Recent development on the Green's function retrieval by wavefield crosscorrelation has substantially advanced the physical research in a multidisciplinary and unprecedented fashion. However, the underlying assumption of the theory that the sources are in the far-field limits the technology to extracting only the high-frequency part of the Green's function in an open system. This critical approximation can be eliminated using the exact boundary integral equation method. A scheme involving the crosscorrelation kernel is proposed to recover the exact Green's function including all-frequency content. Symmetric difference kernels are analytically constructed for sources on a plane or on a circle and can be reduced to the known Dirac delta kernel under the far-field approximation.
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