Conoscopy
Encyclopedia
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 directions image. The earliest references on the use of conoscopy (i.e., observation in convergent light with a polarization microscope with a Bertrand-lens) for evaluation of the optical properties of liquid crystalline phases (i.e., orientation of the optical axes) dates back to 1911 when it was used by Mauging to investigate the alignment of nematic and chiral-nematic phases.
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 into a lateral distribution (directions image) appearing in the back focal plane (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 of the lens
with the distance of their focal point from the optical axis
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 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 (i.e., definition of a measuring spot, or field of measurement) an aperture
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
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
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).
The functional sequence is as follows:
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:
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
, contrast
and chromaticity
with viewing direction
).
A conoscope is an apparatus to carry out conoscopic observations and measurements, often realized by a microscope
Microscope
A microscope is an instrument used to see objects that are too small for the naked eye. The science of investigating small objects using such an instrument is called microscopy...
with a Bertrand lens for observation of the directions image. The earliest references on the use of conoscopy (i.e., observation in convergent light with a polarization microscope with a Bertrand-lens) for evaluation of the optical properties of liquid crystalline phases (i.e., orientation of the optical axes) dates back to 1911 when it was used by Mauging to investigate the alignment of nematic and chiral-nematic phases.
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 into a lateral distribution (directions image) appearing in the back focal plane (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 of the lens
Lens (optics)
A lens is an optical device with perfect or approximate axial symmetry which transmits and refracts light, converging or diverging the beam. A simple lens consists of a single optical element...
with the distance of their focal point from the optical axis
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 or microscope.The optical axis is an imaginary line that defines the path along which light propagates through the system...
being a (monotonous) 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 object of measurement is usually located in the front focal plane of the lens
Lens (optics)
A lens is an optical device with perfect or approximate axial symmetry which transmits and refracts light, converging or diverging the beam. A simple lens consists of a single optical element...
. 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
Aperture
In optics, an aperture is a hole or an opening through which light travels. More specifically, the aperture of an optical system is the opening that determines the cone angle of a bundle of rays that come to a focus in the image plane. The aperture determines how collimated the admitted rays are,...
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
Aperture
In optics, an aperture is a hole or an opening through which light travels. More specifically, the aperture of an optical system is the opening that determines the cone angle of a bundle of rays that come to a focus in the image plane. The aperture determines how collimated the admitted rays are,...
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
Aperture
In optics, an aperture is a hole or an opening through which light travels. More specifically, the aperture of an optical system is the opening that determines the cone angle of a bundle of rays that come to a focus in the image plane. The aperture determines how collimated the admitted rays are,...
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.
| Figure 2: Formation of an image of the object (aperture) 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 (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).
| 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
Liquid crystal display
A liquid crystal display is a flat panel display, electronic visual display, or video display that uses the light modulating properties of liquid crystals . LCs do not emit light directly....
(e.g., variation of luminance
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 or is emitted from a particular area, and falls within a given solid angle. The SI unit for luminance is candela per square...
, contrast
Display contrast
Contrast in visual perception is the difference in appearance of two or more parts of a field seen simultaneously or successively ....
and chromaticity
Chromaticity
Chromaticity is an objective specification of the quality of a color regardless of its luminance, that is, as determined by its hue and colorfulness ....
with viewing direction
Viewing cone
-Viewing direction:When a visual display with non-vanishing size is seen by an observer, every point of the display area is seen from a different direction as illustrated in fig. 1. No two spots on the display are seen from the same direction...
).
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