Algorithm for complete and rapid retrieval of ultrashort pulse amplitude and phase from a sonogram

We describe an algorithm based on principal-component generalized projections that is capable of unambiguous retrieval of the amplitude and phase of an ultrashort pulse from a measurement of its sonogram. Running on a personal computer, the algorithm can complete more than 50 iterations per second which enables real-time display of an ultrashort pulse intensity and phase profile. Retrieval is demonstrated for a range of pulses with commonly encountered phase errors including linear chirp, self-phase modulation, and cubic spectral phase, and experimental results illustrate good agreement between the retrieved pulse characteristics and independent spectral measurements.