The uncertainty factors regarding the laser frequency measuring ability with the optical comb device can be roughly classified into the following two categories:
�@Uncertainty of frequency standard: u1
�AError in synchronization with frequency standard: us2
u1 is obtained by remote calibration; accordingly, u2 evaluation enables the measuring ability to be estimated.
Then, evaluation was conducted according to the device configuration shown in Fig. 6. Another similar type of optical comb device is prepared for comparison, and the two optical comb devices are stabilized by conducting phase synchronization with the same frequency standard. The same stabilized laser is measured with the two optical comb devices at the same time and the obtained two measured values are subtracted. Then, u2 is obtained after u1, which is the common uncertainty factor, and the frequency fluctuation of the stabilized laser are cancelled each other.

Figure 6 Evaluation of error in synchronization with frequency standard

We intercompared our optical comb device with the optical comb device owned by AIST ^{[10] [11]}. Figures 7 and 8 show the measurement results of the two optical comb devices, respectively; Fig. 9 shows the difference of measured values. Figure 10 shows the calculated results of relative stability. The average value of differences between the two optical comb devices is 0.14 Hz. The relative stability at the averaging time of 1000 s is 2.6 Χ 10^-16, and the value will be smaller if the averaging time is extended. As the certainty of synchronization to the frequency standard, u2, is extremely low, the uncertainty of the laser frequency measurement with the optical comb device that we developed is determined only by the uncertainty of the frequency standard, u1, described in (1) above, and that is 1.1 Χ 10^-13 (k=2, at average in a day).

Figure 7 Measured results with optical comb 1 (Mitutoyo)	Figure 8 Measured results with optical comb 2 (AIST)

Figure 9 Difference of measured values with two optical combs (Figs 7-8)	Figure 10 Evaluated results of two optical comb devices' relative stability

The reproducibility of the oscillating frequency of the iodine-stabilized He-Ne laser when the power supply is turned on again was evaluated with our developed optical comb device. Figure 11 shows the evaluation results. The beat frequency of the optical comb device is measured for 86,400s at the average of 1s in each measurement, and the average value of the absolute frequencies is calculated. The standard deviation ((σ) is shown with an error bar. The figure is shown with the uncertainty of 10 kHz and the deviation from the frequency of 476 612 353 604 kHz that is advised by the International Committee for Weights and Measures (CIPM). The difference from the value advised from CIPM is +1.4 kHz. The reproducibility of the frequency of the iodine-stabilized He-Ne laser that we use as a reference standard for common use is high; we confirmed that the fluctuation range of the laser is smaller than the uncertainty of the frequency that is advised by CIPM.

Figure 11 Reproducibility of frequency of iodine-stabilized He-Ne laser

We have developed a laser frequency measuring system with an optical comb device that is traceable to the national standards. This system is an extremely reliable and ideal standard that features small uncertainty, does not need to undergo carrying-in calibration and is calibrated in the operating environment every day. Our laser calibration business with this system was approved as the first business registered with the JCSS in April 2017. We will work further to improve the reliability of our commodities provided to users by utilizing this system in future.
This article is described on the basis of the results of joint research with the National Institute of Advanced Industrial Science and Technology. We deeply appreciate the assistance of Mr. Inaba in the Frequency Measurement Group, Mr. Suzuyama in the Time Standards Group and Mr. Hong, currently a professor at Yokohama National University.

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