Brightness is not what it seems

The light that reaches your retina from a surface depends on two things multiplied together:

light reaching the eye = reflectance of the surface × light falling on it

Reflectance is the fraction of light the surface bounces back (white paper reflects most, charcoal reflects little). The illumination can change a lot, from bright sun to deep shade. The retina cannot tell the two apart from one number. If a patch is dim, is the paper grey, or is it white and in shadow?

Your brain has to decide, and it makes the call using context. The result is called lightness constancy: a white sheet still looks white in the shade, and black coal still looks black in the sun, even though in absolute terms shaded white can reflect less light to your eye than sunlit black.

The checker-shadow illusion, made famous by the vision scientist Edward Adelson, shows the trick. A cylinder casts a shadow on a checkerboard. One square outside the shadow looks dark and one square inside the shadow looks light, and yet on the screen the two squares are exactly the same shade of grey. Your brain knows the second square is in shadow and corrects for it, so the same pixel value looks lighter. The correction is part of how you see, so it works even after you know the answer.

Two more brightness effects come from how neighbouring areas interact:

• Simultaneous contrast: the same grey looks darker on a light background and lighter on a dark one.
• Mach bands: where a smooth ramp of brightness meets a flat area, or where the steps of a grey staircase meet, you see a thin lighter strip on the bright side of the edge and a darker strip on the dark side, even though no such strips exist in the picture. They are named after the physicist and philosopher Ernst Mach, who described them in the 1860s. A common explanation is that neighbouring neurons inhibit each other, which sharpens edges.