English: The physical meaning of the Airy finesse
![{\displaystyle {\mathcal {F}}_{Airy}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/86220527a70b2891ae79671fd44a472567049f8b)
of a Fabry-Pérot resonator.
[1] When scanning the Fabry-Pérot length (or the angle of incident light), Airy distributions (colored solid lines) are created by signals at individual frequencies. The experimental result of the measurement is the sum of the individual Airy distributions (black dashed line). If the signals occur at frequencies
![{\displaystyle \nu _{m}=\nu _{q}+m\Delta \nu _{Airy}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b299bff55e50014c0be5917b18db5589b063ad27)
, where
![{\displaystyle m}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc)
is an integer starting at
![{\displaystyle q}](https://wikimedia.org/api/rest_v1/media/math/render/svg/06809d64fa7c817ffc7e323f85997f783dbdf71d)
, the Airy distributions at adjacent frequencies are separated from each other by the linewidth
![{\displaystyle \Delta \nu _{Airy}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ee2915b8068bf795d79308a19a734dc808cc6d8d)
, thereby fulfilling the Taylor criterion for the spectroscopic resolution of two adjacent peaks. The maximum number of signals that can be resolved is
![{\displaystyle {\mathcal {F}}_{Airy}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/86220527a70b2891ae79671fd44a472567049f8b)
. Since in this specific example the reflectivities
![{\displaystyle R_{1}=R_{2}=0.59928}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d43594c47ed5b55480d45478bd75a3f856a9de84)
have been chosen such that
![{\displaystyle {\mathcal {F}}_{Airy}=6}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3539068c779f30c2e3da5364e9d9ed0604f72b1e)
is an integer, the signal for
![{\displaystyle m={\mathcal {F}}_{Airy}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cb039f2e9ee2f7270b5ab75f78fe665eff083fa4)
at the frequency
![{\displaystyle \nu _{q}+{\mathcal {F}}_{Airy}\Delta \nu _{Airy}=\nu _{q}+\Delta \nu _{FSR}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8ae10aef1da75ac16105fa2dff2e710d1599fe4b)
coincides with the signal for
![{\displaystyle m=q}](https://wikimedia.org/api/rest_v1/media/math/render/svg/28e181bea4627afe393c710b3b55014324c22cc9)
at
![{\displaystyle \nu _{q}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5a35c6e639d10517976ec2b918e859fccf0bd126)
. In this example, a maximum of
![{\displaystyle {\mathcal {F}}_{Airy}=6}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3539068c779f30c2e3da5364e9d9ed0604f72b1e)
peaks can be resolved when applying the Taylor criterion.