A method for correcting slowly varying small-angle scattering curves for collimation effects

A technique has been developed for correcting slowly varying small-angle X-ray scattering curves for the distortions produced by the length of the collimating slits when, as is very often true, slit-width effects are negligible. The method, which is useful with measured scattering curves which decay so slowly with increasing scattering angle that the usual correction procedures do not converge, is based on approximating the measured curve by a polynominal in h², where h = 4πλ⁻¹ sin θ; 2θ is the scattering angle and λ is the X-ray wavelength. The order j of the polynomial is selected to give the best fit to the measured curve over the entire interval of angles for which data are available. The corrected curve is also a polynomial in h² of order j, and the coefficients of this polynomial can be easily evaluated. Tests of the method on a theoretical scattering curve and two experimental curves are described.