We present a study of an adaptive imaging system efficiency when viewing an extended object through a layer of a turbulent medium. We have estimated a change in the size of the region where the influence of weak inhomogeneities can be compensated for when placing a corrector into the region of the layer image center. It is shown that the relative improvement in the system performance due to the displacement of the corrector depends on the layer thickness and its position. A modified version of the correction algorithm is proposed that enables extending the region of the system isoplanatism. Analysis has been made using series expansion of the wave front over Zernike polynomials.