typically much smaller than the intrinsic ellipticity of an image, thus it makes sense to set $\mu_{nm}=f_{nm}$.

Effective Estimation of the Flexion
-----------------------------------

Though the form looks quite complicated, conceptually, computing the flexion is very straightforward. A simplified pipeline may be written as follows:

1.  Generate a catalog of objects and, for each, excise an isolated postage stamp.

2.  Compute the shapelet coefficients of the postage stamp.

3.  Deconvolve the postage stamp with a known PSF kernel.

4.  Compute the transformation matrices associated with each of the four flexion operators, solve the $\chi^2$ minimization (equation \[eq:chi2\]) for $\gamma_{i,j}$, and estimate the flexion.

We discuss each of these steps in turn below. The data used for this analysis was taken using HST and the Advanced Camera for Surveys, and in the particular context of cluster lensing. In this context, the galaxies in which we are interested are potentially blended with much larger and brighter foreground objects. We discuss the specific properties of our data catalog in § \[sec:measurement\], but many of the issues involved are quite generic.

### Catalog Generation and Postage Stamp Cutout

The first step in the process, the generation of a catalog and postage stamps seems quite straightforward. 