Spatially-varying depth and characteristics of observing conditions, such as seeing, airmass, or sky background, are major sources of systematic uncertainties in modern galaxy survey analyses, in particular in deep multi-epoch surveys. We present a f
ramework to extract and project these sources of systematics onto the sky, and apply it to the Dark Energy Survey (DES) to map the observing conditions of the Science Verification (SV) data. The resulting distributions and maps of sources of systematics are used in several analyses of DES SV to perform detailed null tests with the data, and also to incorporate systematics in survey simulations. We illustrate the complementarity of these two approaches by comparing the SV data with the BCC-UFig, a synthetic sky catalogue generated by forward-modelling of the DES SV images. We analyse the BCC-UFig simulation to construct galaxy samples mimicking those used in SV galaxy clustering studies. We show that the spatially-varying survey depth imprinted in the observed galaxy densities and the redshift distributions of the SV data are successfully reproduced by the simulation and well-captured by the maps of observing conditions. The combined use of the maps, the SV data and the BCC-UFig simulation allows us to quantify the impact of spatial systematics on $N(z)$, the redshift distributions inferred using photometric redshifts. We conclude that spatial systematics in the SV data are mainly due to seeing fluctuations and are under control in current clustering and weak lensing analyses. The framework presented here is relevant to all multi-epoch surveys, and will be essential for exploiting future surveys such as the Large Synoptic Survey Telescope (LSST), which will require detailed null-tests and realistic end-to-end image simulations to correctly interpret the deep, high-cadence observations of the sky.
We describe S2LET, a fast and robust implementation of the scale-discretised wavelet transform on the sphere. Wavelets are constructed through a tiling of the harmonic line and can be used to probe spatially localised, scale-depended features of sign
als on the sphere. The scale-discretised wavelet transform was developed previously and reduces to the needlet transform in the axisymmetric case. The reconstruction of a signal from its wavelets coefficients is made exact here through the use of a sampling theorem on the sphere. Moreover, a multiresolution algorithm is presented to capture all information of each wavelet scale in the minimal number of samples on the sphere. In addition S2LET supports the HEALPix pixelisation scheme, in which case the transform is not exact but nevertheless achieves good numerical accuracy. The core routines of S2LET are written in C and have interfaces in Matlab, IDL and Java. Real signals can be written to and read from FITS files and plotted as Mollweide projections. The S2LET code is made publicly available, is extensively documented, and ships with several examples in the four languages supported. At present the code is restricted to axisymmetric wavelets but will be extended to directional, steerable wavelets in a future release.
We develop an exact wavelet transform on the three-dimensional ball (i.e. on the solid sphere), which we name the flaglet transform. For this purpose we first construct an exact transform on the radial half-line using damped Laguerre polynomials and
develop a corresponding quadrature rule. Combined with the spherical harmonic transform, this approach leads to a sampling theorem on the ball and a novel three-dimensional decomposition which we call the Fourier-Laguerre transform. We relate this new transform to the well-known Fourier-Bessel decomposition and show that band-limitedness in the Fourier-Laguerre basis is a sufficient condition to compute the Fourier-Bessel decomposition exactly. We then construct the flaglet transform on the ball through a harmonic tiling, which is exact thanks to the exactness of the Fourier-Laguerre transform (from which the name flaglets is coined). The corresponding wavelet kernels are well localised in real and Fourier-Laguerre spaces and their angular aperture is invariant under radial translation. We introduce a multiresolution algorithm to perform the flaglet transform rapidly, while capturing all information at each wavelet scale in the minimal number of samples on the ball. Our implementation of these new tools achieves floating-point precision and is made publicly available. We perform numerical experiments demonstrating the speed and accuracy of these libraries and illustrate their capabilities on a simple denoising example.
High-precision cosmology requires the analysis of large-scale surveys in 3D spherical coordinates, i.e. spherical Fourier-Bessel decomposition. Current methods are insufficient for future data-sets from wide-field cosmology surveys. The aim of this p
aper is to present a public code for fast spherical Fourier-Bessel decomposition that can be applied to cosmological data or 3D data in spherical coordinates in other scientific fields. We present an equivalent formulation of the spherical Fourier-Bessel decomposition that separates radial and tangential calculations. We propose the use of the existing pixelisation scheme HEALPix for a rapid calculation of the tangential modes. 3DEX (3D EXpansions) is a public code for fast spherical Fourier-Bessel decomposition of 3D all-sky surveys that takes advantage of HEALPix for the calculation of tangential modes. We perform tests on very large simulations and we compare the precision and computation time of our method with an optimised implementation of the spherical Fourier-Bessel original formulation. For surveys with millions of galaxies, computation time is reduced by a factor 4-12 depending on the desired scales and accuracy. The formulation is also suitable for pre-calculations and external storage of the spherical harmonics, which allows for additional speed improvements. The 3DEX code can accommodate data with masked regions of missing data. 3DEX can also be used in other disciplines, where 3D data are to be analysed in spherical coordinates. The code and documentation can be downloaded at http://ixkael.com/blog/3dex.
