The idea of placing a coloured filter in front of a camera to make it more colorimetric has been previously proposed. However, this prior art approach sought to increase the dimensionality of the capture – i.e. to take an image with and without a filter – rather than to change the spectral characteristics of the sensor itself. In this paper, we set out a new method for finding the filter that, in a least-squares sense best achieves the Luther condition. That is, the filter multiplied by the camera spectral sensitivities is 'almost' a linear combination from the colour matching functions of the human visual system. We show that for a given sensor set the best filter and best linear mapping can be found together by solving an alternating least-squares problem. Experiments demonstrate that placing an optimal filter in front of a camera can result in a dramatic improvement in its ability to see the world colorimetrically.