The correction of resolution errors in small-angle scattering using Hermite functions

In a generalization of Guinier's approximation, the scattering functions in small angle scattering are represented by series of Hermite orthonormal functions. This allows a general solution of the slit height problem in terms of a simple coefficient formalism. To correct the slit width resolution error and the polychromatic effect on the basis of Hermite functions, orthonormal systems are constructed which lead to recurrence relations for the coefficients appearing in the solution. The methods have been numerically tested for various types of functions.