Continuous-order derivative for optical signals and images

The derivative operation plays an important role in Fourier optics. For example, it can be used for describing the propagation in free space, analyzing the influence of wave aberrations, visualizing phase structures for edge enhancement, and image deblurring. In many of these applications the order of the derivative operation is performed in an integer number and sometimes in a rational number. Here we propose the use of the derivative operation, whose order is a real number. Consequently, the derivative can be applied in a continuous manner.