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In this paper, we describe an apparatus for correcting the timebase errors when calibrating the response of an equivalent-time sampling oscilloscope using a passively mode-locked erbium-doped fiber laser that is phase locked to a microwave signal generator. This enables us to simultaneously correct both the random jitter and the systematic timebase distortion in the oscilloscope. As a demonstration of the technique, we measure the electrical pulse generated by a fast photodiode that is excited by our laser. We show that the pulse that is reconstructed using our technique has significantly lower uncertainty than the pulse that is reconstructed using a separate correction for timebase distortion followed by jitter deconvolution.