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• Abstract

SECTION I

## INTRODUCTION

The Atacama Large Millimeter/submillimeter Array (ALMA) is a high-frequency/large-scale radio interferometer array which is currently under construction in Northern Chile. ALMA consists of 64 antennas arrayed over baselines that extend up to 14 km and will provide images of the universe in unprecedented detail. Each of the ALMA antennas is equipped with a 10-frequency-band receiver (from 31 to 950 GHz) to transmit signals through optical cables whose maximum length is 15 km. To receive such high frequencies, reference signals (continuous wave signal) are required to be 100 GHz and over for the first local oscillator and a lower frequency (2 GHz) for the second local oscillator and must also be highly stable to maintain signal coherency [10]. To provide the desired characteristics, we have developed a system that generates and transmits reference signals in the form of frequency difference between two coherent optical signals. In a previous paper, the high-frequency signal ($\geq$ 20 GHz) transmission method was shown in [8]. In the presented system using the transmission phase stabilizer for high-frequency signals, the phase of two round-trip signals (signals transmitted from the antenna with a frequency slightly shifted from that of a signal transmitted to the antenna) are separately measured, and then, the phase control is performed on only one of the two optical signals. The previously presented system was for processing high-frequency signals and not for low-frequency signals ($\leq$ 20 GHz). It is difficult to separate low-frequency signals using Fiber Bragg Grating (FBG). This paper discusses a new system for processing and distributing low-frequency reference signals that are highly stable. A unique feature of the new system is to use an Image Rejection Mixer for measuring the phase of round-trip microwave signals that are converted from optical signals. The phase of the two transmitted optical signals is required to be better than $10^{-13}$ for the first local oscillator and $10^{-12}$ for the second local oscillator in the Allan standard deviation [1]. The previously presented system (for high-frequency signals) and the new system described in this paper (for low-frequency signals) have a mutually complementary relationship, and the antenna equipment for phase stabilization is used for both systems. Both systems are alternatives for ALMA; the article of the ALMA baseline plan has been published [3].

SECTION II

## BASIC CONCEPT

We will discuss the microwave signal transmission method for a remote antenna site. The phase reference is a microwave signal (hereafter, it is displayed as M1), and the transmission signal is displayed as microwave M2. The stability of the phase is discussed between M1 and M2.

Two coherent optical signals differing in wavelength are generated from one of the laser beams thus obtained by a two-light wave generator by using a microwave signal. Thus, two optical signals (wavelengths $\lambda_{1}$ and $\lambda_{2}$) that are spaced apart by M1 microwave signal frequencies are generated. The microwave signal M1 is a highly stable signal for transmission. The two-light wave generator is configured to satisfy a condition that the two optical signals be polarized in the same manner. We apply the high extinction ratio Mach–Zehnder $\hbox{LiNbO}_{3}$ (Lithium Niobate: LN) optical modulator to a high-stability and high-frequency two coherent-optical-signals generator [6], [7].

Fig. 1 illustrates the relationship between phases of the microwave and the optical signal. It is assumed that the microwave signal M1 to be input has an angular frequency of $\omega_{0}$ and a phase of zero. If a microwave optical conversion is performed by the two-light wave generator after the phase is shifted by $\Phi$ by the microwave phase shifter, then the two optical signals (wavelengths $\lambda_{1}$ and $\lambda_{2}$) having a phase difference $\Phi$ are output. The phase difference between the two optical signals having the wavelengths $\lambda_{2}$ and $\lambda_{1}$ is $(\omega_{0}t + \Phi)$.

Fig. 1. Configuration of a part of the optical transmission system on the transmitting side. The deferential phase of the two light-wave signals is controlled by the microwave phase shifter. The microwave signal is the phase reference (M1). Blue lines show the electrical signals, and red lines show optical signals.

Fig. 2 is a diagram illustrating the relationship between the phases of the two optical signals that are different in wavelength, which make a round trip through one optical fiber. The left end of Fig. 2 corresponds to the optical signal transmitting side, while the right end corresponds to the receiving side as a transmission destination. The optical frequency difference is extracted as a microwave signal M2 due to the action of the photo-detector as a mixer on the receiving side at the right end. Round trips made by wavelengths $\lambda_{1}$ and $\lambda_{2}$ are illustrated with different lengths in order to indicate that delay amounts of the two optical signals differ due to chromatic/polarization mode dispersion (PMD) [2] based on the wavelength difference.

Fig. 2. Relationship between phases of the two optical signals. This is an optical transmission part connected behind Fig. 1. The right end of the figure corresponds to the receiving side as a transmission destination. The optical frequency difference is extracted as a microwave signal M2. Blue lines show the electrical signals, and red lines show optical signals.

In an optical fiber transmission, the delay amounts of the two optical signals differ, which makes a correction thereof essential. It is possible to separate the two optical signals and assemble a phase control system like the high-frequency signal transmission method [8], but it is difficult to separate the two optical signals at a frequency equal to or lower than 20 GHz. Therefore, the optical signals are converted into microwave signals, and then, the two signals are separated.

It is assumed, as illustrated in Fig. 2, that the optical signal having the wavelength $\lambda_{1}$ which has returned from the round trip through an optical fiber has a phase of $(2\pi m + \phi_{3})$ and that the optical signal having the wavelength $\lambda_{2}$ which has returned from the round trip has a phase of $(2\pi n + \phi_{4} + \Phi)$. In this case, it is assumed that the optical signal of the wavelength $\lambda_{2}$ has an initial phase of $\Phi$ and that m and n are integers.

Here, the optical signal makes a round trip through the one optical fiber, and hence, the transmission destination at the right end is regarded as a midpoint of the round trip. The phase of the optical signal having the wavelength $\lambda_{1}$ at the midpoint is $\phi_{3}/2$ when m is an even number and $((\phi_{3}/2) + \pi)$ when m is an odd number. In the same manner, the phase of the optical signal having the wavelength $\lambda_{2}$ at the midpoint is $((\phi_{4}/2) + \Phi)$ when n is an even number and $((\phi_{4}/2) + \Phi + \pi)$ when n is an odd number. The phase detected by the photo-detector on the receiving side as the transmission destination is obtained as the phase difference signal there between and is hence phase (1) or phase (2): TeX Source \eqalignno{&\left((\phi_{4} - \phi_{3})/2\right) + \Phi&\hbox{(1)}\cr &\left((\phi_{4} - \phi_{3})/2 \right) + \Phi + \pi.&\hbox{(2)}}

This depends upon the combination of (m, n), which may include (odd number, odd number), (odd number, even number), (even number, odd number), and (even number, even number). The phase is (1) in the case of (odd number, odd number) and (even number, even number) and (2) in the case of (odd number, even number) and (even number, odd number) TeX Source $$\phi_{4} - \phi_{3} +2\Phi = 0.\eqno{\hbox{(3)}}$$

If (3) is established by controlling the phase $\Phi$, the phase difference (1) or (2) between the optical fiber transmission signals at the transmission destination becomes 0 or $\pi$, which can compensate an influence of a transmission line as a constant value.

The transmission phase stabilizer for high-frequency, the round-trip phase measurement is separately done on two optical signals. However, the signal separation of two optical-signals to low-frequency signal by using FBG is difficult. The new scheme of the round-trip phase measurement is separately done on a microwave signal with an Image Rejection Mixer.

In actually, at the antenna, the received optical signals are modulated (frequency-shifted) by a microwave signal $M3$ (in Section 3), and the polarization is changed by a Faraday reflector; after that, they are sent back to the ground unit through the same optical cable in a reciprocal process. Frequency-shift is done by an optical modulator (frequency shift by M3). The purpose of these operations is to separate the backscattering signal and the round-trip signal. Delay errors caused by the process will be discussed in Section 3.

SECTION III

## DETAILED DESCRIPTION OF THE SCHEME

Note that the same or equivalent parts across the drawings are denoted by the same reference symbols. The block diagram is shown in Fig. 3. In Fig. 3, after passing through the microwave distributor, the input microwave signal M1 (phase reference) is sent to the microwave phase shifter to be subjected to a phase shift. The microwave signal is lead to the two-light wave generator.

Fig. 3. Configuration of a low-frequency signal optical transmission system. Blue lines show the electrical signals, and red lines show optical signals. The optical modulator is a fiber frequency shifter (or so-called an AO modulator).

In the high-extinction ratio lithium niobate $(\hbox{LiNbO}_{3})$ Mach–Zehnder intensity modulator (produced by Sumitomo Osaka Cement Co.) generates a two-light wave, and the output signal is equivalent to the frequency shift keying (FSK) spectrum. Compared with the optical phase lock scheme, the Mach–Zehnder modulator (shown in Fig. 4) has significant advantages in terms of robustness to mechanical vibration and acoustic noise, stability (free from the influence of the input laser stability), and capability of maintaining the polarization state of the input laser.

Fig. 4. Simplified structure of the two-light wave generator with two arms and electrodes. Optical phase of each arm is controlled by applying DC bias to the electrodes. Amplitude imbalance due to fabrication error is compensated with sub-Mach–Zehnder trimmers. When two lightwaves are in phase, the output optical signals are strengthened with each other. On the other hand, when the phases of the input lightwaves are shifted, the phase-shifted lightwaves are radiated away as higher order waves and do not reach the optical waveguide. This is the main feature of the Mach–Zehnder modulator.

The output spectrum depends on the DC bias voltage applied to the electrodes in the Mach–Zehnder structure. When the bias of the Mach–Zehnder modulator is set to a minimum transmission point (null-bias point), the first-order upper sideband (USB) and lower side band (LSB) components are strengthened, and the carrier is suppressed. As the spectral components generated by the optical modulation are phase-locked, it is possible to construct a robust system without using a complicated feedback control technique.

The two optical signals are vertically polarized waves and pass through the optical coupler and the polarization beam splitter on the transmitting side. After that, the two optical signals pass through the optical fiber and are distributed by the optical coupler on the receiving side, and one set of the two optical signals is guided to the photo-detector and output as the microwave signal M2.

The remaining set of the two optical signals that have been distributed by the optical coupler is frequency-shifted by the frequency of the microwave signal M3 by the optical modulator (usually called an Acoust-Optics modulator or a fiber frequency shifter (FFS): produced by Brimrose Co.) as a round-trip signal and then reflected by the Faraday reflector. The Faraday reflector applies 90° Faraday rotation to the optical signals, and hence, the remaining set of the two optical signals is reflected as optical signals different in polarization by 90°. The reflected optical signals are again frequency-shifted by the frequency of the microwave signal M3 by the optical modulator.

After that, the reflected two optical signals pass through the optical coupler and the optical fiber to be returned to the polarization beam splitter on the transmitting side. In consideration of photo-reversibility, the returned optical signals are the optical signals different in polarization by 90° and, hence, are horizontally polarized waves. Therefore, the optical signals are guided to the optical coupler by the polarization beam splitter.

The two optical signals reflected on the receiving side are mixed by the optical coupler with the optical signals distributed by the optical coupler. The optical signals output from the polarization beam splitter are different in frequency from the optical signal output from the optical coupler by a frequency twice as high as that of the microwave signal M3. The optical signals that have passed through the optical coupler are detected as microwave signals by the photo-detector.

Those signals are subjected to a frequency conversion by the image rejection mixer by using the microwave signal M1 output from the microwave distributor. The filters remove the signal having the same frequency as that of the microwave signal M1 from the sidebands as the DC component. A phase difference between the USB and the LSB is detected by the phase difference detector, and the microwave phase shifter is controlled according to the phase difference detected.

As illustrated in Fig. 5, in order to distinguish between the transmitted light and the reflected light, the optical modulator and the Faraday reflector are used on the receiving side to shift the frequencies of the round-trip optical signals by $2\omega$ (round trip). The shift frequency $\omega$ of the microwave M3 (in Fig. 3) is assumed to be much smaller than the angular frequency $\omega_{0}$ of the microwave signal M1. It is assumed here that a frequency-shifted signal with respect to the optical signal having the wavelength $\lambda_{1}$ is represented as “ $\lambda_{3}$” and that a frequency-shifted signal with respect to the optical signal having the wavelength $\lambda_{2}$ is represented as “$\lambda_{4}$”. If the reflected optical signals and the transmitted optical signals that have been subjected to such a frequency shifting processing are mixed by the optical coupler, the four optical signals having the wavelengths $\lambda_{1}$. $\lambda_{2}$, $\lambda_{3}$, and $\lambda_{4}$ are obtained. Frequency and phase relationships among these optical signals are obtained as follows:

• $(\omega_{0} t + \Phi)$ as a difference between $\lambda_{2}$ and $\lambda_{1}$;
• $(\omega_{0} t + \phi_{4} - \phi_{3} + \Phi)$ as a difference between $\lambda_{4}$ and $\lambda_{3}$;
• $(\omega_{0} t + 2\omega t + \phi_{4} + \Phi)$ as a difference between $\lambda_{4}$ and $\lambda_{1}$;
• $(\omega_{0} t - 2\omega t + \phi_{3} + \Phi)$ as a difference between $\lambda_{2}$ and $\lambda_{3}$.
Fig. 5. Configuration of parts of the low-frequency signal optical transmission system on the transmitting side and a receiving side. Blue lines show the electrical signals, and red lines show optical signals.

Fig. 6 is a diagram illustrating a configuration of parts of the low-frequency signal optical transmission system on the transmitting side and the receiving side. As illustrated in Fig. 6, the photo-detector converts those four optical signals into microwave signals. The (difference between $\lambda_{2}$ and $\lambda_{1}$) and the (difference between $\lambda_{4}$ and $\lambda_{3}$) are the same as the frequency of the input microwave signal M1. The (difference between $\lambda_{4}$ and $\lambda_{1}$) is higher than the frequency of the input microwave signal M1 by $2\omega$, and the (difference between $\lambda_{2}$ and $\lambda_{3}$) is lower than the frequency of the input microwave signal M1 by $2\omega$. These are frequency converted by using the image rejection mixer based on the input microwave signal M1. When signals corresponding to the (difference between $\lambda_{2}$ and $\lambda_{1}$) and the (difference between $\lambda_{4}$ and $\lambda_{3}$), which become a zero-hertz signal, are removed, the following are obtained: $(2\omega t + \phi_{4} + \Phi)$ in a USB signal and $-(-2\omega t - \phi_{3} + \Phi)$ in an LSB signal.

Fig. 6. Configuration of parts of the low-frequency signal optical transmission system on the transmitting side and the receiving side. Blue lines show the electrical signals, and red lines show optical signals.

The LSB signal has a minus sign because the LSB signal is inversed by the image rejection mixer. Here, if a phase-locked loop is configured so that the USB signal and the LSB signal have the same phase, the following equation is obtained: $\phi_{4} - \phi_{3} + 2\Phi = 0$. If the equation is established by controlling the phase $\Phi$, the phase difference $(((\phi_{4} - \phi_{3})/2) + \Phi)$ or $(((\phi_{4} - \phi_{3})/2) + \Phi + \pi)$ between the optical fiber transmission signals at the transmission destination discussed with reference to Fig. 2 becomes 0 or $\pi$, which can compensate an influence of a transmission line as a constant value.

The microwave signal to be transmitted is transmitted as the phase difference between the two optical signals (wavelengths $\lambda_{1}$ and $\lambda_{2}$), and hence, the phase of the transmitted signal at the transmission destination at the right end of the long-distance optical fiber becomes the same as the signal phase on the transmitting side at the left end or a phase shifted precisely by $\pi$. It is possible to perform a long-distance transmission of a low-frequency signal with stability without concern for an influence of the optical fiber. In this case, the influence is commonly exerted on the two optical signals (wavelengths $\lambda_{1}$ and $\lambda_{2}$) from external during the transmission through the optical fiber and is hence canceled as a common noise by using the difference between the two optical signals (wavelengths $\lambda_{1}$ and $\lambda_{2}$) at the transmission destination at the right end.

In order to distinguish between the transmitted optical signals and the reflected optical signals (go and return) in the round trip, it is essential to provide the image rejection mixer on the transmitting side and the optical modulator on the receiving side. The phases of the two optical signals (wavelengths $\lambda_{1}$ and $\lambda_{2}$) caused by the round trip are detected by the photo-detector according to the Michelson interferometer principle as the signal phases of a frequency that is twice as high at the optical modulator on the receiving side (right end) to separate the transmitted light and the received light and converted into microwaves, which are then separated by the image rejection mixer. The microwave phase shifter is controlled to achieve $(\phi_{4} - \phi_{3} + 2\Phi = 0)$, thereby allowing a phase delay to be compensated.

### 1. Delay Errors Caused by the Frequency Shift M3

At the antenna, the received optical signals are modulated (frequency-shifted) by a microwave signal $M3$, and the polarization is changed by a Faraday reflector and then sent back to the ground unit through the optical cable in reciprocal process. The purpose of these operations is to separate the backscatter signal and the round-trip signal. In this subsection, we will discuss the errors caused by these operations. We have to select the shift frequency as small as possible to ignore the chromatic signal delay. We select the shift frequency $(M3)$ from 5 to 25 MHz. Second-order (chromatic) PMD is the wavelength dependence of the propagation delay in the different polarization modes. The birefringence of the optical fiber cable is wavelength dependent; different wavelengths will cause different types of PMD. Deferential group delay is calculated as the covariance of the two deviations of the propagation delay. The deviation of the dual differential propagation delay caused by the phase shift of the second-order PMD is as follows [2]: TeX Source $$\sigma_{\tau 2} = {2\pi c D_{p}^{2} \over \sqrt{3}} \left({1 \over \lambda_{1}^{2}} - {1 \over \lambda_{2}^{2}}\right)\Delta_{\lambda}L\eqno{\hbox{(4)}}$$ where $\Delta_{\lambda}$ is the shift frequency, $D_{p}$ is the fiber PMD parameter of the optical fiber cable $[ps/\sqrt{\hbox{km}}]$, and L is the cable length [in kilometers]. The variation of the delay will have a standard deviation of 0.84 fs (15 km fiber) if we choose a fiber with PMD of 0.079 $ps/\sqrt{\hbox{km}}$, $\lambda_{1} = 1556.2\ \hbox{nm}$: 192.64 THz, $\lambda_{1} - \lambda_{2} = 0.02\ \hbox{nm}$: 2 GHz, and $\Delta_{\lambda} = 5 \times 10^{-4}\ \hbox{nm}$: 50 MHz, which is twice of the shift-frequency. When the $L$ is 15 km, $\sigma_{\tau 2}$ is 5.41E-7 fs. This error is vanishingly small.

### 2. Immunity to the Common-Mode Noise and the Differential-Mode Noise

The optical signal transmission is subject to noises caused due to environmental conditions. Possible noises are common-mode noises and differential-mode noises. The main causes of the common-mode noise are vibrations, acoustic sounds, twists, bending, and swings, while those of the differential-mode noise are the cable length change by temperature and the PMD. Temperature change causes the cable length change, and the cable length change leads the chromatic dispersion, which is the differential-mode noise.

The common-mode noise is referred to as phase shifts of the two coherent light waves ($\lambda_{3}$ and $\lambda_{4}$ in Fig. 7) by equal amounts ($\Delta f_{1}$ and $\Delta f_{2}$ in Fig. 7) and, therefore, does not cause a set of transmission microwave signals to be incoherent. Fig. 7 shows that the microwave frequency of $\lambda_{4} - \lambda_{1}$ becomes higher by $\Delta f_{2}$, and that of $\lambda_{2} - \lambda_{3}$ becomes lower by $\Delta f_{1}$. At the output ports of the image rejection mixer, the USB signal becomes higher by $\Delta f_{2}$, and the LSB signal becomes higher by $\Delta f_{1} (= \Delta f_{2})$. Both sideband signals are shifted in synchronization.

Fig. 7. Common-mode noise and differential-mode noise.

The differential-mode noise is referred to as an independent phase shift of the two coherent-light-waves ($\lambda_{3}$ and $\lambda_{4}$). The amounts of phase shift of $\Delta f_{1}$ and $\Delta f_{2}$ in Fig. 7 are not equal. As a result, both sideband signals are shifted asynchronously.

To successfully perform the signal transmission, a high sensitivity to differential-mode noises is essential. Our new system is designed mainly to detect the differential phase between the USB and the LSB signal phases. It has a relatively low sensitivity to the common-mode noises and insusceptibility to external environmental conditions contributing to common-mode noises.

SECTION IV

## PHASE CONSISTENCY CHECK OF THE TRANSMITTED AND THE ROUND-TRIPPED SIGNALS (OPEN LOOP TEST)

We have carried out the verification test for the differential phase between the 2-GHz transmission signal and the 2-GHz round-trip signal through a 5-km fiber. Fig. 8 shows a block diagram of the open loop test. A 2-GHz synthesizer signal is divided into two signals: One is for the phase stabilizer, and the other is for the transmission signal phase detector. The phase stabilizer signal is transmitted through a 5-km Single-Mode Fiber (SMF) spool, and then, its frequency is shifted by the FFS. The signal is reflected by the Faraday reflection mirror (FRM) and returned to the FFS. After the re-modulation by the shifter, the signal is sent back to the phase stabilizer path through the 5-km SMF cable. This system in the antenna is exactly the same as the high-frequency phase stabilizer [8].

Fig. 8. Phase measurement block diagram.

### 1. Phase Consistency Check of the Transmitted and the Round-Tripped Signals

The differential phase between the signals before/after the roundtrip transmission is detected by the phase stabilizer (roundtrip signal phase). The transmission signal phase is also detected by the phase detector (transmission signal phase). If the basic concept of the phase stabilizer system is correct, the 2-GHz round trip signal phase should be twice that of the 2-GHz transmission signal phase. The detected transmission signal and the round-trip signal phases are shown in Fig. 9.

Fig. 9. Phase measurement results.

### 2. Phase Response Under the Step Phase Shift

The phase stabilizer has a microwave phase shifter. The shift phase is controlled by DC-bias. We checked the phase step response. If the basic concept of the phase stabilizer system is correct, the round-trip signal phase should be twice that of the 2-GHz transmission signal phase. The detected transmission signal and round-trip signal phases are shown in Fig. 10. No contradictions are found from the test result. In the test result, there was a $2\pi$ ambiguity in phase.

Fig. 10. Step response.

### 3. Phase Stability Measurements (Closed Loop Test)

We measured the phase stability of the transmitted signal (2 GHz) at the antenna through the SMF cable (10 km) in the time-domain Allan standard deviation method [1] by a time interval analyzer: TSC-5110A. The measurements were conducted with the phase stabilizer to check the improvement of the phase stabilizer. The phase stability was compared between this system and the conventional system (Ortel 10350A and 10455A). When the optical signal (2 GHz) is transmitted through the SMF cable (10 km) without the stabilizer, the phase stability begins to degrade around some tens of seconds integration time, and a Flicker-FM noise appears. In the case of using the phase stabilizer, the degradation of the phase stability is staved off. The measured phase noise (see Fig. 11) with the stabilizer is the white phase noise.

Fig. 11. Two-gigahertz phase stability that passed through the 10-km fiber with the phase stabilizer.

The closed-loop system is still in the trial phase, and the phase locked loop for the closed loop is under development at the breadboard level. It will be capable of achieving lower phase noise after optimization of the PLL circuit.

SECTION V

## CONCLUSION

The present system can be applied to a signal transmission system using a device, such as an interferometer, to achieve high stability of the reference signal transmission, the transmission, or distribution of the highly stable signal according to the national frequency standard. It can also be applied to a system with transmission delays. The stability of an optical signal is not much of a concern (the optical signal phase stabilized method is described in [3] and [5]), but the stability of the differential light-wave signals is of significance. In the presented system using the transmission phase stabilizer for high-frequency signals [8], the phases of two round-trip signals (signals transmitted from the antenna with a frequency slightly shifted from that of a signal transmitted to the antenna) are separately measured, and then, the phase control is performed only on one of the two optical signals.

The previously presented system was for processing high-frequency signals and not for low-frequency signals ($\leq$ 20 GHz). It is difficult to separate low-frequency signals using the FBG. The new system discussed in this paper processes and distributes low-frequency reference signals that are highly stable. The phase of two round-trip microwave signals that are converted from optical signals is measured separately by an Image Rejection Mixer. The phase control is performed with the microwave phase shifter. We will decide which system to use, i.e., the one with FBG or the one with a phase shifter for low-frequency signals, based on how easily it can be fabricated. In general, the optical transmission phase via fiber is affected by vibration and acoustic noise. The presented systems are insusceptible to these external disturbances and function appropriately, regardless of the ambient conditions under controlled temperature and/or stabilized vibration.

There is insufficient evidence of whether any effort has been made to analyze the environmental perturbations to which the fiber spool is subject and to consider how the system would perform under the thermal fluctuations at ALMA high-site. Therefore, we would like to perform the final test at the ALMA high-site.

### ACKNOWLEDGMENT

The author would like to express his heartiest gratitude to the staff members of Sumitomo Osaka Cement Co., Ltd, as well as the anonymous reviewers for their valuable suggestions.

## Footnotes

Corresponding author: H. Kiuchi (e-mail: hitoshi.kiuchi@nao.ac.jp).

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