We present a differential operator approach for Fourier image processing. We demonstrate that when the mask in the processor Fourier plane is an analytical function, it can be described by means of a differential operator that acts directly on the input field to give the processed output image. In many cases (e.g., Schlieren imaging) this approach simplifies the calculations, which usually involve the evaluation of convolution integrals, and gives a new insight into the image-processing procedure.
© 2007 Optical Society of America
Fourier Optics and Optical Signal Processing
Original Manuscript: November 29, 2006
Revised Manuscript: March 5, 2007
Manuscript Accepted: March 17, 2007
Published: July 11, 2007
Ismael Núñez and José A. Ferrari, "Differential operator approach for Fourier image processing," J. Opt. Soc. Am. A 24, 2274-2279 (2007)