Is it possible to determine the temporal shape of the laser pulse from
the autocorrelation function?
The autocorrelator is used to measure the temporal profile of the pulse.
https://www.rp-photonics.com/autocorrelators.html
https://en.wikipedia.org/wiki/Autocorrelation
basically, you need to rescale x-axis but it dependson how your autocorrelator works.
The autocorrelation gives you an idea of the duration of the pulse but you cannot determine the exact shape of your pulse (several pulse shapes can give you the same autocorrelation trace). Often it is assumed that the pulse coming from a laser has a sech2 shape, and the autocorrelation is fitted based on this assumption. To better determine the temporal shape of the pulse, you need information on its phase. This can be achieved by measuring the FROG trace (Frequency Resolved Optical Gating, which is basically a spectrally resolved autocorrelation with a pulse retrieval algorithm). Other methods such as SPIDER and MIIPS can also provide this information.
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