Scale-Free optics

The most fascinating images and patterns emerge when light diffracts from minute structures [1]. Even the image of an otherwise featureless hole produces enthralling ripples that spread out to invest space and form what is known as an Airy pattern. It is a basic fact that diffraction becomes dominant when the size of the feature becomes micrometric, and the transmitted wave has an angular spread ?? that depends on the size of the aperture d measured in units of the optical wavelength ?, i.e., ?? ??/d. From a practical perspective, diffraction represents a major obstacle to imaging of finer details, and a great research effort is continuously exerted to overcome it. In fact, diffraction spreads the optical wave and blurs the spatial information encoded in the optical beam. Consider an image composed of separate pixels of characteristic size d and spacing l.