Details and Methodology

Since the FARO decided it needed a Florida vacation we have to use the same alignment method employed during aLIGO install.  This is done using a total station for measuring X and Y axis position and ISI yaw, and an autolevel for measuring ISI height and level.

X Axis Position and Yaw

2 sets of crossed scales are used with the total station to make the required measurements.  These scales are mounted in such a way that one edge of the vertical scale lines up with the y-axis centerline of the ISI; a second scale is mounted horizontally to give a reading of the x-axis position of that location.  The 2 sets of scales are mounted to the outermost holes on the +Y and -Y side of the ISI, see the attached picture for an example (the right-most edge of the vertical scales are in line with the ISI y-axis centerline).  The -Y scale mount also has a mounting hole for a corner cube retroreflector, which gives us the ability to used the total station's Electronic Distance Measurement (EDM) function to measure the distance between the total station and the outermost -Y holes of the ISI.

There is a brass monument on the floor to the East of WHAM1 that the total station is set over; this is monument LV25, coordinates [-22726.7, -3050.7] mm.  The total station the sights monument LV26 (cooridnates [-2133.6, -3050.7] mm), which is down by WHAM4, and this line sets our horizontal angle to zero.  The total station is then turned -90° to point at the center of WHAM1.  We then use the total station to read the horizontal scale of each set of crossed scales to get a measurement to calculate x-axis position deviation and ISI yaw; the distance between the outermost holes, 2082.8 mm (taken from the SolidWorks model of the ISI), gives us the needed info to calculate the yaw.  Using the numbers for the final measurements from the above main alog as an example, the calculation looks like this:

• +Y scale reading: 0.0 mm
• -Y scale reading: +0.5 mm
• X axis position deviation: (0.5 + 0.0) / 2 = +0.25 mm
• Yaw: (0.5 - 0.0) / 2082.8 = 240 µrad CCW

Y Axis Position

A corner cube retroreflector is mounted to the -Y scale mount, designed in such a way so the measurement point of the corner cube lines up with the outermost row of holes.  From the SolidWorks model of the ISI this outermost row of holes is 1041.4 mm from the center of the ISI.  The total station occupies monument LV25, which has a y-axis coordinate of -3050.7 mm.  Since the ISI should be at a y-axis coordinate of 0.0 mm, we then use the total station's EDM function to measure the distance from the total station to the corner cube.  The target distance is the y-axis coordinate of monument LV25 minus the y-axis coordinate of the outermost -Y holes of the ISI, or |-3050.7 - (-1041.4)| = 2009.3 mm.  Using the numbers from the Initial measurements (since we did not take a final look at y-axis position yesterday afternoon) in the above main alog as an example, the calculation is:

• Total Station EDM: 2009.7 mm
• Target Distance: 2009.3 mm
• Y axis position deviation: 2009.7 - 2009.3 = +0.4 mm

Z Axis Position and Level

For the z-axis position deviation and ISI level we use an autolevel and a scale set at various points on the ISI.  The autolevel is set to +100.0 mm above the target ISI height using height mark 600 (on the East wall across from WHAM1).  From T1100187 the LHO local coordinate for this height mark is -249.7 mm.  We set a scale on this height mark, with 10.0 mm on the scale lining up with the height mark.  We can then calculate what scale reading required to set the autolevel at +100.0 mm above the target height of the ISI.  The LHO global z-axis coordinate for the WHAM1 ISI is -201.9 mm, but the height mark is in LHO local so we have to translate between the two coordinate systems.  This means we have to add 14.1 mm¹ to the LHO global coordinate to get the LHO local coordinate for the WHAM1 ISI; doing this, the LHO local coordinate for the ISI is -187.8 mm.  Now the delta between the WHAM1 ISI z-axis position and height mark 600 is calculated, then add 100.0 mm to that to set the autolevel 100.0 mm above the target ISI height; we have to also add 10.0 mm since that's where the scale was set on the height mark: |-249.7 - (-187.8)| + 100.0 + 10.0 = 171.9 mm.  So sighting 171.9 mm on the scale we mounted on height mark 600 puts the autolevel 100.0 mm above the target z-axis position of the ISI.

With the autolevel set, we then place a scale at several points on the ISI and use the autolevel to read the scale at each point.  The scale we have for this is in inches, and has tic marks at every 0.01".  Since the autolevel is 100.0 mm above the target ISI height we should be reading 3.94" (100.0 / 25.4 = 3.94) on the scale if the ISI is at the correct height; reading a lower number on the scale means the ISI is too high, and reading a higher number on the scale means the ISI is too low.  The scale is placed at the 4 corners of the ISI, with a reading taken at each point.  These 4 readings are averaged to give the height of the ISI table.  For the table level, the delta between the highest and lowest scale reading is used.  Using the numbers from the final measurements from the above main alog, this calculation looks like:

• -X/+Y scale reading: 3.905"
• -X/-Y scale reading: 3.915"
• +X/+Y scale reading: 3.915"
• +X/-Y scale reading: 3.915"
• Average: 3.913"
  • Z axis deviation: 3.94 - 3.913 = 0.027" => +0.69 mm
• Level: 3.915 - 3.905 = 0.01" => 0.25 mm

1: The 14.1 mm correction comes from removing the global x-axis tilt of -619.5 µrad, done by multiplying the x-axis tilt by the x-axis position of the WHAM1 chamber: -22726.7 * -.0006195 = +14.1 mm.