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The (phase-space) local spectrum of the field scattered by a low-contrast object due to Gaussian beam incidence is evaluated in the high-frequency regime. The scattering problem is linearized using the Born approximation for which the incident field and local transform domain Green's function can be evaluated asymptotically. The scattering phenomenology is described in terms of local samplings of the object function which are localized in the object domain according to the incidence and processing parameters. Application in the field of inverse scattering are expected to yield fast and efficient algorithms due to the availability of analytic solutions for both the incident wave and the local domain Green's function.