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 40m Log Not logged in Message ID: 8630     Entry time: Thu May 23 14:45:08 2013     In reply to: 8621     Reply to this: 8635
 Author: Jenne Type: Update Category: LSC Subject: Sensing matrix scripts calculations make more sense now

I think I have most of the magnitude issues figured out now.

First of all, the lockin outputs are different from the actual responses in the PDs by a factor of 2.

If the optic is driven with amplitude D, it will have a response of `Asin(wt) + Bcos(wt) + other frequency junk`.  The lockin bandpasses the response to get rid of the 'other frequency junk'.  Then creates 2 new signals, one multiplied by cos(wt), the other multiplied by sin(wt).  So, now we have` Asin^2(wt) + Bcos(wt)sin(wt) `and` Asin(wt)cos(wt) + Bcos^2(wt)`.   If I rewrite these, I have `A/2*(1-cos(2wt))+B/2*(sin(2wt) `and` A/2*sin(2wt)+B/2*(1+cos(2wt))`.  We lowpass to get rid of the 2w components, and are left with A/2 for the Q-phase, and B/2 for the I-phase of the lockin outputs.  Since the real amplitudes of the response were A for the Q-phase and B for the I-phase, we need to multiply the lockin outputs by 2.

The other problem was that in the 'uncalibrated' version of numbers that I was printing to compare with Koji's, I had not normalized by the drive amplitude yet.  That happens in the "calibration" part of my script.  So, if I go back to comparing the calibrated versions of our numbers, I get quite close to Koji's answers.

For the PRCL magnitudes, 3 of the 4 numbers match to ~5%.  However, the MICH magnitudes all seem to be off by a factor of 2.  I'm still stuck on this factor of 2, but I'm thinking about it. Also, the phases that Koji and I get are pretty different.

Koji's sensing matrix:

```Sensing Matrix, units = cts/meter, phase in degrees             PRCL Mag   PRCL Phase    MICH Mag   MICH Phase   REFL33_I    3.100E+11  -109.727      4.900E+09    74.434      REFL33_Q    3.300E+09  -141.730      7.900E+08    71.120      REFL55_I    3.200E+11  -109.672      5.900E+08    77.313      REFL55_Q    1.200E+10  -143.169      6.500E+09    91.559  ```

My sensing matrix:

```Sensing Matrix, units = cts/meter, phase in degrees             PRCL Mag   PRCL Phase    MICH Mag   MICH Phase   REFL33_I    3.242E+11  -157.846      1.067E+10    19.010      REFL33_Q    2.217E+09  -104.088      1.683E+09    28.731      REFL55_I    3.371E+11  -157.915      3.645E+09    11.072      REFL55_Q    1.213E+10  -118.348      1.346E+10     2.847 ```

Here are the plotted versions of these matricies:  SOME EDITS:  Koji's measurement was 1Hz away from the violin mode, while mine (him running my script) was at the violin mode, so the sensor TFs were actually taken at slightly different frequencies. This helps explain the discrepancies.

Also, the phase in these plots isn't correct, so I need to figure that out. Corrected version of the 'koji' measurement put in place of the incorrect one.  I convert from radians to degrees for my script, but Koji had already reported his phases in degrees, so when I multiplied by 180/pi, it didn't make any sense. I now convert his numbers to radians before running them through my analysis script.

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