Aplanatic illustration

In geometric optics, an aplanatic imaging is understood to be the imaging of an object point lying on the optical axis through a spherical surface, free of spherical aberration .

To do this, one of the following conditions must be met:

The back focus is zero, i.e. H. the object point and also the image point lie on the vertex of the surface (point of intersection of surface and optical axis).

The angle of incidence is zero, i.e. H. the rays coming from the object point hit the surface perpendicularly and are not refracted; The object and image point lie in the center of curvature of the surface. As in the previous case, the object point is mapped onto itself.

The following applies , where is the back focal length, i.e. the distance between the object point and the vertex of the surface (positive if the object point is behind the surface). is the radius of the surface (positive for convex surface, i.e. when the center of curvature is behind the surface) and are the indices of refraction before and after the surface. The focal length of the image point results . ${\ displaystyle s = {\ frac {n + n '} {n}} r}$ ${\ displaystyle s}$ ${\ displaystyle r}$ ${\ displaystyle n, n '}$ ${\ displaystyle s' = {\ frac {n + n '} {n'}} r}$

Such an aplanatic imaging surface is also called an aplanatic surface . Whether a surface appears aplanatic depends not only on it itself, i.e. on its radius and the refractive indices before and after, but also on the position of the object point. If the back focus changes, the image is generally no longer aplanatic.

A real aplanatic mapping of an object point in front of the system onto an image point behind the system cannot be achieved. From the above conditions it follows that either the object or the image must be virtual . In the case of a real image, an aspherical surface is required in order to completely correct the spherical aberration. But it can also be corrected to a very good approximation by a combination of several spherical surfaces.

Application example

An aplanatic teleconverter can be implemented with a diverging lens . The marginal rays coming from the upstream objective strike the first surface perpendicularly, this is aplanatic according to condition 2, and the second surface is more strongly curved so that it is aplanatic according to condition 3. The overall system of the basic lens and converter is (at least for one light wavelength ) free of spherical aberration, if it is the basic lens too. Such a teleconverter would not be particularly good in practice, because only the spherical aberration is corrected and the other aberrations are not.

literature

Dietrich Kühlke: Optics. Basics and Applications . 2nd, revised and expanded edition. Harri Deutsch, Frankfurt am Main 2004, ISBN 3-8171-1741-8 .
Reinhart Weber: Physics - Volume 1: Classical Physics. Experimental and theoretical basics. Teubner, Wiesbaden 2007, ISBN 978-3-8351-0065-7 .
Eugene Hecht: optics . 4th edition. Oldenbourg, Munich, Vienna 2005, ISBN 3-486-27359-0 , pp. 365 f .
Chris R. Kitchin: Astrophysical Techniques . 3. Edition. Institute of Physics Publishing, Bristol, Philadelphia 1998, ISBN 0-7503-0498-7 , pp. 54, 66 .

Web links

Lexicon of optics