In this article we derive several results concerning diffraction from random surface configurations. First, we describe a practical method for inverting diffraction data in order to obtain an explicit expression for the size distribution of diffracting islands on a substrate. The principle of maximum entropy is used to fix the distribution in the formP=exp[−F(A)], whereF(A) is a polynomial in the island areaA. Then we show that the most general use of the maximum entropy principle requires thatFfor the exact size distribution be a simple, linear function of the geometry of the scatterers. While this result is of considerable practical use, of greater importance is the fact that it puts distinct and well‐defined limits on the possible functional form thatP(A) may exhibit. An example calculation is made using our diffraction data for indium on gallium arsenide.