Abstract
The scattering of a partially-coherent wave from a statistically rough material surface is investigated via derivation of the scattered field cross-spectral density function. Two forms of the cross-spectral density are derived using the physical optics approximation. The first is applicable to smooth-to-moderately rough surfaces and is a complicated expression of source and surface parameters. Physical insight is gleaned from its analytical form and presented in this work. The second form of the cross-spectral density function is applicable to very rough surfaces and is remarkably physical. Its form is discussed at length and closed-form expressions are derived for the angular spectral degree of coherence and spectral density radii. Furthermore, it is found that, under certain circumstances, the cross-spectral density function maintains a Gaussian Schell-model form. This is consistent with published results applicable only in the paraxial regime. Lastly, the closed-form cross-spectral density functions derived here are rigorously validated with scatterometer measurements and full-wave electromagnetic and physical optics simulations. Good agreement is noted between the analytical predictions and the measured and simulated results.
Highlights
Rough surface scattering has been an active area of research for a half century
Concerned with fullycoherent, monochromatic plane-wave scattering from rough surfaces, the common approaches employed by the RF/microwave community to the rough surface scattering problem are physical optics (PO) [1,2,3,4,5,6,7], perturbation [4, 8], and computational/fullwave [9,10,11,12,13,14] methods
Two forms of the scattered-field cross-spectral density (CSD) function were derived in this work using the PO approximation
Summary
Rough surface scattering has been an active area of research for a half century. The first deals with rough surface scattering research performed by the RF/microwave community for synthetic aperture radar and remote sensing applications. The second of the two main groups deals with rough surface scattering research performed by the optics community. This work mainly dealt with how incoherent light interacted with surfaces, modeled via the bidirectional reflectance distribution function (BRDF), for applications in passive visible/near-IR remote sensing and computer graphics [20,21,22,23,24]. With the proliferation of laser-based systems (LIDAR/LADAR and directed energy), the interaction of coherent laser light with rough surfaces, in particular the statistical behaviors of the resulting speckle patterns, gained considerable interest in such fields as metrology and remote sensing. Some of the early notable research in this area was performed by Dainty [25], Goodman [26], Parry [27], Fujii and Asakura [28,29], Pedersen [30], and Yoshimura et al [31]
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