Estimation accuracy of Horn and Schunck's classical optical flow algorithm depends on many factors including the brightness pattern of the measured images. Since some applications can select brightness functions with which to `paint' the object, it is desirable to know what patterns will lead to the best motion estimates. In this paper we present a method for determining this pattern a priori using mild assumptions about the velocity field and imaging process. Our method is based on formulating Horn and Schunck's algorithm as a linear smoother and rigorously deriving an expression for the corresponding error covariance function. We then specify a scalar performance measure and develop an approach to select an optimal brightness function which minimizes this performance measure from within a parametrized class. The resulting optimal performance is demonstrated using simulations, and a discussion of these results and potential future research is given.