High-frequency expressions in the caustic region are derived for the wave reflected by a circular and a parabolic cylindrical reflector using Maslov's method when a plane wave is incident obliquely. Maslov's method is a systematic procedure for predicting the field in the caustic region combining the simplicity of ray and generality of the transform method. Numerical computations are made for the field pattern around the caustic or cusp region and the variation of peak positions of the reflected field with respect to the incident angle. three spatial dimensions can be obtained by solving which are valid near the caustics for the waves re-Hamilton's canonical equations. But information of flected by the cylindrical reflectors are derived. Field the ray trajectory is included in both space coordi-distributions around the caustic and cusp are calcunates R = (x, y, z) and wave vector P = (Px, Py, Pz), lated numerically, and the results are shown schesince R and P are related to each other by the ca-matically. The variation of peak positions of the renonical equations. We can therefore replace a part of flected waves with respect to incident angles is also the components of (x, y, z) by corresponding compo-discussed. nents of (p •,, py, Pz), e.g., (x, p>,, z), (p•, py, z) to describe a ray. These are refered to as hybrid coordi-2. STATEMENT OF THE PROBLEM nates or mixed coordinates. Ray expression described 2.1. Summary of basic expressions

High-frequency solutions for a field generated by a reflector and by a phase transformer are derived using Maslov's method. Derived results are compared with those obtained by other more standard methods when they are available. Agreement is complete for a field generated by a reflector. The results demonstrate that Maslov's method provides an alternative tool for evaluating diffraction images of reflector antennas.

Maslov's method is applied to derive expressions for the wave reflected by a spherical reflector when the plane wave is incident along the axis of the reflector. A relatively simple expression is derived which is valid in the caustic region. An asymptotic my expression is also derived which can be used in the region far from the caustic. Field distributions around the cusp region are calculated numerically and the results are compared with those obtained by other methods when they are available. Agreement among them is fairly good.

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