X-ray diffraction from Anodisc membrane filters is measured and analyzed. The patterns are consistent with pores of constant diameter and a Gaussian distribution of pore-pore spacing. The mean distance between pores, measured using x rays is 0.37 microm compared to 0.32 microm calculated from the nominal density of pores/cm(2). The results may be modeled both in terms of the convolution of a structure factor of the pores with the resolution function, and by modeling the source as a collection of incoherent sources with an ideal monochromator crystal. The incoherent source analysis provides an explanation for the common observation that the resolution function in many x-ray spectrometers is better fit to a sum of Lorentzians, rather than a single Lorentzian.