To meet the constant demands of high-capacity telecommunications infrastructure, data rates beyond 1 terabit per second per wavelength channel and optical multiplexing are widely applied. However, these features pose challenges for existing data acquisition and optical performance monitoring techniques because of bandwidth limitation and signal synchronization. We designed an approach that would address these limitations by optically converting the frequency limit to an unlimited time axis and combining this with a chirped coherent detection to innovatively obtain the full-field spectrum. With this approach, we demonstrated a real-time Fourier-domain optical vector oscilloscope, with a 3.4-terahertz bandwidth and a 280-femtosecond temporal resolution over a 520-picosecond record length. In addition to on-off keying and binary phase-shift keying signals (128 gigabits per second), quadrature phase-shift keying wavelength division-multiplexed signals (4 × 160 gigabits per second) are simultaneously observed. Moreover, we successfully demonstrate some high-precision measurements, which indicate them as a promising scientific and industrial tool in high-speed optical communication and ultrafast optical measurement.