Linear filter analysis of methods for ultrashort-pulse-shape measurements

We analyze the properties required of a linear interferometer composed of time-stationary and time-nonstationary filters and a square-law, integrating detector in order that it may be used for the complete characterization of ultrashort optical pulses. Some general conditions for measurements are formulated for various schemes, and, in particular, time-nonstationary filtering is shown always to be necessary. The roles of both phase-only time nonstationarity and amplitude time gating are investigated in the context of known measurement schemes, and the known nonlinear schemes are shown to be members of a larger class of methods that use amplitude time-nonstationary filters.