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The optical phase$\mathrm{\varphi <\#comment/>}$is a key quantity in the physics of light propagating through a turbulent medium. In certain respects, however, the statistics of the phasefactor,$\mathrm{\psi <\#comment/>}=\exp <\#comment/>(i\mathrm{\varphi <\#comment/>})$, are more relevant than the statistics of the phase itself. Here, we present a theoretical analysis of the 2D phase-factor spectrum$F_{\mathrm{\psi <\#comment/>}}(\mathit{\kappa <\#comment/>})$of a random phase screen. We apply the theory to four types of phase screens, each characterized by a power-law phase structure function,$D_{\mathrm{\varphi <\#comment/>}}(r)=(r/r_c{)}^{\mathrm{\gamma <\#comment/>}}$(where$r_c$is the phase coherence length defined by$D_{\mathrm{\varphi <\#comment/>}}(r_c)=1{\mathrm{r}\mathrm{a}\mathrm{d}}^2$), and a probability density function$p_{\mathrm{\alpha <\#comment/>}}(\mathrm{\alpha <\#comment/>})$of the phase increments for a given spatial lag. We analyze phase screens with turbulent ($\mathrm{\gamma <\#comment/>}=5/3$) and quadratic ($\mathrm{\gamma <\#comment/>}=2$) phase structure functions and with normally distributed (i.e., Gaussian) versus Laplacian phase increments. We find that there is a pronounced bump in each of the four phase-factor spectra$F_{\mathrm{\psi <\#comment/>}}(\mathrm{\kappa <\#comment/>})$. The precise location and shape of the bump are different for the four phase-screen types, but in each case it occurs at$\mathrm{\kappa <\#comment/>}\sim <\#comment/>1/r_c$. The bump is unrelated to the well-knownmore »“Hill bump” and is not caused by diffraction effects. It is solely a characteristic of the refractive-index statistics represented by the respective phase screen. We show that the second-order$\mathrm{\psi <\#comment/>}$statistics (covariance function, structure function, and spectrum) characterize a random phase screen more completely than the second-order$\mathrm{\varphi <\#comment/>}$counterparts.

During propagation through atmospheric turbulence, variations in the refractive index of air cause fluctuations in the time-of-flight of laser light. These timing jitter fluctuations are a major noise source for precision laser ranging, optical time transfer, and long-baseline interferometry. While there exist models that estimate the turbulence-induced timing jitter power spectra using parameters obtainable from conventional micrometeorological instruments, a direct and independent comparison of these models to measured timing jitter data has not been done. Here we perform this comparison, measuring turbulence-induced optical pulse timing jitter over a horizontal, near-ground path using frequency comb lasers while independently characterizing the turbulence along the path using a suite of micrometeorological sensors. We compare the power spectra of measured optical pulse timing jitter to predictions based on the measured micrometeorological data and standard turbulence theory. To further quantitatively compare the frequency comb data to the micrometeorological measurements, we extract and compare the refractive index structure parameter,C_n², from both systems and find agreement to within a factor of 5 for wind speed >1 m/s, and further improvement is possible as wind speed increases. These results validate the use of conventional micrometeorological instruments in predicting optical timing jitter statistics over co-located laser beam paths.