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Entry  Wed Jun 13 19:00:26 2012, Sarah, DailyProgress, Laser, Transfer Functions 12x
    Reply  Fri Jun 22 22:34:28 2012, tara, DailyProgress, NoiseBudget, RIN coupling to Frequency noise 
    Reply  Wed Jun 27 18:51:56 2012, Sarah, DailyProgress, Laser, Transfer Functions Slide1.pngtf_oa_calc_measured.pngTF_allfreq.pngTF_fit_allfreq.pngnb_allfreq.png
       Reply  Fri Jul 6 18:59:49 2012, tara, DailyProgress, Laser, Transfer Functions IMG_1447.jpgRIN_Fnoise.pngRIN_Fnoise.png
          Reply  Tue Jul 10 02:55:37 2012, tara, DailyProgress, Laser, Transfer Functions 
             Reply  Mon Jul 16 19:08:34 2012, tara, DailyProgress, NoiseBudget, Transfer Functions (RIN to Frequency noise via photothermal) 
                Reply  Tue Jul 17 19:05:32 2012, tara, DailyProgress, NoiseBudget, Transfer Functions (RIN to Frequency noise via photothermal) 7x
                   Reply  Tue Jul 24 17:02:35 2012, Sarah, DailyProgress, NoiseBudget, Transfer Functions (RIN to Frequency noise via photothermal) 8x
                      Reply  Fri Aug 3 02:46:15 2012, tara, DailyProgress, NoiseBudget, Transfer Functions (RIN to Frequency noise via photothermal) RIN_coupling_2012_08_03.pngRIN_coupling.fig
                         Reply  Tue Aug 13 21:45:51 2013, tara, DailyProgress, NoiseBudget, Transfer Functions (RIN to Frequency noise via photothermal) farsi_2013_08_13.pngfarsi_2013_08_13.figRIN_TO_algaas.pngRIN_TO_algaas.fig
                            Reply  Fri Aug 16 04:35:58 2013, tara, DailyProgress, NoiseBudget, Transfer Functions (RIN to Frequency noise via photothermal) RIN_req_algaas.pngRIN_req_algaas.fig
                            Reply  Thu Aug 22 13:36:19 2013, tara, DailyProgress, NoiseBudget, Transfer Functions (RIN to Frequency noise via photothermal) fasi_2013_08_22.pngFarsi_compare.fig
          Reply  Wed Jul 11 11:13:38 2012, Sarah, DailyProgress, Laser, Transfer Functions 7x
          Reply  Sun Jul 15 23:20:32 2012, tara, DailyProgress, NoiseBudget, Transfer Functions (power fluctuation to Frequency noise via photothermal effect) Farsi_compare.pngFarsi_compare.fig
             Reply  Thu Jul 19 03:01:26 2012, tara, DailyProgress, NoiseBudget, Transfer Functions (power fluctuation to Frequency noise via photothermal effect) Farsi_compare.pngFarsi_compare.fig
                Reply  Thu Jul 19 23:56:45 2012, rana, DailyProgress, NoiseBudget, Transfer Functions (power fluctuation to Frequency noise via photothermal effect) 
                   Reply  Fri Jul 20 01:32:45 2012, tara, DailyProgress, NoiseBudget, Transfer Functions (power fluctuation to Frequency noise via photothermal effect) 
Message ID: 1014     Entry time: Fri Jul 6 18:59:49 2012     In reply to: 1005     Reply to this: 1016   1017   1019
Author: tara 
Type: DailyProgress 
Category: Laser 
Subject: Transfer Functions 

I have been thinking that the TF measurement (coupling from RIN to frequency noise) we plotted before has unusable unit [Frequency noise /RIN]. We have to correct it by converting it to [frequency noise/ watt]. With that we can compare the result to other experiment/ calculation or use it in the noise budget.  As an example, I plot the result calculated by Cerdonio etal 2003 here as well.

 

==we use wrong unit==

  I am editing my noise budget code to incorporate the effect from RIN induced noise and find out that, the unit we have in Fnoise/RIN is not making sense. In order to get the noise due to RIN I have to multiply measured RIN to the measured TF, that is    Freq noise due to RIN = [measured TF] x [measured RIN behind CAV] = [Hz/RIN] x [RIN] = Hz. As we can see, it does not change with the input power level. In reality, it should depend on the power level as well.  That is why I think Hz/RIN unit is unusable.

 

==result from Cerdonio==

 Braginsky etal calculated the noise from thermal expansion due to heat absorbed from shot noise. The result was later corrected for all frequency span by Cerdoniot etal in 2003. The result tells us the displacement noise due to shot noise. With some modification, we can apply the result to get the displacement noise due to RIN. This will be compared with the measurement later. [add calculation]

IMG_1447.jpg

fig1: calculation for TF using Cerdonio etal's result.

RIN_Fnoise.png

fig2: calculated TF in unit of [Hz/Watt] (I convert the result from m/watt to Hz/watt). Frequency noise can be calculated by multipling the TF with RIN x Pin. [fig file, code]

==some thing about the measurement setup==

The nice thing from the measurement is that we can see the Cerdonio effect when the thermal diffusion length is comparable to the spot size (around 3Hz) nicely. However, the asymptotic behavior of our measurement does not agree well with the prediction. It has a slope of 1/f0.75 , while we expect 1/f.  I'll find out what's wrong with the setup (bad alignment on EAOM, PDH signal, etc) or other mechanism that might cause this effect.

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