To measure cavity decay time, we are currently just cutting beam by bending a IR card and releasing it towards beam path. This method is not ideal and affect a signal. Since we don't have enough channels on oscilloscopes to conduct measurements at the same time, we cannot distinguish genuine cavity decay time and effect of not-ideal cutting method. Thus I tried to fit a signal obtained by cutting beam by hands. Data is attached as a txt file. Note that this data dosen't contains any effect other than cutting beam.
Two different functions are used for fitting; an error function (erf) and an exponential function. An erf is obtained by integrating a gaussian function. This seems plausible given a laser intensity transverse distribution is typically a gaussian. These functions are shown in a figure attached with resulting fitting parameters. I assumed a constant velocity to cut beam (IR card go across beam crosssection with a constant velocity).
From this calculation, exponential deccay is more fit.
Python codes used is also attached (please change .txt to .py if you try).
According to the esponential fit, the decay time of the "hand cut" is about 0.6 ms which is roughly a factor 5 smaller than the expected decay time of the cavity. We will take some more measurements in order to check the dispersion of such value.
Trying to understand why the best fitting function is not a erf function (given the hypothesis that the beam is cut at constant speed): maybe the exponential decay we see in the data is dominated by the electronics ? one can also try to fit with a function erf + exp.
Constant velocity assumption may be wrong? I'm not very clear. I can try with some acceleration or the combination of erf and exp as you suggested.
According to the fit the decay time is 0.3msec that is a factor of 10 smaller than the cavity decay time.
Actually, there is a factor 2 to take into accunt in the definition of the decay time we used, that is P = P0*exp(-2*t/tau)
(see https://www.osapublishing.org/oe/abstract.cfm?uri=oe-21-24-30114 )
So the decay time from the "hand cutting" fit should be: 2/tau = 3149 => tau = 0.6 ms. Anyway, since I used this definition also for computing the filter cavity decay time (about 2.7ms) if I'm not wrong we have a factor 5 of difference between the two, in any case.