Retroreflector Array Research Articles

Optical parameter design model of hemispherical laser retroreflector arrays for satellite laser ranging

A laser retroreflector array (LRA) with multiple retroreflectors is used to directionally reflect an incident laser beam and aims to enhance the received signal strength into laser ranging ground stations. A comprehensive mathematical equation of the received photons is established by modelling the LRA far field diffraction intensity (FFDI) and the satellite velocity aberration position. Based on this received photon model, a novel method on designing the dihedral angle offset and the aperture of retroreflectors is proposed, which maximizes the received photon under the minimal elevation angle of the ground station. Taking the hemispherical structure parameters of Chinese HY-2 satellite LRA and the specification parameters of the Shanghai Astronomical Observatory, the optimal aperture and the dihedral angle offset of the HY-2 laser retroreflectors are 17 mm and 1.6″, respectively. These two optimal optical parameters make the received photon under the elevation angle of 0° reach ∼0.9 count per laser shot. Until now, ∼851,400 successful observations have been successfully obtained by global ground stations since the first launch of HY-2 satellite series in 2011, which guarantees the high-precise orbit determination of HY-2 satellite series.

Analysis and diagnosis of abnormal SLR validation results for BeiDou-3 SECM-B MEO C225 and C226 satellite orbits

Satellite laser ranging (SLR) is the only stand-alone and external tool for verifying the accuracy of microwave-based GNSS orbits. On February 2, 2023, the International Laser Ranging Service initiated the SLR global tracking campaign for the complete BeiDou-3 medium Earth orbit (MEO) constellation. This initiative provides an opportunity to unveil the potential issue for BeiDou-3 MEO orbit modeling. An examination of the SLR validation results of precise BeiDou-3 MEO orbits across different IGS/Multi-GNSS Experiment (MGEX) analysis centres (ACs) reveals that the SLR residual standard deviation for BeiDou-3 SECM-B MEOs C225 and C226 orbits reaches 18 cm. This figure is approximately four to nine times those for other BeiDou-3 MEOs. This contradicts the fact that the orbit quality of C225 and C226 is comparable to other satellites. By analyzing the correlation between SLR residuals and de-trend clock residuals, detector-specific bias performance, and the distribution characteristics of SLR residuals relative to satellite azimuth and nadir angles, we diagnose that abnormal SLR validation results for C225 and C226 originate from a large deviation in the official horizontal offsets for the laser retroreflector arrays (LRAs) in the satellite reference frame. LRA horizontal offsets for C225 and C226 are estimated based on SLR residuals. With our adjusted LRA offset estimates, the SLR residual metrics for C225 and C226 orbits (across various IGS/MGEX ACs) are comparable to the results obtained for other BeiDou-3 MEOs. Additionally, our adjustments enable the identification of their orbit modeling errors across different IGS/MGEX ACs according to the pattern of SLR residual variation. From the study, spacecraft manufacturers should be encouraged to conduct a comprehensive review of ground calibrations for BeiDou LRA offsets. This is crucial for optimizing BeiDou orbit model and enhancing its applications in high-precision geosciences.

Determination of global geodetic parameters using satellite laser ranging to Galileo, GLONASS, and BeiDou satellites

The new Global Navigation Satellite System (GNSS) satellites, including GLONASS, Galileo, and BeiDou system, are equipped with Laser Retroreflector Arrays (LRA) to support Satellite Laser Ranging (SLR) tracking, which contributes to the estimation of global geodetic parameters. In this study, we estimate the global geodetic parameters using the SLR observations to GNSS satellites and also investigate the effects of different data processing strategies on the estimated Earth Rotation Parameters (ERP), geocenter motion, and terrestrial scale. The results indicate that setting range bias parameters for each satellite-station pair can effectively account for the satellite-specific biases induced by LRAs, leading to smaller Root Mean Square Errors (RMSE) of the post-fit SLR residuals. Furthermore, estimating the range biases for each satellite-station pair improves the accuracy of the estimated station coordinates and ERP. We also examine the impact of different arc lengths on the estimates of ERP, geocenter motion, and terrestrial scale. The results show that extending arc length can significantly reduce the formal error of ERP. The 7-day strategy produces the smallest RMSEs of 473 microarcseconds and 495 microarcseconds for the estimated X- and Y-component of pole coordinates, and 52 microseconds for length-of-day, respectively. However, the estimated geocenter motion is less affected by the arc length, even the shortest 1-day arc strategy can capture the seasonal variations of geocenter motion in Z component. For scale estimation, extending the arc length notably improves the accuracy of the estimated station coordinates and scale, but this advantage becomes less noticeable in longer arcs. The 7-day solution also obtains the closet scale results compared to ITRF2014, with the RMSE of 2.10 × 10–9.

A complete analysis of the link uncertainty budget for pulsed laser time transfer on China space station

High-precision Time-Frequency Rack (HTFR) mission, a part of experiment module II of the China Space Station (CSS), was equipped with a Sr optical clock, H-maser, and laser-cooled microwave clock. To compare time and frequency across widely separated clocks, a microwave link, and a pulsed laser link were both established, which probably enables new possibilities for fundamental science, geodesy, and metrology. Based on the existing relativistic theory for time and frequency transfer, we derive a relativistic model of satellite-ground laser time transfer on CSS (CLT), which can be of direct use in CLT data processing. In addition to first and second-order Sagnac effects, it also includes relativistic rate shifts, atmospheric refraction, and turbulence, laser retroreflector array (LRA) range correction, and position correction between detector and reflector, satisfying the stability evaluation of CSS atomic clocks with fractional frequency stability of 3 × 10−17/10000 s. Additionally, we numerically investigate the link error magnitude and use Monte Carlo simulations to assess the impact of correcting for link errors on the stability of the CLT, taking into account the CSS orbit and attitude determinations as well as the CLT payload calibration parameters. It is shown that the CLT link can be considered to reach a TDEV of approximately 0.1 ps/300 s while meeting the CSS design objectives. The primary factors that influence the stability of the CLT are the position correction between detector and reflector, LRA range correction, and the coupling relation of these two error distributions.

Performance Analysis of Modulating Retroreflector Array for UAV-Based FSO Links

Performance Analysis of Modulating Retroreflector Array for UAV-Based FSO Links

Fifteen Years of Millimeter Accuracy Lunar Laser Ranging with APOLLO: Data Set Characterization

We present data from the Apache Point Observatory Lunar Laser-ranging Operation (APOLLO) covering the 15 yr span from 2006 April through the end of 2020. APOLLO measures the Earth–Moon separation by recording the round-trip travel time of photons from the Apache Point Observatory to five retro-reflector arrays on the Moon. The APOLLO data set, combined with the 50 yr archive of measurements from other lunar laser ranging (LLR) stations, can be used to probe fundamental physics such as gravity and Lorentz symmetry, as well as properties of the Moon itself. We show that range measurements performed by APOLLO since 2006 have a median nightly accuracy of 1.7 mm, which is significantly better than other LLR stations.

Characterization of a retroreflector array for 320-GHz interferometer system in Heliotron J.

A retroreflector array, composed of a cluster of small retroreflectors, is experimentally studied for application to a Michelson-type interferometer system in the fusion plasma experiment. Such a new-type reflector has the potential to be a vital and effective tool at a spatially limited location, such as on the vacuum chamber wall of plasma experimental devices. To investigate the effect of retroreflector array on the reflected beam properties, a tabletop experiment is performed with the retroreflector array composed of 4mm corner-cube retroreflectors and with a 320-GHz (λ ∼ 0.937mm) submillimeter wave source. An imaging camera is utilized to measure the submillimeter wave beam profile and is scanned perpendicularly to the beam propagation direction if necessary. The experimental result exhibits a diffraction effect on the reflected beam, resulting in the emergence of discrete peaks on the reflected beam profile, as predicted in the past numerical study; however, the most reflected beam power converges on the one reflected into the incident direction, resulting from a property as a retroreflector. Furthermore, the dependence of the reflected beam on the incident beam angle is characterized while fixing the detector position, and the retroreflection beam intensity is found to vary due to the diffraction effect. Such an undesired variation of beam intensity induced by the diffraction can be suppressed with a focusing lens placed in front of the detector in the practical application to an interferometer.

Lunar Laser Ranging Retroreflectors: Velocity Aberration and Diffraction Pattern

The Lunar Laser Ranging (LLR) retroreflector arrays have been on the Moon for half a century. During that time, the laser range uncertainty has improved by a factor of 100. Consequently, the science results have also improved by orders of magnitude. New retroreflectors are scheduled to go to the Moon on Commercial Lander Payload Services missions and the Lunar Geophysical Network mission. The new retroreflectors are single 10 cm corner cube retroreflectors that will not spread the laser pulse during reflection like the existing arrays do. Due to the orbital and Earth rotational speeds, there is a velocity aberration of 0.″8–1.″5 for existing stations. Larger corner cubes require attention to ensure that the spread of possible velocity aberration displacements is optimally contained within the diffraction pattern. The diffraction pattern can be changed by making one or more of the rear dihedral angles slightly different from 90°. Improvements in the equipment at the LLR stations and improvements in the data analysis software are also desirable. Future possibilities are described.

The Potential of Focusing Acoustic Retroreflectors for Architectural Surface Treatment

How much sound can a building surface reflect to a source, the location of which is not exactly known? This paper considers this question particularly for a planar surface acting as an array of retroreflectors, or of focusing retroreflectors. The question is investigated using finite-difference time-domain acoustic simulation, using ideal retroreflective patches achieved by space-reversal, and focusing achieved by delays. Extensive (7.2 × 7.2 m) and local (2.4 × 2.4 m) ideal planar reflector arrays were investigated at distances of 1.5 to 4 m from sources that were within a 2.4 × 2.4 m square plane. Patch sizes ranged from 0.3 m squares to the full reflector size. Physically realizable non-ideal focusing retroreflectors based on parabolic trihedra were also investigated. With sufficiently large patches, ideal focusing retroreflector arrays consistently outperform non-focusing retroreflector arrays. A large focusing retroreflector array has the potential to provide retroreflected energy levels (speech and A-weighted) from the first reflection to a source at 2 m distance comparable to the diffuse field energy level of acoustically supportive reverberant rooms. A small focusing retroreflector array returns less sound, but still much more than a single reflection from an equivalent specularly reflecting surface. Results from parabolic trihedra demonstrate that retroreflected energy levels similar to those from ideal surfaces can be achieved by architectural form. Challenges in translating these concepts to practical design solutions are discussed.

Design and analysis of the Macau Science Satellite-1’s laser retro-reflector array

The origin and spatial−temporal variation of the Earth’s magnetic field (EMF) is one of the important scientific problems that has long been unsolved. The Macau Science Satellite-1 (MSS-1) under construction is China’s first high-precision EMF measurement satellite. To satisfy the highly precise requirements of the MSS-1 orbit measurement, a light, high-precision, four-prism laser retro-reflector array was designed. It weighs approximately 285 g, its effective reflection area is greater than 1.77 cm², and its size is 100 × 100 × 41 mm. The laser retro-reflector array has excellent performance, and it can achieve a ranging precision at the subcentimeter level for satellite laser ranging. It will be developed and installed on the MSS-1 as a power-free load for high-precision orbit measurement and accurate orbit calibration. The MSS-1 is planned to be brought into the International Laser Ranging Service observations. More than 31 satellite laser ranging stations in the International Laser Ranging Service around the world will be able to measure the MSS-1 with long arcs, which will support the scientific mission of high-precision EMF exploration.

Station-dependent satellite laser ranging measurement corrections for TOPEX/Poseidon

The TOPEX/Poseidon (T/P) altimetry mission with its main objectives to monitor variations of the global and regional sea level as well as ocean circulation is a milestone in Earth observation. The spacecraft was launched in 1992 and it is the predecessor mission of the Jason series and Sentinel-6A. For laser ranging measurements from the Earth to the spacecraft, T/P was equipped with a non-ideally designed annular retroreflector array. Its large dimensions of over 160 cm in diameter caused huge optical phase centre variations which limit the orbit accuracy. In this study, we developed a continuous, analytical correction function that counteracts both, phase centre variations at the spacecraft and station-related laser ranging measurement errors such as range biases. For most Satellite Laser Ranging (SLR) ground stations that tracked the T/P spacecraft, an individual set of six correction parameters is estimated. The parameters are valid for the entire mission or, in some cases, for a defined period. The developed function uses the observation’s viewing angles to determine a correction value which is added to the range measurement. Applying the measurement correction reduces the overall T/P mission root mean square fit of SLR residuals from 33.78 cm to 1.97 cm (1.59 cm for SLR core stations). External orbits based on the joint analysis of two different space-geodetic techniques are used to validate the quality of our improved orbit solution. The comparisons show good agreement. The mean values of the radial, transverse, and normal components differ by 0.0,-0.1, and -0.2 cm, respectively. To investigate the impact of the corrected orbit on sea level computations, a single-satellite crossover analysis is performed. When using the corrected measurements, the standard deviation of crossover differences reduces from 16 cm to 6 cm. The computed coefficients of the measurement correction function are provided publicly and can be used in any software package to obtain T/P orbits.

Next-generation Laser Ranging at Lunar Geophysical Network and Commercial Lander Payload Service Sites

Five retroreflector arrays currently on the Moon reflect short laser pulses back to Earth, allowing range to be measured. Each array has multiple small corner cubes. Due to variable lunar optical librations of the direction to Earth, the tilted arrays spread return times of single photons in the returned laser pulse, degrading the synthesized multiphoton normal point range accuracy. The Next Generation Lunar Retroreflectors (NGLRs) and MoonLIGHT reflectors currently being fabricated are larger 10 cm single corner cubes that do not spread the pulse. The Lunar Geophysical Network (LGN) mission will place NGLRs at three separated sites on the lunar nearside. The Commercial Lander Payload Service (CLPS) and early Artemis missions will precede the LGN mission. Solutions that include 6 yr of simulated Lunar Laser Ranging (LLR) data to two sites in the north and two in the south show improvement in the uncertainties of many science parameters. Lunar solution parameters include displacement Love numbers h 2 and l 2, tidal dissipation at several frequencies, fluid-core/solid-mantle boundary (CMB) dissipation, and moment of inertia combinations (C–A)/B and (B–A)/C, with principal moments of inertia A < B < C. Submeter-accuracy coordinates of the new reflectors will result from the first month of well-distributed data. There are benefits other than lunar science: gravitational physics includes the equivalence principle; Earth science includes terrestrial tidal dissipation and ranging station positions and motions; and astronomical constants with GM(Earth+Moon) for the gravitational constant times the mass of the Earth–Moon system. Improvements are illustrated for h 2, l 2, (C–A)/B, (B–A)/C, equivalence principle, and GM(Earth+Moon).

The facilities and performance of TianQin laser ranging station

The TianQin Project is aiming at gravitational wave (GW) detection in space. TianQin GW observatory comprises three satellites orbiting on 1 × 105 km Earth orbits to form an equilateral-triangle constellation. In order to minimize the variations in arm lengths and breathing angles, the satellites must be launched and adjusted precisely into an optimized orbit. Therefore, satellite laser ranging must be used to enhance the precision of satellite orbit determination. To develop the capability of satellite laser ranging for TianQin’s orbit, the TianQin Laser Ranging Station has been designed and constructed to perform high-precision laser ranging for TianQin satellites and lunar laser ranging as well. Applying a 1064 nm Nd: YAG laser with 100 Hz repetition frequency, 80 pico-second pulse duration, and 2 × 2 array of superconducting nanowire single-photon detectors, we have obtained the laser echo signals from the five lunar retro-reflector arrays, and the measurement data have been packaged into 234 normal points (NPs), including a few data measured during the full-moon lunar phase. Each NP is calculated from continuous measurement for about ten minutes and the statistical error of the NPs is about 7 mm (1σ).

High-precision physics-based radiation force models for the Galileo spacecraft

We present two new high-precision physics-based radiation force models for the In-Orbit Validation (IOV) and Full Operational Capability (FOC) spacecraft (s/c) of the Galileo Global Navigation Satellite System (GNSS). In both cases, the s/c bus surfaces are covered in material types, i.e., Laser Retro-reflector Array (LRA), Optical Surface Reflector (OSR) and Single-Layer Insulation (SLI) coverings, that were either not encountered or not specifically dealt with in earlier work. To address this, a number of modelling enhancements were proposed and tested, including: a specific model to account for the direct and reflected solar radiation force for LRA surfaces; a design update of the bus model computation process to allow for more than one insulation material; a specific thermal force model for OSR surfaces; a thermal force model for the Navigation Antenna (NAVANT) surface that includes a temperature model derived from on-orbit temperature measurements; and force models to account for thermal emissions from radiator panels on the +X and ±Y surfaces for both IOV and FOC, and on the -Z surface for FOC only. In the UCL2+ model each of these effects are accounted for. The theoretical impact of each modelling concept introduced is assessed, individually, by considering the magnitude of its effect in acceleration-space. The impact on orbit accuracy is confirmed through a rigorous set of Precise Orbit Determination (POD) validation tests, in which observations from all active Galileo s/c over two full years, 2017 and 2018, including during eclipsing periods, are included in the analysis. The UCL2+ approach results in day boundary discontinuities of 22 mm, 17 mm and 27 mm in the radial, across-track and along-track components, respectively. Analysis of the one-way Satellite Laser Ranging (SLR) residuals suggests that radial accuracy at better than 1 cm (3.7 mm mean residuals) and precision at better than 2 cm (17 mm root mean square (rms) error) is achievable with the UCL2+ model.

Mid-infrared DMD-based spectral-coding spectroscopy with a supercontinuum laser source.

We present a mid-infrared spectroscopic system based on a spectral-coding approach enabled by a modified digital micromirror device (DMD). A supercontinuum source offering a confined mid-infrared laser beam is employed to perform gas measurements with this system. The performance, flexibility, and programmability enabled by the DMD is experimentally demonstrated by gas-cell measurements (CO2, CH4, N2O, NO2 and CO). Full spectra are acquired in 14 ms at 10 nm spectral resolution and in 3.5 ms at 40 nm spectral resolution. Further, we employ the system for stand-off open-path spatially resolved CO2 measurements that fully exploit the laser emission properties - the bright and highly-collimated supercontinuum beam is scanned by a galvo mirror over a retroreflector array at a scalable remote distance. The measurement concept models a passing gas emitter under lab conditions; time and spatially resolved CO2 absorbance gas-plume images in the mid-infrared range are obtained.

Geodetic Datum Realization Using SLR‐GNSS Co‐Location Onboard Galileo and GLONASS

AbstractModern satellites of Global Navigation Satellite Systems (GNSS) are equipped with laser retroreflector arrays for Satellite Laser Ranging (SLR). Laser range observations to GNSS satellites allow for the co‐location of two space geodetic techniques onboard navigation satellites. We search for the best network constraining strategy for the SLR and GNSS stations to realize the geodetic datum using combined microwave‐GNSS and SLR‐to‐GNSS measurements. We find that consistent imposing of no‐net‐translation and no‐net‐rotation for the unified GNSS and SLR network provides the best quality of station coordinates and the best common realization of the terrestrial reference frame (TRF). We employ the space ties using solely space geodetic techniques for the SLR and GNSS station coordinates and confront them with the ground‐based measurements, that is, local ties, conducted at the SLR‐GNSS co‐located sites. The common processing of the GNSS and SLR observations allows for the realization of the TRF using space ties that are independent of the a priori coordinates and independent of the errors in local tie measurements. The agreement of space ties with ground measurements is at the level of 1 mm in terms of long‐term mean values for the co‐located station in Zimmerwald, Switzerland. We also revise the approach for handling the SLR range biases which now considers the impact of the SLR observations to GNSS and LAGEOS satellites. The updated SLR range biases improve the agreement between space ties and local ties from 4.4 to 2.4 mm for the co‐located station in Wettzell, Germany.

Earth Rotation Parameters Estimation Using GPS and SLR Measurements to Multiple LEO Satellites

Earth rotation parameters (ERP) are one of the key parameters in realization of the International Terrestrial Reference Frames (ITRF). At present, the International Laser Ranging Service (ILRS) generates the satellite laser ranging (SLR)-based ERP products only using SLR observations to Laser Geodynamics Satellite (LAGEOS) and Etalon satellites. Apart from these geodetic satellites, many low Earth orbit (LEO) satellites of Earth observation missions are also equipped with laser retroreflector arrays, and produce a large number of SLR observations, which are only used for orbit validation. In this study, we focus on the contribution of multiple LEO satellites to ERP estimation. The SLR and Global Positioning System (GPS) observations of the current seven LEO satellites (Swarm-A/B/C, Gravity Recovery and Climate Experiment (GRACE)-C/D, and Sentinel-3A/B) are used. Several schemes are designed to investigate the impact of LEO orbit improvement, the ERP quality of the single-LEO solutions, and the contribution of multiple LEO combinations. We find that ERP estimation using an ambiguity-fixed orbit can attain a better result than that using ambiguity-float orbit. The introduction of an ambiguity-fixed orbit contributes to an accuracy improvement of 0.5%, 1.1% and 15% for X pole, Y pole and station coordinates, respectively. In the multiple LEO satellite solutions, the quality of ERP and station coordinates can be improved gradually with the increase in the involved LEO satellites. The accuracy of X pole, Y pole and length-of-day (LOD) is improved by 57.5%, 57.6% and 43.8%, respectively, when the LEO number increases from three to seven. Moreover, the combination of multiple LEO satellites is able to weaken the orbit-related signal existing in the single-LEO solution. We also investigate the combination of LEO satellites and LAGEOS satellites in the ERP estimation. Compared to the LAGEOS solution, the combination leads to an accuracy improvement of 0.6445 ms, 0.6288 ms and 0.0276 ms for X pole, Y pole and LOD, respectively. In addition, we explore the feasibility of a one-step method, in which ERP and the orbit parameters are jointly determined, based on SLR and GPS observations, and present a detailed comparison between the one-step solution and two-step solution.

Magnification and wavefront aberration correction by a geometric-phase lens in a polarized aerial display using a right-angle prism.

In this paper, geometric-phase lenses, which can not only correct wavefront aberrations but also magnify an aerial image, have been proposed for use in an aerial display system composed of a retroreflector array, an orthogonal-circular polarization grating, a right-angle prism, and a quarter-wave plate. The geometric-phase lenses were demonstrated both experimentally and computationally by arranging them in the aerial display configuration and observing aerial images. We also investigated the relationship between the magnification and the field of view of an aerial image, and it has been found that there is the trade-off relationship between them.

Bound on Lunar Plate Motion

AbstractWe analyzed high accuracy time delays of laser signals sent from the Earth to the retroreflector arrays on the Moon in conjunction with several other sets of solar‐system astrometric data. Using especially the lunar laser ranging data obtained from the Apache Point Observatory telescope site in New Mexico and the Apollo 11 and Apollo 14 retroreflectors on the Moon, we have set a bound on their relative motion along the connecting great circle of 4 mm/yr over a 14‐year period.

50‐4: Optical Design of Corner‐Cube Retroreflectors with Inclined Curved Optical Surfaces for Directional Scattering Projector Screen

An array of hollow corner cube retroreflectors (CCR) with inclined and curved optical surfaces has been designed to realize a directional scattering projector screen. The characteristics of our previously reported projector screen were further modified by emphasizing on the design accuracy and precision of the screen unit cell. The rhombus screen unit cell which is a combination of two directional scattering CCRs with equilateral triangle apertures set back to back, was modified to increase the scattering light. The source of optical noise on the screen and the result of modification are reported.