The knowledge and thus characterization of the temporal modes of quantum
light fields is important in many areas of quantum physics ranging from
experimental setup diagnosis to fundamental-physics investigations. Recent
results showed how the auto-correlation function computed from continuous-wave
homodyne measurements can be a powerful way to access the temporal mode
structure. Here, we push forward this method by providing a deeper
understanding and by showing how to extract the amplitude and phase of the
temporal mode function with reduced experimental resources. Moreover, a
quantitative analysis allows us to identify a regime of parameters where the
method provides a trustworthy reconstruction, which we illustrate
experimentally