Development of a toroidal soft x-ray imaging system and application for investigating three-dimensional plasma on J-TEXT

A toroidal soft x-ray imaging(T-SXRI)system has been developed to investigate threedimensional(3D)plasma physics on J-TEXT.This T-SXRI system consists of three sets of SXR arrays.Two sets are newly developed and located on the vacuum chamber wall at toroidal positionsφof 126.4°and 272.6°,respectively,while one set was established previously atφ=65.50.Each set of SXR arrays consists of three arrays viewing the plasma poloidally,and hence can be used separately to obtain SXR images via the tomographic method.The sawtooth precursor oscillations are measured by T-SXRI,and the corresponding images of perturbative SXR signals are successfully reconstructed at these three toroidal positions,hence providing measurement of the 3D structure of precursor oscillations.The observed 3D structure is consistent with the helical structure of the m/n=1/1 mode.The experimental observation confirms that the T-SXRI system is able to observe 3D structures in the J-TEXT plasma.

GPU-accelerated three-dimensional reconstruction method of the Compton camera and its application in radionuclide imaging

A novel and fast three-dimensional reconstruction method for a Compton camera and its performance in radionuclide imaging is proposed and analyzed in this study. The conical surface sampling back-projection method with scattering angle correction(CSS-BP-SC) can quickly perform the back-projection process of the Compton cone and can be used to precompute the list-mode maximum likelihood expectation maximization(LM-MLEM). A dedicated parallel architecture was designed for the graphics processing unit acceleration of the back-projection and iteration stage of the CSS-BP-SC-based LM-MLEM. The imaging results of the two-point source Monte Carlo(MC) simulation demonstrate that by analyzing the full width at half maximum along the three coordinate axes, the CSS-BP-SC-based LM-MLEM can obtain imaging results comparable to those of the traditional reconstruction algorithm, that is, the simple back-projection-based LM-MLEM. The imaging results of the mouse phantom MC simulation and experiment demonstrate that the reconstruction results obtained by the proposed method sufficiently coincide with the set radioactivity distribution, and the speed increased by more than 664 times compared to the traditional reconstruction algorithm in the mouse phantom experiment. The proposed method will further advance the imaging applications of Compton cameras.

Single exposure passive three-dimensional information reconstruction based on an ordinary imaging system

Existing three-dimensional(3D) imaging technologies have issues such as requiring active illumination, multiple exposures, or coding modulation. We propose a passive single 3D imaging method based on an ordinary imaging system.Using the point spread function of the imaging system to realize the non-coding measurement on the target, the full-focus images and depth information of the 3D target can be extracted from a single two-dimensional(2D) image through the compressed sensing algorithm. Simulation and experiments show that this approach can complete passive 3D imaging based on an ordinary imaging system without any coding operations. This method can achieve millimeter-level vertical resolution under single exposure conditions and has the potential for real-time dynamic 3D imaging. It improves the efficiency of 3D information detection, reduces the complexity of the imaging system, and may be of considerable value to the field of computer vision and other related applications.

Electromagnetic scattering and imaging simulation of extremely large-scale sea-ship scene based on GPU parallel technology

Aiming to solve the bottleneck problem of electromagnetic scattering simulation in the scenes of extremely large-scale seas and ships,a high-frequency method by using graphics processing unit(GPU)parallel acceleration technique is proposed.For the implementation of different electromagnetic methods of physical optics(PO),shooting and bouncing ray(SBR),and physical theory of diffraction(PTD),a parallel computing scheme based on the CPU-GPU parallel computing scheme is realized to balance computing tasks.Finally,a multi-GPU framework is further proposed to solve the computational difficulty caused by the massive number of ray tubes in the ray tracing process.By using the established simulation platform,signals of ships at different seas are simulated and their images are achieved as well.It is shown that the higher sea states degrade the averaged peak signal-to-noise ratio(PSNR)of radar image.

Evaluating the use of three-dimensional reconstruction visualization technology for precise laparoscopic resection in gastroesophageal junction cancer

BACKGROUND Laparoscopic gastrectomy for esophagogastric junction(EGJ)carcinoma enables the removal of the carcinoma at the junction between the stomach and esophagus while preserving the gastric function,thereby providing patients with better treatment outcomes and quality of life.Nonetheless,this surgical technique also presents some challenges and limitations.Therefore,three-dimensional reconstruction visualization technology(3D RVT)has been introduced into the procedure,providing doctors with more comprehensive and intuitive anatomical information that helps with surgical planning,navigation,and outcome evaluation.AIM To discuss the application and advantages of 3D RVT in precise laparoscopic resection of EGJ carcinomas.METHODS Data were obtained from the electronic or paper-based medical records at The First Affiliated Hospital of Hebei North University from January 2020 to June 2022.A total of 120 patients diagnosed with EGJ carcinoma were included in the study.Of these,68 underwent laparoscopic resection after computed tomography(CT)-enhanced scanning and were categorized into the 2D group,whereas 52 underwent laparoscopic resection after CT-enhanced scanning and 3D RVT and were categorized into the 3D group.This study had two outcome measures:the deviation between tumor-related factors(such as maximum tumor diameter and infiltration length)in 3D RVT and clinical reality,and surgical outcome indicators(such as operative time,intraoperative blood loss,number of lymph node dissections,R0 resection rate,postoperative hospital stay,postoperative gas discharge time,drainage tube removal time,and related complications)between the 2D and 3D groups.RESULTS Among patients included in the 3D group,27 had a maximum tumor diameter of less than 3 cm,whereas 25 had a diameter of 3 cm or more.In actual surgical observations,24 had a diameter of less than 3 cm,whereas 28 had a diameter of 3 cm or more.The findings were consistent between the two methods(χ^(2)=0.346,P=0.556),with a kappa consistency coefficient of 0.808.With respect to infiltration length,in the 3D group,23 patients had a length of less than 5 cm,whereas 29 had a length of 5 cm or more.In actual surgical observations,20 cases had a length of less than 5 cm,whereas 32 had a length of 5 cm or more.The findings were consistent between the two methods(χ^(2)=0.357,P=0.550),with a kappa consistency coefficient of 0.486.Pearson correlation analysis showed that the maximum tumor diameter and infiltration length measured using 3D RVT were positively correlated with clinical observations during surgery(r=0.814 and 0.490,both P<0.05).The 3D group had a shorter operative time(157.02±8.38 vs 183.16±23.87),less intraoperative blood loss(83.65±14.22 vs 110.94±22.05),and higher number of lymph node dissections(28.98±2.82 vs 23.56±2.77)and R0 resection rate(80.77%vs 61.64%)than the 2D group.Furthermore,the 3D group had shorter hospital stay[8(8,9)vs 13(14,16)],time to gas passage[3(3,4)vs 4(5,5)],and drainage tube removal time[4(4,5)vs 6(6,7)]than the 2D group.The complication rate was lower in the 3D group(11.54%)than in the 2D group(26.47%)(χ^(2)=4.106,P<0.05).CONCLUSION Using 3D RVT,doctors can gain a more comprehensive and intuitive understanding of the anatomy and related lesions of EGJ carcinomas,thus enabling more accurate surgical planning.

Method of Monitoring Three-dimensional Mining Surface Deformation Based on InSAR

In order to solve the problems of small monitoring range,long time and high cost of existing sedimentation observation methods,based on two-view sentinel No.1 radar images of Guqiao mining area in Huainan City from November 4,2017 to November 28,2017,surface change information was obtained in combination with D-InSAR,and the three-dimensional surface deformation was monitored by two-pass method and single line of sight D-InSAR method.The results show that during the research period of 24 d,the maximum deformation of the mining area reached 71 mm,and the southern subsidence was the most obvious,which was in line with the mining subsidence law.The maximum displacement from the north to the south was about 250 mm,while the maximum displacement from the east to the west was about 80 mm,and the maximum subsidence in the center was 110 mm.It is concluded that D-InSAR technique has a good effect on the inversion of the mining subsidence,and this method is suitable for three-dimensional surface monitoring in areas with similar geological conditions.The monitoring results have certain reference value.

Asymmetric image encryption algorithm based on a new three-dimensional improved logistic chaotic map

Based on some analyses of existing chaotic image encryption frameworks and a new designed three-dimensional improved logistic chaotic map(3D-ILM),an asymmetric image encryption algorithm using public-key Rivest–Shamir–Adleman(RSA)is presented in this paper.In the first stage,a new 3D-ILM is proposed to enhance the chaotic behavior considering analysis of time sequence,Lyapunov exponent,and Shannon entropy.In the second stage,combined with the public key RSA algorithm,a new key acquisition mathematical model(MKA)is constructed to obtain the initial keys for the 3D-ILM.Consequently,the key stream can be produced depending on the plain image for a higher security.Moreover,a novel process model(NPM)for the input of the 3D-ILM is built,which is built to improve the distribution uniformity of the chaotic sequence.In the third stage,to encrypt the plain image,a pre-process by exclusive OR(XOR)operation with a random matrix is applied.Then,the pre-processed image is performed by a permutation for rows,a downward modulo function for adjacent pixels,a permutation for columns,a forward direction XOR addition-modulo diffusion,and a backward direction XOR addition-modulo diffusion to achieve the final cipher image.Moreover,experiments show that the the proposed algorithm has a better performance.Especially,the number of pixels change rate(NPCR)is close to ideal case 99.6094%,with the unified average changing intensity(UACI)close to 33.4634%,and the information entropy(IE)close to 8.

Survey of methods and principles in three-dimensional reconstruction from two-dimensional medical images

Three-dimensional(3D)reconstruction of human organs has gained attention in recent years due to advances in the Internet and graphics processing units.In the coming years,most patient care will shift toward this new paradigm.However,development of fast and accurate 3D models from medical images or a set of medical scans remains a daunting task due to the number of pre-processing steps involved,most of which are dependent on human expertise.In this review,a survey of pre-processing steps was conducted,and reconstruction techniques for several organs in medical diagnosis were studied.Various methods and principles related to 3D reconstruction were highlighted.The usefulness of 3D reconstruction of organs in medical diagnosis was also highlighted.

Three-dimensional positions of scattering centers reconstruction from multiple SAR images based on radargrammetry

A method and procedure is presented to reconstruct three-dimensional(3D) positions of scattering centers from multiple synthetic aperture radar(SAR) images. Firstly, two-dimensional(2D) attribute scattering centers of targets are extracted from 2D SAR images. Secondly, similarity measure is developed based on 2D attributed scatter centers' location, type, and radargrammetry principle between multiple SAR images. By this similarity, we can associate 2D scatter centers and then obtain candidate 3D scattering centers. Thirdly, these candidate scattering centers are clustered in 3D space to reconstruct final 3D positions. Compared with presented methods, the proposed method has a capability of describing distributed scattering center, reduces false and missing 3D scattering centers, and has fewer restrictionson modeling data. Finally, results of experiments have demonstrated the effectiveness of the proposed method.

Application of Three-Dimensional Magnetic Resonance Imaging in the Diagnosis of Perianal Abscess

Perianal abscess is a common disease in anorectal surgery. If the diagnosis is not clear and the cure is thoroughly cleared, the recurrence and spread of anal fistula will cause life-long pain. Objective: To investigate the application of 3.0T MRI 3D CUBE T2WI lipid suppression sequence in the diagnosis of perianal abscess. Methods: Thirty-six patients with perianal abscess confirmed by operation were examined with 2D T2WI and 3D CUBE T2WI lipid suppression sequences before operation. Two imaging techniques were evaluated to show the types of perianal abscess, the number of abscesses, the number of internal orifices of abscess, and the number of fistula branches with anal fistula in abscess. Results: Among 36 cases of perianal abscess, there were 5 cases of anal subcutaneous abscess, 12 cases of ischiorectal space abscess (8 cases complicated with anal fistula), 6 cases of posterior anal space abscess, 5 cases of anal sphincter abscess (3 cases complicated with anal fistula), 2 cases of high intermuscular abscess, 2 cases of rectal submucosal abscess, 3 cases of complex abscess (3 cases complicated with anal fistula), 1 case of misdiagnosis, 2D T2WI lipid suppression sequence and 3D CUBE T2WI suppression. The accuracy of lipid sequence abscess typing was 80.6% (29/36) and 88.9% (32/36), respectively, with no significant difference (P > 0.05). Thirty-six patients were surgically diagnosed as having 32 internal orifices, 68.8% (22/32) and 93.8% (30/32) of 2D T2WI and 3D CUBE T2WI lipid-suppressing sequences, respectively, with significant difference (P Conclusion: 3D CUBE T2WI lipid suppression sequence is superior to 2D T2WI lipid suppression sequence in the classification of perianal abscess, the number of internal orifices of abscess and the number of fistula branches of abscess complicated with anal fistula. It can also determine the number of internal orifices of abscess complicated with anal fistula, the number of fistula branches, the shape of primary and branch fistula and the relationship among pelvic floor muscle tissues. It can provide more accurate images for preoperative and intraoperative clinical surgery.

Real-time Three-Dimensional Color Doppler Flow Imaging： An Improved Technique for Quantitative Analysis of Aortic Regurgitation

The recently introduced real-time three-dimensional color Doppler flow imaging （RT-3D CDFI） technique provides a quick and accurate calculation of regurgitant jet volume （RJV） and fraction. In order to evaluate RT-3D CDFI in the noninvasive assessment of aortic RJV and regurgitant jet fraction （RJF） in patients with isolated aortic regurgitation, real-time three-dimensional echocardiographic studies were performed on 23 patients with isolated aortic regurgitation to obtain LV end-diastolic volumes （LVEDV）, end-systolic volumes （LVESV） and RJV, and then RJF could be calculated. The regurgitant volume （RV） and regurgitant fraction （RF） calculated by two-dimensional pulsed Doppler （2D-PD） method served as reference values. The results showed that aortic RJV measured by the RT-3D CDFI method showed a good correlation with the 2D-PD measurements （r= 0.93, Y=0.89X＋ 3.9, SEE= 8.6 mL, P〈0.001 ）; the mean （SD） difference between the two methods was - 1.5 （9.8） mL. % RJF estimated by the RT-3D CDFI method was also correlated well with the values obtained by the 2D-PD method （r=0.88, Y=0.71X＋ 14.8, SEE= 6.4 %, P〈0. 001）; the mean （SD） difference between the two methods was -1.2 （7.9） %. It was suggested that the newly developed RT-3D CDFI technique was feasible in the majority of patients. In patients with eccentric aortic regurgitation, this new modality provides additional information to that obtained from the two-dimensional examination, which overcomes the inherent limitations of two-dimensional echocardiography by depicting the full extent of the jet trajectory. In addition, the RT-3D CDFI method is quick and accurate in calculating RJV and RJF.

Terahertz Three-Dimensional Imaging Based on Computed Tomography with Photonics-Based Noise Source

Computed tomography has been proven to be useful for non-destructive inspection of structures and materials. We build a three-dimensional imaging system with the photonically generated incoherent noise source and the Schottky barrier diode detector in the terahertz frequency band （90–140GHz）. Based on the computed tomography technique, the three-dimensional image of a ceramic sample is reconstructed successfully by stacking the slices at different heights. The imaging results not only indicate the ability of terahertz wave in the non-invasive sensing and non-destructive inspection applications, but also prove the effectiveness and superiority of the uni-traveling-carrier photodiode as a terahertz source in the imaging applications.

Near-Range Large Field-of-View Three-Dimensional Photon-Counting Imaging with a Single-Pixel Si-Avalanche Photodiode

Large field-of-view（FoV） three-dimensional（3 D） photon-counting imaging is demonstrated with a single-pixel single-photon detector based on a Geiger-mode Si-avalanche photodiode. By removing the collecting lens（CL）before the detector, the FoV is expanded to ±10°. Thanks to the high detection efficiency, the signal-to-noise ratio of the imaging system is as high as 7.8 dB even without the CL when the average output laser pulse energy is about 0.45 pJ/pulse for imaging the targets at a distance of 5 m. A 3 D image overlaid with the reflectivity data is obtained according to the photon-counting time-of-flight measurement and the return photon intensity.

Prenatal Diagnosis of Sirenomelia by Two-Dimensional and Three-Dimensional Skeletal Imaging Ultrasound

Summary： This study sought to evaluate the contribution of two-dimensional ultrasound （2D-US） and three-dimensional skeletal imaging ultrasound （3D-SUIS） in the prenatal diagnosis of sirenomelia. Be- tween September 2010 and April 2014, a prospective study was conducted in a single referral center using 3D-SU1S performed after 2D-US in 10 cases of sirenomelia. Diagnostic accuracy and detailed findings were compared with postnatal three-dimensional helical computed tomography （3D-HCT）, radiological findings and autopsy. Pregnancy was terminated in all 10 sirenomelia cases, including 9 singletons and I conjoined twin pregnancy, for a total of 5 males and 5 females. These cases of sirenomelia were deter- mined by autopsy and/or chromosomal examination. Initial 2D-US showed that there were 10 cases of oligohydranmios, bilateral renal agenesis, bladder agenesis, single umbilical artery, fusion of the lower limbs and spinal abnormalities; 8 cases of dipus or monopus; 2 cases of apus; and 8 cases of cardiac abnormalities. Subsequent 3D-SUIS showed that there were 9 cases of scoliosis, l0 cases of sacrococ- cygeal vertebra dysplasia, 3 cases of hemivertebra, 1 case of vertebral fusion, 3 cases of spina bifida, and 5 cases of rib abnormalities. 3D-SUIS identified significantly more skeletal abnormalities than did 2D-US, and its accuracy was 79.5% （70/88） compared with 3D-HCT and radiography. 3D-SUIS seems to be a useful complementary method to 2D-US and may improve the accuracy of identifying prenatal skeletal abnormalities related to sirenomelia.

Continuous imaging space in three-dimensional integral imaging

We report an integral imaging method with continuous imaging space. This method simultaneously reconstructs real and virtual images in the virtual mode, with a minimum gap that separates the entire imaging space into real and virtual space. Experimental results show that the gap is reduced to 45% of that in a conventional integral imaging system with the same parameters.

Magnetic resonance imaging-three-dimensional printing technology fabricates customized scaffolds for brain tissue engineering

Conventional fabrication methods lack the ability to control both macro- and micro-structures of generated scaffolds. Three-dimensional printing is a solid free-form fabrication method that provides novel ways to create customized scaffolds with high precision and accuracy. In this study, an electrically controlled cortical impactor was used to induce randomized brain tissue defects. The overall shape of scaffolds was designed using rat-specific anatomical data obtained from magnetic resonance imaging, and the internal structure was created by computer- aided design. As the result of limitations arising from insufficient resolution of the manufacturing process, we magnified the size of the cavity model prototype five-fold to successfully fabricate customized collagen-chitosan scaffolds using three-dimensional printing. Results demonstrated that scaffolds have three-dimensional porous structures, high porosity, highly specific surface areas, pore connectivity and good internal characteristics. Neural stem cells co-cultured with scaffolds showed good viability, indicating good biocompatibility and biodegradability. This technique may be a promising new strategy for regenerating complex damaged brain tissues, and helps pave the way toward personalized medicine.

A rapid micro-magnetic resonance imaging scanning for three-dimensional reconstruction of peripheral nerve fascicles

The most common methods for three-dimensional reconstruction of peripheral nerve fascicles include histological and radiology techniques. Histological techniques have many drawbacks including an enormous manual workload and poor image registration. Micro-magnetic resonance imaging（Micro-MRI）, an emerging radiology technique, has been used to report results in the brain, liver and tumor tissues. However, micro-MRI usage for obtaining intraneural structures has not been reported. The aim of this study was to present a new imaging method for three-dimensional reconstruction of peripheral nerve fascicles by ~1T micro-MRI. Freshly harvested sciatic nerve samples from an amputated limb were divided into four groups. Two different scanning conditions（Mannerist Solution/GD-DTPA contrast agent, distilled water） were selected, and both T1 and T2 phases programmed for each scanning condition. Three clinical surgeons evaluated the quality of the images via a standardized scale. Moreover, to analyze deformation of the two-dimensional image, the nerve diameter and total area of the micro-MRI images were compared after hematoxylin-eosin staining. The results show that rapid micro-MRI imaging method can be used for three-dimensional reconstruction of the fascicle structure. Nerve sample immersed in contrast agent（Mannerist Solution/GD-DTPA） and scanned in the T1 phase was the best. Moreover, the nerve sample was scanned freshly and can be recycled for other procedures. MRI images show better stability and smaller deformation compared with histological images. In conclusion, micro-MRI provides a feasible and rapid method for three-dimensional reconstruction of peripheral nerve fascicles, which can clearly show the internal structure of the peripheral nerve.

Three-dimensional time-of-flight magnetic resonance angiography combined with high resolution T2-weighted imaging in preoperative evaluation of microvascular decompression

BACKGROUND Neurovascular compression(NVC) is the main cause of primary trigeminal neuralgia(TN) and hemifacial spasm(HFS). Microvascular decompression(MVD) is an effective surgical method for the treatment of TN and HFS caused by NVC. The judgement of NVC is a critical step in the preoperative evaluation of MVD, which is related to the effect of MVD treatment. Magnetic resonance imaging(MRI) technology has been used to detect NVC prior to MVD for several years. Among many MRI sequences, three-dimensional time-of-flight magnetic resonance angiography(3D TOF MRA) is the most widely used. However, 3D TOF MRA has some shortcomings in detecting NVC. Therefore, 3D TOF MRA combined with high resolution T2-weighted imaging(HR T2WI) is considered to be a more effective method to detect NVC.AIM To determine the value of 3D TOF MRA combined with HR T2WI in the judgment of NVC, and thus to assess its value in the preoperative evaluation of MVD.METHODS Related studies published from inception to September 2022 based on PubMed, Embase, Web of Science, and the Cochrane Library were retrieved. Studies that investigated 3D TOF MRA combined with HR T2WI to judge NVC in patients with TN or HFS were included according to the inclusion criteria. Studies without complete data or not relevant to the research topics were excluded. The Quality Assessment of Diagnostic Accuracy Studies checklist was used to assess the quality of included studies. The publication bias of the included literature was examined by Deeks’ test. An exact binomial rendition of the bivariate mixed-effects regression model was used to synthesize data. Data analysis was performed using the MIDAS module of statistical software Stata 16.0. Two independent investigators extracted patient and study characteristics, and discrepancies were resolved by consensus. Individual and pooled sensitivities and specificities were calculated. The I_(2) statistic and Q test were used to test heterogeneity. The study was registered on the website of PROSERO(registration No. CRD42022357158).RESULTS Our search identified 595 articles, of which 12(including 855 patients) fulfilled the inclusion criteria. Bivariate analysis showed that the pooled sensitivity and specificity of 3D TOF MRA combined with HR T2WI for detecting NVC were 0.96 [95% confidence interval(CI): 0.92-0.98] and 0.92(95%CI: 0.74-0.98), respectively. The pooled positive likelihood ratio was 12.4(95%CI: 3.2-47.8), pooled negative likelihood ratio was 0.04(95%CI: 0.02-0.09), and pooled diagnostic odds ratio was 283(95%CI: 50-1620). The area under the receiver operating characteristic curve was 0.98(95%CI: 0.97-0.99). The studies showed no substantial heterogeneity(I2 = 0, Q = 0.001 P = 0.50).CONCLUSION Our results suggest that 3D TOF MRA combined with HR T2WI has excellent sensitivity and specificity for judging NVC in patients with TN or HFS. This method can be used as an effective tool for preoperative evaluation of MVD.

CROSS-TRACK THREE APERTURES MILLIMETER WAVE SAR SIDE-LOOKING THREE-DIMENSIONAL IMAGING

The airborne cross-track three apertures MilliMeter Wave (MMW) Synthetic Aperture Radar (SAR) side-looking three-Dimensional (3D) imaging is investigated in this paper. Three apertures are distributed along the cross-track direction, and three virtual phase centers will be obtained through one-input and three-output. These three virtual phase centers form a sparse array which can be used to obtain the cross-track resolution. Because the cross-track array is short, the cross-track resolution is low. When the system works in side-looking mode, the cross-track resolution and height resolution will be coupling, and the low cross-track resolution will partly be transformed into the height uncertainty. The beam pattern of the real aperture is used as a weight to improve the Peak to SideLobe Ratio (PSLR) and Integrated SideLobe Ratio (ISLR) of the cross-track sparse array. In order to suppress the high cross-track sidelobes, a weighting preprocessing method is proposed. The 3D images of a point target and a simulation scene are achieved to verify the feasibility of the proposed method. And the imaging result of the real data obtained by the cross-track three-baseline MMW InSAR prototype is presented as a beneficial attempt.

Three-dimensional bistatic interferometric ISA Rimaging

An approach based on interferometry technique is proposed for three-dimensional （3D） bistatic inverse synthetic aperture radar （ISAR） imaging. It is converted to a monostatic problem by using the theory that a bistatic radar equals a monostatic radar located on the bisector of bistatic an- gle. Then, interferometric phases extracted from a pair of cross shaped antennas are used to esti- mate the height and associated rotational velocity. Finally, numerical simulations are provided to e- valuate this method.