Chapter 4Optical Systems in Machine Vision

Karl Lenhardt

Jos. Schneider Optische Werke GmbH, Ringstraße 132, 55543 Bad Kreuznach, Germany

4.1 A Look at the Foundations of Geometrical Optics

4.1.1 From Electrodynamics to Light Rays

The optical system transmits information such as intensity distribution, color distribution, forms, and structures into the image space. This information is finally stored in a single plane, called the image plane.

The usual and most simple treatment of this information transmission – or imaging – is accomplished with the help of light rays. With their introduction, and with the knowledge of the laws of reflection and refraction, one arrives at the field of geometrical optics, in which the object – image relations follow from purely geometrical considerations.

Now, the concept of light rays is a pure hypothetical assumption, which is well suited to work in a first approximation. According to classical physics, light consists of electromagnetic waves of a certain wavelength range:

light = electromagnetic waves with wavelengths c04-math-001

In order to give a general survey on the underlying principles, we will give a very short outline on the approximations that result in the idea of light rays.

The propagation of electromagnetic waves is described by electrodynamics and, in particular, by Maxwell's equations. These are a set of vectorial, linear, and partial ...

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