In order to reduce the size of the HeNe probe I used Jammt to design the optical path.
First I measured the profile without lenses. First plot. The axis is in the translation stage reference. The waist of the HeNe is right at the output of the laser tube.
After some attempts, designs on Jammt and profile measurements, I found a good set of lenses to have the waist about 3 times larger than the pump.
The lenses are a f = -50mm lens and a f = 75mm lens at about 47mm from each other. The second plot shows the final probe profile. The probe size is now 2.8 times larger than the pump.

I aligned the pump and the imaging unit to maximize the signal on the surface reference sample (usual procedure). Then I scanned the bulk calibration sample.

When moving the Imaging Unit with the micometric screw to finely maximize the AC signal, I noticed that there was not a clear maximum in the range. So I unclamped and moved the whole IU much closer to the sample. At about the same position as it was in the very original setup. Now all the conditions are the same as the original setup, or at least as the specs say.
Now I'm wondering if/why it is not possible to have the same size of the image on the detector when we move the telescope further. This is to be cleared.

Then I measured the tama-size sapphire sample again. First with 5W of pump power and then with 10W (max). Noise from chopper (constant phase)  is again a bit high, but let's consider this later.

In the last plot I compare the last sapphire measurement with the one of last week, when the probe was larger. Remider: reducing the pump size without reducing the probe size didn't change the signal.
Now the absorption value is smaller. It's not straightforward to tell a precise ratio, but let's say it is between 1 and 2. It is certainly not a factor of 3, as we would be very happy to have.

I have the feeling that the calibration factor between materials (3.34 according to STPS between sapphire and Schott glass) depends on all the parameters I changed.
What I really don't understand is how the imaging affects the calibration. I thought that the image size depends on the focal lengths of the telescope lenses only, not on the distance of the telescope, but maybe I'm wrong.

The question is: let's call d1 the distance from the sample to the first lens of the telescope and d2 the distance between the two lenses. Is there a d2 for each d1 so that the image on the PD is exactly the same (in sharpness and size)?