Subspace migration for shape reconstruction of a crack with an unknown wavenumber

The results of numerical simulations have confirmed that it is possible to recognize the existence of a perfectly conducting crack via subspace migration when an inaccurate wavenumber is applied, even though the exact shape cannot be retrieved. However, the theoretical reason for this phenomenon has not been confirmed. Due to this reason, we rigorously analyze subspace migration. In this regard, we prove that the imaging function is expressed by the zero-order Bessel function and theoretically identify why such a phenomenon occurs.