Single-shot characterization of noise-like pulses via coherent reference pulse trains

We present a complete single-shot characterization of noise-like pulses, retrieving both their amplitude and phase using spectral interferometry. Our approach eliminates the need for generating individual reference pulses by instead employing a Mamyshev oscillator as the reference source. This approach reveals the dynamics of noise-like pulses, enabling direct access to phase statistics and temporal profiles. We further reconstruct statistically independent modes, which provide a compact and physically meaningful basis for representing noise-like pulse fields.