moments, for example) to compute local gradients in a shear field. BGRT have discussed how flexion may be used to identify substructure in clusters, to normalize the matter power spectrum on sub-arcminute scales via “cosmic flexion” (as an analog to cosmic shear), and to estimate the ellipticity of galaxy-galaxy lenses. As a practical application, flexion has already been used to measure galaxy-galaxy lensing (Goldberg & Bacon, 2005), and is presently being used in cluster reconstruction (Leonard et al., in preparation).

However, there have been several difficulties in the estimation of flexion on real objects. First, the flexion inversion is difficult to describe, contains an enormous number of terms, and thus, is rather daunting to code. Secondly, there has been little discussion of the explicit effects of PSF convolution or deconvolution. Finally, unlike shear, there has, until recently, been no simple form to even approximate what the “flexion” is.

The remainder of this paper will thus be a practical guide to measuring flexion in real images. We begin, below, by reminding the reader of the basic terms involved in flexion analysis. In § \[sec:shapelets\], we review shapelet decomposition, and discuss some of the issues involved in using shapelets to measure flexion. 