Can ultraprecision polishing techniques improve the coherence times of nitrogen-vacancy centers in diamond?

We investigate the correlation between surface roughness and corresponding $T_2$ times of nearsurface nitrogen-vacancy centers (~7 nm/ 5 keV implantation energy) in diamond. For this purpose we compare five different polishing techniques, including both purely mechanical as well as chemical mechanical approaches, two different substrate sources (Diam2tec and Element Six) and two different surface terminations (O- and H-termination) during nitrogen-vacancy forming. All coherence times are measured and compared before and after an oxygen surface treatment at 520 {\deg}C. We find that the coherence times of shallow nitrogen-vacancy centers are surprisingly independent of surface roughness.