This paper details a new extrinsic calibration method for scanning laser rangefinder that is precisely focused on the geometrical ground plane-based estimation. This method is also efficient in the challenging experimental configuration of a high angle of inclination of the LiDAR. In this configuration, the calibration of the LiDAR sensor is a key problem that can be be found in various domains and in particular to guarantee the efficiency of ground surface object detection. The proposed extrinsic calibration method can be summarized by the following procedure steps: fitting ground plane, extrinsic parameters estimation , and extrinsic parameters optimization. Finally, the results are presented in terms of precision and robustness against the variation of LiDAR’s orientation and range accuracy, respectively, showing the stability and the accuracy of the proposed extrinsic calibration method, which was validated through numerical simulation and real data to prove the method performance. With the evolution of technology, the 3D intelligent sensors have posed great challenges in signal processing, especially in their outstanding acquisition performance even in rough environment. Moving to road networks maintenance and transportation safety, the responsibility imposes itself in detecting and locating the road distortion . The literature review in  presentsIn a related context, road defects present a big danger on the traffic circulation ending up with possible traffic accidents. Some traffic accidents result from the presence of disabilities or small obstacles on the roads. In fact, this is one of the major problems that people suffer from in their daily lives. The key problem in this research concerns the characterization of the road surface by detection, localization, and tracking the presence of potentially dangerous areas and road defects using a 3D LiDAR sensor. Although 2D LiDAR sensors can provide 3D data, they require the use of an additional instrument in the form of a tilt unit.Various promising applications, which rely on LiDAR sensors, are developed in different fields: intelligent transportation systems, mobile robotics, and connected vehicles. Thus, LiDAR is a fundamental sensor contributing in multi-vehicles tracking , simultaBasically, LiDAR sensor operation relies on the calibration process which improves the defect detection and other study procedure. Two different types of calibration exist: intrinsic and extrinsic calibration. The intrinsic calibration considers the modeling between the beam creation and measurement of the environment to estimate the sensor–environment relationship in terms of the sensor internal parameters. On the other hand, the extrinsic calibration considers the determination of the relationship between the sensor frame and the world reference frame by rotation and translation transformation.Numerous authors investigated intrinsic and extrinsic calibration methods in LiDAR sensors. An intrinsic calibration technique is presented in . The calOn the other hand, an extrinsic calibration technique is presented in . In thisIn , a numerIn transport applications, many articles use LiDAR to detect and track objects of interest  from 3D measurements. The LiDAR sensor is also used to detect the road, often in addition to camera sensors. In these applications, the idea is to have a thorough view of the driver’s environment over the widest possible horizon. This therefore involves a LiDAR sensor with a low angle of inclination .The perspective of our paper is to propose a calibration method (and road plane estimation) that works under difficult experimental conditions (high angle of inclination). Indeed, we aim at developing a calibration method that allows to determine precisely the road plane in a very close vicinity of the vehicle. The idea in the long term is to detect road defects when driving on the road network. Although developed with this in mind , our method is general enough to be applicable in any wider operational context.In the context of this study (road defects detection), the LiDAR sensor is rotated toward the ground to increase the points’ density covering the defects by the multi elevation laser. This causes a complicated modification in the ground 3D view scene with respect to the LiDAR frame. Therefore, extrinsic calibration was adopted in order to transform the LiDAR frame into a global reference frame, thus modifying the ground impact points transformation into an understandable view scene.To attain the above key objective, a first method was applied by Zaiter et al.  on simulThis paper addresses a new flexible extrinsic calibration method as compared to the previous plane-based methods. The approach developed is generalized to all types of scanning laser rangefinders. It now presents an optimized estimation of all extrinsic calibration parameters (angles and height). This global method can be implemented on different LiDAR sensors (low-cost 3D and full 3D) with various range accuracy. In addition, the proposed technique out performs in high orientation scenarios, which is a very interesting and challenging task that aims to increase the points’ density coverage. The proposed calibration method can be summarized by the following two-fold contributions: (1) ground plane model estimation; and (2) rotation transformation matrix estimation from world ground reference to LiDAR sensor frame. The 3D Euler’s angles (sensor orientation) and the height  are two essential extrinsic parameters required to calibrate the full 3D LiDAR sensors, in order to improve the capability of road defect detection as explained in The structure of this paper is as follows. The synthetic data are generated depending on the features of multi-laser rangefinder or 3D LiDAR sensor, where the environment impact points can be modeled as an intersection between the LiDAR laser beams and the environmental surrounding surfaces. In this work, the LiDAR sensor must be oriented toward the ground to study the road defects. Therefore, the LiDAR laser beams are represented as straight lines and the ground surface as a flat plane in a 3D frame.Practical orientation concept: The LiDAR laser beams Scientific orientation concept: The LiDAR laser beams Depending on the application situation, two concepts can represent the geometrical reflection model between the LiDAR sensor and the ground surface, as shown in Goal: The plane-based extrinsic calibration needs large sparsity area to improve the plane estimation, which requires high altitude and low orientation angles.Constraint: The stated finality of road surface object detection needs high density points to improve the capability of defect coverage points, which requires low altitude and high orientation angles.The four extrinsic parameters  affect the research goals, where the orientation parameter is the strongest influence factor on the ground points distribution process, as shown in Therefore, a trade-off is needed to optimize the extrinsic parameters , providing the suitable coverage points distribution over the ground.Four geometric view patterns are summarized in three cases depending on the variation of pitch angle The study case in this problem focuses on the hyperbolas case, as shown in t is the parameter of the parametric representation.In the following part, the scientific orientation concept is chosen to model the reflections of the laser beams h and rotational matrix The virtual horizontal ground plane The parametric and Cartesian equations of the horizontal ground plane The rotational matrix Therefore, the Cartesian coordinates of the real points cloud In this section, the systematic and random errors Equation , where ρThe 3D transformation from polar coordinates Then, the standard deviation of the error can be derived from polar to Cartesian parameters in Equation , assuminGlennie et al.  showed iIn this study, we then focus on the range error Equation  is then In multi-sensor applications, data acquired from the different sensors must be fused in one common reference frame. In this application, the calibration of LiDAR frame scans is necessary to merge them in one world reference frame, in order to increase the points density coverage on the ground, which facilitates the road defect detection. Therefore, the extrinsic calibration aims to model the relationship between the LiDAR frame and the world reference frame.h. Then, the opt-LGCM is initialized by the estimated extrinsic parameters to optimize them. Finally, the distributed ground noisy points We thus propose the LiDAR/Ground Calibration Method (LGCM) presented in The proposed method consists mainly in two steps. The first, totally unsupervised step, consists of estimating a first value of the steering angles. This first estimate is then used as a basis for the optimization step, which seeks the best orientation parameters. The developed method is therefore totally unsupervised and does not require a priori knowledge of the orientation of the sensor by a tilt unit for example.The first step aims to fit an estimated plane A, B, and D are the plane parameters and w is an additive white Gaussian noise with standard deviation The equation of the estimated plane Therefore, Equation  of the eN is the number of reflected points.The solution of Least Squares estimator for this linear model is expressed as:Rodrigues formula is an efficient rotation transformation that computes the rotation matrix  angle η . Therefot −h cf. c. The obAssuming that Now, by using Equation ,(15)RroThen, the Rodrigues matrix Equation , as showz-axis. This algorithm is called Least Squares Conic Algorithm (LSCA), which takes advantage of the center s characteristic of the geometrical impact patterns  formed by the points After rotating the noisy points Equation . Algorithm 1: Least Squares Conic Algorithm.Input:x,y,z,   Output:1Fit the lines The solution of Least Squares estimator for linear model:2s of each two symmetric lines of Compute the coordinates of the intersection points s of the straight lines Therefore, the intersection points 3s and the origin O by Least Squares estimator.Fit a line The solution of Least Squares estimator: 4y-axis:Finally, compute the angle    Therefore, the third Euler’s angle of rotation (yaw angle) z-axis, as shown in Finally, the points At the end of LGCM approach, a suitable way to estimate the height is to compute the altitude mean of the points Levenberg–Marquardt algorithm is an optimization algorithm that combines gradient descent and Gauss–Newton methods . In addiEquation . The optEquation . In otheThe non-linear function The optimized points Equation :(25)PoptFinally, the Cartesian coordinates of rotated optimized points cloud The proposed calibration method LGCM was applied on two types of data: simulation data were obtained by the modeling mentioned in The extrinsic calibration results are presented in terms of precision and robustness. According to our application, the precision shows the stability of the method with respect to the variation of pitch angle h, estimated height The real height N is the number of impact points.The standard deviation N is the number of impact points.The standard deviation N is the number of impact points.The standard deviation The gain in performance Therefore, the evaluation parameters of the results focus on the point cloud features of the real points In term of precision, the real height In term of robustness, the real height Using the simulation data, the setups used to validate the proposed calibration method are separated in two categories:After analyzing Equation  describeIn The increase of pitch angle The increase of LiDAR range accuracy In terms of precision and robustness, The standard deviation The negligible standard deviation h than the estimated height In terms of precision and robustness, Equation , with reThe 3D point cloud acquisitions were obtained using a multi-lasers rangefinder VLP-16 LiDAR mounted on a vehicle. To obtain a telemetric information about the ground surface and to achieve the application goal, the VLP-16 LiDAR was rotated toward the ground direction with a pitch angle Acquisition 1: The vehicle was at rest on the road.Acquisition 2: The vehicle was moving at a slow speed on the road.The proposed method was applied to two different acquisitions:In the absence of real plane In general, the results prove the efficiency of the optimization algorithm, which is represented by the optimized plane A new extrinsic LiDAR/Ground calibration method for 3D LiDARs is presented in this paper. The solution relies on plane-based modeling of the ground, which allows the estimation of the LiDAR’s orientation and altitude using Rodrigues formula, Least Squares Conic Algorithm for yaw angle estimation and height estimation. The proposed method (LGCM) is extended to an optimized derivation (opt-LGCM) using the Levenberg–Marquardt algorithm and is shown to be a suitable solution to LiDAR/Ground calibration problem. It is implemented on synthetic and real LiDAR telemetric data. The results show the performance in terms of precision and robustness against the variation of LiDAR’s orientation and range accuracy, respectively, proving the stability and the accuracy of the proposed calibration method.


We have designed a fully automated optical microscope running at high-speed and achieving a very high spatial resolution. In order to overcome the resolution limit of optical microscopes, it exploits the localized surface plasmon resonance phenomenon. The customized setup using a polarization analyzer, based on liquid crystals, produces no vibrations and it is capable of probing isolated nanoparticles. We tested its performance with an automated readout using a fine-grained nuclear emulsion sample exposed to 60 keV carbon ion beam and, for the first time, successfully reconstructed the directional information from ultra-short tracks produced by such low-energetic ions using a solid-state tracking detector. Then, it becomes possible to use barycenters of isolated images, thus, providing a better resolution. Recently reported orientation-dependent localization microscopy (ODLM)4 and super-resolution plasmonic imaging microscopy (SRPIM)5 both exploit the localized surface plasmon resonance (LSPR) phenomenon6 for imaging of non-fluorescent metallic NPs in dielectric media.The demand for advanced imaging of nanometer-scale objects at a spatial resolution below the diffraction limit has led to the appearance of various super-resolution techniques. Many of them, such as stimulated emission depletion (STED) microscopy6. Free electrons in metallic NPs have a natural frequency due to the binding force responding to displacement generated by electrostatic attraction in an external electric field. Silver NPs with dimensions from few tens to few hundreds of nanometers undergo a resonance condition at visible wavelengths. In addition, if assuming a non-spherical structure, like an ellipsoid body, the dipole moment depends on the external electric field direction, which can be detected by analysing the angle of linear polarization of the reflected light6. Thus, plasmon resonance provides information at smaller spatial scales than the standard optical imaging.Plasmon resonance is the collective oscillation of free electrons induced by an external electric field8 is composed of tiny silver bromide (AgBr) crystals immersed in a gelatin binder. The crystals act as sensors that are activated by the ionization loss of a passing-through charged particle. The activated state of the crystals is preserved until the emulsion film is chemically developed. Thus, a particle track is recorded, first as a sequence of activated crystals, which later, after the development, becomes a sequence of silver NPs, called grains8. These grains have the form of randomly oriented filaments with typical dimensions equal to several tens of nanometers, depending on the emulsion type8.The nuclear emulsion9, was specifically designed to be used as a detector in the Nuclear Emulsion WIMP Search with directional measurement (NEWSdm) experiment10. This experiment develops the next-generation strategy for directional detection12 of the so-called Weakly Interacting Massive Particle (WIMP)15 with a complementary approach that provides unambiguous signature of the galactic origin of dark matter.The new type of a fine-grained emulsion, called the Nano-Imaging Tracker (NIT)5, the optical resolution of the microscope in green light. These tracks were produced by low-energy (100 keV) carbon ions in an NIT emulsion film. In order to reach and, eventually, overcome the so-called neutrino floor16 the NEWSdm detector must have a high sensitivity and a sufficiently large mass: from 10 to 100 tons, depending on the sensitivity16. The major fraction of events are expected to have track lengths shorter than 200 nm. Therefore, to have a higher sensitivity and also the sensitivity for low-mass WIMPs 16. Such a low threshold requires a super-resolution that, combined with the necessity to analyse several tons of the NIT emulsion, makes the readout an extremely challenging task, impossible without a creation of a high-speed fully automated super-resolution microscopes, like the one we report in this paper.With using the SRPIM technique it was demonstrated the feasibility of reconstructing tracks with lengths shorter than 315 nmnanotracks to distinguish them from other track types that can appear in nuclear emulsion, for example, microtracks, black tracks, etc. Nevertheless, in view of the fact that all the tracks we consider in this paper are nanotracks and to avoid reader’s confusion, we do not call them nanotracks but tracks.In the field of nuclear emulsion analysis sub-micron-length tracks, produced by low-energetic charged particles and composed of silver nano-grains, with typical distances between them being shorter than the optical resolution The microscope, designed and used to carry out the measurements, is shown in the left panel of Fig. We have chosen to use a beamsplitter cube since, unlike a semi-transparent mirror, it does not noticeably distort the polarization of neither the passing-though nor the reflected light. In order to prevent the backreflected light, produced by the faces of the beamsplitter cube, from entering the tube lens and reaching the camera, we have inclined the beamsplitter cube by about mentclass2pt{minimThe LED has a uniform intensity distribution across the whole emitting surface of The microscope is equipped with a fast 4M monochromatic camera with 17, or the sample itself4, inevitably producing noticeable vibrations. Mechanical rotation followed by some idle time to dump vibrations would not only slow down the readout but, potentially, can also lead to localization errors due to the sample drift between consecutive polarization angle measurements. Both vibrations and sample drift, if not corrected, interfere with measurements spoiling the spatial accuracy and, hence, limiting the achievable resolution.All readouts reported so far are implemented by means of mechanical rotation of either an optical element, like the polarization filterWe have designed a polarization analyzer containing no moving parts. Its core is a liquid crystal variable retarder (LCVR), an electrooptical device exploiting anisotropic optical properties of nematic liquid crystals (LC). The retardancy introduced into the light beam passing through a LC cell depends on the orientation of LC molecules with respect to the light beam direction: the retardancy is maximal when the molecules are aligned with the light beam. The orientation of molecules, which are in fact electric dipoles, can be controlled by applying an external electric field to the transparent faces of the LC cell. The rotation of molecules is quite fast and is of the order of 10–20 ms, depending on the LC cell thickness. Therefore, the performance of the designed LC polarization analyzer (LCPA) is equivalent to an ordinary polarization filter vibrationlessly rotating at about 200–400 rpm.I as:The scheme of the LCPA is shown in Fig. mentclass2pt{minimAs it was mentioned before, silver grains in the NIT emulsion are not spherical and have the form of randomly oriented filaments. Since the illumination system uses monochromatic light, a grain becomes detectable when its reflectance is enhanced by the LSPR phenomenon, i.e. when the plasmon resonance peak wavelength matches that of the illuminating light, which happens only at certain polarization angles. In case of several grains being closer than the optical resolution, due to their filament-like shape and random orientation, the contribution of each grain to the brightness of the detected unresolved image is different for different polarization angles. This effect leads to detectable changes in the shape and position of the observed image of unresolved close grains, making their isolation and measurement possible.The analysis method is based on probing the intensity of different polarization components of the light scattered by silver grains. Due to polarization anisotropy of the LSPR phenomenon, the scattered light intensity distribution changes with varying the polarization angle, providing access to the nano-scale details hidden beyond the diffraction limit.In order to test the performance of the designed microscope and the analysis method we used a sample exposed horizontally to carbon ions with energy 60 keV. Carbon ions were implanted in the emulsion films under vacuum in such a way to have reference tracks in the emulsion with the given energy. According to the SRIM simulation, the average path length in the NIT emulsion is equal to 210 nm, with a tail ranging up to 370 nm, as shown in Fig. Figures The spherical shape of the cluster in Fig. barycenter shift as a line connecting the most distant points in these plots. Therefore, the barycenter shift length is defined as the length of this line, while the direction is the line’s angle with the X axis. The event from Fig. Figures It is important to note that the measured value of barycenter shift depends on mutual orientation of grain filaments composing the track: when they are perfectly parallel their brightness changes synchronously and the barycenter shift is minimal, almost close to zero. On the contrary, when they are orthogonal, the barycenter shift is maximal, close to the real length of the horizontal projection of the track. In general case, due to random orientation of filaments, we expect that the barycenter shift is always smaller than the track’s projection at the horizontal plane. Hence, the barycenter shift can be interpreted as a lower limit on the track length.Direction and length of tracks are of great importance for the directional WIMP search since they are related to the direction, mass and energy or the original WIMP that caused the nuclear recoil, which was recorded as a track. Barycenter shift direction can be interpreted as the direction of the track, but barycenter shift length cannot be considered as track length. Nevertheless, there is a strong correlation between them: tracks cannot produce barycenter shifts longer than their own lengths. Therefore, barycenter shift length can be used to separate events with reliable directional information (long tracks) from those with absent or unreliable directional information . Naturally, a part of long tracks that produces short barycenter shifts will be excluded, thus, lowering the overall sensitivity of the emulsion detector, but the remaining part will contain mainly long tracks suitable for WIMP direction measurement.Though the optical resolution is limited by diffraction, and the size of a silver NP cannot be measured directly, its position can be calculated with rather high precision. However, the spatial accuracy is limited by the presence of thermal noise on the camera sensor and by vibrations induced from outside. Indeed, two consecutive position measurements of the same NP do not yield exactly the same result. Nevertheless, the spatial accuracy can be much higher than the optical resolution. As shown in Fig. The microscope was calibrated in a way to have an isotropic response to 40 nm spherical silver NPs. The isotropy of angular measurements is confirmed by the flatness of the barycenter shift direction distribution shown in Fig. We have analyzed the According to the simulation Fig. , the 60 The analysis method was verified by scanning the sample with both the reported microscope and a scanning electron microscope (SEM). A super-resolution image is modelled as a set of brightness-modulated pixels, with each pixel being described with three parameters: average brightness, brightness change amplitude and brightness phase (the polarization angle at which the maximum pixel brightness is reached). With this image model a joint deconvolution of event images shown in Figs. The content of the reconstructed images closely corresponds to that of SEM images. The short barycenter shift event in Fig. We demonstrated that the designed microscope and the developed analysis method are capable of isolating tracks produced by low-energy carbon ions in a completely automated mode. According to the simulations, the major part of tracks have the path length shorter than the diffraction-limited resolution of best conventional optical microscopes. With the chosen threshold of 21 nm, events with the barycenter shifts longer than that, represent tracks produced by carbon ions from the beam. Measured barycenter shift direction corresponds to that of the track. The barycenter shift length depends on mutual orientation of grains composing the track and, therefore, its length is not equal to that of the track, unless the grains are perpendicular to each other. The correlation between the barycenter shift and the actual track length will be investigated with electron microscopes and it will be the subject of a dedicated paper.The reported analysis method has certain limits of applicability. It is optimized for samples in which randomly oriented non-spherical metallic NPs are dispersed in a dielectric media transparent at the illuminating light wavelengths. No barycenter shift will be detected if the two NPs are spherical and also if they are non-spherical but happen to be oriented along the same direction.Further development of the analysis method can help extracting more information about the nano-scale structure of events. For example, from Eq. , since tWe showed that reported microscope can produce super-resolution images by performing a joint deconvolution of images taken at different polarization angles. The achieved resolution was estimated to be about 80 nm and is limited by the hardware pixel size, thus, leaving room for improvement. A new setup with smaller camera sensor pixels and higher optical magnification is required to reveal the full potential of the LSPR-based super-resolution imaging.17, we managed to minimize the effect of vibrations in the designed super-resolution optical microscope. Therefore, it can be used to analyze isolated events when there is no possibility to apply pattern matching algorithms for vibration correction. Better isolation from vibrations coupled with reducing the camera sensor noise can potentially improve the spatial accuracy and lower the detection threshold. The readout speed of the prototype microscope can be further increased by substituting the LCVR with a Pockels cell that has a faster response to the external electric field. We also evaluate the possibility of splitting the field of view into several identical images and analyze each of them with dedicated polarization filters rotated at different polarization angles. The latter will not only permit to analyze all polarization angles simultaneously, but also will allow to use the white light illumination to extend the analysis to multiple wavelengths. The simultaneous acquisition of polarization images will make the microscope insensitive to vibrations and will enable application of novel scanning techniques23, dramatically boosting the readout speed.Unlike previous manual implementations24 technique, with using a coherent optical source, can enable the axial coordinate measurement, thus, providing a full 3D picture of nanostructures under study. Moreover, such a combination can reduce the minimal detectable NP size and will enable the detection of even shorter tracks, resulting in a significant boost of the sensitivity of the NEWSdm nano-emulsion detector.The combination of the reported method and the iSCATThe creation of a fast and completely automated microscope capable of reconstructing low-energy sub-micron ion tracks in nano-grained emulsions paves the way for construction of a solid-state detector exploiting the directionality as an additional parameter enabling the conclusive identification of WIMP events, even in the presence of background. Moreover, this approach can overcome the neutrino floor, thus, enabling the exploration of the WIMP parameter space unreachable by contemporary dark matter search experiments.18. A possibility would be its application in microfluidics to visualize the orientation of non-spherical metallic NPs inside capillars and near membrane walls, where, due to the arising of hydrodynamic interactions between the particle and the walls, the diffusive behavior of a NP in the presence of confining walls is dramatically different from that occurring in the bulk19. Another interesting application could be for the classification and design of magneto-optical materials20, where due to the Kerr effect, the polarization of the reflected light depends on the local magnetic state, making the visualization of magnetic domain structures possible with the reported microscope. Moreover, after minor modifications like the adjustment of the illumination light wavelength and the use of a dichroic mirror instead of the beamsplitter, it will become possible to exploit the designed microscope to study the field-dipole interactions of fluorescent dye molecules21.The reported microscope and analysis method can also be used for applications outside the directional dark matter search for fast automated analysis of materials whose optical properties are anisotropic with respect to the polarization direction. For example, it can be used to reconstruct the spatial orientation of NPs that is of great importance for understanding of certain vital biological mechanisms, such as the heterogeneous local structure deformations of the cell membrane, or the interaction force between proteins and cell membranes, etc. It can be used to verify various hypotheses of the antimicrobial effect of silver NPs that requires the study of the mechanism of the cell membrane penetration, research of the interaction with enzymes and the DNA inside the cell and the understanding of the modulation of cellular signal transduction caused by the presence of silver NPsThe prototype microscope, shown in the left panel of Fig. mentclass2pt{minim26 provides modules for real-time microscope automatization, image acquisition and data analysis.Microscope components are controlled from a workstation (Dell T7500) equipped with a framegrabber (Matrox Radient eCL), a motion control board  and a GPU board (GeForce GTX 780) for accelerated image processing. The LASSO (Large Angle Scanning System for OPERA) software frameworkThe polarization state of incoherent light is described by a Stokes vector. The effect of an optical system on the polarization of light can be determined by constructing the Stokes vector for the input light and convolving it with Mueller matrices representing the optical system. As a result, one gets the Stokes vector of the light leaving the system. The LCPA system can be described mathematically in terms of Mueller matrices as:mentclass2pt{minimThe data acquisition is performed by scanning the entire detector volume with samplings of 60, 43 and In static position, take 8 images varying the polarization angle;If still inside the sample make a step along Z axis, otherwise move along Y or X;Repeat (1) and (2) until the whole sample volume is scanned.The readout speed achieved with these parameters for the reported samples is about 10 s/view.The readout is performed in the following manner: Before the processing, an image of static background is prepared by grabbing a series of images in the absence of a sample. Then, a single image is generated by averaging values of corresponding pixels of the images grabbed during the previous step. The averaging leaves only static features present in images, like dead pixels and images of dust particles attached to the camera sensor as well as the non-uniformity of the illumination brightness level across the image.The first step of image processing involves the subtraction of the pre-generated static background image from every image grabbed, making the illumination brightness distribution flat, removing static image features and leaving only the features belonging to the signal.27 and references therein.In the next step, a flattened image is processed with a A cluster is a tie set of adjacent pixels corresponding to grain’s image projected on the camera sensor. To isolate individual clusters a threshold function is applied to pixels of a filtered image. Tie sets of adjacent pixels with brightness values higher than the predefined one form eventual clusters.f to measure the barycenter coordinates After a cluster is isolated, the corresponding pixels are extracted from the original flattened image along with pixels from the surrounding region of approximately Since the vertical sampling is finer than the depth of field, a single physical grain produces multiple clusters: not only the in-focus one but also those out-of-focus. In order to isolate all clusters belonging to the same grain, a starting cluster is linked with clusters at the adjacent frames that have an offset in XY less than 300 nm. Then, this procedure is repeated for the just linked clusters until there is no more clusters to link. As a result of this procedure, one gets a tree-like collection of clusters that is associated with a grain or, more general, with an event. Thus, an event can contain a single grain, a close unresolved grain pair (a track) or a close resolved grain pair (a microtrack).The barycenter shift analysis procedure is defined only for in-focus clusters and, therefore, it is necessary to find the best focused cluster (BFC) inside the clusters collection tree representing a single grain or an event. A cluster with the highest amplitude, found by the bi-dimensional Gaussian fit, is selected as the BFC by iterating all clusters in the collection.The data acquisition is performed in the same way and with the same parameters as for real measurements. Eight images corresponding to different polarization angles spaced by 8. The energy loss of ionizing particles crossing the films induces along its path atomic-scale perturbations that, after a chemical treatment, produce a sequence of visible grains in the emulsion. A new type of nuclear emulsion the “Nano-Imaging Tracker” (NIT)9 was developed at Nagoya University (Japan) in 2010 intentionally for the directional dark matter search application. The NIT emulsion has grains of 44 nm diameter, respectively, which is about one order of magnitude smaller than the crystal size of the emulsion used in the OPERA experiment28. The overall density is equal to 9. NIT emulsion film was exposed to carbon ion beam of 60 keV at the ion implantation system (NH-20SR-WMH) of the Nagoya University Nano fabrication Platform. The beam during the exposure had angle of Nuclear emulsions are made of small crystals of silver halide  immersed in an organic gelatin


Vehicle platoons involve groups of vehicles travelling together at a constant inter-vehicle distance, with different common benefits such as increasing road efficiency and fuel saving. Vehicle platooning requires highly reliable wireless communications to keep the group structure and carry out coordinated maneuvers in a safe manner. Focusing on infrastructure-assisted cellular vehicle to anything (V2X) communications, the amount of control information to be exchanged between each platoon vehicle and the base station is a critical factor affecting the communication latency. This paper exploits the particular structure and characteristics of platooning to decrease the control information exchange necessary for the channel acquisition stage. More precisely, a scheme based on radio environment map (REM) reconstruction is proposed, where geo-localized received power values are available at only a subset of platoon vehicles, while large-scale channel parameters estimates for the rest of platoon members are provided through the application of spatial Ordinary Kriging (OK) interpolation. Distinctive features of the vehicle platooning use case are explored, such as the optimal patterns of vehicles within the platoon with available REM values for improving the quality of the reconstruction, the need for an accurate semivariogram modeling in OK, or the communication cost when establishing a centralized or a distributed architecture for achieving REM reconstruction. The evaluation results show that OK is able to reconstruct the REM in the platoon with acceptable mean squared estimation error, while reducing the control information for REM acquisition in up to 64% in the best-case scenario. In upcoming years, the transport industry is expected to witness an intense period of change and evolution thanks to the implementation of intelligent transportation systems (ITSs). These systems rely on wireless communications and new computing and sensor technologies to provide a more efficient, safe and comfortable mobility in a variety of vehicular scenarios. In particular, vehicle to vehicle V2V) and vehicle to infrastructure communications (V2I), generally encompassed under the term vehicle to anything communication (V2X), are fundamental for different purposes such as the prevention of collisions between vehicles, emergency notification to distant vehicles, route and track optimization, and automated driving. In this direction, the Third Generation Partnership Project 3GPP) defined the term “enhanced support of V2X communication services”, known as eV2X , which tV and vehGPP definSome autonomous-driving related services require communication among groups of users. For instance, in vehicle platooning, there are two types of platoon nodes known as head/leader (leading vehicle), and follower (the rest of the vehicles). Once the platoon is established, each vehicle must keep a reliable communication within the platoon in order to keep the group structure and carry out coordinated maneuvers . VehiculIn this paper, we elaborate on the benefits of exploiting the particular features of platooning in order to decrease the control information exchange required in the V2X channel acquisition stage, with the focus of reducing the latency while ensuring the reliability of the communication. The possibility of achieving reliable channel state information at each vehicle at a reduced cost would pave the way towards enabling advanced physical-layer functionalities for the entire platoon such as the mobile relay paradigm . In thisTraditionally, one of the key tasks in REM reconstruction is deciding an spatial interpolation method offering a good quality and complexity trade-off when the number of locations (or samples) to be considered increases. The most popular techniques in the literature are nearest neighbor , inverseThe first step in Kriging interpolation is to form an empirical semivariogram, which is later fitted to obtain a theoretical model. The semivariogram model basically characterizes the spatial correlation of the field. In a second step, interpolation is applied by using a weighted average of known field samples to estimate the value of the field in any position. The weights are obtained by minimizing the Kriging variance (best linear unbiased estimation) and hence, the better the semivariogram modeling, the better the Kriging interpolation. Reference  points oIn our target scenario, V2X platoon communications, the REM of interest is reduced to a subset of positions matching the platoon area, and it comprises samples of geo-localized received power due to large-scale channel effects, i.e., path-loss and shadowing. In this framework, we evaluate the potential of OK to reconstruct the REM within the platoon when only a given number of actual REM values are available. The aim is to assess the quality of the reconstructed REM values with different degrees of signaling reduction.a scheme to reduce the control information exchanged for REM reconstruction in platooning based on OK is proposed. The REM reconstruction capability is evaluated via the mean square error and traded-off versus signaling overhead;a suitable semivariogram modeling for OK interpolation in the scenarios under consideration is proposed;an analysis of the optimal patterns of vehicles’ positions for reliable REM reconstruction is performed;expressions for the communication cost related to the REM reconstruction are derived for a centralized and a distributed architecture.The main contributions of this paper are:The remainder of the paper is organized as follows. In this section, the use case and scenario are first presented, corresponding to two particular vehicular platoon setups referred to as the asymmetric and symmetric scenarios. Second, the theoretical framework of OK is briefly reviewed, and the REM modeling is stated (path-loss and shadowing models). Finally, two possible architectures towards the REM reconstruction, namely, centralized and distributed, are analyzed in terms of communication cost.N-vehicle platoon is targeted, with each vehicle of length l, passing through a BS assisting the platooning communication service. The particular use case of a R from the road border. All platoon vehicles are assumed to be perfectly aligned, driving on the centre of the lane and separated of each other a distance equal to L (platoon inter-vehicle distance). The vehicle antennas are located in the middle of the roof, assuming, for simplicity, that their position matches the middle point of the vehicle in both directions. As a result, the antennas of two consecutive vehicles are separated a distance equal to w. This scenario is usually considered as a benchmark for highway communication in the V2X framework [Both in the asymmetric and symmetric case, the BS is located at the origin of coordinates and at a distance ramework . Note thN as:N values. Note that this analysis could be extended by using stochastic geometry and assigning a given probability density function to the relative angle Since in the asymmetric scenario the BS is directly aligned with the platoon leader, the angle is P field values are available at certain vehicles of the reference scenarios depicted in Let us assume that a minimum number of on stage , the vehP is the number of available field values, P field values, and Two steps are required in OK interpolation: semivariogram analysis and Kriging prediction. First, an empirical semivariogram (EV) is formed, which is defined as one half the average squared difference between the field values at points separated by a lag distance :1)γ^(h)γ^(h)(1)γIn this paper, the field value corresponds to large-scale channel parameters, and it is given by:ribution . In the fined by :(4)ρi,j=ver . Considering the unavailability of REM values in the first and last vehicle, which is the worst-case in terms of message exchange, the total number of exchanged messages in the distributed setup is It can be observed that all the messages are transmitted though one-hop communications between neighboring vehicles. As a result, messages traverse exactly the same distance, given by the separation between antennas of consecutive vehicles  programming, obtaining that the power model is the most suited for their scenario. In this work, we deal with two particular features in the model selection step: (a) the number of available REM values to build the EV is small and limited to P, and (b) there is a certain fixed geometry in the EV calculations, which impacts on the model fitting, as it will be next discussed.Once the REM values are available at the BS , or at each vehicle (in the distributed case), the first step to reconstruct the REM in the remaining positions of the platoon is to build the EV in order to provide a semivariogram modeling via a parametric fitting. Reference  presentsIn this contribution, we focus on the basic models as presented in : sphericP is the number of available samples for the REM reconstruction.Once the model is selected, the parameters need to be determined by fitting the semivariogram model to the EV. Available methods include maximum likelihood estimation (MLE), weighted least squares estimation (WLSE) and generalized least squares estimation (GLSE) ,38. For N is set to 10. Two particular cases for the inter-vehicle distance are evaluated: We focus on a snapshot of the platoon service communication, where the vehicles are static in either a symmetric or asymmetric position see . The pardth w=4m . The numP is directly related to the signaling reduction percentage. For instance, with To evaluate the trade-off between signaling reduction when acquiring the REM versus quality of the estimation, we consider in Equation ) to P=9 The small size of the available set of data samples (n is the number of points in the semivariogram (P in our case), p is the number of parameters in the models provided in Two parameters are considered in order to determine which is the best semivariogram model to fit the available set of data: (a) the mean square error (MSE) between the EV (on (AIC) , which don (AIC) . The MSEP, in this example there are L values, the spherical model offers the best fitting for every P. The MSE and AIC results for the asymmetric case are presented in Note that, for a given In this section, patterns of vehicles’ positions with available REM values that provide the best REM reconstruction are first obtained for the scenario parameters and selected semivariogram models of P values ranging between 3 and 9. For the sake of generality, the simulations were performed considering the averaged received power . As previously indicated, for a given number of available REM values to perform the interpolation (P) among P value and each possible combination, the MSE is given by:The REM reconstruction capability of OK in the symmetric and asymmetric scenarios was evaluated with the aim of establishing optimal patterns of vehicles’ positions for Recall that P. The selected vehicle positions are highlighted in blue. Recall that results for the OK in the symmetric scenario were obtained with the spherical model for the semivariogram, whereas the Gaussian model is used in the asymmetric case. It is worth noting that the minimum MSE was also achieved by considering the mirrored patterns. It can be observed that the selected vehicle pattern varied depending on the scenario (symmetric/asymmetric) and inter-vehicle distance value. Comparing first the results in the symmetric scenario, at the top of P always contained the same vehicles selected for P to include the same vehicles selected for D) for this parameter. In particular, D, which generated totally uncorrelated shadowing samples between consecutive vehicle positions, to In this evaluation, the field value was generated following the model from Equation , where ldered in . The shaPrior art has already justified the advantages of OK interpolation with respect to nearest neighbor, inverse distance weighting, natural neighbor and thin plate splines approximations . In these evaluations the parameter B is set to 8 bits, i.e., 1 byte, which allows to represent up to 256 different quantified power values.The worst-case scenario to carry out the reconstruction is considered in order to narrow down the alternatives in the cost evaluation, that is, only quations  and 8)  P=3 REM N, the distance contributions by vehicles from 1 to N in the symmetric setup, but the remaining half of vehicles in the asymmetric case contribute with double distances with respect to the symmetric case.L), the results show that it had a higher impact on the distributed scheme, showing a constant cost gap of more than an order of magnitude for all numbers of vehicles. This result is reasonable, as the distance used for the cost estimation is straightforwardly related to this parameter. It can be further observed that the communication costs of the distributed approach were substantially lower than those calculated for both centralized schemes, despite the fact that the distributed approach exchanged a larger number of messages . TherefN messages), while, in the proposed approach, both in the centralized and distributed architectures, the BS sent only N messages). This equation can also straightforwardly provide the cost of transmitting the pilot messages to only a subset of P vehicles.It has to be noted that the costs in Equation  directlyN pilots in the conventional scheme is P pilots in the proposed approach was N and P pilots were Let us assume the values This work proposes the use of radio environment map (REM) reconstruction techniques to reduce the control information dedicated to the channel acquisition stage in platoon-based cellular vehicle to anything (V2X) communications. Assuming that a minimum number of REM values are available at a subset of the platoon vehicles, Ordinary Kriging (OK) spatial interpolation is then applied to reconstruct the values in the remaining ones. In a first step, different semivariogram fitting functions are evaluated. It is observed that the semivariogram fitting is sensitive to the relative positions between the BS and the platoon vehicles, which requires to consider two different evaluation scenarios separately, here called as symmetric and asymmetric. The fitting results conclude that a spherical model is more suitable in the symmetric scenario, whereas a Gaussian model provides the best fitting in the asymmetric case. This conclusion reinforces the need to carefully perform the semivariogram modeling step when OK is applied as a spatial interpolation technique, and it even paves the way for a dynamic and adaptive semivariogram modeling.After selecting the proper semivariogram fitting, results on the trade-off between REM reconstruction accuracy and signaling reduction are provided. It is shown that the accuracy is highly affected by the selected vehicle positions with available REM values, leading to different optimum vehicle positions’ patterns for the symmetric and asymmetric scenarios. The general trend for these optimum patterns, as the number of available REM values increases, is to include the values for the first and last platoon vehicles, together with an increasing number of available samples in the central area.The OK technique has been later compared to interpolation based on cubic Hermite polynomials (Pchip) in terms of reconstruction accuracy, showing OK superior results at low to medium shadowing correlation distances with the minimum number of available samples. At high correlation distances, both techniques achieve very similar reconstruction results with negligible MSE. The OK technique is also more robust to selecting suboptimum vehicle patterns, as justified by its bounded average MSE values.Finally, a communication cost evaluation related to REM reconstruction in centralized and distributed architectures is provided, showing that the centralized scheme in the asymmetric scenario involves the highest costs. Considering also the cost of initial pilot transmissions from the BS in the analysis, it is observed that, for The work presented in this exploratory paper paves the way towards enabling advanced physical-layer functionalities for the platoon V2X scenario. More precisely, two particular use cases are envisaged by the authors of this paper: mobile relays (where the entire platoon would cooperate with the base station to improve the communication link of a poor coverage vehicle outside the platoon); and intra-platoon relaying, where platoon vehicles with good quality channels would act as relays for platoon vehicles with low quality channels. To this end, our future work will address the need to include time effects via stochastic modeling of the platoon location, as well as exploring the capability of advanced forms of Kriging such as Regression Kriging. A more complete analysis of the signaling reduction versus performance trade-off will be also carried out through system-level evaluations.


Tracking moving masses in several degrees of freedom with high precision and large dynamic range is a central aspect in many current and future gravitational physics experiments. Laser interferometers have been established as one of the tools of choice for such measurement schemes. Using sinusoidal phase modulation homodyne interferometry allows a drastic reduction of the complexity of the optical setup, a key limitation of multi-channel interferometry. By shifting the complexity of the setup to the signal processing stage, these methods enable devices with a size and weight not feasible using conventional techniques. In this paper we present the design of a novel sensor topology based on deep frequency modulation interferometry: the self-referenced single-element dual-interferometer (SEDI) inertial sensor, which takes simplification one step further by accommodating two interferometers in one optic. Using a combination of computer models and analytical methods we show that an inertial sensor with sub-picometer precision for frequencies above 10 mHz, in a package of a few cubic inches, seems feasible with our approach. Moreover we show that by combining two of these devices it is possible to reach sub-picometer precision down to 2 mHz. In combination with the given compactness, this makes the SEDI sensor a promising approach for applications in high precision inertial sensing for both next-generation space-based gravity missions employing drag-free control, and ground-based experiments employing inertial isolation systems with optical readout. Precision interferometry with a dynamic range over multiple fringes is the core metrology technique employed in space-based detectors, such as the Laser Interferometer Space Antenna (LISA) , to measStandard two-beam interferometers have an operating range that is typically less than a quarter of a wavelength of pathlength difference. To increase the sensing range over many fringes, several techniques exist, such as homodyne quadrature interferometry  or hetererometry ,11.In DFM, a strong frequency modulation is applied to the laser input beam in an unequal arm-length interferometer. This modulation is embedded in the output signal in the form of components at multiple higher harmonics of the modulation frequency. The signal phase reallocates the complex amplitudes of these components in a predictable manner, which allows the extraction of the phase in real time or in post-processing by fitting the complex amplitudes of the modulation harmonics using, e.g., a Levenberg–Marquardt (least-squares) routine. This scheme requires fewer optical components, allowing for compact optical layouts or even single-element interferometers .As with any interferometer with arms of unequal length, laser frequency noise is converted into phase (and displacement) readout noise. Typically, in order to reach sub-picometer precision, interferometric inertial sensors rely on using pre-stabilized lasers, which adds to their complexity and cost. Previous DFM-based inertial sensors  made useIn C is the interferometric contrast or fringe visibility. The amplitude and phase can be read out via an in-phase/quadrature (I/Q) demodulator phasemeter [There are several techniques to increase the working range of two beam interferometers . For exaasemeter  applied However, the preparation of such laser beams with a frequency offset is not trivial and requires complex optics and electronics, and it is therefore not ideal for scaling to multi-DOF test mass (TM) read out. Meanwhile, optical fibers offer the most convenient way to deliver laser beams, but the length fluctuations of fibers can adversely affect phase measurements. Several techniques can be used to cancel fiber-induced phase noise, such as using an offset phase-locked loop  or an ac is the speed of light and N harmonics of the modulation frequency before being low-pass filtered. The resulting demodulated signal for each harmonic is given by the quadrature k, m, By applying a strong sinusoidal frequency modulation to the laser input of an unequal arm-length interferometer, with modulation frequency the form (2)Pout∝m measurement, which encodes the delay in light travel time between the interferometer arms. This measurement can be performed, e.g., by making a separate measurement of the frequency modulation depth m of m stability a control system applies a feedback signal to the laser controller acting on Apart from providing a high resolution and high dynamic range displacement measurement through the readout of the interferometric phase on index .DFM interferometry has been implemented previously on a single-element interferometer consisting of a custom-made triangular prism capable of sensing the motion of a test mass with sub-picometer precision . The smaFor the next generation of these devices, we incorporate both the inertial sensor and the reference interferometer in the same optic. This is made possible by a custom-design prism . Using oThere are many possible prism geometries capable of accommodating two unequal arm-length interferometers. We settle for a heptagonal prism with three main optical surfaces (c is the speed of light); and the m, as described at the end of The reference interferometer serves two purposes. First, it is used to compensate the very slow laser frequency drift by feeding back a control signal to the source. Secondly, it is used to remove the coupling of the remaining laser frequency noise from the TM IFO measurements, which appears as an unavoidable source of noise due to the unequal arm-length. The latter is done by combining the differential phase measurements of both interferometers in post-processing,With frequency noise suppressed by combining the signals from the TM and reference interferometers, the main noise sources are thermal , electronic  and optical  in nature. All of these sources are investigated in To reach sufficient modulation depth in centimeter-scale setups such as SEDI, the frequency modulation applied to the laser beam must be at the GHz level, which can make the search for a suitable laser source slightly challenging. We have opted for the commercially available 1064.5 nm external cavity diode laser Vortex Plus TLB 6821 , which we have verified experimentally to provide sufficient modulation strength for our purpose. The photodiodes are based in InGaAs with a small active area diameter of 0.5 mm to achieve high bandwidth and interferometric contrast, and a trans-impedance amplifier is applied to each photocurrent signal channel. The signals are subsequently digitized using a data acquisition system with a sample rate of 250 kHz, and the digital signals are demodulated by a software phasemeter that decimates the data rate down to 100 Hz and implements the non-linear fit algorithm or Kalman filter.For reaching displacement sensitivities on the order of .g., see ). Beams A disadvantage of any experiment using complex optical elements is dealing with manufacturing tolerances and imperfections. For example, relative alignment errors between the three optical surfaces of the OH can cause a bad overlap between the interferometer arms and lead to poor interferometric contrast. Similarly, the perpendicularity of the optical surfaces with respect to the base of the prism is essential to maintain both interferometers in-plane, as small deviations from such perpendicularity can cause the beams to veer off-plane significantly.s is the macroscopic accumulated optical pathlength difference during beam propagation through the setup  , and in rometers .The nominal parameters used in the simulation are listed in the An automatic beam tracing routine is used to propagate the beams within the optical system formed by the fiber injectors, the OH and the QPDs . We intrA ghost beam having perfect overlap with the nominal beam and having a power above nt level . Hence, loor see . This opTo analyze the sensitivity of the detector to manufacturing tolerances of the prism, we inject different types of geometrical errors into the OH model. Among the geometrical parameters that are critical to the performance of the device, we distinguish between two types: relative alignment errors between the optical surfaces, parameterized by angles α and γ a; and deα and γ b. The foIn the ut plane . We intrut plane . Hence, On the other hand, manufacturing imperfections affecting the perpendicularity of the optical surfaces with respect to the base of the prism are more difficult to compensate for. The input beam couplers are able to introduce small vertical beam angles, as well as small vertical beam shifts. Typically, however, this is avoided at all costs, since it requires rotating the lens held in the fiber coupler assembly, and therefore introduces astigmatism; it also tends to introduce strong couplings between some of the DOFs of the fiber coupler which are very difficult to control during construction. The in-plane interferometer design therefore takes priority, and we set a tolerance specification on the perpendicularity of the optical surfaces based on the degradation of the interferometric contrast that we deem allowable.To properly characterize this effect, we perform a Monte Carlo simulation where we inject errors in the form of deviations from perpendicularity into all three optical surfaces following a uniform distribution, and compute the resulting interferometric signals . We findHaving determined the feasibility of manufacturing, we turn our attention to the main noise sources of the SEDI inertial sensor. The largest entry in the noise budget, that emerges from having an interferometer of unequal arm lengths, is the laser frequency noise. This source of noise is mitigated by the dual interferometer configuration (see Equation ). FigureThe second entry in the noise budget is thermal noise, which can be very severe in optical setups employing large continuous optics like the SEDI sensor. Thermal noise is generally compound of two effects: mechanical deformation due to thermal expansion and refractive index variations. The latter is specially relevant in this experiment due to the interferometers’ long arms having significant intra-prism optical pathlengh, as listed in We also calculate the displacement noise stemming from the angular and translational jitter noise of the fiber injector optical subassemblies (FIOS), which makes the next entry in the noise budget. Lastly, we also obtain the coupling between the angular motion of the test mass and the displacement measured by the sensor, or tilt-to-length (TTL) coupling, which takes the value of As the experiment is scaled, however, we may take advantage of signal combinations with a lower total noise floor. For example, by probing a test mass from opposite sides as depicted in On the other hand, the similarity between the temperature fluctuations in the left and right OHs is in principle unknown, making thermal noise a potentially limiting noise source. Expanding the thermal noise coupling term from Equation  yields. Since the details of this mechanism are still unknown, we consider a worst-case scenario in which all of the prism’s base surface area is perfectly coupled to the surrounding environment. A spectrum of random temperature fluctuations, relaxed towards lower frequencies, is applied uniformly to the base of the prism, and the resulting temperature response is measured throughout the prism.The transfer function of temperature fluctuations is computed as a volume average for the whole prism, as well as locally along the interferometer arms. The former is used to compute the spectrum of displacement noise due to the thermal expansion of the prism, and the latter is used to compute the spectrum of displacement noise due to the local refractive index change. We find that under these assumptions the temperature fluctuations in both interferometers are fully correlated within the frequency band of interest. In the interest of generality, however, we also analyze the situation where the correlation in temperature noise between TM IFO and Ref IFO follows an arbitrary shape, as we report in The final performance of the SEDI inertial sensor , is derived for a single OH and the dual-OH setup of We found that, due to these imperfections, the test mass TTL coupling could increase to the picometer level, and imperfections causing deviations from the nominal geometry of the kind that can be parameterized by γ see  were speThe final results, including inherent imperfections in the construction, are shown in We presented the design of the SEDI inertial sensor that is being built at the Albert-Einstein-Institute to measure test mass displacements with a precision greater than Due to the intrinsic minimalism of this optical setup, this device can be integrated into an optical readout platform that features multiple optical heads and is able to interrogate several degrees of freedom of a mechanical system. We demonstrate how two of these optical heads can work together to suppress residual thermal noise and achieve sub-picometer precision above 2 mHz, and up to the The perpendicularity of the three optical surfaces has been identified as the most critical manufacturing specification. This parameter has a large impact on the resulting interferometric contrast. This is a common issue in interferometers employing a single optical element. It was found that using smaller beams helps increase the likelihood of obtaining a good contrast from the manufactured prism. Another potential limitation of the device is that assembly requires accurate relative positioning of the fiber injectors and optical head in order to take full advantage of the stray light noise suppression strategy, and adjusting each fiber injector is a tedious job requiring a specialist with ample experience. An alternative to using two fiber injectors is using a fiber injector and a beamsplitter and mirror, which could simplify the assembly process at the expense of having to deal with additional ghost beams from the added beamsplitter.The potential applications of this new sensor cover many areas of science and technology. In experimental gravitational physics, and notably in next-generation space-based gravity missions, the SEDI sensor offers a scalable solution for multi-channel test mass readout. Satellites employing drag-free control to trail a free-floating test mass in order to follow an undisturbed geodesic require measuring the motion of said test mass in several degrees of freedom with high precision and large dynamic range. The reduced size and weight of the SEDI sensor means that several optical heads can be applied to offer increased sensitivity and redundancy in these measurements, making it a suitable candidate for these applications.The same measurement principle applies to inertial isolation systems on the ground, where the inertial stability of a reference mass can be transferred to an actively controlled platform through a high-gain feedback system. This is a key resource in many experiments that require suppression of seismic noise, notably in gravitational-wave detection, where the seismic activity at low frequency presents an important impediment to the discovery potential of ground-based detectors.Beyond space-based gravity missions or ground-based gravitational-wave detection experiments, the SEDI inertial sensor can find applications in fields across multiple disciplines. For instance, the first planned application of the sensor is its integration into the torsion balance facility being developed at the same institute. The inertial member of the torsion balance is suspended from a tungsten fiber and consists of a symmetric crossbar with cubic test masses at the end of each arm. Two SEDI sensors will be applied to opposite sides of one of the cubic test masses in a similar fashion to the case that is reported in this article . This wi


Inductive measurement of magnetic fields is a diagnostic technique widely used in several scientific fields, such as magnetically confined fusion, plasma thrusters and particle accelerators, where real time control and detailed characterization of physics phenomena are required. The accuracy of the measured data strongly influences the machine controllability and the scientific results. In the framework of the assembly modifications of the RFX-mod experiment, a complete renew and improvement of the magnetic diagnostic system, from the probes moved inside the vacuum vessel to the integrator modules, has been carried out. In this paper, the whole system making up the magnetic diagnostics is described, following the acquisition chain from the probe to the streamed data and illustrating the requirements and conflicting limitations which affect the different components, in order to provide a comprehensive overview useful for an integrated design of any new systems. The characterization of a prototypical implementation of the whole acquisition chain is presented, focusing on the flexible ADC architecture adopted for providing a purely numerical signal integration, highlighting the advantages that this technology offers in terms of flexibility, compactness and cost effectiveness, along with the limitations found in existing implementation in terms of ADC noise characteristics and their possible solutions. Magnetic field measurements are extensively used in the domain of magnetically confined fusion ,2,3, plaMany papers address inductive sensors and their applications . In thisThe paper is organized as follows. In Inductive sensors are a widely used means of measuring magnetic fields and related quantities, having the important advantages to be linear up to the range of hundreds of kHz and are easily calibrated accurately. These consist of different forms of conducting loops, each measuring the voltage induced by a changing magnetic field. Inductive sensors are simple and inexpensive, allowing many channels to be used for spatially detailed measurements. Despite the wide variety of applications, all of these measurements are based on the principle of a simple inductive loop. Essentially, three different kind of inductive sensors can be distinguished. Generally, the word “loop” denotes a large size probe made of a small number of turns for magnetic flux or averaged field measurement. Pick-up or Mirnov coils are small size coils with a large number of turns for localized magnetic field measurements. The so-called Rogowski coils are part of the inductive sensor category as well, and they consist of a particular winding around a closed path allowing the measurement of currents flowing inside that path.V at the terminals of a n turn conducting loop is equal to the rate of change of the magnetic flux According to Faraday’s law, the voltage difference V from the coil with the known initial conditions  the higher the coil sensitivity. However, the optimization of the coil performance certainly is not a trivial process, characterized by a trade-off among several conflicting requirements, such as sensitivity, frequency spectrum, spatial and time resolution, and limiting constraints, such as available room, distances to be covered by transmission lines, etc.For example, magnetic sensors intended for both plasma active control and magneto- hydrodynamics (MHD) study need to be installed inside the vacuum chamber in order to allow measurements of actual magnetic field fluctuations. This will necessarily impose limitation on the coil size, as well as limitation on the allowed materials. A single system capable of meeting both the purposes needs a high time resolution and a broad frequency range, from 0 to 100s kHz (very high-frequency phenomena necessarily require ad hoc probes). As examined in depth in Magnetic probe signals might require to be pre-amplified near the machine before the long transmission line. Then, they are either amplified to be used as the time derivative of the field or integrated to obtain the field itself. Some channels can also require to be attenuated in order to study fast events which would lead to saturation of amplifiers or ADCs. Signals are generally passed through a low pass passive filter along the acquisition chain as well. Each of these elements, represented in N, its inductance l is its axial length and l, cross dimensions a and b and wire diameter d [d and l, taking as a reference the inductance of a circular coil r, the following approximate formula is used:Magnetic pickup coils are used to detect magnetic phenomena with frequencies ranging from a few Hz to many MHz. However, size and shape affect the frequency response of the probe. While the effective area ameter d . At consThe rectangular coil formula instead is:C of the cable connecting the coil to the termination will also help to maximize the bandwidth.A possible way to improve sensitivity without limiting the bandwidth is to increase the actual cross section of the coil The dynamic range requirements for the signal acquisition system demands a careful evaluation of both the minimum detectable and the maximum expected signal, in particular when its numerical integration is considered. The maximum level of the expected signals has to be somehow estimated and will define in particular the filter and attenuator design. On the other hand, the minimum signal requirement involves the sensitivity to slowly changing magnetic fields at low intensity and thus constrains in particular the coil effective area and the noise rejection of the system and possible amplifiers. The minimum required signal amplitude implies an effective probe area typically of a few hundred square centimeters, which can also allow bandwidth on the order of some hundreds of kHz. High bandwidth measurements of fast phenomena are obtained by high frequency pick up coils usually based on a special design that guarantees high bandwidth, typically higher than 300 kHz.In addition, the magnetic probe size and shape are in general a compromise between the required effective area of the winding and the available space. Indeed, for several reasons, the sensors should be as close as possible to the magnetic source which often means in a vacuum, narrow and harsh environment. Highly compact, radiation hard magnetic probes have been built, for example, by employing a thick film technology , to builIt is worth noting that the electrical parameters of the probe are temperature dependent. Indeed, the coil inductance tends to increase with increased temperature, as well as the cable resistance, because of the thermal expansion of the copper which the coil cable is made of. The design of probes for high temperature operation  must take particular care in the selected material, especially in terms of relative thermal expansion, which may significantly change the effective area of the probe. In particular, the material adopted for the former which the winding is wrapped around has to show a similar thermal expansion to that of the adopted cable, since repeated relative expansions lead to a change in the electrical characteristics of the coil and the consequent loss of calibration .A further ploy in magnetic probe design is the choice of an even number of layers in order to minimize the collecting area in perpendicular directions with respect to the coil axis and therefore the cross talk with perpendicular magnetic fields.The ideal circuit model of an air-core inductive sensor consists of a linear inductor with self-inductance Equation . By assuEquation  implies f. This transfer function is given byThe frequency response of a real magnetic probe already in a frequency range up to few tens of kHz cannot be reduced to a simple first-order transfer function. An equivalent circuit able to reproduce a typical measured frequency response is sketched in This transfer function displays a resonance at M between the coil and the shield  is considered.The shielding effect introduced by a potential protective conducting container enclosing the coil or by the cable sheath when the coil is wound with a coaxial cable can be modeled by a magnetically coupled circuit with inductance By neglecting the self inductance Equation  is reducThe frequency response amplitude of an ideal and a real (shielded and non-shielded) inductive sensor is presented in The above is valid for an ideal measurement of the voltage on an open-ended coil sensor or for the voltage measurement across an infinitely large impedance put between the coil terminals. Instead, in real application, no matter how large the input impedance of the amplifier or digitizer that follows the coil, this will inevitably be of finite value. Besides, as clarified below, the sensor coil is often loaded by a terminating impedance see  which isThe transmission line generally connects the probes directly to the electronics input stage. It usually consists of a thin twisted pair cable, possibly with individual pair shielding. The line has a variable length which can be of some tens to about a hundred meters and has a characteristic impedance on the order of a hundred ohms. As already mentioned, due to the harsh operating conditions the probes undergo inside the vacuum chamber, different cable technologies are adopted for the cable sections internal and external to the chamber, usually characterized by different electrical properties. In some cases the distance between the chamber and the processing unit may be covered with multiple cables as well, again with various electrical properties. Generally, at high frequencies the inhomogeneity of the cables might become important due to wave propagation and reflection effects.As sketched in ℓ is the distance between the conductors and d is the diameter of the conductor. An alternative formula is based on the knowledge of the inductance and capacitance of the line:The characteristic transmission line impedance is expressed byAs already stated, typical values are Assuming a frequency-invariant transmission line per unit length inductance acitance . The ana R/L=G/C  and thisC are reported on the top and on the bottom, respectively.Therefore, by considering purely resistive terminating and electronics impedance ectively :10)|H*||H*|RX anIn general, the effect of the transmission line is to downshift the resonance of the coil from the frequency observed in the absence of the transmission line. For When the probe and the connections are defined, a matching/filtering circuit must be designed to guarantee the minimum attenuation for the acquisition band signals and, on the contrary, the maximum attenuation for the resonance peaks of the probe and for the higher frequency out-of-band signals. The simplest solution would be loading the line with a resistance of value equal to that of the characteristic line impedance .Analog integrators based on a pre-compensation circuit: The output voltage is measured before each pulse during a time interval when no excitation is applied, sampled and held by analog or digital means, and then looped back to the amplifier during the pulse ,21.Analog or hybrid analog–digital implementations measure both the signal and the drift, alternatively ,23 or coThe measured signal is chopped early in the data acquisition chain and the digital de-chopping operation ideally removes any DC offset voltages introduced anywhere along the measurement chain ,26,27.First, a careful choice of the input electronics is required to mitigate the root of the problem. Then, different strategies and precautions can be adopted. In particular, there are three state-of-the-art integrator concepts developed for magnetic field measurements for real-time control purposes:Both the last two techniques imply an expensive design and a complex implementation that are not compatible with a very large number of sensors to be integrated. In addition, only offset sources internal to the integrator are taken into account, while external ones remain in the signal.A feedback circuit that adjusts the input offset to minimize the output voltage is a straightforward means for compensating the drift error. The feedback circuit is activated between experiments, when the sensor gives no significant signal, while it is disabled during the experiment and the latest measured offset is maintained by an analog or digital sample-and-hold circuit. However, this is based on two assumptions: the temperature in the integrator rack does not change significantly during the time of an experiment, so that the compensation value held before the start is relevant for the entire pulse duration, and the compensation value measured before the pulse itself remains stable during the pulse. This kind of integrator has proved to be able to achieve output drifts of few mV in 1000-s pulses ,21. SuchSeveral schemes adopting the digital technology have been implemented, hybrid solutions in combination with analog circuits or pure digital implementations, in order to go beyond the analog limitations. Analog integration with a digital feedback circuit gets rid of the changes in the compensation caused by capacitor leakage current over time. For instance, in , two anaThe integrator droop is instead completely eliminated by the full digital integration. In the basic scheme, the input is periodically sampled and the digitized signal is then numerically integrated. However, digitization of the raw sensor signal has drawbacks as well. Indeed, new errors are introduced by the finite time resolution, the finite bit resolution and the voltage saturation of the ADC. Significant errors can result in the integrated signal during transient events with timescales comparable to the sampling interval and then persist throughout the pulse. Time resolution errors can be mitigated by choosing a sampling rate fast enough with respect to the phenomena to be observed. Voltage saturation of the ADC may also occur in case of fast events which tends to produce large To, in principle, completely eliminate the integrator drift, the ADC input can be rapidly chopped at high frequency alternating between the filtered sensor loop and a matched dummy load  or betweN is the cycle number. At a fixed sampling rate, this means a drift error growing with If the errors introduced by the finite resolution of the ADC are measured and corrected periodically during the pulse, they can be assumed uncorrelated from one measurement cycle to the next. When integrated, the resulting accumulated error is proportional to urements . A digitIt is clear that digital technology schemes can have several advantages, in particular related to long lasting applications, but an accurate digital integration of the coil sensor signal requires a careful choice of the integration period, sampling frequency and triggering time, especially in the presence of complex and unknown frequency content in the processed signal. Moreover, good quality digital data acquisition (DAQ) components are typically very expensive when high dynamic, wide bandwidth and high precision are required. Furthermore, the injection of high-frequency noise from the chopping, as well as the loss of bandwidth and phase lag due to the necessary filtering affect this integration method.Ensuring the highest signal to-noise ratio of the acquired signal is essential in order to perform correct integration. Noise is an unwanted signal disturbance that can cause important variations in the acquired data, even making them completely unusable. In particular, it is a critical parameter in the integration process since, in carrying out the operation, its effects add up and makes an important distortion of the resulting signal, especially if the acquisition continues for several seconds. Many sources of noise affect the signal from a pickup coil, such as magnetic and electrostatic pickup from imperfect shielding, inductive common mode signals from possible extended cabling, electronic noise, thermal noise, radiation induced electromotive force (RIEMF), etc. These generally add up in a background incoherent white noise, which is a random signal having equal intensity at almost all frequencies, therefore having constant power spectral density. The In Magnetic confined fusion machines require real-time feedback control systems characterized by a response time of the order of 1 ms for both protection needs and the study of fast physics phenomena. RFX-mod stands out among other magnetically confined plasma machines for its advanced and flexible systems for active feedback MHD control, based on a network of 192 independently driven saddle coils , a state-of-the-art digital real-time control system and a comprehensive set of diagnostics. This makes RFX-mod an excellent test bench where challenging regimes in both Reversed Filed Pinch (RFP) and Tokamak configurations can be achieved. RFP plasmas with a dominant helical shape, opening a natural connection to the stellarator geometry, and stable low q Tokamak plasmas have been obtained thanks to the interplay of the extended magnetic measurement system and the non-axisymmetric coils in counteracting the growth of the plasma instability. The innovative and powerful feature of RFX-mod is the capability of operating under challenging boundary conditions: many input signals, many modes to control and fast response required.As anticipated in previous paragraphs, an upgrade of RFX-mod presently being implemented foresees a modification of the machine assembly see  based onThe RFX-mod2 assembly modifications are an opportunity for the complete renewal and improvement of the magnetic diagnostic system, from the probes moved inside the vacuum vessel to the integrator modules. The greatly increased number of magnetic sensors  can have large effects on the plasma behavior. The ability to detect these features is thus needed for example to allow the characterization of the structure of these small error field components and the correction of misalignments of the sensors.As the minimum detectable reference signal, we choose a trapezoidal 1 mT field with a slow trapezoidal evolution: 1 s ramp-up, 1 s steady state and 1 s ramp-down .To build a model of the acquisition chain, the electrical parameters of a coil prototype , as shown in The three coils of the prototypes have been tested with an impedance analyzer HP4198A by 400 automatic measurements of the impedance between 100 Hz and 10 MHz. The measured parameters of the equivalent RLC circuit for the three windings are reported in The twisted coil cable is used without transition up to the vacuum feed-through, covering a distance between 2 and 3 m. A characteristic impedance between 150 and 200 A passive snubber filter with two branches and related cut-off frequencies A passive attenuator has been adopted to adapt the output voltage from the filter to the ADC input. It consists of a simple resistive divider with the addition of a capacitor in parallel to the grounded resistance in order to filter out the remaining spurious voltage peaks. The resistor values have been chosen according to the ADC dynamic range, considering the requirement of being able to distinguish 1 mT/s which translate to 0.02 mV with a 200 cmAs a guiding reference case, the performance in terms of noise level and integrator drift of the existing conditioning system of RFX-mod  is shownThe noise characteristic of a precision ADC  has been measured by taking advantage of the existing modules of the ATCA-MIMO system ,30; the The module has been interfaced with a readily available Red Pitaya board , prepariThe frequency domain analysis  shows twn steps For short time integration, the noise spectrum involved is in the high frequency range, i.e., dominated by the white noise. In this case, the numerical integration of a sampled sequence In the case of RFX-mod2 signals, the integration time lasts several seconds and the desired frequency range extends well below the typical An estimation of the expected output with the reference signal of As a final proof of concept, the complete signal acquisition chain has been deployed in a test bench environment with the actual prototype of the probes. The test was carried out with a solenoid connected to a laboratory power supply. The current on the solenoid was modified by manually changing the power supply settings.The direct acquired signal is reported in The existing legacy architecture of RFX-mod ,32, wherAs mentioned in e plasma ,34.The basic architecture of the proposed system resembles that of the ATCA-MIMO , originaWe are planning to switch to a slightly different and more modern architecture, maintaining the basic feature of the single isolated ADC module for each channel, which is expected to highly improve the noise immunity. The system management is performed through a commercially available System-On-Module , integrating both FPGA and CPU cores, which allows to set-up a self-contained acquisition 6U eurocard board, managing up to eight channels each see .This solution easily provides both the autonomous local storage for transient recording function, as well as the ability to send a real-time data stream of decimated and integrated signals to the control servers through standard gigabit Ethernet interface. The use of a configurable FPGA is intended to handle ADC conversion and provide a set of on-line functions directly performed at the FPGA logic level, including the numeric integration in real-time, the recording of the derivative signal The synchronization of the system can be handled directly by extracting the timing information from a variety of the central time sources, such as an external timing highway or by using the PTP protocol through the Ethernet interface.the management of a circular data buffer and the DMA transfer in RAM of pre and post trigger samples after the trigger has been received;anti-aliasing filtering and subsequent sub-sampling of the samples to be streamed, where the resulting samples are enqueued in a FIFO accessed by the processor;digital integration for deriving magnetic field measurements from the coil signals (it is worth noting that in this case a single ADC stage will generate two ADC channels);ROI detection in case ADC triggers are derived from the signal itself ; andclock and trigger extraction in the case a highway signal is provided by the timing system, encoding both clock and triggers.The time critical functions carried out by the FPGA in this context are:the management of the configuration setting, received via TCP/IP or HTTP, where the processor validates the configuration and writes the identified registers in the FPGA;off-line data readout of acquired samples in transient recording and communication via TCP/IP with the central data acquisition system; andnetwork data streaming of sub-sampled data read from the FIFO and sent in UDP packets to the active plasma control system.The less critical functions that will be carried out by the processor unit are:The flexibility provided by the configurable FPGA also allows the inclusion of more sophisticated triggering mechanisms and a deeper integration with the timing systems. An example is given by the acquisition of fast transients requiring high speed sampling only in a given, dynamic ROI. This technique has been applied to NIO experiment , a smallMany experimental applications involve the study and/or control of magnetic fields whose range and frequency spectra demand the use of inductive sensors for their characterization. Inductive sensors indeed have the important advantages of robustness, operation and design simplicity, wide frequency bandwidth and large dynamics. However, inductive probes exhibit some shortcomings as well: a probe fixed in space can detect only time varying magnetic fields, although with a frequency down to mHz range, and, since the output signal depends on the time derivative of the magnetic field, it is frequency dependent. This in turn requires the integration of the sensor output with the possible introduction of additional errors in the signal processing and evidently the accuracy of the measured data strongly influences the machine controllability and the scientific results.The probes of the new magnetic measurement system of the upgraded RFX-mod2 experiment have been moved inside the vacuum vessel, adopting materials suitable for high temperature applications presenting low outgassing rate and similar thermal expansion coefficients for both the winding cable and the reel. The careful design of the coils allowed obtaining a high frequency band despite the stringent limitations in terms of available room. The probe-transmission line system has been characterized and the associated filters and attenuator accordingly designed. The complete replacement of existing analog integrators with direct numerical integration of the digitally acquired signal has been chosen in view of a significant reduction of the hardware complexity.The architecture of a new flexible ADC device has been presented, aimed at reducing the number of actual ADC channels by integrating high speed transient recording and data streaming for real-time plasma control. In addition, the same ADC will be used to acquire both magnetic fields and their time derivatives, providing FPGA based digital integration for the derivation of the former, providing a significant cost reduction with respect to the duplication of devices for transient recording and streaming.A complete acquisition chain has been built, testing the frequency response and dynamic range of the system in bench tests. A complete isolated ADC module has been interfaced to an embedded SoC DAQ board, exploiting a Xilinx FPGA real-time numerical elaboration, which also allows the inclusion of more sophisticated triggering mechanisms and a deeper integration with the timing systems. The feasibility of the numerical integration approach to recover the RFX magnetic field has been proved with an experimental testbed, useful to evaluate the ADC noise impact on the integration results as well. In conclusion, it has been shown that a direct digital integration appears feasible, even if it seems to require the state-of-the-art components to recover high dynamic range and wide frequency spectrum signals at the same time in a single channel. An accurate design of the input stage is mandatory; the management of the noise from the DC/DC converter is important; and the evaluation of the ADC characteristics must lead the choice of technology, matching the desired input dynamic range and the bandwidth attenuation . The need of high quality components has been shown to be related with the