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Let $M$ be a scattering manifold, i.e., a Riemannian manifold withasymptotically conic structure, and let $H$ be a Schr\"odinger operator on $M$.We can construct a natural time-dependent scattering theory for $H$ with asuitable reference system, and the scattering matrix is defined accordingly. Wehere show the scattering matrices are Fourier integral operators associated toa canonical transform on the boundary manifold generated by the geodesic flow.In particular, we learn that the wave front sets are mapped according to thecanonical transform. These results are generalizations of a theorem by Melroseand Zworski, but the framework and the proof are quite different. These resultsmay be considered as generalizations or refinements of the classicaloff-diagonal smoothness of the scattering matrix for 2-body quantum scatteringon Euclidean spaces.

Microlocal properties of scattering matrices for Schrödinger equations on scattering manifolds