Weak gravitational lensing is a very promising probe for cosmology that relies on highly precise shape measurements. Several new instruments are being deployed and will allow for weak lensing studies on unprecedented scales, and at new frequencies. In particular, some of these new instruments should allow for the blooming of radio-weak lensing, specially the SKA with many Petabits per second of raw data. Hence, great challenges will be waiting at the turn. In addition, processing methods should be able to extract the highest precision possible and ideally, be applicable to radio-astronomy. For the moment, the two methods that already exist do not satisfy both conditions. In this paper, we present a new plug-and-play solution where we add a shape constraint to deconvolution algorithms and results show measurements improvement of at least 20%.
Space test of the Equivalence Principle: first results of the MICROSCOPE mission
P. Touboul, G. Metris, M. Rodrigues, Y. André, Q. Baghi, J. Bergé, D. Boulanger, S. Bremer, R. Chhun, B. Christophe, V. Cipolla, T. Damour, P. Danto, H. Dittus, P. Fayet, B. Foulon, P.-Y. Guidotti, E. Hardy, P.-A. Huynh, C. Lämmerzahl, V. Lebat, F. Liorzou, M. List, I. Panel, S. Pires, B. Pouilloux, P. Prieur, S. Reynaud, B. Rievers, A. Robert, H. Selig, L. Serron, T. Sumner, P. Viesser
The Weak Equivalence Principle (WEP), stating that two bodies of different compositions and/or mass fall at the same rate in a gravitational field (universality of free fall), is at the very foundation of General Relativity. The MICROSCOPE mission aims to test its validity to a precision of 10^-15, two orders of magnitude better than current on-ground tests, by using two masses of different compositions (titanium and platinum alloys) on a quasi-circular trajectory around the Earth. This is realised by measuring the accelerations inferred from the forces required to maintain the two masses exactly in the same orbit. Any significant difference between the measured accelerations, occurring at a defined frequency, would correspond to the detection of a violation of the WEP, or to the discovery of a tiny new type of force added to gravity. MICROSCOPE's first results show no hint for such a difference, expressed in terms of Eötvös parameter δ = [-1 +/- 9(stat) +/- 9 (syst)] x 10^-15 (both 1σ uncertainties) for a titanium and platinum pair of materials. This result was obtained on a session with 120 orbital revolutions representing 7% of the current available data acquired during the whole mission. The quadratic combination of 1σ uncertainties leads to a current limit on δ of about 1.3 x 10^-14.
Weak Lensing provides a unique method to directly map the distribution of dark matter in the universe. Ongoing efforts are made to improve the detection of cosmic shear on existing telescopes and future instruments dedicated to survey are planned. Several methods are used to derive the lensing shear from the shapes of background galaxies. But the shear map obtained is always noisy, and when it is converted into a map of the projected mass map, the result is dominated by the noise.
MRLens offers a new algorithm for the reconstruction of Weak Lensing mass maps.
MRLens (Multi-Resolution tools for gravitational Lensing) is a software written in C++ with an IDL interface. This method uses the Multiscale Entropy concept (which is based on wavelets) and the False Discovery Rate (FDR) which allows us to derive robust detection levels in wavelet space. MRLens has been used to process the COSMOS map (see Figure above)..
More than a software dedicated to a new reconstruction method, MRLens software includes many other tools useful to process, analyze and visualize lensing data. The user manual introduces Weak Lensing field and describes the MRLENS tools. Some results are presented and an accurate description of IDL routines are available.
System Requirements : 1- Make sure you have approximately 400 MB of disk space available. After installation MRLENS package occupies approximately 56 MB or 205MB (version with data) of disk space. 2- The binaries C++ called by IDL routines are not available under all the systems therefore you cannot use the package on all platforms. The supported platforms are : SUN-Solaris, PC-Linux, Mac OS X. Next release will include PC Windows.
Software Requirements : The IDL MRLENS software requires that IDL (version 6.0 or later) to be installed on your computer. Starting IDL using the script program mrl.pro allows the user to add the MRLENS software to the IDL environment. Thus, all routines described in the user manual can be called. An online help is available by using the mrh.pro program.oftwares are required:
This package is a compilation of some algorithms and methods which were developed and/or used successfully in the applications reported in the 2 following publications:
Weak Lensing Mass Reconstruction using Wavelets, J.-L. Starck, S. Pires and A. Réfrégier, Astronomy and Astrophysics, March 2006
Map of the universe's Dark Matter scaffolding, R. Massey, J. Rhodes, R. Ellis, N. Scoville, A. Leathaud, A. Finoguenov, P. Capak, D. Bacon, H. Aussel, J.-P. Kneib, A. Koekemoer, H. McCracken, B. Mobasher, S. Pires, A. Réfrégier, S. Sasaki, ,J.-L. Starck, Y. Taniguchi and J. Taylor, Nature, January 2007
Sunyaev-Zeldovich cluster reconstruction in multiband bolometer camera surveys, S. Pires, J.-B. Juin, D. Yvon, Y. Moudden, S. Anthoine and E. Pierpaoli, Astronomy and Astrophysics, April 2006 More than a software dedicated to a new reconstruction method, this package includes many other tools useful to process, analyze and visualize lensing data.
Please acknowledge use of the code in any resulting work, citing Starck, et al, 2006. We would be interested to collaborate with anyone requiring more advanced applications, and are always interested to hear about new applications. For questions and feedback or to be informed of the forthcoming versions, send an email to Sandrine Pires.
The analysis of weak lensing data requires to account for missing data such as masking out of bright stars. To date, the majority of lensing analyses uses the two point-statistics of the cosmic shear field. These can either be studied directly using the two-point correlation function, or in Fourier space, using the power spectrum. The two-point correlation function is unbiased by missing data but its direct calculation will soon become a burden with the exponential growth of astronomical data sets. The power spectrum is fast to estimate but a mask correction should be estimated. Others statistics can be used but these are strongly sensitive to missing data.
The solution that is proposed by FASTLens is to properly fill-in the gaps with only NlogN operations, leading to a complete weak lensing mass map from which we can compute straight forwardly and with a very good accuracy any kind of statistics like power spectrum or bispectrum. The inpainting method relies strongly on the notion of sparsity and on the construction of sparse representations in large redundant dictionaries.
Simulated mass map with the mask pattern of CFHTLS data on D1 field (on the left), inpainted maps map (on the right).
FASTLens (Fast STatistics for weak Lensing) is a package written in C++ that includes:
- An inpainting code to derive complete weak lensing mass maps from incomplete shear maps
- A power spectrum estimator
- A bispectrum estimator (for equilateral and isoscele configurations)
We propose also a new method to compute fastly and accurately the power spectrum and the bispectrum with a polar FFT algorithm.
The user manual introduces the missing data problem in statistic estimation and presents the available routines. An accurate description of IDL routines is given.
The IDL FASTlens software requires IDL (version 6.0 or later) to be installed on your computer. The binaries C++ called by IDL routines are not available under all the systems therefore you cannot use the package on all platforms. The supported platforms are : PC-Linux and Mac OS X.
Please acknowledge use of the code in any resulting work, citing Pires, et al, 2009. We would be interested to collaborate with anyone requiring more advanced applications, and are always interested to hear about new applications. For questions and feedback or to be informed of the forthcoming versions, send an email to Sandrine Pires.