Corner Cube Reflector Research Articles

Analysis of the Effect of Tilted Corner Cube Reflector Arrays on Lunar Laser Ranging

This paper primarily investigates the effect of the tilt of corner cube reflector (CCR) arrays on lunar laser ranging (LLR). A mathematical model was established to study the random errors caused by the tilt of the CCR arrays. The study found that, ideally, when the laser ranging pulse width is 10 picoseconds or less, it is possible to distinguish from which specific corner cubes within the CCR array each peak in the echo signal originates. Consequently, partial data from the echo can be extracted for signal processing, significantly reducing random errors and improving the single-shot precision of LLR. The distance obtained by extracting part of the echo can be reduced to the center position of the array, thereby providing multiple higher-precision ranging results from each measurement. This not only improves the precision of LLR but also increases the data volume. A simulation experiment based on the 1.2 m laser ranging system at Yunnan Observatories was conducted. By extracting one peak for signal processing, the single-shot precision improved from 32.24 mm to 2.52 mm, validating the theoretical analysis results. Finally, an experimental laser ranging system based on a 53 cm binocular telescope system was established for ground experiments. The experimental results indicated that the echo signal could identify the tilt state of the CCR array. By extracting the peak returned by the central CCR for signal processing, the ranging precision was greatly improved. Through theoretical analyses, simulation experiments, and ground experiments, a solution to reduce the random errors caused by the tilt of the CCR array was provided. This offers an approach to enhance the single-shot precision of future LLR and provides a reference for upgrading ground-based equipment at future laser ranging stations.

Retroreflective optical ISAC using OFDM: channel modeling and performance analysis.

In this Letter, we propose and investigate a retroreflective optical integrated sensing and communication (RO-ISAC) system using orthogonal frequency division multiplexing (OFDM) and corner cube reflector (CCR). To accurately model the reflected sensing channel of the RO-ISAC system, both a point source model and an area source model are proposed according to the two main types of light sources that are widely used. Detailed theoretical and experimental results are presented to verify the accuracy of the proposed channel models and evaluate the communication and sensing performance of the considered RO-ISAC system.

Analysis and experimental verification of the polarization characteristics of cube-corner reflectors

The polarization effect of cube-corner reflectors (CCRs), which influences the performance of optical systems, requires comprehensive analysis. This study developed a model for the polarization state of uncoated solid and hollow CCRs using the Jones matrix derivation and Zemax software simulations. The accuracies of theoretical analyses and simulations were verified using an experimental setup. Theoretical analysis, simulation, and experimental results revealed that hollow CCRs are insensitive to the polarization state of the incident light, exhibiting average variations of 0.8° and 0.7° in the polarization direction and ellipticity, respectively. Contrastingly, the high sensitivity of solid CCRs to the polarization state of the incident light varied across different incident regions. The propagation paths 2–1–3 and 3–1–2 with minor polarization effects involved light that entered from one side of the CCR, traversed the bottom, and emitted from the other side. In these regions, the average variations in the polarization direction and ellipticity were 10.7° and 6.6°, respectively, whereas more affected regions exhibited corresponding values of 44.8° and 20.0°. These findings guide the enhancement and optimization of the performance of optical systems using CCRs.

A Wollaston Prism and Corner Cube Reflector Cooperative Sensing Heterodyne Interferometer for Simultaneous Measurement of Straightness Errors and Displacement

A Wollaston Prism and Corner Cube Reflector Cooperative Sensing Heterodyne Interferometer for Simultaneous Measurement of Straightness Errors and Displacement

Near-infrared lunar laser ranging: Research on pointing error of Lunokhod 2 corner reflector based on effective echo signal broadening

The effective echo intensity of lunar laser ranging (LLR) has always been a concern, which not only reflects the detection ability of the LLR system but also affects the ranging uncertainty of LLR. The initial pointing of the corner-cube reflector (CCR) has a certain relationship with the echo intensity and ranging uncertainty of LLR. In our previous work, we analyzed the pointing error of the CCR array by studying the change in echo signal intensity. This paper will continue to research the initial pointing error of the CCR array from the perspective of ranging uncertainty. In this paper, based on the ranging system of the TianQin laser ranging station, the ranging uncertainty is obtained by analyzing the data, and finally, the pointing error of the CCR array is researched by summarizing the variation law of the ranging uncertainty. Firstly, the delay model introduced by the pointing error of the corner reflector is established, and the theoretical uncertainty introduced by the pointing error of the corner reflector is calculated. Secondly, the ranging uncertainty is analyzed through the experiment of LLR. Finally, the pointing error of the CCR array is calculated by inversion of ranging uncertainty. Theoretical analysis and experimental measurement results show that there is a pointing error in the L2 (Lunokhod 2) corner reflector, and its pointing error is about 5° ∼ 10°. This study is of great guiding significance for analyzing and studying the ranging uncertainty of LLR and arranging the next generation of LLR reflectors.

Injection-seeded, Q-switched Ho:YAG laser based on alignment-insensitive corner cone reflectors

This paper demonstrates a single-frequency injection-seeded laser with a Q-switched Ho:YAG laser consisting of two corner cube reflectors. As a seed laser, the Ho:YAG NPRO has an available output power of 1.8 W and operates at 2090.6964 nm. The single-frequency pulse energy obtained in the case of injection-seeded is 6.8 mJ, the pulse width is 166 ns, and the Q-switched Ho:YAG laser operates at a repetition rate of 100 Hz. The Ho:YAG single-pass amplifier scales single-frequency energy from 6.8 mJ to 32.3 mJ. The pulsed spectrum has a half-width of 2.84 MHz. The Ho:YAG amplifier has a beam quality of 1.1 and 1.17 in the x and y axes.

Robust free-space optical frequency transfer in time-varying link distances conditions

Future inter-satellite clock comparison on high orbit will require optical time and frequency transmission technology between moving objects. Here, we demonstrate robust optical frequency transmission under the condition of variable link distance. This variable link is accomplished by the relative motion of a single telescope fixed on the experimental platform to a corner-cube reflector (CCR) installed on a sliding guide. Two acousto–optic modulators with different frequencies are used to separate forward signal from backward signal. With active phase noise suppression, when the CCR moves back and forth at a constant velocity of 20 cm/s and an acceleration of 20 cm/s2, we achieve the best frequency stability of 1.9 × 10−16 at 1 s and 7.9 × 10−19 at 1000 s indoors. This work paves the way for future studying optical frequency transfer between ultra-high-orbit satellites.

Acousto-Optic Q-Switched Ho:YLF Ring Laser Based on Anti-Misalignment Resonant Cavity

An acousto-optic Q-switching Ho:YLF ring oscillator at 2066.33 nm with two anti-misalignment corner cube reflectors (CCRs) pumped by a 1940 nm thulium-doped fiber laser is demonstrated. The depolarization effect of the CCR is expressed in the form of equivalent transmission, and the transmission from two output directions of the oscillator is changing synchronously and periodically as the waveplate angle changes. In the experiment, under the pump power of 21.76 W, the optimum bidirectional energy of 3.13 mJ for a pulse duration of 122 ns at a repetition rate of 50 Hz is realized. The pulse energy reduction percentage at 50 Hz is 8% by changing the horizontal drift angle of one of the CCRs to 4.5°. The beam quality factor M2 is calculated to be about 1.10, revealing that the Ho laser is working in a fundamental transverse mode.

Distant RF field sensing with a passive Rydberg-atomic transducer

We combine a rubidium vapor cell with a corner-cube prism reflector to form a passive RF transducer, allowing the detection of microwave signals at a location distant from the active components required for atomic sensing. This compact transducer has no electrical components and is optically linked to an active base station by a pair of free-space laser beams that establish an electromagnetically induced transparency scenario. Microwave signals at the transducer location are imprinted onto an optical signal which is detected at the base station. Our sensing architecture with a remote standalone transducer unit adds important flexibility to Rydberg-atom based sensing technologies, which are currently subject to significant attention. We demonstrate a ∼30 m link with no particular effort and foresee significant future prospects of achieving a much larger separation between the transducer and the base station.

Lunar laser ranging: The pointing error analysis to Lunokhod 1 and Lunokhod 2

The corner-cube reflectors (CCRs) are small optical instruments designed to accurately measure the distance between the Earth and the Moon. Signals from L1 (Lunokhod 1) and L2 (Lunokhod 2) can be used for higher precision analysis of lunar libration than Apollo reflector. Here, we describe the optical performance of L1 and L2 at near-infrared wavelength. Theoretically, because of the initial direction and lunar librations, the surfaces of these arrays do not, in general, point directly to the Earth. The laser incident angles for the CCRs and the far-field diffraction patterns (FFDP) of individual CCRs of possible incident angles are calculated. Finally, extract the optical cross-section as a function of incident angles. In the experiment, for the first time, superconducting nanowire single-photon detectors (SNSPDs) at a wavelength of 1064 nm are designed and fabricated aiming at lunar laser ranging (LLR), and the effective echo rates of L1 and L2 are measured. Using experimental results to check the orientation of the CCRs. The experimental results show that there is an error in the initial pointing of the CCRs, the initial pointing angles of L1 and L2 are about from 10o to 40o.

Application of optical switching technology inalunar laser ranging system based on a superconducting detector.

The TianQin laser ranging station has successfully obtained the effective echo signals of the all five corner-cube reflectors on the lunar surface by using a 1064nm Nd:YAG laser with 100Hz repetition frequency and a 2×2 array of superconducting nanowire single-photon detectors (SNSPDs). The application of the SNSPD in the lunar laser ranging system (LLRS) has demonstrated its detection ability, but it loses its superconducting state and cannot work under strong stray light conditions. In this paper, a high-speed optical switch experimental device based on 100Hz is developed to solve the application problem of the SNSPD in the LLRS, and its main technical parameters are tested. The results show that the maximum running distance of the switch is 200µm; the switching time is better than 2ms; and the extinction ratio is better than 57dB. Moreover, the application of the high-speed optical switch experimental device in the lunar laser ranging system is designed, and the effective detection time between two laser pulses (10ms) is determined to be 6.1ms.

Development of SMA Spring Linear Actuator for an Autonomous Lock and Release Mechanism: Application for the Gravity-Assisted Pointing System in Moon to Earth Alignment of Directional Devices

The next generation lunar reflector (NGLR) experiment is one of the experiments selected by NASA in the framework of the commercial lunar payload services (CLPS) initiative. The experiment, inspired by the lunar laser ranging (LLR) experiments of the Apollo era, is basically a single cube corner reflector (CCR) capable of reflecting a beam coming from a laser station on Earth that must be deployed on the Moon and pointed toward the mean Earth direction. In this work, a prototype of an actuator for the lock and release system of the reflector package was conceived, built, and tested in laboratory conditions. Since the entire pointing system must be passive, the actuator is designed to be operated by an SMA spring actuated by the thermal radiation of the Sun and regolith on the Moon. In lab conditions, the prototype, activated by a heat gun, showed the capability of the SMA spring to operate a lock and release pin, whose diameter is 4 mm, subjected to a preload of F = 7 N exerted by the releasing spring.

Autocollimation angle-measurement method with a large range based on spot deformation.

A novel hollow cylindrical cube-corner reflector (HCCCR) for the autocollimator (AC) is proposed. The angle measuring range of AC will be effectively increased by using the parallel propagation characteristics of the reflected light and the incident light in local area of this reflector. And the yaw and pitch angles of HCCCR will be measured through the morphological changes of the reflected beam. The experimental results show that the measuring range of the autocollimation angle measurement method is extended from ±30' to ±30°, and the dynamic measurement distance is 0.2∼5m, the measurement accuracy of pitch angle and yaw angle is better than 69" and 51", respectively.

Development of a magnetic cardan suspension coupled with a single actuated axis for gravity assisted pointing of directional devices: A case study of Moon to Earth alignment for a laser ranging reflector

A new class of Lunar Laser Ranging (LLR) experiments has been recently investigated by the international Space Agencies, in order to deploy a set of Next Generation Lunar Reflector (NGLR) on the Moon surface, funded under NASA's Commercial Lunar Payload Services (CLPS) program (Currie et al., 2020). In principle the Cube Corner Reflector (CCR) arrays deployed by Apollo and Lunokhod missions in the 70’s will be flanked (at different locations) by single bigger reflectors, thus removing the systematic errors in the Time of Flight (TOF) measurement induced by the Moon librations (Turyshev et al., 2012).In this paper we describe a mechanism formed by a passive cardan magnetic suspension, dedicated to the alignment of the CCR toward the mean Earth direction. The suspension is able to compensate for the misalignment due to the slope of the landing site that can be different at each site (Zupp, 2013). If proper control of azimuth angle of the spacecraft at touchdown cannot be guaranteed, an additional motor to rotate the magnetic suspension must be provided by the lander, for the alignment toward the mean Earth direction.Once the landing site is defined, the geometry of the retroreflector housing, together with that of the cardan suspension, will autonomously (without human intervention) and passively (without provision of electrical power by the lander) provide the right elevation angle just by gravity, no matter what the morphology of the site is.The mechanical performances of the magnetic suspension have been preliminarily investigated in (Ancillai et al., 2020). The solution presented can be applied to any directional device, requiring pointing capability, like antennas, and can be adopted with low friction rolling bearings as well.

Resistance of a corner cube reflector with a dielectric antireflection coating to the space environment

Subject of study. The negative effect of corpuscular radiation of outer space on the optical properties of a corner cube reflector with a multilayer dielectric coating is studied. Aim. The feasibility of applying a bilayer antireflection dielectric coating for radiation with a wavelength of 532 nm on the input face of a corner cube reflector operated in a high-orbit spacecraft is investigated. Method. Electron–proton irradiation simulating the effect of hot magnetospheric plasma on corner cube reflectors with and without antireflection coatings was carried out using a simulation stand. Because the corner cube reflector is made of KU-1 radiation-resistant quartz glass, special attention was devoted to the formation of electrostatic discharges that accompany the irradiation of the samples. Main results. The induced optical density of the coating of the input face of corner reflectors caused by magnetospheric plasma particles increased with the distance from the geometric center of the aperture of the input face to the metal frame. This can be explained by the fact that discharges with the maximum intensity were observed in the vicinity of the frame, resulting in the destruction of the near-surface layers of the irradiated samples. It has been experimentally established that the antireflection effect of a bilayer coating, which comprises HfO2 (thickness of approximately 25 nm) and SiO2 (thickness of approximately 100 nm), leveled with increasing irradiation dose. Practical significance. The results demonstrate that the use of the investigated bilayer antireflection coating is advisable in optical systems of a high-orbit spacecraft with an active lifetime not exceeding 6 years or under conditions of lower dose load.

Development of a combined interferometer using millimeter wave solid state source and a far infrared laser on ENN’s XuanLong-50 (EXL-50)

A millimeter wave solid state source—far infrared laser combined interferometer system (MFCI) consisting of a three-channel 890 GHz hydrogen cyanide (HCN) laser interferometer and a three-channel 340 GHz solid state source interferometer (SSI) is developed for real-time line-integrated electron density feedback and electron density profile of the EXL-50 spherical tokamak device. The interferometer system is a Mach–Zehnder type, with all probe-channels measured vertically, covering the plasma magnetic axis to the outermost closed magnetic plane. The HCN laser interferometer uses an HCN laser with a frequency of 890 GHz as a light source and modulates a 100 kHz beat signal by a rotating grating, giving a temporal resolution of 10 μs. The SSI uses two independent 340 GHz solid-state diode sources as the light source, the frequency of the two sources is adjustable, and the temporal resolution of SSI can reach 1 μs by setting the frequency difference of the two lasers at 1 MHz. The main optical path of the two interferometers is compactly installed on a set of double-layer optical platform directly below EXL-50. Dual optical path design using corner cube reflectors avoids the large support structures. Collinear the probe-beams of two wavelengths, then the phase error caused by vibration can be compensated. At present, the phase noise of the HCN Interferometer is 0.08 rad, corresponding to a line-integrated electron density of 0.88 × 1017 m−2, one channel of measuring result was obtained by the MFCI system, and the highest density measured is about 0.7 × 1019 m−2.

Roll angle autocollimator measurement method based on a cylindrical cube-corner reflector with a high resolution and large range.

A novel high-resolution and large-range autocollimator measurement system for roll angle is proposed. The system retains the basic internal structure of the traditional autocollimator (AC), which only uses a novel non-standard cylindrical cube-corner reflector (CCCR) instead of the planar reflector. In the article, the mathematical relationship between the structure of this special reflector and the spatial coordinate vector change of the reflected beam is deduced, and the measurement formula of the roll angle autocollimator (RAC) measurement system is established based on this mathematical relationship. The effectiveness of the measurement system and method is verified by experiments. Experimental results show that this method can effectively enhance the range to ±20°, and the whole measurement accuracy is 6.1", the measuring resolution is 1".

Optical wireless sensor networks using tunable optical filters

A novel decision gathering scheme for optical wireless sensor networks (OWSNs) is proposed and thoroughly analyzed in this article. The proposed technique relies on a tunable optical filter (TOF) that is mounted on each sensor node. Specifically, the received laser signal from a central unit at any particular node is modulated through the TOF, where it is either rejected or passed in accordance to the sensed result. The output of the TOF is passed to a corner cube reflector (CCR) that reflects the optical signal either back to the central unit or to another node in the OWSN. Three different setups are considered to implement the proposed scheme and the pros and cons of each setup are thoroughly discussed. It is revealed that the energy requirement of each sensor node is minimized as energy is only consumed in the process of sensing and adjusting the TOF. The performance of the proposed scheme is analyzed through a mathematical framework to derive the average decision error rate (DER) for all setups. Moreover, simulation results analyze the impact of key system parameters including atmospheric turbulence, transmit power, link distance, filter efficiency and detection threshold.

Roll angle of autocollimator measurement method based on hollow cube corner reflector

Roll angle of autocollimator measurement method based on hollow cube corner reflector

Experimental research on a multi-aperture phase modulation technique based on a corner-cube reflector array.

In this paper, a novel phase modulation technique based on a corner-cube reflector (CCR) array is proposed and demonstrated experimentally. The piezoceramics are linked behind each CCR. When the beams irradiate on the CCR array, the phase modulation can be realized by applying a voltage to piezoceramics to control the spatial location of each CCR. The piston phase errors of the device itself are compensated by employing the stochastic parallel gradient descent (SPGD) algorithm. Then, the piezoceramics are loaded with preset voltages to obtain the expected phase, and the anticipative optical field is generated. In the experiment, the piston phase errors of the 7-way and 19-way CCR array are corrected well. In order to further verify the phase control capability of the device, a vortex beam carrying orbital angular momentum (OAM) of 1 is generated by utilizing the 6-way CCR array. The experimental results confirm the feasibility of the concept.