  Stabilized optical frequency combs (OFC) can have remarkable levels of
coherence across their broad spectral bandwidth. We study the scaling of the
optical noise across hundreds of nanometers of optical spectra. We measure the
residual phase noise between two OFC's (having offset frequencies $f^{(1)}_0 $
and $f^{(2)}_0$) referenced to a common cavity-stabilized narrow linewidth CW
laser. Their relative offset frequency $ \Delta f_0 = f^{(2)}_0 - f^{(1)}_0 $,
which appears across their entire spectra, provides a convenient measure of the
phase noise. By comparing $\Delta f_0$ at different spectral regions, we
demonstrate that the observed scaling of the residual phase noise is in very
good agreement with the noise predicted from the standard frequency comb
equation.
