The transition of the powertrain from combustion to electric systems increases the demand for reliable copper connections. For such applications, laser welding has become a key technology. Due to the complexity of laser welding, especially at micro welding with small weld seam dimensions and short process times, reliable in-line process monitoring has proven to be difficult. By using a green laser with a wavelength of [lambda] = 515 nm, the welding process of copper benefits from an increased absorption, resulting in a shallow and stable deep penetration welding process. This opens up new possibilities for the process monitoring. In this contribution, the monitoring of the capillary depth in micro copper welding, with welding depth of up to 1 mm, was performed coaxially using an optical coherence tomography (OCT) system. By comparing the measured capillary depth and the actual welding depth, a good correlation between two measured values could be shown independently of the investigated process parameters and stability. Measuring the capillary depth allows a direct determination of the present aspect ratio in the welding process. For deep penetration welding, aspect ratios as low as 0.35 could be shown. By using an additional scanning system to superimpose the welding motion with a spacial oscillating of the OCT beam perpendicular to the welding motion, multiple information about the process could be determined. Using this method, several process information can be measured simultaneously and is shown for the weld seam width exemplarily.