Derivation of infinite-slit-smeared small-angle scattering from porous surface and porous mass fractals

Small-angle X-ray scattering (SAXS) is often used to study porous and aggregated fractal materials. Typically when q is small or when large primary-beam intensities are required, the small-angle geometry employed introduces infinite-slit-height smearing into the experimental data. Herein, simple derivations for infinite-slit-height-smeared SAXS from porous surface and mass fractals are presented, including an approximation for aggregated mass fractals. The models allow rapid analysis of background-subtracted data without the need for deconvolution. An equation is derived that allows analysis of normalization from deconvolution routines applied to porous-fractal data. This model is tested using simulated and experimental SAXS data.