  We investigate the potential of the so-called XFROG cross-correlation
technique originally developed for ultrashort laser pulses for the recovery of
the amplitude and phase of the condensate wave function of a Bose-Einstein
condensate. Key features of the XFROG method are its high resolution,
versatility and stability against noise and some sources of systematic errors.
After showing how an analogue of XFROG can be realized for Bose-Einstein
condensates, we illustrate its effectiveness in determining the amplitude and
phase of the wave function of a vortex state. The impact of a reduction of the
number of measurements and of typical sources of noise on the field
reconstruction are also analyzed.
