Theory of sonogram characterization of optical pulses

We derive a formula for retrieving the amplitude and phase of an optical pulse from its sonogram, When the transfer function of the frequency filter is known, the pulse amplitude and phase are completely retrieved from the sonogram without iterative calculations by using the derived formula. Based on this formula, we find that the width of a sampling pulse, which is used for cross-correlation measurement of the sonogram, must be much shorter than the width of the pulse under test, and that it is not necessarily possible to reconstruct the pulse when we use the pulse under test itself as a sampling pulse, Finally, we discuss possible schemes for sonogram characterization of optical pulses.