Scattering from a Surface Fractal

The scattered intensity I (q) can be obtained by substituting (5.124) into (5.61) and performing the integration. Here, again, we simply quote the final result, which is 

The exponent — (6—ds) for surface fractals, given by Equation (5.125), can also be understood by the following simplified argument. The surface area of a surface fractal depends on the scale with which the object is viewed. In the scattering measurement, as we increase q, we are in effect looking at the object at an ever decreasing size scale. The effective surface area S perceived therefore varies, as a function of q, as 

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