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Message ID: 4214     Entry time: Thu Jan 27 21:10:47 2011
Author: Osamu 
Type: Update 
Category: 40m Upgrading 
Subject: Calibrated noise of green 

I calibrated noise spectrum of green lock.

1. Measurement of conversion factor of ADC input from V to ct:

As a preparation, first I measured a conversion factor at ADC input of C1;GCX1SLOW_SERVO1.

It was measured while the output of AI ch6 as the output of C1;GCX1SLOW_SERVO2 with 1Hz, 1000ct(2000ct_pp) was directly connected into AA ch7 as the input of C1;GCX1SLOW_SERVO1. Amplitude at the output at AI ch6 was 616mVpp measured by oscilloscope, and C1;GCX1SLOW_SERVO1_IN1 read as 971.9ct_pp. So the conversion factor is calculated as 6.338e-4[V/ct].

2. Injection of a calibration signal:

When Green laser was locked to cavity with fast PZT and slow thermal, I injected 100Hz, 1000ct EXC at ETMX ASL. The signal was measured at C1:GCX1SLOW_SERVO1_IN1 as 5.314ct_rms. It can be converted into 3.368e-3Vrms using above result, and then converted into 3368Hz_rms using PZT efficiency as 1MHz/V. This efficiency was obtained from Koji's knowledge, but he says that it might have 30% or higher error. If somebody get more accurate value, put it into the conversion process from V to Hz here.

3. Conversion;

Frequency of green f=c/532nm=5.635e14[Hz] is fluctuating with above 3368Hz_rms,so the fluctuation ratio is 3368/5.635=5.977e-12, and it corresponds to length fluctuation of 37.5m. So, cavity fluctuation will be 5.977e-12*37.5=2.241e-10m_rms by 100Hz, 1000ct EXC at ETMX ASL.

4. Results;

Finally, we knew 5.314ct corresponds to 3368Hz and 2.241e-10m, so conversion factor from ct to Hz and ct to m are ;

633.8[Hz/ct] @ C1:GCX1SLOW_SERVO1

4.217e-11[m/ct] @ C1:GCX1SLOW_SERVO1

 

5. Calibration:

You can measure green noise spectrum at C1;GCX1SLOW_SERVO1_IN1 during lock,  and mutiply above result to convert Hz or m.

This calibration is effective above corner frequency of slow and fast servo around 0.5Hz and UGF of fast servo around 4kHz.

I show an example of calibrated green noise.

20110127_Calibrated_grrennoise.jpg

20110127_Calibrated_grrennoise.pdf

Each color show different band-width. Of course this results of calibration cactor does not depend on band-width. Noise around 1.2Hz is 6e-8Hz/rHz. It sounds a bit too good by factor ~2. The VCO efficiency might be too small.

 

Note that there are several assumptions in this calibration;

1. TF from actual PZT voltage to PZT mon is assumed to be 1 in all frequency. Probably this is not a bad assumption because circuit diagram shows monitor point is extracted PZT voltage directly.

2. However above assumption is not correct if the input impedance of AI is low.

3. As I said, PZT efficiency of 1MHz/V might be wrong.

 

I also measured a TF from C1:SUS-ETMX_ALS_EXC to C1:GCX1SLOW_SERVO1_IN1. It is similar as calibration injection above but for wide frequency. This shows a clear line of f^-2 of suspension.

20110127_TF_ETMXSUSEXC_to_PZTOUT.pdf

 

Files are located in /users/osamu/:20110127_Green_calibration.

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