I have estimated how the mode profile of the PRM reflection should be, as shown in the plot blow.
A conclusion here is :
we should be able to constrain the PRM curvature situation if measurements are precise and accurate enough with a level of less than ~ 100 um
In the calculation two cases are considered :
(1) PRM has the correct curvature of +122 m. This is shown as solid curves in the plot.
(2) PRM has a wrong curvature of - 122 m (mirror is flipped) This is shown as dashed curves in the plot.
The plot above shows beam radii of the PRM reflections for vertical and horizontal profiles in each case.
The x-axis is distance from PRM in meter and the y-axis is the beam radii in mm.
As for the initial beam parameter, I used the measured values ( see the wiki), which are that of after the beam exits from the mode matching telescope and before it goes to PRM.
(1) If PRM has the correct curvature, the reflection after it passes MMT1 will have ~ 1.6 mm beam radii.
This is intuitively correct because the beam profiles should match to that of the MC exiting beam ( see the wiki), which has waist size of 1.5 - 1.6 mm if everything is perfect. (2) When PRM is flipped, the beam starts converging at the beginning as PRM act as a convex mirror, resulting in smaller beam sizes after it comes out from the telescope.
Roughly speaking the waist sizes will be different by ~ 5 mm between those two cases, so our measurement should be more precise and accurate than this number.
Note:
I have omitted the effect from the PRM thickness. Therefore PRM is dealt as just a curved reflector with RoC of +/- 122 m in the calculation.
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