Corner Cube Reflector Research Articles

Spin parameters of LAGEOS-1 and LAGEOS-2 spectrally determined from Satellite Laser Ranging data

The Satellite Laser Ranging (SLR) measures distance to the spacecrafts equipped with Corner Cube Reflectors (CCRs). The range measurements contain information about the spin parameters of the observed satellites. In this paper we present results of the spin rate and the spin axis orientation determination of LAGEOS-1 and LAGEOS-2 by frequency analysis of the SLR data.Analysis of 6734 passes of LAGEOS-1 (L1; January 5, 1984–December 30, 1997) and 12156 passes of LAGEOS-2 (L2; October 24, 1992–June 30, 2008) indicates the exponential slowing down of the satellites. The inertial spin period of the LAGEOS satellites can be expressed by the functions: TL1=0.6188667·exp (0.328951·Y) (s), TL2=0.7673569·exp (0.455635·Y) (s), where Y is year since launch (L1: 1976.3415, L2: 1992.8085). The slowing down rate of the satellites is not constant but varies in time by about 50%.Applying the apparent corrections to the observed spin rates allows to identify precession of the spin axes of the satellites around the southern pole of the inertial reference frame. The direction of rotation around the spin axis of LAGEOS-1 is clockwise, and counter-clockwise for LAGEOS-2. The obtained results are compared (and present good agreement) with the predictions given by the LOSSAM model.

Fabry–Perot displacement interferometer for the measuring range up to 100 mm

Current commercial laser interferometers have demonstrated outstanding measuring performances for high precision measurements, but they are very sensitive to environmental or mechanical effects. Owing to the fact that the most laser interferometers are based on the structure of Michelson interferometer, the above-mentioned influences from measuring arms will undisputedly lead to significant errors. To realize the high precision measurement, the environmental conditions must be strictly demanded. As a result of that limit, it’s inconvenient for industrial applications. In comparison with such non-common optical path structure, conventional Fabry–Perot interferometer with common optical path can effectively reduce the measuring errors resulting from environmental disturbances.To minimize the environmental and mechanical effects, a new interferometric displacement system with the structure of common optical path is proposed. By the optical interference principle and the corner cube reflector, the novel system with the common optical path can be designed. Hence, the novel interferometer can hold the advantage of large measurement range, and the signal pattern is nearly the same with that of Michelson interferometer. Because of the folded optical cavity, the resolution of the multi-interference interferometer with corner-cube can be enhanced to λ/16.Through this development, a high accurate interferometric displacement measurement system can be available under ordinary environmental conditions without the compensation requirement of the tilt angles and its prominent measurement characterizations have been proven. It will be demonstrated that measurement range is larger than 100mm and the standard deviation of the comparison experiment is about 0.211μm (within half wavelength) in the whole measuring range.

Formation of polarization-symmetrical beams using cube-corner reflectors

We consider the basic properties and features of beams with a defined type of polarization symmetry, in particular beams formed by Laguerre-Gauss modes of the second-order. On the whole the polarization structure of such beams does not have a certain polarization state. We have shown the approach to such beams' formation with the use of cube-corner reflectors, with the faces having a special dielectric interference coating.

Multi-interferometric displacement measurement system with variable measurement mirrors

Laser interferometers have been widely implemented for the displacement sensing and positioning calibration of the precision mechanical industry, due to their excellent measuring features and direct traceability to the dimensional definition. Currently some kinds of modified Fabry-Perot interferometers with a planar mirror or a corner cube prism as the measurement mirror have been proposed. Each optical structure of both models has the individual particularity and performance for measuring applications. In this investigation, a multi-interferometric displacement system has been proposed whose measurement mirror can be quickly and conveniently altered with a planar mirror or a corner cube reflector depending on the measuring demand. Some experimental results and analyses about the interpolation error and displacement measurements with both reflectors have been demonstrated. According to the results, suggestions about the choice of a measuring reflector and interpolation model have been presented. With the measuring verifications, the developed system with a maximum standard deviation less than 0.2081 μm in measuring range of 300 mm would be a compact and robust tool for sensing or calibrating the linear displacement of mechanical equipment.

Spectral filter for signal identification in the kHz SLR measurements of the fast spinning satellite Ajisai

The high repetition rate satellite laser ranging (SLR) measurements to the fast spinning satellites contain a frequency signal caused by the rotational motion of the corner cube reflector (CCR) array. The spectral filter, developed here, is based on the Lomb algorithm, and is tested with the simulated and the observed high repetition rate SLR data of the geodetic satellite Ajisai (spin period ∼2s). The filter allows for the noise elimination from the SLR data, and for identification of the returns from the single CCRs of the array – even for the low return rates. Applying the spectral filter to the simulated SLR data increases the S/N ratio by a factor 40–45% for all return rates. Filtering out the noise from the observed data strengthens the frequency signal by factor of ∼25 for the low return rates, which significantly helps to determine the spin phase of the satellite. The spectral filter is applied to the Graz SLR data and the spin rates of Ajisai are determined by two different methods: the frequency analysis and the phase determination of the spinning retroreflector array.The analysis of more than 8years of the Graz SLR measurements indicates an exponential spin rate trend: f=0.67034 exp(−0.0148542 Y) [Hz], RMS=0.085mHz, where Y is the year since launch. The highly accurate spin rate information demonstrates periodic changes related to the precession of the orbital plane of Ajisai, as it determines the amount of energy received by the satellite from the Sun. The rate of deceleration of Ajisai is not constant: the half life period of the satellite’s spin oscillates around 46.7years with an amplitude of about 5years.

Corner cube reflector lateral displacement evaluation simultaneously with interferometer length measurement

The novel corner cube reflector (CCR) system for a distance measuring interferometer is presented. The proposed system allows reflector lateral displacement evaluation (relative to the beam axis) simultaneously with the interferometer length measurement. Laser beam in measuring arm of the interferometer is divided into two parallel beams that are used for the interferometer distance measurement and lateral shifts of the assembly in relation to the beam axis.The CCR assembly is based on applying a position sensitive detector placed behind the CCR that has truncated vertex. Due to the proposed configuration of the cube corner and photodetector, the rotations of the CCR assembly does not cause error in the lateral displacement measurement in relation to the beam axis.The theoretical analysis and experimental verification of the system metrological feasibilities are presented. The general limitations and design problems are shown. The proposed system can be used basically for measurement and compensation of global or local cosine errors especially in short range of the interferometer displacement measurement, where known techniques are ineffective. Possible applications of the system for Coordinate Measuring Machines accuracy testing are indicated.

Cube-corner reflectors with interference dielectric coating

The cube-corner reflectors (CCRs) with a special interference dielectric coating intended for ring retroreflector systems of space vehicles with uniaxial orientation are considered. The diffraction patterns of radiation reflected from the CCRs with different face coatings are studied. It is shown that the choice of the angle between the faces, the size and the coating of CCR faces allow essential variation in the diffraction pattern, thereby providing its optimisation for solving different navigation problems.

Ring retroreflector system consisting of cube-corner reflectors with special coating

The ring retroreflector system (RS) consisting of cube-corner reflectors (CCRs) with a special coating of reflecting surfaces, intended for uniaxially Earth-oriented navigation satellites, is considered. The error of distance measurement caused by both the laser pulse delay in the CCR and its spatial position (CCR configuration) is studied. It is shown that the ring RS, formed by the CCR with a double-spot radiation pattern, allows the distance measurement error to be essentially reduced.

On the possibility of using a corner-cube reflector in resonators of high-power repetitively pulsed lasers

An optical cavity with a highly reflecting mirror in the form of a hollow corner-cube reflector (CCR) made of uncooled plane metal mirrors, which, in combination with a plane semitransparentoutput mirror, ensures complete filling of the output laser beam aperture, is studied. It is shown that, both in the pulsed and repetitively pulsed regimes of high-power far- and mid-IR lasers, it is possible to achieve beam divergence close to the diffraction limit (taking into account the drift of the radiation pattern axis) and dependent only on the quality of surfaces and accuracy of alignment of the hollow CCR mirrors and the resonator.

Development and testing of the pneumatic lunar drill for the emplacement of the corner cube reflector on the Moon

Lunar Laser Ranging provides a highly accurate measurement of the distance between ground stations on Earth and reflectors on the surface of the Moon. Since retroreflectors were initially placed during the Apollo missions, the ground stations improved the ranging accuracy by a factor of 200 and now the Apollo-era arrays on the Moon pose a significant limitation to the ranging accuracy. The new Lunar Laser Ranging Retroreflector (i.e. the Lunar Laser Ranging retroreflector for the 21st century or LLRRA-21) would provide extensive new information on the lunar interior, general relativity, and cosmology.During the day/night lunar cycle, when the thermal variation of the surface is approximately 300°C, the regolith will rise and fall by almost 500μm. Yet, it is estimated that the thermal variation 0.5m to 1m below the surface is less than much 1°C. Thus for the lunar emplacement to support 10s of microns ranging accuracy, the reflectors must be anchored to that thermally stable mass at 0.5m or greater depth.In this paper, we present a novel method of deploying LLRRA-21 with a Corner Cube Reflector (CCR) on the Moon. The emplacement approach uses a gas-powered drill consisting of a >50cm long, slim, hollow rod with a perforated anchor-cone at its lower end and the CCR mounted to the top. Gas supplied from a small tank is directed into and down the rod and out through the cone, lofting the soil out of the hole and allowing the rod to sink under its own weight to a depth of 0.5m.To determine the system performance, we conducted several tests in compacted JSC-1a lunar soil simulant and inside a vacuum chamber. In several tests, the rod successfully sunk under its own weight of 16N to a depth of 50cm in 4–6min.The pneumatic system is the game-changer for subsurface access. The extremely low mass and volume required to reach 50cm, along with very simple penetration method allow the CCR to remain in a variety of payload architectures.

Lunar Gravity and Rotation Measurements by Japanese Lunar Landing Missions

Measurements of lunar gravity and rotation are important because they provide information of the physical state of the lunar interior. Previously only passive LLR (Lunar Laser Ranging) using CCR (corner cube reflectors) has been applied for the detailed study of lunar librations, rotation variability. As for candidate instruments for SELENE-2 (forthcoming lunar landing mission by JAXA) and future lunar missions, we propose VLBI (inverse-VLBI and differential VLBI) for gravity measurement to constrain tidal Love number, LLR (Lunar Laser Ranging) and ILOM (In-situ Lunar Orientation Measurement) for libration measurements.

Diffraction polarization optical elements with radial symmetry

Diffraction polarization optics elements with radial symmetry are considered by an example of corner cube reflectors. Diffraction patterns in the far zone of the radiation that is reflected from the angle reflectors with different coatings of their faces are studied. It is shown that the optimal choice of the coating can significantly change the form of the diffraction pattern and, hence, optimize the pattern for various navigation problems.

The Study of Optical Properties of Laser Identification Friend or Foe System

The optical properties is essential to the process of identification in Laser Identification Friend or Foe (Laser-IFF) system. The corner cube reflector (CCR), composed of three mutually orthogonal reflective micromirrors, is extensively used in Laser-IFF system for it can reflect incident light at any angle to its incoming direction. So the micromachined CCR array is set to be the most important component of the responder. And assuming the Laser-IFF system is used in missiles, we present an analysis of the optical properties about the responder sectional area, the signal power of the responder and the echo power from the responder to the inquirer, considering at different effect distances between the inquirer and responder, divergence half-angle, CCR arrays reflectivity and other factors. Further field testing about the system can reference obtained experimental results and conclusions.

A low-finesse Fabry–Pérot interferometer for use in displacement measurements with applications in absolute gravimetry

A low-finesse Fabry–Perot interferometer is used to determine long and fast displacements. Two corner cube reflectors form the traveling-wave cavity and one beam splitter couples the input collimated laser beam. Given the retro-directive property of corner cube reflectors, the cavity operates at the edge of stability over an extended scanning range. The in-line scheme with a single fixed optical component makes the proposed interferometer robust and easy to align and use. These characteristics are particularly useful in applications running in noisy environments, such as in on-field absolute gravimetry. Experimental data showing the performances reached in a transportable ballistic gravimeter are also presented.

An approximate three-dimensional analytical propagation formula for Gaussian beams through a cube corner reflector

Based on the idea that the propagation of Gaussian beams passing through a cube corner reflector can be approximately regarded as a propagation of Gaussian beams passing through a hexagon aperture which is the intersection of three parallelogram apertures, and by using the method of expanding the aperture function into a finite sum of complex Gaussian functions, an approximate analytical propagation formula of Gaussian beams propagating through a cube corner reflector is derived and illustrated with numerical examples. It is found that the aberrance of the intensity distribution pattern becomes obvious with the increase of the incidence angle and orientation angle, and the aberrance brought by the incidence angle is larger that that by the orientation angle at same values.

Low-profile, high-gain and broadband array of corner cube reflector antenna based on substrate integrated waveguide

A novel array of a corner-cube reflector antenna targeting the 10.7–13.5 GHz frequency band is presented. The proposed antenna has the advantages of low-profile, broadband and high gain with linear polarisation. The substrate integrated waveguide (SIW) technology is employed effectively for feeding the antenna. The proposed antenna is formed of four corner-cube reflectors which are fed by SIW lines. The concept is validated by simulations and measurements.

Simultaneous Remote Energy Supply and Motion Control of Micro Vehicles with Laser

This paper proposes a method for simultaneous laser energy transmission and motion control of micro vehicles. Both the energy transmission and the remote control are achieved simultaneously with the same light path of two lasers. A green laser and a laser diode are used independently for the navigation and the energy transmission, respectively. Core technology of the system is the laser tracking, in which the direction of the tracking laser beam is changed by a galvano mirror so as to keep chasing the position of the corner-cube reflector mounted on the vehicle. In addition, by using a pulsing oscillation of the tracking laser, the vehicle is able to receive operation commands as a frequency change of the pulse. A beam of the laser diode runs parallel to the tracking beam and is radiated to the solar cells mounted on the vehicle. Then the photoelectrically converted power is supplied for the DC motors and control circuits on the vehicle. Experiments with a small wheeled-vehicle were conducted, and the results show that proposed system exhibits sufficient performance for controlling and supplying power to the micro vehicle.

In-vessel optic system Design of FIR interferometer/polarimeter system for KSTAR

An FIR interferometer/polarimeter system will be constructed in the Korea Superconducting Tokamak Advanced Research (KSTAR) device for electron density profile measurements. Due to the complex inner-wall geometry and long diagnostics ports, a specially designed in-vessel optic system is necessary to ensure a sufficient number of beam lines for inversion of the density profile. A single channel on the vertical center line and seven channels on the tangential plane will be placed using corner-cube reflectors mounted on the vacuum vessel. To avoid interferences with in-vessel structures such as neutral beam protection tiles and diagnostics systems, the positions of these beam lines are designed carefully using an in-vessel beam positioning module placed inside a narrow diagnostics port. Since these in-vessel optic components must be mounted on the vacuum vessel, a vibration compensation system needs to be integrated on the module. Designs of the corner-cube reflectors and the beam positioning modules have been performed for these purposes. A prototype corner-cube reflector will be installed on KSTAR before the 2010 campaign and vibration compensation performance and surface degradation due to plasma will be tested.

Spin axis orientation of Ajisai determined from Graz 2 kHz SLR data

The Graz 2 kHz Satellite Laser Ranging (SLR) measurements allow determination of the spin axis orientation of the geodetic satellite Ajisai. The high repetition rate of the laser makes it possible to determine the epoch time when the laser is pointing directly between two corner cube reflector (CCR) rings of the satellite. Identification of many such events during a few (up to 3) consecutive passes allows to state the satellite orientation in the celestial coordinate system. Six years of 2 kHz SLR data (October 2003–October 2009) delivered 331 orientation values which clearly show precession of the axis along a cone centered at 14 h56 m2.8 s in right ascension and 88.512° in declination (J2000.0 celestial reference frame) and with an half-aperture angle θ of 1.405°. The spin axis precesses with a period of 117 days, which is equal to the period of the right ascension of the ascending node of Ajisai’s orbit. We present a model of the axis precession which allows prediction of the satellite orientation – necessary for the envisaged laser time transfer via Ajisai mirrors.

In Situ Measurements of Lunar Rotation for the Study of the Interior of the Moon

Measurements of physical and free librations of lunar rotation are important because they provide information of the physical state of the lunar interior. For example, we can discuss if the lunar core is molten from the amplitudes of libration terms. Previously only passive LLR (Lunar Laser Ranging) using CCR (corner cube reflectors) has been applied for the detailed study of lunar librations. As for candidate instruments for SELENE-II (forthcoming lunar landing mission by JAXA), we propose detailed measurements of lunar rotation by ILOM (In-situ Lunar Orientation Measurement) and IVLBI (Inverse-VLBI) in addition to LLR.