Previous analysis had some biased due to the calibration of our signals.The new calibration should take into account non ideal PBS and differents photodetectors.

We can express our 2 signals as :

DC = (Rs * Is + Rp * Ip ) * p(t) * Ks

AC = ( (1 - Rs) * Is + (1-Rp) * Ip ) * p(t) * Kp

where

Rs and Rp are PBS reflectivities for s and p polarizations

Ks and Kp are gain of the photodetector for respective s and p polarization readout

p(t) time-varying power fluctuations.

By measuring all these parameters, we can then reconstruct Is and Ip powers from our lockin amplifiers signal.

After carefully aligning the QWP and HWP to have linear s polarization, we measured AC and DC signals for 10 mn while injecting first s then p polarizations.

The measurements are attached in figure 1.

From these measurements, I could compute all the coefficients as shown in figure 2.

Note that here p1 are power fluctuations while injecting s polarization and p2 the one when injecting p polarization.

Using the mean of each of these coefficients, I show in figure 3 Is and Ip, the respective s and p polarizations when injecting s polarization.

As expected, Is = 1 and Ip = 0 and are independent on power fluctuations as well.

Rs and Rp coefficients are compatible with their specifications.

Also, during this calibration we found that the old lockin amplifier readout seems noisier than the new one.

Especially, we could barely see the power fluctuations that were hidden inside the noise (at that time we had about 2 nW of power reaching the photodetector but still a factor 50 above dark noise)

Following this calibration we started the AZTEC #3 birefringence measurement.