GP2 is oriented at the maximum signal, so its response should be close to (and never higher than) the Earth rotation rate. https://doi.org/10.1140/epjc/s10052-019-7089-5, DOI: https://doi.org/10.1140/epjc/s10052-019-7089-5. Increase the life, safety and performance of Dassault aircraft with our dedicated solutions. 53(31), 76107618 (2014), A. Beghi, J. Belfi, N. Beverini, B. Bouhadef, D. Cuccato, A. Read more. Assuming that RLG is at the steady state [17], the solutions are the following: The validity of the above solutions has been previously tested with a Monte Carlo simulation and with the experimental data of the RLG G-Pisa, which was a 5.40 m perimeter RLG [18, 23]. MathSciNet If a pure frequency oscillation is maintained, these small lock-in intervals can accumulate. : The ring laser gyroscope consists of a ring laser having two independent counter propagating resonant modes over the same path; the difference in the frequencies is used to detect rotation. GP2 is an apparatus with comparatively low quality mirrors and located in a noisy environment [25, 26], while GINGERINO is located in a very quiet place [24, 27], and is presently equipped with state of the art mirrors. Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Ring laser gyroscopes for inertial navigation. Since 2011 we are studying the feasibility of the Lense Thirring test at the level of \(1\%\) with an array of large frame RLGs [5,6,7]. Forced dithering can largely overcome this problem. Remotely-operated vehicles and autonomous underwater vehicles Surveying equipment Pros: Extremely precise rotational rate information No moving parts Doesn't rely on inertial resistance to movement Typically shows higher resolution than RLG Cons: Longer production times due to higher calibration requirements In this case the standard method evaluates the Earth rotation rate with a relative systematic error of 6 part in \(10^{-3}\), while in the new way 1 part in \(10^{-4}\) is obtained, a factor 60 improvement in accuracy, with a sensitivity in the range of 2 nrad/s with tens of seconds integration time. Rev. Figure4 shows the histogram of the Sagnac frequency data of GP2 analysed with the two methods. Gyroscope sensor resolution depends largely on spin rate of the rotor. Advantages:-can be a very accurate system, but actual accuracy is operator dependent;-can be road tested at surface. Its rotational sensitivity is superior (~ 0.1 o /Hr) and faster compare to conventional gyroscope. As a consequence, the third gimbals movement will tamper with the movement of the other two and the gyroscope. Di Virgilio, U. Giacomelli, E. Maccioni, A. Simonelli, F. Stefani, G. Terreni, Analysis of 90 day operation of the gingerino gyroscope. Figure6 shows corresponding split mode and mode jumps. Figure3, showing the power spectral density (PSD) as a function of frequency, demonstrates that, for GINGERINO and above 200 mHz, the difference between the two methods is less than 0.1 nrad/s in 1 s measurement. Courtesy of Engineering 360. These gyroscopes and accelerometers also output analogue data that can be integrated into velocity and direction information. 2.1 Introduction. A Constant Stream of Trendy Photonics Articles, 3790 El Camino Real, #538, Palo Alto, CA 94306 USA, Optical Gyroscopes: Measuring Rotational Changes With Sagnac Effect, VLC Enabled Indoor Navigation Systems for Visually Impaired People, Using Light Polarization to Explore Earths Final Frontier, Neural Imaging with Visible Light: Advanced Implantable Sensor, Flaw Detection in Laser Powder Bed Fusion, Plasma Light Sources Entering the Tech Industry: A Testament to Moores Law, Transmyocardial Surgery: Using Lasers to Increase Vascular Flow, Neural Networks for Real-Time Sensing of Particle Pollution, Infrared Imaging: See the Invisible Light from Biology to Technology, Futuristic Farming: Photonics Technologies in Land and Crops, Optical Illusions: 10 of the Most Recognizable Illusions, Non-Ablative Fractional Lasers Fighting Colorectal Cancer. This paper presents a mathematical approach to measure the Sagnac frequency taking into account the laser dynamics. Ring laser gyroscopes (RLG) have demonstrated to currently be the most sensitive device for testing rotational motion with respect to an inertial frame. The two ASD are approximately equal above 200mHz, the main differences are at low frequency. Rather, an external laser injects counter-propagating beams into an optical fiber ring, where rotation causes a relative phase shift between those beams when interfered after their pass through the fiber ring. We will indicate them in the following as the mono-beam signals. Other disadvantages of the laser light therapy are temporary pain, redness, swelling and sometimes dry skin. Immediately, much interest was gained in the potential for gyroscopes and autopilot technologies. This issue has been addressed several times [9, 16,17,18,19], but no general solution exists. High-Accuracy Ring Laser Gyroscopes: Earth Rotation Rate and Relativistic Effects, N Beverini et al 2016 J. It provides an output of the compensated measured rotation in a digital data stream. Accordingly INS are used to help ships, aircraft, and guided missiles through missions where GPS is not safe to use. Phys. Crewed, uncrewed and satellite solutions for space missions. Fly longer, safer and more efficiently with Honeywell solutions and upgrades for Pilatus aircraft. Hurst, N. Rabeendran, K.U. For example, a lot of wear and tear occurs due to how things are mechanically mounted onto the platform. Since Eq. In our present analysis, we assume \(\beta _1 = \beta _2 = \beta \), and \(\theta _{21} = \theta _{12}=\theta \). Advantages of Ring Laser Gyro are as follows : It gives digital output with angle increments It has very high sensitivity It has stable input axis easy detection over a wide range of measurement (from 10-3"/h to thousands of " i s ) It is insensitive to accelerations as it has no moving parts. Appendix A describes methods to identify and eliminate those portions of data. In other words, the interferometer will measure a signal with varying amplitudes and a phase shift that gives the angular velocity of the object in question. Zendri, M. Allegrini, J. Belfi, N. Beverini, B. Bouhadef, G. Carelli, I. Ferrante, E. Maccioni, R. Passaquieti, F. Stefani, M.L. DiVirgilio, A. Ortolan, A. Porzio, S. Solimeno, M. Cerdonio, J.P. It is interesting to observe that the average value of the frequency \(\omega _{s0}\) is higher, this is what we expect when the noise is dominated by backscatter. The discussion is composed of two main parts. The four mirrors are placed at the corner of the square ring, they are contained inside small vacuum chambers, which are connected by pipes. Safety, tracking and power for helicopter operators. Google Scholar, A.D.V. The term called \(\omega _{s0}\), which is the dominant one and does not contain any laser parameter, is evaluated in details and expressed as a function of the available measurements; this term has been evaluated for the two RLG prototypes GINGERINO and GP2, and compared with the standard analysis method. Slider with three articles shown per slide. Large frame rings utilise the Earth rotation rate as bias. Gyroscopes are devices utilized for measuring and maintaining orientation of an object in inertial space, at any given time. Menegozzi, W.E. 15, in the fit \(\xi =0.16\)). This is a huge increase in sensitivity, and this direct comparison is the current drive behind the interest of making atom-based interferometers in general. Further efforts will be devoted to analyse the data of GINGERINO using the full set of terms. Many tens of thousands of RLGs are operating in inertial navigation systems and have established high accuracy, with better than 0.01/hour bias uncertainty, and mean time between failures in excess of 60,000 hours. If the gyroscope is in motion, the beams will be traveling different distances (like in special relativity). Stedman, Z. Li, C.H. Wells, Measuring gravitomagnetic effects by a multi-ring-laser gyroscope. Thus the laser gyroscope is more rugged than conventional gyros, offering the obvious advantages of much greater reliability and lower maintenance requirements. Any improvement in the accurate evaluation of the backscatter noise, and in general of the systematics induced by the non linear dynamics of the lasing process, is advantageous for increasing the performance of both large and small frame RLGs. When the gyroscope is still, the beams will all run the same distances on all sides. Hence it helps in determining direction of the Earth's poles based on measurements of angular velocity only. When the ring laser is hardly rotating, the frequencies of the counter-propagating laser modes become almost identical. Other two photodiodes monitor at one of the output corners (top-left) the laser output power of the two beams (\(PH_{1}\), \(PH_{2}\)). With the new analysis the average rotation rate is evaluated with a relative systematic error of 1 part in \(10^{-4}\), while with 6 part in \(10^{-3}\) with the standard analysis: a factor 60 improvement in accuracy has been achieved. 8 can be expanded in K and \(\delta _{ns}\) at first and second order, obtaining: Equation9 is composed of six terms, which can be independently evaluated, and analysed. 9 is valid for \(K \ll L \omega _m\); referring to our smaller prototype G-Pisa (perimeter 5.40 m), and utilising published parameters [17], we obtain K \(\sim 6\) rad m/s, to be compared with \(\omega _m L\sim 3600\) rad m/s: consequently Eq. In this article we will explore the operating principle of ring laser gyroscopes and two different navigation and munition transportation applications. Honeywell Oil, Gas and Mining Solutions and Systems. Presently there is large interest in this kind of device, large scale apparatus should further improve their sensitivity and accuracy for geodetic and fundamental physics application, and small scale and transportable devices at nrad/s sensitivity are required to improve the low frequency response of gravitational wave antennas, for the development of inertial platforms, and for seismology [11,12,13,14,15]. Korth, A. Heptonstall, E.D. Typical rates are 400Hz, with a peak dither velocity on the order of 1 degree per second. The present analysis is dedicated to the evaluation of the Sagnac signal taking into account the dynamics of the ring laser. 33, 035004 (2016), D. Martynov, N. Brown, E. Nolasco-Martinez, M. Evans, Passive optical gyroscope with double homodyne readout. Therefore, in order to have the possibility to correct it with common statistical methods, the term \(\xi \) has been added. An interferometer will measure the recombined signal at the exit. 57(20), 58445851 (2018), J. Belfi, N. Beverini, D. Cuccato, A. D 84, 122002 (2011), A. Tartaglia, A. It has following attributes or properties. When a ring laser gyro is in motion, the beams of light travel different distances. However, it is necessary to consider the presence of noise in the mono-beams signals, which can be due to the inherent noise of the photodiodes or by the discharge fluorescence, which cannot be completely removed. This introduces a tiny separation between the frequencies of the counter-propagating beams, a motion of the standing wave pattern within the ring, and thus a beat pattern when those two beams interfere outside the ring. The operating principles of the ring laser are developed and discussed, with special emphasis given to the problems associated with the achievement of greater sensitivity and stability. The systematics of RLG depends on the size and the mirror quality, large frame RLGs are usually closer to behave in an ideal manner. The reconstruction of those terms will be addressed in future work, and applied to the analysis of the data of GINGERINO. Davis, the very first usable gyrocompass goes back as far as 1904 and was invented by German inventor Hermann Anschtz-Kaempfe. Another example of a Honeywell INS is the HG1900 IMU and the HG1700. Sci. Systematics induced by the non linear dynamics of the laser, mainly due to back scatter light, induces non linear terms in the output of high sensitivity RLGs, severely limiting the development of RLGs with sensitivity of the order of nrad/s level, which in principle should have a large range of applications. Determining \(\omega _{s0}\) requires in turn to evaluate \(r_1\) and \(r_2\). First-principle treatments of the nature of quantum noise in the ring laser gyro and various methods designed to avoid low-rotation . Figure 13 shows a schematic of a frequency stabilized ring laser. In fact, as more R&D goes into creating new models of RLGs, they are getting smaller and smaller. Part of Springer Nature. They are largely utilised for inertial navigation, and applications in geodesy, geophysics and even for General Relativity tests are foreseen [4]. The average value of K is very small for frequencies much below Sagnac frequency, since the average value of sinus and co-sinus oscillating at the Sagnac frequency goes to zero for frequency much below \(f_s\). To illustrate, the fluids in the human ear act as the inertial body and hairs in the ear act as the sensors. Without loss of generality we can define \(\delta _{ns} = \sigma _2 - \sigma _1 + \tau _{21} I_2- \tau _{12}I_1 \), which is usually referred to as null shift; it is generally accepted that \(\delta _{ns}\) is a small quantity to be neglected [9, 17, 20]. Inertial sensors are important at application level and also in fundamental physics. The advantage of using an RLG is that there are no moving parts (apart from the dither motor assembly (see further description below), and laser-lock), compared to the conventional spinning gyroscope. Analytical solutions can be derived in the case the backscattered light is equal in the two counter propagating modes, or the ratio between the intensities of the two modes is constant, conditions which are not fulfilled in the actual generation of RLGs [17]. In any case, when \(| K | \ll L \omega _m\) and \( \delta _{ns} \ll \omega _m\), Eq. The general equations are. In particular, the inertial body for ring laser gyroscopes are actually completely immobile. RLGs, while more accurate than mechanical gyroscopes, suffer from an effect known as "lock-in" at very slow rotation rates. Bottom: the relative phase between the two modes \(\epsilon \) is shown. However, self-contained gyroscopes can protect these missions from any unwanted electronic interference. Usually for top quality mirrors losses are minimised, but there are no requirements for the transmission. Google Scholar, J. Belfi, N. Beverini, G. Carelli, A. Phys. So again, the effects is bigger for a bigger detector, and commercially available laser gyroscope have a size of the order of 10 cm, and that gives a fringe shift several orders of magnitude too small to be measurable. For that reason, RLGs are perfect for integration in Inertial Navigation Systems. Figure1 shows the typical lay-out of a square cavity RLG. This manuscript has no associated data or the data will not be deposited. In addition, the accelerometers work just as they do with the stabilized platforms to give velocities and direction. One of the contributions, called \(\omega _{s0}\), is the dominant one, the others being small corrections. Improvements of a factor 10-100 would make these instruments able to measure . Opt. This eliminates the need for gimbals used in stabilized platform INS that typically have reliability issues. Before RLG technology, mechanical gyroscopes were the norm. The ring laser gyro. Specifically, these gyros can provide guidance to stabilize aircraft flights or even autopilot operations. Basic Eng. However, each split-beam will be running in opposite directions. To take on this challenge, Honeywell, one of the worlds top RLG producers, has utilized Micro Electro-Mechanical Systems (MEMS)to create an INS with RLGs (HG1930 Gun Hard IMU) that can withstand 20,000 times the force of gravity. Phys. Anyone you share the following link with will be able to read this content: Sorry, a shareable link is not currently available for this article. Ring laser gyroscope in usage for aircraft.Courtesy of Rogoway. As the military remains a large consumer of ring laser gyros, market projections will continue to steadily climb upward in the coming decades. In: 2016 IEEE Conference on Control Applications (CCA), Sept 2016, pp. With autopilot, pilots can relieve fatigue and strain on long flights. Ring laser gyroscopes, which measure angular rotation rates, are among the most sensitive ones. Macek and D.T.M. A Mk 84 bomb fitted with JDAM kit. Stedman, Ring-laser tests of fundamental physics and geophysics. Eur. The standard analysis leads to a broader and highly irregular distribution, typical of non linear system. This work opens up the window for the development of high sensitivity transportable RLGs, for applications in seismology, as environmental monitors to improve the low frequency performance of the test mass suspension of the gravitational wave antennas, and for the development of inertial platforms in general. 1, and eventually a locking of the two laser frequencies when the \(f_s\) value become lower than \(f_{lock}= r_{1,2} c/ (\pi L)\) [9]. Courtesy of Tampere University of Technology. Interferometers are typically used for highly sensitive measurements which cannot be achieved in other ways, such as identifying variations on microscopic organisms or detecting gravitational waves, and have wide applicability. Ruggiero, Testing general relativity by means of ring lasers. In the present analysis it will not be neglected: \(\delta _{ns}\) will be considered a perturbation of \({\dot{\psi }}\), defining a new variable \(\dot{\psi _0} \simeq {\dot{\psi }}-\delta _{ns}\) (\({\dot{\psi }}\) being the frequency effectively measured by the interferogram, called also \(\omega _m\)). Maximize safety and optimize the efficiency of Embraer jets with our leading technology solutions. Comparison of the old and new analysis of GINGERINO data. The resonator incorporates polarization rotation (via a nonplanar geometry) which splits the fourfold-degenerate cavity mode (two directions, two polarizations each) into right- and left-circular-polarized modes separated by many hundreds of MHz, each having two counterpropagating beams. Stabilized platform INS contain three or more accelerometers, as well as three or more gimballed spinning mass gyros which maintain platform alignment and stability when the aircraft is in motion. Large area ring laser reach sensitivities at the level of fractions of prad/s, allowing measurements of relevant geophysical signals. The analytical expansion for the whole set of 6 terms is reported. INS are guiding systems for ships, spacecraft, aircraft and missiles that help maintain an accurate position in situations and environments where GPS technology cannot be used. We apply this technique to data from two ring laser prototypes, and compare the precision of the measurement of the angular rotation rate obtained with the new and the standard methods. Ser. Additionally, the entire unit is compact, lightweight and highly durable, making it suitable for use in mobile systems such as aircraft, missiles, and satellites. Our solutions for Airbus platforms enhance fuel efficiency, boost safety and simplify maintenance. 31(22), 225003 (2014), NBeverini, GCarelli, ADi Virgilio, UGiacomelli, EMaccioni, F.Stefani, JBelfi. Phys. As more R&D is going into INS systems and GPS free devices, ring laser gyros are continually growing smaller and more convenient for air and spacecraft applications. Regular gyroscopes do this by a method similar to the way the human ear detects motion. As a consequence, the beams will have destructive interference and a net phase difference by an amount proportional to the rotation rate (Sagnac effect). Power Boeing aircraft with dedicated products and solutions ranging from APUs to flight controls. Often, GPS is unavailable or unreliable in battlefields as GPS spoofing and tampering technologies are becoming more advanced. Petermann-factor sensitivity limit near an exceptional point in a Brillouin ring laser gyroscope Nat Commun. Large frame RLGs are instruments dedicated to the study of phenomena with typical frequency below 20 Hz; we have checked that the two methods are equivalent in the high frequency band of interest. See here how our solutions help you maximize operational safety and efficiency. Dither does not fix the lock-in problem completely, as each time the direction of rotation is reversed, a short time interval exists in which the rotation rate is near zero and lock-in briefly can occur. RLG consists of a laser with a cavity comprising of three or four mirrors, depending if the cavity is triangular or square, rigidly attached to a frame; large frame RLGs are utilised to measure the Earth rotation rate, being attached to the Earth crust. Equation1 connects \(\varOmega \) with the scale factor S, which depends on the geometry, and \(\lambda \), quantities than can be measured. They are also more lightweight and tend to be more compact, which is most ideal for efficient air vehicles. Appl. The difference in frequency is proportional to the rotation rate. For reduced size RLG and when the mirrors are not top quality, deviations from the ideal case are more relevant. \end{aligned}$$, $$\begin{aligned} K(t) = \sqrt{\frac{\alpha _1}{\alpha _2}} c r_1 \sin (\epsilon -t \omega _s)-\sqrt{\frac{\alpha _2}{\alpha _1}} c r_2 \sin (t \omega _s+\epsilon ), \end{aligned}$$, $$\begin{aligned} \omega _s= & {} \frac{\omega _m}{2} + \sqrt{\frac{8 c^2 r_1 r_2 \cos (2 \epsilon )+(K-L (\omega _m +\delta _{ns}))^2}{4 L^2}}\nonumber \\&-\frac{K}{2L}+\frac{\delta _{ns}}{2} \end{aligned}$$, $$\begin{aligned}&\omega _s \simeq \omega _{s0} +\omega _{ns1} +\omega _{ns2} + \omega _{K1}+\omega _{K2}+\omega _{nsK} \end{aligned}$$, $$\begin{aligned}&\omega _{s0} = \left( \frac{1}{2} \sqrt{\frac{8 c^2 r_1 r_2 \cos (2 \epsilon )}{L^2}+\omega _m ^2}+\frac{\omega _m }{2} \right) \\&\omega _{ns1} = -\delta _{ns}\times \left( \frac{\omega _m }{2 \sqrt{\frac{8 c^2 r_1 r_2 \cos (2 \epsilon )}{L^2}+\omega _m ^2}}+\frac{1}{2}\right) \nonumber \\&\omega _{ns2} = \delta _{ns}^2\times \frac{2 c^2 r_1 r_2 \cos (2 \epsilon )}{(8 c^2 r_1 r_2 \cos (2 \epsilon )+L^2 \omega ^2) \sqrt{\frac{8 c^2 r_1 r_2 \cos (2 \epsilon )}{L^2}+\omega _m ^2}}\nonumber \\&\omega _{K1} = K\times \left( -\frac{\omega _m }{2 L \sqrt{\frac{8 c^2 r_1 r_2 \cos (2 \epsilon )}{L^2}+\omega _m ^2}}-\frac{1}{2 L} \right) \nonumber \\&\omega _{K2} = K^2\times \frac{2 c^2 r_1 r_2 \cos (2 \epsilon ) \sqrt{\frac{8 c^2 r_1 r_2 \cos (2 \epsilon )}{L^2}+\omega _m ^2}}{ (8 c^2 r_1 r_2 \cos (2 \epsilon )+L^2 \omega _m ^2 ){}^2}\nonumber \\&\omega _{ns K}= \frac{ \delta _{ns} K}{2\sqrt{8 c^2 r_1 r_2 \cos {2 \epsilon }+L^2{\omega _m}^2}}\nonumber \end{aligned}$$, \(\frac{8 c^2 r_1 r_2 \cos (2 \epsilon )}{L^2} \ll \omega _m^2\), $$\begin{aligned} r_1= & {} \frac{ I_{S2} \omega _m}{\frac{ 2 c \sqrt{ PH_{1} PH_{2}}}{L}} \end{aligned}$$, $$\begin{aligned} r_2= & {} \frac{ I_{S1} \omega _m}{\frac{ 2 c \sqrt{ PH_{1} PH_{2}}}{L}} \end{aligned}$$, $$\begin{aligned} \omega _{s0} = \frac{1}{2} \sqrt{(1+\xi ) \frac{ 2 I_{S1} I_{S2} \omega _m^2 \cos (2 \epsilon )}{ PH_{1} PH_{2}}+\omega _m^2}+\frac{\omega _m}{2} \end{aligned}$$, $$\begin{aligned} \omega _{s0}= & {} \frac{1}{2} \sqrt{\frac{ 2 \omega _m^2 I_{S1} I_{S2} \cos (2 \epsilon )}{ I_{1} I_{2}}+\omega _m^2}+\frac{\omega _m}{2} + \omega _{s \xi } \end{aligned}$$, $$\begin{aligned} \omega _{s \xi }= & {} \xi \times \frac{ I_{S1} I_{S2} \omega _m ^2 \cos (2 \epsilon )}{2 I_{1} I_{2} \sqrt{\frac{ 2 I_{S1} I_{S2} \omega _m^2 \cos (2 \epsilon )}{ I_{1} I_{2}}+\omega _m^2}} \end{aligned}$$, \(\varOmega _\oplus = 7.292115\times 10^{-5}\), $$\begin{aligned}&\delta I_{S1} \sim \frac{\delta _1 I_{S2} \omega ^2 \cos (2 \epsilon ))}{8 PH_{1}^2 PH_{2} \sqrt{\frac{I_{S1} I_{S2} \omega ^2 \cos (2 \epsilon )}{2 PH_{1} PH_{2}}+\omega ^2} } \end{aligned}$$, $$\begin{aligned}&\delta PH_{1} \sim \frac{\delta _{1} I_{S1} I_{S2} \omega ^2 \cos (2 \epsilon )}{8 {PH_{1}}^2 PH_{2} \sqrt{\frac{I_{S1} I_{S2} \omega ^2 \cos (2 \epsilon )}{2 {PH_{1}} PH_{2}}+\omega ^2}} \end{aligned}$$, https://doi.org/10.1140/epjc/s10052-019-7089-5, Long-term performance analysis of BDS-3 precise point positioning (PPP-B2b) service, Assessment of Galileo High Accuracy Service (HAS) test signals and preliminary positioning performance, Correcting antenna phase center effects to reconcile the code/phase bias products from the third IGS reprocessing campaign, Characteristics of the IGS receiver clock performance from multi-GNSS PPP solutions, Bridging astronomical, astrometric and geodetic scheduling for VGOS, BDS-3 precise orbit and clock solution at Wuhan University: status and improvement, Comment on Tidally Synchronized Solar Dynamo: A Rebuttal by Nataf (Solar Phys. 8, provided that \(r_1\), \(r_2\), \(\epsilon \), \(\delta _{ns}\), and the average value of K are available, which is in principle feasible utilising the mono-beam signals and the measured losses of the cavity and employing numerical recursive methods to evaluate K. In the following Eq. Opt. Our avionics enhance safety, operational efficiency and passenger comfort for the Bombardier family. We discuss a novel technique to analyse data, able to reduce non-linear laser effects. Note, VIR-019A-07 (2005), J.Belfi, N. Beverini, et al. (submitted), J. Belfi, N. Beverini, F. Bosi, G. Carelli, D. Cuccato, G. De Luca, A. In reality, the "rings" are usually triangles, squares, or rectangles filled with inert gases through which the beams are reflected by mirrors..
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