Recently a ray-optical procedure has been developed to determine the modes scattered by an obstacle in a homogeneously filled, perfectly conducting waveguide from knowledge of the free-space diffraction pattern ƒ(θ) of the obstacle. The present paper extends the procedure to two-dimensional waveguides or ducts filled with a weakly inhomogeneous medium and bounded by impedance walls. As in previous studies for simpler cases, the analysis deals initially with radiation from a nonisotropic line source with free-space radiation pattern ƒ(θ); it involves the ray-optical construction of the solution, ray-modal conversion, comparison with the asymptotic form of the rigorous solution for an isotropic source (ƒ(θ) = 1), and a semiheuristic modification to make the result applicable even to lower-order modes. While the method applies most directly to real rays and propagating modes, the result is extended subsequently to complex modes descriptive of evanescent, lossy, or leaky wave processes. Moreover, special attention is given to commonly ignored ray-optical phenomena associated with impedance boundaries. Application of the results is illustrated briefly by considering scattering due to a perfectly conducting strip obstacle located inside an inhomogeneous, lossless waveguide. Detailed calculations for this and other examples are to be presented in a future publication.
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