In this paper, we present a novel approach to Fourier transform spectral interferometry based on single-shot detection of broadband pulses. It allows heterodyne detection with non-phase-stabilised setups, which use ps- and fs-pulsed laser sources. This approach can tremendously simplify the implementation of complex techniques such as heterodyne Fourier transform four-wave mixing and pave the way to novel phase-sensitive diagnostics for lasers and optical setups.

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