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Entry  Wed Nov 25 16:40:32 2015, yutaro, Update, LSC, round trip loss of Y arm 
    Reply  Wed Nov 25 23:34:52 2015, yutaro, Update, LSC, round trip loss of Y arm 14.png
       Reply  Fri Nov 27 03:38:23 2015, yutaro, Summary, LSC, round trip loss of Y arm image1.png
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          Reply  Sat Nov 28 11:46:40 2015, yutaro, Update, LSC, possible error source of loss map measurement 
          Reply  Mon Nov 30 10:41:45 2015, yutaro, Update, LSC, Does a baffle in front of ETMY have effect on loss map measurement? 
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          Reply  Mon Dec 7 11:11:25 2015, yutaro, Summary, LSC, round trip loss of X arm image1-2.JPGsymmetry.png
Message ID: 11810     Entry time: Wed Nov 25 16:40:32 2015     Reply to this: 11816
Author: yutaro 
Type: Update 
Category: LSC 
Subject: round trip loss of Y arm 

I measured round trip loss of Y arm. The alignment of relevant mirrors was set ideal with dithering (no offset).

Summary:

 round trip loss of Y arm: 166.2 +/- 9.3 ppm

(In the error, only statistic error is included.)

How I measured it: 

I compared the power of light reflected by Y arm (measured at AS) when the arm was locked (P_L) and when ETMY was misaligned (P_M). P_L and P_M can be described as 

P_M=P_0(1-T_\mathrm{ITM})

P_L=P_0\left[1-(1-\alpha)\frac{4T_\mathrm{ITM}}{T_\mathrm{tot}^2}T_\mathrm{loss}\right].

The reason why P_L takes this form is: (1-alpha)*4T_ITM/(T_tot)^2 is intracavity power and then product of intracavity power and loss describes the power of light that is not reflected back. Here, alpha is power ratio of light that does not resonate in the arm (power of mismatched mode and modulated sideband), and T_tot is T_ITM+T_loss. Transmissivity of ETM is included in T_loss. I assumed alpha = 7%(mode mismatch) + 2 % (modulation) (elog 11745)

After some calculation we get

1-P_L/P_M\simeq \frac{4(1-\alpha) T_\mathrm{loss}}{T_\mathrm{ITM}}-T_\mathrm{ITM}.

Here, higher order terms of T_ITM and (T_loss/T_ITM) are ignored. Then we get

(1-\alpha) T_\mathrm{loss}=\frac{T_\mathrm{ITM}}{4}(1-P_L/P_M+T_\mathrm{ITM}).

Using this formula, I calculated T_loss. P_L and P_M were measured 100 times (each measurement consisted of 1.5 sec ave.) each and I took average of them. T_ETM =13.7 ppm is used.

Discussion: 

-- This value is not so different from the value ericq reported in July (elog 10248).

-- This method of measuring arm loss is NOT sensitive to T_ITM.  In contrast, the method in which loss is obtained from finesse (for example, elog 11740) is sensitive to T_ITM.

In the method I'm now reporting, 

\Delta T_\mathrm{loss}/T_\mathrm{loss}\simeq\Delta T_\mathrm{ITM}/T_\mathrm{ITM},

but in the method with finesse,

\Delta T_\mathrm{loss}\simeq\Delta T_\mathrm{ITM}.

In the latter case, if relative error of T_ITM is 10%, error of T_loss would be 1000 ppm.

So it would be better to use power of reflected light when you want to measure arm loss.  

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