is still several orders of magnitude lower than the scatter in intrinsic flexion of galaxies.

We are not surprised by this since, for example, PSF distortions arising from variable sizes in chips is likely to scale as the variation in PSF ellipticity. In ACS, chip distortions produce ellipticities of order $1\%$, and vary on scales of 100’s of pixels, producing an induced flexion of $\sim 10^{-4}\ pix.^{-1}$. From the ground, the atmospheric distortions are expected, on average, to be even more isotropic.

There is another reason to suppose that PSF flexion contributions will be unimportant. In shear measurements, the PSF ellipticity typically varies smoothly and somewhat symmetrically around the center of a field, mimicking (or partially reversing) the overall behavior of the expected shear field. Since flexion probes smaller scale effects, the induced flexion by the PSF will, on average, cancel out.

This is not to say that we cannot deal with PSF flexion inversion. Refregier (2003) describes an explicit deconvolution algorithm (see also Refregier and Bacon 2003, and references therein). In shapelet space, equation (\[eq:PSFdef\]) can be re-written as: $$f_{nm} = \sum_{n'm'n''m''} C_{nmn'm'n''m''} P_{n'm'}f^{(0)}_{n''m''}$$

Where $C_{nmn'm'n''m''}$ is the 2-dimensional convolution tensor: $$C_{nmn'm'n''m''}(\gamma,\alpha,\beta)=2\pi(-1)^{n+m}i^{n+m+n'+m'+n''+m''}\int
d^2{\bf x}{\cal B}_{n''m''}({\bf x}/\gamma){\cal B}_{n'm'}({\bf
x}/\alpha){\cal B}_{nm}({\bf 