Fresnel integrals and the problem of calculating the field of an electromagnetic wave reflected from a rough surface

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The scattering of electromagnetic waves from rough surfaces

A method is presented which can be used for the calculation of the distribution of energy reflected from irregular surfaces. The formulation is useful for the first boundary value problem and can be used in either two‐ or three‐dimensional problems with any given incident field. The solution is reduced to quadrature with negligible error when the average square of the slope of the reflecting surface is small and when the wavelength of the incident radiation is not small compared with the displacement of the surface from its average value. A numerical example is worked, the sinusoidal surface, and is compared with experiment and with a method due to Rayleigh. It is found that the Fourier transform method is preferable to previous methods, notably those which can be classified physical optics (such as Rayleigh's), since the error in the transform method is of second order in the surface slope whereas the error in previous methods is of first order in the same quantity.

Fourier Transform Method for the Treatment of the Problem of the Reflection of Radiation from Irregular Surfaces

A full-wave solution is developed for problems of radio wave propagation over rough surfaces characterized by variable impedance and height parameters. The analysis, which is suitable for problems involving both the radiation fields as well as the ground waves, is compared with earlier solutions to these problems. The full-wave solutions which satisfy the exact boundary conditions are shown to be consistent with the reciprocity relationships for the general case.

http://ieeexplore.ieee.org/iel6/8/25506/01140201.pdf

Fresnel integrals and the problem of calculating the field of an electromagnetic wave reflected from a rough surface

References

The scattering of electromagnetic waves from rough surfaces

Fourier Transform Method for the Treatment of the Problem of the Reflection of Radiation from Irregular Surfaces

Radio wave propagation over a rough variable impedance boundary: Part I--Full-wave analysis

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