In this paper, we extend the recently introduced linear technique for temporal phase reconstruction using optical ultrafast differentiation (PROUD) to achieve full characterization of ultrashort optical pulses with durations down to the picosecond regime using a well-characterized temporal stretcher (e.g., dispersive optical fiber). The proposed method is experimentally demonstrated by precisely characterizing the amplitude and phase temporal profiles of microwatt-power picosecond pulses ranging from 4 to 20ps with both continuous and discrete temporal phase variations. Using this simple mechanism, the same PROUD setup can be used to characterize optical pulses with durations ranging from the picosecond to the nanosecond regime. We provide a comprehensive mathematical analysis of this general PROUD technique: we evaluate in detail the influence of the key specifications (e.g., different sources of noise) of the used components and instruments, namely, optical differentiator, linear temporal stretcher, and time-domain intensity test equipment, on the performance of the PROUD measurement system, particularly in terms of phase sensitivity in the optical pulse characterization.
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