  We argue that a finite iteration of any surface fractal can be composed of
mass-fractal iterations of the same fractal dimension. Within this assertion,
the scattering amplitude of surface fractal is shown to be a sum of the
amplitudes of composing mass fractals. Various approximations for the
scattering intensity of surface fractal are considered. It is shown that
small-angle scattering (SAS) from a surface fractal can be explained in terms
of power-law distribution of sizes of objects composing the fractal (internal
polydispersity), provided the distance between objects is much larger than
their size for each composing mass fractal. The power-law decay of the
scattering intensity $I(q) \propto q^{D_{\mathrm{s}}-6}$, where $2 <
D_{\mathrm{s}} < 3$ is the surface fractal dimension of the system, is realized
as a non-coherent sum of scattering amplitudes of three-dimensional objects
composing the fractal and obeying a power-law distribution $d N(r) \propto
r^{-\tau} dr$, with $D_{\mathrm{s}}=\tau-1$. The distribution is continuous for
random fractals and discrete for deterministic fractals. We suggest a model of
surface deterministic fractal, the surface Cantor-like fractal, which is a sum
of three-dimensional Cantor dusts at various iterations, and study its
scattering properties. The present analysis allows us to extract additional
information from SAS data, such us the edges of the fractal region, the fractal
iteration number and the scaling factor.

Statistical Mechanics;Mesoscale and Nanoscale Physics