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Abstract
Scalar diffraction theory is usually introduced using the classical Green function approach as a solution to a boundary value problem. I propose a different approach first proposed by Duffieux and later put on a solid mathematical foundation by Arsac and which exploits the close connection between Fourier theory and linear systems theory; it is based on elementary distribution theory, where scalar diffraction appears naturally as a convolution of the diffracting screen with an optical propagator. All the classical expressions such as Rayleigh's integral formula and the Kirchhoff-Sommerfeld diffraction integral are easily derived as special cases. The fact that diffraction appears naturally as a convolution facilitates the integration of diffraction theory with linear systems theory, which has come to play a major role in fourier optics.
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Henri H. Arsenault "Alternate way to teach Fourier optics", Proc. SPIE 2525, 1995 International Conference on Education in Optics, (13 October 1995); https://doi.org/10.1117/12.224070
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KEYWORDS
Diffraction
Convolution
Fourier optics
Fourier theory
Fourier transforms
Linear filtering
Free space
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