Overcoming noise in pulse retrieval: introducing the line-search FROG algorithm

The most widely used frequency-resolved optical gating (FROG) retrieval algorithm solves the trace inversion problem to retrieve the phase distribution of the ultrashort pulse electric field by using preprocessed measured data in each iterative step to improve subsequent guesses. Such algorithms work very well for measurements with high signal-to-noise ratios but can become less reliable in extracting weaker signals buried in noisy data. We introduce the line-search FROG (LSF) algorithm, which enhances noise robustness by treating measurement data passively, using it solely for error evaluation rather than iterative correction. The gradient-free LSF algorithm requires no preprocessing of the measurement data and thus does not make assumptions about the noise in the measured traces. We show that LSF achieves comparable FROG error metrics to a ptychographic retrieval algorithm and COPRA, while producing higher-quality pulse reconstructions with reduced noise contaminations. It is applicable to all FROG geometries, supports blind FROG retrieval, and can reconstruct pulses from incomplete datasets.