Factorial constraints of transparency

The present paper reports the results of an experiment designed to determine the constraints of the factorial pattern of data that a valid model for the perceived extent of achromatic transparency, rated, must predict. Consider a transparent achromatic disk in the middle of two adjoining achromatic rectangles with the common border of the rectangles dividing the disk in half. Let a and b be the l-minances of the left and right rectangles, respectively, and let p and q be the lu-minances of the left and right halves of the disk, respectively. By varying p and q factorially for different pairs of a and b and plotting mean rated as a function of p, we have found that a valid model of transparency must meet the constraints that (i) the rated extent of transparency of the disk varies essentially linearly with p, (ii) that factorial curves converge upward as p increases, and (iii) that the mean slope of factorial curves increases as the difference between a and b decreases. A new model of transparency is proposed which satisfies these constraints.