blocking circular object.) the integral that needs to be solved is given by: Numerical calculation of the integral using the trapezoidal rule or Simpson's rule is not efficient and becomes numerically unstable especially for configurations with large Fresnel number. However, it is possible to solve the radial part of the integral so that only the integration over the azimuth angle remains to be done numerically. For a particular angle one must solve the line integral for the ray with origin at the intersection point of the line P0P1 with the circular object plane. The contribution for a particular ray with azimuth angle and passing a transparent part of the object plane from to is: So for each angle one has to compute the intersection point(s) of the ray with the circular object and then sum the contributions for a certain number of angles between 0 and . Results of such a calculation are shown in the following images. The images are simulations of the Arago spot in the shadow of discs of diameter 4 mm, 2 mm, and 1 mm, imaged 1 m behind each disc. The disks are illuminated by light of wavelength of 633 nm, diverging from a point 1 m in front of each disc. Each image is 16 mm wide. Experimental aspects Intensity and size 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. This means that one can compensate for a reduction in the source's wavelength by increasing the distance l between 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): where r is the distance of the point P1 on the screen from the optical axis d is the diameter of circular object λ is the wavelength b is the distance between circular object and screen. The following images show the radial intensity distribution of the simulated Arago spot images above: The red lines in these three graphs correspond to the simulated images above,