# In interferometry, what is the origin of the name “Airy function”?

In interferometry (specifically, in the domain of Fabry-Perot cavities), the function $$f(\phi) = \frac{1}{1 + F \sin^2 \phi},$$ which describes the shape of the resonant structure of the cavity, is often called the "Airy function" (for instance, in Wolfram Mathworld). However, it is obviously quite different from the special functions Ai(x) that usually go by that name.

This function resembles probability density function of the wrapped Cauchy distribution.

How did it get the name "Airy function"?

I've heard that Fabry and Perot gave it this name in one of their original papers (maybe this one? PDF, in French, which I can't read), in honor of (the same) George Biddell Airy who had earlier considered similar interferometers. It would be great if someone could help ferret out the first reference to that function by this name.

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In the paper in French he uses the term "Airy formulas" like a well known name for these formulas... maybe defined in one of his earlier paper ? – Cedric H. Nov 9 '10 at 20:40
According to this page: skullsinthestars.com/2008/10/16/…, the first paper is called "C. Fabry and A. Perot, “Sur les franges des lames minces argentées et leur application a la mesure de petites épaisseurs d’air,” Ann. Chim. Phys. 12 (1897), 459.". – Robert Smith Nov 9 '10 at 20:54

I have noticed this in the literature as well. It always seemed glossed over - but thanks to your PDF of the Fabry-Perot paper (in french) - and google translate, we have the relevant passage:

"Les franges par transmission, complementaires des precedentes, ont l'aspect de lignes brillantes tres fines se detachant sur un fond tres sombre.

ces phenomenes sont dus aux reflections multiples et s'expliquent facilement au moyen des formules d'Airy, en tenant compte de ce que, au voisinage de la reflexion totale, la coefficient de reflexion prend une valeur voisine de l'unite."

which becomes:

"Transmission fringes, complementary previous ones, have the appearance of very fine bright lines set against a very dark background.

these phenomena are due to multiple reflections and are easily explained using the formulas of Airy, taking into account that, in the vicinity of total reflection, the reflection coefficient takes a value close to unity."

which means that Fabry and Perot simply named the transmission function after Airy sometime around 1897.

According to Wikipedia, the conventional notation for Ai and Bi was introduced by Sir Harold Jeffreys, FRS (22 April 1891 – 18 March 1989).

So the special functions that we know and love - received their names after Fabry-Perot noticed that the transmission function for fringes looked like those related to the ones Airy had written about.

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edit this is the wrong Airy function, answer is only kept for discussion

According to the german wikipedia entry on Airy function (-> google translation), it is named after the british Astronomer George Biddell Airy.

update http://wordiq.com/definition/Airy_function cites Airy (1838). On the intensity of light in the neighbourhood of a caustic. Transactions of the Cambridge Philosophical Society, 6, 379—402., which may simply be the first publication with these functions thus justifying the naming, but I haven't read it and can only guess. I found it on the archive after some searching: http://www.archive.org/details/transactionsofca06camb (page 379 ff)

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Yes, but who named it, and when/where? – nibot Nov 10 '10 at 16:15
@nibot: wordiq.com/definition/Airy_function cites Airy (1838). On the intensity of light in the neighbourhood of a caustic. Transactions of the Cambridge Philosophical Society, 6, 379—402., which may simply be the first publication with these functions thus justifying the naming, but I haven't read it and can only guess – Tobias Kienzler Nov 11 '10 at 8:06
That's the well-known Airy function Ai(x), which is different from this other Airy function 1/(1+F sin^2 x) that I'm asking about. – nibot Nov 12 '10 at 17:31
@nibot: true, sorry about that. But I never heard this formula being called Airy function before, can you name other sources beside the (this time uninformative) wolfram site? – Tobias Kienzler Nov 15 '10 at 8:25