AbstractThe optimal performance of high-brightness free-electron lasers (FELs) is limited by the microbunching instability, which can cause variations in both the slice energy spread and longitudinal profile of electron beams. In this paper, we perform 2D Fourier analysis of the full bunch longitudinal phase space, such that modulations in both planes can be studied simultaneously. Unlike the standard 1D analysis, this method is able to reveal modulations in a folded phase space, which would otherwise remain uncovered. Additionally, the plasma oscillation between energy and density modulations is also revealed by this method. The damping of the microbunching instability, through the use of a laser heater, is also analysed with this technique. We confirm a mitigation of the amplitude of modulation and a red-shift of the microbunching frequency as the energy spread added increases. As an outcome of this work, a systematic experimental comparison of the development of the instability in the presence of different compression schemes is here presented for the first time.