Second-harmonic frequency-resolved optical gating ($I(\omega ,\tau )=|\int A(t)A(t-\tau )e^{-i\omega t}dt{|}^2$)

The self-gated second-harmonic spectrogram has the displayed ideal form. Its delay marginal is proportional to the intensity autocorrelation by the Parseval identity. Absolute time and wave phase are undetermined; $A(t)$ and $A^{\ast }(-t)$ also give the same record. Finite crystal acceptance and spatial walk-off modify the ideal gate.