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In 1950, Giuliano Toraldo di Francia published a paper [1] with the title "Parageometrical Optics" followed by several other papers on the subject, I dare say culminating in a beautiful design work of a microwave antenna [2]. Toraldo also presented his ideas in a rather brief chapter in his otherwise excellent book "Onde Elettromagnetiche" published in 1953. His work on parageometric optics seems to have preceded or at least be simultaneous with Keller's Geometric Theory of Diffraction.

Parageometric optics is supposed to be an extension of conventional geometric optics to include diffraction effects. In his analysis, Toraldo shows that the various diffractive orders resulting from an arbitrary (amplitude/phase) transparency illuminated by a plane wave will follow Malus' law for the associated ray systems having orthogonal surfaces and thus the propagation of diffraction orders can be treated individually and "geometrically" and, furthermore, the transparency can be of arbitrary (smooth) shape.

It seems to me that since 1960 or so nothing has been written on the subject, and by now is completely forgotten despite its eminent intuitive appeal; Born&Wolf does not mention it at all, not even as a pedagogic device. My question is why? Is anything fundamentally so wrong with it that the idea is not worth discussing?

[1]:"Parageometrical Optics", JOURNAL OF THE OPTICAL SOCIETY OF AMERICA, 1950 vol.40, 9

[2]: "An Application of Parageometrical Optics to the Design of a Microwave Mirror", IRE Trans. Antennas and Propagation, January 1958

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  • $\begingroup$ Might help to have a link to the original article in full text. It's on page 600 here: archive.org/details/… $\endgroup$
    – uUnwY
    Jan 17, 2022 at 8:16

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