The Shear TEsting Programme 1: Weak lensing analysis of simulated ground-based observations

TL;DR

STEP addresses the accuracy and reliability of weak-lensing shear measurements by performing blind analyses of simulated ground-based images across multiple pipelines. The study finds that several methods achieve percent-level accuracy while additive PSF systematics can be suppressed to very low levels, but calibration bias remains the dominant source of error. The authors provide detailed descriptions of each pipeline and quantify biases, weights, and selection effects to benchmark current capabilities and guide improvements. The results highlight the need for linear, well-calibrated shear estimators for upcoming wide-field cosmic shear surveys and outline plans for future STEP investigations with more realistic morphologies and space-based PSFs.

Abstract

The Shear TEsting Programme, STEP, is a collaborative project to improve the accuracy and reliability of all weak lensing measurements in preparation for the next generation of wide-field surveys. In this first STEP paper we present the results of a blind analysis of simulated ground-based observations of relatively simple galaxy morphologies. The most successful methods are shown to achieve percent level accuracy. From the cosmic shear pipelines that have been used to constrain cosmology, we find weak lensing shear measured to an accuracy that is within the statistical errors of current weak lensing analyses, with shear measurements accurate to better than 7%. The dominant source of measurement error is shown to arise from calibration uncertainties where the measured shear is over or under-estimated by a constant multiplicative factor. This is of concern as calibration errors cannot be detected through standard diagnostic tests. The measured calibration errors appear to result from stellar contamination, false object detection, the shear measurement method itself, selection bias and/or the use of biased weights. Additive systematics (false detections of shear) resulting from residual point-spread function anisotropy are, in most cases, reduced to below an equivalent shear of 0.001, an order of magnitude below cosmic shear distortions on the scales probed by current surveys. Our results provide a snapshot view of the accuracy of current ground-based weak lensing methods and a benchmark upon which we can improve. To this end we provide descriptions of each method tested and include details of the eight different implementations of the commonly used Kaiser, Squires and Broadhurst (1995) method (KSB+) to aid the improvement of future KSB+ analyses.

Figures (5)

• Figure 1: SkyMaker PSF models, as described in Table \ref{['tab:psfs']}. The upper panel shows the PSF core distortion, with contours marking $3\%$, $25\%$ and $90\%$ of the peak intensity. The lower panel shows the extended diffraction spikes, with contours marking $0.003\%$, $0.03\%$, $0.3\%$, $3\%$ and $25\%$ of the peak intensity.
• Figure 2: Examples of two analyses of PSF 3 simulations using KSB+ (HH implementation, upper panel) and BJ02 (MJ implementation, lower panel) comparing the measured shear $\gamma_1$ and input shear $\gamma_1^{\rm true}$. The best-fit to equation \ref{['eqn:m1c1']} is shown dashed, and the optimal result (where $\gamma_1 = \gamma_1^{\rm true}$) is shown dot-dashed. Both analyses have additive errors that are consistent with shot noise (fitted y-offset parameter $c$) and low 1% calibration errors (fitted slope parameter $m$). The weighting scheme used in the BJ02 analysis introduces a non-linear response to increasing input shear (fitted quadratic parameter $q$), reducing the shear recovery accuracy for increasing shear. The accuracy of the KSB+ analysis responds linearly to increasing input shear and so these results were re-fit with a linear relationship, i.e. $q=0$.
• Figure 3: Measures of calibration bias $\langle m \rangle$, PSF residuals $\sigma_c$ and non-linearity $\langle q \rangle$ for each author (key in Table \ref{['tab:methods']}), as described in the text. For the non-linear cases where $\langle q \rangle \ne 0$ (points enclosed within a large circle), $\langle q \rangle$ is shown with respect to the right-hand scale. In short, the lower the value of $\sigma_c$, the more successful the PSF correction is at removing all types of PSF distortion. The lower the absolute value of $\langle m \rangle$, the lower the level of calibration bias. The higher the $q$ value the poorer the response of the method to stronger shear. Note that for weak shear $\gamma < 0.01$, the impact of this quadratic term is negligible. Results in the shaded region suffer from less than $7\%$ calibration bias. These results are tabulated in Table \ref{['tab:mcq']}.
• Figure 4: Measures of selection bias $\langle m_{\rm selc} \rangle$, for each author (key in Table \ref{['tab:methods']}), as described in the text. The lower the absolute value of $\langle m_{\rm selc} \rangle$ the lower the level of selection bias. Selection bias can be compared to the calibration bias $\langle m_{\rm uncontaminated} \rangle$ measured from catalogues cleansed of false detections and stellar contamination. Unbiased shear measurement methods, where the shear is measured accurately but the source selection criteria are potentially biased, would fall along the 1:1 line over-plotted. These results are tabulated in Table \ref{['tab:mcq']}.
• Figure 5: An example plot of the difference between measured shear $\gamma_1$ and input shear $\gamma_1^{\rm true}$ as a function of galaxy $I$ band magnitude. This plot is taken from the KSB+ analysis of HH using the PSF 0 simulations with an input shear $\gamma_1^{\rm true} = 0.05$. The dot-dashed line shows the average $\gamma_1-\gamma_1^{\rm true}$ measured from the full galaxy sample.