  We present detailed studies of the coherence properties of an ultra-broadband
super-continuum, enabled by a new approach involving continuous wave laser
sources to independently probe both the amplitude and phase noise quadratures
across the entire spectrum. The continuum coherently spans more than 1.5
octaves, supporting Hz-level comparison of ultrastable lasers at 698 nm and
1.54 {\mu}m. We present the first numerical simulation of the accumulated comb
coherence in the limit of many pulses, in contrast to the single-pulse level,
with systematic experimental verification. The experiment and numerical
simulations reveal the presence of quantum-seeded broadband amplitude noise
without phase coherence degradation, including the discovery of a dependence of
the super-continuum coherence on the fiber fractional Raman gain.
