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Concept
Talbot effect
Summary
The Talbot effect is a diffraction effect first observed in 1836 by Henry Fox Talbot. When a plane wave is incident upon a periodic diffraction grating, the image of the grating is repeated at regular distances away from the grating plane. The regular distance is called the Talbot length, and the repeated images are called self images or Talbot images. Furthermore, at half the Talbot length, a self-image also occurs, but phase-shifted by half a period (the physical meaning of this is that it is laterally shifted by half the width of the grating period). At smaller regular fractions of the Talbot length, sub-images can also be observed. At one quarter of the Talbot length, the self-image is halved in size, and appears with half the period of the grating (thus twice as many images are seen). At one eighth of the Talbot length, the period and size of the images is halved again, and so forth creating a fractal pattern of sub images with ever-decreasing size, often referred to as a Talbot carpet. Talbot cavities are used for coherent beam combination of laser sets.
Lord Rayleigh showed that the Talbot effect was a natural consequence of Fresnel diffraction and that the Talbot length can be found by the following formula:
where is the period of the diffraction grating and is the wavelength of the light incident on the grating. However, if wavelength is comparable to grating period , this expression may lead to errors in up to 100%. In this case the exact expression derived by Lord Rayleigh should be used:
The number of Fresnel zones that form first Talbot self-image of the grating with period and transverse size is given by exact formula . This result is obtained via exact evaluation of Fresnel-Kirchhoff integral in the near field at distance .
Due to the quantum mechanical wave nature of particles, diffraction effects have also been observed with atoms—effects which are similar to those in the case of light. Chapman et al.
Official source
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