Abstract
The one-dimensional stochastic Helmholtz equation is solved first by a two-variable expansion. This gives the one-dimensional equivalent of the Debye asymptotic expansion. Then the one-dimensional Born result is derived for the stochastic Helmholtz equation. It is shown that imposing the traditional single-scattering condition on the Debye result produces the Born result. The coefficient of intensity variation V is calculated for both approximations, and it is again shown that the Debye result reduces to the Born result under the single-scattering condition. It is emphasized that the Debye result avoids the long-range and high-frequency restrictions of the Born result, which arise from the cumulative phase effects.
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