The new optimization is less sensitive to the values of refractive indices, but the overall error will not change much if other material parameters have the uncertainties as we estimate.
Summary: see update of error analysis in PSL:1356. The issues from the previous entry are cleared
1) show error analysis
Today Tara showed me where to find isopropanol in order to clean the Peltier element. After cleaning it carefully, the TEC controller worked fine again! I am going to avoid using the silicone thermal paste for now in order to avoid this same problem, but if it becomes necessary I will add small amounts very carefully. I'm not sure how safe it is to clean the Peltier element often. The thermistor is being held onto the diode mount with aluminum tape.
I worked on tuning the PID gain on the TEC controller. It seems a lot less stable than before, having a hard time settling on one temperature. Perhaps this is because I am not using the silicone thermal paste. I want to continue tweaking these settings, although I have them at something reasonably workable right now. It takes a minute or two for temperatures to settle, but they seem stable once a temperature has been reached.
I cleared off a shelf in the ATF lab to keep my things. The collimating lens and lens adapter arrived, and Tara and I had to search for awhile to figure out where he put it (since they arrived while I was away). I put the lens into the lens adapter, and put this into the lens mount. Immediately, I noticed 2 problems which need to be fixed immediately:
Today I tried to calibrate the PID gain for the TEC controller. I noticed some connections needed repairing to I resoldered them, and checked every single connection.
However, the TEC controller still couldn't turn the Peltier element on, citing a "OPEN" problem (I believe according to the manual this means that something about the TEC connections are wrong). I checked these several times with my past notes and the instruction manual, but could not fix the problem. Then I tried cleaning the silicone thermal paste off of the Peltier element and was able to briefly make the Peltier element turn on. As soon as I tried reinstalling this in the ECDL setup, it stopped working. I was able to get the element working again briefly, but it was never stable (would stop working after a minute). I believe that I can use isopropyl alcohol without damaging any parts, but I want to do more reading online before I try this so that I am sure. It seems that trying to wipe the silicone paste out is insufficient, as I spent awhile trying this to recreate my results.
I'm trying to find another optimization that is less sensitive to change in nH and nL. Here is a few thought and a few examples.
We have seen that uncertainties (withing +/- 1%)in nH and nL result in higher TO noise (up to 10 time as much) in the coating. So we are trying to see if there is another possible optimized structure that is less sensitive to the values of n. We estimate the value of nH to be 3.51 +/- 0.03, and nL to be 3.0 +/-0.03. (The numbers we have used so far are nH/nL = 3.51/3.0, while G.Cole etal use nH/nL = 3.48/2.977.
The algorithm is similar to what I did before[PSL]. But this time the cost function is taken from different values of refractive indices. The values of nH and nL used in this optimization are
The cost function is the sum of the TO noise level at 100Hz, Transmission, and reflected phase, calculated from 9 possible pairs of nH and nL values. The weight number from each parameters (which parameter is more important) are chosen to be 1, as a test run. I have not had time to try other values yet, but the prelim result seems to be ok.
[Details about the codes, attached codes]
Note about the calculation,
The calculation follows these facts:
==results from QWL (55layers) and 4 other optimized coatings.==
Each plot has three traces (blue, black, red) for different values of nH (3.48, 3.51, 3.54). nL is varied on x-axis from 2.97 to 3.03. The first result is from QWL coating, with 55 layers. This serves as a reference, to see how much each property changes with the uncertainty in nH and nL.
I tried to change the cost function in the optimization code and numbers of layer to see if better optimized structure can be done. The optimized structure (V3,4,5) seems to be less sensitive to the values of n, see below.
Above: from QWL coatings, 55 layers. nominal transmission = 100ppm. We can see that the transmission of QWL coatings is still quite sensitive to uncertainties in nH and nL.
Above: First optimization reported before, TO noise is larger by a factor of 10 in certain case, and transmission can be up to 500 ppm. This coating is very sensitive to the change in refractive indices.
Above: opt3, obtained from the code using the new cost function discussed above. 55 layers, nominal transmission = 150ppm. The TO noise is less dependent on nH and nL, but the transmission is still quite high.
Above: opt4, the weight parameter for transmission is changed to 3, 57 layers.
above opt5,the weight parameter for transmission is changed to 50, Lower/Upper thickness bound = 0.1/0.5 lambda, 59 layers
Above: Opt6, the weight parameter for transmission is changed to 500, Lower/Upper thickness bound = 0.1/1.2 lambda, 59 layers
From the results, optimized structure # 3,4,5 seem to be good candidates. So I ran another monte carlo error analysis on opt1 (as a reference), opt3, opt4, and opt5, assuming errors in both material properties and coating thickness. Each one has 5e4 runs. Surprisingly, the results from all designs are very similar (see the plot below). It is possible that, by making the coatings less sensitive to changes in nH/nL, it is more sensitive to other parameters (which I have to check like I did before). Or the properties are more dependent on coating thickness, not material parameters (this is not likely, see psl:1345). Or perhaps, there might be a mistake in the monte carlo run. I'll check this too.
I'll update the coating structure and forward it in google doc soon.
OK, I borrowed a Watec from the ATF. It is more sensitive than the jWin I was using, but judging by the graininess we appear to be close to the camera's noise floor. For the attached pictures I turned up the power on the RFPD from 1.0 mW to 1.5 mW, and that seemed to help a little.
No (as I already told Tara).
The PD reflection is distorted and must be dumped in razor dump or black glass.
The mirror leakthrough can be detected easily by a CCD. CCD can easily see uW beams, but you have to use something beyond the $10 ones that Frank bought.
I placed a CCD camera behind the steering mirror directly before the south RFPD in the hopes of getting a handle on the shape of the refl beam while the refcav is locked or unlocked. Unfortunately I think the transmission through the mirror is too low; you can barely make out the refl spot when the cavity is unlocked, and it disappears when the cavity is locked.
Previously (PSL:798), Frank and Tara used a CCD camera to monitor the reflection off the RFPD itself. This reflection has enough power to be seen on an IR card, so perhaps this is the way to go (if we trust the face of the RFPD to not distort the beam).
Last week I talked to an engineer at Newport, and he agreed that the discrepancy (1 µW/V versus 30 µW/V) seemed unusual. Tara and I are sending this EOAM back to Newport for inspection; it should ship out today. We await Newport's diagnosis with bated breath.
I also mentioned to Newport that this EOAM has a minor annoyance with the two hex screws on the bottom of the case: the screw heads jut out slightly from the case rather than sitting inside the countersink (didn't think to take a picture, sorry). This causes the EOAM to have a slight roll when sitting on its kinematic mount. Tara was able to add a washer to the 1/4-20 screw holding the EOAM in order to mostly cancel this roll, but it would be nice to not have to deal with it in the first place.
If that's true, then it means that a 1% deviation in the index of refraction of the low index material can by a 10x increase in the TO noise. Is this really true?
That surprises me too, but, that's what the calculation gives me. It is also strange that deviation in nH has smaller effect on to TO noise than nL does. I'm checking it. I ran the code one more time, and still got the same result.
Note: when I calculate the error in refractive indices, I assume that the physical thickness is constant = x * lambda/ n_0. Where x is the optical thicknesss. But if the the actual refractive index is not n_0, it means the optical length is not x, but x*n/n_0. I think this is a valid assumption, if they control the physical thickness during the manufacturing process.
update:Tue Sep 24 02:09:28 2013
The TO noise level does really change a lot when nL is nL + sigma (nL=3.0+ 0.03), dark green trace. Most of the change comes from TR noise level (not shown in the plot). TE noise remains about the same level. It might be worth a try to find another optimization that is less sensitive to the change in value of n. I'll spend sometime working on it.
I removed 29 cm of SMA cable between the south RFPD RF output and the south TTFSS PD input in order to make the PDH error signal more symmetric. Relevant oscilloscope traces attached.
The numbers in the table are the ratio between the TO noise when the parameter is changed by 1sigma and the TO noise calculated form the nominal value.
About the Poisson's ratios, Matt asked me to check for the values between 0.024 to 0.32, and the TO cancellation becomes much worse. I looked up papers about AlGaAs' Poisson's ratios. Most of the literature report the value ~0.32. I think we don't have to worry about it that much.
Krieger etal 1995 Table2, and ref 16 17 thereof.
Wasilewski et al1997 page 6, also discuss about the calculation and the measurement of poisson value in GaAs and AlAs, the value is still in the range of 0.27-0.33, not 0.024. The value of 0.27 is already considered very low.
zhou and usher has a calculation for poisson's ratio of AlAs. they report ~0.32, see table 2. and there references.
So I don't think Poisson's ratios of the materials will be a problem for us, since the reported numbers agree quite well.
I don't understand these values for n.
How can nH be 3 or 11? Isn't just that nL is ~1.45 and nH is ~2 ? I would guess that the sigma for these is only ~1% of the mean values.
In our meeting, Eric mentioned that there might be some uncertainty in how the average coating properties are calculated.
To see how much it matters, I set the average properties to either that of the high-index (H) or low-index (L) material, and calculated the ratio of the new thermo-optic noise to the original calculation (TO'/TO) and the ratio of the new thermo-optic noise to the unchanged Brownian noise (TO'/Br) for Tara's optimized coating structure. The results are in the table below:
C = Heat Capacity/Volume, k = thermal conductivity, alpha/a = thermal expansion
alphaBar_c and alphaBar_k are more complicated, since they take into account the Poisson ratio and Young's modulus of the coating materials, and may be wildly different from the thermal expansion coefficient. alphaBar_c is an average of alphaBar_k values, and when I use "alphaBar_k = alphas", I'm indicating that alphaBar_k is an array, and I have replaced that array with an array of the corresponding thermal expansion coefficients. As we can see in the final four rows of the table, alphaBar_c has a much smaller affect if we use an alphaBar_k value with all its added moduli and ratios instead of just regular thermal expansion. alphaBar_k_TR is the array of values used in the "Yamamoto Correction" to calculate the appropriate alphaBar for the thremo-refractive noise.
This all indicates to me that while most of the averages won't have much effect on our cancellation, a mistake in the calculation of alphaBar_k will.
The difference between alphaB_k and alphaBar_k_TR (in the last two rows of the table) is also interesting. Kazuhiro Yamamoto tells us this equation is correct, and explains the correction here. It's apparently because there is no added strain in the substrate due to the change in the refractive index, while there is strain for the thermal expansion.
I'm using Matt's code to do error analysis for AlGaAs coatings. This time I vary materials' parameters and compare the thermo optic noise, reflected phase and transmission. There is no alarming parameter that will be critical in TO optimization, but the values of refractive indices will change the transmission considerably.
Eric, Matt and I discussed about this to make sure that even with the errors in some parameters, the optimization will still work.
Parameters in calculation and one sigma estimated from Matt
% Coating stuff
betaL = 1.7924e-4 +/- 0.07e-4; %dn/dT
betaH = 3.66e-4 +/-0.07e-4 ;
CL = 1.6982e6 +/- 5% ; % Heat Capacity per volume
CH = 1.754445e6 +/- 5%;
kL = 69.8672 +/- 5% ; % Thermal Conductivity
kH = 55 +/- 5%;
alphaL = 5.2424e-6 +/- 5%; % Thermal expansion
alphaH = (5.73e-6 ) +/- 5%;
sigmaL = 0.32 +/- 10%; % Poisson Ratio
sigmaH = 0.32 +/- 10% ;
EL = 100e9 +/-20e9; % Young's modulus
EH = 100e9 +/-20e9;
nH = 3.51 +/-0.03 ; % Index of refraction
nL = 3.0 +/-0.03 ;
* Note: when I change nH and nL value, I keep the physical thickness of the layers constant. This is done under the assumption that the manufacturing process controls the physical thickness. The optical thickness in the calculation will be changed, as the actual dOpt = physical thickness * actual n / lambda. And averaged values of coatings will depend on physical thickness.
This is fixed in Line 120-180
== Effect on TO cancellation from each parameters==
First, I calculate the TO cancellation when one of the parameter changes. Some parameters, for examples, Poisson ratios, Young's moduli, are chosen to be the same for both AlAs and GaAs. In this test, I vary only one of them individually, to see which parameters are important. The numbers indicate the ratio between the PSD of TO noise with change in the parameter and the optimized TO noise . Not the standard deviation of the parameters.
Turns out that the change in Young's moduli and Poisson's ratios are quite important.
==Effect on TO cancellation, from all paramerters==
Then, I calculate the TO noise when all parameters vary in Gaussian distribution, similar to what I did before,all parameters are uncorrelated. The histograms from 1000 runs are shown below.
I'll try more run overnight. Each run takes about 1 second.
== combined effect from errors in layer thickness and material parameters==
Since the comparison does not need to calculate the thermal fluctuations and finite size correction all the time, I cut that calculation out and save some computation time. Now I compare errors from
Each simulation contains 5e4 runs. The Transmission varies a lot depending on the material parameters ( mostly refractive indices, see the cyan plot).
The cancellation seems still ok. Most of the time it will not be 10 times larger than the optimized one. Only the transmission that seems to be a problem, but this is highly depends on refractive indices. It's weird that the error makes the mean of the transmission smaller.
Details for AlGaAs coatings order
Above, plot of ratio of power due to finite size mirror P(r) / P0, P(r) is the power of the beam at radius r from the center. G Cole said that the wafer can be made to 8mm diameter. diameter between 5-8 mm should be good for us.
Tara noticed an accidental re-definition in my old code. I fixed it, and updated the svn. This fixes most of the discrepancies, but shifts the difference in thermo-optic to the low-frequency region.
Attachment 1 is the comparison from case 3 between mine and Tara's calculations of his optimized coating structure.
Attachment 2 is the comparison from case 2 between mine and Tara's calculations of a 55-layer 1/4-wavelength stack.
I discussed the calculation with Matt. The error in TO noise is large because it is a fraction of something small. Mostly it comes from TE part. The error in TO noise appears large (10%-20%) because the TO level is small. Otherwise, the rests are in good agreement, and I think we should be able to order soon.
Below, summary of the calculation, dTE is alpha_effective * coating thickness, dTO is beta effective * lambda. 0.2% difference in dTE and 0% difference in dTR can cause error upto 40% in dTO when dTE and dTR cancel each other really well. But this will be insignificant, since the final TO levels are still in the same magnitude.
The summary of the TO cancellation is in wiki page AlGaAs
I checked the calculation. I think most of the discrepancies are from the thick coating correction calculation (from Evans etal paper). The error is frequency dependent, and the calculations that involve frequency dependence are temperature fluctuation and thick coating correction. The temperature fluctuations are the same from our results. So it is most likely the thick coating correction. I checked and the corrections did differ at high frequency.
I need to take a closer look to tell exactly where the errors are. Since the error is small and only at high frequency (around the shot noise limit, 10kHz), I don't think it will be a problem for us.
Yesterday I measured the noise of the refcav PDH loops. Because of RFAM effects, possible nonlinearity in the RFPD response, etc., the correct way to measure the loop noise is to take the PSD of the error signal (Common OUT1 on the TTFSS) while the cavity is unlocked but light is still incident on the cavity and on the RFPD.
For these measurements, the south TTFSS gain was 642 common and 702 fast, and the north TTFSS gain was 802 common and 835 fast; these are the highest gain settings I could achieve before the loops started to oscillate when locked. There was 1 mW of light incident on each cavity.
Plots and data are attached. I've converted from voltage to frequency using the slopes I found in PSL:1339. Current thoughts:
Optimized coatings structure.
I took measurements of the carrier and sideband power transmitted through each cavity in order to get the modulation depth Γ of the EOMs. The modulation depth is related to the transmitted powers by Γ2/4 = PSB/Pcar. [Edit: I checked last night in Mathematica, and it seems the approximation Γ ≈ J1(Γ)/J0(Γ) is good to about 1% for Γ < 0.3.]
First I aligned the cavities to get good refl visibility (about 90%). Then I aligned the transmitted beams onto the ISS transmission PDs. Then I unplugged the EOM HV actuation on the TTFSS.
To get the transmitted carrier power, I locked each cavity as usual and then wrote down the voltage on the ISS PD. To get the sideband power, I flipped the sign of the fast actuation on the TTFSS, thereby making the servo lock on the sideband. I then wrote down the voltage on the ISS PD. I also blocked each transmitted beam to get the dark voltage on the ISS PDs.
For posterity, I also took triangle-wave sweeps of the ISS transmission, the refl DC, and the error signal. The oscilloscope traces are attached. [Edit: from a quick look at the error signal traces, I get slopes of (164±10) kHz/V for the south cavity and (199±12) kHz/V for the north cavity.]
In other news, the south PDH error signal looks a bit asymmetric; I think it might need a phase adjustment.
combined PDFs with pdftk:
pdftk *.pdf cat output MattThermal.pdf
and saved as PDF-X for thumbnail compatibility
Neither Tara nor I can get the north New Focus 4104 to put out a significant amount of power modulation, despite going through (what we think is) the biasing procedure several times. We're getting modulation on the order of 1 µW/V, compared to 30 µW/V when we first installed the south EOAM (PSL:1287).
To review, these New Focus EOAMs consist of two lithium niobate crystals mounted with their fast and slow axes orthogonal to each other. If the crystals are the same length, then with zero applied voltage the EOAM should have no birefringence. Any applied voltage causes the EOAM to become birefringent; the voltage required to produce a λ/4 retardation between the two optical axes is called the quarter- wave voltage, and the voltage required to produce a λ/2 retardation is called the half-wave voltage (Vπ).
To use the EOAM for intensity modulation, we put down a HWP before the EOAM to make sure the input beam is either p- or s-polarized relative to the optics on the table. The EOAM crystals are mounted at 45 deg., so the input beam therefore is projected in equal parts onto the EOAM's two optical axes. After the EOAM there is a QWP with its fast and slow axes aligned to the EOAM's optical axes [Edit: actually the manual says to align the QWP axes to be horizontal and vertical wrt the table, which I don't understand. At any rate, neither configuration makes the EOAM work.], and following that there is a PBS which passes only p-polarized light. The intensity of the light transmitted through the PBS is a linear function of the EOAM birefringence only when the beam entering the PBS is nearly circularly polarized, so the purpose of the QWP is to optically bias the beam so that we can actuate around zero volts on the EOAM. (The alternative is to have no QWP and instead electrically bias the EOAM to its quarter-wave voltage.)
Anywho, the procedure that Tara and I have gone through is
After this, the setup should now give linear intensity modulation when a few volts are applied to the EOAM. For the south EOAM this procedure worked fine—by applying a few volts to the EOAM we could see the power change on the ThorLabs power meter. But with the north EOAM the power changes are much, much smaller.
In preparation for tomorrow's sprinkler installation, we have removed any extraneous optics, cables, and electronic equipment on and around the table. Everything on the table is now covered by a drop cloth.
I made a quick inverting op-amp integrator which kicks in at 860 Hz at has gain 10 at infinity. The feedback is a 5.6 kΩ resistor in series with a 33 nF capacitor. On the inverting input there is a 560 Ω resistor.
I put this after the SR560 with gain set to 100 and bandwidth set to 30 kHz. It seems like this gives good RIN suppression.
I changed the values so that the feedback is 13 kΩ in series with 1.2 nF, and the inverting input is 1.3 kΩ. This puts the zero at 10 kHz.
I duplicated this with a second OP27 on the same circuit board, so now there is an integrator for each cavity.
Last night the best results seemed to be achieved with the SR560s set to G = 100 with a pole at 10 kHz.
The cause of the peaks around 1kHz in RIN is solved, PMC is the reason. After damping it, the peaks disappears.
Short notes from tonight measurement:
need to buy:
I'm trying to understand the measured RIN in the setup. The evidence suggests that the measured RIN in 100Hz- 6kHz, is real intensity noise and not associated with alignment + jitter.
As seen in PSL:1329 that we might be limited by RIN at high frequency, I tried to figure out what cause the shape of the RIN around kHz to be mechanical -like peaks. So the problem can be minimized, and does not have to rely on ISS that much.
My assumption was that they were from mirror mounts, because
So to test this, I measured RIN before and after ACAV (NOTE:ACAV path has PMC in it), when
above, beam path in front of ACAV, before the beam enters ACAV. The PD for RIN measurement is circled in blue.
above, beam path behind ACAV.
If the measured RIN was from the jitter, RIN after the cavity should change with the alignment, and RIN before the cavity should not change much. I made sure that the spotsize on both PDs are significantly smaller than the PD to make sure that any jitter in front of the cavity should not change the power level that much.
==comments about the result==
==To do next==
The measured RIN is measured and converted to frequency noise via photo thermal effect then compared to beat. The effect seems to be significant now since we lost the common mode rejection.
I measured RIN after ACAV (there is only one PD behind ACAV right now. we will add another one for RCAV soon). The magnitude is comparable from what we measured before but the peaks seem to change, see PSLPSL:1326, :PSL:1308, (8"cavity) PSL:742 .
The peaks around kHz are more clear. I'm not sure where they are from, but I think it is associated with vibration on mirror mounts that causes beam jitter. Because the peaks look like mechanical peaks, and this time the cavities are shorter, the beamsize is smaller from 8" cavities, the same beam misalignment will cause the power coupled into the cavities to change more compared to that of 8" cavity. We can check that by mis-aligning the input beam a bit, and see if RIN becomes larger or not.
The coupling from RIN to frequency noise is discussed in PSL:1328
I applied that to the measurement and here is the result. Note, only the effect from one cavity (ACAV) is taken into account.
The peaks seems to match up, especially around 20-30Hz and around 1kHz, see the zoomed in picture below. This makes me think that we might be limited by RIN noise now.
To Do next:
I've taken the above RIN data and combined it with the intensity-to-frequency TF in PSL:1316 to arrive at an estimate of the RIN-induced frequency noise.
By eye, I fitted the magnitude of the transfer function from Tara's farsi.m code to the following model:
The first attachment shows this fit compared to the original TF.
I used this TF (along with the dc power 0.74 mW incident on the cavity) to convert the measured RIN (suppressed and unsuppressed) into frequency noise. I multiplied the result by a fudge factor of 3 to account for the fact that the TF we measured was a factor of 3 higher than the expectation.
The result is shown in the second attachment. Since this only with G = 500, Chas's high-gain ISS board should crush the RIN well below the expected Brownian noise.
Short note from tonight measurement:
1) scattered bump from dc to 100Hz is mostly from seismic. It is worse during the day. It gets smaller at around 3-4 am. Unless we have a better seismic isolation, we might not be able to see anything below 100Hz.
2) RIN shape from RCAV changes, reasons still unknown. (DC level 0.7 V)
3) I might see the effect from RIN induced TO noise at frequency ~ 1-3 kHz. (compare RIN and beat).
I'll get into details tomorrow.
At Tara's suggestion, I implemented a simple ISS by feeding the output of the PDA10CS into an SR560 (ac-coupled) with some gain, and then the output of the SR560 into the EOAM.
I found that by turning on a 6 dB, 30 kHz low-pass filter on the SR560, I could put the gain at 500 without saturating the SR560 output. No inversion is necessary because positive voltage on the EOAM decreases the beam power (so there is already a minus sign in the loop).
I monitored the RIN by feeding the output of the PDA10CS into the SR785. The in-loop RIN is suppressed by a factor of 6 or so. Once Chas's board is here, the suppression should be much greater (since the gain will be 106 at low frequencies).
The shape of the RIN spectrum has changed compared to the previous RIN measurement. The 2 kHz peak is gone, and the shelf from 100 Hz to 1 kHz has dropped. Maybe it's because Tara has damped a lot of the mechanical resonances of the table optics with rubber stoppers. The low-frequency RIN remains at a few times 10−4/rtHz. According to Tara, this is probably induced by seismic coupling (not by fluctuations from the laser), and so the right way to make it go away is to float the table.
There is a minor mystery here. Based on the previous RIN measurement, I expect the dark noise of the PDA10CS to be at 7×10−7/rtHz or so abve 1 kHz. Why have I apparently been able to measure below this noise floor in the attached plot?
I used the black voltage calibrator to give the south EOAM a DC voltage, and then used the ThorLabs power meter to read off the DC power level before the PBS that used for picking off the RFPD path.
I find the volts-to-watts conversion is (5.93±0.12)×10−6 W/V. This will, of course, change if we change the input power level into the EOAM. I guess if there's a more lasting message here, it's that we've got the orientation of the QWP after the EOAM in a pretty good place, since there's no visible nonlinearity in the attached plot.
Can you please explain how the seismic noise coupling is estimated for the noise budget?
Since the cavities are now on the same stack it seems tricky. I guess that some stack tilts produce differential vertical accelerations on the cavities. How much of the noise below 100 Hz is from scattered light?
The estimated seismic noise in the plot uses the coupling calculated by COMSOL model, see PSL:1060 and PSLL1065. It is the coupling between acceleration to the cavity displacement noise. It is just an upper bound of the seismic noise, no common mode rejection is used in the calculation. (I have to check if the seismic noise data in the noise budget is from floated or unfloated table). So far, only displacement noise from vertical seismic motion is calculated in the noise budget.
I'm certain that the noise bump below 100 Hz is mostly scattered light induced by any vibration on the chamber. The reasons are:
So I don't think we really hit the actual seismic-driven displacement noise yet ,and what we see is mostly from seismic-driven scattered light which I don't know how to calculate. I ordered a new set of table leg to replace the current ones that leak. They should be here next month.
Coating optimization and error analysis are updated, see PSL:1320.
It's a quiet night, so I went down the lab to measure the beat signal. We are getting close. I think I have to review my noise budget calculation and estimate the error in the measurement carefully.
So after a few things Evan and I did a few days ago:
Then I measured the beat signal.
We reduce some noise from scattered light at frequency below 100 Hz, we are limited by some white noise at high frequency ~ above 1 kHz.
fig1: measurement vs noise budget
fig2: zoom in. The slope of the measured signal agrees well with the slope of thermal noise.
I updated the optimization and error analysis. The error in optimized structure is comparable to that of a standard quarter wave length structure.
After a discussion with Rana, Garrett, and Matt, I fixed the thermo-optic calculation, and the error analysis done in PSL:PSL:1315. The modifications are
1) fix the TO calculation (Yamamoto TR correction): There is a modification for TR correction that is not in Evans etal 2008, paper. I contacted M. Evans to ask about the details of this correction which is done in GWINC.
2) Try another optimized coatings with the correct TO calculation: After the correction, I ran doAlGaAs.m code, cf PSL:1269 using fmincon function , to find another optimized structure. The result is shown below.
above) layer structure in optical thickness, the .fig and .mat file are attached below. Note .mat file contains 54 layers, you need to add 1/4 cap to the first entry to calculate the noise budget.
above) noise budget of the optimized coating.
3) Repeat the error analysis : This time I used the following assumptions (from G Cole)
Fig1: Above, percentage of error distribution between the two materials used in the calculation. nH(red) has 2 sigma = 1% and nL(blue) has 2sigma=1%.The same error distributions are used for both optimized layers and QWL layers in comparion, see fig2.
The section below is the algorithm used to distribute the error, this one makes the error between the two materials to be the same sign. The whole code can be found on svn.
mu1 = 0;
sigma1 = 0.5; % 2sigma is 1percent;
mu2 = 0;
sigma2 = 1;
run_num = 5e4; % how many test we want
errH = normrnd(mu1,sigma1,[run_num,1]); %errH in percent unit
errL = normrnd(mu2,sigma2,[run_num,1]); %errL in percent unit
errL = abs(errL).*sign(errH); %make sure that errH and errL have the same sign
dOpt = xout; % xout from doAlGaAs (optimized layer)
dOpt = [ 1/4 ; dOpt]; % got 54 layer no cap from doALGaAs, need to add the cap back
dOpt_e = zeros(length(dOpt),1);
for ii = 1:run_num;
dOpt_e(1:2:end)= dOpt(1:2:end)*(1+ errH(ii)/100 );
dOpt_e(2:2:end)= dOpt(2:2:end)*(1+ errL(ii)/100 );
This time I calculated the change in reflection phase (TOP left), the ratio between TO noise from the coatings with error and the coatings with no error(top right), transmission (bottom left), and ratio of BR noise ( bottom right). The result from the optimized coating(blue) is compared with the QWL coating (black).
Fig2: Error analysis, in 5e4 run. Blue: from optimized coatings Black:from 55 QWL coatings, from 5x10^4 runs.
Reflection phase: The reflection phase can be away up to ~6 degree. The power at the surface will be ~Finesse/pi * Power input * sin^2 (6degree) ~ 50mW. Seems high, but this is about a regular power used in the lab.
Ratio of PSD TO/TO_0 : At worse, it seems the PSD TO noise will be ~ a factor of 10 higher than the design. However, this will be still lower than BR noise. I plotted only the error distribution for optimized coatings because for QWL coatings, the ratio will be about the same, since TO is dominated by TE.
Transmission: Most of the results are within 197-200 ppm. The optimized coating has transmission ~ 197ppm. The QWL with 55 layers has transmission ~100ppm.
Ratio of BR: not much change here.
The turbo pump is removed, and the ion pump is on. The initial value is ~7mA.
I removed the turbo pump and turn on the ion pump, see the procedure on wiki page. The initial value on the ion pump is ~ 7mA, similar to the last time we opened the chamber although this time I left the turbo pump on 4 days instead of 2 days. So I think this is the limit of this turbo pump.
Here is a summary for how I verify the codes for TO calculation.
So far, we have been using a set of modified GWINC codes to calculate TO noise, but I have not mentioned how did I make sure that the codes were reliable. So I'll try to explain how I check the codes here.
==What do we compute?==
For the TO nosie calculation and the optimization, we are interested in:
==Beta calculation check==
For TR coefficient we can compare GWINC with an analytical result (see Gorodetsky,2008, and Evans 2008) (when # of layers ~ 50 or more), see psl:1181. I tried the solution with nH, 1/4 cap and nL, 1/4 and 1/2 cap. All results agree.
==Alpha calculation check==
There is no complication in this calculation. The effective alpha is just the sum of all layers. This calculation is quite straight forward.
This was done by reducing the coating layers to one or two layers and comparing with an analytical solution by hand. I checked this and the results agreed.
So I think the calculations for TO noise is valid, the noise estimated from the optimized coatings is done with some error check (previous entry). I think we should be ready to order.
We modified the EOM driver, so that the resonant frequency is now~ 14.75MHz. The full test will be done later.
As mentioned in PSL:1311, the resonant frequency on the EOM driver was not at 14.75MHz. Evan and I discussed about how to modify it and decided tof change L4 from 1.4uH to 3 uH, see the schematic here.
above, the driver after the inductor was replaced. The new one has a shield to reduce any magnetic field leakage. The legs are not fit with the footprint on the PCB, so I had to solder it to another wire to reach the footprint.
above: the TF of the driver measured between the drive and the mon output. Red trace shows the TF before the modification. Yellow trace shows the TF after the modification, notice the peak is at 14.75MHz, the Q is about the same.
Last week we tried measuring a transfer function which takes intensity fluctuation induced at the south EOAM and returns frequency fluctuation as read out by Tara's beat setup. This is therefore meant to be the measurement corresponding to Tara's code farsi.m (on the SVN at CTNLab/simulations/misc).
We used the SR785 in swept-sine mode. As measured previously, the EOAM response is 3×10−5 W/V (although I think this number should be rechecked, since we've fooled around with the EOAM in the meantime). The beat PLL readout is 7.1 kHz/V (when the Marconi is set to its 10 kHz setting). [Edit, 2013–10–18: by comparing with the newer measurement in PSL:1368, I think the Marconi must have actually been at the 1 kHz setting, so the conversion factor is 710 Hz/V and the transfer function measurement below is a factor of 10 too high.] These two numbers give the conversion factor necessary to convert from V/V into Hz/W.
The attached plot shows the measurement and the expectation from Tara's code. Here I'm using the version of the code as checked out last night, and in my local copy of the code I changed the cavity length to 1.45″ and the input power to 1 mW. Below 200 Hz, the agreement in magnitude is good: the overall shapes agree the values are within a factor of 3 of each other. The phase also appears to be good below 40 Hz or so. Above 200 Hz the transfer function is apparently dominated by some other effect.
Since the optimized layer structure is designed, I'm checking how the coatings properties change with error in layer thickness.
G.Cole said that they can control each layer thickness within 0.3%. So I tested the optimized coatings properties by adding some random number within +/- 0.5% on each layer thickness. The results are shown below for 10 000 test.
The error check does the following:
The figure below is an example of the varying layer thickness added by rand command. They are confined within 0.5%.
1) result from the error in thickness control
Above: histograms of the important values. top left, reflected phase. top right, ratio between PSD of Brownian noise and Thermo optic noise at 100 Hz. Bottom left, transmission. Bottom right, total coating thickness error.
comments: this test is chosen for 0.5% error which is almost a factor of 2 worse than what they claimed (0.3%), so the actual result should be better. I assumed 0.5% errof because of the irregular layer structure of the optimized coatings, there might be some more error in the manufacturing process.
2) result from different calculated Beta values:
Here I checked what happen if the beta calculation was wrong, and the error is still within 0.5% in each layer.
In Evans paper, the effect from "Thermo-refractive" comes from the phase changes of the wave travels in each layer. So it includes the effect from dn/dT and dz. The effective beta for each layer is given as
where alpha bar is
Where s denotes substrate, k denotes the material in each layer (high or low indices).
So my, calculation & optimization have been using these equations.
However, in the original GWINC code for TO calculation, the calculation [B8], alphabark( used in dTR) is not the same as A1, but rather.
alphaH * (1 + sigH) / (1 - sigH)
see getCoatLayerAGS.m. Line 16-17.
This is used in the calculation for beta effective in getCoatTOphase. Line73-74. Notice that for dTE, the alpha_bar_k is the same as used in Evans. (line 77).
the comment says "Yamamoto thermo-refractive correction". I emailed kazuhiro yamamoto, but never got a response back. So I keep using the same formula as in Evans because I don't see the reason why the expansion contribution should be different between TE and TR.
So this is the nb plot for TO noise from the optimized coating, if using yamamoto TR correction.
Above: nb from the optimized coatings, using Yamamoto TR correction. The cancellation becomes worse, but TO is still lower than other noise.
Finally, I repeat the same error analysis for random noise in the thickness (+/- 0.5%).
Most of the parameters behave similarly, except the cancellation (upper right plot). Now BR is only ~ x12 larger than TO noise because of the worse cancellation. Good news is, it still below Brownian noise, the cancellation still somehow works.
[Tara, Koji, Evan]
On Friday when the vacuum chamber was open, we took some impulse response measurements of the seismic isolation stack. We used a HeNe laser and a PDA100A as a shadow sensor for recording the responses.
The measurement setups were as follows:
For each setup, two ringdows were taken with the scope AC coupled (we'll call them measurements A and B).
I used scipy.optimize.curve_fit to fit each ringdown to the sum of two damped harmonic oscillators:
where θ is the Heaviside step function. In the table below I've collected the fitted frequencies and Q factors. In the first attachment I've plotted the ringdowns, their Fourier transforms (with no windowing—very crude, but it is only intended as a very rough guide), and the fits (in red).
f1 = 10.5 Hz; Q1 = 0.2
f2 = 7.2 Hz; Q2 = 0.3
f1 = 3.6 Hz; Q1 = 0.16
f2 = 10.4 Hz; Q2 = 0.2
f1 = 10.4 Hz, Q1 = 0.2
f2 = 7.0 Hz; Q2 = 0.12
f1 = 10.5 Hz; Q1 = 0.3
f2 = 6.7 Hz; Q2 = 0.08
f1 = 3.6 Hz; Q1 = 0.4
f2 = 7.3 Hz; Q2 = 0.3
f2 = 7.3 Hz; Q2 = 0.4
f1 = 3.5 Hz; Q1 = 0.5
f2 = 3.9 Hz; Q2 = 0.3
f1 = 3.5 Hz; Q1 = 0.6
f2 = 4.4 Hz; Q2 = 0.17
f1 = 4.2 Hz; Q1 = 0.5
f2 = 6 Hz; Q2 = 0.4
f1 = 3.4 Hz; Q1 = 0.2
f2 = 4.3 Hz; Q2 = 0.6
I haven't assigned error bars here because I think I may be overfitting; the amplitude and phase parameters and the offset parameter have huge uncertainties (many times the nominal value). However, by eye the fits of the ringdowns appear to be pretty good, and so I am inclined to believe the fitted frequency values.
I closed the chamber. The turbo pump is on and pumping down.
I realigned the beams so the visibilities for both cavities were 80% or more. This made sure that the beams' path would be close to the optimized path.
Now, the window reflection won't overlap with the cavity reflection, and can be dumped properly.
Note about a few things to do:
FYI for torque wrench setting for CTN cavity:
The CTN cavity is 10" OD, the Torque required is 190 InchPound.
Tara and I opened the CTN vacuum can this afternoon. Previously, the reflection from the vacuum window was overlapping with the reflection from the south refca, so Tara repositioned the seismic isolation stack in order to get rid of this overlap. We have now realigned into the two refcavs, and neither show any reflection overlap. The attached picture shows the two reflections at the PBS pickoff for the RFPD path for the south cavity. The large spot is the refcav reflection. Slightly to the left of it you can kind of make out a much smaller spot, which is the reflection from the vacuum window.
For the north cavity, the refcav reflection is currently clipping on the QWP nearest to the vacuum can, while the vacuum window reflection makes it through the QWP and onto the RFPD path. So evidently there's no overlap here either.
We also took some measurements of the impulse response of the seismic isolation stack, but that will be covered in a subsequent elog post.
The bump at 2kHz in the beat signal that I saw before was also from RFAM. By adjusting the 1/2 waveplate in front of the sideband EOM, the bump disappears. I still don't understand why adjusting the EOAM can reduce the bump from RFAM.
As I planned to add the eom driver to the BB EOM for sideband in RCAV path, I wanted to see the improvement without worrying about the EOAM optimzation. So I removed the EOAM, but I still saw the bump I observed before. This time it came from the RFAM. By adjusting the wave plate to match the polarization of the input beam to the EOM axis, the bump is gone.
above: From right to left, 1) laser for RCAV, 2)&3) 1/2 and 1/4 wave plates, 4) lense, 5) Faraday isolator, 6) 1/2 wave plate, 7)BB EOM for frequency locking, 8) BB EOM for side band, the EOM driver is attached to the side (in aluminum foil wrapped box). RFAM is minimized by adjusting (6) 1/2 wave plate.
I added the EOM driver, however it was not yet modified for 14.75 MHz, so the amplification is small, see PSL:1234 . After adjusting the phase of the demodulated sigmal, the error signal slope is increased by a factor of 2. Then I remeasured the beat signal, and the beat was better by ~ a factor of 2 at high frequency. So I think now the signal is gain limited (in RCAV loop) at high frequency. This makes me confused why the error noise from RCAV loop does not match the beat signal in PSL:1307. I have to re check my work.
The next few things to do are:
I went through all the code with Evan and found another mistake. This time the code should be correct, and the result is close to what we measured a year ago.
The calculation in PSL:1014 is wrong. There should be no square root for the absorption power (Finesse/pi * absorption). With that correction, and an assumption of absorption of 18ppm in the mirrors (9ppm on each) with Finesse of 7000, see PSL:425. The result matches with the calculation quite well.
The validity of this result depends on the absorption factor and cavity finesse. The finesse was measured, but the absorption measurement has never been done. So it might be good to think about how to measure that.
We did the same measurement with the current ACAV 1.45" cavity. Evan will post the result later.