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 rays through the center of the lens remain unchanged,
- the rays through the front focal point are transformed into parallel rays.
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:
- the first lens forms the directions image,
- the second lens together with the first projects an image of the object,
- the aperture allows selection of the area of interest on the object,
- the third lens together with the second images the directions image on a 2-dimensional optical sensor.
- maximum angle of light incidence as high as possible,
- diameter of measuring spot up to several millimeters,
- achromatic performance for all angles of inclination,
- minimum effect of polarization of incident light.
Modern advanced conoscopic devices are used for rapid measurement and evaluation of the electro-optical properties of LCD-screens.
Literature
- Pochi Yeh, Claire Gu: "Optics of Liquid Crystal Displays", John Wiley & Sons 1999, 4.5. Conoscopy, pp. 139
- Hartshorne & Stuart: "Crystals and the Polarizing Microscope", Arnold, London, 1970, 8: The Microscopic Examination of Crystals, Conoscopic Observations
- C. Burri: "Das Polarisationsmikroskop", Verlag Birkhäuser, Basel 1950