Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Department of Electrical and Computer Engineering

First Advisor

Milo W. Hyde, PhD.


Much of the rough surface scattering theory developed to date considers only the effects of fully coherent and fully incoherent illumination in the formation of solutions— a problem studied in earnest since the late 1800’s. In response, this dissertation extends the theory currently available in modeling rough surface scattering to include the effects of partially coherent illumination. Such illumination plays a pivotal role in our understanding of active-illumination systems, similar to those found in directed-energy and remote-sensing applications, which use the light scattered from distant targets for tactical purposes. Specifically, this dissertation uses the physical optics approximation (Kirchhoff boundary conditions) to determine a 3D vector solution for the far-field scattering of electromagnetic beam illumination with partial spatial coherence from statistically rough surfaces. The analysis considers three different material substrates: dielectrics, conductors, and a perfect electrical conductor. It also makes use of a Gaussian Schell-model form for the incident-field cross-spectral density matrix. In so doing, this dissertation develops closed-form expressions for the scattered field cross-spectral density matrix with two analytical forms—one applicable to smooth-to moderately rough surfaces and the other applicable to very rough surfaces. The analysis shows that these closed-form expressions are, in general, complicated functions of both the source (size and coherence properties) and surface parameters (surface height standard deviation and correlation length). Under appropriate conditions, the analysis also compares the 3D vector solution to previously validated solutions and empirical measurements. The results show good agreement.

AFIT Designator


DTIC Accession Number



Mark F. Spencer is a 2022 recipient of the AFIT Young Alumni Award, for achievements of alumni who have made outstanding contributions in their career within ten years of graduating from AFIT.