[Manasa, Sendhil, Yuta]

We calibrated oplev for PRM. Calibration factor for C1:SUS-PRM_OL(PIT|YAW)_IN1 are;
  OLPIT: 15.6 +/- 0.3 counts/mrad
  OLYAW: 17.8 +/- 0.3 counts/mrad

We needed these values for g-factor measurement of PRC using angle dithering method.

What we did:
  1. Adjusted QPD offsets (C1:SUS-PRM_OL[1-4]_OFFSET) by zeroing the output when turned oplev laser was turned off.
  2. Centered PRM oplev beam on QPD using steering mirror.
  3. Mounted PRM oplev QPD on a xy-stage and centered the beam on QPD.
  4. Moved QPD in x and y using micrometers and measured dependance of C1:SUS-PRM_OL(PIT|YAW)_IN1 on QPD displacement.
  5. Measured the path length of PRM oplev returning beam. We get the in-vac path length using optical layout CAD. We measured out of vac path using scale and tape measure.
  6. Dismounted PRM QPD from the stage and put it back to the original position.

Result:
  1. Figures below are OLPIT/OLYAW dependance on micrometer displacement moved in x and y. Error bars are measured fluctuation in the signal.


moved in x:       moved in y:


  2. We fitted the result by error function to get slope at zero crossing point. We also linear-fitted the other degree of freedom to get cross coupling between x and y. Slopes we get were;

micrometer    OLPIT          OLYAW
moved in x    4.68 +/- 0.08  0.01 +/- 0.03
moved in y   -5.32 +/- 0.10  0.11 +/- 0.03    (counts/mm)

  3. Measured the path length of PRM oplev returning beam was 3340 +/- 20 mm. This gives you the calibration factors above.

Discussion:
  [Precision] According to Jamie's calculation, expected g-factor for PRC in PR2-flipped PRMI is 0.966/0.939 (elog #8068). We care about the g-factor change in ~0.01. Also, intra-cavity power dependance on mirror angle is proportional to 1/(1-g). So, we need to calibrate mirror angle in ~few 10 % of precision in order to get useful g-factor from angle dithering measurement. Measurement precision here meets this requirement.

  [x/y coupling] Measured x/y coupling was less than 2 %. We assumed gains in 4 QPD quadrants are same, and assumed QPD is mounted well in x/y axes. These assumptions are OK considering precision we need.

  [x/y difference] Calibration factors for OLPIT/OLYAW are different by ~10 %. This is not so crazy considering the incident angle on the QPD (~20 deg) and elliptic beam shape.