Combs spanning an octave in frequency (i.e., a factor of two) can be used to directly measure (and correct for drifts in) f 0 . Thus, octave-spanning combs can be used to steer a piezoelectric mirror within a carrier–envelope phase-correcting feedback loop. Any mechanism by which the combs' two degrees of freedom ( f r and f 0 ) are stabilized generates a comb that is useful for mapping optical frequencies into the radio frequency for the direct measurement of optical frequency.