The luminance conditions of transparency

In two experiments the luminance conditions for the occurrence of phenomenal transparency in achromatic flat patterns was studied. Let a, p, q and b be, respectively, the luminances of the parts A, P, Q, and B of a pattern comprising a transparent square on a two-part background, where P and Q are the parts of the square on backgrounds A and B, respectively. The results showed that magnitude of p-a, magnitude of q-b, and magnitude of p-q were quantitative conditions of transparency. Metelli has proposed two ordinal conditions of transparency, magnitude of a-b > magnitude of p-q and p > q if a > b (or p < q if a < b). Alternatively, Masin and Fukuda have proposed the single ordinal condition p [symbol: see text] (a, q) [or q [symbol: see text] (p,b)]. The results showed that this second condition best predicted the occurrence of transparency.