The Lunar Laser Ranging Experiment

Application of optical switching technology in a lunar 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 1064 nm Nd:YAG laser with 100 Hz 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 100 Hz 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 200 µm; the switching time is better than 2 ms; and the extinction ratio is better than 57 dB. 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 (10 ms) is determined to be 6.1 ms.

A way forward for fundamental physics in space

Space-based research can provide a major leap forward in the study of key open questions in the fundamental physics domain. They include the validity of Einstein’s Equivalence principle, the origin and the nature of dark matter and dark energy, decoherence and collapse models in quantum mechanics, and the physics of quantum many-body systems. Cold-atom sensors and quantum technologies have drastically changed the approach to precision measurements. Atomic clocks and atom interferometers as well as classical and quantum links can be used to measure tiny variations of the space-time metric, elusive accelerations, and faint forces to test our knowledge of the physical laws ruling the Universe. In space, such instruments can benefit from unique conditions that allow improving both their precision and the signal to be measured. In this paper, we discuss the scientific priorities of a space-based research program in fundamental physics.

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.

Lunar laser ranging based on a 100 Hz repetition frequency

High-repetition-rate lunar laser ranging (LLR) has great prospects and significance. We have successfully obtained the effective echo signals of all five corner-cube reflectors (CCRs) on the lunar surface by using a 100 Hz repetition rate. This method can effectively improve the detection ability but has some defects: for example, the main wave and echo signals overlap. In this paper, the frequency selection and signal overlap are theoretically analyzed. The results show that the existing target prediction accuracy can meet the requirement of a 100 Hz repetition rate LLR. In the experiment, the use of a high-repetition-rate pulse laser allowed us to obtain detailed CCR information, such as the column number of CCRs, which will prove that the effective echo signals of LLR are reflected by the CCRs. Finally, we propose to use the resolved data to calculate the precision of inner coincidence and believe the accuracy can be within a millimeter.

Nanometric Precision Distance Metrology via Hybrid Spectrally Resolved and Homodyne Interferometry in a Single Soliton Frequency Microcomb

Laser interferometry serves a fundamental role in science and technology, assisting precision metrology and dimensional length measurement. During the past decade, laser frequency combs-a coherent optical-microwave frequency ruler over a broad spectral range with traceability to time-frequency standards-have contributed pivotal roles in laser dimensional metrology with ever-growing demands in measurement precision. Here we report spectrally resolved laser dimensional metrology via a free-running soliton frequency microcomb, with nanometric-scale precision. Spectral interferometry provides information on the optical time-of-flight signature, and the large free-spectral range and high coherence of the microcomb enable tooth-resolved and high-visibility interferograms that can be directly read out with optical spectrum instrumentation. We employ a hybrid timing signal from comb-line homodyne, microcomb, and background amplified spontaneous emission spectrally resolved interferometry-all from the same spectral interferogram. Our combined soliton and homodyne architecture demonstrates a 3-nm repeatability over a 23-mm nonambiguity range achieved via homodyne interferometry and over 1000-s stability in the long-term precision metrology at the white noise limits.

A Study into the Effects of Factors Influencing an Underwater, Single-Pixel Imaging System’s Performance

Underwater detection has always been a challenge due to the limitations caused by scattering and absorption in the underwater environment. Because of their great penetration abilities, lasers have become the most suitable technology for underwater detection. In all underwater laser applications, the reflected laser pulse which contains the key information for most of the system is highly degraded along the laser’s propagation path and during reflection. This has a direct impact on the system’s performance, especially for single-pixel imaging (SPI) which is very dependent on light-intensity information. Due to the complications in the underwater environment, it is necessary to study the influential factors and their impacts on underwater SPI. In this study, we investigated the influence of the angle of incidence, target distance, and medium attenuation. A systematic investigation of the influential factors on the reflectance and ranging accuracy was performed theoretically and experimentally. The theoretical analysis was demonstrated based on the bidirectional reflection distribution function (BRDF) and laser detection and ranging (LADAR) model. Moreover, 2D single-pixel imaging (SPI) systems were setup for experimental investigation. The experimental results agree well with the theoretical results, which show the system’s dependency on the reflection intensity caused by the angle of incidence, target distance, and medium attenuation. The findings should be a reference for works looking to improve the performance of an underwater SPI system.

Small and lightweight laser retro-reflector arrays for lunar landers

A set of small and lightweight laser retro-reflector arrays (LRAs) was fabricated and tested for use on lunar landers under NASA's Commercial Lunar Payload Service program. Each array contains eight 1.27-cm-diameter corner cube retro-reflectors mounted on a dome-shaped aluminum structure. The arrays are 5.0 cm in diameter at the base, 1.6 cm in height, and 20 g in mass. They can be tracked by an orbiting laser altimeter, such as the Lunar Orbiter Laser Altimeter, from a distance of a few hundred kilometers or by a landing lidar on future lunar landers. The LRAs demonstrated a diffraction-limited optical performance. They were designed and tested to survive and function on the Moon for decades, well after the lander missions are completed.

General Relativity Measurements in the Field of Earth with Laser-Ranged Satellites: State of the Art and Perspectives

Recent results of the LARASE research program in terms of model improvements and relativistic measurements are presented. In particular, the results regarding the development of new models for the non-gravitational perturbations that affect the orbit of the LAGEOS and LARES satellites are described and discussed. These are subtle and complex effects that need a deep knowledge of the structure and the physical characteristics of the satellites in order to be correctly accounted for. In the field of gravitational measurements, we present a new measurement of the relativistic Lense-Thirring precession with a 0.5 % precision. In this measurement, together with the relativistic effect we also estimated two even zonal harmonics coefficients. The uncertainties of the even zonal harmonics of the gravitational field of the Earth have been responsible, until now, of the larger systematic uncertainty in the error budget of this kind of measurements. For this reason, the role of the errors related to the model used for the gravitational field of the Earth in these measurements is discussed. In particular, emphasis is given to GRACE temporal models, that strongly help to reduce this kind of systematic errors.

An embedded microretroreflector-based microfluidic immunoassay platform

We present a microfluidic immunoassay platform based on the use of linear microretroreflectors embedded in a transparent polymer layer as an optical sensing surface, and micron-sized magnetic particles as light-blocking labels. Retroreflectors return light directly to its source and are highly detectable using inexpensive optics. The analyte is immuno-magnetically pre-concentrated from a sample and then captured on an antibody-modified microfluidic substrate comprised of embedded microretroreflectors, thereby blocking reflected light. Fluidic force discrimination is used to increase specificity of the assay, following which a difference imaging algorithm that can see single 3 μm magnetic particles without optical calibration is used to detect and quantify signal intensity from each sub-array of retroreflectors. We demonstrate the utility of embedded microretroreflectors as a new sensing modality through a proof-of-concept immunoassay for a small, obligate intracellular bacterial pathogen, Rickettsia conorii, the causative agent of Mediterranean Spotted Fever. The combination of large sensing area, optimized surface chemistry and microfluidic protocols, automated image capture and analysis, and high sensitivity of the difference imaging results in a sensitive immunoassay with a limit of detection of roughly 4000 R. conorii per mL.

Improved time-of-flight range acquisition technique in underwater lidar experiments

This paper presents an underwater lidar time-of-flight ranging system that combines the variable forgivable factor recursive least-squares (VFF-RLS) adaptive filter algorithm and the constant fraction discriminator (CFD) timing technology. The effectiveness of suppressing the backscattering and increasing timing accuracy is experimentally verified in the water basin under the different target distances, especially near the detection limit. The classical RLS is creatively transformed by introducing the VFF, which is highly correlated to the target echo at any distance. The improvement of the signal-to-backscatter ratio always exceeds 18.9 dB. The Monte Carlo simulation proves the applicability of the proposed method in the media of different turbidity. The influences of the selective timing methods on the walk error and time jitter are compared, and the optimum zero point of CFD is achieved by the slope analysis of leading (falling) edge in experimental target pulses.

An absolute method for determination of misalignment of an immersion ultrasonic transducer

An absolute methodology has been developed for quantification of misalignment of an ultrasonic transducer using a corner-cube retroreflector. The amplitude based and the time of flight (TOF) based C-scans of the reflector are obtained for various misalignments of the transducer. At zero degree orientation of the transducer, the vertical positions of the maximum amplitude and the minimum TOF in the C-scan coincide. At any other orientation of the transducer with the horizontal plane, there is a vertical shift in the position of the maximum amplitude with respect to the minimum TOF. The position of the minimum (TOF) remains the same irrespective of the orientation of the transducer and hence is used as a reference for any misalignment of the transducer. With the measurement of the vertical shift and the horizontal distance between the transducer and the vertex of the reflector, the misalignment of the transducer is quantified. Based on the methodology developed in the present study, retroreflectors are placed in the Indian 500MWe Prototype Fast Breeder Reactor for assessment of the orientation of the ultrasonic transducer prior to the under-sodium ultrasonic scanning for detection of any protrusion of the subassemblies.

Measuring coalignment of retroreflectors with large lateral incoming-outgoing beam offset

A method based on phase-shifting Fizeau interferometry is presented with which retroreflectors with large incoming-outgoing beam separations can be tested. The method relies on a flat Reference Bar that is used to align two auxiliary mirrors parallel to each other to extend the aperture of the interferometer. The method is applied to measure the beam coalignment of a prototype Triple Mirror Assembly of the GRACE Follow-On Laser Ranging Interferometer, a future satellite-to-satellite tracking device for Earth gravimetry. The Triple Mirror Assembly features a lateral beam offset of incoming and outgoing beam of 600 mm, whereas the acceptance angle for the incoming beam is only about ±2 mrad. With the developed method, the beam coalignment of the prototype Triple Mirror Assembly was measured to be 9 μrad with a repeatability of below 1 μrad.

Next-generation hollow retroreflectors for lunar laser ranging

The three retroreflector arrays put on the Moon 40 years ago by the Apollo astronauts and the French-built arrays on the Soviet Lunokhod rovers continue to be useful targets, and have provided the most stringent tests of the Strong Equivalence Principle and the time variation of Newton's gravitational constant, as well as valuable insight into the Moon's interior. However, the precision of the ranging measurements are now being limited by the physical size of the arrays and a new generation of retroreflectors is required to make significant advances over current capabilities. Large single-cube retroreflectors represent the most promising approach to overcoming current limitations, and hollow retroreflectors in particular have the potential to maintain their good optical performance over the nearly 300 K temperature swing that occurs during the lunar cycle. Typically, epoxies are used for aligning and bonding hollow retroreflectors, but their thermal stability will predominantly be limited by the difference of the coefficient of thermal expansion (CTE) between the epoxy and the glass. A relatively new bonding method known as hydroxide catalysis bonding (HCB) has been used to adhere complex optical components for space-based missions. HCB has an extremely thin bond, a low CTE, and a high breaking strength that makes it an ideal candidate for bonding hollow retroreflectors for lunar laser ranging (LLR). In this work, we present results of a feasibility study of bonded Pyrex and fused silica hollow retroreflectors using both epoxy and HCB methods, including the results of thermally cycling the hollow retroreflectors from 295 to 185 K. Finally, we discuss the potential for using these retroreflectors for future LLR.

Geodetic imaging with airborne LiDAR: the Earth's surface revealed

The past decade has seen an explosive increase in the number of peer reviewed papers reporting new scientific findings in geomorphology (including fans, channels, floodplains and landscape evolution), geologic mapping, tectonics and faulting, coastal processes, lava flows, hydrology (especially snow and runoff routing), glaciers and geo-archaeology. A common genesis of such findings is often newly available decimeter resolution 'bare Earth' geodetic images, derived from airborne laser swath mapping, a.k.a. airborne LiDAR, observations. In this paper we trace nearly a half century of advances in geodetic science made possible by space age technology, such as the invention of short-pulse-length high-pulse-rate lasers, solid state inertial measurement units, chip-based high speed electronics and the GPS satellite navigation system, that today make it possible to map hundreds of square kilometers of terrain in hours, even in areas covered with dense vegetation or shallow water. To illustrate the impact of the LiDAR observations we present examples of geodetic images that are not only stunning to the eye, but help researchers to develop quantitative models explaining how terrain evolved to its present form, and how it will likely change with time. Airborne LiDAR technology continues to develop quickly, promising ever more scientific discoveries in the years ahead.

Lunar laser ranging: the millimeter challenge

Lunar laser ranging has provided many of the best tests of gravitation since the first Apollo astronauts landed on the Moon. The march to higher precision continues to this day, now entering the millimeter regime, and promising continued improvement in scientific results. This review introduces key aspects of the technique, details the motivations, observables, and results for a variety of science objectives, summarizes the current state of the art, highlights new developments in the field, describes the modeling challenges, and looks to the future of the enterprise.

Suspended, micron-scale corner cube retroreflectors as ultra-bright optical labels

Corner cube retroreflectors are objects with three mutually perpendicular reflective surfaces that return light directly to its source and are therefore extremely bright and easy to detect. In this work, we have fabricated suspended corner cube retroreflectors, 5 microns in size, consisting of a transparent epoxy core and three surfaces coated with gold as ultra-bright labels for use in a rapid, low-labor diagnostic platform. The authors have demonstrated that individual cubes are easily imaged using low-cost, low numerical aperture objectives in suspension and that they remain suspended over long periods of time. Moreover, we have demonstrated that the gold outer surfaces can be decorated with proteins, and that individual cubes can be bound to magnetic sample preparation particles bearing antibodies which recognize these proteins. The bound cubes can be imaged and tracked as they move through solution in response to an external magnetic field, and we have, as such, demonstrated the principle of the new biosensing approach.

Tests of Gravity Using Lunar Laser Ranging

Lunar laser ranging (LLR) has been a workhorse for testing general relativity over the past four decades. The three retroreflector arrays put on the Moon by the Apollo astronauts and the French built arrays on the Soviet Lunokhod rovers continue to be useful targets, and have provided the most stringent tests of the Strong Equivalence Principle and the time variation of Newton's gravitational constant. The relatively new ranging system at the Apache Point 3.5 meter telescope now routinely makes millimeter level range measurements. Incredibly, it has taken 40 years for ground station technology to advance to the point where characteristics of the lunar retroreflectors are limiting the precision of the range measurements. In this article, we review the gravitational science and technology of lunar laser ranging and discuss prospects for the future.

Dragging of inertial frames

The origin of inertia has intrigued scientists and philosophers for centuries. Inertial frames of reference permeate our daily life. The inertial and centrifugal forces, such as the pull and push that we feel when our vehicle accelerates, brakes and turns, arise because of changes in velocity relative to uniformly moving inertial frames. A classical interpretation ascribed these forces to acceleration relative to some absolute frame independent of the cosmological matter, whereas an opposite view related them to acceleration relative to all the masses and 'fixed stars' in the Universe. An echo and partial realization of the latter idea can be found in Einstein's general theory of relativity, which predicts that a spinning mass will 'drag' inertial frames along with it. Here I review the recent measurements of frame dragging using satellites orbiting Earth.

Beam quality of a nonideal atom laser

We study the propagation of a noninteracting atom laser distorted by the strong lensing effect of the Bose-Einstein condensate (BEC) from which it is outcoupled. We observe a transverse structure containing caustics that vary with the density within the residing BEC. Using the WKB approximation, Fresnel-Kirchhoff integral formalism, and ABCD matrices, we are able to describe analytically the atom-laser propagation. This allows us to characterize the quality of the nonideal atom-laser beam by a generalized M2 factor defined in analogy to photon lasers. Finally we measure this quality factor for different lensing effects.

Progress in lunar laser ranging tests of relativistic gravity

Analyses of laser ranges to the Moon provide increasingly stringent limits on any violation of the equivalence principle (EP); they also enable several very accurate tests of relativistic gravity. These analyses give an EP test of Delta(MG/MI)EP=(-1.0+/-1.4) x 10(-13). This result yields a strong equivalence principle (SEP) test of Delta(MG/MI)SEP=(-2.0+/-2.0) x 10(-13). Also, the corresponding SEP violation parameter eta is (4.4+/-4.5) x 10(-4), where eta=4beta-gamma-3 and both beta and gamma are post-Newtonian parameters. Using the Cassini gamma, the eta result yields beta-1=(1.2+/-1.1) x 10(-4). The geodetic precession test, expressed as a relative deviation from general relativity, is Kgp=-0.0019+/-0.0064. The search for a time variation in the gravitational constant results in G /G=(4+/-9) x 10(-13) yr(-1); consequently there is no evidence for local (approximately 1 AU) scale expansion of the solar system.

Lunar Laser Ranging: A Continuing Legacy of the Apollo Program

On 21 July 1969, during the first manned lunar mission, Apollo 11, the first retroreflector array was placed on the moon, enabling highly accurate measurements of the Earthmoon separation by means of laser ranging. Lunar laser ranging (LLR) turns the Earthmoon system into a laboratory for a broad range of investigations, including astronomy, lunar science, gravitational physics, geodesy, and geodynamics. Contributions from LLR include the three-orders-of-magnitude improvement in accuracy in the lunar ephemeris, a several-orders-of-magnitude improvement in the measurement of the variations in the moon's rotation, and the verification of the principle of equivalence for massive bodies with unprecedented accuracy. Lunar laser ranging analysis has provided measurements of the Earth's precession, the moon's tidal acceleration, and lunar rotational dissipation. These scientific results, current technological developments, and prospects for the future are discussed here.

Application of space technology to geodynamics

Measurements of the movement and deformation of tectonic plates are needed for many research areas in geodynamics, but observations with adequate accuracy and frequency of measurement are not feasible if classical geodetic methods are used. Long-baseline microwave interferometry and laser ranging to Earth satellites are among the new techniques that have been developed within the past decade to make the required measurements. Fixed and mobile stations using both these methods have been constructed in several countries and are now being used in an internationally coordinated research program. Baseline length accuracy better than 2 to 3 centimeters (1 standard deviation) is expected within the next 5 years.

Earth Rotation Measured by Lunar Laser Ranging

The estimated median accuracy of 194 single-day determinations of the earth's angular position in space is 0.7 millisecond (0.01 arc second). Comparison with classical astronomical results gives agreement to about the expected 2-millisecond uncertainty of the 5-day averages obtained by the Bureau International de l'Heure. Little evidence for very rapid variations in the earth's rotation is present in the data.

Cube corner retroreflector test and analysis

Cube corner retroreflectors with nominal dihedral angles of 90 degrees 0' 1.5'' were fabricated, tested, and analyzed to determine the return energy in the annular ring of the far field diffraction pattern required by the Laser Geodynamic Satellite. Performance was assessed for variations in the dihedral angles, optical surfaces, and thermal environment. Despite relatively high independent axial and radial sensitivities, the changes caused by the anticipated thermal environment were found to be negligible; however, there were substantial variations between the analytical predictions and measured performance.

Operation and performance of a lunar laser ranging station

The Lunar Laser Ranging Experiment has been in continuous operation for about 4 years using the McDonald Observatory 2.7-m telescope. Occupying only a small percentage of the available telescope time, the system is now measuring 350 lunar ranges per year, each with an accuracy of from 10 cm to 15 cm. This article tabulates the observed signal strengths, the success ratios, and the major operating restrictions that have characterized the daily performance of the experiment. These empirical data can be used to optimize the design of such installations in the future.