Field and intensity correlation in random media

We have obtained the spectral and spatial field correlation functions, $C_E\left(\Delta \omega \right)$ and $C_E\left(\Delta x\right),$ respectively, from measurement of the microwave field spectrum at a series of points along a line on the output of a random dielectric medium. $C_E\left(\Delta \omega \right)$ and $C_E\left(\Delta x\right)$ are shown to be the Fourier transforms, respectively, of the time of flight distribution, obtained from pulsed measurements, and of the specific intensity. Unlike $C_E\left(\Delta \omega \right),$ the imaginary part of $C_E\left(\Delta x\right)$ is shown to vanish as a result of the isotropy of the correlation function in the output plane. The complex square of the field correlation function gives the short-range or $C_1$ contribution to the intensity correlation function C. Longer-range contributions to the intensity correlation function are obtained directly by subtracting $C_1$ from C and are in good agreement with theory.