Abstract
By the use of the spectral representation of the Rayleigh diffraction formula, an analytic representation of the solution of the boundary value problem for the Helmholtz equation in the half-space is shown when the boundary values are given on a non-singular curved boundary surface. The solution and the boundary values are mutually connected by a linear transformation which makes one-to-one correspondence in two dimensional space, if the region of the curved boundary surface is bounded. In the special case that a curved boundary surface is represented approximately by a plane and the spatial frequencies of the specified boundary values are limited to be low, the linear transformation is expressed approximately by the Fresnel transform.
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