Summary:
For a cold interferometer with no self heating (ie IFO power) onto the surfaces, the TCS settings are as follows. What is being used for the calculations come from the Nebula page and the Finesse aLIGO parameter files and the contrast defect is calculated using the amplitude overlap described here. Depending on the various configurations of the interferometer, the amount of calculated contrast defect will be different:
| Configuration | Required CO2 Power(Watts) |
Required RH Power(Watts) |
Calculated Static Contrast Defect (PPM) | Description |
| Xarm and Yarm Locked | 0.0 | 0.269 on ITMY | 3.86 | Propagate the arm modes to the beam splitter and measure the mode overlap, this will not see the CO2 lensing and is dominated by the ITM+ETM radii of curvature. |
| PRX,PRY, IMC Locked | 0.094 on ITMX (Annular) | 0.0 | 186 | After turning on the ring heaters to adjust the ring heaters for the X-arm and Y-arm modes. Lock PRX and PRY individually and take the overlap between the two modes at the ITM HR surfaces. This is sensitive to both the thermal lensing of the ring heaters and the CO2 laser, however, we'll want to compensate the ITM RH configuration for sideband. |
| Simple Michelson, only IMC locked |
0.100 on ITMY (Annular) |
0.0 | 160 | Propagate the IMC mode towards the ITMs and take their overlap at the HR surface, because this is not resonant, the overlap will be proportional to just the difference in ITM radii of curvature. However, this overlap is sensitive to the substrate thermal lensing, but we won't be using this configuration anyway. |
Details:
Generally, the contrast defect is ratio of the power at the AS port to the REFL port when locked on a dark fringe, in other words, it's the amount of junk light that is present in the interferometer.
This junk light is a symptom of a few different causes, for example, an imbalance of reflectivities between the ITMX/ITMY will cause non-perfect destructive interference at the AS port and AS-AIR camera will see a round beam. Another cause of contrast defect could be misalignment between the ITMs+BS which will result in seeing a 01/10 higher order mode. But if both of those causes are fixed with stringent designs specs and alignment loops closed, then what is left over will be dominated by mode mismatch which can be fixed by a combination of RH and CO2 lasers. Because this model doesn't take into account the self heating, these numbers will have to be adjusted based off the amount of optical absorption on the HR surfaces as well as the substrate.
The power required for the lensing is calculated using the TCS actuator calibrations:
Where 
is the calibration factor in microdiopters/watt.
It seems, according to alog-43005, that the radii of curvature reported by the nebula page might not be correct since most of the phase change seen by the beam (both sb and carrier) in the simple michelson configuration is due to the ITM ROCs.
