I calculated thermal noise in mode cleaner (MC) mirrors and compared it with the measured MC noise. Thermal noise won't be a significant noise source for MC.

== Motivation==

 There is an idea of using MC and a refcav to measure coating thermal noise. One laser is frequency locked to MC, another laser is locked to an 8" refcav. Then the two transmitted beams are recombined so that we can readout the frequency noise. In this case, the transmitted beam from MC is a better reference (less frequency noise) than the beam from refcav. However, we need to make sure that we understand the noise sources, for example brownian noise, thermoelastic noise in both substrates and coatings, in MC more thoroughly.

==Calculation==

I used Rana's code for MC's technical noise sources from, svn. The same plot can be found in appendix C of his thesis. Then I added my calculation to the plot.  Jenne pointed me to 40m:2984 for the spot size and the cavity length. The spot radius on MC1 and MC3 is ~ 1.5mm, and ~3.4 mm@MC2, The round trip length is ~27m, thus the frequency fluctuation due to thermal noise is lower than that of refcav by 2-3 orders of magnitude. I calculated Brownian noise in coatings, Brownian noise in substrate, Thermoelastic noise in substrate. I assumed that the coatings are SiO2/Ta2O5, quarter stacks, coatings thickness for MC1/3 = 5um, for MC2 = 8um. The code can be found in the attachment.

==result==

Total thermal noise on MC (Brownian + Thermoelastic on substrate and coatings of MC1-MC3) is plotted in dashed red. It is already below 10^-5 Hz/rtHz at ~20 Hz. This is sufficiently low compared to other noise sources. Beat signal from CTN measurement with 8" cavities is plotted in pink, the estimated coating brownian noise is plotted in a yellow strip. They are well above the measured MC noise between 100 Hz to a few kHz. Measuring coating thermal noise on 8" refcav seems plausible with this method. We can beat the two transmitted beams from IMC and refcav and readout the beat signal to extract the displacement noise of refcav. I'll discuss this with Koji if this is a good surf project.

[the internal thermal noise in the original plotted is removed and replaced with the total thermal noise plot instead]

 note:I'm not sure about the current 40m MC configuration. The parameters used in this calculation are summarized in mcnoiseS2L1.m (in the svn page).