we wanted to calculate the right telescope with 2 spherical lenses.

1) we have the FP cavity mode size which is 0.58mm at the input mirror and 0.7mm at the output mirror.

2) we planned to measure the laser beam at the output of the amplifier working at P=1W (2nd stage ON only).

we did several measurements at different positions from the amplifier output.
for each of these measurements, we were able to fit the intensity profile I = I0 * exp(-2 *r^2 / w^2) on x or y axis, then we have w(z).
attached files give an example of the beam image at z=40mm and an example of the beam fits for w and y.

with all the w(z) measurements, we were able to fit the divergence of the beam => 2.3 mrad
attached file show the radius measurements and the divergence fit.
with this divergence, we should find a waist bigger than 140 µm (value for M²=1).

unfortunately the smallest beam radius measured is 116 µm which would give a M²<1 that is not allowed !
then it seems the measurements have not been done correctly... :-(

we will try to do them again... maybe at P=10W or 50W ?!?