  Given a galaxy image, one cannot simply measure its flexion. An image's spin
one and three shape properties, typically associated with F- and G-flexion, are
actually complicated functions of the galaxy's intrinsic shape and the
telescope's PSF, in addition to the lensing properties. The same is true for
shear. In this work we create a completely analytic mapping from apparent
measured galaxy flexions to gravitational flexions by (1) creating simple
models for a lensed galaxy and for a PSF whose distortions are dominated by
atmospheric smearing and optical aberrations, (2) convolving the two models,
and (3) comparing the pre- and post-convolved flexion-like shape variations of
the final image. For completeness, we do the same for shear. As expected,
telescope astigmatism, coma, and trefoil can corrupt measurements of shear, F-
flexion, and G-flexion, especially for small galaxies. We additionally find
that PSF size dilutes the flexion signal more rapidly than the shear signal.
Moreover, mixing between shears, flexions, and asymmetric aberrations can
create additive offsets in lensing measurements that vary with both galaxy size
and galaxy ellipticity and flexion values. But all is not lost; by measuring
the patterns, we can correct for them.
