The dual-space resolution bias correction algorithm: applications to powder data

A reciprocal-space resolution bias correction algorithm has been recently suggested, providing suitable corrections for the classical atomic scattering factors. The Fourier maps calculated by using as coefficients the structure factors obtained by the modified scattering factors proved to be less resolution biased. In this paper the correction has been generalized in order to apply it to the experimental structure factor moduli; in this way more useful electron density maps may be calculated. In a less recent paper a direct-space resolution bias correction algorithm was devised and tested on a large set of powder patterns; the algorithm implies the modification of the electron density maps to reduce the truncation errors in the Fourier syntheses. In the present paper direct and reciprocal resolution bias correction algorithms are combined into the dual-space resolution bias correction algorithm. The usefulness of the new algorithm is checked on a set of powder patterns.