The Federal Bureau of Mines has derived a mathematical expression for the emulsion calibration curve used in optical emission spectroscopy. Employing a two-step preliminary curve method, an approximation of the first derivative of the calibration curve is formed and integrated. The final equation is I = (1 + βS)−α where I is the line intensity, S is the transform that linearizes the preliminary curve, and α and β are constants.
Jack R. Woodyard, B. C. Piper, and K. R. Stever, "The Functional Form of the Emulsion Calibration Curve," Appl. Spectrosc. 33, 25-28 (1979)