Personal web page : http://jstarck.cosmostat.org
Laboratory link : http://www.cosmostat.org
The Euclid satellite, to be launched in 2022, will observe the sky in the optical and infrared, and will be able to map large scale structures and weak lensing distortions out to high redshifts. Weak gravitational lensing is thought to be one of the most promising tools of cosmology to constrain models. Weak lensing probes the evolution of dark-matter structures and can help distinguish between dark energy and models of modified gravity. Thanks to the shear measurements, we will be able to reconstruct a dark matter mass map of 15000 square degrees. These shear measurements are derived from the galaxy shapes, which are blurred by the PSF (point-spread function) of the optical imaging system. One of the main problems to achieve the scientific goals is therefore the need to model the point spread function (PSF) of the instrument with a very high accuracy. The PSF field can be estimated from the stars contained in the acquired images. It has to take into account the spatial and spectral variation of the PSF. An additional problem to take care of is the subsampling of the images. Once the PSF is correctly modelled, we need to derive the shear from galaxy shapes.
In a recent paper (Schmitz et al 2018) we shown that optimal transport (OT) techniques allow to extremely well represent the evolution of the PSF with the wavelength and on-going work (Morgan et al, 2018) consists in building a 3D Euclid PSF modelling, which takes into account both the spatial variation of the PSF and the PSF wavelength dependency. However even if OT produces beautiful results, its use is extremely limited in practice due to a prohibitive computational cost, and we cannot consider to use our OT PSF modeling for the huge Euclid set.
The goal of the PhD consists first in finding an efficient way to build such a 3D PSF model. A solution could be to use the Deep Wasserstein Embedding technique (Courty, Flamary and Ducoffe, 2017) to get an approximation mechanism that allows to break the complexity. The second step will be to interpolate, from the reconstructed 3D PSFs at stars position, the PSF at any position in the field. This will done by extending to the third dimension the 2D interpolation on a Graph Laplacian we proposed in (Schmitz, Starck and Ngole, 2018), which allows us to interpolate the PSF on the adequate manifold. The final step will be to quantify the modelling errors by studying using simulations the propagation of the reconstructed PSFs errors to cosmological parameters.