A novel approximation for the delays used in focused beamforming is presented that is based on weighting the terms of the conventional Fresnel approximation. The objective is to enlarge the validity region of the Fresnel approximation in order to investigate wider scanning regions. A least-squares solution provides the exact weight values by the minimization of the mean-square error computed over the desired scanning region and on the basis of the array geometry. The attractive results obtained by applying the proposed approximation to a linear array are presented.