An equation for the irradiance due to a square array of circular apertures is derived from scalar Fresnel–Kirchhoff diffraction theory. Each aperture is illuminated by coherent radiant energy of constant amplitude and constant phase. Phase differences between the apertures produce a focus. The array equation was solved with an IBM 7094 computer. The results are presented in a plot of relative irradiance at the focus versus a parameter containing focal distance, wavelength, and aperture diameter for different numbers of elements. Also given are plots of the Fresnel diffraction patterns along the optic axis and in the focal plane for arrays of 16 and 64 elements.
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Lee et al. (1967) studied this question.
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