Electron backscatter diffraction (EBSD) has become the preferred technique for characterizing the crystallographic orientation of individual grains in polycrystalline microstructures due to its ability to rapidly measure orientations at specific points in the microstructure at resolutions of approximately 20-50nm depending on the capabilities of the scanning electron microscope (SEM) and on the material being characterized. Various authors have studied the angular resolution of the orientations measured using automated EBSD. These studies have stated values ranging from approximately 0.1° to 2° [1-6]. Various factors influence the angular resolution achievable. The two primary factors are the accuracy of the detection of the bands in the EBSD patterns and the accuracy of the pattern center (PC) calibration. The band detection is commonly done using the Hough transform. The effect of varying the Hough transform parameters in order to optimize speed has been explored in a previous work . The present work builds upon the earlier work but with the focus towards achieving the best angular resolution possible regardless of speed. This work first details the methodology used to characterize the angular precision then reports on various approaches to optimizing parameters to improve precision.