Limitations to testing the equivalence principle with satellite laser ranging

We consider the possibility of testing the equivalence principle (EP) in the gravitational field of the Earth from the orbits of LAGEOS and LAGEOS II satellites, which are very accurately tracked from ground by laser ranging. The orbital elements that are affected by an EP violation and can be used to measure the corresponding dimensionless parameter η are semimajor axis and argument of pericenter. We show that the best result is obtained from the semimajor axis, and it is limited—with all available ranging data to LAGEOS and LAGEOS II—to η ≃ 2 × 10⁻⁹, more than 3 orders of magnitude worse than experimental results provided by torsion balances. The experiment is limited because of the non uniformity of the gravitational field of the Earth and the error in the measurement of semimajor axis, precisely in the same way as they limit the measurement of the product GM of the Earth. A better use of the pericenter of LAGEOS II can be made if the data are analyzed searching for a new Yukawa-like interaction with a distance scale of one Earth radius. It is found that the pericenter of LAGEOS II is 3 orders of magnitude more sensitive to a composition dependent new interaction with this particular scale than it is to a composition dependent effect expressed by the η parameter only. Nevertheless, the result is still a factor 500 worse than EP tests with torsion balances in the gravitational field of the Earth (i.e. at comparable distance), though a detailed data analysis has yet to be performed. While EP tests with satellite laser ranging are not competitive, laser ranging to the Moon has been able to provide a test of the EP almost 1 order of magnitude better than torsion balances. We show that this is due to the much greater distance of the test masses (the Earth and the Moon) from the primary body (the Sun) and the correspondingly smaller gradients of its gravity field. We therefore consider a similar new experiment involving the orbit of LAGEOS: testing LAGEOS and the Earth for an EP violation in the gravitational field of the Sun. We show that this test may be of interest, though it is a factor 300 less sensitive than in the case of the Moon due to the fact that LAGEOS is closer to the Earth than the Moon and consequently its orbit is less affected by the Sun. The limitations we have pointed out for laser ranging can be overcome by flying in low Earth orbit a spacecraft carrying concentric test masses of different composition with the capability, already demonstrated in ground laboratories, to accurately sense in situ any differential effects between them. An erratum to this article can be found at     

月球激光测距中的关键物理与技术问题

根据国际上公开发表利用的1969—1972年美国Apollo 11、14、15宇航员放置在月球上的三个角反射器以及1970—1971年苏联无人登月车放置的两个角反射器进行的月球激光测距的论文和技术文献,讨论了月球激光测距中的几个关键物理和技术问题,主要包括:1)角反射器阵列指向与其月面位置的精确定位;2)角反射器激光回波信号的确认;3)接收信号强度与信噪比;4)测距结果的精度;5)满月时为什么不适于测距;6)地球大气对激光测月及其精度的影响。现有技术文献对一些关键的技术细节描述尚不完备,判定接收信号来自角反射器对激光的反射缺乏直接的物理证据,现在声称的距离测量精度与激光本身特性的关系尚需进一步分析。     

Polarization analysis of the beam-steering device of quantum optical systems

Optics and Spectroscopy - Polarization analysis of the laser radiation of quantum optical systems intended for pulsed laser ranging of satellites orbiting the Earth is conducted. The polarization...     

An overview of the laser ranging method of space laser altimeter

Space laser altimeter is an active remote sensing instrument to measure topographic map of Earth, Moon and planetary. The space laser altimeter determines the range between the instrument and laser footprint by measuring round trip time of laser pulse. The return pulse reflected from ground surface is gathered by the receiver of space laser altimeter, the pulsewidth and amplitude of which are changeable with the variability of the ground relief. Meantime, several kinds of noise overlapped on the return pulse signal affect its signal-to-noise ratio. To eliminate the influence of these factors that cause range walk and range uncertainty, the reliable laser ranging methods need to be implemented to obtain high-precision range results. Based on typical space laser altimeters in the past few decades, various ranging methods are expounded in detail according to the operational principle of instruments and timing method. By illustrating the concrete procedure of determining time of flight of laser pulse, this overview provides the comparison of the employed technologies in previous and undergoing research programs and prospect innovative technology for space laser altimeters in future.     

基于自混合效应的激光测距仪设计

给出了一个基于自混和效应的激光测距仪设计。通过使用差频模拟锁相环（APLL）独特的优点来处理信号,明显地提高系统的测距精度和扩大测量的动态范围。同时通过选取合适的三角波电流调制频率fm=400-600Hz．来对测量系统的性能进一步的进行了优化。实验结果表明,当采样时间是0．1s时,整个系统的测量动态范围也能达到50-500mm,且精度为2mm。     

Lumped parameter model for multimode laser cutting

A lumped parameter mathematical model is developed to relate the cut depth to the laser cutting parameters and material properties. The model takes into account the threshold power of the incident laser beam for the initiation of cutting and modifies an earlier cutting model so that it applies to a wide set of process parameters ranging from low to high laser powers and slow to fast cutting speeds. Plain steel is taken as an example to show the effects of various process parameters such as the laser power, spot size and cutting speed on the cut depth. Special emphasis is given to the effect of laser mode structure on its cutting capability.     

Effect of energy above laser-induced damage thresholds in the micromachining of silicon by femtosecond pulse laser

A 400 nm second harmonic Ti : sapphire femtosecond laser was applied to structure silicon base on a direct-write process in air. A series of lines were ablated with pulses of 300-fs duration at varying power densities ranging from 50 to 100 nJ of energy on 2″ silicon (1 1 1) wafers. In this event, we investigate and report extensive laser induced thermal damage and redeposition encompassing the ablated lines at high energy levels above the damage threshold of the silicon. In addition, the effect of polarisation on the direction of micromachining is also observed and discussed. The resolution and quality of these lines were also found to hold a linear relationship to the laser energy up to its thermal threshold limit.     

The centennial of the Sagnac experiment in the optical regime: From a tabletop experiment to the variation of the Earth's rotation

The investigation of non-reciprocal behavior of optical beams in a rotating reference frame was the main motivation of the historic tabletop experiment of George Sagnac. His ground-breaking experiment was extended to a very large installation more than a decade later, which was sensitive enough to allow Michelson, Pearson and Gale to resolve the rotation rate of the Earth by an optical interferometer. With the advent of lasers in the early sixties of the last century, rotating laser cavities with a ring structure demonstrated superior performance and very soon matured to a point where mechanical gyroscopes were quickly superseded by laser gyroscopes in aircraft navigation. When vastly upscaled ring lasers were taken back to the laboratory at the end of the 20th century, the goal of applying the Sagnac effect to geodesy for the monitoring of tiny variations of Earth's rotation was the main motivation. The large-ring laser G, which is the most stable instrument out of a series of instruments built by the New Zealand–German collaboration, routinely resolves the rotation rate of the Earth to better than eight orders of magnitude. Since G is directly referenced to the Earth rotation axis, the effect of diurnal polar motion, the Chandler and the Annual wobbles as well as tilts from the solid Earth tides can be found in the interferogram obtained from the ring laser. G has also demonstrated high sensitivity to rotations associated with seismic events. The toroidal eigenmodes of the Earth when they are excited by large earthquakes have been resolved. A surprisingly large amplitude has been measured for Love wave signals contained in the microseismic background signal. This paper summarizes the recent development of highly sensitive large Sagnac gyroscopes, and presents unique results from the measurements of rotations of the earth.     

激光雷达干扰效果评估方法研究

研究了光电干扰对测距和跟踪测量激光雷达干扰效果的评估方法.在深入分析激光雷达光电干扰机理的基础上,提出了相应的干扰效果评估准则.对激光测距机的距离欺骗干扰效果采用测距误差-干扰成功率准则或准测率准则定量评估,对测距机的激光盲干扰效果依据盲激光对测距准确度、测距功能的影响程度进行评估.对于跟踪测量激光雷达,根据实施干扰后其跟踪误差是否超出正常跟踪准确度的三倍判定一次干扰是否有效,再依据多次试验的干扰成功率的大小评估干扰效果.     

测距光束光斑漂移的数值仿真

针对远距离激光测距,如地球同步卫星测距、激光测月,利用基于傅里叶变换的分步传播方法对测距光束在湍流大气中的上行传播进行数值仿真.根据大气结构常数廓线,采用等Rytov指数间隔法分布相位屏,与理论值比对的结果表明相位屏的分布合理.在此基础上,对光束的光斑漂移进行分析,得到光斑漂移量与准直测距光束束腰的定量关系,为测距激光...     

Influence of Noncommutativity on the Motion of Sun-Earth-Moon System and the Weak Equivalence Principle

Features of motion of macroscopic body in gravitational field in a space with noncommutativity of coordinates and noncommutativity of momenta are considered in general case when coordinates and momenta of different particles satisfy noncommutative algebra with different parameters of noncommutativity. Influence of noncommutativity on the motion of three-body Sun-Earth-Moon system is examined. We show that because of noncommutativity the free fall accelerations of the Moon and the Earth toward the Sun in the case when the Moon and the Earth are at the same distance to the source of gravity are not the same even if gravitational and inertial masses of the bodies are equal. Therefore, the Eotvos-parameter is not equal to zero and the weak equivalence principle is violated in noncommutative phase space. We estimate the corrections to the Eotvos-parameter caused by noncommutativity on the basis of Lunar laser ranging experiment results. We obtain that with high precision the ratio of parameter of momentum noncommutativity to mass is the same for different particles.     

脉冲激光探测平面目标特性对测距分布的影响

针对脉冲激光近程探测系统平面目标特性影响测距分布的问题,推导了平面目标脉冲响应方程和脉冲激光回波方程,分析了不同平面目标倾斜角、激光发射发散角和激光发射脉宽对激光回波展宽的影响.基于脉冲激光回波方程和恒阈值时刻鉴别方法,推导了平面目标的测距概率密度函数解析式,并理论仿真分析了不同平面目标倾斜角、激光发射功率、激光发射发散角及阈噪比对测距统计特性分布的影响.运用蒙特卡罗算法进行全波形模拟测距实验;搭建脉冲激光测距实验环境,进行20 m测距实验.实验结果表明:理论仿真、蒙特卡罗模拟实验与实际实验的测距概率密度分布基本一致,随着平面目标倾斜角的增大,测距均值和测距方差增大;当倾斜角度为0°,20°,40°,60°时,回波信噪比高于阈噪比,测距分布呈现高斯分布;当倾斜角度为70°时,回波信噪比低于阈噪比,分布不再呈现高斯分布,呈现上升沿缓下降沿陡的分布特性.研究结果为研究目标平面特性对脉冲激光探测测距分布的影响提供了理论依据.     

基于光子数目比较的激光测距法

提出了一种新颖的激光测距方法。该方法避开了传统激光测距法中使用复杂辅助电子设备对脉冲计时或比较相位差的过程,而主要通过光学手段分析和提取待测距离信息,最终通过比较大量光子数目的方法求得待测距离。并利用单轴晶体的双折射和全内双反射性质,用特殊结构的单块LiNbO3晶体设计了实施该方法的主体装置。结果表明,该激光测距法同目前普遍使用的激光测距法相比,不但简化了结构,而且有很高的测距精度,从而为激光测距开拓了一种新的思路。     

The effect of the relativistic transformation law of angles on laser ranging of satellites moving in circular orbits equipped with a single retroreflector

It is shown that due to the relativistic transformation law of angles, a laser pulse reflected from a moving retroreflector propagates not strictly back, but at a small angle to the direction of the laser station. For this reason, the ray located on the periphery of a pulse reaches the receiving telescope of the laser station instead of the central ray of a pulse. As a result, the flux of electromagnetic energy received by the laser station is certainly less than the flux of energy in the vicinity of the central ray. The energy flux attenuation coefficient is assessed on the basis of numerical analysis. It is shown that if the receiving telescope is separated from the laser station in order to be mobile and is moving along the Earth’s surface so that the center of each spot formed by a pulse of the reflected light hits the telescope, then the electromagnetic energy flux during laser probing of the satellite will be higher by more than 100 times in comparison with the energy flux received by the stationary telescope of the laser station. From our study it follows that the maximum speed of motion of the centers of spots on the Earth’s surface does not exceed 8 km/h.     

高分辨率调频连续波激光绝对测距研究

大空间精密测量在重大装备制造、空间科技、国防工业等方面发挥着重要作用,激光高精度绝对长度测量是大空间精密测量领域的重要研究课题.调频连续波激光测距是近年来激光绝对测距研究的热点,它克服了脉冲法测量分辨率低和相位法激光测距存在2π缠绕模糊度问题的缺点,有着测量精度高、量程大的优点.本文研究了调频连续波激光测距的原理,分析了影响其测距分辨率的主要原因,证明了利用等光频间隔采样来抑制激光调制非线性对测距结果影响的可行性.该方法可以提高测距分辨率,且系统构成简单、实用性强.搭建了光纤调频连续波激光测距系统,并加入了辅助干涉光路对测量信号进行等光频间隔采样.利用该系统进行了测距分辨率实验,实验结果表明,本系统测量分辨率可以达到50μm,测量范围达到了10m.     

Gravitational Acceleration of Spinning Bodies from Lunar Laser Ranging Measurements

The Sun's 1/c ² order gravitational gradient accelerations of Earth and Moon, dependent on the motions of the latter bodies, act upon the system's internal angular momentum. Not only does this gravitational spin-orbit force (which plays an important part in calculating gravity wave signal templates from astrophysical sources) slightly accelerate the Earth-Moon system as a whole, it more robustly perturbs the internal Earth-Moon dynamics with a 5 cm amplitude, synodically oscillating range contribution which is presently measured to 4 cm precision by more than three decades of accumulated lunar laser ranging data.     

Testing Photons Coupled to Weyl Tensor with Gravitational Time Advancement

Classical Solar System tests of photons coupled to Weyl tensor with two polarizations were studied in a recent work. A coupling strength parameter α in this model was firstly obtained as |α|<4×10¹¹ m² by using available datasets in the Solar System. In this paper, a new test called by gravitational time advancement is proposed and investigated to test such the coupling. This new test, which is quite different from Shapiro time delay, depends strongly on round-trip proper time span (not coordinate time one) of flight of radio pulses between an observer on the Earth and a distant spacecraft. For ranging a spacecraft getting far away from the Sun, two special cases (the superior/inferior conjunctions) are used to analyse the observability in the advancement contributed by the Weyl coupling. We found that the situation of the inferior conjunction is more suitable for detecting the advancement caused by such the Weyl coupling. In either case, two kinds of polarizations make the advancement in the model smaller or larger than the one of general relativity. Although the observability in the advancement could be out of the reach of already existing technology, the implement of planetary laser ranging and optical clocks might provide us more insights on such the Weyl coupling in the near future.     

How to detect the Chandler and the annual wobble of the Earth with a large ring laser gyroscope

We demonstrate a 16 m(2) helium-neon ring laser gyroscope with sufficient sensitivity and stability to directly detect the Chandler wobble of the rotating Earth. The successful detection of both the Chandler and the annual wobble is verified by comparing the time series of the ring laser measurements against the "C04 series" of Earth rotation data from the International Earth Rotation and Reference System Service.     

基于重采样技术的调频连续波激光绝对测距高精度及快速测量方法研究

调频连续波激光测距方法可以实现高精度的大尺寸绝对距离测量, 且测量过程无需合作目标, 在大空间坐标精密测量领域有很高的研究价值. 而如何提高测量分辨率和实用化一直是近年来调频连续波激光绝对测距研究的热点. 本文研究了调频连续波激光测距的原理, 基于双光路调频连续波激光测距系统, 提出了通过信号拼接提高测量分辨率的信号处理优化方案, 该方案可以提高测距分辨率, 且可以降低对激光器的性能要求; 提出了可实现高速测量的简易测量方法. 设计加工了双光路光纤调频连续波激光测距系统, 利用该系统进行了测距分辨率及测距误差标定实验, 实验结果表明: 优化方案可以有效地提高测量分辨率和测量效率, 在26 m测量范围内, 测距分辨率达到了50 μm, 测距误差不超过100 μm; 快速测量方案有较高实用价值.     

脉冲串互相关方法在远程激光测距中的应用

基于单脉冲激光测距在远程激光测距中的局限性,提出了一种基于发射脉冲串与回波脉冲串互相关的信号处理方法。该方法将多个激光发射脉冲和回波脉冲作为一次连续信号同时数字化,然后进行互相关处理。采用激光强度与发射间隔可调的激光系统来模拟不同反射强度、不同距离的测距回波信号;通过处理不同信噪比的回波信号,来探究本方法对于回波信号信噪比的提升能力以及对于尖峰噪声的抑制能力。实验结果表明,该方法能够有效提高回波信号的信噪比,信噪比为0.11的弱回波信号经过处理后信噪比被提升到5.92,从而扩展了激光测距系统的测程,有效降低了探测系统的探测虚警率,提高了远程激光测距系统的弱回波探测能力。