Camera distortion self-calibration using the plumb-line constraint and minimal Hough entropy

In this paper we present a simple and robust method for self-correction of camera distortion using single images of scenes which contain straight lines. Since the most common distortion can be modelled as radial distortion, we illustrate the method using the Harris radial distortion model, but the method is applicable to any distortion model. The method is based on transforming the edgels of the distorted image to a 1-D angular Hough space, and optimizing the distortion correction parameters which minimize the entropy of the corresponding normalized histogram. Properly corrected imagery will have fewer curved lines, and therefore less spread in Hough space. Since the method does not rely on any image structure beyond the existence of edgels sharing some common orientations and does not use edge fitting, it is applicable to a wide variety of image types. For instance, it can be applied equally well to images of texture with weak but dominant orientations, or images with strong vanishing points. Finally, the method is performed on both synthetic and real data revealing that it is particularly robust to noise.Comment: 9 pages, 5 figures Corrected errors in equation 1

A Multiwavelength Analysis of the Strong Lensing Cluster RCS 022434-0002.5 at z=0.778

We present the results of two (101 ks total) Chandra observations of the z=0.778 optically selected lensing cluster RCS022434-0002.5, along with weak lensing and dynamical analyses of this object. An X-ray spectrum extracted within R(2500) (362 h(70)^(-1) kpc) results in an integrated cluster temperature of 5.1 (+0.9,-0.5) keV. The surface brightness profile of RCS022434-0002.5 indicates the presence of a slight excess of emission in the core. A hardness ratio image of this object reveals that this central emission is primarily produced by soft X-rays. Further investigation yields a cluster cooling time of 3.3 times 10^9 years, which is less than half of the age of the universe at this redshift given the current LCDM cosmology. A weak lensing analysis is performed using HST images, and our weak lensing mass estimate is found to be in good agreement with the X-ray determined mass of the cluster. Spectroscopic analysis reveals that RCS022434-0002.5 has a velocity dispersion of 900 +/- 180 km/s, consistent with its X-ray temperature. The core gas mass fraction of RCS022434-0002.5 is, however, found to be three times lower than expected universal values. The radial distribution of X-ray point sources within R(200) of this cluster peaks at ~0.7 R(200), possibly indicating that the cluster potential is influencing AGN activity at that radius. Correlations between X-ray and radio (VLA) point source positions are also examined.Comment: 32 pages, 9 figures. Accepted for publication in The Astrophysical Journa

Hubble Space Telescope weak lensing study of the z=0.83 cluster MS 1054-03

We have measured the weak gravitational lensing signal of MS 1054-03, a rich and X-ray luminous cluster of galaxies at a redshift of z=0.83, using a two-colour mosaic of deep WFPC2 images. The small corrections for the size of the PSF and the high number density of background galaxies obtained in these observations result in an accurate and well calibrated measurement of the lensing induced distortion. The strength of the lensing signal depends on the redshift distribution of the background galaxies. We used photometric redshift distributions from the Northern and Southern Hubble Deep Fields to relate the lensing signal to the mass. The predicted variations of the signal as a function of apparent source magnitude and colour agrees well with the observed lensing signal. We determine a mass of (1.2+-0.2)x10^15 Msun within an aperture of radius 1 Mpc. Under the assumption of an isothermal mass distribution, the corresponding velocity dispersion is 1311^{+83}_{-89} km/s. For the mass-to-light ratio we find 269+-37 Msun/Lsun. The errors in the mass and mass-to-light ratio include the contribution from the random intrinsic ellipticities of the source galaxies, but not the (systematic) error due to the uncertainty in the redshift distribution. However, the estimates for the mass and mass-to-light ratio of MS 1054-03 agree well with other estimators, suggesting that the mass calibration works well. The reconstruction of the projected mass surface density shows a complex mass distribution, consistent with the light distribution. The results indicate that MS 1054-03 is a young system. The timescale for relaxation is estimated to be at least 1 Gyr. Averaging the tangential shear around the cluster galaxies, we find that the velocity dispersion of an Lstar galaxy is 203+-33 km/s.Comment: 21 pages, Latex, with 27 figures (3 figures bitmapped), ApJ, in press. Version (with non-bitmapped figures) available at http://www.astro.rug.nl/~hoekstra/papers.htm

Means of confusion: how pixel noise affects shear estimates for weak gravitational lensing

Weak-lensing shear estimates show a troublesome dependence on the apparent brightness of the galaxies used to measure the ellipticity: In several studies, the amplitude of the inferred shear falls sharply with decreasing source significance. This dependence limits the overall ability of upcoming large weak-lensing surveys to constrain cosmological parameters. We seek to provide a concise overview of the impact of pixel noise on weak-lensing measurements, covering the entire path from noisy images to shear estimates. We show that there are at least three distinct layers, where pixel noise not only obscures but biases the outcome of the measurements: 1) the propagation of pixel noise to the non-linear observable ellipticity; 2) the response of the shape-measurement methods to limited amount of information extractable from noisy images; and 3) the reaction of shear estimation statistics to the presence of noise and outliers in the measured ellipticities. We identify and discuss several fundamental problems and show that each of them is able to introduce biases in the range of a few tenths to a few percent for galaxies with typical significance levels. Furthermore, all of these biases do not only depend on the brightness of galaxies but also on their ellipticity, with more elliptical galaxies often being harder to measure correctly. We also discuss existing possibilities to mitigate and novel ideas to avoid the biases induced by pixel noise. We present a new shear estimator that shows a more robust performance for noisy ellipticity samples. Finally, we release the open-source python code to predict and efficiently sample from the noisy ellipticity distribution and the shear estimators used in this work at https://github.com/pmelchior/epsnoiseComment: integrated the origin of the moment correlation (thanks to Alan Heavens). source code at https://github.com/pmelchior/epsnois

Correction of image radial distortion based on division model

This paper presents an approach for estimating and then removing image radial distortion. It works on a single image and does not require a special calibration. The approach is extremely useful in many applications, particularly those where human-made environments contain abundant lines. A division model is applied, in which a straight line in the distorted image is treated as a circular arc. Levenberg–Marquardt (LM) iterative nonlinear least squares method is adopted to calculate the arc’s parameters. Then “Taubin fit” is applied to obtain the initial guess of the arc’s parameters which works as the initial input to the LM iteration. This dramatically improves the convergence rate in the LM process to obtain the required parameters for correcting image radial distortion. Hough entropy, as a measure, has achieved the quantitative evaluation of the estimated distortion based on the probability distribution in one-dimensional θ Hough space. The experimental results on both synthetic and real images have demonstrated that the proposed method can robustly estimate and then remove image radial distortion with high accurac

The Magnetic Distortion Calibration System of the LHCb RICH1 Detector

The LHCb RICH1 detector uses hybrid photon detectors (HPDs) as its optical sensors. A calibration system has been constructed to provide corrections for distortions that are primarily due to external magnetic fields. We describe here the system design, construction, operation and performance.Comment: 9 pages, 14 figure

Variation of the Diameter of the Sun as Measured by the Solar Disk Sextant (SDS)

The balloon-borne Solar Disk Sextant (SDS) experiment has measured the angular size of the Sun on seven occasions spanning the years 1992 to 2011. The solar half-diameter -- observed in a 100-nm wide passband centred at 615 nm -- is found to vary over that period by up to 200 mas, while the typical estimated uncertainty of each measure is 20 mas. The diameter variation is not in phase with the solar activity cycle; thus, the measured diameter variation cannot be explained as an observational artefact of surface activity. Other possible instrument-related explanations for the observed variation are considered but found unlikely, leading us to conclude that the variation is real. The SDS is described here in detail, as is the complete analysis procedure necessary to calibrate the instrument and allow comparison of diameter measures across decades.Comment: 41 pages; appendix and 2 figures added plus some changes in text based on referee's comments; to appear in MNRA