Conoscopy 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'' (i.e., observation in convergent light with a polarization microscope with a
Bertrand lens A phase telescope or Bertrand lens is an optical device used in aligning the various optical components of a light microscope. In particular it allows observation of the back focal plane of the objective lens and its conjugated focal planes. The pha ...
) for evaluation of the optical properties of
liquid crystalline phases (i.e., orientation of the optical axes) is in 1911 when it was used by
Charles-Victor Mauguin to investigate the alignment of
nematic
Liquid crystal (LC) is a state of matter whose properties are between those of conventional liquids and those of solid crystals. For example, a liquid crystal may flow like a liquid, but its molecules may be oriented in a crystal-like way. The ...
and
chiral-nematic phases.
[Mauguin, C.: Sur les cristaux liquides de Lehmann]
Bull. Soc. Fr. Miner. 34, 71–117 (1911)
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A beam of convergent (or divergent) 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
In Gaussian optics, the cardinal points consist of three pairs of points located on the optical axis of a rotationally symmetric, focal, optical system. These are the '' focal points'', the principal points, and the nodal points. For ''ideal'' ...
into a lateral distribution (''directions image'') appearing in the back focal plane
In Gaussian optics, the cardinal points consist of three pairs of points located on the optical axis of a rotationally symmetric, focal, optical system. These are the '' focal points'', the principal points, and the nodal points. For ''ideal'' ...
(which is more or less curved). The incoming elementary parallel beams (illustrated by the colors blue, green and red) are converging in the back focal plane
In Gaussian optics, the cardinal points consist of three pairs of points located on the optical axis of a rotationally symmetric, focal, optical system. These are the '' focal points'', the principal points, and the nodal points. For ''ideal'' ...
of the lens
A lens is a transmissive optical device which focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (''elements''), ...
with the distance of their focal point from the optical axis
An optical axis is a line along which there is some degree of rotational symmetry in an optical system such as a camera lens, microscope or telescopic sight.
The optical axis is an imaginary line that defines the path along which light propa ...
being a (monotonous) function of the angle of beam inclination.
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 object of measurement is usually located in the front focal plane
In Gaussian optics, the cardinal points consist of three pairs of points located on the optical axis of a rotationally symmetric, focal, optical system. These are the '' focal points'', the principal points, and the nodal points. For ''ideal'' ...
of the lens
A lens is a transmissive optical device which focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (''elements''), ...
. In order to select a specific area of interest on the object (i.e., definition of a measuring spot, or field of measurement) an aperture
In optics, an aperture is a hole or an opening through which light travels. More specifically, the aperture and focal length of an optical system determine the cone angle of a bundle of rays that come to a focus in the image plane.
An op ...
can be placed on top of the object. In this configuration only rays from the measuring spot (aperture) hit the lens.
The image of the aperture
In optics, an aperture is a hole or an opening through which light travels. More specifically, the aperture and focal length of an optical system determine the cone angle of a bundle of rays that come to a focus in the image plane.
An op ...
is projected to infinity while the image of the directional distribution of the light passing through the aperture (i. e. directions image) is generated in the back focal plane of the lens. When it is not considered appropriate to place an aperture
In optics, an aperture is a hole or an opening through which light travels. More specifically, the aperture and focal length of an optical system determine the cone angle of a bundle of rays that come to a focus in the image plane.
An op ...
into the front focal plane of the lens, i.e., on the object, the selection of the measuring spot (field of measurement) can also be achieved by using a second lens. An image of the object (located in the front focal plane of the first lens) 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.
A third lens transforms the rays passing through the aperture (located in the plane of the image of the object) into a second directions image which may be analyzed by an image sensor (e.g., electronic camera).
{, class="wikitable"
, -
,
, 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 (transformation of directions into locations),
* the second lens together with the first projects an image of the object,
* the aperture allows selection of the area of interest (measuring spot) on the object,
* the third lens together with the second images the directions image on a 2-dimensional optical sensor (e.g., electronic camera).
This simple arrangement is the basis for all conoscopic devices (conoscopes). It is not straight forward however to design and manufacture lens systems that combine the following features:
* maximum angle of light incidence as high as possible (e.g., 80°),
* diameter of measuring spot up to several millimeters,
* achromatic performance for all angles of inclination,
* minimum effect of polarization of incident light.
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 (e.g., variation of luminance
Luminance is a photometric measure of the luminous intensity per unit area of light travelling in a given direction. It describes the amount of light that passes through, is emitted from, or is reflected from a particular area, and falls with ...
, contrast and chromaticity with viewing direction).
References
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, (ii) Conoscopic Observations (in convergent light)
* C. Burri: "Das Polarisationsmikroskop", Verlag Birkhäuser, Basel 1950
External links
Polariscope/Conoscope - Gemology Project
Microscopy