Theory Of Physical Optics Research Articles

Rubinowicz transform of the MTPO surface integrals

The surface integral of the modified theory of physical optics is reduced to a line integral by using the Rubinowicz transform for the incident scattered fields by an arbitrary aperture in a black surface. The integral theorem of Kirchhoff is applied to the scattering geometry and the diffracted fields are expressed in terms of a line integral along the contour of the diffracting edge.

Integral representation of the edge diffracted waves along the ray path of the transition region

The expression of the edge diffracted fields, in terms of the Fresnel integral, is transformed into a path integral. The obtained integral considers the integration of the incident field along the ray path of the transition region. The similarities of the path integral with Kirchhoff's theory of diffraction and the modified theory of physical optics are examined.

Modified diffraction theory of Kirchhoff

The diffraction theory of Kirchhoff is reinterpreted and a new form of a surface diffraction integral is developed by using the axioms of the modified theory of physical optics, which leads to the exact scattered fields by conducting bodies. The new integral is arranged according to the interpretation of Young, and the diffracted waves are expressed in terms of a line integral. The method is applied to the diffraction problem by a semi-infinite edge contour.

Scattering of a line source by a cylindrical parabolic impedance surface

The scattering of the radiated fields of a line source by a cylindrical parabolic reflector, which has impedance boundary conditions on its surface, is obtained by using the surface integrals of the modified theory of physical optics. The reflected geometrical optics and edge diffracted fields are evaluated by using the asymptotic methods. The scattered fields are plotted numerically for various parameters such as surface impedance and angles of the edges.

The theory of the boundary diffraction wave for wedge diffraction

A new potential function, line integration which gives the edge diffracted fields, is constructed for wedge diffraction by using the method of modified theory of physical optics. The surface integrals are transformed into line integrals by the technique of asymptotic reduction. As an application of the novel potential function, the diffracted field is obtained for the geometry of a wedge for arbitrary incidence of plane waves.

Uniform line integral representation of edge-diffracted fields

A uniform line integral representation is derived for edge-diffracted fields by using the modified theory of physical optics and uniform asymptotic evaluation methods. The method is applied to the problem of diffraction of plane waves by a semi-infinite edge, which creates tip-diffracted fields with edge-diffracted waves. The uniform diffracted fields are plotted and examined numerically.

Diffraction of evanescent plane waves by a resistive half-plane

Diffraction of evanescent plane waves by a resistive half-plane is examined. The scattering integrals are constructed with the modified theory of physical optics. These integrals are evaluated uniformly by using an unusual method. The scattered fields of evanescent waves are obtained by giving the angle of incidence a complex value. The diffracted waves are plotted numerically for different parameters of the incident field.

Scattering of a Gaussian beam by an impedance half-plane

The diffraction of a Gaussian beam by an impedance half-plane is studied through the method of the modified theory of physical optics. An electric line source, which is defined in the complex space, is used to represent the Gaussian beam. The uniform evaluation of the diffraction integral is performed and the scattering patterns of the field are investigated for various numerical parameters of the incident wave.

On the Geometrical Optics (Hagfors' Law) and Physical Optics Approximations for Scattering From Exponentially Correlated Surfaces

High-frequency approximations to the physical optics (PO) theory of scattering from exponentially correlated rough surfaces are examined and used to interpret the expected accuracy of the PO theory. As an introduction, a review of the PO theory for Gaussian-correlated surfaces is provided, and in this process an analytical summation of the PO series for specular scattering from Gaussian-correlated surfaces is obtained. A similar form is then derived for specular scattering from exponentially correlated surfaces and contrasted to the Gaussian case. These series allow the accuracy of the leading order term (i.e., the geometrical optics limit) in the high-frequency approximation of PO scattering for Gaussian or exponentially correlated surfaces to be investigated analytically. The leading order term in the high-frequency expansion for general PO scattering from exponentially correlated surfaces (Hagfors' Law) is then reviewed and interpreted in terms of a recently published theory of PO for surfaces with infinite rms slopes. The approximate ldquocutoffrdquo wavenumber from Hagfors' Law at which the high-frequency portion of the spectrum of an exponentially correlated surface can be truncated without producing large errors in PO predicted scattering is also discussed. Using this cutoff wavenumber, an approximate region of validity of the complete PO theory for exponentially correlated surfaces is obtained. The validity condition indicates that, for fixed surface statistics, the PO method produces accurate predictions of true surface scattering only up to a specific frequency, and that PO is inaccurate in the high-frequency limit. Comparisons of PO predictions with those of a Monte Carlo numerical simulation are used to show that the validity condition derived appears to provide a reasonable indication of PO accuracy. These results have important implications for current investigations of scattering from exponentially correlated surfaces and for the use of Hagfors' Law, as it is traditional to accept PO as the appropriate high-frequency limit in most existing approximate models of surface scattering.

Diffraction of homogeneous and inhomogeneous plane waves by a planar junction between perfectly conducting and impedance half-planes

The problem of diffraction of homogeneous and inhomogeneous plane waves at the discontinuity formed by perfectly conducting and impedance half-planes is examined by the method of modified theory of physical optics (MTPO). The MTPO integral of the reflected scattered waves by the perfectly conducting half-plane is reconstructed in order to include the effect of the diffracted wave coming from the edge of the impedance half-plane. The integrals are evaluated by a uniform asymptotic method. The results are plotted numerically and compared with the literature.

Validation of Design Techniques on a Quasi-Optics Test Bench

A two channel Quasi-Optics Network (QON) with a Frequency Selective Surface (FSS) to act as filter has been designed, constructed and tested in order to examine several aspects of the design, including the accuracy of the design software, the effectiveness of the FSS and the effect of moving components along the ray path in a QON. The QON was designed to feed an offset reflector system which required an input beamwidth of 20 degrees at −8.68 dB. The two channels were the atmospheric sounding channels at 54 GHz (5 GHz bandwidth) and 89 GHz (3 GHz bandwidth). Gaussian beam techniques were used to design the QON with the final optimisation carried out using Physical Optics and Physical Theory of Diffraction. The measurements were carried using the facilities at National Physical Laboratory, London and Queen Mary, University of London. Agreement between predicted and measured performance was good, thus validating the design method, the equipment manufacture and the assumptions.

Scattering from a cylindrical reflector: modified theory of physical optics solution

The problem of scattering from a perfectly conducting cylindrical reflector is examined with the method of the modified theory of physical optics. In this technique the physical optics currents are modified by using a variable unit vector on the scatterer's surface. These current components are obtained for the reflector, which is fed by an offset electric line source. The scattering integral is expressed by using these currents and evaluated asymptotically with the stationary phase method. The results are compared numerically by using physical optics theory, geometrical optics diffraction theory, and the exact solution of the Helmholtz equation. It is found that the modified theory of physical optics scattering field equations agrees with the geometrical optics diffraction theory and the exact solution of the Helmholtz equation.

Edge-dislocation waves in the diffraction process by an impedance half-plane

Edge-dislocation waves, created in the diffraction of plane waves by an impedance half-plane, are examined by the method of modified theory of physical optics. The integrals, obtained by a related technique, are decomposed according to their boundaries and evaluated by using uniform asymptotic methods. The results are plotted and are investigated numerically.

Fourth-Order Small-Slope Theory of Sea-Surface Brightness Temperatures

A derivation of the fourth-order term in the small-slope approximation (SSA) of thermal emission from the sea surface is presented. It is shown that this term has the form of a fourfold integration over a product of two sea spectra for a Gaussian random process sea, thereby describing emission interaction effects among pairs of sea waves. An approximation for long-long wave interactions (i.e., the optical limit) is considered and shown to match the physical optics theory. Interaction effects between long and short waves are also considered, both through numerical and approximate evaluations of the fourth-order theory. The approximation developed has a form similar to an expanded model and enables comparisons of short-wave tilting effects between the two models in terms of spectrum independent functions. The weighting functions obtained are found to be similar, but not identical, for the SSA and two-scale theories. In addition, azimuthal harmonics from the fourth-order SSA expansion of long-short wave interactions for a particular sea-surface model are compared against the full fourth-order theory and the two-scale model. Results again show the SSA and two-scale models to yield similar, but not identical, predictions

Modified theory of physical optics solution of impedance half plane problem

The scattering of electric polarized plane waves from an impedance half plane problem is examined by the method of modified theory of physical optics (MTPO). Two integrals, consisting of incident and reflected scattered fields, are obtained. These integrals are evaluated asymptotically by the methods of stationary phase and edge point. The obtained scattered fields are compared with the exact solution numerically.

Modified theory of the physical-optics approach to the impedance wedge problem

The problem of a wedge with equal face impedances is examined with a modified theory of physical optics. The surface integral is constructed by use of the impedance boundary condition. The aperture equivalent current is estimated from the behavior of the reflected diffracted field. The integrals obtained are evaluated asymptotically and compared with the exact solution numerically.

Modified theory of physical optics approach to wedge diffraction problems

The problem of diffraction from a perfectly conducting wedge is examined with the modified theory of physical optics (MTPO). The exact wedge diffraction coefficient is compared with the asymptotic edge waves of MTPO integral and related surface currents are evaluated. The scattered electric fields are expressed by using these current components. The total, incident and reflected diffracted fields are compared with the exact series solution of the wedge problem, numerically.

Modified theory of physical optics

A new procedure for calculating the scattered fields from a perfectly conducting body is introduced. The method is defined by considering three assumptions. The reflection angle is taken as a function of integral variables, a new unit vector, dividing the angle between incident and reflected rays into two equal parts is evaluated and the perfectly conducting (PEC) surface is considered with the aperture part, together. This integral is named as Modified Theory of Physical Optics (MTPO) integral. The method is applied to the reflection and edge diffraction from a perfectly conducting half plane problem. The reflected, reflected diffracted, incident and incident diffracted fields are evaluated by stationary phase method and edge point technique, asymptotically. MTPO integral is compared with the exact solution and PO integral for the problem of scattering from a perfectly conducting half plane, numerically. It is observed that MTPO integral gives the total field that agrees with the exact solution and the result is more reliable than that of classical PO integral.

A study of the higher-order small-slope approximation for scattering from a Gaussian rough surface

Results from the first three terms of the small-slope approximation (SSA) for incoherent electromagnetic scattering from a penetrable randomly rough interface are discussed. Surface roughness is characterized as a Gaussian random process with an isotropic Gaussian correlation function. Sample results illustrate parameter spaces for which each correction term is appreciable. Reduction of the SSA to the physical optics theory is also discussed for both perfectly conducting and dielectric surfaces.

A UTD-PO solution for diffraction of plane waves by an array of perfectly conducting wedges

In this paper, a formulation for plane wave incidence by an array of perfectly conducting wedges is proposed. The solution takes the advantages of the uniform theory of diffraction (UTD) and physical optics (PO), and allows for numerical evaluation of a large number of perfectly conducting wedges. The solution has the major advantage of shortening the computing time over existing formulation when the number of wedges is very large. The source is assumed to be above, below, or level with the edge height. The technique proposed is validated with numerical results from technical literature. Results for cases not previously reported in the technical literature are also presented.