## 5. SummaryIn this paper we have studied possible systematic errors arising from the correction for anisotropic point-spread functions in weak lensing analyses based on the well-known Kaiser et al. (1995) method. While such effects are small, generally below a few percent in the deduced gravitational shear components , they are at a level that is important for studies such as galaxy-galaxy lensing, lensing by large-scale structure or cluster lensing at large radii. We have traced the effect to the treatment in KSB of the PSF as a convolution of a compact anisotropic function with a more extended, circular function. We have presented a new algorithm with which to carry out the PSF-correction in a single fitting step. It makes no assumptions about the PSF other than that it is well-measured. We show with simulated images that the low-level residuals left in the KSB analysis can thus be avoided, and that the noise properties of this algorithm compare well with those of KSB. The new algorithm is mathematically exact (in the sense that it
will recover the correct shear value from a PSF-smeared image) when
applied to instrinsically circular sources, provided the radial
profile of the source can be modelled well. In the practical situation
in which galaxies have intrinsic elongations but random orientations,
we have shown that nearly unbiased results (down to a few tenths of a
percent in shear) can also be obtained. This galaxy-by-galaxy
application of the algorithm therefore allows observations with
spatially varying PSF and/or shear fields to be handled. © European Southern Observatory (ESO) 1999 Online publication: December 2, 1999 |