Scattering-type scanning near-field optical microscopy enables the measurement of optical constants of a surface beyond the diffraction limit. Its compatibility with pulsed sources is hampered by the requirement of a high-repetition rate imposed by lock-in detection. We describe a sampling method, called quadrature-assisted discrete (quad) demodulation, which circumvents this constraint. Quad demodulation operates by measuring the optical signal and the modulation phases for each individual light pulse. This method retrieves the near-field signal in the pseudoheterodyne mode, as proven by retraction curves and near-field images. Measurement of the near-field using a pulsed femtosecond amplifier and quad demodulation is in agreement with results obtained using a CW laser and the standard lock-in detection method.