† Corresponding author. E-mail:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11655001 and 11605065).
Over the past 50 years, lunar laser ranging has made great contributions to the understanding of the Earth–Moon system and the tests of general relativity. However, because of the lunar libration, the Apollo and Lunokhod corner-cube retroreflector (CCR) arrays placed on the Moon currently limit the ranging precision to a few centimeters for a single photon received. Therefore, it is necessary to deploy a new retroreflector with a single and large aperture to improve the ranging precision by at least one order of magnitude. Here we present a hollow retroreflector with a 170-mm aperture fabricated using hydroxide-catalysis bonding technology. The precisions of the two dihedral angles are achieved by the mirror processing with a sub-arc-second precision perpendicularity, and the remaining one is adjusted utilizing an auxiliary optical configuration including two autocollimators. The achieved precisions of the three dihedral angles are 0.10 arc-second, 0.30 arc-second, and 0.24 arc-second, indicating the 68.5% return signal intensity of ideal Apollo 11/14 based on the far field diffraction pattern simulation. We anticipate that this hollow CCR can be applied in the new generation of lunar laser ranging.
Over the past five decades, lunar laser ranging (LLR) has been making great contributions to the study of the Earth–Moon system and the gravitational physics, such as the test of the equivalent principle, time-rate-of-change of the gravitational constant G, geodetic precession, and test of the Newton inverse-square law.[1,2] Ranging precision has been improved from a few decimeters to the centimeter level along with the progress of the ground-based laser ranging facilities.[3] Nevertheless, to test the parameters of gravitational physics with a higher precision, the millimeter-level ranging precision is necessary.
Nowadays, the corner cube retroreflector (CCR) arrays placed on the Moon by the United States of America and the former Soviet Union last century has become the dominating error source (15 mm–45 mm) according to the analysis of APOLLO (Apache Point Observatory Lunar Laser-ranging Operation).[4] As seen from the Moon’s surface, the Earth’s center appears to move around its mean position with ± 6.9° in the north-south direction and ± 8.2° in the east-west direction due to the combined effects of the perturbed orbit and the obliquity of the ecliptic for the Moon. This phenomenon is the so-called “lunar libration”, which causes the tilt of the CCR array plane with respect to the orientation of the Earth, resulting in a spread of the arrival time as each CCR is at a slightly different distance from the Earth.[5,6] Moreover, the reflecting performance of these CCR arrays has attenuated to a factor of 1/10 after more than four decades' operation.[7]
Thus, upgrading the CCR array is a feasible approach for achieving millimeter precision LLR. Recently, several research teams have proposed replacing the CCR arrays with a single, wide aperture CCR to overcome the current ranging uncertainty.[5–9] Turyshev et al.[5] designed a hollow CCR with a 170-mm aperture that showed a similar reflection performance to Apollo 15. Currie et al.[6,8] developed a solid CCR prism with a 100-mm aperture for the new generation of LLR, which had 20% reflection performance of the initial Apollo 11/14. Araki et al.[9] proposed to develop a hollow CCR with a 200-mm aperture for the future LLR and had been focusing on the choice of the material and the thermal simulation for years.
Compared with a solid CCR, hollow CCR is probably a better choice to avoid the effect of the gradient and the variation of refraction index caused by the fluctuation of lunar temperature (100 K–400 K), as well as to get a smaller weight. Consequently, the flatness of the reflecting surface and the precision of the dihedral angle are the main two decisive factors determining the optical performance of a hollow CCR.
In this paper, we present the manufacture of a hollow CCR with a 170-mm aperture and sub-arc-second angle precision using hydroxide-catalysis bonding (HCB) technology. In contrast to the previous reports, we put forward (i) special processing and measurement techniques of sub-arc-second precision perpendicularity, and (ii) adjusting method for the third angle using two autocollimators. The hollow CCR can be potentially applied for the next generation of LLR.
The velocity aberration, caused by the different motion velocity of the moon and the ranging station, introduces a location deviation between the ranging station and the center of the diffraction pattern when a laser ranging pulse arrives back to Earth.[10] The velocity aberration for lunar laser ranging mainly varies between 0.7 arc-second–1.4 arc-second, which is determined by the latitude of the ranging station.[11] Generally, slight angle errors of the CCR can compensate this location deviation so that the ranging station can be located in the area where most return photons can be received.
According to the calculation by Otsubo et al.,[11] to acquire a similar optical response to Apollo CCR arrays for future LLR, the optimized aperture and the dihedral angle offset (deviation from a perfect right-angle) of a single CCR are 150 mm–250 mm and about 0.3 arc-second–0.4 arc-second, respectively. We plan to develop a hollow CCR with a 170-mm aperture. It is a choice that takes both the reflecting area and the technology difficulty into consideration. Based on our numerical simulation in Table
Many research groups experimentally studied the fabrication of a hollow CCR with high angle precision.[12–16] Preston and Merkowitz[12,13] developed several 40-mm aperture hollow CCRs using both hydroxide-catalysis bonding and epoxy bonding methods, and the best prototype realized the dihedral angle offsets of 0.93 arc-second, 0.52 arc-second, and 1.58 arc-second, respectively. Oreb et al.[14,15] developed a double hollow corner cube (three mirrors were bonded onto a base glass forming two hollow CCRs) using optical contact with an approximately 73-mm aperture (minor axis of an ellipse-shaped aperture) for NASA’s Space Interferometer Mission (SIM). The dihedral angle offsets were within 0.4 arc-second and then went up to 1.68 arc-second, 0.03 arc-second, and 1.68 arc-second, and 1.90 arc-second, 0.07 arc-second, and 0.50 arc-second respectively for another prototype when the HCB technology was employed later.[16]
We developed a method for manufacturing hollow CCR with sub-arc-second precision using HCB technology, because its high strength and low coefficient of thermal expansion are desirable for enduring vibration, impact, and extreme temperature fluctuation during a space-based mission.[5,12,13,17,18] As shown in Fig.
There are two key technical issues for this method. First, it is really difficult to process two lateral mirrors (mirror 2 and mirror 3 in Fig.
To resolve the first issue, we designed an auxiliary fixture as shown in Fig.
To resolve the second issue, Burke et al.[16] adjusted the third dihedral angle of a hollow CCR using a laser interferometer based on estimating the shape of interferometric fringes. Here, we employed two autocollimators marked as “a” and “b” as shown in Fig.
Figure
The far field diffraction pattern of this hollow CCR is calculated as shown in Fig.
A hollow corner cube retroreflector with a 170-mm aperture was developed using the HCB technology. The dihedral angle offsets of 0.10 arc-second, 0.30 arc-second, and 0.24 arc-second were realized, which completely met the requirement (required by the lunar libration) of ≤ 0.7 arc-second for LLR. The 68.5% relative intensity of Apollo 11/14 arrays can be expected at least, indicating the potential application in the next generation of LLR.
The thermal cycle test with temperature ranging from − 40 °C to +75 °C was carried out. The changes of dihedral angle did not exceed 0.2 arc-second. In our future work, thermal cycle testing with simultaneous FFDP measurement will be operated to verify its optical performance in the actual lunar environment ( − 170 °C to +130 °C).[19] The robotic way of deploying the CCR on the Moon and the pointing to the Earth also need to be considered. Additionally, to meet the launch requirement, this hollow corner cube retroreflector also needs to be tested with a series of experiments including acceleration, vibration, impact, and solar radiation.[20–22]
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