J. Kissel

I've arrived at numbers for refining the calibration of the ETM OPTICALIGN alignment offset sliders, using the same method as was used for the ITMs and BS (see LHO aLOGs 14265 and 14321, respectively). The new slider gains should be 
EX P =  15.344 [ct/urad]
   Y =  44.044 [ct/urad]
EY P =  19.341 [ct/urad]
   Y =  51.013 [ct/urad]
which are comparable to the ITMs' calibration, as expected.

I have not installed these new gains, nor have I corrected the saved alignment offsets since it will be too disruptive to commissioning. These can be installed at anyone's convenience, but I'll install them in week if know one's gotten around to it. 
The to-do list:
- Record current OPTICALIGN OUT values (in [ct]), to confirm you get the same answer after updates
- Install above calibration gains
- Restore to ALIGNED via guardian, enter in predicted offset values (in [urad]) below (adjust, if necessary, to get the previously recorded output value in [ct])
- Save ALIGNED value using pull-down menu in IFO_ALIGN MEDM screen
- Restore to MISALIGNED via guardian, enter in predicted offset values (in [urad]) below (adjust, if necessary, to get the previously recorded output value in [ct])
- Save MISALIGNED value using pull-down menu in IFO_ALIGN MEDM screen
- svn commit the updated aligned and misaligned .snap files in the ${userapps}/release/sus/h1/burtfiles/ directory
- IF AMBITIOUS (and commissioning team gives you some time) -- perform refinement of optical lever calibration with these new values, as was done with the ITMs and BS (see LHO aLOGs 14312 and 14387).

Details
-----------
The current alignment offset slider calibrations for both EX and EY are
23.219 [ct/"urad"]
51.689 [ct/"urad"]
and currect stored alignment offsets are
                  P       Y    ["urad"]
EX Aligned     274.1    63.9
   Misaligned  240.0   102.0

EY Aligned      83.4   -64.8
   Misaligned   62.0   -7.72

The ETM alignment slider values to hit the center of the ITM baffle PDs are
         P     Y     ["urad"]
EX PD1 261.4  79.75
   PD4 285.2  49.1
delta  23.8   30.65  
claimed displacement = 2*delta
       47.6   61.3

EY PD1  70.5   -83.5
   PD4 100.5   -48.0
delta   30.0    35.5  
claimed displacement = 2*delta
        60.0    71.0
where the factor of two to calculate the displacement is from the single-bounce, optical lever effect.

We know from D1200313 and D1200296 the ITMX and ITMY (respectively) PDs 1 and 4 are 11.329 [inches] = 0.287757 [m] apart vertically, and 11.313 [inches] = 0.28735 [m] horizontally on both ITM baffles, implying an angular displacement -- over the L = 3994.5 [m] arm lengths -- of
P   0.287757 [m] / 3994.5 [m] = 72.03 [urad]
Y   0.28735 [m]  / 3994.5 [m] = 71.94 [urad]

which means the correction factor for the OPTICALIGN gain is
EX P  47.6  ["urad"] / 72.03 [urad] = 0.661 ["urad"/urad]
EX Y  61.3  ["urad"] / 71.94 [urad] = 0.852
EY P  60.0  ["urad"] / 72.03 [urad] = 0.833
EY Y  71.0  ["urad"] / 71.94 [urad] = 0.987
or

EX P = 1.5132 [urad/"urad"]               
EX Y = 1.1736             
EY P =  1.2005
EY Y = 1.0132

which are corrections comparable to the ITMs (good sanity check, since they have the same actuation chain, and used the same offset calibrations prior to the refinement).
So the new alignment slider calibation gains should be
       Old Cal               Correction            New Cal
EX P 23.219 [ct/"urad"] * 0.661 ["urad"/urad] =  15.344 [ct/urad]
   Y 51.689 [ct/"urad"] * 0.852 ["urad"/urad] =  44.044 [ct/urad]
EY P 23.219 [ct/"urad"] * 0.833 ["urad"/urad] =  19.341 [ct/urad]
   Y 51.689 [ct/"urad"] * 0.987 ["urad"/urad] =  51.013 [ct/urad]
and the predicted alignment offsets that need be installed are
    old offsets ["urad"] * correction factor [urad / "urad"] = new offsets [urad]

                 P       Y    [urad]
EX Aligned     414.77    74.993
   Misaligned  363.17    119.71

EY Aligned      100.12  -65.655
   Misaligned   -77.792   -7.822