and the green lines were computed by applying the corresponding parameters to the squared Bessel function given above. Finite source size and spatial coherence The main reason why the Arago spot is hard to observe in circular shadows from conventional light sources is that such light sources are bad approximations of point sources. If the wave source has a finite size S then the Arago spot will have an extent that is given by Sb/g, as if the circular object acted like a lens. At the same time the intensity of the Arago spot is reduced with respect to the intensity of the undisturbed wave front. Defining the relative intensity as the intensity divided by the intensity of the undisturbed wavefront, the relative intensity for an extended circular source of diameter w can be expressed exactly using the following equation: where and are the Bessel functions of the first kind. is the radius of the disc casting the shadow, the wavelength and the distance between source and disc. For large sources the following asymptotic approximation applies: Deviation from circularity If the cross-section of the circular object deviates slightly from its circular shape (but it still has a sharp edge on a smaller scale) the shape of the point-source Arago spot changes. In particular, if the object has an ellipsoidal cross-section the Arago spot has the shape of an evolute. Note that this is only the case if the source is close to an ideal point source. From an extended source the Arago spot is only affected marginally, since one can interpret the Arago spot as a point-spread function. Therefore, the image of the extended source only becomes washed out due to the convolution with the point-spread function, but it does not decrease in over all intensity. The circular object's surface roughness The Arago spot is very sensitive to small-scale deviations from the ideal circular cross-section. This means that a small amount of surface roughness of the circular object can completely cancel out the bright spot. This is shown in the following three diagrams which are simulations of the Arago spot from a 4 mm diameter disc (g = b = 1 m): The simulation includes a regular sinusoidal corrugation of the circular shape of amplitude 10 μm, 50 μm and 100 μm, respectively. Note, that the 100 μm edge corrugation almost completely removes the central bright spot. This effect can