Novel formula for retrieving amplitude and phase of an optical pulse from its sonogram without iterative calculations

Summary form only given. Sonogram characterization is one of the methods for measuring the amplitude and phase of an ultra-short optical pulse. After a pulse is frequency-filtered, the intensity waveform of the filtered pulse is measured by the cross-correlation method to obtain the sonogram. it has been shown that an iterative algorithm, in which the window function for frequency filtering is assumed to be unknown, can be employed for pulse reconstruction from the sonogram.In this paper, we derive a novel formula for retrieving the pulse from its sonogram. When the window function for frequency filtering is given, as is always the case in the sonogram measurement, the pulse amplitude and phase are completely retrieved from the sonogram without iterative calculations by using the derived formula. This formula can also be applicable to the XFROG characterization of an optical pulse where we know the temporal gate function for measuring the spectrogram.