Angular memory effect and its interferometric application in rough surface mean height profiling

It is well known that the scattered wave from a random medium will exhibit the speckle phenomenon. The backscattered power is the average quantity over many realizations. Less obvious is the correlation of these speckle patterns. In this thesis, we will show that under some conditions, there is strong correlation between these seemingly random speckle patterns. By taking the wave correlation, we may have additional parameters besides the intensity measurement for parameter retrieval.; We propose a novel method of taking the correlation of the scattered waves at different incident and observing angles and/or different frequencies and/or different polarizations. In particular, the angular correlation leads to the "angular memory effect". This effect represents the ability of the scattered wave to "remember" and "follow" small changes in the incident direction. The remarkable property of this effect is that it exists even under a strong multiple scattering region. The condition for strong correlation is the conservation of the horizontal wavevectors. This condition depends only on the scattering geometry, and is independent of the surface properties. Using rough surfaces as the scattering medium, we will perform analytical, numerical, and experimental studies of this effect. We will employ the fully polarimetric second-order Kirchhoff approximation which consists of the first- and second-order terms.; We will combine both the angular and frequency correlation to find the mean topography height of a rough surface. The interferometric phase from the correlation of two waves at two different observing angles and/or different frequencies is linearly related to the mean topography height. This phase is independent of the surface properties and the polarization. The magnitude of the correlation gives the degree of correlation. Knowledge of the magnitude is important since it is related to the accuracy of the phase measurement. The degree of correlation depends on the surface statistics, the polarization, and the scattering geometry. We will show that the degree of correlation is greatest when the scattering angles satisfy the condition for the angular memory effect. Millimeter-wave (MMW) experiments and Monte-Carlo simulations will be performed to verify the theoretical prediction. Extension of the angular memory interferometry to pulse systems will be carried out. Besides the "spatial diversity" obtained from the angular memory effect, the "temporal diversity" which arises from the temporal correlation (or the "frequency diversity" from the frequency correlation in a wide-band system) provides additional measurement. This extra information can be implemented to obtain a very robust interferometric system.