Spatial Filtering in Optical Image Processing

Lidiya Mishchenko

Dr. John Noe
Dr. Harold Metcalf
Laser Teaching Center
Stony Brook University

Abbe's theory of image formation states that objects illuminated by a plane wave form diffraction patterns in the back focal plane (or the Fourier plane) of an objective lens. A faithful image of the object can only be formed (with the help of a second lens) when all the diffracted orders are allowed to pass through the objective lens. The purpose of the project was to observe how different spatial frequencies of the aforementioned diffraction pattern contribute to image formation.

High-pass filters involve obstructing lower spatial frequencies located in the middle of the object's diffraction pattern in the Fourier plane. This kind of filtering results in edge enhancement of an object. Edge enhancement can be used to easily locate and define the edges of fine objects. Low-pass filters block out higher spatial frequencies located at the edges of the diffraction pattern in the Fourier plane. Blocking out higher spatial frequencies leads to degradation of the image quality. All lenses are of finite size, so all image formation involves low-pass filtering to some degree, and all lenses contribute to image degradation of the original object. Low-pass spatial filtering can be used to filter out grain noise highlighted by higher spatial frequencies in photographic emulsions.

Using various high-pass and low-pass spatial filters, processed images of objects were taken and analyzed using a CCD camera. The experimental results clearly supported Abbe's theory of image formation. Low-pass spatial filtering of an image of a Ronchi grating (with an iris acting as a filter) showed expected image blurring. High-pass filtering of an edge of an object (with circular obstructions in the middle of a transparent material acting as filters) showed edge enhancement, also as predicted. This experiment effectively illustrated that low spatial frequencies are important in forming the basic layout of an image, while higher spatial frequencies form the finer details, precisely defining the edges of the object.

Amplitude spatial filtering is closely related to the more general field of Fourier optics, as well as optical imaging. The concepts of amplitude filtering, combined with those of phase filters, lead to the development of complex holographic optical filter systems, which have applications in pattern recognition and intricate data processing.

This work was supported by a grant from the National Science Foundation (Phy-0243935).

Lidiya Mishchenko
June 2004
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