## 1 Introduction  
Time and frequency distribution is a key enabling technology for remote clock synchronization, which finds applications in telecommunication, navigation, grid deployment, remote sensing, precision measurement, and fundamental research. With the advent of optical atomic clocks [1; 2; 3; 4] and their much higher stability over traditional atomic clocks operating at microwave frequencies, it has become increasingly clear that future remote clock synchronization, especially on the backbone level, must be accomplished in the optical domain. Recently, remote distribution of optical-frequency references has attracted considerable interest [5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19]. There are in general two possible transfer media: _optical fiber_ and _free space_. An optical fiber provides a light transfer path isolated from the surrounding environment, minimizing excess noises added to the clock signals during beam propagation and hence maximizing the fidelity of the delivered frequency references. Coherent optical links spanning well over 100 km have been experimentally demonstrated by a number of groups [5; 6; 7; 8; 9]. On the other hand, free-space clock distribution benefits from its flexibility and low overhead cost, and has proved to be a feasible option for short-distance, _ad hoc_ networks or networks among mobile hubs, despite its much poorer link fidelity due primarily to air turbulence [15; 16; 17; 18; 19]. It is also the only option for space-terrestrial network synchronization [17]. So far, most of the effort in both fiber-optic and free-space clock distribution has been devoted to the realization of faithful delivery of a _single-frequency optical carrier_[5; 6; 7; 8; 9; 10; 15; 17]. An alternative approach, meanwhile, transfers _multiple frequency references_ simultaneously in the form of an optical frequency comb (OFC) [13; 14; 16; 18; 19]. The advantage of the latter scheme rests on its ability to directly synchronize clocks operating at different wavelengths, for example between an Hg\({}^{+}\) clock and a Ca clock [20], or even in different domains, for example between an optical atomic clock and a traditional atomic clock, such as a Cs clock [1]. As a result, direct distribution of an OFC can potentially suit a broader range of network synchronization scenarios. One of the most important issues in remote clock distribution is the _excess phase noise_, which refers to the extra phase noise added to the original highly-coherent frequency references by the transfer media due to fluctuations inherent to them or external perturbations. For a multifrequency clock transfer scheme, characterizing the excess phase noise is more challenging because multiple waves are simultaneously involved and the phase noise added by the transfer medium to each wave may not necessarily be the same. On top of that, dispersion could further complicate the problem. Therefore, in general, the instability of a multi-frequency clock transfer link is characterized by the long-term error of the clock (e.g., the Allan deviation) rather than the phase noise spectrum [13]. However, under certain conditions, phase noise can be directly measured in a multifrequency scheme with a well-defined meaning. We have recently proposed a multiheterodyne technique for direct phase noise characterization of a multifrequency clock distribution system [19]. In essence, multiheterodyne is a generalization of the optical heterodyne technique used for characterizing single-carrier clock distribution systems [14]. It measures the coherent superposition of the optical heterodyne signals generated by multiple frequency components. When the refractive index fluctuation of the transfer medium is small enough so that its impact to all of the involved frequency components can be treated as approximately equal, the multiheterodyne signal becomes a close representation of the optical heterodyne signal produced by individual frequency components [19].