  We account for all the image distortions relevant to weak gravitational
lensing to second order. Besides the familiar shear, convergence, rotation and
flexions, we find a new image distortion with two distinct descriptions, the
twist and the turn. Like rotation, this distortion is not activated
gravitationally to first order, but will be activated by systematic effects. We
examine the rotational properties of twist and turn, and their effect on images
in real and shapelet space. We construct estimators for the new distortion,
taking into account the centroid shift which it generates. We then use these
estimators to make first constraints on twist using the STAGES HST survey; we
find that the mean twist estimator is consistent with zero. We measure
correlation functions for our twist estimator on the survey, again finding no
evidence of systematic effects.
