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Multi-conjugated adaptive optics (MCAO) yield nearly diffraction-limitedimages at 2$\mu$m wavelengths. Currently, GeMS/GSAOI at Gemini South is theonly MCAO facility instrument at an 8m telescope. Using real data and for thefirst time, we investigate the gain in depth and S/N when MCAO is employed for$K_{\rm s}$-band observations of distant galaxies. Our analysis is based on theFrontier Fields cluster MACS J0416.1-2403, observed with GeMS/GSAOI (neardiffraction-limited) and compared against VLT/HAWK-I (natural seeing) data.Using galaxy number counts, we show that the substantially increased thermalbackground and lower optical throughput of the MCAO unit are fully compensatedfor by the wavefront correction, because the galaxy images can be measured insmaller apertures with less sky noise. We also performed a direct comparison ofthe signal-to-noise ratios (S/N) of sources detected in both data sets. Forobjects with intrinsic angular sizes corresponding to half the HAWK-I imageseeing, the gain in S/N is 40 per cent. Even smaller objects experience a boostin S/N by a up to a factor of 2.5 despite our suboptimal natural guide starconfiguration. The depth of the near diffraction limited images is moredifficult to quantify than that of seeing limited images, due to a strongdependence on the intrinsic source profiles. Our results emphasize theimportance of cooled MCAO systems for $K_{\rm s}$-band observations withfuture, extremely large telescopes.

Multi-conjugated adaptive optics imaging of distant galaxies -- A comparison of Gemini/GSAOI and VLT/HAWK-I data