When characterising a digital camera spectrally or colourimetrically, the camera response to a generally diffusely reflecting colour chart is often employed. The recorded responses to the light incident from each colour patch are typically not linearly related to the power of the irradiance on the chart, and the irradiance varies with position on the chart. This necessitates a linearisation of the responses. We present a new single image colour chart-based estimation method of responses, that are linearly related to camera response values known as ground truth. The method estimates the spatial geometry of the irradiance incident on the chart attenuated by lens vignetting and compensates individually for volumetric and per colour channel non-linearities, including compensation for physical scene and camera properties in a pipeline of successive signal transformations between the estimated linear and the given recorded responses. The estimation is controlled by introducing a novel Additivity Principle of linear responses, which is derived from the spectral reflectances of the coloured surfaces on the colour chart, observing that linear relations of the spectral reflectances are equal to the relations of the corresponding linear responses. Crucially, the additivity principle is not subject to metamerism. The method is fundamentally solely reliant on a one-shot set of one triplet of response values sampled from each patch of a colour chart with known spectral reflectances, where rendition level, gray scale, illuminant, camera sensor curves, irradiance geometry, vignetting, moderate specular reflection, colour space, colour correction, gamut correction and noise level are unknown.