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Astron. Astrophys. 352, 355-362 (1999)

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1. Introduction

Gravitational lensing is one of the most powerful and direct methods for studying the gravitational potentials of massive objects in the universe. An important type of lensing study is `weak lensing.' It is the study of mild systematic distortions of background sources as their light rays are perturbed by gravitational fields on their way to us. Weak lensing has already provided important results in the study of galaxy clusters (e.g., Tyson et al. 1990; Bonnet et al. 1993; Fahlman et al. 1994; Squires et al. 1997; Fischer et al. 1997; Clowe et al. 1998; Hoekstra et al. 1998), halos of individual galaxies (e.g., Brainerd et al. 1996), and large-scale structure (Schneider et al. 1998). As the techniques are becoming better understood, research is progressing to the search for weaker and weaker distortions, which would enable the outer regions of galaxy clusters and galaxy halos, as well as lensing signals from large-scale structure (e.g., Jain & Seljak 1997; Kaiser 1998), to be studied.

To be able to detect such very weak signals, it is important to accurately remove the dominant systematic effect affecting weak lensing measurements: anisotropy of, and smearing by, the point-spread function (PSF). In this paper we will first investigate the limits of the most commonly-used technique for weak lensing analysis, devised by Kaiser et al. (1995, henceforth KSB). We will show that after PSF anisotropy correction, residual effects on the order of 1% shear are difficult to avoid with this method, even for moderately elongated PSF's. Since the ability to detect percent signals is important for a variety of scientific questions, we have therefore devised a new method which does not have such residuals, but which nevertheless has noise properties comparable to those of the KSB method.

There are several other methods for PSF anisotropy correction in the literature. The Autocorrelation Function method of Van Waerbeke et al. (1997) is a variant of the KSB method in which not individual galaxy images, but the autocorrelation function of many of them, is analyzed. The Bonnet & Mellier (1995) method uses a different aperture weighting function from KSB, and treats the PSF convolution as a shear term. Fischer & Tyson (1997) convolve the image with a kernel constructed to make the PSF rounder again. A more sophisticated such kernel has recently been presented by Kaiser (in preparation).

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© European Southern Observatory (ESO) 1999

Online publication: December 2, 1999