() (/s) (τ/s) .(9)We nd coecients =6.8×10 , =2.2×10 and =3.4×10 . ese relate [26] [27] to a PSD of()=ℎ +ℎ/+ℎ⁄ (10)with coecients ℎ=9.3×10Hz , ℎ=4.1×10 and ℎ=9.1×10 Hz , calculated as elabo ra ted in the appendix. By taking the discrete Fourier transform of () , can now be calculated for an arbitrary distribu-tion of measurement time. Although the method is gener-ally robust, the ℎ⁄ term representing FWFM varies rapidly for near-zero frequencies. e numerical evaluation of eq.(8) is more consistent if the frequency resolution of the discrete Fourier transform is increased by zero-padding () . We then nd agreement to better than 10% with a statistical analysis using Monte Carlo methods. For this, we generate random noise series according to the PSD coef-cients using the method described in Ref. [28].Within this framework, we can now investigate eective distributions of measurement time. is is shown in Fig.4. While a dense, even distribution throughout the eval u a tion period, e.g. daily measurements, yields the best re sults, this is not ecient when considering the eort re quired to ini-tiate and maintain optical lattice clock opera tion. A divi-sion of the assumed 16 h measurement time discussed in Section 4 into four operating intervals of 4 h is sucient to obtain =1.1×10 for a 35 d period. Here we take FiF3Representative maser stability Colored marks and guides show individual Hadamard deviations extracted from continuous DMTD data using a four-corner-hat method [26]. Heavy open circles represent the mean vari ance of maser-to-maser frequency differences. The thick solid line and shaded area represent the fitted maser model in cluded in Fig.2 and Fig.5, which includes instabilities from white frequency noise (WFN), flicker fre-quen cy noise (FFN) and flicker-walk frequency modulation noise (FWFM). For averaging times the maser instability exceeds that of the GPS link (thin solid line). The plotted data includes a correction for > ai [23].FiF4Dead time uncertainty with distribution of mea sure ments (a) and (b) Maser frequency evaluation over a period of 35 d by identical total measurement times, either as a single interval (a) or equally distributed over 4 intervals (b), given in terms of the differential weighting function () , re-normalized to 1. We describe the (identical) separation of the intervals by the span from the beginning of the first interval to the end of the last. (c) and (d) Corresponding squared sensitivity function |()| obtained by Fourier transform of () . Shortening the unobserved intervals (where <0 ) causes the sensitivity to extend to higher Fourier frequencies (d), where both FFN and FWFM are of smaller magnitude (solid lines). (e) Overall stochastic uncertainty (solid lines) and contribution from (dashed lines) as a function of . Colors and symbols indicate different numbers of intervals. Values represent an ensemble of =3 , where four intervals are sufficient to reach =1.14×10 . For any number of intervals, a suitable choice of allows for .954-4 光 – マイクロ波リンクとTAI校正
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