Inner products and orthogonality in color recording filter design

We formalize ideas of orthogonality and inner products implicit in the development of a number of figures of merit (FOM) of color recording filters. We show that, in negligible measurement noise, the data dependence of each FOM based on linear color correction is equivalent to a choice of inner product (and hence of orthogonality). Further, we show that optimal sensors with respect to noise sensitivity are simply defined as orthogonal with respect to this inner product. We also develop the idea of a generalized Q-factor by generalizing the Euclidean inner product to include all inner products. Simulations demonstrate the utility of our analytical results.