Краткое изложение:
Light-matter interaction is exploited in spectroscopic techniques to access
information about molecular, atomic or nuclear constituents of the sample of
interest. While scattered light carries both amplitude and phase information of
the electromagnetic field, most of the time the latter is lost in intensity
measurements. However, often the phase information is paramount to reconstruct
the desired information of the target, as it is well known from coherent x-ray
imaging. Here we introduce a new phase retrieval algorithm which allows us to
reconstruct the field phase information from two-dimensional time- and
energy-resolved spectra. We apply this method to the particular case of x-ray
scattering off M\"ossbauer nuclei at a synchrotron radiation source. Knowledge
of the phase allows also for an excellent reconstruction of the energy spectra
from experimental data, which could not be achieved with this resolution
otherwise. Our approach provides an efficient novel data analysis tool which
will benefit x-ray quantum optics and M\"ossbauer spectroscopy with synchrotron
radiation alike.