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Temporal imaging systems are outstanding tools for single-shot observation ofoptical signals that have irregular and ultrafast dynamics. They allow longtime windows to be recorded with femtosecond resolution, and do not rely oncomplex algorithms. However, simultaneous recording of amplitude and phaseremains an open challenge for these systems. Here we present a new heterodynetime-lens arrangement that efficiently records both the amplitude and phase ofcomplex signals, while keeping the performances of classical time-lens systems($\sim 200$~fs) and field of view (tens of ps). Phase and time are encoded ontothe two spatial dimensions of a camera. We demonstrate direct application ofour heterodyne time lens to turbulent-like optical fields and optical roguewaves generated from nonlinear propagation of partially coherent waves insideoptical fibres. We also show how this phase-sensitive time-lens system enablesdigital temporal holography to be performed with even higher temporalresolution (80 fs).

Phase and Amplitude single-shot measurement by using heterodyne time-lens and ultrafast digital time-holography