Editing Optical autocorrelation (section)

==Interferometric autocorrelation==
[[Image:optical-interferometric-autocorrelation-setup.png|thumb|upright=1.2|Setup for an interferometric autocorrelator, similar to the field autocorrelator above, with the following optics added: '''L''': converging [[lens (optics)|lens]], '''SHG''': second-harmonic generation [[crystal]], '''F''': spectral [[filter (optics)|filter]] to block the fundamental wavelength.]]

As a combination of both previous cases, a nonlinear crystal can be used to generate the second harmonic at the output of a Michelson interferometer, in a ''collinear geometry''. In this case, the signal recorded by a slow detector is

: <math>I_M(\tau) = \int_{-\infty}^{+\infty}|(E(t)+E(t-\tau))^2|^2dt</math>

<math>I_M(\tau)</math> is called the interferometric autocorrelation. It contains some information about the phase of the pulse: the fringes in the autocorrelation trace wash out as the spectral phase becomes more complex.<ref>{{Cite journal | doi=10.1364/OE.479638| title=Neural-network-powered pulse reconstruction from one-dimensional interferometric correlation traces| year=2023| last1=Kolesnichenko| first1=Pavel| last2=Zigmantas| first2=Donatas| journal=Optics Express| volume=31| issue=7| pages=11806–11819| pmid=37155808| arxiv=2111.01014| bibcode=2023OExpr..3111806K}}</ref>

[[Image:optical-interferometric-autocorrelation.png|thumb|upright=1.75|left|Two [[ultrashort pulse]]s (a) and (b) with their respective interferometric autocorrelation (c) and (d). Because of the phase present in pulse (b) due to an instantaneous frequency sweep ([[chirp]]), the fringes of the autocorrelation trace (d) wash out in the wings. Note the ratio 8:1 (peak to the wings), characteristic of interferometric autocorrelation traces.]]
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