The following is a short summary of an approach to commissioning the H1 ITMY CO2 mask, D1900030. The purpose of the mask is to reduce the scattering of sidebands into higher order spatial modes. However, when the mask is simply applied by itself, it creates a strong positive quadratic lens. A combination of the ITMY RH, ITMX CO2 central heating and ITMX RH must be used to minimize the overall effect of the COMMON & DIFFERENTIAL MICH lenses and the COMMON and DIFFERENTIAL ITM curvatures.

First Step: Mask application to reduce HOM and maintain current quadratic lens in ITMY 

The application of the mask is illustrated in the attached PDFs. An example of the application is shown here:

• Upper left: The single-pass (SP) optical path distortion from self-heating (point absorbers) scaled to 30W of input power and assuming PRG of 40. The Gaussian weighted RMS OPD of this distortion is 25nm (where the Gaussian beam radius = 54mm). Contour spacing is 5nm.
• Upper middle: "OPD Now": The SP OPD plus 0.75W of RH power. RMS OPD = 22nm. This is what we currently have on ITMY - hence the name "OPD Now". The scatter from this OPD to LG10 is calculated (i.e. the effective lens of this OPD) as that's a number that we're going to come back to.
• Upper right: The steady-state SP OPD from the CO2 mask when a total of 450mW is applied to the ITM. The RMS distortion from this is 25nm. Note that this is the power applied to the test mass (not the power transmitted through the mask. i.e. be sure to account for the efficiency of transmission from the mask to the ITM).
• Lower left: The "OPD Now" distortion plus the CO2 mask OPD. This removes a lot of the intermediate HOM but leaves some of the very high spatial frequencies. As can be seen, there is a strong positive lens in the OPD now. 
• Lower middle: The amount of additional RH OPD required to be added to the previous plot so that the scatter into LG10 (or the effective lens of the new OPD) is the same as what we currently have in "OPD Now".
• Lower right: the sum of "OPD Now", the CO2 mask OPD and the additional RH power. This has the same effective lens as "OPD Now" but has a much lower overall RMS wavefront error of approximately 8nm.

Note that (a) the color scales have been set to the same level [-70, 70]nm for comparison between different plots [so there is some saturation in some of the plots], (b) contours are set to 5nm spacing in all plots, (c) DC levels have been subtracted from each image so that the Gaussian weighted mean value is 0nm.

Once this step has been applied, the ITMY substrate lens should be same as it currently is. This will maintain the COMMON and DIFFERENTIAL MICH lenses. However, the application of ITMY RH will change the ITMY ROC and, hence, the COMMON and DIFF ITM ROC will need to be corrected. Which will be dealt with in step 2.

The attached PDFs show the effect for differing CO2 powers ranging from 50mW to 750mW. The minimum RMS OPD is achieved around 450mW.