The OMC calibration was performed by injecting a line at 119Hz in each of the OMCs PZT.

The amplitude of the modulation in meters can be measured from the height of the 2f line (2*119Hz = 238Hz).
The starting point is the Airy peak formula:
dP/P0 = 1/[1 + (2 F/pi)^2 sin^2(2 pi l / lambda)] - 1

which for a monochromatic small modulation simplifies to
dP/P0 = - (4 F)^2 * (l / lambda)^2

which means that the RMS of the length modulation l_mod in meters is:
l_mod = lambda/(4*F)*AS_PD(at mod frequency)/P0
where AS_PD is the amplitude spectrum of the PD signal (ie sqrt(PSD_PD*dF))

comparing this to the amplitude spectrum density of the calibration line as seen in the error point spectrum allows to calibrate the error point into meters.

The same can be done for the high frequency (10-15kHz) dither line to estimate its modulation depth.

In addition, looking at the height of the 1f calibration line at 119Hz, we can estimate the total RMS of the locking accuracy, as the linear coupling is:
l_RMS = lambda^2/l_mod/(32*Finesse^2)*AS_PD(1f)/P0

Figure 1 shows the 4 spectrum data points from the error point and PD used for OMC1 and Figure 3 is the same for OMC2.
Figure 2 shows the calibrated error spectrum and its RMS for OMC1 and Figure 4 for OMC2.

For OMC1 the calibration is
calib_factor = 5.6908e-07
the calibration modulation depth
l_mod = 9.0512e-13 m
the error point dither modulation depth
l_err_mod = 8.4857e-12 m
and the total estimate RMS is
l_RMS = 6.4433e-11 m
this is much higher than expected, from figure 2 the measured RMS below 200Hz is 1.47e-12 m which added in quadrature to the high frequency dither yields 8.62e-12m, so most of the RMS is not explained. The PZT actuation gain is 5e-11 m/V at 119Hz and 5e-11 m/V at 13kHz.

For OMC2 the calibration is
calib_factor = 7.0264e-07
the calibration modulation depth
l_mod = 2.0625e-12 m
the error point dither modulation depth
l_err_mod = 1.7311e-12 m
and the total estimate RMS is
l_RMS = 3.4853e-12 m
this is about where it should be, from figure 4 the measured RMS below 200Hz is 2.64e-12 m which added in quadrature to the high frequency dither yields 3.16e-12, so most of the RMS is explained. The PZT actuation gain is 1e-10 m/V at 119Hz and 3e-10 m/V at 15kHz.

Figure 5, looking at the high frequency PD spectrum, the OMC1 modulation 1f, 2f, 3f are shown in red, and for OMC2 in black. The OMC2 3f line is buried in noise, but for OMC1 it is quite high. So maybe something is saturating in the dither actuation which could explain the excess length noise coupling in OMC1.

At the next opportunity we should make these calibration measurements, and an OMC scan at the same time. To compare that the two methods of calibration give the same result. Also, the OMC1 line should be reduced to get rid of the high harmonics and we should explore with lock offsets and calibration line heights to check that the calibration method really works (doesn't depend on the calibration line height) and that the total lock RMS estimate is correct. Note that I haven't paid much attention for conversion from modulation depth to RMS and for power spectral leakage, so the value here might be wrong by factors ~sqrt(2).

The scripts to analyze the calibration are in /users/mwas/OMC/OMC_calibration_20180406