I realized that we have not checked the eigenmodes of 1.45" cavity yet, so I used comsol to find out several modes. The lowest mode is ~ 46kHz, and the first longitudinal mode is about 60kHz. The frequencies are high enough so that the thermal noise calculation in dc- 10kHz frequency band can be done with quasi-static assumption.
1) I tried a simple cylindrical shape, with the dimension of the spacer. The result for the first longitudinal mode is 74KHz, the analytical result is ~ 77kHz, see PSL:1135. It seems that COMSOL's result and the analytical results are comparable.
2) Then I simulated the whole reference cavity. The lowest body mode is ~ 47kHz. The body expand-contract radially, and should not change the cavity beamline length that much. The first longitudinal mode is ~ 60kHz. The color on the surface shows the rms displacement from all direction.
open loop gain transfer function of RCAV is measured.
1) how to measure OLG TF
The requirement assumes that the residual frequency noise is 5% or less in the total noise. The servo performance is definitely ok for 1.45 inch cavity.
We heard back from G. Cole about the thickness resolution in the AlGaAs coating manufacturing process will be around 0.5 A. So I'm checking how the noise budget will change by rounding up the physical thickness in opt V4 to the next 0.5A. The design will still work. The round up thickness is added in the google document (for opt v4 only).
The estimated growth rate of the crystal is 4.8A/s and shutter speed is assumed to have 0.1 sec time step. This means the smallest step of the thickness control is ~0.5A. So I round up the physical thickness to the next 0.5 A and calculate the coating properties.
1) Rounding up to the next 0.5 Angstrom. The truncating process acts like a random thickness variation in the optimized coatings with maximum error ~ 0.25 Angstrom. The averaged layer thickness is ~ 800 Angstrom.
2)Results when the layers physical thickness are round up to the closest 0.5 A. The noise budget does not change much.
The coatings properties still hold, even with random error in parameters, thickness.
Note: For the error calculation I did before I used 1 sigma to be 1% for AlGaAs, and 0.5% for GaAs. The thinnest layer is AlGaAs at 35 A, so its sigma is about 0.35 A. The average thickness is 90 Angstrom, so the average error is about 0.9 A. The estimated error in the calibration process is already larger than the error from the truncation(0.25A). That's why the error analysis results are still valid.
I got a chance to measure beat measurement. The noise budget is updated and contains all dominant noise traces.
== Beat measurement ==
1) at DC to 10Hz, the contribution is mostly from RIN driven Photothermal noise and a bit of seismic noise, a small peaks around 10Hz is probably from the stack, not the cavity sagging. The hump from DC to ~ 50Hz disappear when it is quiet. I think it is mostly scattered light associated with the seismic noise, not displacement noise due to the vibration.
2) 10Hz to 1kHz is pretty much Coating Brownian noise.
3) At 1kHz and above, it is PLL readout noise and residual frequency noise from the laser, where the gain cannot suppress enough noise. This is mostly from ACAV. The residual frequency noise = free running noise / (1+ OLGTF). The measurement of the open loop gain is explained below.
==TTFSS Loop characterization==
The OLG TF of TTFSS is measured up to 10MHz and compared with the calculation. The schematic explaning how TTFSS actuates on the laser is shown below.
The freqeuncy discriminator can be measured from the slope of the error signal (from Common out1) while scanning the laser. For RCAV Dv = 1/ (194 kHz/V) and 1/(164kHz/V) for ACAV. with 1mW input power.
The adjustable gain stage can be tuned by turning the dial knob. At 400, gain=1, and the gain changes by 10dB with every 250click.
The PZT actuator has a gain of 4.5MHz/V (measured), and the EOM actuator is 15mRad/V (or 15mHz/f Hz/V) (taken from the spec sheet).
OLG measurement is taken: RCAV OLG is measured and plotted against the theoretical approximation, see the below figure.
above: RCAV OLG TF. Note: The calculation and the measurement do not include the integrator with corner frequency at 4.6kHz.
There are some problems with ACAV loop and I could not increase the gain up as much as it used to be and the UGF is around only 200kHz , but the measurement matches the calculation. Right now RCAV servo has a better loop performance.
The calculated OLG TF trace(green) should go down at 1MHz or above because of the opamps' bandwidth. I used ideal Op Amps in the simulation because I don't have some op amps in my liso library. I'll see if I can fix it.
I'm trying to record beat measurement for a few days. The data will be taken from ATF using mDV. There are a few issues about mDV right now, I'm looking into it and asking around.
There is a problem with gps.m that converts the string to gps second. It is used in get_data where we specify the start time. I tried enter the gps second manually but it returns an empty time struct, and the get_data cannot be used.
A reminder entry: psl:978
I looked into the uncertainty in coating thickness of the QWL SiO2/Ta2O5 coating The thickness of 4.53 +/- 0.07 um (~1.5%)seems to be appropriate.
The thermal noise level is directly proportional to the coating thickness, so we want to estimate its uncertainty. The error in the thickness is from
The errors in nL and nH are quite small, nL ~ 1.45 +/ 0.01, nH ~ 2.06+/- 0.01. (From the literature). I also looked around the error in IBS thickness control, they are usually better than 0.1 nm, IBS, but that is the current technology. In literature around 2000s, 2% error seems to be the number estimated for the thickness control (Sullivan 2000, Badoil 2007). As a quick check, I used the same assumption for error propagation similar to that of AlGaAs coating. The result gives ~ 4.53 +/- 0.07 um for coating thickness.
Note that the error here is smaller than the difference in coating thickness for the coatings with or without half wave cap.
For 28 Layer (with cap), the coating thickness is 4.53 um, for 28 layer QWL, the coating thickness is 4.35 um. But after digging up all the information from REO, and peter king they agree that it is 28 QWL with half wave cap. I tried to compare the calculation and the photothermal TF measurement, but the effect is too small to be conclusive about the structure. So the biggest error might come from the fact that the coating has cap or not. The error is about 4%.
Spacer in BR noise
== COMSOL vs result from Kessler etal 2012==
The analytical result from kessler2012, assume the force acts on whole surface of the spacer (with bore hole), I check this with COMSOL by comparing the result, similar to what I did in PSL:1075. The result agrees well within 2%. This verifies that COMSOL model is correct
==thermal noise level vs annulus thickness==
Typically, the contact surface between the spacer and the mirror is only a thin annulus, see psl:1199 . And the noise level is dependent on the actual area of contact. So I run the simulation to see the dependent of the stored energy (U) vs the annulus thickness. The annulus thickness is about 2 mm +/- 0.2 mm. The displacement noise is proportional to sqrt(U).
fig1: The stored energy as calculated by COMSOL, fitted with cubic polynomial.
The error from the contact area, the simulation result are small ~3% and 2%. These are smaller than the uncertainty of loss in bulk fused silica (can be from 10^-6 to 10^-7). The effect is still small in the total noise.
I"m packing the mirrors so that they are ready to be shipped to G. Cole. The mirrors are packed properly, see picasa.
I'm trying to estimate the coupling between seismic to displacement noise of the cavity using COMSOL.
From the design, the strain due to the seismic noise is about 2e-11. But we want to see what happen if the support positions are moved away from the specified points a bit. This time the model is a whole cavity, not just 1/8 as I did before. This is to see results of the mis-positioned support points. However, COMSOL has some problems
Right now I have ~30 data points after 4 hrs of running the simulation. I'll get a bit more data and will see how it goes when I histogram it.
I tried to estimate the coupling from seismic to displacement noise. With the common mode rejection taken into account, the coupling from vertical acceleration to differential length between the two cavities is about 6x10^-12.
Since we measured thermal noise from the coating(QWL, SiO2/Ta2O5), we want to extract loss angles of each materials. The losses are about a factor of 2 higher than the numbers reported in the literature.
So far, there are 3 calculations we have been using for coating noise estimation.
In essence, both Harry's and Hong's result can be written as a linear combination of phiL and phiH. I used Harry result to compare with Hong to see if there is any differences in the result or not, but both gave me the same answer.
The calculation is attached below. I made sure that the calculation from Hong and Harry are correct by choosing the elastic properties of the coatings to be the same as that of substrate and checking the the results agree with Nakagawa's. So the code should be correct.
Then, I varied phiL and phiH to match the measurement. The measurement is represented by the prediction by Nakagawa with the fitted loss (phiC = 4.15e-4).
Both calculations gave the similar relation between phiH (phi tantala) and phiL (phi silica) to match the measurement:
phiH = -1.4 phiL + 9.7 (Hong)
phiH = -1.44 phi L + 9.77 (Harry) (assume sigma1 = sigma 2 = 0)
The problem is if we use the nominal numbers from various reports, phiL ~ 1e-4, phiH ~ 4e-4. The result will be off by almost a factor of 2. For example, for phiL = 1e-4, this means phi H has to be 8.4e-4. Or if phi H is chosen to be 4e-4, phi L will be ~4e-4 as well. It seems that our result is higher than the predictions (under some assumptions).
Table1 below shows some possible values of phiL and phiH extracted from our result and the calculation.
But we have good evidences from Numata and short/long cavities (spot size dependent) to believe that the measurement is real coating thermal noise . The reason why the prediction is smaller than the measurement could be that the losses is actually higher in our coating. Most ring down measurements were done after 2002 while our coatings were fabricated around 1997. Coating vendors might become more careful about loss and improved their process. But the result from Numata was out in 2003, and it is about the same as ours, so I'm really not sure what can we say about this.
==numbers from literature==
Penn2003: (disc ring down) phiL = (0.5 +/- 0.3) x10^-4 , phiH = (4.4 +/- 0.2) x10^-4
Numata2003 (direct measurement) phiC = 4.4e-4;
Crooks2004(disc ring down) phiL = 0.4+/-0.3 x10^-4, phiH = (4.2+/-0.4)x10^-4 (the frequency dependent part is ignored)
Crooks2006: (disc ring down) phiL = (1.0 +/- 0.2) x10^-4 phiH = (3.8 +/- 0.2) x10^-4 (small change in TE calculation from previous paper)
Martin2009 : (blade) phiH = 3+/- 0.5 x10^-4 (at 300K)
Martin2010: (blade) phiH = (2.5-5) x10^-4 ( heat treated at 600C, several frequencies)
LMA2014: (blade) phiL = (0.43+/-0.02) x10^-4 phiH = (2.28 +/- 0.2) x10^-4
I checked Brownian coating noise level with uncertainties in coating parameters. The measured result is barely at the edge of the confident interval.
Hong2013 look into coating noise level when materials' parameters are changed. One example is the Young's modulus of Ta2O5. With the assumption phi bulk = phi shear, if Y_Ta2O5 is varied between 70e9 to 280e9 (nominal value = 140e9), coating thermal noise can be changed by a factor of 0.9 to 1.5 from the nominal value (in PSD m^2/Hz unit). It seems that the range is quite large compared to the numbers measured by various groups, (see PSL895 for error in material parameters). I used a smaller range, but I varied other parameters as well.
==Note about uncertainties in calculation==
I used rand command in Matlab to generate random values. The reasons are 1) for reported loss angles, say 4+/- 2e-4, if I use Gaussian dist, with sigma =2, mean = 4, sometimes the generated value will be negative, and 2) since we are only trying to see the possible range of the estimated noise level, not the real statistic value, rand should be ok at this point.
==1:fixed loss angles==
First I checked how much the parameters effect the calculation if the loss angles are fixed (phi silica = 1e-4, phi tantala = 4e-4). Y tantala is chosen between (70-280 GPa), Y silica is varied between72e9 +/- 10%, Poisson's ratio are varied between 10percent for coating materials. All substrate parameters are fixed, since they should be relatively well measured compared to that of the coatings. The result is around 0.5-0.85 of the measurement (in PSD m^2/Hz).
For a more conservative value of Ta2O5 ( 140+/-40 GPa), the result is a factor of 0.5-0.64 of the measurement.
==2:varied loss angles==
In this study, I varied loss angles of phi_silica = [0.8-1.2] x10^-4, phi_ta2O5 = [3,5]x10^-4, these numbers are reported from several measurement. Then I change the uncertainties range of Y_Ta2O5 in my calculation
==note and comment==
Both Hong's and Harry's calculation provide quite the same value (within 3%). So I show only histogram obtained from Hong's calculation. I don't know why the study shown in Hong paper choose the value of Y tantala between 70-280 GPa, most of the measurements report smaller uncertainty. But with that higher value of Y_Ta2O5, it can explain the measured noise level from our measurement. However, I doubt that this argument is valid, since most of the ring down measurements to evaluate phi_Ta2O5 assume Y_tantala ~ 140GPa. Then the loss angle of Ta2O5 should carry some information about Y_Ta2O5 in it and cannot be treated as an independent parameter like this calculation. I'll look into the ring down papers to see how much Y_Ta2O5 affects the extraction of its loss angle.
I'm checking how loss angle of Ta2O5 is related to its Young's modulus (as used in ring down measurements), then I use that relation in error calculation for BR noise in coating. The uncertainties in Young's moduli of SiO2/Ta2O5 might lead to errors in loss angles and BR noise in coating.
Many ring down measurements (see Penn2003, Crooks2004, Crooks2006), observed loss from a disc substrate with multilayer coatings of Ta2O5/SiO2. The loss in the coating (ring down mode) is written as
phi_c = (phi1*Y1*d1 + phi2*Y2*d2 )/ (Y1*d1 + Y2*d2) --------(1)
Where phi_c is determined from the measurement. Y is the young's modulus, phi is loss angle of material, d is physical thickness of the material.
Then phi1 and phi2 is determined with the assumption that Y1 and Y2 are known.
So, the reported value of phi Ta2O5 is directly related to its Young's modulus. The uncertainty calculation of BR noise where Y, phi are varied independently might not reflect the real situation.
For example, I recalculated phi_c (of QWL structure) using phiH phiL of 4e-4, 1e-4. YH = 140 Gpa, YL = 72GPa. Then I rearranged eq(1) so that phiH can be written as a function of YH to see how the loss angle of Ta2O5 (H) will change with its Young's modulus assuming that YL and phiL are fixed.
fig1: How phi Ta2O5 changes with Young's modulus.
==BR calculation with loss parametrized by Young's modulus==
With the loss angles parametrized by the Young's modulus, I calculate the estimated thermal noise compared to our measurement (using Hong2013)
fig2: ratio of BR calculated and our result.
It is interesting that, even with the lower phiH as YH increases, the total BR noise increases. And the nominal value that we have been using (YTa2O5 = 140 GPa) yields almost the minimum value of BR noise calculation.
So far, the calculation is done assuming phiL = 1e-4, YL = 72e9. The next step is to varied phiL, YL, phiH, YH all together ( with the constraint given by eq1) and see how BR noise changes.
I'm also checking how large the errors are in the measurements for Young's modulus (both SiO2/Ta2O5). Crooks2006 reports the value of Young's modulus of Ta2O5 with the assumption that Y_SiO2 is 72e9. This might give another constraint.
Ta2O5 Young's modulus is quoted to be 140 GPa from this paper Martin1993, but that is the value of Ta2O5 deposited on Silicon substrate cf fig5, top plot. The deposition technique is IAD. I'm not sure if it is the same as ion beam sputtering or not. I'm looking into it.
Anyway, the Young's modlus of Ta2O5 can be down to 70 GPa for IAD technique on glass substrate, as the paper says in the conclusion section.
Note that Crooks2006 mentions other papers measure YTa2O5 to be around 100-110 GPa as well. I'm looking into it.
I just talked to Matt and learned that:
The measurement from Penn extracts phi1 and phi2 from
phi_c = (Y1 *d1*phi1 + Y2*d2*phi2) / (d1*Y1 + d2*Y2).
Phi_c is calculated from the total phi of the ring down system.
The dissipated energy comes from two part, the substrate and the coating. With the assumption that phi sub is much smaller than phi coat, we can write
phi_total (measured from ring down) = |energy in coating| / |Energy in substrate| * coating loss, and the ratio Ec/Es can be obtained from FEA. For drum head mode it is ~ 1500 (From Penn paper), see the picture, top panel.
This Ec/Es also depends on the Young's moduli, so the calculated phi_c also has Y as a parameter. The calculation I did before takes phi_c from the reported values, so it is not correct.
To get the correct phi_c, the ratio of Ec/Es has to be changed with Y. Crooks PDH thesis has an analytical expression for the drum head mode of a cylindrical substrate. The analytical result is comparable to the FEA result used in Penn2003 within 5%. Note that the young's modulus of the coating is the volume average (Yc tc = y1*t1 +y2*t2) where tc is the total thickness, tx = thickness of material x. See the middle panel in the picture above.
For the next step, instead of using the report value of phi1,phi2 and Y1,Y2 to reconstruct phi_c (Penn2003). I will use the measured phi_tot (for drum mode) then use that as a constraint on Y1, Y2, phi1, and Phi2 instead, see bottom panel in the picture. This should give a correct dependent among these variables.
I used results from ring down measurement in Penn 2003, without assuming the values of YL,YH. If the actual Young's moduli of both materials are about 60% of their nominal values, the calculation of BR noise will match our measurement within 3%.
I used ring down drumhead mode from sample C2 and F2 since the phi_coating as reported in the paper is about the same as the phi_coating obtained from the analytical result (see previous entry). With these two eqs, I can write
Ysub * D/3 * phitot_1 = phiL*YL*dL_1 + phiH*YH*dH_1-------(1) (see previous entry, last eq).
Ysub * D/3 * phitot_2 = phiL*YL*dL_2 + phiH*YH*dH_2-------(2) .
phi tot_1 and _2 are 1/Qtot from the two samples. D is the thickness of the substrate (0.25 cm). dL and dH are the physical thickness of siO2 and Ta2O5 in each sample.
For any fixed values of YH and YL, the two eqs will solve for a pair of phiL and phiH.
First, I checked the validity of these two ring down measurements by using YL = 72 GPa, YH= 140GPa. The results are
PhiL = 1.29e-4, phiH = 4.13e-4. These numbers agree with the reported values.
Then, I varied YH from 0.5*YH_0 to 2*YH_0 and YL from 0.5*YL_0 to 2*YL_0 ( YH_0 = 140GPa, YL_0 = 72GPa), and solved for the corresponding phiL and phiH. Then with all 4 parameters, BR noise can be calculated.
Below is a plot of ratio of BR calculation and our measurement, vs YH. Each trace represents different value of YL.
Each point on the plot will have information about phiL and phiH. If YL = 43 GPa (0.6*72GPa) and YH = 84 GPa (0.6*140GPa), the loss angles extracted from the ring down measurements are phiL = 2.15e-4 and phiH = 6.9 e-4. All these four parameters give the estimated BR noise comparable to our measurement to 2% (in PSD unit).
I'm trying to explain why our measurement is larger than the estimated calculation using numbers from literature. But we have good reasons to believe that the measurement is really BR coating since
It is possible that loss angles in our coating is lossier than usual. But there are still other possible explanations. The results from ring down measurements rely on the values of Young's moduli of the coating materials. If the actual values divert from the nominal values, the losses will be changed as well. So I used the result from the ring down measurement, without assuming any values of YH and YL, then extracted values of phiH and phiL using different combinations of YH and YL and calculated the coating noise according to each set of parameters. If YL and YH have lower Young's moduli than their nominal values, coating BR noise will be higher and agree with our measurement.
One might argue that 0.6 YL and 0.6 YH are too low. Ta2O5 was measured with nano indentation to be ~ 140 GPa (Abernathy). Other references measured Ta2O5 ~ 100 GPa (see ref 16, 20 in Crooks2006 paper). So, uncertainty around 40% might be possible.
In addition, this calculation also assume phi_bulk = phi_shear. But the different value of phiB/phiS can also change the calculation between 0.5*S_0 to 1.6*S_0, for different values of phi bulk/phi shear ratio is varied by a factor of 5(see Hong2013). These values also change the noise level significantly.
So with the uncertainties in Young's moduli, the loss angles from ring down measurements can be changed significantly. If the Young's moduli of the coatings are smaller than the nominal values, the loss angles calculated from a ring down result will be higher, and it resuls in a higher level of coating BR noise calculation.
I'm surprised that for the value of 0.6*YL_0 and 0.6*YH_0 used above, with the loss angles of phiH = 6.89e-4 and phiL = 2.15 e-4, the calculated BR noise is almost the same as when I use the nominal value of YH,YL with the same loss (2.15 and 6.89e-4) see, PSL:1408. I double checked the result, but I did not see anything wrong in the calculation. It turns out that the BR calculation is not very sensitive to YL, YH, but it is directly proportional to phiH, phiL. However, the values of phiH, phiL obtained from a ring down measurement are very sensitive to YL and YH as we can see from the plot above.
Heat treatment after coating changes loss angles of both SiO2 and Ta2O5. Our coating might really have higher loss (maybe because of the low temp annealing), regardless of the actual values of coatings Young's moduli.
I went through the paper by LMA2014 that measured loss in SiO2 and Ta2O5 using interferometry on a cantilever blade. They could also extract Young's moduli from thin film SiO2 and Ta2O5, their results are ~ 70GPa and 118 GPa respectively.
One interesting result is that losses are reduced with heat treatment after coating process.
SiO2 loss before heat treatment is ~ 6e-4, and it goes down to ~ 0.6e-4 after the annealing (from broadband measurement).
From ring down measurement, SiO2 before heat treatment is ~ 4e-4. no result for the measurement after annealing.
For Ta2O5,from broadband measurement, the loss after heat treatment is ~ 4.7e-4, no result from the before heat treatment is reported.
From ring down, the loss is ~ 11.4e-4 before annealing, and down to ~ 4.9e-4 after annealing.
Their annealing process is described in the paper. I should find out more how losses of both materials change with different heat treatment i.e. time/ temperature/cooling, then see if any information about our mirrors can be retrieved from REO or not.
Right now, we have only the information about phiH and phiL as phiH = a*phiL + b. I still need another relation to get phiH and phiL individually. My plan is finding information about heat treatment vs loss, like the picture below (I still need to find for Ta2O5). Otherwise, it is hard to say anything about the loss from each material.
Most reports have different annealing temp, (I'm not considering time/ heating rate/ cooling rate right now, but they might be important) So I can compare loss vs annealing temp.
It is hard to extract the similar plot as above for Ta2O5 from Martin2010 paper. I'll try to ask Ian Martin if he can give me the raw data.
From the loss vs annealing temp I found out below, it seems that the annealing temp for our mirrors will be less than 300C. Since at 300C, silica loss is ~ 1.5e-4, tantala loss is ~ 4e-4. These numbers give the estimated BR noise below our measurement.
ref: silica loss with vs different heat treatment temperature. https://dcc.ligo.org/DocDB/0010/G1000356/001/PennCoatingMarch10.pdf
Martin2010: Class. Quantum Grav. 27 (2010) 225020 (13pp): Tantala loss with different heat treatment temperature
Zach helped me re-setting up the channels for PSL lab. The two channels are:
The sampling rate is set to 10kHz (8192 Hz).
Anti-alias, provided by foton, cheby2, low pass at 4096 Hz, is induced in both channels.
calibration 2^15 count for 20 V -> 20V/ 2^15 = 6.1035e-4 V/count
==Note about start configuring MDV==
Run this from the terminal on ws2:
Then, start matlab and run:
(there are some error messages about the paths that can't be added (matapps_SDE, matapps_path , frame cache, ligotools_matlab, home_pwd.) ,but they are irrelevant.
Now gps and get_data commands are working. We checked with the test signal and see both time domain, and frequency domain. The anti-alias filter is working fine.
I plotted our measurement together with other experiments. The source file and fig files are attached below.
Details about each experiment (cavity length, wavelength), are included in the source file.
Add the measurement from AlGaAs coating, and Silicon refcav (see CRYO:1045). The source file, figs, and eps files are attached in the zip file.
Here is a prelim result for AlGaAs TO opt for ETM coating.
The optimization is named opt_ETM5 in .mat file. The structure is in optical length unit ( the physical thickness = (opt length) * 1064e-9 / n). The first layer is the air-coating GaAs layer . For the current optimization (opt_ETM5.mat) the transmission is 5.4 ppm, the reflected phase is off by about 2 degrees.
ETM parameters used in the optimization
Note about optimization:
To run the code:
I did an optimized structure for ITM and plotted the estimated noise budget of AdvLIGO using optimized AlGaAs coating on ETM and ITM. More details will be added later.
Above: Optimized structure of ITM
Above: AdvLIGO with Optimized AlGaAs coatings on SiO2 substrate, room temp. The plot is generated by GWINC.
I'm working on estimating aLIGO sensitivity when material uncertainties are taken into account. I have a result for a reference cavity, uncertainty due to Ta2O5's Young's modulus might have smaller effect than we previously expected. All plots and code are attached below.
GWINC does not take any uncertainties in material parameters into account, so its noise budget does not have any error bar. We want to know how the noise budget might change due to imprecise knowledge of the material parameters. One particular issue is coating thermal noise that is dominating around 30 - 200 Hz, so we want to know how its level will change with material parameters. Some import ant parameters are loss angles and Young's moduli of each material.
In Hong et al 2013 paper, there is a plot of the calculated coating Brownian noise vs Ta2O5's Young's modulus (YH). The calculated coating BR noise is calculated with the corresponding YH while other parameters are fixed. This would be ok if each parameters were independently measured. In reality, loss angles are measured from ring down measurements, and YH and YL are used to calculated the material loss angles (phiH/phiL), see Penn et al. 2003. So to make the calculation reflects the real situation, we should take the correlation between phiH/phiL and YH/YL into account when we calculate coating BR noise. So the goal is to estimate coating BR noise for aLIGO with some uncertainties from loss angles and Young's moduli of the coatings.
calculate BR noise vs YL and YH (see PSL:1408 for the original code) using numbers from our setup (these can be changed later when we want to apply for aLIGO calculation). The code calculates BR noise with phiL = 1e-4, phiH = 8e-4. the numbers are from our measurement and another ring down measurement. This does not take the correlation between loss any YL/YH into account. I do this to compare my code to Hong's result, and they agree. YL and YH are varied between 80% and 120% of their nominal values (YL = 72 GPa, YH = 140 GPa).
above: Fig1:Thermal noise level of 28 Layer QWL structure, spot size = 180 um as a function of YH and YL
above:Fig2: three slices from the 3-d plot for different values of YL, Y_L min and Y_L max are 80% and 120% of the nominal value.
above:Fig3: three slices from the 3-d plot for different values of YH, Y_H min and Y_H max are 80% and 120% of the nominal value.
Next, let's assume that the values of SiO2 are well measured and the error is much smaller than those of Ta2O5, so we can fix phiL and YL. Then recalculate BR noise when phiH and YH are correlated. I use a calculation from ring down measurement (see PSL:1412 or Harry 2002 or Penn 2003). The equation is
constant = phi_parallel = (YL*dL*phiL + YH*dH*phiH) / (YL*dL + YH*dH)
from this equation, we can write phiH as a function of YH assuming that other parameters are constant. Currently, I'm using numbers from CTN setup.
above: Coating BR noise as phi_H is varied along Y_H (green) compared with the previous calculation (Blue) from fig 2. The two traces cross at YH = 140 GPa. Note that in this plot, YH is varied between 50% and 200% of the nominal value. We see that the uncertainty of coating noise due to YH becomes smaller compared to the previous calculation done in Hong paper.
==what to do next==
From fig3, uncertainty in YL does not change the BR noise level that much, but this calculation assumes no correlation between YL and phiL. I have not been able to include uncertainty in YL and see the effect on phiL yet, because that will need more constraint equation. But I should check if it will greatly change phiL and affect the total BR noise calculation or not.
I'm estimating the BNS range of aLIGO. Here is a quick note about the calculation.
For example, the normal configuration for aLIGO will have BNS in spiral range equal to 178.29 Mpc (based on the current code available on gwinc.
That GWINC link is more than a year old. You're best off just updating your CVS checkout of the code, or getting a new zip file from someone else if your CVS is broken. When I run gwinc with nomm.m, I get R_BNS = 189.5 Mpc.
I just saw you comment. I'll find an update version for GWINC.
Anyway, I have a code to plot the result. I will use it on an updated code.
Some material parameters in the calculation are:
In the IFOModel_rnd.m file which is a copy of IFOModel.m for material params, I use normrnd(mean,sigma) to generate the random value of the material parameters.
Note, for loss angle of SiO2, I have to use abs command to make sure that all the generated values are greater than zero.
This is because the mean is comparable to the standard deviation, and sometime it gives negative values.
Note: I have not taken the coherent between the loss and Young's modulus of Ta2O5 into account yet. I have to read how they measure this more carefully.
Here are prelim results from the above numbers.
above: a histogram of BNS range, due to uncertainties in loss angles/young's moduli of the coatings.
The mean of the histogram is slightly less than the nominal value from GWINC because the mean values of loss angles for fused silica (6e-5) is slightly higher than the original value (4e-5) used in the code.
above: histograms and Gaussian fits for BR noise (blue/green) and total noise and its Gaussian fit (red/cyan) at 100 Hz in the strain unit.
Manassa is helping me installing a camera for scattering measurement. The work is in progress.
I'm borrowing a Prosilica gc750 from the 40m. It will be used for scattering measurement on AlGaAs samples. It is a good idea to have a setup that can quantitatively measure scatter loss on mirrors.
First I tried to install it on the small Acer laptop used with win cam, but it did not work. I'm not sure if the ethernet card of the laptop does not support the camera or not. Now I'm trying to install it on my mac book instead, since Manassa claimed that it worked on her macbook.
I'll write a step by step installation guide once we succeed.
==note about the AlGaAs samples==
I used a green laser pointer to check scattering loss on one sample. I couldn't see any green spot of the laser with my eyes. This means that the scattering is probably less than 100 ppm (according to Josh). Once we use the camera to measure it and it turn out to be smaller. We will probably go to Fullerton to have the samples measured there for better accuracy.
The calculation for LIGO astronomical reach with uncertainties are updated. See the details below.
I got the updated GWINC from Nic. When I run the nomm file, the BNS range is 189.5 Mpc. The nominal value of the refractive index for nH in the code is 2.06 which is the value for the pure Ta2O5. The refractive index for Ta2O5 doped with TiO2 25% (Ta2O5:TiO2) is 2.119 (see Harry et al 2007 paper). So when I changed nH to 2.119, the BNS range became 192 Mpc due to the thinner coating.
The ring down measurements from Harry 2007 paper measure parallel loss of the coating from multilayer coating, then extract PhiH from the measurement. Again, this is done by assuming the knowledge of phiL, YL and YH. The loss angle of silica (phiL) used in the paper is 1e-4 (from Crooks 2006 paper) while the value in GWINC is 0.4e-4. In this calculation, I use phiL = 1e-4 because of a couple reasons:
So the value phiL = 1e-4 is only used for extracting phiH as a function of YH, while phiL = 0.4e-4 is used as a nominal value in noise budget calculation.
Running the code
The calculation is done in the code name BNS_score.m (see the attached zipped file). The file calls on IFOModel_rnd2.m that generates random material parameters by normrnd command. The plot can be made by running plot_hist.m file.
fig1: histograms and gaussian fits for coating BR noise and total noise at 100Hz.
fig2: The astronomical range for BNS, in MPC unit.The histogram is from 20k samples. The average is at 189.2 Mpc, while the mode is around 188 MPc.
I'm setting up a scattered light measurement for AlGaAs samples. The methods are summarized below.
I discussed with Manasa about the setup and how to do the measurement. The goal is to measure scattered losses from AlGaAs samples from a normal incident beam. The setup is shown below.
The setup is in the ATF lab, on the unused optical table. It is too crowded on CTN table. So I will need a to borrow a 1064 laser from somewhere.
The incident beam will have to be slightly angle from the normal angle in order to dump the beam properly.
The arm holds the camera, it can rotate to change the angle to cover the measurement from around 10 degrees to ~70 degrees.
==measurement and data analysis==
How hot do you need to heat it? if the thermal expansion of aluminum/steel is much higher than that of fused silica, then just heating the end cap might be a better idea. Thermal conductivity is also better.
I took some hard yellow foam, made it into a U-shape, and wrapped it with a combination of aluminum and duct tape.
This insulation fits snugly over the PMC and its copper shield. In retrospect, the foam is probably a little too thick. I had to temporarily move the beam dump at the input of the Faraday isolator.
Putting 20 V across the 105 Ω heater produces a change of 5 V on the PMC PZT (when locked). So we need better insulation or more heating.
The CTE of fused quartz is something like 0.5×10−6 K−1, and the CTE of steel is more like 15×10−6 K−1. So I suspect there's not much point in heating the glass spacer if I'm going to leave the steel end cap open to air.
A possible solution is to put a heater on the end cap, but I worry that the differential expansion of steel vs. glass will cause the end cap to pop off the spacer (it looks like it's only held on by epoxy).
A better solution is to improve the insulation on the back end of the PMC. I'll do that next.
I'm testing the setup and a code for extracting scattered light from the images.
I used a red laser pointer to test the scattered light setup. Then took a picture with no light (fig1) and a picture with the incident light (fig2). The scattered light can be extracted by subtract fig1(background) from fig2.
The snapshots saved by SampleViewer are in .bmp file. When it is read by MATLAB, the file will contain 480x752x3 matrix element, Each are varied between 0 and 255. The values are proportional to the brightness (how many photons hit the cell). 480x752 is the resolution of the image, x3 are for R G B color. In our case, the image is greyscale and the values are identical. The code can be found in the attached file.
fig1: The test mirror without incident beam taken as a background image. The image is enhanced by a factor of 5 (by matlab).
fig2: The test mirror with a red incident beam around the center. The image is enhanced by a factor of 5.
fig3: the image is created by subtracting data of fig1 (background) from fig2 (scattered light) and enhanced by a factor of 100. The scattered light on both surfaces can be seen clearly around the center.
==To do next==
I'm checking the linearity of power and exposure on the camera. The ccd counts are quite linear with the exposure setup, but I have to check the power again.
==ccd count vs exposure setup==
The exposure time on the camera can be set to adjust the brightness of the image. Since we might have to adjust it to make sure that the images won't be saturated, it is necessary to check if the ccd count response linearly to the exposure setup or not.
I used a silver mirror as a test sample. The incident power is constant, and the camera position is fixed. Then adjust the exposure from 5k to 30k. I'm not sure if it is in nano second or microsecond unit. [Edit, 20140725: according to page 18 of the manual for the Prosilica GC750, the available exposure options are 30 µs to 60 s, in 1 µs increments. —Evan] But from fig1, the ccd count is quite linearly proportional to the exposure value.
It turns out that when I try to calibrate a sample, the incident power on the sample has to be more (so the power meter can measure some scattered power) and the camera can be saturated. The exposure value has to be around 1000, and I have not checked the response at this level. I might have to remeasure it.
==ccd count vs power==
This measurement is similar to the above. But this time the incident power (to the sample) is varied. The result is not linear. I check the images and see that the bright spot moves. The camera might move during the measurement. I'll repeat this again. It will be complicated for the calibration if the ccd count is not linear with the power.
== To do==
I rechecked the CCD response vs exposure time and power. The results are linear.
After some adjustments (strain relief on the camera's cables, clamping down the camera properly), I made sure that the camera is more stable and repeated the measurement. The CCD response is linear with the incident power on the sample (this is under the assumption that the scattered power is directly proportional to the incident power).
Fig1: CCD response vs incident power. The camera response is linear.
== AlGaAs Samples==
I prepared the sample for measurements. All the samples are quite dirty, especially on the flat sides. So I wiped all of them. I still cannot get rid off some water marks on the annulus of the mirror. It might cause some problems when I optical contact the mirrors. I'll try to clean them later.
fig2: one of the AlGaAs mirrors before cleaning.
I put one of the samples in the scattered light setup. The transmitted beam has a lot of diffused light behind the mirror. The amount of the diffused light changes with the beam direction. I'm not sure exactly why. I'll try to investigate it more. But the scattered light from the sample is very small. Most of the light is from debris on the surface, not the micro roughness of the sample. The amount of scattered light significantly changes with the beam position on the mirror.
fig3: diffused light behind the mirror. It might come from the reflection inside the substrate because the incident beam is not normal to the surface.
I used the setup to measure scattered loss from an REO mirror (mirror for iLIGO refcav, the one we measured coating thermal noise) and get 6 ppm. This number agrees quite well with the previous Finesse measurement.
Finesse measurement from REO mirrors = 9700 , see PSL:424 The absorption loss in each mirror is ~ 5 ppm ( from photo thermal measurement, see PSL:1375). The measured finesse infers that the roundtrip loss is ~ 24 ppm, see here. So each mirror has ~ 12 ppm loss. With ~ 5ppm absorption loss, we can expect ~ 6-7 ppm loss for scattered loss. So this measurement roughly says that our scattered light setup and calibration is ok.
I turned the ion pump for vacuum chamber on. The initial current is 7.3mA ( the value before opening the chamber was 7 uA)
The turbo pump was turned off.
I used optimization codes for ETM. The optimization reduce the PSD of Brownian noise by ~ 3/4 (in units of [m^2/Hz]) from QWL structure.
Since we have not had all the material parameters for aSi:H at 120K with 1550nm, the optimization here is for room temperature with 1550 nm (for Brownian noise only).
fig1: optical thickness for ETM with minimized BR noise. The transmission is 5.4 ppm and the reflected phase is ~ 179 degree.
Parameters/configuration used in the optimization:
It is remarkable that 5ppm transmission can be achieved with just 17 layers of coatings due to the largely different values between nL and nH. This makes the total thickness down to ~ 3 um.
BR noise from the optimized coating is 3.3x 10^-42 [m^2/Hz] at 100 Hz. This is converted to the strain of ~ 5x10^-25 [1/sqrt Hz] for 4 km interferometer.
Note: for QWL structure, with 14 layers + half wave cap of SiO2 (total of 15 layers), the transmission is ~5.2 ppm and the coating Brownian noise is 4.2x10^-42 [m^2 /Hz]. So the optimization reduced the PSD of BR noise by ~ 25%.
Perl scripts for controlling the vacuum tank and slow feedback to the two lasers are acting weird. Usually we can run three scripts simultaneously, but I just notice that only two can be run at the same time. When I restarted the script for acav feedback, the vac temp control stopped. When I restarted the vac temp control, acav slow feedback stopped. I'll check this later.
RCAV transPD_DC :0.54 V
ACAV transPD_DC: 0.16 V (loop might oscillate when DC level was measured, need to double check)
We measured the transmission of the vacuum windows. The total transmission through two windows is 0.975 +/- 0.002.
If we assume that both windows have the same transmission, the transmission for each window will be 0.988.
[Antonio,Tara] We glue PMC back mirror to PZT and wait for it to settle.
Since we have all parts for the steel PMC (body/PZT/Mirrors) we start putting it together. The first step is using epoxy to glue the back mirror to the PZT.
There is a little problem. The soldering tin on the PZT gets a bit to the edge of the PZT, see picture. When we put the PZT on the steel end cap, one side of the soldering tin electrically connects to the end cap.
So we decide to put a kapton tape as an insulator between the pzt and the end cap. (We thought about resoldering the tin, but we were not sure if we would make it worse).
It is quite hard to center the mirror-pzt on the end cap, so we plan to use a fixture to keep the mirror center at the end cap. It will be something similar to the plastic piece we used for cavity-mirror assembly.
We want the mirrors' positions to be as precise as possible to reduce clipping loss, and beam alignment problem.
See the rest of the picture in Picasa
Note about epoxy: The epoxy we use is EP-30 (suggested by Rick Savage, provided by Callum). There's a test procedure to check if we mix the epoxy correctly or not.
After mixing the epoxy, you have to put a small amount of epoxy in an oven at 200 F for 15 minutes to check if the mixture is good or not.
If the epoxy in test came out smooth and hard, it is good. You can proceed with the work. We tested that, and our mixture was good.
We ordered fixtures for gluing mirror-pzt-end cap. Waiting for the glue to settle.
The glue is dry and the back PMC mirror is steady. we are ordering the o-ring for clamping flat mirrors on the pmc. See more pictures here.
To do next:
We tested one of the two new PMCs. finesse is ~ 500 and the PZT works fine.
We assembled two new PMCs for testing how the new designed PMC would be. They looked great. The PZT wires were connected to BNC connectors.
We temporarily put the new PMC in the north path. The Faraday isolator (as an extra back reflection protection) was removed, and replaced by the new PMC. (The original marking for the PMC is still visible on the table, where the waist radius is 370 um). We used a post to clamped the PMC on the 2" block.
As a quick test, we have not mode matched the beam into the PMC yet. We just maximized the coupling by using two steering mirrors in front of the PMC.
The measured finesse for the new PMC is ~ 300. The previous calculation was wrong because of the wrong calibration.
Finesse measurement revisited: I rechecked the Finesse measurement and found that I got the same result, so I realized that the calibration might be wrong. So here is the explanation
PZT range revisited: I mentioned in the previous entry that I can find several (4-5) TEM00 within 0-100 V applied to the PZT. This number should be wrong because we can expect only ~ 6 resonance over 200 V (3 um), or ~ 3 resonance over 100 V. It turned out that what I saw was not real TEM 00, but something else that made me think I saw some hysteresis.
To Do Next: Anyway, the PMC/PZT are good. We will try to lock it tomorrow.
We are hacking the PMC card, to try to lock the PMC without using a computer.
Aidan helped me try to lock the PMC with the current equipment (LIGO PMC card, the schematic can be found here). Since, the computer for controlling the card is not here and we cannot put it back together within one week I have left, we are trying to use the card and send in signals to control the card manually. For today test, we used a spare PMC left on the crate (I think Frank used it to drive the PZT for shaking the table, long time ago. It might be modifed from what we saw on the schematic.)
We tested the control signal for the high voltage output using the following procedures.
The HV drive is working and linear with the input control [HV = -24.1*Vin + 40] (Vin = [-6,2] V, HV = [4,185] V). At first, we injected the signal at INOFFSET2 (through R4), but we couldn't see the signal out. I'm not sure why, but we are working on it.
I checked the VME crate, and made sure that the PMC cards/ LO were functioning.
There was a problem with the VME crate and we couldn't turn on the kepco power supply for +/- 24 V for the PMC servo cards and 21.5 MHz LO on the crate. There were wires that connected to the power supply and the loose ends shorted together. I fixed that by taping over the wires. Now the power is up +/- 24V.
Summary of the crate status:
I showed Antonio how to do optical contact (refcav-mirror setup). The videos and pictures are posted on Google photo
I used a blank plane mirror (from coastline optics, intended for AlGaAs coating) and bonded it on the spare 1.45" refcav. It took me 4-5 tries and I scratched one mirror (I put it back and marked the box) before I could get a reliable bond. In the videos, I added comments for each failure. Mostly I think the problem is only cleanliness of the tools and the solvent.
After that I removed the mirror from the refcav. First I tried to use a setup to push the mirror along the mirror surface. To my surprise, the mirror did not pop out, but just slid off of center and still stuck on the surface of the refcav.
So I used a razor blade to wedge in between the mirro and the refcav, add some isopropanol. With little effort, the mirror popped out nice and easy. The edge of the HR surface of the mirror is beveled, so it is easy to wedge in a razor blade without scratching the refcav or mirror's surfaces.
To sum up, before trying to do the optical bond we should
To do the bond
Trouble shooting: If you can't form the bond
We still need two SMA cables. One connects between 21.5Mhz EOM and PMC servo card, another one connects between PMC PD and the servo card.
The 21.5 and 35.5 local oscillator were in the wrong slots, we fixed them.
The 21.5 MHz photo diode that detects the reflected beam from PMC saturates at 15 mW.
Now I'm trying to optimize the PMC setup so that we have maximum transmittedd power.
I don't know why I can't lock the PMC. After changing the 21.5 MHz card because of the loosen SMA connector, the 21.5 MHz EOM is working.
The error signal looks good. I adjusted the gain, flipped the phase by 180 degree, and still cannot lock the cavity.
(The medm was frozen this morning, Peter helped reset it back to work this after noon.) It might be insufficient amount of power coupling into the cavity.
The minimum reflected beam I could get is only ~1/2 of the total DC power, I'll try to align the beam and move the lens a little bit more to see if I can optimize it better.
So I skip this PMC part for now, and pre align the path to mode cleaner. The mode matching is ok. Two lens, f1=114.5 and f2=286.3 mm are good. A CCD behind the cavity is set in place.
After adding another 1/2 plate to have P wave into the cavity, I can lock the PMC cavity. It's been 30 minutes so far.
There is only one transmitted beam now (there were two when I used S wave.)
When I work or knock on the table, sometime the beam switches to another mode (might be it's side band.)
It's very close to the main TEM00 mode. I need to adjust the DC offset a little bit to get back.
The incoming power is 9 mW, and the Transmitted beam has ~ 6 mW.
RF Amp: 7V
Phase shift: 2.87 + 180
Gain: 27.91 dB
DC offset: -2.3 V
I tried to pre align the ref cavity. It's harder than I thought, can't see the beam that well. I'll have to check the manual for the laser controller, so that I can
scan the RefCav when I align the beam into the cavity.