Radius Error Research Articles

Improving the accuracy of mirror measurements by removing noise and lens distortion

Telescope mirrors determine the imaging quality and observation ability of telescopes. Unfortunately, manufacturing highly accurate mirrors remains a bottleneck problem in space optics. One main factor is the lack of a technique for measuring the 3D shapes of mirrors accurately for inverse engineering. Researchers have studied and developed techniques for testing the quality of telescope mirrors and methods for measuring the 3D shapes of mirrors for centuries. Among these, interferometers have become popular in evaluating the surface errors of manufactured mirrors. However, interferometers are unable to measure some important mirror parameters directly and accurately, e.g. the paraxial radius, geometry dimension and eccentric errors, and these parameters are essential for mirror manufacturing. In this paper, we aim to remove the noise and lens distortion inherent in the system to improve the accuracy of a previously proposed one-shot projection mirror measurement method. To this end, we propose a ray modeling and a pattern modeling method. The experimental results show that the proposed ray modeling and pattern modeling method can improve the accuracy of the one-shot projection method significantly, making it feasible as a commercial device to measure the shapes of mirrors quantitatively and accurately.

Spatial Detection of Vehicles in Images using Convolutional Neural Networks and Stereo Matching

Convolutional Neural Networks combined with a state of the artstereo-matching method are used to find and estimate the 3D positionof vehicles in pairs of stereo images. Pixel positions of vehiclesare first estimated separately in pairs of stereo images usinga Convolutional Neural Network for regression. These coordinatesare then combined with a state-of-art stereo-matching method todetermine the depth, and thus the 3D location, of the vehicles. Weshow in this paper that cars can be detected with a combined accuracyof approximately 90% with a tolerated radius error of 5%,and a Mean Absolute Error of 5.25m on depth estimation for carsup to 50m away.

Technique for measuring the three-dimensional shapes of telescope mirrors

Telescope mirrors determine the imaging quality and the observation ability of the telescopes. Unfortunately, manufacturing highly accurate mirrors remains a bottleneck problem in space optics. One primary cause is the lack of a technique to robustly measure the three-dimensional (3-D) shapes of mirrors for inverse engineering. After centuries of study, researchers developed different techniques for testing the quality of telescope mirrors and proposed different methods for measuring the 3-D shapes of mirrors. Among them, interferometers become popular in evaluating the surface errors of the manufactured mirrors. However, interferometers could not measure some important mirror parameters, e.g., paraxial radius, geometry dimension, and eccentric errors, directly and accurately although these parameters are essential for mirror manufacturing. For those methods that could measure these parameters, their measurement accuracies are far beyond satisfactory. We present a technique for robust measurement of the 3-D shapes of mirrors with single-shot projection. Experimental results show that this technique is significantly more robust than state-of-the-art techniques, which makes it feasible for commercial devices to measure the shapes of mirrors quantitatively and robustly.

X-RAY SPECTRAL AND OPTICAL PROPERTIES OF A ULX IN NGC 4258 (M106)

ABSTRACT We study the X-ray and optical properties of the ultraluminous X-ray source (ULX) X-6 in the nearby galaxy NGC 4258 (M106) based on the archival XMM-Newton, Chandra, Swift, and Hubble Space Telescope (HST) observations. The source has a peak luminosity of L X ∼ 2 × 1039 erg s−1 in the XMM-Newton observation of 2004 June. Consideration of the hardness ratios and the spectral model parameters shows that the source seems to exhibit possible spectral variations throughout the X-ray observations. In the images from the HST/Advanced Camera for Surveys, three optical sources have been identified as counterpart candidates within the 1σ error radius of 0.″3. The brightest one has an absolute magnitude of M V ≈ −7.0 and shows extended structure. The remaining two sources have absolute magnitudes of M V ≈ −5.8 and −5.3. The possible spectral types of the candidates from brightest to dimmest were determined as B6–A5, B0–A7, and B2–A3. The counterparts of the X-ray source possibly belong to a young star cluster. Neither the standard disk model nor the slim disk model provides firm evidence to determine the spectral characteristics of ULX X-6. We argue that the mass of the compact object lies in the range 10–15 M ☉, indicating that the compact source is most likely a stellar-mass black hole.

A high-accuracy roundness measurement for cylindrical components by a morphological filter considering eccentricity, probe offset, tip head radius and tilt error

A morphological filter is proposed to obtain a high-accuracy roundness measurement based on the four-parameter roundness measurement model, which takes into account eccentricity, probe offset, probe tip head radius and tilt error. This paper analyses the sample angle deviations caused by the four systematic errors to design a morphological filter based on the distribution of the sample angle. The effectiveness of the proposed method is verified through simulations and experiments performed with a roundness measuring machine. Compared to the morphological filter with the uniform sample angle, the accuracy of the roundness measurement can be increased by approximately 0.09 μm using the morphological filter with a non-uniform sample angle based on the four-parameter roundness measurement model, when eccentricity is above 16 μm, probe offset is approximately 1000 μm, tilt error is approximately 1″, the probe tip head radius is 1 mm and the cylindrical component radius is approximately 37 mm. The accuracy and reliability of roundness measurements are improved by using the proposed method for cylindrical components with a small radius, especially if the eccentricity and probe offset are large, and the tilt error and probe tip head radius are small. The proposed morphological filter method can be used for precision and ultra-precision roundness measurements, especially for functional assessments of roundness profiles.

On the Local Convergence of an Eighth-order Method for Solving Nonlinear Equations

Abstract We present a local convergence analysis of an eighth-order method for approximating a locally unique solution of a non-linear equation. Earlier studies such as have shown convergence of these methods under hypotheses up to the seventh derivative of the function although only the first derivative appears in the method. In this study, we expand the applicability of these methods using only hypotheses up to the first derivative of the function. This way the applicability of these methods is extended under weaker hypotheses. Moreover, the radius of convergence and computable error bounds on the distances involved are also given in this study. Numerical examples are also presented in this study.

Measurement and algorithm for localization of aspheric lens in magnetorheological finishing

Unlike traditional machinery manufacturing generally using simple features of workpiece as the alignment reference, optical manufacturing, which prioritizes shape tolerances of the machining surface over position tolerances between workpiece geometry features, chooses the machining surface itself as the alignment reference. Thus, the manual alignment of workpiece in optical manufacturing could be very time-consuming when the machining surface is aspheric. Workpiece localization technology is able to automate the workpiece alignment and improve its efficiency. However, there are no relevant reports about application of this technology in the field of optical manufacturing. In this work, the workpiece localization problem for aspheric surface in magnetorheological finishing (MRF) is investigated from aspects of measurement and algorithm. The probe radius error is compensated by applying the polynomial fitting method. A new localization algorithm is proposed in order to improve the computational efficiency for the localization of aspheric surface. Simulation and experiment results verify the validity of the proposed methods. The accurate and efficient workpiece localization in MRF has been achieved and applied in real application which proves its practicability.

Ball convergence of some fourth and sixth-order iterative methods

We present a local convergence analysis for some families of fourth and sixth-order methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Earlier studies [V. Candela and A. Marquina, Recurrence relations for rational cubic methods II: The Chebyshev method, Computing 45 (1990) 355–367; C. Chun, P. Stanica and B. Neta, Third order family of methods in Banach spaces, Comput. Math. Appl. 61 (2011) 1665–1675; J. M. Gutiérrez and M. A. Hernández, Recurrence relations for the super-Halley method, Comput. Math. Appl. 36 (1998) 1–8; M. A. Hernández and M. A. Salanova, Modification of the Kantorovich assumptions for semilocal convergence of the Chebyshev method, J. Comput. Appl. Math. 126 (2000) 131–143; M. A. Hernández, Chebyshev’s approximation algorithms and applications, Comput. Math. Appl. 41 (2001) 433–455; M. A. Hernández, Second-derivative-free variant of the Chebyshev method for nonlinear equations, J. Optim. Theory Appl. 104(3) (2000) 501–515; J. L. Hueso, E. Martinez and C. Teruel, Convergence, efficiency and dynamics of new fourth and sixth-order families of iterative methods for nonlinear systems, J. Comput. Appl. Math. 275 (2015) 412–420; Á. A. Magre nán, Estudio de la dinámica del método de Newton amortiguado, Ph.D. thesis, Servicio de Publicaciones, Universidad de La Rioja (2013), http://dialnet.unirioja.es/servlet/tesis?codigo=38821 ; J. M. Ortega and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables (Academic Press, New York, 1970); M. S. Petkovic, B. Neta, L. Petkovic and J. Džunič, Multi-Point Methods for Solving Nonlinear Equations (Elsevier, 2013); J. F. Traub, Iterative Methods for the Solution of Equations, Automatic Computation (Prentice-Hall, Englewood Cliffs, NJ, 1964); X. Wang and J. Kou, Semilocal convergence and [Formula: see text]-order for modified Chebyshev–Halley methods, Numer. Algorithms 64(1) (2013) 105–126] have used hypotheses on the fourth Fréchet derivative of the operator involved. We use hypotheses only on the first Fréchet derivative in our local convergence analysis. This way, the applicability of these methods is extended. Moreover the radius of convergence and computable error bounds on the distances involved are also given in this study. Numerical examples illustrating the theoretical results are also presented in this study.

On-machine contact measurement for the main-push propeller blade with belt grinding

A main-push propeller blade (MPPB) with a free-form surface has great volume and weight, severe casting deformation and pore shrinkage, and loading and unloading difficulties. It is thus difficult to measure and evaluate accurately for manufacturing, especially for precision grinding. On-machine contact measurement (OMCM) is proposed in this paper and has been used successfully for belt grinding equipment. This paper establishes a method of improving the surface precision of the MPPB. First, the principle of the five-axis OMCM for the MPPB surface with belt grinding is illustrated. The path planning, point distribution, and radius error compensation are then analyzed and optimized for OMCM. Finally, an experiment for the belt grinding of an MPPB is conducted after OMCM. The experimental results show that the measurement precision is enhanced, and the measuring efficiency is advanced, the surface roughness Ra < 0.6 μm, the errors of profile precision of the MPPB are ±0.5 mm, and the tolerances on the curvature geometry and the surface finish all meet requirements of OMCM after belt grinding. The effectiveness and practicability of the method are thus fully verified.

Estimating Stellar Parameters and Interstellar Extinction from Evolutionary Tracks

Abstract Developing methods for analyzing and extracting information from modern sky surveys is a challenging task in astrophysical studies. We study possibilities of parameterizing stars and interstellar medium from multicolor photometry performed in three modern photometric surveys: GALEX, SDSS, and 2MASS. For this purpose, we have developed a method to estimate stellar radius from effective temperature and gravity with the help of evolutionary tracks and model stellar atmospheres. In accordance with the evolution rate at every point of the evolutionary track, star formation rate, and initial mass function, a weight is assigned to the resulting value of radius that allows us to estimate the radius more accurately. The method is verified for the most populated areas of the Hertzsprung-Russell diagram: main-sequence stars and red giants, and it was found to be rather precise (for main-sequence stars, the average relative error of radius and its standard deviation are 0.03% and 3.87%, respectively).

Local convergence for a derivative free method of order three under weak conditions

A local convergence analysis for a family of a third-order method in order to approximate a solution of a nonlinear equation is presented in this paper. We use hypotheses only on the first derivative in contrast to earlier studies such as Parhi and Gupta (2007, 2010) and Zhu and Wu (2003) using hypotheses only on the first derivative. This way the applicability of these methods is extended under weaker hypotheses. Moreover the radius of convergence and computable error bounds on the distances involved are also given in this study. Numerical examples are also presented in this study.

Application of gradient-based Hough transform to the detection of corrosion pits in optical images

In this paper, we introduce a circle detection technique named Hough transform to automatically recognize the corrosion pits in microscopic images. All the points in the input image are transformed into a parameter space, which is represented by a two-dimensional accumulative array with the same size of the original image. Local extreme values in the accumulative array, which represent the candidates of corrosion pits, are located using a maxima searching algorithm. The accuracy of detecting the number, radius and coordinate of pits from simulated images was examined. The results show that more than 95% of pits were successfully detected and the average errors of radius and coordinate are less than 10%, while these errors have negligible effect on the pit size distribution. The introduced method can also differentiate pits from scratches or inclusions, as indicated by the 100% accuracy of pit detection, from the simulated images presented in this study. Therefore, it is believed that the gradient-based Hough transform is a powerful method for the recognition of corrosion pits in microscopic images, making the statistical analysis of pit size and pit locations easier and more efficient.

Artificial Neural Networks for Data Analysis of Magnetic Measurements on East

The problem of the reconstruction of the parameters characterizing the plasma shape in a tokamak device is of paramount importance both for present day experiments and for future reactor. The plasma shape can only be evaluated by diagnostic data, such as poloidal flux and magnetic field measured respectively by the flux loops and magnetic probes located on the vacuum vessel outside the plasma. The aim of the present paper is to take a step forward in the application of the neural network approach for the identification of non-circular plasma equilibrium and data analysis for the problem of the optimal location of a limited number of magnetic sensors. We have adopted a machine learning method, back-propagation neural network, to analyze the magnetic diagnostic data. The database has been generated by means of a specially adapted version of an MHD equilibrium code EFIT with reference to the EAST geometry and stored in the EAST mdsplus database. The network uses external magnetic measurements as input data and the selected plasma parameters as output data to train and test. Then a novel strategy is implemented for the selection of the optimum location of a limited number of magnetic probes based data analysis of the network. The average accuracy of the identification procedure is quite good (e.g., the maximum relative error is 0.260 % of internal inductance), with a contrast of the computation results of EFIT as desired output. It has been shown that the degradation of the performance is rather small (e.g., RMS error of minor radius vary from 4.307 to 4.765 %) when the number of magnetic probes is reduced by nearly half.

Robust global error bounds for uncertain linear inequality systems with applications

In this paper, we examine global error bounds for a linear inequality system in the face of data uncertainty by building upon recent developments in robust optimization, where the uncertain parameters are assumed to be in prescribed uncertainty sets. We present necessary and sufficient dual conditions for the existence of robust global error bounds. As a consequence, we obtain a robust Hoffman error bound in the case of commonly used interval data uncertainty, extending the well-known Hoffman's error bound. We then introduce the notion of radius of robust global error bound under interval data uncertainty and present a formula for finding the radius by examining the stability of robust global error bounds. It provides the radius of the largest interval uncertainty set in which the uncertain system admits a robust global error bound. As an immediate application to robust linear programming, we provide conditions for robust feasibility and give a formula for radius of robust feasibility of an uncertain linear program.

Distortion Correction of Visante Optical Coherence Tomography Cornea Images.

Quantitative biometry measurements from uncorrected anterior segment optical coherence tomography (AS-OCT) images are inaccurate because of spatial and optical distortions. Prior reported distortion correction equations for the Visante AS-OCT were not reproducible. The goal was to calculate the distortions and provide equations to correct corneal parameters for the Visante AS-OCT to get a central corneal radius of curvature from young and older subjects. Five contact lenses (CLs) of known front and back radii of curvature and central thickness were imaged using the Visante AS-OCT (Carl Zeiss, Dublin, CA). Contact lens surface coordinates from Visante images were identified and fitted with a circle using custom Matlab image analysis software. Spatial and optical distortions of the Visante image of the CL radii of curvature and thickness were calculated and corrected. Visante images were also captured from 24 younger (aged 21 to 36 years) and 30 older (aged 36 to 48 years) human subjects. Corneal radii of curvature and thickness measurements from these subjects were corrected, and intrasession and intersession repeatabilities of the corneal parameters were calculated. Root mean square error of radius and power of the CL surfaces after distortion correction were 0.02 mm and 0.18D for the front and 0.011 mm and 0.11D for the back, respectively. Intraclass correlation coefficient for intrasession and intersession repeatability for all the corneal parameters from the human subjects was greater than 0.88 in both age groups. A distortion correction algorithm was developed for the Visante AS-OCT and applied to extract human corneal radius of curvature measurements.

Ball convergence for Traub-Steffensen like methods in Banach space

Abstract We present a local convergence analysis for two Traub-Steffensen-like methods in order to approximate a locally unique solution of an equation in a Banach space setting. In earlier studies such as [16, 23] Taylor expansions and hypotheses up to the third Fréchet-derivative are used. We expand the applicability of these methods using only hypotheses on the first Fréchet derivative. Moreover, we obtain a radius of convergence and computable error bounds using Lipschitz constants not given before. Numerical examples are also presented in this study.

Non-cooperative Interference Radio Localization with Binary Proximity Sensors

Interference can cause serious problems in our daily life. Traditional ways in localizing a target can’t work well when it comes to the source of interference for it may take an uncooperative or even resistant attitude towards localization. To tackle this issue, we take the BPSN (Binary Proximity Sensor Networks) and consider a passive way in this paper. No cooperation is needed and it is based on simple sensor node suitable for large-scale deployment. By dividing the sensing field into different patches, when enough patches are formed, good localization accuracy can be achieved with high resolution. Then we analyze the relationship between sensing radius and localization error, we find that in a finite region where edge effect can’t be ignored, the trend between sensing radius and localization error is not always consistent. Through theoretical analysis and simulation, we explore to determine the best sensing radius to achieve high localization accuracy.

THE DETECTION OF A SN IIn IN OPTICAL FOLLOW-UP OBSERVATIONS OF ICECUBE NEUTRINO EVENTS

The IceCube neutrino observatory pursues a follow-up program selecting interesting neutrino events in real-time and issuing alerts for electromagnetic follow-up observations. In March 2012, the most significant neutrino alert during the first three years of operation was issued by IceCube. In the follow-up observations performed by the Palomar Transient Factory (PTF), a Type IIn supernova (SN) PTF12csy was found $0.2^\circ$ away from the neutrino alert direction, with an error radius of $0.54^\circ$. It has a redshift of $z=0.0684$, corresponding to a luminosity distance of about $300 \, \mathrm{Mpc}$ and the Pan-STARRS1 survey shows that its explosion time was at least 158 days (in host galaxy rest frame) before the neutrino alert, so that a causal connection is unlikely. The a posteriori significance of the chance detection of both the neutrinos and the SN at any epoch is $2.2 \, \sigma$ within IceCube's 2011/12 data acquisition season. Also, a complementary neutrino analysis reveals no long-term signal over the course of one year. Therefore, we consider the SN detection coincidental and the neutrinos uncorrelated to the SN. However, the SN is unusual and interesting by itself: It is luminous and energetic, bearing strong resemblance to the SN IIn 2010jl, and shows signs of interaction of the SN ejecta with a dense circumstellar medium. High-energy neutrino emission is expected in models of diffusive shock acceleration, but at a low, non-detectable level for this specific SN. In this paper, we describe the SN PTF12csy and present both the neutrino and electromagnetic data, as well as their analysis.

Ball convergence theorems for Maheshwari-type eighth-order methods under weak conditions

We present a local convergence analysis for a family of Maheshwari-type eighth-order methods in order to approximate a solution of a nonlinear equation. We use hypotheses up to the first derivative in contrast to earlier studies such as Cordero et al. (J Comput Appl Math 291(1):348–357, 2016), Maheshwari (Appl Math Comput 211:283–391, 2009), Petkovic et al. (Multipoint methods for solving nonlinear equations. Elsevier, Amsterdam, 2013) using hypotheses up to the seventh derivative. This way the applicability of these methods is extended under weaker hypotheses. Moreover the radius of convergence and computable error bounds on the distances involved are also given in this study. Numerical examples are also presented in this study.

NEWLY DETERMINED EXPLOSION CENTER OF TYCHO’S SUPERNOVA AND THE IMPLICATIONS FOR PROPOSED EX-COMPANION STARS OF THE PROGENITOR

`Star G', near the center of the supernova remnant of Tycho's SN1572, has been claimed to be the ex-companion star of the exploding white dwarf, thus pointing to the progenitor being like a recurrent nova. This claim has been controversial, but there have been no confident proofs or disproofs. Previously, no has seriously addressed the question as to the exact explosion site in 1572. We now provide accurate measures of the supernova position by two radically different methods. Our first method is to use the 42 measured angular distances between the supernova in 1572 and bright nearby stars, with individual measures being as good as 84 arc-seconds, and all resulting in a position with a 1-$\sigma$ error radius of 39 arc-seconds (including systematic uncertainties). Our second method is to use a detailed and realistic expansion model for 19 positions around the edge of the remnant, where the swept-up material has measured densities, and we determine the center of expansion with a chi-square fit to the 19 measured radii and velocities. This method has a 1-$\sigma$ error radius of 7.5 arc-seconds. Both measures are substantially offset from the geometric center, and both agree closely, proving that neither has any significant systematic errors. Our final combined position for the site of the 1572 explosion is J2000 $\alpha$=0h 25m 15.36s, $\delta=64^{\circ} 8' 40.2"$, with a 7.3 arc-second 1-sigma uncertainty. Star G is rejected at the 8.2-$\sigma$ confidence level. Our new position lies mostly outside the region previously searched for ex-companion stars.