Summary:

There is ~ 7% variation in the power seen by the MC2 trans QPD, depending on the WFS offsets applied to the MC2 PIT/YAW loops. Some more interpretation is required however, before attributing this to spot-position-dependent loss variation inside the IMC cavity.

Analysis:

Attachment #1: This shows a scatter plot of the MC2 transmission and IMC REFL average values after the WFS loops have converged to the set offset positions. The size of the points are proportional to the normalized variance of the quantity. The purpose of this plot is to show that there is significant variation of the transmission, much more than the variance of an individual datapoint during the course of the averaging (again, the size of the circles is only meant to be indicative, the actual variance in counts is much smaller and wouldn't be visible on this plot scale). For a critically coupled cavity, I would have expected that the TRANS/REFL to be perfectly anti-correlated, but in fact, they are, if anything, correleated. So maybe the WFS loops aren't exactly converging to optimize the inoput pointing for a given offset? 

Attachment #2: Maps of the transmission/reflection as a function of the (YAW, PIT) offset applied. The radial coordinate does not yet mean anything physical - I have to figure out the calibration from offset counts to spot position motion on the optic in mm, to get an idea for how much we scanned the surface of the optic relative to the beam size. The gray circles indicate the datapoints, while the colormaps are scipy-based interpolation. 

Attachment #3: After talking with Koji, I explicitly show the correlation structure between the IMC REFL DCMON and MC2 TRANS. The shaded ellipses indicate the 1, 2 and 3-sigma bounds for the 2D dataset going radially outwards. The correlation coefficient for this dataset is 0.46, which implies moderate positive correlation. 🤔 

Scan algorithm:

The following was implemented in a python scipt:

1. Choose 2 independent random numbers from the uniform distribution in the interval [-0.5, 0.5] (in uncalibrated counts).
2. One of these numebrs is set as the error point offset for the QPD spot-centering PITCH WFS loop, while the other is the YAW offset.
3. Wait for 600 seconds - this long wait is required because the step-response time for these loops is long. 
4. If there is an MC unlock event - wait till the MC relocks, and then another 600 seconds, to give the WFS loops sufficient time to converge.
5. Once the WFS loops have converged, average a few data channels (MC TRANS, REFL, WFS loop error points etc) for 10 seconds, and write these to a file.

I am now setting the offsets to the WFS QPD loop to the place where there was maximum transmission, to see if this is repeatable. In fact it was. Looking at the QPD segment outputs, I noticed that the MC2 transmission spot was rather off-center on the photodiode. So I went to the MC2 in-air optical table and centered the beam till the output on the 4 segments were more balanced, see Attachment #4. Then I re-set the MC2 QPD offsets and re-enabled the WFS servos. The transmission is now a little lower at ~14,500 counts (but still higher than the ~14200 counts we had before), presumably because we have more of the brightest part of the beam falling on the gap between quadrants. For a more reliable measurement, we should use a single-element photodiode for the MC2 transmission.