Adaptive optics are regularly used in ground-based astronomical telescopes. These applications are characterized by a very narrow (~1 arcmin) field of view. For economic reasons, commercial space- based earth-observing optical systems must have a field of view as large as possible. We develop a new error function that is an extension of conventional adaptive optics for wide field-of-view optical systems and show that this new error function enables diffraction-limited performance across a large field of view with only one deformable mirror. This new error function allows for reprogramming of aberration control algorithms for particular applications by the use of an addressable weighting function.