Likelihood-enhanced fast translation functions

This paper is a companion to a recent paper on fast rotation functions [Storoni et al. (2004), Acta Cryst. D60, 432-438], which showed how a Taylor-series expansion of the maximum-likelihood rotation function leads to improved likelihood-enhanced fast rotation functions. In a similar manner, it is shown here how linear and quadratic Taylor-series expansions and least-squares approximations of the maximum-likelihood translation function lead to likelihood-enhanced translation functions, which can be calculated by FFT and which are more sensitive to the correct translation than the traditional correlation-coefficient fast translation function. These likelihood-enhanced translation targets for molecular-replacement searches have been implemented in the program Phaser using the Computational Crystallography Toolbox (cctbx).