Second-generation exoplanet imagers using extreme adaptive optics and coronagraphy have demonstrated their great potential for studying close circumstellar environments and for detecting new companions and helping to understand their physical properties. However, at very small angular separation, their performance in contrast is limited by several factors: diffraction by the complex telescope pupil not perfectly canceled by the coronagraph, residual dynamic wavefront errors, chromatic wavefront errors, and wavefront errors resulting from noncommon path aberrations (NCPAs). In a previous work, we demonstrated the use of a Zernike wavefront sensor called ZELDA for sensing NCPAs in VLT/SPHERE and their compensation. In the present work, we move to the next step with the on-sky validation of NCPA compensation with ZELDA. We start by reproducing previous results on the internal source and show that the amount of aberration integrated between 1 and 15 cycles/pupil is decreased by a factor of five, which translates into a gain in raw contrast of between 2 and 3 below 300 mas. On sky, we demonstrate that NCPA compensation works in closed loop, leading to an attenuation of the amount of aberration by a factor of approximately two. However, we identify a loss of sensitivity for the sensor that is only partly explained by the difference in Strehl ratio between the internal and on-sky measurements. Coronagraphic imaging on sky is improved in raw contrast by a factor of 2.5 at most in the ExAO-corrected region. We use coronagraphic image reconstruction based on a detailed model of the instrument to demonstrate that both internal and on-sky raw contrasts can be precisely explained, and we establish that the observed performance after NCPA compensation is no longer limited by an improper compensation for aberration but by the current apodized-pupil Lyot coronagraph design. [abridged]
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