![]() 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). 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. It also makes use of a Gaussian Schell-model form for the incident-field cross-spectral density matrix. The analysis considers three different material substrates: dielectrics, conductors, and a perfect electrical conductor. 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. 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. In response, this dissertation extends the theory currently available in modeling rough surface scattering to include the effects of partially coherent illumination. 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. Outputs of this study has potential application on deriving the requirements of optical systems on aircrafts like laser range finder, laser designator, optical communication systems and directed infrared countermeasure (DIRCM). Furthermore, the beam width of the PCLGSMvB increasing as the structural constant increases and it means that the beam can resist to stronger fluctuation of turbulence. Also, we found that the spreading of PCLGSMvB is related with their initial parameters, and it will be spread faster with smaller source coherence width, larger mode order n, and longer wavelength. If the source coherent width is very small, the shape of PCLGSMvB is converted to a Gaussian shape and keeps its form upon propagation. When the source coherence width is high, the profile of PCLGSMvB changes from initially dark hollow into two spot beams at short propagation distances. Our results show that the spectral density of the corresponding beam can change their form shape during its propagation as the source coherence varies. In this study, based on the generalized Huygens-Fresnel principle, the evolution properties, such as spectral density, degree of coherence, and beam width of the propagation of partially coherent Laguerre-Gaussian Schell model vortex beam (PCLGSMvB) in jet engine exhaust are studied. ![]()
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