Inverse problem for the reduced wave equation with fixed incident field. III

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Abstract
The inverse problem for the reduced wave equation Δu+k2n2(x)u=0, x∈R3, is examined for the case where measurements of the amplitude of the scattered field (produced by a fixed incident field at a single frequency) are obtained at a finite number of points. A strategy is given for the recovering of the phase data through the minimization of a quadratic form involving comparison data. The problem is then reduced to the problem treated in previous papers where the complex-valued quantities us(xl) are known at a finite number of points. A relationship between the smallest eigenvalue of the ‘‘measurement’’ matrix and ∥K∥2 is given.

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