  Dispersion scan is a self-referenced measurement technique for ultrashort
pulses. Similar to frequency-resolved optical gating, the dispersion scan
technique records the dependence of nonlinearly generated spectra as a function
of a parameter. For the two mentioned techniques, these parameters are the
delay and the dispersion, respectively. While dispersion scan seems to offer a
number of potential advantages over other characterization methods, in
particular for measuring few-cycle pulses, retrieval of the spectral phase from
the measured traces has so far mostly relied on the Nelder-Mead algorithm,
which has a tendency of stagnation in a local minimum and may produce ghost
satellites in the retrieval of pulses with complex spectra. We evaluate three
different strategies to overcome these retrieval problems, namely
regularization, use of a generalized-projections algorithm, and an evolutionary
retrieval algorithm. While all these measures are found to improve the
precision and convergence of dispersion scan retrieval, differential evolution
is found to provide the best performance, enabling the near-perfect retrieval
of the phase of complex supercontinuum pulses within less than ten seconds,
even in the presence of strong detection noise and limited phase-matching
bandwidth of the nonlinear process.
