STABLE DESMEARING OF SLIT-COLLIMATED SAXS PATTERNS BY ADEQUATE NUMERICAL CONDITIONING

Small-angle X-ray scattering (SAXS) patterns from slit cameras ('Kratk y cameras') require a subsequent desmearing procedure in order to obta in the pinhole scattering curve that is suitable for subsequent struct ure analysis. Since the corresponding integral equation contains a sin gularity, its solutions are usually unstable and fail if large noise i s present. It is demonstrated how analytical stability can be achieved by physically reliable conditioning of the experimental data, introdu ction of the Moore-Penrose pseudoinverse of the equation's discretized integral operator and solving the equation by a FFT algorithm. This e nsures the consistency of the solution as well as its stability, and h ence its convergence. This solution can account for arbitrarily nonsym metrical primary-beam profiles. The algorithm does not require anteced ent smoothing of the scattering curve. It allows on the contrary low-p ass filter smoothing during desmearing but remains stable despite larg e noise contributions.