Point spread function calibration requirements for dark energy from cosmic shear

Abstract

Context. The control of systematic effects when measuring background galaxy shapes is one of the main challenges for cosmic shear analyses. Aims. Study the fundamental limitations on shear accuracy due to the measurement of the point spread function (PSF) from the finite number of stars that are available. We translate the accuracy required for cosmological parameter estimation to the minimum number of stars over which the PSF must be calibrated. Methods. We characterise the error made in the shear arising from errors on the PSF. We consider different PSF models, from a simple elliptical Gaussian to various shapelet parametrisations. First we derive our results analytically in the case of infinitely small pixels (i.e. infinitely high resolution), then image simulations are used to validate these results and investigate the effect of finite pixel size in the case of the elliptical Gaussian PSF. Results. Our results are expressed in terms of the minimum number of stars required to calibrate the PSF in order to ensure that systematic errors are smaller than statistical errors when estimating the cosmological parameters. On scales smaller than the area containing this minimum number of stars, there is not enough information to model the PSF. This means that these small scales should not be used to constrain cosmology unless the instrument and the observing strategy are optimised to make this variability extremely small. The minimum number of stars varies with the square of the star Signal-to-Noise Ratio, with the complexity of the PSF and with the pixel size. In the case of an elliptical Gaussian PSF and in the absence of dithering, 2 pixels per PSF full width at half maximum (FWHM) implies a 20% increase of the minimum number of stars compared to the ideal case of infinitely small pixels; 0.9 pixels per PSF FWHM implies a factor 100 increase. Conclusions. In the case of a good resolution and a typical Signal-to-Noise Ratio distribution of stars, we find that current surveys need the PSF to be calibrated over a few stars, which may explain residual systematics on scales smaller than a few arcmins. Future all-sky cosmic shear surveys require the PSF to be calibrated over a region containing about 50 stars. Due to the simplicity of our models these results should be interpreted as optimistic and therefore provide a measure of a systematic "floor' intrinsic to shape measurements.

Optimal Capture of Non-Gaussianity in Weak-Lensing Surveys: Power Spectrum, Bispectrum, and Halo Counts

“…Mellier 1999;Bartelmann & Schneider 2001;Refregier 2003;Hoekstra & Jain 2008;Munshi et al 2008) and has been shown to be the most promising probe of dark energy (Albrecht et al 2006;Peacock et al 2006). Surveys' optimization and systematics minimizations in both software and hardware have been investigated (Heymans et al 2006;Massey et al 2007a;Amara & Réfrégier 2007, 2008Paulin-Henriksson et al 2008;Amara et al 2009;Bridle et al 2009), favoring wide surveys, with well-controlled, stable Point Spread Function, with comprehensive photometric redshift follow-up. Those characteristics are shared by ambitious upcoming large area surveys, such as the Large Synoptic Survey Telescope (LSST) 5 , the Panoramic Survey Telescope & Rapid Response System (Pan-STARRS) 6 , Euclid 7 and the Joint Dark Energy Mission (JDEM) 8 .…”

Testing PSF Interpolation in Weak Lensing with Real Data

“…The quality of the reconstruction can be checked by directly comparing the recovered PSF image and the original star image, in terms of their sizes, ellipticities, or other properties (Hoekstra 2004;Wittman 2005;Van Waerbeke et al 2005;Heymans et al 2012;Hamana et al 2013). The residual PSF ellipticity error can be used to estimate the induced shear recovery error through the shear susceptibility factor (Paulin-Henriksson et al 2008;Rowe 2010) in certain shear measurement methods.…”

Optimal point spread function modeling for weak lensing: complexity and sparsity

“…In Paulin-Henriksson et al (2008) (P1 hereafter), we investigated the link between systematic errors in the power spectrum and uncertainties in the PSF correction phase. The framework is the following.…”