thumb|Photo of the Arago spot in a shadow of a 5.8 mm circular obstacle.
In optics, the Arago spot, Poisson spot, or Fresnel spot is a bright point that appears at the center of a circular object's shadow due to Fresnel diffraction.
In astronomy, the Arago spot can also be observed in the strongly defocussed image of a star in a Newtonian telescope. There, the star provides an almost ideal point source at infinity, and the secondary mirror of the telescope constitutes the circular obstacle.
thumb|Formation of the Arago spot by the interfering edge waves
When light shines on the circular obstacle, Huygens' principle says that every point in the plane of the obstacle acts as a new point source of light. The light coming from points on the circumference of the obstacle and going to the center of the shadow travels exactly the same distance, so all the light passing close by the object arrives at the screen in phase and constructively interferes. This results in a bright spot at the shadow's center, where geometrical optics and particle theories of light predict that there should be no light at all.
Arago later noted that the phenomenon (later known as "Poisson's spot" or the "spot of Arago") had already been observed by Joseph-Nicolas Delisle
thumb|left|700px|Numerical simulation of the intensity of monochromatic light of wavelength λ = 0.5 μm behind a circular obstacle of radius .
Experimental aspects
Intensity and size
400px|thumb|right|Arago spot experiment. A point source illuminates a circular object, casting a shadow on a screen. At the shadow's center a bright spot appears due to [[diffraction, contradicting the prediction of geometric optics.]]
For an ideal point source, the intensity of the Arago spot equals that of the undisturbed wave front. Only the width of the Arago spot intensity peak depends on the distances between source, circular object and screen, as well as the source's wavelength and the diameter of the circular object. <!--The shape of the Poisson spot's intensity distribution will in fact be similar for experimental setups with the same Fresnel number.--> This means that one can compensate for a reduction in the source's wavelength by increasing the distance between the circular object and screen or reducing the circular object's diameter.
The lateral intensity distribution on the screen has in fact the shape of a squared zeroth Bessel function of the first kind when close to the optical axis and using a plane wave source (point source at infinity):
<math display="block">I_\text{rel}(w) = J_0^2\left(\frac{w R \pi}{g \lambda}\right) + J_1^2\left(\frac{w R \pi}{g \lambda}\right)</math>
where <math>J_0</math>and <math>J_1</math>are the Bessel functions of the first kind. <math>R</math> is the radius of the disc casting the shadow, <math>\lambda</math> the wavelength and <math>g</math> the distance between source and disc. For large sources the following asymptotic approximation applies: Another is to probe aberrations in laser beams by using the spot's sensitivity to beam aberrations.
See also
- Aragoscope
- Occulting disk
References
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