This experiment suggests that two conditions must be fulfilled for transparency to be seen. First, there must be figural complexity and segmentation to justify this interpretation (hence no transparency in a). Second, the luminance ratios have to be right (no transparency is visible in b or d).
Transparency is infrequent in nature, but shadows are not. It is possible that the “laws” of perception we have explored so far evolved mainly to deal with shadows and to distinguish them from “real” objects, which would also produce luminance differences in the visual scene as a result of differences in reflectance (for instance, a zebra’s stripes or a white cat on a black mat).
The shadow cast by an object such as a tree could, in theory, be pitch black if there were a single distant light source, without scattering or reflections. Ordinarily, however, ambient light from the environment falls on the shadow so that a dark, but not black, shadow results. If the tree shadow falls on a sidewalk and darker grass (e), the manner in which the magnitude and sign of luminance vary along the shadow’s boundary would be identical on both sides of the boundary, the shadow side and the light side. This covariation of luminance clues the brain that it is a shadow, not an object or texture.
It turns out that the luminance changes in transparency mimic those seen in shadows. The visual system may have evolved to discover and react appropriately to shadows rather than to transparent filters. If it could not, you might try to grab a shadow or gingerly step over it to avoid tripping, not realizing that it is not an object at all.
Interestingly, although our perceptual mechanisms seem to be aware of the physics of transparency pertaining to luminance, they appear to be blind to the laws pertaining to color “transparency.” In f and g, we have two bars crossing each other, both with luminance of, say, 50 percent of the background. We have contrived it so that in g the overlapping region has 25 percent of the background luminance, as it should be if we were dealing just with luminance. But if the colors of the two filters are different—as they are—the overlap zone should be pitch black, not gray. The reason is that the red filter transmits only long (“red”) wavelengths when white light shines through it and the blue filter transmits only short (“blue”) wavelengths. So if you cross the filters, no light passes through; the overlap zone would be black. In fact, transparency is seen not when the midzone is black but when it is 25 percent (g). Apparently, the visual system continues to follow the luminance rule and ignores the color incompatibilities.
A curious effect occurs if you place a gray cross on a white background when the middle of the cross is a lighter shade of gray (h). Instead of seeing the lighter cross for what it is, the brain prefers to see it as if there were a circular piece of frosted glass or vellum superimposed on the larger gray cross. To achieve this perception, the brain has to “hallucinate” an illusory frosted glass spreading, even in the area surrounding the central region of the cross. The effect is especially compelling if you have a patch of several such crosses (i).
Once again the luminance ratios between the surround (white), the cross (dark gray) and the central region (light gray) have to be just right for the effect to occur; if they are wrong, the effect disappears (j). In other words, the ratios must be compatible with what would occur with actual translucent surfaces (for example, fog or frosted glass). The effect is even more striking if there is a chromatic component to the display (k).
Thus, even though the visual system does not know about color subtraction, if the luminance ratios are right, then the colors are “dragged along” with the spread of luminance.