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Entry  Wed Feb 4 17:45:39 2009, Yoichi, Update, General, Mode matching of the upgraded IFO 
    Reply  Wed Feb 4 19:22:57 2009, Yoichi, Update, General, Do we need off-axis parabolic mirrors ? 
       Reply  Thu Feb 5 10:42:33 2009, Yoichi, Update, General, Do we need off-axis parabolic mirrors ? No way ! 
Message ID: 1272     Entry time: Wed Feb 4 19:22:57 2009     In reply to: 1271     Reply to this: 1274
Author: Yoichi 
Type: Update 
Category: General 
Subject: Do we need off-axis parabolic mirrors ? 
I also estimated the mode matching degradation caused by the astigmatism.
Since the incident angles to the mode matching mirrors are not 0, the effective focal lengths in the incident plane and the perpendicular plane are different.
This effect leads to astigmatism of the beam.
When there is astigmatism, the maximum achievable mode matching rate becomes less than 100%.
According to my calculation, the mode matching cannot be better than 94% for the input beam.
For the output mode matching, we can theoretically achieve more than 99% even with the astigmatism.
The difference comes from the fact that the OMMT is longer, thus the incident angle is smaller.

If we don't like this 94%, we have to use off-axis parabolic mirrors, or modify the IMMT to a longer one.
I prefer to make it longer. Just 5" elongation will increase the mode matching rate to 99.4%.
We have a room for this 5" elongation.

Again, the details of the calculation are added to the Mathematica notebook below.


Quote:
I did mode matching calculations for the new optical layout.
For the input mode matching, we have to change the focal length of the second mirror from 687mm to 315mm and the distance between the two MMT mirrors from 137mm to 149.2mm.
For the mode matching to the OMC, we only have to change the distance between the OMMT mirrors from 384mm to 391mm. No need to change the mirrors.

Details of the calculations can be found in
http://lhocds.ligo-wa.caltech.edu:8000/40m/Upgrade_08/Optical_Layout?action=AttachFile&do=get&target=NewRecyclingCavities.zip
(Mathematica notebook)
or if you prefer PDF, here
http://lhocds.ligo-wa.caltech.edu:8000/40m/Upgrade_08/Optical_Layout?action=AttachFile&do=get&target=NewRecCav.pdf
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