It is well understood that the color values from a digital camera are functions of the camera's spectral sensitivities, the reflectances of the objects in the scene as well as illumination and any filter that is placed between the object and the sensor. It is vital to select the correct illumination to optimize a color reproduction pipeline. In practice, the choice of the illumination is limited to the spectra of available light sources.<br/> In this paper, we optimize a camera's colorimetric performance by theoretically mounting a filter to the lens. An ideal spectrum of the filter is obtained using the Luther optimization condition. By using variational calculus we reduce the optimization problem to a system of non linear equations on a Lie group. We solve the system of equations by applying Newton's method on a Lie group with a left invariant Riemannian structure. As expected from the literature, our experiments show quadratic convergence.<br/> A second approach is a redesign of the set-up. This redesign gives us a quadratic optimization problem that is easier to solve. Constraints to this optimization problem gives us control on the transparency of the filter.