When distinguishing between fat and water in acquired MR data, a modified Dixon technique includes acquiring first and second signals Ii and I2, calculating the first and second components B and S of the signals Iχ and I2, where one of the first and second components corresponds to fat and the other corresponds to water, deriving two differential phase error candidates from them, and selecting a phase error candidate based on the assumption of smoothness of the disturbing field inhomogeneity. The exact determination of the absolute values of the water and fat components is then made by solving three signal equations for two variables that respectively correspond to water and fat, and is performed using for example a least square minimization with a Newton method.