For a small planar source, an accurate description of the far-field error in terms of the source error was presented based on a far-field asymptotic solution of the Helmholtz equation. The "critical point" of the far-field phase error was derived, analyzed and proposed to decide the off-center source error with the "relative error volume". Numerical results were also given to examine this method. It is shown that the off-center distance influences the far-field errors significantly, which can be used to describe the source error and analyze the far-field errors, and the source error for the inverse problem can be estimated by the "critical point".