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A main science goal for the Large Synoptic Survey Telescope (LSST) is to measure the cosmic shear signal from weak lensing to extreme accuracy. One difficulty, however, is that with the short exposure time ($simeq$15 seconds) proposed, the spatial variation of the Point Spread Function (PSF) shapes may be dominated by the atmosphere, in addition to optics errors. While optics errors mainly cause the PSF to vary on angular scales similar or larger than a single CCD sensor, the atmosphere generates stochastic structures on a wide range of angular scales. It thus becomes a challenge to infer the multi-scale, complex atmospheric PSF patterns by interpolating the sparsely sampled stars in the field. In this paper we present a new method, PSFent, for interpolating the PSF shape parameters, based on reconstructing underlying shape parameter maps with a multi-scale maximum entropy algorithm. We demonstrate, using images from the LSST Photon Simulator, the performance of our approach relative to a 5th-order polynomial fit (representing the current standard) and a simple boxcar smoothing technique. Quantitatively, PSFent predicts more accurate PSF models in all scenarios and the residual PSF errors are spatially less correlated. This improvement in PSF interpolation leads to a factor of 3.5 lower systematic errors in the shear power spectrum on scales smaller than $sim13$, compared to polynomial fitting. We estimate that with PSFent and for stellar densities greater than $simeq1/{rm arcmin}^{2}$, the spurious shear correlation from PSF interpolation, after combining a complete 10-year dataset from LSST, is lower than the corresponding statistical uncertainties on the cosmic shear power spectrum, even under a conservative scenario.
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Reconstruction of the point spread function (PSF) is a critical process in weak lensing measurement. We develop a real-data based and galaxy-oriented pipeline to compare the performances of various PSF reconstruction schemes. Making use of a large amount of the CFHTLenS data, the performances of three classes of interpolating schemes - polynomial, Kriging, and Shepard - are evaluated. We find that polynomial interpolations with optimal orders and domains perform the best. We quantify the effect of the residual PSF reconstruction error on shear recovery in terms of the multiplicative and additive biases, and their spatial correlations using the shear measurement method of Zhang et al. (2015). We find that the impact of PSF reconstruction uncertainty on the shear-shear correlation can be significantly reduced by cross correlating the shear estimators from different exposures. It takes only 0.2 stars (SNR > 100) per square arcmin on each exposure to reach the best performance of PSF interpolation, a requirement that is generally satisfied in the CFHTlenS data.
We investigate the impact of point spread function (PSF) fitting errors on cosmic shear measurements using the concepts of complexity and sparsity. Complexity, introduced in a previous paper, characterizes the number of degrees of freedom of the PSF. For instance, fitting an underlying PSF with a model with low complexity will lead to small statistical errors on the model parameters, however these parameters could suffer from large biases. Alternatively, fitting with a large number of parameters will tend to reduce biases at the expense of statistical errors. We perform an optimisation of scatters and biases by studying the mean squared error of a PSF model. We also characterize a model sparsity, which describes how efficiently the model is able to represent the underlying PSF using a limited number of free parameters. We present the general case and illustrate it for a realistic example of PSF fitted with shapelet basis sets. We derive the relation between complexity and sparsity of the PSF model, signal-to-noise ratio of stars and systematic errors on cosmological parameters. With the constraint of maintaining the systematics below the statistical uncertainties, this lead to a relation between the required number of stars to calibrate the PSF and the sparsity. We discuss the impact of our results for current and future cosmic shear surveys. In the typical case where the biases can be represented as a power law of the complexity, we show that current weak lensing surveys can calibrate the PSF with few stars, while future surveys will require hard constraints on the sparsity in order to calibrate the PSF with 50 stars.
The weak-lensing science of the LSST project drives the need to carefully model and separate the instrumental artifacts from the intrinsic lensing signal. The dominant source of the systematics for all ground based telescopes is the spatial correlation of the PSF modulated by both atmospheric turbulence and optical aberrations. In this paper, we present a full FOV simulation of the LSST images by modeling both the atmosphere and the telescope optics with the most current data for the telescope specifications and the environment. To simulate the effects of atmospheric turbulence, we generated six-layer phase screens with the parameters estimated from the on-site measurements. For the optics, we combined the ray-tracing tool ZEMAX and our simulated focal plane data to introduce realistic aberrations and focal plane height fluctuations. Although this expected flatness deviation for LSST is small compared with that of other existing cameras, the fast f-ratio of the LSST optics makes this focal plane flatness variation and the resulting PSF discontinuities across the CCD boundaries significant challenges in our removal of the systematics. We resolve this complication by performing PCA CCD-by-CCD, and interpolating the basis functions using conventional polynomials. We demonstrate that this PSF correction scheme reduces the residual PSF ellipticity correlation below 10^-7 over the cosmologically interesting scale. From a null test using HST/UDF galaxy images without input shear, we verify that the amplitude of the galaxy ellipticity correlation function, after the PSF correction, is consistent with the shot noise set by the finite number of objects. Therefore, we conclude that the current optical design and specification for the accuracy in the focal plane assembly are sufficient to enable the control of the PSF systematics required for weak-lensing science with the LSST.
This is the third paper on the improvements of systematic errors in our weak lensing analysis using an elliptical weight function, called E-HOLICs. In the previous papers we have succeeded in avoiding error which depends on ellipticity of background image. In this paper, we investigate the systematic error which depends on signal to noise ratio of background image. We find that the origin of the error is the random count noise which comes from Poisson noise of sky counts. Random count noise makes additional moments and centroid shift error, and those 1st orders are canceled in averaging, but 2nd orders are not canceled. We derived the equations which corrects these effects in measuring moments and ellipticity of the image and test their validity using simulation image. We find that the systematic error becomes less than 1% in the measured ellipticity for objects with $S/N>3$.
Weak gravitational lensing (WL) is one of the most powerful techniques to learn about the dark sector of the universe. To extract the WL signal from astronomical observations, galaxy shapes must be measured and corrected for the point spread function (PSF) of the imaging system with extreme accuracy. Future WL missions (such as the Wide-Field Infrared Survey Telescope, WFIRST) will use a family of hybrid nearinfrared CMOS detectors (HAWAII-4RG) that are untested for accurate WL measurements. Like all image sensors, these devices are subject to conversion gain nonlinearities (voltage response to collected photo-charge) that bias the shape and size of bright objects such as reference stars that are used in PSF determination. We study this type of detector nonlinearity (NL) and show how to derive requirements on it from WFIRST PSF size and ellipticity requirements. We simulate the PSF optical profiles expected for WFIRST and measure the fractional error in the PSF size and the absolute error in the PSF ellipticity as a function of star magnitude and the NL model. For our nominal NL model (a quadratic correction), we find that, uncalibrated, NL can induce an error of 0.01 (fractional size) and 0.00175 (absolute ellipticity error) in the H158 bandpass for the brightest unsaturated stars in WFIRST. In addition, our simulations show that to limit the bias of the size and ellipticity errors in the H158 band to approximately 10% of the estimated WFIRST error budget, the parameter of our quadratic NL model must be calibrated to about 1% and 2.4%, respectively. We present a fitting formula that can be used to estimate WFIRST detector NL requirements once a true PSF error budget is established.
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