Looking back at elog 12528, the uncertainty in the armloss number from the individual quantities in the equation for  can be written as:
![\delta\mathcal{L}^2=\left(\frac{T_1(1-\frac{P_L}{P_M}-2T_1)}{4\gamma}\right)^2\left(\frac{\delta T_1}{T_1}\right)^2+T_2^2\left(\frac{\delta T_2}{T_2}\right)^2+\left(\frac{T_1(1-\frac{P_L}{P_M}-T_1)}{4\gamma}\right)^2\left(\frac{\delta\gamma}{\gamma}\right )^2+\left(\frac{T_1}{4\gamma}\right )^2\left[\left(\frac{\delta P_L}{P_L}\right )^2+\left(\frac{P_L}{P_M} \right )^2\left(\frac{\delta P_M}{P_M}\right )^2\right ]](https://latex.codecogs.com/gif.latex?%5Cdelta%5Cmathcal%7BL%7D%5E2%3D%5Cleft%28%5Cfrac%7BT_1%281-%5Cfrac%7BP_L%7D%7BP_M%7D-2T_1%29%7D%7B4%5Cgamma%7D%5Cright%29%5E2%5Cleft%28%5Cfrac%7B%5Cdelta%20T_1%7D%7BT_1%7D%5Cright%29%5E2+T_2%5E2%5Cleft%28%5Cfrac%7B%5Cdelta%20T_2%7D%7BT_2%7D%5Cright%29%5E2+%5Cleft%28%5Cfrac%7BT_1%281-%5Cfrac%7BP_L%7D%7BP_M%7D-T_1%29%7D%7B4%5Cgamma%7D%5Cright%29%5E2%5Cleft%28%5Cfrac%7B%5Cdelta%5Cgamma%7D%7B%5Cgamma%7D%5Cright%20%29%5E2+%5Cleft%28%5Cfrac%7BT_1%7D%7B4%5Cgamma%7D%5Cright%20%29%5E2%5Cleft%5B%5Cleft%28%5Cfrac%7B%5Cdelta%20P_L%7D%7BP_L%7D%5Cright%20%29%5E2+%5Cleft%28%5Cfrac%7BP_L%7D%7BP_M%7D%20%5Cright%20%29%5E2%5Cleft%28%5Cfrac%7B%5Cdelta%20P_M%7D%7BP_M%7D%5Cright%20%29%5E2%5Cright%20%5D)
Making some generous assumption about the individual uncertainties and filling in typical values we get in our measurements, results in the following uncertainty budget:
In my recent round of measurements I had a 2.5% uncertainty in the ASDC reading, which completely dominates the armloss assessment.
The most recent numbers are 57 ppm for the YARM and 21 ppm for the XARM, but both with an uncertainty of near 150 ppm, so while these numbers fit well with Gautam's estimate of the average armloss via PRG, it's not really a confirmation.
I set the whitening gain in ASDC to 24 dB and ran LSC offsets, and now I'm getting a relative uncertainty in measured reflected power of .22%, which would be sufficient for ~25ppm accuracy according to the above formula. I'm going to start a series of measurements tonight when I leave, should be done in ~2 hours (10 pm) the latest.
If anybody wants to do some night work: I misaligned ITMY by a lot to get its reflection off ASDC. Approximate values are saved as a restore point. Also the whitening gain on ASDC will have to be rolled back (was at 0dB) and LSC offsets adjusted. |