Coherence

In physics, coherence means a property of waves – coherent waves are able to interfere as they have a constant phase relation.

Physicists distinguish between two types of coherence:

  • spatial (transverse) coherence
  • temporal (longitudinal, spectral) coherence

In order to observe interference patterns both types of coherence must exist.

Some light sources such as lasers already have a high spatial and temporal coherence due to their design. For some years such sources are also available for atoms; they are based on Bose-Einstein condensates and are able to emit coherent matter waves. However, for large molecules we often have to work with incoherent thermal sources. In the case of such sources, say, the wave functions of two molecules leaving the souce from two far apart regions of the oven nozzle do not have a pre-defined phase relation to each other.

Spatial Coherence

Each point of the source opening can create its own interference pattern. In the case of incoherent sources they overlap without being influenced, without constant phase relation. Together they can form an image without contrast. However, you can improve the spatial coherence by reducing the real or even just the apparent size of the source opening. The latter can be achieved by increasing the distance between source and the diffractive object.

In the following applet you can see the two most extreme directions of propagation (black lines) of waves moving from the source on the left to the detector on the right. Find out how you can improve the spatial coherence:


Source-opening - +
Detector-opening - +
Distance - +

Spacial coherence

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Temporal coherence

Temporal coherence depends on how similar the frequencies and, therefore, the wavelengths are. If there is a vast difference in wavelengths the waves are diffracted unequally and produce different interference patterns. These patterns overlap and reduce the contrast of the pattern. In the forward direction the phase relations change with time which, in turn, makes a stable interference pattern impossible.

coherence

  1. The waves on the top left have neither a combined wavelength nor a combined direction of propagation. They are temporally and spatially incoherent.
  2. Although all waves on the top right propagate in the same direction they have different wavelengths. They are temporally incoherent but spatially coherent.
  3. On the bottom left one can watch monochromatic waves which all have the same wavelength. Spatially, however, the waves are incoherent since they propagate in different directions.
  4. On the bottom right both the propagation directions and the wavelengths are identical. Therefore, the waves are spatially and temporally coherent.

Coherence

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