Euclid: Nonparametric point spread function field recovery through interpolation on a graph Laplacian

Abstract

Context. Future weak lensing surveys, such as the Euclid mission, will attempt to measure the shapes of billions of galaxies in order to derive cosmological information. These surveys will attain very low levels of statistical error and systematic errors must be extremely well controlled. In particular, the point spread function (PSF) must be estimated using stars in the field, and recovered with high accuracy.Aims. This paper's contributions are twofold. First, we take steps toward a non-parametric method to address the issue of recovering the PSF field, namely that of finding the correct PSF at the position of any galaxy in the field, applicable to Euclid. Our approach relies solely on the data, as opposed to parametric methods that make use of our knowledge of the instrument. Second, we study the impact of imperfect PSF models on the shape measurement of galaxies themselves, and whether common assumptions about this impact hold true in a Euclid scenario. Methods. We use the recently proposed Resolved Components Analysis approach to deal with the undersampling of observed star images. We then estimate the PSF at the positions of galaxies by interpolation on a set of graphs that contain information relative to its spatial variations. We compare our approach to PSFEx, then quantify the impact of PSF recovery errors on galaxy shape measurements through image simulations. Results. Our approach yields an improvement over PSFEx in terms of PSF model and on observed galaxy shape errors, though it is at present not sufficient to reach the required Euclid accuracy. We also find that different shape measurements approaches can react differently to the same PSF modelling errors.

Probabilistic Modeling and Inference for Sequential Space-Varying Blur Identification

“…This is at the exception of [16], [23], [18], that jointly restore the image and a piecewise-constant map, obtained through a segmentation-based strategy, describing the non-stationary blur effects. Though image restoration is a problem of high interest, in certain applications such as microscopy or astronomical imaging, an accurate qualitative and quantitative knowledge of the blur effects is key for a better understanding and improving (e.g., through calibration) of the imaging device [19], [38], [39], [40]. For performing blur identification, it is necessary to make structural assumptions on the blur map to be estimated.…”

“…This problem is typically addressed using optimization-based methods [25], [34]. We also refer the reader to [38] and references therein, for a review of the problem and recent insights, in the particular context of astronomical imaging. In the aforementioned works, no parametric model of the PSF was assumed though it is highlighted in [38] as a promising research direction.…”

“…We also refer the reader to [38] and references therein, for a review of the problem and recent insights, in the particular context of astronomical imaging. In the aforementioned works, no parametric model of the PSF was assumed though it is highlighted in [38] as a promising research direction. Moreover, most available techniques address the problem in a batch manner, requiring the loading of the full image before the starting of the identification process, which can be at the price of a high memory cost in high resolution imaging or even incompatible with an on-the-fly image acquisition (e.g., satellite imaging).…”

“…lens aberrations [19], or atmospheric turbulence [20], [21], [22]. Such image degradation sources give rise to a so-called spatially variant blur [23], [24].…”

Particle Filtering for Online Space-Varying Blur Identification

“…In most realistic scenarios, the PSF cannot be considered constant throughout the field-of-view due to various reasons such as defocus [12,13], moving objects or cameras [14], anisotropic optical lens aberrations [15], or atmospheric turbulence [16,17]. This non-stationary behavior gives rise to the so-called spatially variant blur [18].…”