  We formulate theoretically and demonstrate experimentally an all-optical
method for reconstruction of the amplitude, phase and coherence of frequency
combs from a single-shot measurement of the spectral intensity. Our approach
exploits synthetic frequency lattices with pump-induced spectral short- and
long-range couplings between different signal components across a broad
bandwidth of of hundreds GHz in a single nonlinear fiber. When combined with
ultra-fast signal conversion techniques, this approach has the potential to
provide real-time measurement of pulse-to-pulse variations in the spectral
phase and coherence properties of exotic light sources.
