution are a function of the sum of the reciprocal transmitter and receiver distances. This behavior suggests that the departures are related to the sphericity of the transmitting and receiving beams.