Conoscopic holography

The conoscopic holography is an optical measuring principle for the contactless measurement of form and shape deviations. The principle is based on the interference of two light waves. Coherent light is a prerequisite for interference . This light is generated by a laser (Fig. 1). The measuring principle is used, for example, to measure the roughness of technical surfaces. The basic principle of holography was discovered in 1948 by Dennis Gábor . In the mid-1980s, G. Sirat and Demetri Psaltis published the theory of conoscopic holography.

Construction of a conoscopic sensor

With the help of the laser beam, a point of light is generated on a measurement object, the light of which is diffuse, i.e. H. in all directions, reflects back (picture "Schematic structure"). Part of the light reflected back from this point of light is captured by the lens of the sensor and falls on a crystal. There, the incoming light rays are first split into partial rays and then superimposed again after exiting the crystal. An interference pattern is created there, which is recorded with the help of a CCD sensor and evaluated electronically. Information about the angle of the incoming light beam is stored in the interference pattern. This angle is analyzed in the conoscopic system. The measuring process is based on the reconstruction of the distance of the light point from the angle information.

Schematic structure of a conoscopic sensor

Beam refraction on a birefringent crystal

In order to be able to better understand the system functionality, the measuring principle should be explained using the beam path ( see beam optics ) of a single light beam (picture “splitting”). A single beam was reflected in the direction of the sensor at a distance z from the measurement object (light point = measurement point). This light beam hits a birefringent crystal at an angle  ( refractive indices and ). At the surface of the crystal the beam is split into two partial beams - an ordinary beam and an extraordinary beam (see birefringence ). Both partial beams are refracted in the direction of the optical axis, the extraordinary beam part being refracted more strongly than the ordinary beam part. Both partial beams propagate in the crystal in different ways and emerge from the crystal at different locations. Instead of the original light point, a viewer on the side of the crystal opposite the light point would see two separate light points which are at a distance Δz from one another. The distance Δz depends on the crystal properties and the angle of incidence  . By cutting with the optical axis, the original distance z from the light point to the sensor can be reconstructed. ${\displaystyle \Theta }$ ${\displaystyle n_{o}}$ ${\displaystyle n_{ao}}$ ${\displaystyle \Theta }$

Splitting of a light beam on the surface of a birefringent crystal. Each reflected beam contains information about the location of the point of light.

Reconstruction of the distance z

Conoscopy is used to reconstruct the distance z. In contrast to orthoscopy, conoscopy does not observe an enlarged image of the object, but an interference figure. Imagine the two points of light as sources from which light waves are emitted in a spherical shape (picture “Distance”). Comparable as if two stones were thrown at the same time at a distance of Δz into a still water. The bank edge corresponds to the viewing plane. At the edge of the shore, interference can be observed wherever the waves from the two sources overlap. If two light waves interfere, a bright point results in an otherwise dark environment. Transferred to the sum of all light rays diffusely reflected from the measuring point, this means: Each reflected ray is split in the crystal into a regular and an extraordinary partial beam. This means that there is also a separate interference pattern for each beam. The conoscopic image is generated by collecting all interfering partial beams. It consists of concentric rings that become increasingly narrow towards the outside. Such a pattern is also called a Fresnel zone plate or Gabor zone lens. The size of the rings depends on the position of the measuring point in space.

The distance between the emitted spherical waves is λ / 2, where λ is the wavelength of the laser light source. Light waves interfere on a viewing plane. The collection of all interference patterns results in a Fresnel zone plate. The distance between the light sources can be reconstructed from the interference pattern.

The distance between the object point and the receiver (CCD array) (Rao) correlates with the mean radius of the interference ring of the mth order (R _m ):

${\displaystyle R_{\text{ao}}={\sqrt {\left(m\cdot {\frac {\lambda }{2}}\right)^{2}-{R_{m}}^{2}}}}$

As a rule of thumb, the further away the measuring point is from the receiver, the larger the rings of the Fresnel zone plate become.

Advantages over other distance measuring methods

The main difference to classic laser triangulation is that triangulation only measures the angle of a single beam, while the conoscopic system detects and evaluates the angle of each diffuse reflected beam. This procedure is much more stable and robust compared to triangulation, since angle errors are averaged out. Compared to the laser focus principle or some variants of the confocal technology , no moving parts are required, which disadvantageously restrict the measuring range. The measuring range of the conoscopic sensor can be changed by exchanging the lenses.

Individual evidence

1. ↑ K. Buse, M. Luenneman: 3D Imaging: Wave Front Sensin Utilizing a Birefringent Crystal . In: Physical Review Letters , The American Physical Society, Vol. 85, 16/2000, pp. 3385-3387.
2. ↑ L. Mugnier: Conoscopic Holography: Toward Three-Dimensional Reconstructions of opaque objects . In: Applied Optics , Optical Society of America, Vol. 34, 8/1995, pp. 1363-1371.
3. ↑ D. Gabor: A New Microscopic Principle . In: Nature , No. 161, 1948, pp. 777-778.
4. ↑ D. Gabor: Holography - 1948-1971 . In: Proc. of the IEE Electronics , Vol. 60, 1972, No. 6, pp. 655-668.
5. ↑ G. Sirat, D. Psaltis: Conoscopic Holography . In: Optics Letters , USA, 10/1985, pp. 4-6.
6. ↑ G. Sirat, D. Psaltis: Conoscopic Holograms . In: Optics Communications , Netherlands, vol. 65, 4/1988, pp. 243-249.