We demonstrate a novel algorithmic approach for second-harmonic-generation (SHG) frequency-resolved optical gating(FROG) that always converges and is also faster for complex pulses. It takes advantage of the Paley-Weiner Theorem forgenerating significantly better initial guesses. It also uses a multi-grid approach, which allows the algorithm to operateinitially on smaller arrays for early iterations and only on the complete array for the final few iterations. We tested it onsets of twenty thousand noisy FROG traces and have achieved 100% convergence even for pulses with time-bandwidthproducts of 100.
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