Читать книгу Optical Engineering Science - Stephen Rolt - Страница 102

We wish to construct a simple magnification system with a simple conic mirror. The system magnification is to be two and the object distance 100 mm. There is to be no on axis aberration. What is the prescription of the mirror, i.e. base radius and conic constant?

It is assumed that object and image are located the same side of the mirror, so that, in this context, the image distance is −200 mm. The overall set up is illustrated in the diagram:

The base radius of the conic mirror is very simple to calculate as it follows the simple paraxial formula, as replicated in Eq. (5.6):

This gives R = −133 mm.

We now need to calculate the conjugate parameter, t:

From Eq. (5.5) it is straightforward to see that k = −(1/t)² and thus k = −0.1111. The shape is that of a slightly prolate ellipsoid.

The practical significance of a perfect on axis set up described in this example, is that it forms the basis of an ideal manufacturing test for such a conic surface. This will be described in more detail later in this text.