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We derive asymptotic expressions for the scattering effects of small inhomogeneities in the context of the two dimensional Helmholtz equation. Asymptotic refers to the limit as the inhomogeneity size tends to zero. One novelty is that these asymptotic formulas also apply to large frequency, not just finite or zero frequency, as has been considered previously. The derived formulas are compared to numerically simulated solutions of the Helmholtz equation.

High frequency perturbation formulas for the effect of small inhomogeneities