Babinet's principle

In physics, Babinet's principle is a theorem concerning diffraction that states that the diffraction pattern from an opaque body is identical to that from a hole of the same size and shape except for the overall forward beam intensity.

Assume B is the original diffracting body, and B' is its complement, i.e., a body that is transparent where B is opaque, and opaque where B is transparent. The sum of the radiation patterns caused by B and B' must be the same as the radiation pattern of the unobstructed beam. In places where the undisturbed beam would not have reached, this means that the radiation patterns caused by B and B' must be opposite in phase, but equal in amplitude.

Diffraction patterns from apertures or bodies of known size and shape are compared with the pattern from the object to be measured. For instance, the size of red blood cells can be found by comparing their diffraction pattern with an array of small holes. One consequence of Babinet's principle is a paradox that in the diffraction limit, the radiation removed from the beam due to a particle is equal to twice the particle's cross section times the flux. This is because the amount of radiation absorbed or reflected is the same as the amount diffracted.

The principle is most often used in optics but it is also true for other forms of electromagnetic radiation and is, in fact, a general theorem of diffraction and holds true for all waves. Babinet's principle finds most use in its ability to detect equivalence in size and shape.

The effect can be simply observed by using a laser. First place a thin (approx. 0.1 mm) wire into the laser beam and observe the diffraction pattern. Then observe the diffraction pattern when the laser is shone through a narrow slit. The slit can be made either by using a laser printer or to print onto clear plastic film or by using a pin to draw a line on a piece of glass that has been smoked over a candle flame.

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