  Through examining the product of the mathematical variance of intensity with
respect to time and frequency, we arrive at a temporal characterization of
laser pulses through parameters for pulse duration, group delay dispersion and
temporal form. These statistics, which are sufficient to predict subsequent
pulse behavior, are recoverable in a simple experiment, measuring the
two-photon-induced photocurrents in three nonlinear diodes. With only two
photodiodes, we demonstrate that pulse durations as low as several tens of
femtoseconds can be easily measured in a single shot if the usual assumptions
of pulse form and dispersion are made as in the more difficult autocorrelation
setup.
