Longitudinal electron pulse characterization. (a) and (b) Energy spectra depending on the time delay between the excitation of an optical field (50-fs optical pulse duration, electron-light interaction facilitated by reflection off a thin silicon membrane) and the arrival time of the electron pulses (photoemission laser pulse duration: 100 fs). Photon sidebands on the energy-gain and -loss side are formed during temporal overlap, yielding an electron-light cross correlation. For low-charge electron pulses (a), short cross-correlation times are observed, substantially broadening for higher bunch charges (b). Color scale is chosen to highlight the temporal width of photon-sideband intensity on the gain-side of the spectra. (c) and (d) Space-charge induced spectral and temporal broadening is observed in the electron energy spectra (c) and temporal electron pulse profiles [(d) extracted from the delay-dependent intensity of higher order photon sidebands]. (e) Electron pulse duration (FWHM) scales linearly with its energy width. Dotted lines: position of spectral and temporal profiles shown in (c) and (d), respectively. (f) Electron pulse chirp (blue symbols) is derived from the inclination of the photon sidebands. The experimental data are well described by an analytical model (black line) considering an energy-independent shear amplitude due to pulse propagation and a space-charge-induced spectral broadening close to the emitter tip.