  I study how pulse to pulse phase coherence in a pulse train can survive
super-broadening by extreme self phase modulation (SPM). Such pulse trains have
been used in phase self-stabilizing schemes as an alternative to using a
feedback process. However, such super-broadened pulses have undergone
considerable distortion, and it is far from obvious that they necessarily
retain any useful phase information. I propose measures of phase coherence
(i.e. supercontinuum coherence) applicable to such pulse trains, and use them
to analyze numerical simulations comparable to self-stabilization experiments.
