In this paper , we develop a new gravitational lensing inversion technique .
While traditional approaches assume that the lensing field varies little across a galaxy image , we note that this variation in the field can give rise to a “ Flexion ” or bending of a galaxy image , which may then be used to detect a lensing signal with increased signal to noise .
Since the significance of the Flexion signal increases on small scales , this is ideally suited to galaxy-galaxy lensing .
We develop an inversion technique based on the “ Shapelets ” formalism of Refregier ( 2003 ) .
We then demonstrate the proof of this concept by measuring a Flexion signal in the Deep Lens Survey .
Assuming an intrinsically isothermal distribution , we find from the Flexion signal alone a velocity width of v _ { c } = 221 \pm 12 km / s for lens galaxies of r < 21.5 , subject to uncertainties in the intrinsic Flexion distribution .