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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 
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Message ID: 1856     Entry time: Sat Aug 12 19:11:56 2017     Reply to this: 1859   1919
Author: Craig, awade 
Type: Summary 
Category: NoiseBudget 
Subject: Noise Budget Summary 

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)

COATINGS THERMAL NOISE BUDGET

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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