The diffraction pattern which represents the image of a luminous point produced by an instrument free from aberrations and having a circular aperture, when observed out of focus, has been calculated by A. E. Conrady, A. Buxton, and G. Lansraux. Conrady and Buxton used numerical integration. Such a process yields a sequence of values of the complex amplitude at a particular point in the diffraction pattern for a particular lack of focus, and for any given integration, the distance W of the point under consideration from the center of the pattern, and the lack of focus ψ, are functions of the upper limit of integration. If ψ is plotted against W, the path obtained is a parabola, ψ = aW2.
The author has found a method whereby any desired path can be followed instead of a parabola. In particular, if the point of observation is near the edge of the purely geometrical diffusion disk and remains at a constant distance from it as ψ changes, then, for large values of ψ, the form of the diffraction fringes is approximately independent of ψ and their intensity is inversely proportional to ψ2.
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