Vogel spiral-based tilt-scan averaging approach for robust and efficient diffraction contrast suppression in DPC STEM

We theoretically investigated how the arrangements of tilt points affect the suppression of diffraction contrast in tilt-scan-averaged differential phase contrast scanning transmission electron microscopy (tDPC STEM). To examine the effectiveness of tilt-point arrangement, we compared three sampling patterns: conventional 4-fold, 6-fold symmetric concentric patterns and the Vogel spiral pattern based on Fermat's spiral with the golden angle. Multislice simulations were performed for GaN, GaAs, Si, and SrTiO3 crystals. Although all patterns approached similar converged values with sufficiently high tilt numbers, their convergence behaviors differed markedly. The concentric patterns exhibited non-monotonic decay and showed discrete fluctuations in residual diffraction contrast, whereas the Vogel spiral showed a smoother and more monotonic decrease over a wide range of tilt numbers. This behavior was consistently observed across the crystals with different crystal symmetries. These results show that rotationally asymmetric and uniformly distributed tilt sampling is advantageous for the robust diffraction-contrast suppression in DPC STEM, and identify the Vogel spiral as an effective tilt pattern for this purpose.