Improved model for improving the inter-instrument agreement of spectrocolorimeters

A proposal by Robertson slightly modified by Berns and Petersen, to use spectral differences to predict systematic errors in spectrophotometers has found limited success in practical application. Porter suggested a way to improve the level of agreement between standardizing laboratories based on the Berns and Petersen method but suggested using derivatives calculated from piecewise polynomial splines. He did not know it at the time, but such a model was already in use. That model now has over five years of successful field testing and this paper discloses how the model was developed, the efficiency with which it can reduce systematic errors and the kinds of errors that cannot presently be corrected by computational comparison of reflectance or transmittance factor readings. For instruments of the same basic design, this model will produce a reduction of the systematic errors in colorimetric coordinates on the order of factors of 2–3. The magnitude of the initial color differences appears to be irrelevant. The corrective power of the model is limited by the numerical noise generated by the process of simulating analytical derivatives. We show that instruments with average color differences of 1.0 CIELAB unit can be reduced to a level of 0.5–0.3 units. Our testing has included a large variety of material samples including textiles, plastics, inks, paints and ceramics. Over 400 samples have been measured in proving this method. In addition, the model has been in place in industrial environments where multiple instruments of different manufacturer have been made to operate successfully from the same set of laboratory standards at reproducibility levels that rival those of national standards laboratories.