Fit beam waist going to FC

[Yuhang, Eleonora P]

We measured the beam size of OPO TEM00 transmission after PBS (setting the initial position in the z0 of OPO), that will be sent to the filter cavity. We acquired 7 data points (fig 3) for two perpendicular axes of the beam (W and V) and we made the fit, as shown in fig 1.

Beam parameters estimated by the fit:
- w0 = (0,21 +/- 0,06) mm (in W direction)
- z0 = (0,10 +/- 0,29) m (in W direction)

- w0 = (0,21 +/- 0,09) mm (in V direction)
- z0 = (0,10 +/- 0,45) m (in V direction)

This estimation is not reliable as we can see from the errors.

We did the simulation about the beam propagation after the OPO, fig 2. The reference position is the beam waist position inside OPO.
Beam parameters in OPO (initial beam):
- w0 = 0,034 mm
- z0 = 0 m

Beam parameters after the lens (z = 0,13m, focal 100mm) after OPO (resulting beam):
- w0 = 0,113 mm
- z0 = 0,56 m


Comparing the above results, we found that the discrepancy is not too large.
One reason should be that also a small change in position of the lens after OPO changes a lot the beam parameters, because we don't know exactly the position of beam waist inside OPO. Another reason can be the not really good quality of the measurements, because the beam size was fluctuating a lot, maybe because of the movement on the hand during the acquisition.

Since the first and last points are quite far from the line of the fit, we need to acquire more data to have a better estimation.

Next step:
- To acquire few points also between the second and the third mirrors, fixing the position of the camera every point.
- To do again the fit and compare the results with what we expect.