Intensity Profile of Lambert's Scatterer

[0207]

I wish to understand the intensity profile of a lambertian scatterer.
how can a surface look the same when viewed from any angle, when its intensity profile shows that the intensity decreases with the viewing angle?

 

[Andy Resnick]

A lambertian surface has the property that the intensity of scattered light varies linearly with the cosine of the angle between incidence and reflection.

Because this dependence is the same as the geometrical change of a surface element as it is tilted with respect to the line of sight (i.e. the projected area), the two terms cancel and the surface appears to have a constant brightness. Thus, the moon appears flat, and a piece of printer paper likewise appears to have constant brightness without regard to viewing angle.