Equivalence of least-squares estimation of eye aberrations in linearly transformed reference frames

Zernike aberrations, estimated with respect to the wavefront sensor's reference frame by least-squares, are currently transformed to other frames using algebraic relationships. Obviously, they can also be estimated directly with respect to the transformed frames. In this paper, we demonstrate the equivalence between these two approaches in terms of bias and noise propagation, when the reference frames are related by a linear conformal transformation of coordinates.