= Fresnel diffraction by an opaque disk
{c}
Under the same scalar paraxial assumptions as <Fresnel diffraction by a circular aperture>, <Babinet's principle> gives the complementary opaque-disk field $U_d/U_0=e^{i\pi N_F}$ on axis. Its axial intensity equals the unobstructed intensity, producing the <Arago spot> inside the geometric shadow. The off-axis pattern depends on the full Fresnel integral; it is not obtained by subtracting aperture intensities from the incident intensity. Finite source size, misalignment and imperfect circular edges reduce the ideal spot contrast.
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