Amplitude ambiguities in second-harmonic generation frequency-resolved optical gating

We construct field shapes with distinct amplitude profiles that have nearly identical second-harmonic generation frequency-resolved optical gating (SHG FROG) traces. Although such fields are not true mathematical ambiguities, they result in experimentally indistinguishable FROG traces. These fields are neither time-reversed copies nor pulselets with a mere relative phase difference, which are well known nontrivial ambiguities for SHG FROG. We also show that for certain example fields, second-order interferometric autocorrelation is more sensitive to the pulse shape than is SHG FROG.