Lightness constancy through transparency: internal consistency in layered surface representations

Asymmetric lightness matching was employed to measure how the visual system assigns lightness to surface patches seen through partially-transmissive surfaces. Observers adjusted the luminance of a comparison patch seen through transparency, in order to match the lightness of a standard patch seen in plain view. Plots of matched-to-standard luminance were linear, and their slopes were consistent with Metelli's alpha. A control experiment confirmed that these matches were indeed transparency based. Consistent with recent results, however, when observers directly matched the transmittance of transparent surfaces, their matches deviated strongly and systematically from Metelli's alpha. Although the two sets of results appear to be contradictory, formal analysis reveals a deeper mutual consistency in the representation of the two layers. A ratio-of-contrasts model is shown to explain both the success of Metelli's model in predicting lightness through transparency, and its failure to predict perceived transmittance--and hence is seen to play the primary role in perceptual transparency.