Methods for improving the accuracy of Commission Internationale de L’Eclairage tristimulus values of object color by calculation – Part I: Improvement on measurement bandpass and intervals

Color is one of the most important appearance properties of objects. To digitize color, measuring and calculating tristimulus values are the most basic work besides obtaining reflectance spectrum. However, the accuracy of tristimulus values varies with instruments, measuring, and calculation methods. Textiles and some other application of color demand high color quality due to their special utilization. The series of our studies aim to analyze and evaluate some mathematical solutions in order to improve the accuracy of tristimulus values. The studies include two parts: (1) Part I concentrates on measurement bandpass and intervals and their corresponding improvement algorithms, (2) Part II focuses on the influence of measurement ranges and their truncation errors and some algorithms to overcome the truncation errors. In Part I (current article), measurement errors caused by bandpass and test intervals in the spectrophotometer are analyzed. Then, algorithms including two bandpass corrections (3-point correction and 5-point correction), three interpolations (third-order polynomial interpolation Lagrange and Spline, a fifth-order polynomial interpolation Sprague), two Oleari deconvolution methods (zero- and second-order), and three optimization weighting table methods (ASTM Table 6, Table LLR, and Table LWL) are studied systemically by programming MATLAB software and basing on measuring the spectral reflectance of 1301 chips in Munsell Color Book with Commission Internationale de L’Eclairage (CIE) 1964 color-matching functions and D65 standard illuminant. The results show that all algorithms mentioned above yield very positive effects, and among them, Table LWL performs best with reducing the bandpass error and intervals error to 7‰ of its original error and is recommended.