The first half of this paper explores the origin of systematic biases in the measurement of weak gravitational lensing. Compared to previous work, we expand the investigation of point spread function ...instability and fold in for the first time the effects of non-idealities in electronic imaging detectors and imperfect galaxy shape measurement algorithms. Together, these now explain the additive
and multiplicative
systematics typically reported in current lensing measurements. We find that overall performance is driven by a product of a telescope/camera's absolute performance, and our knowledge about its performance.
The second half of this paper propagates any residual shear measurement biases through to their effect on cosmological parameter constraints. Fully exploiting the statistical power of Stage IV weak lensing surveys will require additive biases
and multiplicative biases
. These can be allocated between individual budgets in hardware, calibration data and software, using results from the first half of the paper.
If instrumentation is stable and well calibrated, we find extant shear measurement software from Gravitational Lensing Accuracy Testing 2010 (GREAT10) already meet requirements on galaxies detected at signal-to-noise ratio = 40. Averaging over a population of galaxies with a realistic distribution of sizes, it also meets requirements for a 2D cosmic shear analysis from space. If used on fainter galaxies or for 3D cosmic shear tomography, existing algorithms would need calibration on simulations to avoid introducing bias at a level similar to the statistical error. Requirements on hardware and calibration data are discussed in more detail in a companion paper. Our analysis is intentionally general, but is specifically being used to drive the hardware and ground segment performance budget for the design of the European Space Agency's recently selected Euclid mission.
We present first results from the third GRavitational lEnsing Accuracy Testing (GREAT3) challenge, the third in a sequence of challenges for testing methods of inferring weak gravitational lensing ...shear distortions from simulated galaxy images. GREAT3 was divided into experiments to test three specific questions, and included simulated space- and ground-based data with constant or cosmologically varying shear fields. The simplest (control) experiment included parametric galaxies with a realistic distribution of signal-to-noise, size, and ellipticity, and a complex point spread function (PSF). The other experiments tested the additional impact of realistic galaxy morphology, multiple exposure imaging, and the uncertainty about a spatially varying PSF; the last two questions will be explored in Paper II. The 24 participating teams competed to estimate lensing shears to within systematic error tolerances for upcoming Stage-IV dark energy surveys, making 1525 submissions overall. GREAT3 saw considerable variety and innovation in the types of methods applied. Several teams now meet or exceed the targets in many of the tests conducted (to within the statistical errors). We conclude that the presence of realistic galaxy morphology in simulations changes shear calibration biases by ∼1 per cent for a wide range of methods. Other effects such as truncation biases due to finite galaxy postage stamps, and the impact of galaxy type as measured by the Sérsic index, are quantified for the first time. Our results generalize previous studies regarding sensitivities to galaxy size and signal-to-noise, and to PSF properties such as seeing and defocus. Almost all methods’ results support the simple model in which additive shear biases depend linearly on PSF ellipticity.
We present a joint weak lensing and X-ray analysis of 4 deg2 from the CFHTLS and XMM-LSS surveys. Our weak lensing analysis is the first analysis of a real survey using shapelets, a new generation ...weak lensing analysis method. We create projected mass maps of the images, and extract six weak-lensing-detected clusters of galaxies. We show that their counts can be used to constrain the power-spectrum normalization σ8= 0.92+0.26−0.30 for Ωm= 0.24. We show that despite the large scatter generally observed in the mass–temperature (M–T) relation derived from lensing masses, tight constraints on both its slope and normalization M* can be obtained with a moderate number of sources provided that the covered mass range is large enough. Adding clusters given by Bardeau et al. to our sample, we measure M*= 2.71+0.79−0.61× 1014h−1M⊙. Although they are dominated by shot noise and sample variance, our measurements are consistent with currently favoured values, and set the stage for future surveys. We thus investigate the dependence of those estimates on survey size, depth and integration time, for joint weak lensing and X-ray surveys. We show that deep surveys should be dedicated to the study of the physics of clusters and groups of galaxies. For a given exposure time, wide surveys provide a larger number of detected clusters and are therefore preferred for the measurement of cosmological parameters, such as σ8 and M*. We show that a wide survey of a few hundred square degrees is needed to improve upon current measurements of these parameters. More ambitious surveys covering 7000 deg2 will provide the 1 per cent accuracy in the estimation of the power-spectrum and the M–T relation normalizations.
We present the results of the Gravitational LEnsing Accuracy Testing 2008 (GREAT08) Challenge, a blind analysis challenge to infer weak gravitational lensing shear distortions from images. The ...primary goal was to stimulate new ideas by presenting the problem to researchers outside the shear measurement community. Six GREAT08 Team methods were presented at the launch of the Challenge and five additional groups submitted results during the 6-month competition. Participants analyzed 30 million simulated galaxies with a range in signal-to-noise ratio, point spread function ellipticity, galaxy size and galaxy type. The large quantity of simulations allowed shear measurement methods to be assessed at a level of accuracy suitable for currently planned future cosmic shear observations for the first time. Different methods perform well in different parts of simulation parameter space and come close to the target level of accuracy in several of these. A number of fresh ideas have emerged as a result of the Challenge including a re-examination of the process of combining information from different galaxies, which reduces the dependence on realistic galaxy modelling. The image simulations will become increasingly sophisticated in future GREAT Challenges, meanwhile the GREAT08 simulations remain as a benchmark for additional developments in shear measurement algorithms.
The Shear Testing Programme (STEP) is a collaborative project to improve the accuracy and reliability of weak-lensing measurement, in preparation for the next generation of wide-field surveys. We ...review 16 current and emerging shear-measurement methods in a common language, and assess their performance by running them (blindly) on simulated images that contain a known shear signal. We determine the common features of algorithms that most successfully recover the input parameters. A desirable goal would be the combination of their best elements into one ultimate shear-measurement method. In this analysis, we achieve previously unattained discriminatory precision via a combination of more extensive simulations and pairs of galaxy images that have been rotated with respect to each other. That removes the otherwise overwhelming noise from their intrinsic ellipticities. Finally, the robustness of our simulation approach is confirmed by testing the relative calibration of methods on real data.
Weak-lensing measurements have improved since the first STEP paper. Several methods now consistently achieve better than 2 per cent precision, and are still being developed. However, we can now distinguish all methods from perfect performance. Our main concern continues to be the potential for a multiplicative shear calibration bias: not least because this cannot be internally calibrated with real data. We determine which galaxy populations are responsible for bias and, by adjusting the simulated observing conditions, we also investigate the effects of instrumental and atmospheric parameters. The simulated point spread functions are not allowed to vary spatially, to avoid additional confusion from interpolation errors. We have isolated several previously unrecognized aspects of galaxy shape measurement, in which focused development could provide further progress towards the sub-per cent level of precision desired for future surveys. These areas include the suitable treatment of image pixellization and galaxy morphology evolution. Ignoring the former effect affects the measurement of shear in different directions, leading to an overall underestimation of shear and hence the amplitude of the matter power spectrum. Ignoring the second effect could affect the calibration of shear estimators as a function of galaxy redshift, and the evolution of the lensing signal, which will be vital to measure parameters including the dark energy equation of state.
The GRavitational lEnsing Accuracy Testing 2008 (GREAT08) Challenge focuses on a problem that is of crucial importance for future observations in cosmology. The shapes of distant galaxies can be used ...to determine the properties of dark energy and the nature of gravity, because light from those galaxies is bent by gravity from the intervening dark matter. The observed galaxy images appear distorted, although only slightly, and their shapes must be precisely disentangled from the effects of pixelisation, convolution and noise. The worldwide gravitational lensing community has made significant progress in techniques to measure these distortions via the Shear TEsting Program (STEP). Via STEP, we have run challenges within our own community, and come to recognise that this particular image analysis problem is ideally matched to experts in statistical inference, inverse problems and computational learning. Thus, in order to continue the progress seen in recent years, we are seeking an infusion of new ideas from these communities. This document details the GREAT08 Challenge for potential participants. Please visit www.great08challenge.info for the latest information.
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GRavitational lEnsing Accuracy Testing 2010 (GREAT10) is a public image analysis challenge aimed at the development of algorithms to analyze astronomical images. Specifically, the challenge is to ...measure varying image distortions in the presence of a variable convolution kernel, pixelization and noise. This is the second in a series of challenges set to the astronomy, computer science and statistics communities, providing a structured environment in which methods can be improved and tested in preparation for planned astronomical surveys. GREAT10 extends upon previous work by introducing variable fields into the challenge. The "Galaxy Challenge" involves the precise measurement of galaxy shape distortions, quantified locally by two parameters called shear, in the presence of a known convolution kernel. Crucially, the convolution kernel and the simulated gravitational lensing shape distortion both now vary as a function of position within the images, as is the case for real data. In addition, we introduce the "Star Challenge" that concerns the reconstruction of a variable convolution kernel, similar to that in a typical astronomical observation. This document details the GREAT10 Challenge for potential participants. Continually updated information is also available from www.greatchallenges.info.
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