Curvature sensors, adaptive optics, and Neumann boundary conditions

We consider the Neumann boundary-value problem for curvature adaptive optics systems. We show that, because curvature sensors average over extended regions of the wave front, inconsistent data for the solution of the Neumann problem result when the measurements are treated as local. Because this inconsistency is generally resolved passively in the adaptive mirror itself, it can be interpreted as an uncontrolled degree of freedom of the system. We offer several procedures for treating the data in a more consistent fashion.