Coherent transfer of the phase through interferometric FSHG within the time window available for temporal convolution: A spectral phase filter (a 50 mm fused silica rod introducing positive group-delay dispersion) is inserted in the delayed Michelson arm before the nonlinear stage. Left column: XFROG spectrograms of the fundamental (a) and FSHG pulses (c) revealing the distribution of both pulse sequences at ω0 and 2ω0. (b) Spectrum (solid line) and phase (dashed line) of individual pulses (black F1, red F2) retrieved from XFROG reconstruction. The delayed pulse at ω0 (F2) has a positive chirp. (d) Its quadratic phase is transferred from F2 to the second harmonic pulses H12 and H2, where the phase stroke is doubled. H12 is leaving the system 2 ps before F2.