Spatial Filtering Experiments for Undergraduate Laboratories

Abstract

Experiments in the spatial filtering of optical images, which are suitable for an upper division undergraduate laboratory, are presented. These experiments exploit the spatial coherence of laser radiation for their success. It is shown that the field distribution across the aperture of a lens, and the field distribution across the focal plane are a Fourier transform pair. Since a lens resolves an image into its Fourier components, filtering operations can be performed at the transform plane which enhance or eliminate selected components of the image. A second lens performs another transformation that recreates the original image, plus the effects of whatever filtering operation which has been performed. Three examples of experiments that use this principle are described. The irregularities across the wavefront of a laser output beam are eliminated. A two-dimensional pattern is filtered so only the information in one dimension is transmitted. The squares which make up a self-portrait are subtracted, leaving a continuous rendition.