Achromatic-point prediction.

Abstract

This paper constitutes a mathematical elaboration, in a form permitting direct predictions of data, of the empirical discoveries of Helson and Michels concerning the “effect of chromatic adaptation on achromaticity.” An equation is developed permitting the chromaticity of a test spot that appears achromatic against an extended chromatic background to be predicted from the background chromaticity and the luminance ratio of spot to background. The technique for numerical solution of the equation is explained, and a family of curves allowing approximate solution by interpolation is presented. If the luminance of the achromatic spot is no greater than that of the background, the achromatic chromaticity always lies more than 34 of the way along the line directed from the absolute (black background) neutral point to the background point, regardless of the color of the background. As part of a discussion of additional numerical methods useful in applying the model to data, general least-squares formulas are presented for the coordinates of the point best representing the common intersection of any set of given lines; and for the line, passing through a specified point, that best fits a set of given points by the criterion of perpendicular deviations.