A high resolution autofocussing method for synthetic aperture sonar (SAS) has been developed for use in the Sapphires (Synthetic Aperture Processing High Resolution Sensor) SAS system jointly developed by FOI and SAAB underwater systems under a contract from the Swedish Defence Materiel Administration (FMV). The method is based on a frequency domain formulation and can correct for range and azimuth errors of the positioning system in the slant plane. The theoretical foundation for the method is developed and examples of application are presented using simulated data produced by a sonar simulation software (SAFIX) developed in the Sapphires project.