Differentiation by spatial filtering

A simple procedure for generating filters to perform first- and second- order differentiation has been presented. The procedure is based on the dependence of the diffraction efficiency on the grating constant of a binary grating. The influence of the finite or zero transmittance of the central region of the filter and also of the finite size of the filter on the quality of differentiation has been studied. It is shown that false information is obtained when the sizeable central region of the filter has zero transmittance. The experimental results for first- and second-order differentiation are presented. © 1977 Taylor & Francis Group, LLC.