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 $0.37\hspace{0.5em}\mu \mathrm{m}$ compared to $0.32\hspace{0.5em}\mu \mathrm{m}$ calculated from the nominal density of $\mathrm{pores}/{\mathrm{cm}}^2.$ 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.

• Received 30 October 2001

DOI:https://doi.org/10.1103/PhysRevE.65.046615