## Designing 3D printable Lieberkühn Reflectors for macro- and micro-photography

Designing a Lieberkühn Reflectors for macro- and micro-photography

A Lieberkühn Reflector gets its name from one Johann Nathaniel Lieberkühn, who invented the speculum that bears his name which you may recognize from reflective headband decorations for doctor costumes. The name is generally changed from “speculum” to “reflector” when referring to optical reflectors used in photography and microscopy, perhaps because the term has drifted from its original Latin root meaning “mirror” to refer to probing instruments for dilating orifices.

Lieberkühn reflectors were a way to bathe an opaque specimen in fill light. Lieberkühn reflectors and their use have unfortunately fallen by the wayside with the advent of modern conveniences like LEDs and fiber optic illumination. The above example from the collection of the Royal Microscopical Society displays a Lieberkühn on a simple microscope. In use, the reflector would be pointed towards the specimen, and fed light by a second mirror like the one on the rightmost microscope. Both of the microscopes pictured were on display at the Museum of the History of Science in Oxford

The working part of the Lieberkühn reflector is a parabolic mirror, which doesn’t add the spherical aberrations of hyper- or hypo-bolic configurations. As an added benefit, mirrors don’t tend to add chromatic dispersion or other aberrations associated with refraction (though they can effect polarisation). A parabola can be described as a a particular slice through a cone , but for the purposes of my first prototype, the functional description in cartesian coordinates will do.

$y = alpha x^2$
Where $alpha$ depends on the focal length of the parabola.
$alpha = 1 /4 f$

To get a functional, 3-dimensional mirror, I describe the parabola in terms of the focal length and a given radius as a 2D trace and spin it with rotate_extrude() in OpenSCAD. Leaving an aperture in the middle leaves room for light to reach the objective. The reflector shown below has a 4mm central aperture for the objective, 16mm focal length and 32mm diameter.

I have sent a few prototypes (matched to particular lenses or objectives) to Shapeways for prototyping. After some characterisation these will appear on theBilder shoppe.