  We present a common pulse retrieval algorithm (COPRA) that can be used for a
broad category of ultrashort laser pulse measurement schemes including
frequency-resolved optical gating (FROG), interferometric FROG, dispersion
scan, time domain ptychography, and pulse shaper assisted techniques such as
multiphoton intrapulse interference phase scan (MIIPS). We demonstrate its
properties in comprehensive numerical tests and show that it is fast, reliable
and accurate in the presence of Gaussian noise. For FROG it outperforms
retrieval algorithms based on generalized projections and ptychography.
Furthermore, we discuss the pulse retrieval problem as a nonlinear
least-squares problem and demonstrate the importance of obtaining a
least-squares solution for noisy data. These results improve and extend the
possibilities of numerical pulse retrieval. COPRA is faster and provides more
accurate results in comparison to existing retrieval algorithms. Furthermore,
it enables full pulse retrieval from measurements for which no retrieval
algorithm was known before, e.g., MIIPS measurements.
