Simple additivity is often used as basic model for digital display characterization. However, such a simple model cannot all the time satisfy the needs of demanding color management applications.This paper presents an enhanced method to characterize the XYZ to RGB transform of a digital display. This parametric method exploits the independence between the luminance variation of the electro-optic response and the colorimetric responses for certain display types.3-DMD projectors are the reference for high grade color management. However, the model is more generally applicable to Digital Displays (and not only projectors), including Single DMDs, CRTs, LCDs, etc, if the independence condition is satisfied.While the problem to solve is a 3D to 3D transformation (from XYZ to RGB), the proposed parametric model is the composition of a 2D transform followed by a 1D transform. The 2D transform manages the chromatic aspects and, in succession, the 1D transform manages the Luminance variations.This parametric digital model is applicable in the field of Color Management, with the objective to calibrate Digital Displays and apply a reference look such as a film look.