We decided not to care about the mode after MMT1.

So far Koji, Alberto and I have measured the beam profile after MMT1,

but we are going to stop this measurement and go ahead to the next step i.e. putting MMT2

There are two reasons why we don't care about the profile after MMT1:

     (1) it is difficult to fit the measured data

     (2) The position of MMT1 is not critical for the mode matching to the IFO.

The details are below.

(1) difficulty in fitting the data

The precision of each measured point looked good enough, but the fitting result varies every measurement.

The below shows the data and their fitted curves. 

In the label, "h" and "v" stand for "horizontal" and "vertical" respectively.

The solid curves represent the fitting results, varying by each measurement.

In order to increase the reliability of the fitting, we had to take some more data at further distance.

But we couldn't do it, because the beam radius already becomes 3 mm even at 2 m away from MMT1 and at this point it starts to be clipped on the aperture of the beam scan.

Thus it is difficult to increase the reliability of the fitting. 

Once if we put MMT2 the beam should have a long Rayleigh range, it means we can measure the profile at further distance, and the fitting must be more reliable.

(2) positioning of MMTs

Actually the position of MMT1 is not so critical for the mode matching. 

The most important point is the separation distance of MMT1 and MMT2.

As written in Jenne's document, if we slide the positions of MMT1 and MMT2 while keeping their appropriate separation distance, the mode match overlap still stays above 99%

This is because the beam coming from MC3 is almost collimated (ZR~8m), so the position of MMTs doesn't so matter. 

To confirm it for the real case, I also computed the mode overlap while sliding the position of MMTs by using real data. The below is the computed result.

It is computed by using the measured profile after MC3 (see the past entry).

The overlap still stay above 99% when the distance from MC to MMT is between 1300 and 3000mm.

This result suggests to us putting MMT1 as we like.