A method for calibrating a computed tomographic imaging apparatus having a gantry, a radiation source operable at a plurality of kVp's, and a detector array having a plurality of detector elements includes using a system detection function to estimate signals of each detector element that would have been detected through air and through a given thickness of water to determine estimated datasets. The estimated datasets are used to determine data pair sets each comprising a normalized water projection value and an ideal projection value for each detector element. The method further includes determining and storing a representation of a mapping function of the normalized water projections values to the ideal projection values in a memory of the computed tomographic imaging apparatus as a spectral calibration of the computed tomographic imaging apparatus.