In the complete reconstruction of ultrashort optical pulses based on temporal interferometry, the chromatic dispersion and the optical time delay are two key factors, which determine the measurement accuracy. Due to the higher order dispersion, the wavelength-to-time mapping becomes nonlinear, leading to a nonuniformly spaced interference pattern and a decreased fringe visibility in the time domain, even though the input pulse is transform limited. On the other hand, an estimation of the time delay difference with a minor deviation from the true value will result in an artificial linear chirp in the reconstructed phase of the pulse under test. In this paper, a rigorous mathematical analysis on the nonlinear frequency-to-time mapping is performed, with which the phenomena of a nonuniformly spaced interference pattern and a decreased fringe visibility are explained. A frequency-to-time mapping function including higher order dispersion is developed. With a general mapping function, using a transform-limited pulse as the reference signal, we propose a method for real-time tracking of the system parameters, including the chromatic dispersion corresponding to all the optical devices incorporated in the system and the time delay introduced by the interferometer. Finally, a complete reconstruction of a 237 fs optical pulse is demonstrated experimentally with an average angular error of 0.18 rad ranging from 190.65 to 193.85 THz.
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