Fig. 4: Retrieval of a few-cycle low-dispersion pulse for n = 2 and s = 0.5 in the presence of noise.

a Reference (dark blue) and retrieved (orange) IAC traces in the time domain for a strong noise background (σ = 0.02) according to Eq. (7). b Reference (red) and retrieved (green) field spectra and the fundamental component filter used (dashed gray line). Magnitudes are shown as solid lines and phases as dotted lines. c Reference (red) and retrieved (green) temporal profiles of the electric field intensity and phase. The linear component of the temporal phase (\(\omega _0t\)) has been removed. d Error quantities as defined in Eqs. (10–12). The phase error is shown in radians, while the other errors are dimensionless (but are all shown on the same scale). e Field error as a function of the balance factor s for different noise values shown for n = 2 (left) and n = 3 (right). Error bars denote standard deviations. The case corresponding to the example shown in a-d is marked by a red circle