out using the $\chi^2$ minimization technique described previously. However, we have found that truncating the shapelet series prior to the flexion measurement yields a more accurate and robust measure of the flexion than using the full series. Excluding the higher order shapelet modes avoids contamination of the flexion signal by small scale substructure and by noise (particularly in dimmer objects). We exclude all shapelet modes with $n > n_{max}/5$ in our flexion measurement. This effectively increases $\theta_{min}$ to 2 pixels, without affecting the accuracy of the reconstruction.

### PSF Deconvolution

One of the complications in measuring properties of lensed images is that, in practice, they are convolved with a PSF: $$f({\bf \theta})=\int d^2\theta' P({\bf \theta-\theta'}) f^{(0)}({\bf
  \theta})\ .
\label{eq:PSFdef}$$ In principle, the PSF can be estimated through measurement of stars, but in deep, small-field, high galactic-latitude observations, stars may be scarce, and thus PSF estimation may rely partly on numerical analysis of the instrument (e.g. the Tiny Tim algorithm, Krist, J. 1993).

In reality, though, this should rarely be an issue. Estimations of the PSF flexion from Tiny Tim yield values of $\sigma_{aF,psf}\simeq
7\times 10^{-4}$. This represents the maximum induced flexion which can arise from convolution with the PSF, and 