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Entry  Sat Aug 12 19:11:56 2017, Craig, awade, Summary, NoiseBudget, Noise Budget Summary noiseBudget.pdfExperimentalSetup.pdf
    Reply  Mon Aug 14 21:38:51 2017, Craig, awade, Summary, NoiseBudget, Noise Budget Summary 
    Reply  Fri Sep 15 02:05:46 2017, Craig, Summary, NoiseBudget, Noise Budget Summary 20170915_012259noiseBudget.pdf
       Reply  Fri Sep 15 14:45:54 2017, rana, Summary, NoiseBudget, Noise Budget Summary 
       Reply  Fri Sep 15 20:42:55 2017, Craig's left brain, Summary, NoiseBudget, Text wrapping 
Message ID: 1919     Entry time: Fri Sep 15 02:05:46 2017     In reply to: 1856     Reply to this: 1921   1923
Author: Craig 
Type: Summary 
Category: NoiseBudget 
Subject: Noise Budget Summary 

The noise budget posted in the previous noisebudget elog has been described by experts as "bunk".  I am here to right the ship with a more correct noise budget.  I have committed the corrected noisebudget code in the CTN_noisebudget git under /CTN_noisebudget/noisebudget/noisebudget.ipynb.

In particular, the pink curve in the new noise budget is the real COATING THERMO-OPTIC NOISE.  It is far lower than before.  This is why the optimized coating layers were created in the first place: to strategically cancel coating thermoelastic and coating thermorefractive noise.  Recall that thermo-optic = thermoelastic + thermorefractive, and they can cancel if their phases are carefully controlled.

With lowered COATING THERMO-OPTIC NOISE, we can now think about measuring COATING BROWNIAN NOISE for the AlGaAs coatings. 

I have included a new trace: the SEPT 2017 BEAT MEAS.  These are just some preliminary PLL noise limited spectra to keep you excited for great low noise measurements to come.


I spent a bunch of time making an interactive noise budget bokeh plot.  HERE IT IS. 

Advantages: You can scroll over and see exact numbers at whatever frequency you want.  You can pan and zoom.  You can click the legend to remove lines you don't want to see.  It looks nice.  We can host these on our 40m server soon (I'm hosting this on the ldas cluster, so you have to login).

Disadvantages: File is huge (~20 Mb) and takes a long time to load.  Interactivity is choppy.  Panning causes lines to disappear.  Tick labels are cancerous.  The dark background is good only if I can figure out how to make the entire background dark, this means making custom CSS files and I'm no html expert.



This is an overview of the old noise budget made by Evan and Tara.  The plot is the result of noisebudgetQWL.ipynb written by Evan.  QWL stands for quarter wavelength, referring to the coating layers' thickness (see Fig 2 of Evan's paper).

Each curve is given an brief statement about it's origin.  Here is a link to Tara's paper on the PSL Lab setupHere is a link to Evan's paper.  These papers have convenient tables with parameter values for the setup and reference cavities. 

The x axis is frequency in Hz, the y axis is the ASD in Hz / rtHz, aka frequency noise.  Many of the thermal noises are reported as length noise.  To convert from length to frequency noise, use Delta f / Delta L = c / (L * lambda)


TOTAL EXPECTED (blue):  Sum of all expected noises.  This does not equal the actual measurement in red, meaning not all sources of noise are accounted for in this plot.  One suspicious missing noise source is scattering.  Not much has been done to mitigate scattering in the PSL Lab setup.

MEASUREMENT (red): Actual beatnote measurement measured using a phase locked loop with the cavities' transmission radio-frequency photodetector (See Fig 2).  The two lasers are locked to their respective cavities to reduce the free-running laser noise via PDH control loop gain.  By suppressing laser noise, we can reveal the residual cavity length noise, hopefully dominated by broadband thermal noise.

COATING BROWNIAN (green): Theory curve of the estimated coating brownian noise.  Brownian noise magnitude is governed by a material's mechanical loss.  "Mechanical loss" refers to rate at which kinetic energy in a material is "lost" to thermal energy.  Unclear why Equation 8 in Tara's paper and Equation 3 in Evan's paper are different, I think it has to do with assumptions about the coating and substrate Young's modulus and Poisson ratio being the same.  In the noisebudgetQWL.ipynb, Tara's coating brownian noise equation is used.

COATING THERMO-OPTIC (pink): Theory curve of the estimated thermo-optic noise.  Thermo-optic noise comes from temperature fluctuations in a material causing cavity length changes.  This seems to be the key curve to all Tara and Evan's work.  The idea here, originated by Evans et al., seems to be that thermoelastic noise and thermorefractive noise can cancel one another in thin enough coatings.  Given by Equation 9 in Tara's paper and Equation 4 in Evan's. 

SUBSTRATE BROWNIAN (yellow): Theory curve of the estimated substrate brownian noise.  Like the coating brownian, but refers to noise originating from the fused silica making up most of the mirror.  Equation 5 in Tara's paper.

SUBSTRATE THERMOELASTIC (teal): Theory curve of the estimated substrate thermoelastic noise.  Thermoelastic noise refers to how temperature fluctuations cause a material to modulate its length.  Governed by the coefficient of thermoelasticity alpha = 1/L(dL/dT)  Equation 6 in Tara's paper. 

Incidentally, I will mention THERMOREFRACTIVE noise here since there is no curve dedicated directly to it, but it is important to thermo-optic noise.  Thermorefractive noise comes from temperature fluctuations changing the refractive index n of a material light is passing through.  Governed by the coefficient of thermorefractivity beta = dn/dT

POUND DREVER HALL SHOT NOISE (orange): Theory curve of shot noise.  Shot noise refers to the Poisson statistics of fluctuations in the number of photons incident on a photodetector.  This noise PSD is flat in frequency, but falls as 1/f^2 in power.  To convert from the power PSD to frequency PSD, multiply the power PSD by (1 + f^2/fc^2)/(2 P0 Gamma/fc)^2 where fc is the cavity pole, Gamma is the modulation depth, and P0 is the incident power on the cavity. Equation 20 of Tara's paper.

PHASE LOCKED LOOP OSCILLATOR NOISE (grey):  Measured noise from the PLL, presumably originating from the voltage-controlled oscillator (VCO).  Figure 5 in Tara's paper shows the PLL and the various noises found in it, including photocurrent shot noise, photodiode amplifier noise, and VCO frequency noise.  Unclear what the 707 Hz/V means, probably is the VCO control slope (i.e. if I want to change my VCO freq 707 Hz, I raise the control voltage by 1 V).

PHASE LOCKED LOOP READOUT (purple): Theory curve of the PLL readout noise.  The PSD for this noise rises as f^2, due to the fact that the PLL is a phase detector but the noise budget is in units of Hz/rtHz.  This curve is poorly documented compared to the rest of them (Evan calls it a "magic number" curve).  To convert from phase noise to frequency noise, multiply the phase PSD by f^2.

SEISMIC COUPLING (black): Measured curve of the seismic coupling into the experiment.  The raw data taken appears to be seismic velocity in units of m / (s * rtHz) as a function of frequency.  Then, seismic acceleration is obtained by multiplying the raw seismic velocity data by 2*pi*f.  Then the two stacks (?) and a spring (??) TF are modeled with hard-coded resonant frequencies and Q's and multiplied together to give a final seismic TF falling as 1/f^6.  The final seismic PSD is found by squaring the product of seismic acceleration, the 1/f^6 seismic TF, and an additional hard-coded seismic coupling factor dependent on the cavity length with units  m/(m s**-2).

PHOTOTHERMAL NOISE, ISS ON (brown):  Measured curve of the photothermal noise.  Photothermal noise originates from fluctuations in laser intensity causing changes in the amount of laser power absorbed by the coatings, which causes coating temperature fluctuations.  Seems to be the expected limiting noise at low frequency.  The raw measurement was of relative intensity noise from both lasers.  To get the photothermal noise PSDs for each path, the RINs from each path are multiplied by the absolute laser power absorbed by the coatings squared, a "total photothermal TF" squared, and converted from length PSDs in units of m^2/Hz to frequency PSDs Hz^2/Hz.  The "total photothermal TF" is the sum of the coatings photothermal thermoelastic TF, coatings photothermal thermorefractive TF, and subtrate photothermal thermoelastic TF.  Each of these photothermalTFs are from units of transmitted cavity power to beatnote frequency fluctuations, (i.e. Hz/W).  The process of measuring these three TFs is explained in Evan's paper, section VI, subsection A.  It seems that the successful cancellation of expected photothermal noise was the main success of Evan's paper.

RESIDUAL NPRO NOISE (dark green): Theory curve for the residual NonPlanar Ring Oscillator (NPRO) laser noise.  The freerunning ASD of the NPRO is reported to by 10**4/f with units of Hz/rtHz.  This is then divided by the PDH control loop gain for both paths, squared into a PSD, and summed together into a final NPRO residual PSD. 



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