kiwamu.izumi@LIGO.ORG - posted 12:44, Thursday 06 April 2017 - last comment - 10:39, Monday 10 April 2017(35364)
Double checking the HWS coordinate
WP 6562; Nutsinee, Kiwamu,
As a follow up of Aidan's analysis (35336), we did a simple measurement in this morning for determining the HWS coordinate.
- Preliminary result (currently being double checked with Aidan):
- The vertical coordinate needs to be flipped. This is consistent with what Aidan reported (35043).
- The horizontal coordinate does not need to be flipped. This is opposite to what Aidan concluded based on a CO2 measurement (35336).
[Measurement]
- We tilted ITMX in yaw toward positive values by 15 urad.
- We then observed the displacement in the Hartman spots in HWSX.
- The spots moved toward the right (i.e. all the vectors in the Hartman image pointed toward the right).
- This indicates that there is no need to switch the left and right.
[Verification measurement]
- We tilted ITMX in pitch this time toward negative values by 15 urad.
- The spots moved upward (i.e. the vectors pointed upward).
- This means that the y coordinate is up-side-down. The y-axis needs to be flipped.
I've independently checked my analysis and disagree with the above aLOG. I get the same orientation that I initially calculated in aLOG 35336.
After discussing the matter with Kiwamu, it turned out there was some confusion over the orientation of the CCD. The following analysis should clear this up.
1. ABCD matrix for ITMX to HWSX (T1000179):
So, nominally the X&Y coordinates are inverted by this matrix. However, the X coordinates will be inverted in horizontal reflection off a mirror. Fortunately, there are an even number of horizontal reflections (plus the periscope but the upper and lower mirrors cancel each other).
Therefore, we can illustrate the optical system of the HWS as below:
As viewed from above, the return beam propagates from ITMX back toward the HWSX (from right to left in this image). A positive rotation of ITMX in YAW is a counter-clockwise rotation of ITMX when viewed from above. So the return beam rotates down in the image as illustrated. The conjugate plane of the HWS Hartmann plate (plane A) is at the ITMX HR surface (plane A'). The conjugate plane of the HWS CCD (plane B) is approximately 3m from the ITMX HR surface (going into the PRC - plane B').
The even mirror reflections cancel each other out. The only thing left is the inversion from the ABCD matrix. Hence, the ray that rotates counter-clockwise at ITMX rotates clockwise at the HWS - as illustrated here. In this case, towards the right of the HWS CCD.
Lastly, the HWS CCD coordinate system is defined as shown here (with the origin in the lower-left). I verified this in the lab this morning.
Therefore: the orientation in aLOG 35336 is correct.