Intermittent maser evaluatione reporting interval used by BIPM consists of ve-day periods that begin at UTC 0:00:00 for modied Julian dates (MJD) ending in 4 or 9. However, any measurement that spans only one or two such periods is likely to be limited by the timing uncertainty of the satellite link to BIPM. As described in Section 2, the link used by NICT is characterized by a frequency uncertainty =2.0×10 over . For , this is de gra ded to =6.1×10 .As originally discussed in Ref. [24], the maser charac-terization does not require continuous operation of the optical clock, as the maser stability is sucient to act as a ywheel oscillator between measurements. We consider the maser frequency uctuations aer removal of a persistent linear dri to represent stationary stochastic processes. Following the approach discussed in the supple-ment of Ref. [15], the average frequency over an arbitrary distribution of observation time can then be written as=()() ,(6)with normalized weighting function()=during measurement intervals0elsewhere (7)Here is the combined averaging time. e place-holder refers to either the sampled intervals ( ) or the full evaluation period ( ). e frequency average over the sampled intervals then deviates from the true average by . e expectation value of is zero, and we consider the variance =〈〉 to represent the uncertainty due to unobserved stochastic behavior during measurement dead times. is relates directly to the power spectral density (PSD) () describing the maser frequency noise:=()|()| .(8)Here () is the Fourier transform of the dierential weighting function ()()() . Straight for ward application of Parseval’s theorem then immediately con-rms two expectations: e rst is that better agree ment of () and () , which reduces the integral over () , likewise reduces |()| , and therefore (generally) . e second is that for white frequency noise, where ()=const , only the integral over the squared sensitiv-ity function |()| (and thus () ) is relevant, while the distribution of sampling time is not. For the typical case of , it is therefore sucient to handle the white frequency noise contribution based on the observed Allan deviation as discussed in the previous section.We extract the typical maser stability based on fre-quency dierences recorded by the DMTD system. Using data from more than two years of simultaneous operation for four masers (HMJST#03, HMJST#12, HMJST#13, and HMJST#15), we average the Hadamard variances to extract a representative single-HM instability shown in Fig.3. We interpret this as a combination of white fre quen cy noise (WFN), icker frequency noise (FFN), and icker-walk frequency modulation noise (FWFM) and we t the data according to5FiF2Stability of a maser frequency evaluation over a 10 d period The linear drift of the maser leads to an increasing Allan deviation for averaging times t>10 s (gray solid diamonds). After subtraction of a linear trend, the instability reaches a plateau near 2×10 , representing the maser flicker noise floor (red circles). Correcting for non-linear drift based on an ensemble of 5 masers further reduces the observed instability (blue squares). The contributions from NICT-Sr1 (solid blue line) and the phase lock of the frequency comb’s carrier-envelope offset and repetition rate (open triangles) do not significantly contribute to the measurement instability. Open diamonds indicate a subset of data evaluated at a time step of 1 s, where an initial slope of σ(τ)=1×10/τ indicates a significant phase noise contribution. The brown line represents the maser noise model discussed later in the text, with (drift-corrected) instabilities in the shaded region indicating instability above expectation.94 情報通信研究機構研究報告 Vol. 65 No. 2 （2019）4 原⼦周波数標準
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