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Four-view split-image fragment tracking in hypervelocity impact experiments
International Journal of Impact Engineering 135 (2020) 103405
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International Journal of Impact Engineering journal homepage: www.elsevier.com/locate/ijimpeng
Four-view split-image fragment tracking in hypervelocity impact experiments
T
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Erkai Watsona, , Nico Kunerta, Robin Putzara, Hans-Gerd Maasb, Stefan Hiermaiera a b
Fraunhofer Institute for High-Speed Dynamics, Ernst Mach-Institut, EMI, 79104 Freiburg, Germany Technische Universität Dresden, Institute of Photogrammetry and Remote Sensing, 01062 Dresden, Germany
A R T I C LE I N FO
A B S T R A C T
Keywords: Hypervelocity impact Fragmentation Particle tracking Velocity distribution Image splitting 3d measurement
Fragmentation is a significant phenomenon caused by hypervelocity impact and has applications in orbital debris and planetary impact research, among many others. In particular, the velocity distribution of fragments created by hypervelocity impact is not thoroughly understood. In this paper, we present an experimental setup and analysis method for tracking and measuring individual fragment velocities in 3D. The setup uses two synchronized high-speed cameras with split images, yielding four views, to record image sequences of the in-flight fragments. We analyze the image sequences by identifying fragments and their trajectories in each view, matching the fragments found in different views, and finally triangulating for their 3D positions. The result is a method able to measure fragments’ 3D velocities in the highly transient hypervelocity process.
1. Introduction
Velocimetry (PIV) and Particle Tracking Velocimetry (PTV) are two non-intrusive imaging techniques originally developed for experimental fluid dynamics, that have been used to measure the velocity of fragments in HVI experiments. PIV works with interrogation areas and uses convolution to find the motion vector of small areas in each image between frames [11]. In general, PIV is considered well suited to images with a high fragment density. In the realm of HVI, 3D PIV has been used to study crater formation in sand [12]. This technique is able to measure the flow-field of the ejected sand particles, but cannot resolve individual fragment velocities. Alternately, PTV identifies and tracks individual particles [13] and is therefore more suited to the study of HVI fragmentation of solids where the size of the fragment is also of interest. A combined 2D PIV/ PTV technique has been used to study HVI crater growth in sand, allowing the velocities and position of a small subset of sand grains to be measured [14]. In a later paper, the method was extended to 3D using four views to find the 3D locations of individual sand particles and using PIV to help link particles between two frames to find their velocities [15]. In other research, a PTV technique has been applied to HVI experiments in geological materials in 2D, where both velocities and sizes of the ejected fragments are determined [16,17]. A similar 2D PTV algorithm was applied to the study of debris cloud formations in HVI of satellite shields [18]. In these studies, a robust particle tracking is achieved by taking advantage of the constant velocities of the ejected fragments to help filter out outliers. Particle tracking in 3D with two
Hypervelocity impacts (HVI) often cause significant fragmentation to occur in both target and projectile materials. The study of fragmentation processes extends to numerous applications such as orbital debris or planetary impact. In orbital debris research, understanding the effects of HVI fragmentation, which can causes the break-up of large dense debris into thousands of smaller but still satellite-lethal fragments, is important to modeling the environment [1,2]. In planetary impact research, the correlation between fragment sizes and velocities for impacts on celestial bodies [3–5] or the momentum transfer enhancing effect that fragmentation and backward ejection of material have on celestial bodies and spacecraft [6] are still poorly understood. Fragmentation caused by HVI is challenging to study experimentally because of the highly transient nature of the process and the large number of fragments involved. Traditional HVI experiment instrumentation, such as high-speed cameras and radiographs, allow researchers to study morphological aspects of the debris cloud, like its shape or expansion velocities [7,8], but are not able to quantify the fragments or measure their individual velocities. High-speed images are often supplemented by witness plates or soft catchers which can provide insight into the composition of the ejected fragments and the spray angle of the debris [9,10], but also provide little time resolved data. Recent advances in high-speed camera technology have opened up new measurement methods to HVI experiments. Particle Image
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Corresponding author. E-mail address: [email protected] (E. Watson).
https://doi.org/10.1016/j.ijimpeng.2019.103405 Received 19 July 2019; Accepted 2 October 2019 Available online 03 October 2019 0734-743X/ © 2019 Elsevier Ltd. All rights reserved.
International Journal of Impact Engineering 135 (2020) 103405
E. Watson, et al.
Fig. 1. The experimental setup consists of two synchronized high-speed cameras. Both cameras have their images split into two views with the help of a mirror rig shown in Fig. 2A. This results in four separate views of the backward ejecta emanating from the target.
what is available in the high-speed cameras, and the aperture size is kept at a minimum, limited by the illumination requirements of the experiment. The effects of focal length and distance to the target counteract each other such that a larger focal length with a larger distance leads to a very similar DoF as a smaller focal length and closer distance. The end effect is that magnification must be sacrificed to increase DoF. This leads to a tradeoff between image magnification (and thus spatial resolution and accuracy) and DoF. As we would like to maximize the magnification of the high-speed images, we choose the minimum DoF needed which leads to a magnification with 0.4 mm/ pixel. Once the positions and setting of the cameras are determined, all cameras must be calibrated to determine their intrinsic and extrinsic parameters. The intrinsic parameters are the internal camera parameters such as focal length, principal point, and lens distortions, while the extrinsic parameters refer to the rotation and translation of each camera center with respect to the world coordinate system. We calibrate the cameras with a 2D pattern checkerboard pattern [21]. Camera calibration images are taken before and after each experiment, thereby allowing us to determine if there was any disruption of the setup. In each image, we set the pixels in the unused half to zero and treat each view as a virtual camera with its own calibration and intrinsic parameters. This gives the advantages of having the distortion model partly compensate for any mirror surface irregularities [22]. Because of large focal length of our cameras, we assume the principal point of each camera to be at the center of the image [23]. Radial and tangential distortion are corrected for with Brown's distortion model [24].
synchronized high-speed cameras was demonstrated by measuring the 3D velocities of aluminum debris cloud fragments by using a priori knowledge of the fragment trajectories [19]. In this paper, we present further developments of a 3D particle tracking technique for measuring the 3D fragment positions and velocities generated by HVI experiments. We improve on previous work, by developing experimental setups and algorithms that use high-speed images taken from up to four views to measure the fragments. Increasing the number of perspectives from two to four views allows more fragments to be correctly matched and triangulated from the low resolution and noisy images typical of high-speed recordings. 2. Experimental setup The experimental setup for multi-view fragment tracking involves high-speed cameras and backlit flash lighting to create shadowgraph images of the HVI fragments. An experimental setup with two highspeed cameras is shown in Fig. 1. Two Shimadzu high-speed cameras, capable of micro- to nanosecond exposure times and framerates of up to 10 million frames per second are synchronized and used to record the ejected fragments. In this paper, we will use one specific experiment to describe a method for measuring individual fragment velocities in a HVI experiment. The experiment involved the impact of a 3 mm aluminum sphere on a 5 mm thick CFRP plate at 7.2 km/s. The image sequence was taken at 250,000 fps with a field of view of approximately 70 × 100 mm in each view. The target chamber was evacuated to 120 mbar. The goal of this experiment was to measure the properties of the backward ejecta that is accelerated up-range from the CFRP target plate. Although 3D particle measurements with two views is possible, using three or four views greatly decreases the number of ambiguities that arise in stereo image matching of detected particles [20]. In order to increase the number of perspectives with a limited number of cameras, the images of each high-speed cameras is split using a custom built mirror rig shown in Fig. 2A, yielding four views from two cameras. One constraint in the image splitting setup is the need of a large Depth of Field (DoF), the distance about the plane of focus where objects appear acceptably sharp. A large DoF is needed to produce two completely separate images without having objects in one view overlap into the other view; that is, both the splitting mirrors and the target must be in focus. Fig. 2B and C show an example of different DoF and the effect on image overlap. Because the splitting mirrors must be placed outside the target chamber, a minimum DoF of 50 cm is required. The DoF is affected by the lens aperture, the focal length, the distance to the target, and the sensor size. Sensor size is fixed, defined by
3. Method The analysis of the multi-view high-speed images can be separated into three main parts: object detection, object tracking and multi-view correspondence establishment. After fragments are detected in the object detection step, two different strategies may be used for object tracking and correspondence establishment [25]: Object tracking in 2D image space followed by multi-view correspondence establishment of trajectories, or 3D object coordinate determination by multi-view correspondence establishment of detected objects, followed by tracking in 3D object space. In our approach, we chose to perform object tracking in the 2D image space because of the straight line trajectories followed by each fragments. Fig. 3 shows a set of raw images from the high-speed image sequences. These images will serves as inputs to the algorithm.
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International Journal of Impact Engineering 135 (2020) 103405
E. Watson, et al.
Fig. 2. A) Mirror rig for splitting an image into two views. B) and C) Split-images of a Siemens star showing the effect of Depth of Field on image overlap due to the splitting. In image B, a small Depth of Field (f/2.8) results in a large area of overlap, marked in red, where View 3 blurs with View 4. Increasing the Depth of Field in Image C (f/16) significantly decreases the overlap and increases the usable area of the two views.
vacuum in the target chamber experience only negligible aerodynamics drag forces, so their velocities remain essentially constant. Fragments also travel in a straight line due to the negligible effects of gravity at the short time scales of the experiment. These two assumptions are more formally addressed in [19]. The fact that fragments travel in straight lines allows us to take a trajectory based linking approach. We implement this by plotting all identified points from each of the four image sequences into a 3D-XYT space representing 2D space and time. Points in this XYT space that lie on a line represent the same fragment in different images traveling in a straight line and at constant velocity. To find these straight lines in the XYT space, we use a random sample consensus algorithm (RANSAC) [26]. As points forming straight lines are found, they are removed from the XYT space point cloud and saved, thereby reducing the search space and preventing repeated matches from being recorded. The RANSAC analysis is performed in parallel on a graphics-processing unit (GPU). A minority of the outputs of the RANSAC algorithm will be false matches that need to be filtered out. We filter the trajectories by examining their angle in the XYT space. All trajectories are expected to converge in one location in XYT, which represents the 2D launch location of the fragments and the launch time of the fragments. Trajectories that do not intersect this point, to within a certain
3.1. Object detection To identify the fragments in each image, we apply the following steps:
• Apply a top-hat filter to preserve intensity peaks and eliminate other features • Remove background pixels below given threshold • Apply Gaussian blur to remove small variations in intensity • Find all local maxima in the image • Apply Gaussian fit for subpixel accuracy These steps are applied to every frame of each image sequence, which results in a list of detected fragments with their 2D locations and times. 3.2. Object tracking Once fragments have been identified in each frame of the image sequence, they need to be tracked from frame to frame. We base our fragment tracking on the assumption that each fragment travels in a straight line and at a constant velocity. Fragments traveling through the
Fig. 3. High-speed images of the ejected fragments seen from two synchronized cameras and four different viewing angles. These images sequences will be used to measure the velocity of the recorded fragments. 3
International Journal of Impact Engineering 135 (2020) 103405
E. Watson, et al.
one of the black points in View 2 into View 3 and 4. Since only one point in View 2 actually corresponds to the point in View 1, only one of the transferred point should match the actual location of fragments in Views 3 and 4. A closer examination of View 4 in Fig. 4, shows that of the three transferred locations (line intersections), only one of them is close to the location of a fragment. (Note: the fourth line and intersection happened to lie outside the image). In View 3 of Fig. 4, we see that there are two transferred points that closely match an actual fragment locations, this causes an ambiguity. To determine the “best” corresponding fragment in the other views, we measure the distance between the found point and the transferred point (in this case in Views 3 and 4) and save it along with identifier of the fragment in the three views. Therefore, in the example of Fig. 4, the distances between each green point in View 3 and the nearest intersection would be saved together with the trajectory number of the red point and the black point in Views 1 and 2. The same is done for View 4. The process of finding correspondence candidates is repeated for every trajectory found in View 1. The results are sets of three trajectories (from three different views) that are assigned a score based on the distance between transferred point and detected point and number of instances that those trajectories are detected repeatedly in different image frames. The same set must be found a minimum of four frames and have a maximum distance of 5 pixels. A weighting factor is applied to the instance and distance parameters to assign each set a final score. The sets with the highest scores are chosen as corresponding trajectories. Fig. 5 shows a subset of the trajectories that were corresponded in three views. Due to the search method of starting in View 1 and using View 2 to transfer points into View 3 or 4, all trajectories are corresponded in Views 1 and 2, but the third view could be either in View 3 or View 4. In Fig. 5, each trajectory has a unique color so they can be identified in each view. The first few trajectories are numbered to aid in finding the trajectory in the other views. Once the correspondences are determined, we can triangulate to find the 3D positions of the fragments.
tolerance level, are considered false matches and removed. In some cases, the image processing chain will identify a fragment in a few frames, and then skip a frame or two, before identifying the fragment again in the following frames. This happens when the fragment is tumbling or changes in intensity. These missing points are searched for in a separate step where we predict the location of the missing fragments and perform a careful search in that region by applying a 2DGaussian fit to test for the contour of the fragment. A more in-depth description of all aspects of the trajectory identification is presented in [19]. 3.3. Trajectory correspondence In photogrammetry, correspondence refers to identifying parts of a 3D scene in one image that correspond to parts in another image. Once such a correspondence is made in at least two views, then the 3D location of that point can be determined via triangulation, assuming the relative locations of the two views are known. Therefore, solving the correspondences between trajectories in the four different views is a key step to measuring the fragments’ 3D potions and velocities. Solving for correspondences is challenging because the same points of the 3D scene can look very different in different views and be in different locations on the image. This problem is particularly challenging when the points of interest have little or no distinguishable features to help in the matching and no interconnected structures to act as guides between points, as is the case with the experimental HVI images. In such cases, only the location of the points in each image can be used to find correspondences and eliminate ambiguities. In this paper, we determine the correspondences of the fragments based not simply on individual fragments, but also consider the fragment's trajectory. This means that the correspondence is not made on a frame-by-frame basis, but rather the match is considered over all frames. Searching for the correspondences in this way greatly decreases the likelihood of ambiguities. To determine the trajectory correspondences, we begin with an identified fragment in View 1 and project its epipolar line on the three other images. Fig. 4 shows one such point in View 1 marked with a red circle. The epipolar line of this point is shown in Views 2, 3, and 4 as a red line. We then search in the three other views for fragments less than five pixels from this epipolar line. These points are marked with colored circles in Fig. 4 and are all saved into a database. Next, epipolar lines are plotted in View 3 and 4 for each point that is found in View 2. The points in View 2 are marked with black circles in Fig. 4 and the epipolar lines from these points are shown as black lines in Views 3 and 4 of Fig. 4. In a system of cameras with at least three views, if the location of a point is known in two views, then that point can be transferred into a third view with what is known as point transfer. The transferred point can be found geometrically as the intersection of two epipolar lines from two cameras in the third view [13] and is known as epipolar transfer. In View 3 and 4 of Fig. 4, each intersections of the black lines with the red line is the transferred point of the red point in View 1 and
4. Results and measurement accuracies Fig. 6a shows the fragments triangulated into their 3D locations. The coordinate system is centered about Camera 1, View 1. With the known 3D locations and the known frame rate of the synchronized cameras, an individual velocity vector for each fragment can be calculated. Fig. 6b shows a histogram of the velocities of the fragments from the experiment. The measured velocities fall within the expected range for the cone stage of the backward ejecta velocities as predicted from empirically based models [28]. The fastest and slowest fragments are not measured in this experiment because of constraints of the cameras. The majority of the slow, late-time, spall ejecta which travels around 10–100 m/s do not make it into the field of view before the recording is over because the camera can only record 128 frames. On the other extreme, the fastest fragments tend to be the smallest fragments, typically smaller than one pixel (0.4 mm), and are therefore not reliably tracked. Fragments with velocities away from either extreme
Fig. 4. One image of the experimental sequence showing the steps used to correspond trajectories between all views. See main text for details. 4
International Journal of Impact Engineering 135 (2020) 103405
E. Watson, et al.
Fig. 5. A subset of corresponded trajectories in all four views are overlaid on the high-speed images. Views 1 and 2 contain all corresponded trajectories with the third image correspondence being either in View 3 or View 4. Each trajectory's colors are the same in all four views and the first few are numbered to facilitate finding the same trajectory in different views.
originate at later times from the very edge of the crater and their launch angle is increased by the carbon fiber filaments still attached to the undamaged part of the target. Eventually the fibers break allowing long fragments to be launched at a high angle and giving them a noticeable rotational component which can be easily seen in the high-speed videos. We determine the measurement accuracies of this method by evaluating control images with the same camera setup used for the experiment. A set of three images containing a checkerboard pattern and seen from all four views are given as control image inputs. This represents 144 control points with known relative positions. We identify and correspond all 144 points and triangulate to find their 3D
should be well represented in the histogram. Fig. 6c shows a histogram of the launch angle of each fragment. This is the angle formed between the trajectory and the central impact axis of the experiment. The peak of the histogram occurs at about 30° which agrees with empirical findings performed with witness plates on aluminum targets [27,28]. Fig. 6d shows a 2D histogram of the number of fragments with given velocities and launch angles. In this figure, we can see that the fastest fragments, which belong to the cone part of the ejecta, tend to cluster close to 30° while the slower ejecta, which may contain a mix of cone and spall ejecta, have a much wider spread in launch angle. The fragments launched at very large angles (> 60°) are caused by the fibrous structure of the CFRP target. These fragments
Fig. 6. a) The 3D position of fragments. Points of the same color belong to one trajectory. b) Histogram showing the velocity of the fragments measured. c) Histogram of fragments’ launch angle with respect to the central axis. d) 2D histogram of fragment velocity and launch angle. 5
International Journal of Impact Engineering 135 (2020) 103405
E. Watson, et al.
Fig. 7. Histograms of 3D measurement errors calculated from 144 control points. Errors are calculated from different view pairs used to triangulate for the 3D position. Views 1-2 and 3-4 have poor accuracy due to the small base between the two views leading to poor depth estimation. Mean and standard distribution of the error are listed in each plot.
uncertainties from the high-speed cameras ( ± 10 ns) are negligible compared to the position uncertainties of the fragments, then the velocity uncertainty becomes
coordinates. These coordinates are then compared to the known locations of the control points resulting in a position error estimate. The triangulation can be made between any two views, and depending on a number of factors, different pairs yield different errors. Fig. 7 shows histograms of the errors measured using all view pairs. Triangulations from the majority of these views lead to a 2σ error of approximately 300 µm or 0.75 pixels, which represents a 0.4% error over the image. Mean and standard deviations of the control point errors for individual views are shown in Fig. 7. Two potential sources of error in the high-speed images are not accounted for in error estimate derived from the checkerboard: the effect of camera synchronization and the effects of slightly shifted fragment centers. Camera synchronization error would lead to the fragment location being seen in one view at a slightly different time as in the other view. This would lead to a shift in the triangulated 3D position that would constitute an error. The amount of shift would be dependent on the time offset of the images and the velocity of the fragment, but the error would be correlated in successive timesteps, partially mitigating its effect when calculating the velocity of the fragment. The second error not accounted for are errors caused by fragment correspondences that are centered on different points of the same fragment. Accurate triangulation requires that the same point be identified in both images. Therefore, using slightly different points of the same fragment to triangulate for position would lead to errors. Due to these two sources of error, we cannot assume that the fragment locations are known to the same accuracy as derived from the checkerboard pattern, but are likely to be in the same order of magnitude. A quantitative investigation of these error sources is planned for the near future. The error in the velocity is derived from the position and time error as, 2
ϵv =
ϵv =
ϵx , t
where t is the time of the measurement. In this experiments, frame-toframe time of the high-speed cameras was 4 µs and the average trajectories were tracked over 24 frames corresponding to 96 µs. If we assume that the fragment position error is 1 mm, this leads to a velocity error of 10.4 m/s. 5. Conclusion This paper describes the setup and analysis method for measuring individual fragment velocities in 3D from HVI experiments. The setup makes use of two synchronized high-speed cameras whose images are further split in half yielding four completely separate views. Having these views allows the majority of the identified fragment positions to be determined in 3D without ambiguity. The steps taken to identify, link, correspond, and triangulate each fragment are described in detail. The final result is an approach that is able to measure fragment positions in 3D with sub-millimeter accuracy and 3D velocities with an accuracy of ± 10 m/s. In this paper we have focused exclusively on the method and steps needed to obtain the fragmentation data. The developments described herein will allow further insights into the fragmentation process as well as applied study to a variety of HVI scenarios ranging from satellite breakup, to momentum transfer, to crater formation. Acknowledgments
2
⎛ ∂v ϵx ⎞ + ⎛ ∂v ϵt ⎞ , ⎝ ∂x ⎠ ⎝ ∂t ⎠
The authors would like to acknowledge the excellent work of the laboratory personnel, especially of Mr. Benjamin Berger who operated the accelerator during the impact tests. Part of the work described herein was carried out under a program funded by, the European Space Agency under the project “Microparticle impact related attitude
where v is the velocity and ϵ v , ϵx , and ϵt are the velocity, positions, and time uncertainties respectively. If we assume that the timing 6
International Journal of Impact Engineering 135 (2020) 103405
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disturbances”, ESA Contract No. 4000124111/18/NL/GLC.
[13] Maas HG, Gruen A, Papantoniou D. Particle tracking velocimetry in 3-dimensional flows. 1. Photogrammetric determination of partacle coordinates. Exp Fluids 1993;15(2):133–46. [14] Hermalyn B, Schultz PH. Time-resolved studies of hypervelocity vertical impacts into porous particulate targets: effects of projectile density on early-time coupling and crater growth. Icarus 2011;216(1):269–79. [15] Hermalyn B, Heineck JT, Schairer ET, Peter H. Measurement of ejecta from hypervelocity impacts with a generalized high-speed two-frame 3D hybrid particle tracking velocimetry method. 17th international symposium on applications of laser techniques to fluid mechanics. 2014. [16] Gulde M, Kortmann L, Ebert M, Watson E, Wilk J, Schäfer F. Robust optical tracking of individual ejecta particles in hypervelocity impact experiments. Meteorit Planet Sci 2017;9:1–9. [17] Schimmerohn M, Watson E, Gulde M, Kortmann L, Sch F. Measuring ejecta characteristics and momentum transfer in experimental simulation of kinetic impact. Acta Astronaut 2018. March. [18] Watson E, Gulde M, Kortmann L, Higashide M, Schaefer F, Hiermaier S. Optical fragment tracking in hypervelocity impact experiments. Acta Astronaut 2019;155:111–7. [19] Watson E, Gulde M, Kortmann L, Higashide M, Schaefer F, Hiermaier S. Optical fragment tracking in hypervelocity impact experiments. Acta Astronaut 2019;155:111–7. [20] Maas H. Complexity analysis for the establishment of image correspondences of dense spatial target fields. Int Arch Photogramm Remote Sens 1992;29:102–7. [21] Zhang Zhengyou. Flexible camera calibration by viewing a plane from unknown orientations. Proc. seventh IEEE int. conf. comput. vis. vol.1. 1999. p. 666–73. [22] Putze T, Raguse K, “Configuration of multi mirror systems for single high speed camera based 3D motion analysis,” p. 64910L–64910L–10, 2007. [23] Ruiz a, Lopez-de-Teruel PE, Garcia-Mateos G. A note on principal point estimability. Proc. 16th Int. Conf. Pattern Recognition (ICPR). 2002. p. 11–5. [24] Brown D. Decentering distortion of lenses. Photom Eng 1966;32(3):444–62. [25] Gruen A. Digital photogrammetric techniques for high-resolution three-dimensional flow velocity measurements. Opt Eng 1995;34(7):1970–6. [26] Fischler MA, Bolles RC. Random sample consensus: a paradigm for model fitting with applicatlons to image analysis and automated cartography. Commun ACM 1981;24:381–95. [27] Nishida M, Hiraiwa Y, Hayashi K, Hasegawa S. Ejecta cone angle and ejecta size following a non-perforating hypervelocity impact. Procedia Eng 2015;103:444–9. [28] Rival M, Mandeville J. Modeling of ejecta produced upon hypervelocity impacts. Space Debris 1999:45–57.
References [1] Ausay E, Cornejo A, Horn A, Palma K, Sato T, Blake B, Pistella F, Boyle C, Todd N, “A comparison of the socit and debrisat experiments,” no. April, pp. 18–21, 2017. [2] Flegel S, Gelhaus J, Wiedemann C, Vörsmann P, Oswald M, Stabroth S, Klinkrad H, Krag H. The master-2009 space debris environment model. Eur Space Agency 2009;672. April. [3] Chappaz L, Melosh HJ, Vaquero M, Howell KC. Transfer of impact ejecta material from the surface of Mars to Phobos and Deimos. Adv Astronaut Sci 2012;143(10):1627–46. [4] Head JN, Melosh HJ. Launch velocity distribution of the martian clan meteorites. Lunar and planetary science XXXI. 2000. [5] Buhl E, Sommer F, Poelchau MH, Dresen G, Kenkmann T. Ejecta from experimental impact craters: particle size distribution and fragmentation energy. Icarus 2014;237:131–42. [6] Michel P, Kueppers M, Sierks H, Carnelli I, Cheng AF, Mellab K, Granvik M, Kestilä A, Kohout T, Muinonen K, Näsilä A, Penttila A, Tikka T, Tortora P, Ciarletti V, Hérique A, Murdoch N, Asphaug E, Rivkin A, Barnouin O, Bagatin AC, Pravec P, Richardson DC, Schwartz SR, Tsiganis K, Ulamec S, Karatekin O. European component of the aida mission to a binary asteroid: characterization and interpretation of the impact of the Dart mission. Adv Space Res 2018;62(8):2261–72. [7] Piekutowski AJ. Characteristics of debris clouds produced by hypervelocity impact of aluminum spheres with thin aluminum plates. Int J Impact Eng 1993;14(1–4):573–86. [8] Zhang Q, Chen Y, Huang F, Long R. Experimental study on expansion characteristics of debris clouds produced by oblique hypervelocity impact of LY12 aluminum projectiles with thin LY12 aluminum plates. Int J Impact Eng 2008;35(12):1884–91. [9] Higashide M, Kusano T, Takayanagi Y, Arai K, Hasegawa S. Comparison of aluminum alloy and CFRP bumpers for space debris protection. Procedia Eng 2015;103:189–96. [10] Nishida M, Kato H, Hayashi K, Higashide M. Ejecta size distribution resulting from hypervelocity impact of spherical projectiles on CFRP laminates. Procedia Eng 2013;58:533–42. [11] Raffel M, Willert CE, Wereley ST, Kompenhans J. Particle image velocimetry: a practical guide. Berlin Heidelberg: Springer; 2007. [12] Heineck JT, Schultz PH, Anderson JLB. Application of three-component PIV to the measurement of hypervelocity impact ejecta. J Vis 2002;5(3):233–41.
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Contents lists available at ScienceDirect
International Journal of Impact Engineering journal homepage: www.elsevier.com/locate/ijimpeng
Four-view split-image fragment tracking in hypervelocity impact experiments
T
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Erkai Watsona, , Nico Kunerta, Robin Putzara, Hans-Gerd Maasb, Stefan Hiermaiera a b
Fraunhofer Institute for High-Speed Dynamics, Ernst Mach-Institut, EMI, 79104 Freiburg, Germany Technische Universität Dresden, Institute of Photogrammetry and Remote Sensing, 01062 Dresden, Germany
A R T I C LE I N FO
A B S T R A C T
Keywords: Hypervelocity impact Fragmentation Particle tracking Velocity distribution Image splitting 3d measurement
Fragmentation is a significant phenomenon caused by hypervelocity impact and has applications in orbital debris and planetary impact research, among many others. In particular, the velocity distribution of fragments created by hypervelocity impact is not thoroughly understood. In this paper, we present an experimental setup and analysis method for tracking and measuring individual fragment velocities in 3D. The setup uses two synchronized high-speed cameras with split images, yielding four views, to record image sequences of the in-flight fragments. We analyze the image sequences by identifying fragments and their trajectories in each view, matching the fragments found in different views, and finally triangulating for their 3D positions. The result is a method able to measure fragments’ 3D velocities in the highly transient hypervelocity process.
1. Introduction
Velocimetry (PIV) and Particle Tracking Velocimetry (PTV) are two non-intrusive imaging techniques originally developed for experimental fluid dynamics, that have been used to measure the velocity of fragments in HVI experiments. PIV works with interrogation areas and uses convolution to find the motion vector of small areas in each image between frames [11]. In general, PIV is considered well suited to images with a high fragment density. In the realm of HVI, 3D PIV has been used to study crater formation in sand [12]. This technique is able to measure the flow-field of the ejected sand particles, but cannot resolve individual fragment velocities. Alternately, PTV identifies and tracks individual particles [13] and is therefore more suited to the study of HVI fragmentation of solids where the size of the fragment is also of interest. A combined 2D PIV/ PTV technique has been used to study HVI crater growth in sand, allowing the velocities and position of a small subset of sand grains to be measured [14]. In a later paper, the method was extended to 3D using four views to find the 3D locations of individual sand particles and using PIV to help link particles between two frames to find their velocities [15]. In other research, a PTV technique has been applied to HVI experiments in geological materials in 2D, where both velocities and sizes of the ejected fragments are determined [16,17]. A similar 2D PTV algorithm was applied to the study of debris cloud formations in HVI of satellite shields [18]. In these studies, a robust particle tracking is achieved by taking advantage of the constant velocities of the ejected fragments to help filter out outliers. Particle tracking in 3D with two
Hypervelocity impacts (HVI) often cause significant fragmentation to occur in both target and projectile materials. The study of fragmentation processes extends to numerous applications such as orbital debris or planetary impact. In orbital debris research, understanding the effects of HVI fragmentation, which can causes the break-up of large dense debris into thousands of smaller but still satellite-lethal fragments, is important to modeling the environment [1,2]. In planetary impact research, the correlation between fragment sizes and velocities for impacts on celestial bodies [3–5] or the momentum transfer enhancing effect that fragmentation and backward ejection of material have on celestial bodies and spacecraft [6] are still poorly understood. Fragmentation caused by HVI is challenging to study experimentally because of the highly transient nature of the process and the large number of fragments involved. Traditional HVI experiment instrumentation, such as high-speed cameras and radiographs, allow researchers to study morphological aspects of the debris cloud, like its shape or expansion velocities [7,8], but are not able to quantify the fragments or measure their individual velocities. High-speed images are often supplemented by witness plates or soft catchers which can provide insight into the composition of the ejected fragments and the spray angle of the debris [9,10], but also provide little time resolved data. Recent advances in high-speed camera technology have opened up new measurement methods to HVI experiments. Particle Image
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Corresponding author. E-mail address: [email protected] (E. Watson).
https://doi.org/10.1016/j.ijimpeng.2019.103405 Received 19 July 2019; Accepted 2 October 2019 Available online 03 October 2019 0734-743X/ © 2019 Elsevier Ltd. All rights reserved.
International Journal of Impact Engineering 135 (2020) 103405
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Fig. 1. The experimental setup consists of two synchronized high-speed cameras. Both cameras have their images split into two views with the help of a mirror rig shown in Fig. 2A. This results in four separate views of the backward ejecta emanating from the target.
what is available in the high-speed cameras, and the aperture size is kept at a minimum, limited by the illumination requirements of the experiment. The effects of focal length and distance to the target counteract each other such that a larger focal length with a larger distance leads to a very similar DoF as a smaller focal length and closer distance. The end effect is that magnification must be sacrificed to increase DoF. This leads to a tradeoff between image magnification (and thus spatial resolution and accuracy) and DoF. As we would like to maximize the magnification of the high-speed images, we choose the minimum DoF needed which leads to a magnification with 0.4 mm/ pixel. Once the positions and setting of the cameras are determined, all cameras must be calibrated to determine their intrinsic and extrinsic parameters. The intrinsic parameters are the internal camera parameters such as focal length, principal point, and lens distortions, while the extrinsic parameters refer to the rotation and translation of each camera center with respect to the world coordinate system. We calibrate the cameras with a 2D pattern checkerboard pattern [21]. Camera calibration images are taken before and after each experiment, thereby allowing us to determine if there was any disruption of the setup. In each image, we set the pixels in the unused half to zero and treat each view as a virtual camera with its own calibration and intrinsic parameters. This gives the advantages of having the distortion model partly compensate for any mirror surface irregularities [22]. Because of large focal length of our cameras, we assume the principal point of each camera to be at the center of the image [23]. Radial and tangential distortion are corrected for with Brown's distortion model [24].
synchronized high-speed cameras was demonstrated by measuring the 3D velocities of aluminum debris cloud fragments by using a priori knowledge of the fragment trajectories [19]. In this paper, we present further developments of a 3D particle tracking technique for measuring the 3D fragment positions and velocities generated by HVI experiments. We improve on previous work, by developing experimental setups and algorithms that use high-speed images taken from up to four views to measure the fragments. Increasing the number of perspectives from two to four views allows more fragments to be correctly matched and triangulated from the low resolution and noisy images typical of high-speed recordings. 2. Experimental setup The experimental setup for multi-view fragment tracking involves high-speed cameras and backlit flash lighting to create shadowgraph images of the HVI fragments. An experimental setup with two highspeed cameras is shown in Fig. 1. Two Shimadzu high-speed cameras, capable of micro- to nanosecond exposure times and framerates of up to 10 million frames per second are synchronized and used to record the ejected fragments. In this paper, we will use one specific experiment to describe a method for measuring individual fragment velocities in a HVI experiment. The experiment involved the impact of a 3 mm aluminum sphere on a 5 mm thick CFRP plate at 7.2 km/s. The image sequence was taken at 250,000 fps with a field of view of approximately 70 × 100 mm in each view. The target chamber was evacuated to 120 mbar. The goal of this experiment was to measure the properties of the backward ejecta that is accelerated up-range from the CFRP target plate. Although 3D particle measurements with two views is possible, using three or four views greatly decreases the number of ambiguities that arise in stereo image matching of detected particles [20]. In order to increase the number of perspectives with a limited number of cameras, the images of each high-speed cameras is split using a custom built mirror rig shown in Fig. 2A, yielding four views from two cameras. One constraint in the image splitting setup is the need of a large Depth of Field (DoF), the distance about the plane of focus where objects appear acceptably sharp. A large DoF is needed to produce two completely separate images without having objects in one view overlap into the other view; that is, both the splitting mirrors and the target must be in focus. Fig. 2B and C show an example of different DoF and the effect on image overlap. Because the splitting mirrors must be placed outside the target chamber, a minimum DoF of 50 cm is required. The DoF is affected by the lens aperture, the focal length, the distance to the target, and the sensor size. Sensor size is fixed, defined by
3. Method The analysis of the multi-view high-speed images can be separated into three main parts: object detection, object tracking and multi-view correspondence establishment. After fragments are detected in the object detection step, two different strategies may be used for object tracking and correspondence establishment [25]: Object tracking in 2D image space followed by multi-view correspondence establishment of trajectories, or 3D object coordinate determination by multi-view correspondence establishment of detected objects, followed by tracking in 3D object space. In our approach, we chose to perform object tracking in the 2D image space because of the straight line trajectories followed by each fragments. Fig. 3 shows a set of raw images from the high-speed image sequences. These images will serves as inputs to the algorithm.
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Fig. 2. A) Mirror rig for splitting an image into two views. B) and C) Split-images of a Siemens star showing the effect of Depth of Field on image overlap due to the splitting. In image B, a small Depth of Field (f/2.8) results in a large area of overlap, marked in red, where View 3 blurs with View 4. Increasing the Depth of Field in Image C (f/16) significantly decreases the overlap and increases the usable area of the two views.
vacuum in the target chamber experience only negligible aerodynamics drag forces, so their velocities remain essentially constant. Fragments also travel in a straight line due to the negligible effects of gravity at the short time scales of the experiment. These two assumptions are more formally addressed in [19]. The fact that fragments travel in straight lines allows us to take a trajectory based linking approach. We implement this by plotting all identified points from each of the four image sequences into a 3D-XYT space representing 2D space and time. Points in this XYT space that lie on a line represent the same fragment in different images traveling in a straight line and at constant velocity. To find these straight lines in the XYT space, we use a random sample consensus algorithm (RANSAC) [26]. As points forming straight lines are found, they are removed from the XYT space point cloud and saved, thereby reducing the search space and preventing repeated matches from being recorded. The RANSAC analysis is performed in parallel on a graphics-processing unit (GPU). A minority of the outputs of the RANSAC algorithm will be false matches that need to be filtered out. We filter the trajectories by examining their angle in the XYT space. All trajectories are expected to converge in one location in XYT, which represents the 2D launch location of the fragments and the launch time of the fragments. Trajectories that do not intersect this point, to within a certain
3.1. Object detection To identify the fragments in each image, we apply the following steps:
• Apply a top-hat filter to preserve intensity peaks and eliminate other features • Remove background pixels below given threshold • Apply Gaussian blur to remove small variations in intensity • Find all local maxima in the image • Apply Gaussian fit for subpixel accuracy These steps are applied to every frame of each image sequence, which results in a list of detected fragments with their 2D locations and times. 3.2. Object tracking Once fragments have been identified in each frame of the image sequence, they need to be tracked from frame to frame. We base our fragment tracking on the assumption that each fragment travels in a straight line and at a constant velocity. Fragments traveling through the
Fig. 3. High-speed images of the ejected fragments seen from two synchronized cameras and four different viewing angles. These images sequences will be used to measure the velocity of the recorded fragments. 3
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one of the black points in View 2 into View 3 and 4. Since only one point in View 2 actually corresponds to the point in View 1, only one of the transferred point should match the actual location of fragments in Views 3 and 4. A closer examination of View 4 in Fig. 4, shows that of the three transferred locations (line intersections), only one of them is close to the location of a fragment. (Note: the fourth line and intersection happened to lie outside the image). In View 3 of Fig. 4, we see that there are two transferred points that closely match an actual fragment locations, this causes an ambiguity. To determine the “best” corresponding fragment in the other views, we measure the distance between the found point and the transferred point (in this case in Views 3 and 4) and save it along with identifier of the fragment in the three views. Therefore, in the example of Fig. 4, the distances between each green point in View 3 and the nearest intersection would be saved together with the trajectory number of the red point and the black point in Views 1 and 2. The same is done for View 4. The process of finding correspondence candidates is repeated for every trajectory found in View 1. The results are sets of three trajectories (from three different views) that are assigned a score based on the distance between transferred point and detected point and number of instances that those trajectories are detected repeatedly in different image frames. The same set must be found a minimum of four frames and have a maximum distance of 5 pixels. A weighting factor is applied to the instance and distance parameters to assign each set a final score. The sets with the highest scores are chosen as corresponding trajectories. Fig. 5 shows a subset of the trajectories that were corresponded in three views. Due to the search method of starting in View 1 and using View 2 to transfer points into View 3 or 4, all trajectories are corresponded in Views 1 and 2, but the third view could be either in View 3 or View 4. In Fig. 5, each trajectory has a unique color so they can be identified in each view. The first few trajectories are numbered to aid in finding the trajectory in the other views. Once the correspondences are determined, we can triangulate to find the 3D positions of the fragments.
tolerance level, are considered false matches and removed. In some cases, the image processing chain will identify a fragment in a few frames, and then skip a frame or two, before identifying the fragment again in the following frames. This happens when the fragment is tumbling or changes in intensity. These missing points are searched for in a separate step where we predict the location of the missing fragments and perform a careful search in that region by applying a 2DGaussian fit to test for the contour of the fragment. A more in-depth description of all aspects of the trajectory identification is presented in [19]. 3.3. Trajectory correspondence In photogrammetry, correspondence refers to identifying parts of a 3D scene in one image that correspond to parts in another image. Once such a correspondence is made in at least two views, then the 3D location of that point can be determined via triangulation, assuming the relative locations of the two views are known. Therefore, solving the correspondences between trajectories in the four different views is a key step to measuring the fragments’ 3D potions and velocities. Solving for correspondences is challenging because the same points of the 3D scene can look very different in different views and be in different locations on the image. This problem is particularly challenging when the points of interest have little or no distinguishable features to help in the matching and no interconnected structures to act as guides between points, as is the case with the experimental HVI images. In such cases, only the location of the points in each image can be used to find correspondences and eliminate ambiguities. In this paper, we determine the correspondences of the fragments based not simply on individual fragments, but also consider the fragment's trajectory. This means that the correspondence is not made on a frame-by-frame basis, but rather the match is considered over all frames. Searching for the correspondences in this way greatly decreases the likelihood of ambiguities. To determine the trajectory correspondences, we begin with an identified fragment in View 1 and project its epipolar line on the three other images. Fig. 4 shows one such point in View 1 marked with a red circle. The epipolar line of this point is shown in Views 2, 3, and 4 as a red line. We then search in the three other views for fragments less than five pixels from this epipolar line. These points are marked with colored circles in Fig. 4 and are all saved into a database. Next, epipolar lines are plotted in View 3 and 4 for each point that is found in View 2. The points in View 2 are marked with black circles in Fig. 4 and the epipolar lines from these points are shown as black lines in Views 3 and 4 of Fig. 4. In a system of cameras with at least three views, if the location of a point is known in two views, then that point can be transferred into a third view with what is known as point transfer. The transferred point can be found geometrically as the intersection of two epipolar lines from two cameras in the third view [13] and is known as epipolar transfer. In View 3 and 4 of Fig. 4, each intersections of the black lines with the red line is the transferred point of the red point in View 1 and
4. Results and measurement accuracies Fig. 6a shows the fragments triangulated into their 3D locations. The coordinate system is centered about Camera 1, View 1. With the known 3D locations and the known frame rate of the synchronized cameras, an individual velocity vector for each fragment can be calculated. Fig. 6b shows a histogram of the velocities of the fragments from the experiment. The measured velocities fall within the expected range for the cone stage of the backward ejecta velocities as predicted from empirically based models [28]. The fastest and slowest fragments are not measured in this experiment because of constraints of the cameras. The majority of the slow, late-time, spall ejecta which travels around 10–100 m/s do not make it into the field of view before the recording is over because the camera can only record 128 frames. On the other extreme, the fastest fragments tend to be the smallest fragments, typically smaller than one pixel (0.4 mm), and are therefore not reliably tracked. Fragments with velocities away from either extreme
Fig. 4. One image of the experimental sequence showing the steps used to correspond trajectories between all views. See main text for details. 4
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Fig. 5. A subset of corresponded trajectories in all four views are overlaid on the high-speed images. Views 1 and 2 contain all corresponded trajectories with the third image correspondence being either in View 3 or View 4. Each trajectory's colors are the same in all four views and the first few are numbered to facilitate finding the same trajectory in different views.
originate at later times from the very edge of the crater and their launch angle is increased by the carbon fiber filaments still attached to the undamaged part of the target. Eventually the fibers break allowing long fragments to be launched at a high angle and giving them a noticeable rotational component which can be easily seen in the high-speed videos. We determine the measurement accuracies of this method by evaluating control images with the same camera setup used for the experiment. A set of three images containing a checkerboard pattern and seen from all four views are given as control image inputs. This represents 144 control points with known relative positions. We identify and correspond all 144 points and triangulate to find their 3D
should be well represented in the histogram. Fig. 6c shows a histogram of the launch angle of each fragment. This is the angle formed between the trajectory and the central impact axis of the experiment. The peak of the histogram occurs at about 30° which agrees with empirical findings performed with witness plates on aluminum targets [27,28]. Fig. 6d shows a 2D histogram of the number of fragments with given velocities and launch angles. In this figure, we can see that the fastest fragments, which belong to the cone part of the ejecta, tend to cluster close to 30° while the slower ejecta, which may contain a mix of cone and spall ejecta, have a much wider spread in launch angle. The fragments launched at very large angles (> 60°) are caused by the fibrous structure of the CFRP target. These fragments
Fig. 6. a) The 3D position of fragments. Points of the same color belong to one trajectory. b) Histogram showing the velocity of the fragments measured. c) Histogram of fragments’ launch angle with respect to the central axis. d) 2D histogram of fragment velocity and launch angle. 5
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Fig. 7. Histograms of 3D measurement errors calculated from 144 control points. Errors are calculated from different view pairs used to triangulate for the 3D position. Views 1-2 and 3-4 have poor accuracy due to the small base between the two views leading to poor depth estimation. Mean and standard distribution of the error are listed in each plot.
uncertainties from the high-speed cameras ( ± 10 ns) are negligible compared to the position uncertainties of the fragments, then the velocity uncertainty becomes
coordinates. These coordinates are then compared to the known locations of the control points resulting in a position error estimate. The triangulation can be made between any two views, and depending on a number of factors, different pairs yield different errors. Fig. 7 shows histograms of the errors measured using all view pairs. Triangulations from the majority of these views lead to a 2σ error of approximately 300 µm or 0.75 pixels, which represents a 0.4% error over the image. Mean and standard deviations of the control point errors for individual views are shown in Fig. 7. Two potential sources of error in the high-speed images are not accounted for in error estimate derived from the checkerboard: the effect of camera synchronization and the effects of slightly shifted fragment centers. Camera synchronization error would lead to the fragment location being seen in one view at a slightly different time as in the other view. This would lead to a shift in the triangulated 3D position that would constitute an error. The amount of shift would be dependent on the time offset of the images and the velocity of the fragment, but the error would be correlated in successive timesteps, partially mitigating its effect when calculating the velocity of the fragment. The second error not accounted for are errors caused by fragment correspondences that are centered on different points of the same fragment. Accurate triangulation requires that the same point be identified in both images. Therefore, using slightly different points of the same fragment to triangulate for position would lead to errors. Due to these two sources of error, we cannot assume that the fragment locations are known to the same accuracy as derived from the checkerboard pattern, but are likely to be in the same order of magnitude. A quantitative investigation of these error sources is planned for the near future. The error in the velocity is derived from the position and time error as, 2
ϵv =
ϵv =
ϵx , t
where t is the time of the measurement. In this experiments, frame-toframe time of the high-speed cameras was 4 µs and the average trajectories were tracked over 24 frames corresponding to 96 µs. If we assume that the fragment position error is 1 mm, this leads to a velocity error of 10.4 m/s. 5. Conclusion This paper describes the setup and analysis method for measuring individual fragment velocities in 3D from HVI experiments. The setup makes use of two synchronized high-speed cameras whose images are further split in half yielding four completely separate views. Having these views allows the majority of the identified fragment positions to be determined in 3D without ambiguity. The steps taken to identify, link, correspond, and triangulate each fragment are described in detail. The final result is an approach that is able to measure fragment positions in 3D with sub-millimeter accuracy and 3D velocities with an accuracy of ± 10 m/s. In this paper we have focused exclusively on the method and steps needed to obtain the fragmentation data. The developments described herein will allow further insights into the fragmentation process as well as applied study to a variety of HVI scenarios ranging from satellite breakup, to momentum transfer, to crater formation. Acknowledgments
2
⎛ ∂v ϵx ⎞ + ⎛ ∂v ϵt ⎞ , ⎝ ∂x ⎠ ⎝ ∂t ⎠
The authors would like to acknowledge the excellent work of the laboratory personnel, especially of Mr. Benjamin Berger who operated the accelerator during the impact tests. Part of the work described herein was carried out under a program funded by, the European Space Agency under the project “Microparticle impact related attitude
where v is the velocity and ϵ v , ϵx , and ϵt are the velocity, positions, and time uncertainties respectively. If we assume that the timing 6
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disturbances”, ESA Contract No. 4000124111/18/NL/GLC.
[13] Maas HG, Gruen A, Papantoniou D. Particle tracking velocimetry in 3-dimensional flows. 1. Photogrammetric determination of partacle coordinates. Exp Fluids 1993;15(2):133–46. [14] Hermalyn B, Schultz PH. Time-resolved studies of hypervelocity vertical impacts into porous particulate targets: effects of projectile density on early-time coupling and crater growth. Icarus 2011;216(1):269–79. [15] Hermalyn B, Heineck JT, Schairer ET, Peter H. Measurement of ejecta from hypervelocity impacts with a generalized high-speed two-frame 3D hybrid particle tracking velocimetry method. 17th international symposium on applications of laser techniques to fluid mechanics. 2014. [16] Gulde M, Kortmann L, Ebert M, Watson E, Wilk J, Schäfer F. Robust optical tracking of individual ejecta particles in hypervelocity impact experiments. Meteorit Planet Sci 2017;9:1–9. [17] Schimmerohn M, Watson E, Gulde M, Kortmann L, Sch F. Measuring ejecta characteristics and momentum transfer in experimental simulation of kinetic impact. Acta Astronaut 2018. March. [18] Watson E, Gulde M, Kortmann L, Higashide M, Schaefer F, Hiermaier S. Optical fragment tracking in hypervelocity impact experiments. Acta Astronaut 2019;155:111–7. [19] Watson E, Gulde M, Kortmann L, Higashide M, Schaefer F, Hiermaier S. Optical fragment tracking in hypervelocity impact experiments. Acta Astronaut 2019;155:111–7. [20] Maas H. Complexity analysis for the establishment of image correspondences of dense spatial target fields. Int Arch Photogramm Remote Sens 1992;29:102–7. [21] Zhang Zhengyou. Flexible camera calibration by viewing a plane from unknown orientations. Proc. seventh IEEE int. conf. comput. vis. vol.1. 1999. p. 666–73. [22] Putze T, Raguse K, “Configuration of multi mirror systems for single high speed camera based 3D motion analysis,” p. 64910L–64910L–10, 2007. [23] Ruiz a, Lopez-de-Teruel PE, Garcia-Mateos G. A note on principal point estimability. Proc. 16th Int. Conf. Pattern Recognition (ICPR). 2002. p. 11–5. [24] Brown D. Decentering distortion of lenses. Photom Eng 1966;32(3):444–62. [25] Gruen A. Digital photogrammetric techniques for high-resolution three-dimensional flow velocity measurements. Opt Eng 1995;34(7):1970–6. [26] Fischler MA, Bolles RC. Random sample consensus: a paradigm for model fitting with applicatlons to image analysis and automated cartography. Commun ACM 1981;24:381–95. [27] Nishida M, Hiraiwa Y, Hayashi K, Hasegawa S. Ejecta cone angle and ejecta size following a non-perforating hypervelocity impact. Procedia Eng 2015;103:444–9. [28] Rival M, Mandeville J. Modeling of ejecta produced upon hypervelocity impacts. Space Debris 1999:45–57.
References [1] Ausay E, Cornejo A, Horn A, Palma K, Sato T, Blake B, Pistella F, Boyle C, Todd N, “A comparison of the socit and debrisat experiments,” no. April, pp. 18–21, 2017. [2] Flegel S, Gelhaus J, Wiedemann C, Vörsmann P, Oswald M, Stabroth S, Klinkrad H, Krag H. The master-2009 space debris environment model. Eur Space Agency 2009;672. April. [3] Chappaz L, Melosh HJ, Vaquero M, Howell KC. Transfer of impact ejecta material from the surface of Mars to Phobos and Deimos. Adv Astronaut Sci 2012;143(10):1627–46. [4] Head JN, Melosh HJ. Launch velocity distribution of the martian clan meteorites. Lunar and planetary science XXXI. 2000. [5] Buhl E, Sommer F, Poelchau MH, Dresen G, Kenkmann T. Ejecta from experimental impact craters: particle size distribution and fragmentation energy. Icarus 2014;237:131–42. [6] Michel P, Kueppers M, Sierks H, Carnelli I, Cheng AF, Mellab K, Granvik M, Kestilä A, Kohout T, Muinonen K, Näsilä A, Penttila A, Tikka T, Tortora P, Ciarletti V, Hérique A, Murdoch N, Asphaug E, Rivkin A, Barnouin O, Bagatin AC, Pravec P, Richardson DC, Schwartz SR, Tsiganis K, Ulamec S, Karatekin O. European component of the aida mission to a binary asteroid: characterization and interpretation of the impact of the Dart mission. Adv Space Res 2018;62(8):2261–72. [7] Piekutowski AJ. Characteristics of debris clouds produced by hypervelocity impact of aluminum spheres with thin aluminum plates. Int J Impact Eng 1993;14(1–4):573–86. [8] Zhang Q, Chen Y, Huang F, Long R. Experimental study on expansion characteristics of debris clouds produced by oblique hypervelocity impact of LY12 aluminum projectiles with thin LY12 aluminum plates. Int J Impact Eng 2008;35(12):1884–91. [9] Higashide M, Kusano T, Takayanagi Y, Arai K, Hasegawa S. Comparison of aluminum alloy and CFRP bumpers for space debris protection. Procedia Eng 2015;103:189–96. [10] Nishida M, Kato H, Hayashi K, Higashide M. Ejecta size distribution resulting from hypervelocity impact of spherical projectiles on CFRP laminates. Procedia Eng 2013;58:533–42. [11] Raffel M, Willert CE, Wereley ST, Kompenhans J. Particle image velocimetry: a practical guide. Berlin Heidelberg: Springer; 2007. [12] Heineck JT, Schultz PH, Anderson JLB. Application of three-component PIV to the measurement of hypervelocity impact ejecta. J Vis 2002;5(3):233–41.
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