Test of the Singh-Anderson Model of Transparency

Abstract

A new model of achromatic transparency has been recently proposed by Singh and Anderson as an alternative to the model proposed long ago by Metelli. The study reported here compared these models using achromatic stimuli consisting of a transparent disk on a background formed by two adjoining rectangles, with the common border of the rectangles dividing the disk in half. Let a and b denote the luminances of the left and right parts of the background, respectively, and let p and q denote the luminances of the left and right parts of the disk, respectively. The value of b was varied for fixed values of a, p, and q. For these values the Singh-Anderson model predicts that the perceived extent of transparency T of the disk is constant with b, while Metelli's model predicts that T decreases as b increases. Participants rated T. The results confirm the prediction of Metelli's model. It is also shown that the Singh-Anderson model is invalid in principle in that, unlike Metelli's model, it fails to capture the principle of independence of the effects of a, b, p, and q on T.