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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: 1274     Entry time: Thu Feb 5 10:42:33 2009     In reply to: 1272
Author: Yoichi 
Type: Update 
Category: General 
Subject: Do we need off-axis parabolic mirrors ? No way ! 
I made a mistake in estimating the astigmatism problem.
If we use the current MMT1 as it is, this one is already an off-axis parabolic (OAP) mirror.
In this case, the astigmatism of this mirror is very small (if we use it with the correct angle). I did not include this effect in the previous calculation.
It turned out that the maximum achievable mode matching becomes far smaller (only 77%) if we use the OAP for MMT1 and a spherical mirror for MMT2.
This is not acceptable.
The reason behind this is that when we use spherical mirrors for both MMT mirrors, the astigmatism caused by the MMT1 is somewhat canceled by the astigmatism of MMT2. We don't get this cancellation if we mix OAP and spherical mirrors.

We should either (1) change MMT1 to a spherical mirror and keep the length of the input MMT as it is, or (2) change MMT1 to a spherical mirror and elongate the length of the input MMT.
In the case of (1) the maximum achievable mode matching is 94%. The focal length of MMT2 should be 315.6mm.
If we do (2), the mode matching rate can be as high as 99.8%. The focal lengths are MMT1 = -301.3mm, MMT2=558mm. The distance between the mirrors is 262mm.
We have enough space to do this elongation. But we have to mechanically modify the MMT mount.
I prefer (2).

As usual, the document on the Wiki was updated to include the above calculations.
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