[astro-ph/0506112] The Shear TEsting Programme 1: Weak lensi
Posted: June 16 2005
This is an interesting (though rather technical) paper that compares various methods of estimating averaged galaxy cosmic shear.
The errors on the recovered shear depend on the weighting scheme used for averaging over galaxies. The ellipticity-dependent weighting scheme used by BJ02 was found to bias the results for larger shears (because the weights depend on the shear). They recommend using a shape-independent weighting to avoid the problem. Perhaps an alternative would be to iterate on the shear and weight?: ie. estimate the shear with shape- independent weighting, then re-estimate the shear using un-sheared shape weights (where the un-shearing is done using the previous shear estimate). Iterate until the weighted shear estimate converges. I'd have though this would remove most of the bias by making the weighting almost independent of shear (i.e. weighting only on the psf-rounded instrinsic ellipticity which is perfectly valid and reduces the shape noise).
Comment: I'm not very convinced by the tests of PSF removal in this study: since the simulation has constant PSF, methods which are more realistic (allowing rapid spatial variations) are bound to do worse in the test compared to simpler schemes, whereas is reality they might do much better. Wouldn't it be better to allow people to use the fact that the PSF is constant? (therefore testing the already-hard problem of smeared shape estimation without confusion from the also hard but irrelevant problem of spatial modelling).
One result is that Shapelet methods need to use very high order (12th) to get sensible answers. This presumably reflects a relatively poor match between the fundamental low order Shapelet sizes/shapes and the actual PSF/galaxy shapes, and sounds like very bad news for doing reliable spatial interpolation of the PSF. Perhaps one could instead do a PCA on Shapelet coefficients to identify which combinations are relevant, then define a new smaller basis of PCA functions which are much better matched to the images? One could test for spatial dependence of the PSF components, then only interpolate those which are found to vary spatially (e.g. those from focus/atmosphere, but not components describing diffraction spikes/pixelization/CCD artefacts).
The errors on the recovered shear depend on the weighting scheme used for averaging over galaxies. The ellipticity-dependent weighting scheme used by BJ02 was found to bias the results for larger shears (because the weights depend on the shear). They recommend using a shape-independent weighting to avoid the problem. Perhaps an alternative would be to iterate on the shear and weight?: ie. estimate the shear with shape- independent weighting, then re-estimate the shear using un-sheared shape weights (where the un-shearing is done using the previous shear estimate). Iterate until the weighted shear estimate converges. I'd have though this would remove most of the bias by making the weighting almost independent of shear (i.e. weighting only on the psf-rounded instrinsic ellipticity which is perfectly valid and reduces the shape noise).
Comment: I'm not very convinced by the tests of PSF removal in this study: since the simulation has constant PSF, methods which are more realistic (allowing rapid spatial variations) are bound to do worse in the test compared to simpler schemes, whereas is reality they might do much better. Wouldn't it be better to allow people to use the fact that the PSF is constant? (therefore testing the already-hard problem of smeared shape estimation without confusion from the also hard but irrelevant problem of spatial modelling).
One result is that Shapelet methods need to use very high order (12th) to get sensible answers. This presumably reflects a relatively poor match between the fundamental low order Shapelet sizes/shapes and the actual PSF/galaxy shapes, and sounds like very bad news for doing reliable spatial interpolation of the PSF. Perhaps one could instead do a PCA on Shapelet coefficients to identify which combinations are relevant, then define a new smaller basis of PCA functions which are much better matched to the images? One could test for spatial dependence of the PSF components, then only interpolate those which are found to vary spatially (e.g. those from focus/atmosphere, but not components describing diffraction spikes/pixelization/CCD artefacts).