Conoscopy: Definition, Use, Equipment, Characteristics and Origins

It is an optical technique for making observations of a transparent specimen in a cone of converging rays of light.

The various directions of light propagation are simultaneously observable.

This means that it is a transformation of a directional distribution of light rays in the front focal plane into a lateral distribution (image of directions) that appears in the back focal plane (which is more or less curved).

Ultimately, this method is performed through a conoscope , which is a device for carrying out conoscopic observations and measurements, often performed using a microscope with a Bertrand lens for image observation.

Characteristics of a conoscope

A converging (or diverging) beam of light is a linear superposition of many plane waves on a cone of solid angles.

The incoming elementary parallel beams converge at the rear focal plane of the lens, the distance of their focal point from the optical axis being a (monotonic) function of the beam angle tilt.

This transformation can be easily deduced from two simple rules for the thin positive lens:

  • The rays through the center of the lens remain unchanged.
  • Rays through the front focal point transform into parallel rays.

The measurement object is generally located in the front focal plane of the lens. To select a specific area of ​​interest on the object such as a measurement point, or measurement field, an aperture can be placed at the top. In this configuration, only the rays from the measurement point (aperture) hit the lens.

The image of the aperture is projected to infinity while the image of the directional distribution of light passing through the aperture. That is why it is generated in the back focal plane of the lens.

When it is not considered appropriate to place an aperture in the front focal plane of the lens, that is, in the object, the selection of the measurement point or 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 at the back focal plane of the second lens.

For example, a magnification, M, of this imaging is given by the ratio of the focal lengths of the L1 and L2 lenses, M = f2 / f1.

A third lens transforms the rays that pass through the aperture, located in the image plane of the object, into a second directional image that can be analyzed by an image sensor and can be generated by an electronic camera.

The functional sequence is as follows:

  • The first lens forms the image of directions, that is, transformation of directions into locations.
  • The second lens together with the first one projects an image of the object.
  • The aperture allows selection of the area of ​​interest or measurement point on the object.
  • The third lens, together with the second, represents the image of the indications on a two-dimensional optical sensor, such as the electronic camera.

This simple arrangement is the basis for all conoscopic devices. However, it is not easy to design and manufacture lens systems that combine the following characteristics:

  • Maximum angle of incidence of light as high as possible, for example 80 °.
  • Diameter of the measuring point up to several millimeters.
  • Achromatic performance for all tilt angles.
  • Minimal effect of incident light polarization.

The design and manufacture of this type of complex lens system requires assistance through numerical modeling and a sophisticated manufacturing process.

Modern advanced conoscopic devices are used for the rapid measurement and evaluation of the electro-optical properties of LCD displays, that is, the variation of luminance, contrast and chromaticity with the viewing direction.


The first time that the technique of conoscopy was used, such as observation in convergent light with a polarization microscope with a Bertrand lens for the evaluation of the optical properties of the liquid crystalline phases for the orientation of the optical axes was in 1911 by the researcher Mauging to analyze the alignment of the nematic and chiral-nematic phases.