Prof William Shaw

Environmental/Applied Electromagnetics

Background

The theme of my work remains focused on scattering from rough "ocean-like" surfaces. This is the fundamental mathematical theory behind such applications as radar imaging of the ocean, using synthetic aperture radar to view the ocean in fine detail (at night, and through cloud!) Andrew Dougan and I pioneered the application to the electromagnetic case of the half-space (and indeed more accurate still) Green's functions, in the context of ocean-surface scattering. The case of a perfect conductor was discussed in the following paper

Half-space Green's functions and applications to scattering of electromagnetic waves from ocean-like surfaces., Shaw, W.T. and Dougan, A.J., 1995, Waves in Random Media Vol. 5 p. 341

The link above contains the abstract and a link to a downloadable PDF if you have IOP access.

A related matter concerns the eveluation of statistical Kirchhoff integrals. Andy Dougan and I published a paper on this:

The failure of specular limit formulae for Kirchhoff integrals associated with Gaussian surfaces with ocean-like spectra, Shaw, W.T. and Dougan, A.J., 1995, Waves in Random Media Vol. 5 p. 1.

This paper made it clear that some of the asymptotic techniques often used to estimate scattering amplitudes are actually wrong due to subtle non-differentiability issues with the correlation structure of the ocean. A completely different approach that gets around the difficulty for the more interesting case of high incidence angles was developed by myself, Andrew Dougan and Robert Tough and was published by the IEEE (your access to IEEE links may depend on your organizations level of subscription to IEEE journals):

Analytical expressions for correlation functions and Kirchhoff integrals for Gaussian surfaces with ocean-like spectra, Shaw, W.T., Dougan, A.J. and Tough, R.J.A., 1996. IEEE Transactions on Antennas and Propagation, Vol 44, No 11, p. 1454.

The extension of the half-space model to a dielectric, which is perhaps one of our most important contributions, is given in a special issue of IEEE Trans AP on ocean scattering

Green's function refinement as an approach to radar backscatter: general theory and applications to low grazing angle scattering from the ocean, Shaw, W.T., Dougan, A.J. 1998. IEEE Transactions on Antennas and Propagation, Vol 46, No 1, p.57.

This work is important as it generalized Dennis Holliday's team's 1986 work in the International Journal of Remote Sensing to cope with (a) dielectric effects and (b) make Dennis's team's essentially "Kirchhoff" theory compatible with perturbation theory for high-contrast dielectrics.

These articles published in IEEE Trans AP are copyright IEEE. A lot of our early work and the work of others makes use of simple tangent plane approximations for the electromagnetic fields. This needs to be improved for all sorts of reasons, including penetration of the media for dielectrics. When the media is a high-contrast medium compared to empty space, one can make use of asymptotic methods to derive a family of impedance boundary conditions. The ideas behind this date back to the 1940s and the work of the Russian theorists Shchukin, Leontovich and Rytov. However, all the implementations we found required the introduction of orthogonal curvilinear coordinates, or the identification of principle curvature axes on the surface, in order to develop a detailed model. Dougan and I recently got round this and developed methods valid in a general vector basis, which is much more useful for doing scattering theory from general surfaces. The paper was published by the IEEE in May 2005:

Curvature Corrected Impedance Boundary Conditions in an Arbitrary Basis, Shaw, W.T. and Dougan, A.J., IEEE Transactions on Antennas and Propagation, Vol. 53, May 2005, pp 1699-1705.

Extending these models to work with Doppler spectra is the subject of the working paper cited below.

Working Paper

Modelling Doppler Spectra for scattering from rough surfaces A working paper on modelling coherence functions and Doppler spectra for scattering from dynamics rough surfaces (i.e. the ocean) is available here. This is work with Andrew Dougan.