  We demonstrate a dual-comb vibrometer where the pulses of one frequency-comb
are split into pulse pairs. We introduce a delay between the two pulses of each
pulse pair in front of the sample, and after the corresponding two consecutive
reflections at the vibrating sample surface, the initially introduced delay is
cancelled by a modified Sagnac geometry. The remaining phase difference between
the two pulses corresponds to the change in the axial position of the surface
during the two consecutive reflections. The Sagnac geometry reduces the effect
of phase jitter since both pulses propagate through nearly the same optical
path (in opposite directions), and spurious signals are eliminated by time
gating. We determine the amplitude of a surface vibration on a
surface-acoustic-wave device with an axial precision of 4 pm. This technique
enables highly accurate determination of extremely small displacements.
