Conoscopy


Conoscopy "cone, spinning top, pine cone" and σκοπέω is an optical technique to make observations of a transparent specimen in a cone of converging rays of light. The various directions of light propagation are observable simultaneously.
A conoscope is an apparatus to carry out conoscopic observations and measurements, often realized by a microscope with a Bertrand lens for observation of the direction's image. The earliest reference to the use of conoscopy for evaluation of the optical properties of liquid crystalline phases is in 1911 when it was used by Charles-Victor Mauguin to investigate the alignment of nematic and chiral-nematic phases.
A beam of convergent light is known to be a linear superposition of many plane waves over a cone of solid angles. The raytracing of Figure 1 illustrates the basic concept of conoscopy: transformation of a directional distribution of rays of light in the front focal plane into a lateral distribution appearing in the back focal plane. The incoming elementary parallel beams are converging in the back focal plane of the lens with the distance of their focal point from the optical axis being a function of the angle of beam inclination.
Figure 1: Imaging of bundles of elementary parallel rays to form a directions image in the back focal plane of a positive thin lens.

This transformation can easily be deduced from two simples rules for the thin positive lens:
The object of measurement is usually located in the front focal plane of the lens. In order to select a specific area of interest on the object an aperture can be placed on top of the object. In this configuration only rays from the measuring spot hit the lens.
The image of the aperture is projected to infinity while the image of the directional distribution of the light passing through the aperture is generated in the back focal plane of the lens. When it is not considered appropriate to place an aperture into the front focal plane of the lens, i.e., on the object, the selection of the measuring spot can also be achieved by using a second lens. An image of the object is generated in the back focal plane of the second lens. The magnification, M, of this imaging is given by the ratio of the focal lengths of the lenses L1 and L2, M = f2 / f1.
Figure 2: Formation of an image of the object by addition of a second lens. The field of measurement is determined by the aperture located in the image of the object.

A third lens transforms the rays passing through the aperture into a second directions image which may be analyzed by an image sensor.
Figure 3: Schematic raytracing of a complete conoscope: formation of the directions image and imaging of the object.

The functional sequence is as follows:
This simple arrangement is the basis for all conoscopic devices. It is not straight forward however to design and manufacture lens systems that combine the following features:
Design and manufacturing of this type of complex lens system requires assistance by numerical modelling and a sophisticated manufacturing process.
Modern advanced conoscopic devices are used for rapid measurement and evaluation of the electro-optical properties of LCD-screens.

Literature