J. Kissel, J. Driggers

There's been some confusion about why the ITM ISIs are performing so differently. This resurrected memories of mistrust in the optical lever calibration, that I'd talked to Thomas about in June (see LHO aLOG 12216). That aLOG leaves it at "we should confirm the calibrations once we have arms again." The idea will be to cross-check the calibration  using the alignment sliders, which can be precised calibrated using the green beam and baffle PDs as a 4 [km] optical lever. The details of the process are below, but in summary, the refined calibration of the sliders is
IX P = 15.589 [ct/urad]
IX Y = 43.835 [ct/urad]
IY P = 19.920 [ct/urad]
IY Y = 46.700 [ct/urad]
which, for IX P is a ~50% correction, but the rest is a ~10-20% correction.

We have updated both the OPTICALIGN [ct/urad] gains, and corrected the "cal" [ct/urad] FM0 in the M0 LOCK P and Y filter banks, saved the newly corrected alignment offsets, and confirmed that the refinement of gain and slider value brings the optic to the same place.

DETIALS
------------

Currently, the alignment slider calibration gains are
P  23.219 [ct/"urad"]
Y  51.689 [ct/"urad"]
based on dead-reckoned knowledge of the actuation chain (see LHO aLOG 4730).

Keita, Alexa, and Shiela recently went through the exercise of finding the green beam down the arms (see LHO aLOG 14201 for ITMX, and LHO aLOG 14161 for ITMY) using baffle PDs and the SUS alignment sliders. 

From these aLOGs, we know that the ETMY baffle PDs, and ETMX ERM Pattern are at the following ITM alignment slider values:
                 P ["urad"]     Y ["urad"]
ETMX Top Stop     65.2     
ETMX Bot Stop     84.2
ETMX Lef Stop               -20.2
ETMX Rig Stop                3.8
ETMY PD1          165      -105.3
ETMY PD4          197       -139
for displacement claimed by the sliders of
      delta ["urad"]
EX P   -19 * 2 = -38
EX Y   -24 * 2 = -48
EY P   -32 * 2 = -64
EY Y   33.7* 2 = 67.4 
where the factor of 2 comes from the single bounce, optical lever effect.

From an older aLOG when Keita had performed a similar calibration (see attachment to 9087), we know the ETMX baffle PDs are a distance 11.76 [inches] = 0.2987 [m] apart in vertical, and 11.77 [inches] = 0.29895 [m] in horizontal. From D0900949, we know the pattern has an inner-most diameter of 226 [mm] = 0.226 [m]. The length of the arms is 3994.5 [m], confirmed by older measurements during the HIFO days (see LHO aLOG 9635 and 11611).
That means the physical displacements are
EX P   0.226 [m] / 3994.5 [m] = 56.6 [urad]
EX Y   0.226 [m] / 3994.5 [m] = 56.6 [urad]
EX P   0.298 [m] / 3994.5 [m] = 74.6 [urad]
EX Y   0.298 [m] / 3994.5 [m] = 74.6 [urad]

Hence the slider gains should be corrected by
IX P   56.6 / 38   = 1.49 [urad / "urad"]
IX Y   56.6 / 48   = 1.18 [urad / "urad"]
IY P   74.6 / 64   = 1.17 [urad / "urad"]
IY Y   74.6 / 67.4 = 1.11 [urad / "urad"]
or
IX P  0.67138 ["urad"/urad]
IX Y  0.84806 ["urad"/urad] 
IY P  0.85791 ["urad"/urad]
IY Y  0.90349 ["urad"/urad]



The new slider gains are therefore
IX P   23.219 [ct/"urad"] * 0.67139 ["urad"/urad] = 15.589 [ct/urad]
IX Y   51.689 [ct/"urad"] * 0.84806 ["urad"/urad] = 43.835 [ct/urad]
IY P   23.219 [ct/"urad"] * 0.85791 ["urad"/urad] = 19.920 [ct/urad]
IY Y   51.689 [ct/"urad"] * 0.90349 ["urad"/urad] = 46.700 [ct/urad]

Which means the former alignment values, in ["urad"],
                     P               Y
IX Aligned         75.4            -7.6
IX Misaligned        0            -52.75
IY Aligned         182.4          -116.6
IY Misaligned        0               0
now become (["urad"] slider value * [urad/"urad"] = [urad] slider value)

                      P            Y
IX Aligned         112.35       -8.968
IX Misaligned        0         -62.245
IY Aligned         213.41     -129.43
IY Misaligned        0           0   

We have updated both the OPTICALIGN [ct/urad] gains, and corrected the "cal" [ct/urad] FM0 in the M0 LOCK P and Y filter banks, saved the newly corrected alignment offsets, and confirmed that the refinement of gain and slider value brings the optic to the same place.