We present a differential wavefront sampling method for the efficient alignment of centred optical systems. Using the inter-element effects reported in our previous study, this method generates a linear symmetric matrix that relates the optical wavefront to misalignments within the system. The solution vector of this matrix equation provides a unique description of decentre and tilt misalignments of the system. We give a comparison of this approach to the existing method in the first case study and then illustrate characteristics of the new approach using the subsequent four case studies and Monte-Carlo alignment simulations. The results reveal superiority of the method over the existing one in misalignment estimation accuracy and demonstrate the practical feasibility and robustness.