FRAUNHOFER DIFFRACTION PATTERNS FROM APERTURES ILLUMINATED WITH NONPARALLEL LIGHT

The size of the Fraunhofer diffraction pattern produced when a circular aperture is illuminated with a diverging beam of light, in contrast with a parallel beam, is derived on the basis of simple lens theory by introducing the concept of a virtual diffraction pattern. The results of the simple analysis agree with the diffraction pattern size determined by a formal analysis of the light wave amplitude. The formal analysis reveals a general scale factor relating the Fraunhofer diffraction pattern size for an aperture illuminated with parallel light to the size for nonparallel illumination. The diffraction pattern intensity is independent of the position of the aperture in its plane, based on a property of the Fourier transform. The invariance in intensity for nonparallel illumination of the aperture is also shown by a simple argument based on the Abbe theory of image formation by diffraction. Finally, some experimental results are given. © 1979, American Association of Physics Teachers. All rights reserved.