Spatial image differentiation using programmable binary optical elements.

Spatial differentiation can be performed by imaging an input pattern with a binary optical element consisting of Fresnel lenses having identical focal lengths but different center locations. Each of these lenses forms an image of the object at a different transverse location in the image plane. If the two lenses have a phase shift of pi rad, the two images will be subtracted, resulting in an image that is differentiated in the direction of the shifted lens positions. We show experimental results in which the optical element is written onto a programmable magneto-optic spatial light modulator.