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ID Date Author Type Category Subject
2556   Thu Mar 12 11:06:35 2020 anchalDailyProgressBEATLowest ever beatnote spectrum today!

Last night I switched off all the fans in the lab and we have reached the lowest ever recorded beatnote noise.

Latest BN Spectrum: CTN_Latest_BN_Spec.pdf

Daily BN Spectrum: CTN_Daily_BN_Spec.pdf

Relevant posts:

CTN: 2551 : Comparison between Out of loop vs In loop RIN

Attachment 1: CTN_Noise_Budget_March11-2020.pdf
2559   Thu Mar 12 19:11:00 2020 shrutiDailyProgressISSRemoved half-wave plate in north path

[Anchal, Shruti]

We realized that the half-wave plates before the EOAMs probably had no real function in the setup and therefore we proceeded to remove the one from the north path at (39,121) aka row 39, column 121 of the Optical layout.

After this was done, we had to re-adjust the quarter wave-plate (39,112) after the EOAM (39,115) to make sure that the EOAM was still functioning about the 50% transmission point. The beam going into the PMC was also re-aligned by adjusting the two mirrors at (32,92) and (37,92). Finally, the mirror at (43,88) was adjusted to align the beam reflecting from the PMC into the photo-diode.

We were able to re-lock the north PMC and north cavity after increasing the power in that path by adjusting some waveplates.

As may be expected, the sign of the ISS feedback had to be inverted. The ISS actuates on the EOAM; removing the half-wave plate would have switched the circularity of the polarization of the beam entering the PBS at (39,110), so the sign of the voltage that would have previously caused the transmission to increase would now cause it to decrease and vice versa.

2560   Mon Mar 16 16:16:17 2020 anchalDailyProgressISSAdded true OOL transmission PD for South Path

Today, I added a new out-of-loop transmission PD (Thorlabs PDA10CS) for the south path. This will be helpful in future measurements of RIN coupling to beatnote noise. This PD is added at (1, 40) using the dumped light. The optical layout would be updated in a few days. I've confirmed that this photodiode is reading the same RIN as read earlier in CTN:2555. I've also connected Acromag channel for South Transmission DC to this photodiode, so the transmitted power channels and the mode matching percentage channel of South Cavity are meaningful again.

2561   Tue Mar 17 18:03:22 2020 anchalDailyProgressISSAdded true OOL transmission PD for North Path

Today, I added a new out-of-loop transmission PD (Thorlabs PDA10CS) for the north path. This will be helpful in future measurements of RIN coupling to beatnote noise. This PD is added at (8, 42) using the dumped light. The optical layout would be updated in a few days. I've also connected Acromag channel for North Transmission DC to this photodiode, so the transmitted power channels and the mode matching percentage channel of North Cavity are meaningful again.

ISS Gain for the Northside has been increased to 2x10000 since half of the light is now being used by the OOL PD.

Attachment 1: IMG_20200317_180420.jpg
2562   Wed Mar 18 12:51:22 2020 anchalDailyProgressBEATSuper beatnote measurement analysis results

On March 13th around 7:30 pm, I started a super measurement of the beatnote spectrum for over 2 days. The script superBNSpec.py took a beatnote spectrum every 15 minutes for a total of 250 measurements. The experiment was stable throughout the weekend with no lock loss or drift of the beatnote frequency. All data with respective experimental configuration files are present in the Data folder. HEPA filters were on during this measurement.

### Analysis and Inference:

• I first plotted time series of how beatnote frequency ASD at 300 Hz varies over the 2 days.
• Remember, this is a median measurement done using function modPSD which uses modWelch function we wrote a while back (See CTN:2399).
• Then I plotted the same for a bunch of frequencies from 200 Hz to 1 kHz.
• It is clear that the time of the day does not have any major or meaningful effect on the beatnote spectrum. It mostly remains the same.
• Finally, I took the median of the 250 ASD measurements.
• I also calculated lower and upper bounds using RMS of difference between 250 upper and lower bounds and the median calculated above.
• All the noise peaks are intact indicating that all noise sources are stationary and REAL (in Will Farr's language).

Data

Attachment 1: CTN_Beatnote_SuperMeasurement_March13-16.pdf
2563   Thu Mar 19 15:34:41 2020 anchalDailyProgressNorth CavityNorth path's buggy nature solved

I found out that since the slow PID of the FSS used Cavity reflection DC level, it is important that this path remains rigid and undisturbed from any testing. In CTN:2559, when Shruti and I were realigning North PMC, we used  BNC-T (which was permanently attached to the rack) to pick-off North cavity reflection DC signal. During this putting on and off the cable, we made the BNC-T itself loose and the connection to acromag card became buggy.

I have fixed this by connecting the acromag cards directly to the cable coming from the table behind the rack. Now connections/disconnections at the front of the rack shouldn't disturb this vital connection. Still, we need to be careful about this from next time. I had no idea what went wrong and was about to start a full-scale investigation into PMC and FSS loops. Thankfully, I figured out this problem before that.

Attachment 1: IMG_20200319_154013.jpg
2564   Sun Mar 22 17:23:29 2020 anchalDailyProgressNorth CavityNorth path's buggy nature NOT solved

It seems like this was never properly solved. On Friday, the same problem was back again. After trying relocking PMC and FSS on the north path without any luck, I switched off the laser to standby mode and after a minute restarted it and the problem went away. I have a strong suspicion that this problem has something to do with the laser temperature controller on the laser head itself. During the unstable state, I see a spike that starts a large surge in error signal of FSS loop which occurs every 1 second! (so something at 1 Hz). The loop actually kills the spike successfully withing 600-700 ms but then it comes back again. I'm not sure what's wrong, but if this goes on and the lockdown is enforced due to Corona virus, I won't even able to observe the experiment from a distance :(. I have no idea what went wrong here.

2565   Wed Mar 25 15:50:57 2020 anchalDailyProgressNorth CavityNorth path's buggy nature NOT solved

Today, magically almost, the North Path was found to be locking nicely without the noise. I was waiting for the beatnote to reach the detector's peak frequency when in about 40 min, it started going haywire again. No controls were changed to trigger any of this and as far as I know, nobody entered the lab. Something is flakey or suddenly some new environmental noise is getting coupled to the experiment. Attached is the striptool screenshot of the incident and the data dumped. In the attached screenshot, channel names are self-explanatory, all units on y axis are mW on left plot (note the shifted region, but same scale of North Cavity Transmission Power) and MHz on the right plot for Beatnote Frequency.

I know for sure that everything until PMC is good since when only PMC is locked, I do not see huge low frequency noise in the laser power transmitted or reflected from the PMC. But whatver is this effect, it makes the FSS loop unstable and eventually it unlocks, then locks again and repeats.

Evidences

Attachment 1: Screen_Shot_2020-03-25_at_3.48.24_PM.png
2566   Mon Apr 13 16:52:30 2020 anchalDailyProgressBEATBeatnote measurements back on track

Since this morning atleast, I'm not seeing the North Path unstability (see CTN:2565) and the beatnote is stable and calm at the setpoint. Maybe the experiment just needed some distance from me for few days.

So today, I took a general single shot measurement and even after HEPA filers being on at 'Low', the measurement is the lowest ever, especially in the low-frequency region. This might be due to reduced siesmic activity around the campus. I have now started another super beatnote measurement which would take measurement continuously every 10 min is the transmission power from the cavities look stable enough to the code.

there is a new broad bump though arounf 250-300 Hz which was not present before. But I can't really do noise hunting now, so will just take data until I can go to the experiment.

Latest BN Spectrum: CTN_Latest_BN_Spec.pdf

Daily BN Spectrum: CTN_Daily_BN_Spec.pdf

Relevant post:

CTN:2565: North path's buggy nature NOT solved

Attachment 1: CTN_Latest_BN_Spec.pdf
2567   Tue Apr 14 12:24:16 2020 anchalDailyProgressNorth CavityNorth path's buggy nature Strikes Again!

Today at sharp 8:30 am, perfectly fine running experiment went bad again. The North path became buggy again with strong low frequency oscillations in almost all of the loops except the temperature control of vacuum can. The temperature control of beatnote frequency felt a step change and hence went into oscillations of about 65 kHz.

Not sure what went wrong, but 8:30 am might be the clue here. But can't change/test anything until I can go to the lab.

Data

Attachment 1: NorthPathWentBuggy.pdf
2568   Thu Apr 16 18:08:56 2020 anchalDailyProgressNorth CavityNorth path stopped being buggy

On wednesday around noon, the North Path got back to stability. I captured this process by going back to the FB data. The process of coming back to stability is not so instantaneous as the other way round. Also, in this process, the path becomes stable, then unsable and stable and so one with the duration od unstability decreasing until it vanishes. Attached are plots of about 14 hours of curucial channels. If anyone has any insights on what might be happening, let me know.

Data

Attachment 1: NorthPathStoppedBeingBuggy.pdf
2571   Wed May 13 18:07:32 2020 anchalDailyProgressNoiseBudgetBayesian Analysis

I did this analysis last with bare-bones method in CTN:2439. Now I've improved this much more. Following are some salient features:

• Assuming Uniform prior distribution of Bulk Loss Angle since the overlap with Penn et al. is so low that our measurement is inconsistent with theirs ((5.33 +- 0.03) x 10-4 )if we take into account their extremely low standard deviation associated to bulk loss angle.
• Assuming Normal Distributed prior distribution for Shear Loss Angle matching Penn et al. reported value of (2.6 +- 2.6) x 10-7. This is done because we can faithfully infere only one of the two loss angles.
• The likelihood function is estimated in the following manner:
• Data cleaning:
• Frequency points are identified between 50 Hz to 700 Hz where the derivative of Beat Note Frequency noise PSD with respect to frequency is less than 2.5 x 10-5 Hz2/Hz2..
• This was just found empirically. This retains all low points in the data away from the noise peaks.
• Measured noise Gaussian:
• At each "clean" frequency point, a gaussian distribution of measured beat note frequency noise ASD is assumed.
• This gaussian is assumed to have a mean of the corresponding measured 'median' value.
• The standard deviation is equal to half of the difference between 15.865 percentile and 84.135 percentile points. These points correspond to mean +- standard deviation for a normal distribution
• Estimated Gaussian and overlap:
• For an iterable value of Bulk and Shear Loss Angle, total noise is estimated with estimated uncertainty. This gives a gaussian for the estimated noise.
• The overlap of two Gaussians is calculated as the overlap area. This area which is 0 for no overlap and 1 for complete overlap is taken as the likelihood function.
• However, any estimate of noise that goes above the measured nosie is given a likelihood of zero. Hence the likelihood function in the end looks like half gaussian.
• The likelihood for different clean data points is multiplied together to get the final likelihood value.
• The Product of prior distribution and likelihood function is taken as the Bayesian Inferred Probability (unnormalized).
• The maximum of this distribution is taken as the most likely inferred values of the loss angles.
• The standard deviation for the loss angles is calculated from the half-maximum points of this distribution.

Final results are calculated for data taken at 3 am on March 11th, 2020 as it was found to be the least noise measurement so far:

Bulk Loss Angle: (8.8 +- 0.5) x 10-4.

Shear Loss Angle: (2.6 +- 2.85) x 10 -7.

Figures of the analysis are attached. I would like to know if I am doing something wrong in this analysis or if people have any suggestions to improve it.

The measurement instance used was taken with HEP filter on but at low. I expect to measure even lower noise with the filters completely off and optimizing the ISS as soon as I can go back to lab.

Other methods tried:

Mentioning these for the sake of completeness.

• Tried using a prior distribution for Bulk Loss Angle as a gaussian from Penn et al. measured value. The likelihood function just became zero everywhere. So our measurements are not consistent at all. This is also because the error bars in their reported Bulk Loss Angle are extremely
• Technically, the correct method for likelihood estimation would be following:
• Using the mean ($\mu$) and standard deviation ($\sigma$) of estimated total noise, the mean of the measured noise would be a gaussian distribution with mean $\mu$ and variance $\sigma^2/N$ where N is the number of averaging in PSD calculation (600 in our case).
• If standard deviation of the measured noise is $\sigma_m$, then $(N-1)\sigma_m^2/\sigma^2$would be a $\chi^2_{(N-1)}$ distribution with N-1 degrees of freedom.
• These functions can be used to get the probability of observed mean and standard deviation in the measured noise with a prior distribution of the total estimated noise distribution.
• I tried using this method for likelihood estimation and while it works for a single frequency point, it gives zero likelihood for multiple frequency points.
• This indicated that the shape of the measured noise doesn't match well enough with the estimated noise to use this method. Hence, I went to the overlap method instead.

Analysis Code

Attachment 1: CTN_Bayesian_Inference_Analysis_Of_Best_Result.pdf
2572   Fri May 15 12:09:17 2020 aaronDailyProgressNoiseBudgetBayesian Analysis

Wow, very suggestive ASD. A couple questions/thoughts/concerns:

• It's typically much easier to overestimate than underestimate the loss angle with a ringdown measurement (eg, you underestimated clamping loss and thus are not dominated by material dissipation). So, it's a little surprising that you would find a higher loss angle than Penn et all. That said, I don't see a model uncertainty for their dilution factors, which can be tricky to model for thin films.
• If you're assuming a flat prior for bulk loss, you might do the same for shear loss. Since you're measuring shear losses consistent with zero, I'd be interested to see how much if at all this changes your estimate.
• I'm also surprised that you aren't using the measurements just below 100Hz. These seem to have a spectrum consistent with brownian noise in the bucket between two broad peaks. Were these rejected in your cleaning procedure?
• Is your procedure for deriving a measured noise Gaussian well justified? Why assume Gaussian measurement noise at all, rather than a probability distribution given by the measured distribution of ASD?
• It's not clear to me where your estimated Gaussian is coming from. Are you making a statement like "given a choice of model parameters \phi_bulk and \phi_shear, the model predicts a measured ASD at frequency f_m will have mean \mu_m and standard deviation \sigma_m"?
• I found taking a deep dive into Feldman Cousins method for constructing frequentist confidence intervals highly instructive for constructing an unbiased likelihood function when you want to exclude a nonphysical region of parameter space. I'll admit both a historical and philosophical bias here though :)
• Can this method ever reject the hypothesis that you're seeing Brownian noise? I don't see how you could get any distribution other than a half-gaussian peaked at the bulk loss required to explain your noise floor.
• I think you instead want to construct a likelihood function that tells you whether your noise floor has the frequency dependence of Brownian noise.
2573   Fri May 15 16:50:24 2020 anchalDailyProgressNoiseBudgetBayesian Analysis

It's typically much easier to overestimate than underestimate the loss angle with a ringdown measurement (eg, you underestimated clamping loss and thus are not dominated by material dissipation). So, it's a little surprising that you would find a higher loss angle than Penn et all. That said, I don't see a model uncertainty for their dilution factors, which can be tricky to model for thin films.

Yeah but this is the noise that we are seeing. I would have liked to see lower noise than this.

If you're assuming a flat prior for bulk loss, you might do the same for shear loss. Since you're measuring shear losses consistent with zero, I'd be interested to see how much if at all this changes your estimate.

Since I have only one number (the noise ASD) and two parameters (Bulk and Shear loss angle), I can't faithfully estimate both. The dependence of noise due to the two-loss angles is also similar to show any change in frequency dependence. I tried giving a uniform prior to Shear Loss Angle and the most likely outcome always hit the upper bound (decreasing the estimate of Bulk Loss Angle). For example, when uniform prior to shear was up to 1x 10-5, the most likely result became $\Phi_B$ = 8.8x10-4, $\Phi_S$ = 1 x 10-5. So it doesn't make sense to have orders of magnitude disagreement with Penn et al. results on shear loss angle to have slightly more agreement on bulk loss angle. Hence I took their result for the shear loss angle as a prior distribution. I'll be interested in knowing if their are alternate ways to do this.

I'm also surprised that you aren't using the measurements just below 100Hz. These seem to have a spectrum consistent with brownian noise in the bucket between two broad peaks. Were these rejected in your cleaning procedure?

Yeah, they got rejected in the cleaning procedure because of too much fluctuations between neighboring points. But I wonder if that's because my empirically found threshold is good only for 100 Hz to 1kHz range because number of averaging is lesser in lower frequency bins. I'm using a modified version of welch to calculate the PSD (see the code here), which runs welch function with different npersegment for the different range of frequencies to get the maximum averaging possible with given data for each frequency bin.

Is your procedure for deriving a measured noise Gaussian well justified? Why assume Gaussian measurement noise at all, rather than a probability distribution given by the measured distribution of ASD?

The time-series data of the 60s for each measurement is about 1 Gb in size. Hence, we delete it after running the PSD estimation which gives out the median and the 15.865 percentile and 84.135 percentile points. I can try preserving the time series data for few measurements to see how the distribution is but I assumed it to be gaussian since they are 600 samples in the range 100 Hz to 1 kHz, so I expected the central limit theorem to kick-in by this point. Taking out the median is important as the median is agnostic to outliers and gives a better estimate of true mean in presence of glitches.

It's not clear to me where your estimated Gaussian is coming from. Are you making a statement like "given a choice of model parameters \phi_bulk and \phi_shear, the model predicts a measured ASD at frequency f_m will have mean \mu_m and standard deviation \sigma_m"?

Estimated Gaussian is coming out of a complex noise budget calculation code that uses the uncertainties package to propagate uncertainties in the known variables of the experiment and measurement uncertainties of some of the estimate curves to the final total noise estimate. I explained in the "other methods tried" section of the original post, the technically correct method of estimation of the observed sample mean and sample standard deviation would be using gaussian and $\chi^2$distributions for them respectively. I tried doing this but my data is too noisy for the different frequency bins to agree with each other on an estimate resulting in zero likelihood in all of the parameter space I'm spanning. This suggests that the data is not well-shaped either according to the required frequency dependence for this method to work. So I'm not making this statement. The statement I'm making is, "given a choice of model parameters $\Phi_{B}$ and $\Phi_{S}$, the model predicts a Gaussian distribution of total noise and the likelihood function calculates what is the overlap of this estimated probability distribution with the observed probability distribution.

I found taking a deep dive into Feldman Cousins method for constructing frequentist confidence intervals highly instructive for constructing an unbiased likelihood function when you want to exclude a nonphysical region of parameter space. I'll admit both a historical and philosophical bias here though :)

Thanks for the suggestion. I'll look into it.

Can this method ever reject the hypothesis that you're seeing Brownian noise? I don't see how you could get any distribution other than a half-gaussian peaked at the bulk loss required to explain your noise floor. I think you instead want to construct a likelihood function that tells you whether your noise floor has the frequency dependence of Brownian noise.

Yes, you are right. I don't think this method can ever reject the hypothesis that I'm seeing Brownian noise. I do not see any other alternative though as such as I could think of. The technically correct method, as I mentioned above, would favor the same frequency dependence which we are not seeing in the data :(. Hence, that likelihood estimation method rejected the hypothesis that we are seeing Brownian noise and gave zero likelihood for all of the parameter space. Follow up questions:

• Does this mean that the measured noise is simply something else and the experiment is far from being finished?
• Is there another method for calculating likelihood function which is somewhat in the midway between the two I have tried?
• Is the strong condition in likelihood function that "if estimated noise is more than measured noise, return zero" not a good assumption?
2574   Fri May 22 17:22:37 2020 anchalDailyProgressNoiseBudgetBayesian Analysis

I talked to Kevin and he suggested a simpler straight forward Bayesian Analysis for the result. Following is the gist:

• Since Shear Loss Angle's contribution is so little to the coatings' brownian noise, there is no point in trying to estimate it from our experiment. It will be unconstrained in the search always and would simply result in the whatever prior distribution we will take.
• So, I accepted defeat there and simply used Shear Loss Angle value estimated by Penn et al. which is 5.2 x 10-7.
• So now the Bayesian Analysis is just one dimensional for Bulk Loss Angle.
• Kevin helped me inrealizing that error bars in the estimated noise are useless in bayesian analysis. The model is always supposed to be accurate.
• So the log likelihood function would be -0.5*((data - model)/data_std)**2) for each frequency bin considered and we can add them all up.
• Going to log space helped a lot as earlier probablitis were becoming zero on multiplication but addition of log likelihood is better between different frequencies.
• I'm still using the hard condition that measured noise should never be lower than estimated noise at any frequency bin.
• Finally, the estimated value is quoted as the most likely value with limits defined by the region covering 90% of the posterior probability distribution.

This gives us:
$\huge \Phi_B = 8.9^{8.9}_{3.7} \times 10^{-4}$

with shear loss angle taken from Penn et al. which is 5.2 x 10-7. The limits are 90% confidence interval.

Now this isn't a very good result as we would want, but this is the best we can report properly without garbage assumptions or tricks. I'm trying to see if we can get a lower noise readout in next few weeks, but otherwise, this is it, CTN lab will rest afterward.

Analysis Code

Attachment 1: CTN_Bayesian_Inference_Analysis_Of_Best_Result.pdf
2575   Mon May 25 08:54:26 2020 anchalDailyProgressNoiseBudgetBayesian Analysis with Hard Ceiling Condition

I realized that using only the cleaned out frequencies and a condition that estimated power never goes above them at those places is double conditioning. In fact, we can just look at a wide frequency band, between 50 Hz to 600 Hz and use all data points with a hard ceiling condition that estimated noise never goes above the measured noise in any frequency bin in this region. Surprisingly, this method estimates a lower loss angle with more certainty. This happened because, 1) More data points are being used and 2) As Aaron pointed out, there were many useful data bins between 50 Hz and 100 Hz. I'm putting this result separately to understand the contrast in the results. Note that still we are using a uniform prior for Bulk Loss Angle and shear loss angle value from Penn et al.

The estimate of the bulk loss angle with this method is:

$\huge \Phi_B = 6.1^{6.1}_{5.2} \times 10^{-4}$

with shear loss angle taken from Penn et al. which is 5.2 x 10-7. The limits are 90% confidence interval. This result has an entire uncertain region from Penn et al.  within it.

Which is a more fair technique: this post or  CTN:2574 ?

Analysis Code

Attachment 1: CTN_Bayesian_Inference_Analysis_Of_Best_Result_Hard_Ceiling.pdf
2576   Tue May 26 15:45:18 2020 anchalDailyProgressNoiseBudgetBayesian Analysis

Today we measured further low noise beatnote frequency noise. I reran the two notebooks and I'm attaching the results here:

### Bayesian Analysis with frequency cleaning:

This method only selects a few frequency bins where the spectrum is relatively flat and estimates loss angle based on these bins only. This method rejects any loss angle vaue that results in estimated noise more than measured noise in the selected frequency bins.

$\huge \Phi_B = 8.9^{8.9}_{5.0} \times 10^{-4}$

with shear loss angle taken from Penn et al. which is 5.2 x 10-7. The limits are 90% confidence interval.

### Bayesian Analysis with Hard Ceiling:

This method uses all frequency bins between 50 H and 600 Hz and uses them to estimate loss angle value This method rejects any loss angle value that results in estimated noise more than measured noise in the selected frequency bins.

$\huge \Phi_B = 6.1^{6.1}_{5.1} \times 10^{-4}$

with shear loss angle taken from Penn et al. which is 5.2 x 10-7. The limits are 90% confidence interval.

Analysis Code

Attachment 1: CTN_Bayesian_Inference_Analysis_Of_Best_Result.pdf
Attachment 2: CTN_Bayesian_Inference_Analysis_Of_Best_Result_Hard_Ceiling.pdf
2577   Thu May 28 14:13:53 2020 anchalDailyProgressNoiseBudgetBayesian Analysis

I'm listing first few comments from Jon that I implemented:

• Data cleaning can not be done by looking at the data itself. Some outside knowledge can be used to clean data. So, I removed all the empirical cleaning procedures and instead just removed frequency bins of 60 Hz harmonics and their neighboring bins. With HEPA filters off, the latest data is much cleaner and the peaks are mostly around these harmonics only.
• I removed the neighboring bins of 60 Hz harmonics as Jon pointed out that PSD data points are not independent variables and their correlation depends on the windowing used. For Hann window, immediate neighbors are 50% correlated and the next neighbors are 5%.
• The Hard ceiling approach is not correct because the likelihood of a frequency bin data point gets changed due to some other far away frequency bin. Here I've plotted probability distributions with and without hard ceiling to see how it affects our results.

### Bayesian Analysis (Normal):

$\huge \Phi_B = (8.1 \pm 2.25) \times 10^{-4}$

with shear loss angle taken from Penn et al. which is 5.2 x 10-7. The limits are 90% confidence interval.

Note that this allows estimated noise to be more than measured noise in some frequency bins.

### Bayesian Analysis (If Hard Ceiling is used):

$\huge \Phi_B = 5.82^{5.82}_{4.56} \times 10^{-4}$

with shear loss angle taken from Penn et al. which is 5.2 x 10-7. The limits are 90% confidence interval.

### Remaining steps to be implemented:

There are more things that Jon suggested which I'm listing here:

• I'm trying to catch next stable measurement with saving the time series data.
• The PSD data points are not normal distributed since "PSD = ASD^2 = y1^2 + y2^2. So the PSD is the sum of squared Gaussian variables, which is also not Gaussian (i.e., if a random variable can only assume positive values, it's not Gaussian-distributed)."
• So I'm going to take PSD for 1s segements of data from the measurement and create a distribution for PSD at each frequency bin of interest (50Hz to 600 Hz) at a resolution of 1 Hz.
• This distribution would give a better measure of likelihood function than assuming them to be normal distributed.
• As mentioned above, neighboring frequency bins are always correlated in PSD data. To get rid of this, Jon suggested following
"the easiest way to handle this is to average every 5 consecutive frequency bins.
This "rebins" the PSD to a slightly lower frequency resolution at which every data point is now independent. You can do this bin-averaging inside the Welch routine that is generating the sample distributions: For each individual PSD, take the average of every 5 bins across the band of interest, then save those bin-averages (instead of the full-resolution values) into the persistent array of PSD values. Doing this will allow the likelihoods to decouple as before, and will also reduce the computational burden of computing the sample distributions by a factor of 5."
• I'll update the results once I do this analysis with some new measurements with time-series data.

Analysis Code

Attachment 1: CTN_Bayesian_Inference_Analysis_Of_Best_Result_New.pdf
2578   Sun May 31 11:44:20 2020 AnchalDailyProgressNoiseBudgetBayesian Analysis Finalized

I've implemented all the proper analysis norms that Jon suggested and are mentioned in the previous post. Following is the gist of the analysis:

• All measurements taken to date are sifted through and the sum of PSD bins between 70 Hz to 600 Hz (excluding 60 Hz harmonics and region between 260 Hz to 290 Hz (Known bad region)) is summed. The least noise measurement is chosen then.
• If time-series data is available (which at the moment is available for lowest noise measurement of May 29th taken at 1 am), following is done:
• Following steps are repeated for the frequency range 70 Hz to 100 Hz and 100 Hz to 600 Hz with timeSegement values 5s and 0.5s respectively.
• The time series data is divided into pieces of length timeSegment with half overlap.
• For each timeSegment welch function is run with npersegment equal to length of time series data. So each welch function returns PSD for corresponding timeSegement.
• In each array of such PSD, rebining is done by taking median of 5 consecutive frequency bins. This makes the PSD data with bin widths of 1 Hz and 10 Hz respectively.
• The PSD data for each segement is then reduced by using only the bins in the frequency range and removing 60 Hz harmonics and the above mentioned bad region.
• Logarithm of this welch data is taken.
• It was found that this logarithm of PSD data is close to Gaussian distributed with a skewness towards lower values. Since this is logarithm of PSD, it can take both positive and negative values and is a known practice to do to reach to normally distributed data.
• A skew-normal distribution is fitted to each frequency bin across different timeSegments.
• The fitted parameters of the skew-normal distribution are stored for each frequency bin in a list and passed for further analysis.
• Prior distribution of Bulk Loss Angle is taken to be uniform. Shear loss angle is fixed to 5.2 x 10-7 from Penn et al..
• The Log Likelihood function is calculated in the following manner:
• For each frequency bin in the PSD distribution list, the estimated total noise is calculated for the given value of bulk loss angle.
• Probability of this total estimated noise is calculated with the skew-normal function fitted for each frequency bin and logarithm is taken.
• Each frequency bin is supposed to be independent now since we have rebinned, so the log-likelihood of each frequency bin is added to get total log-likelihood value for that bulk loss angle.
• Bayesian probability distribution is calculated from sum of log-likelihood and log-prior distribution.
• Maximum of the Bayesian probability distribution is taken as the most likely estimate.
• The upper and lower limits are calculated by going away from most likely estimate in equal amounts on both sides until 90% of the Bayesian probability is covered.

### Final result of CTN experiment as of now:

$\huge \Phi_B = (8.81 \pm 1.52) \times 10^{-4}$

with shear loss angle taken from Penn et al. which is 5.2 x 10-7. The limits are 90% confidence interval.

The analysis is attached. This result will be displayed in upcoming DAMOP conference and would be updated in paper if any lower measurement is made.

Analysis Code

Thu Jun 4 09:17:12 2020 Result updated. Check CTN:2580.

Attachment 1: CTN_Bayesian_Inference_Final_Analysis.pdf
2579   Mon Jun 1 11:09:09 2020 ranaDailyProgressNoiseBudgetBayesian Analysis Finalized

what is the effective phi_coating ? I think usually people present bulk/shear + phi_coating.

2580   Thu Jun 4 09:18:04 2020 AnchalDailyProgressNoiseBudgetBayesian Analysis Finalized

### Final result of CTN experiment as of June 4th 9 am:

$\huge \Phi_B = (8.74 \pm 1.51) \times 10^{-4}\quad,rad$

with shear loss angle taken from Penn et al. which is 5.2 x 10-7. The limits are 90% confidence interval.

The analysis is attached. This result will be displayed in upcoming DAMOP conference and would be updated in paper if any lower measurement is made.

### Adding Effecting Coating Loss Angle (Edit Fri Jun 5 18:23:32 2020 ):

If all layers have an effective coating loss angle, then using gwinc's calculation (Yam et al. Eq.1), we would have effective coating loss angle of:

$\huge \Phi_\text{c} = (4.95 \pm 0.86) \times 10^{-4}$

This is worse than both Tantala (3.6e-4) and Silica (0.4e-4) currently in use at AdvLIGO.

Also, I'm unsure now if our definition of Bulk and Shear loss angle is truly same as the definitions of Penn et al. because they seem to get an order of magnitude lower coating loss angle from their bulk loss angle.

Analysis Code

Attachment 1: CTN_Bayesian_Inference_Final_Analysis.pdf
2582   Thu Jun 11 14:02:26 2020 AnchalDailyProgressNoiseBudgetBayesian Analysis Finalized

I realized that in my noise budget I was using higher incident power on the cavities which was the case earlier. I have made the code such that now it will update photothermal noise and pdhShot noise according to DC power measured during the experiment. The updated result for the best measurement yet brings down our estimate of the bulk loss angle a little bit.

### Final result of CTN experiment as of June 11th 2 pm:

$\huge \Phi_B = (8.69 \pm 1.51) \times 10^{-4}\quad rad$

with shear loss angle taken from Penn et al. which is 5.2 x 10-7. The limits are 90% confidence interval.

The analysis is attached.

### Adding Effecting Coating Loss Angle (Edit Fri Jun 5 18:23:32 2020 ):

If all layers have an effective coating loss angle, then using gwinc's calculation (Yam et al. Eq.1), we would have an effective coating loss angle of:

$\huge \Phi_c = (4.92 \pm 0.86) \times 1^{-4} \quad rad$

This is worse than both Tantala (3.6e-4) and Silica (0.4e-4) currently in use at AdvLIGO.

Also, I'm unsure now if our definition of Bulk and Shear loss angle is truly the same as the definitions of Penn et al. because they seem to get an order of magnitude lower coating loss angle from their bulk loss angle.

Analysis Code

Attachment 1: CTN_Bayesian_Inference_Final_Analysis.pdf
2583   Fri Jun 12 12:34:08 2020 anchalDailyProgressNoiseBudgetResolving discrepancy #1 concretly

I figured out why folks befor eme had to use a different definition of effective coating coefficent of thermal expansion (CTE) as a simple weighted average of individual CTE of each layer instead of weighted average of modified CTE due to presence of substrate. The reason is that the modification factor is incorporated in another parameter gamma_1 and gama_2 in Farsi et al. Eq, A43. So they had to use a different definition of effective coating CTE since Farsi et al. treat it differently. That's my guess anyway since thermo-optic cancellation was demonstrated experimentally.

Quote:

## Discrepancy #1

Following points are in relation to previously used noisebudget.ipynb file.

• One can see the two different values of effective coating coefficient of thermal expansion (CTE) at the outputs of cell 9 and cell 42.
• For thermo-optic noise calculation, this variable is named as coatCTE and calculated using Evans et al. Eq. (A1) and Eq. (A2) and comes out to (1.96 +/- 0.25)*1e-5 1/K.
• For the photothermal noise calculation, this variable is named as coatEffCTE and is simply the weighted average of CTE of all layers (not their effective CTE due to the presence of substrate). This comes out to (5.6 +/- 0.4)*1e-6 1/K.
• The photothermal transfer function plot which has been used widely so far uses this second definition. The cancellation of photothermal TF due to coating TE and TR relies on this modified definition of effective coating CTE.

Following points are in relation to the new code at https://git.ligo.org/cit-ctnlab/ctn_noisebudget/tree/master/noisebudget/ObjectOriented.

• In my new code, I used the same definition everywhere which was the Evans et al. Eq. (A1) and Eq. (A2). So the direct noise contribution of coating thermo-optic noise matches but the photothermal TF do not.
• To move on, I'll for now locally change the definition of effective coating CTE for the photothermal TF calculation to match with previous calculations. This is because the thermo-optic cancellation was "experimentally verified" as told to me by Rana.
• The changes are done in noiseBudgetModule.py in calculatePhotoThermalNoise() function definition at line 590 at the time of writing this post.
• Resolved this discrepancy for now.

Quote:

The new noise budget code is ready. However, there are few discrepancies which still need to be sorted.

The code could be found at https://git.ligo.org/cit-ctnlab/ctn_noisebudget/tree/master/noisebudget/ObjectOriented

Please look into How_to_use_noiseBudget_module.ipynb for a detailed description of all calculations and code structure and how to use this code.

### Discrepancy #1

In the previous code, while doing calculations for Thermoelastic contribution to Photothermal noise, the code used a weighted average of coefficients of thermal expansion (CTE) of each layer weighted by their thickness. However, in the same code, while doing calculations for thermoelastic contribution to coating thermo-optic noise, the effective CTE of the coating is calculated using Evans et al. Eq. (A1) and Eq. (A2). These two values actually differ by about a factor of 4.

Currently, I have used the same effective CTE for coating (the one from Evans et al)  and hence in new code, prediction of photothermal noise is higher. Every other parameter in the calculations matches between old and new code. But there is a problem with this too. The coating thermoelastic and coating thermorefractive contributions to photothermal noise are no more canceling each other out as was happening before.

So either there is an explanation to previous codes choice of using different effective CTE for coating, or something else is wrong in my code. I need more time to look into this. Suggestions are welcome.

### Discrepancy #2

The effective coating CTR in the previous code was 7.9e-5 1/K and in the new code, it is 8.2e-5 1/K. Since this value is calculated after a lot of steps, it might be round off error as initial values are slightly off. I need to check this calculation as well to make sure everything is right. Problem is that it is hard to understand how it is done in the previous code as it used matrices for doing complex value calculations. In new code, I just used ucomplex class and followed the paper's calculations. I need more time to look into this too. Suggestions are welcome.

2584   Mon Jun 15 16:43:58 2020 AnchalDailyProgressNoiseBudgetBetter measurement on June 14th

### Final result of CTN experiment as of June 15th 5 pm:

$\huge \Phi_B = (8.28 \pm 1.45)\times 10^{-4}\quad rad$

with shear loss angle taken from Penn et al. which is 5.2 x 10-7. The limits are 90% confidence interval.

The analysis is attached.

### Adding Effecting Coating Loss Angle (Edit Fri Jun 5 18:23:32 2020 ):

If all layers have an effective coating loss angle, then using gwinc's calculation (Yam et al. Eq.1), we would have an effective coating loss angle of:

$\huge \Phi_c = (4.69 \pm 0.82) \times 10^{-4} \quad rad$

This is worse than both Tantala (3.6e-4) and Silica (0.4e-4) currently in use at AdvLIGO.

Also, I'm unsure now if our definition of Bulk and Shear loss angle is truly the same as the definitions of Penn et al. because they seem to get an order of magnitude lower coating loss angle from their bulk loss angle.

Analysis Code

Attachment 1: CTN_Bayesian_Inference_Final_Analysis.pdf
2585   Mon Jun 15 17:58:02 2020 anchalDailyProgressDocumentationCTN paper

I've just finished a preliminary draft of CTN paper. This is of course far from final and most figures are placeholders. This is my first time writing a paper alone, so expect a lot of naive mistakes. As of now, I have tried to put in as much info as I could think of about the experiment, calculations, and analysis.
I would like organized feedback through issue tracker in this repo:
https://git.ligo.org/cit-ctnlab/ctn_paper
Please feel free to contribute in writing as well. Some contribution guidelines are mentioned in the repo readme.

2586   Tue Jun 23 17:28:36 2020 AnchalDailyProgressNoiseBudgetBetter measurement on June 22nd (as I turned 26!)

### Final result of CTN experiment as of June 23  5 pm:

$\huge \Phi_B = (8.18 \pm 1.42) \times 10^{-4} \quad rad$

with shear loss angle taken from Penn et al. which is 5.2 x 10-7. The limits are 90% confidence interval.

The analysis is attached.

### Adding Effecting Coating Loss Angle (Edit Fri Jun 5 18:23:32 2020 ):

If all layers have an effective coating loss angle, then using gwinc's calculation (Yam et al. Eq.1), we would have an effective coating loss angle of:

$\huge \Phi_c = (4.13 \pm 0.80) \times 10^{-4} \quad rad$

This is worse than both Tantala (3.6e-4) and Silica (0.4e-4) currently in use at AdvLIGO.

Also, I'm unsure now if our definition of Bulk and Shear loss angle is truly the same as the definitions of Penn et al. because they seem to get an order of magnitude lower coating loss angle from their bulk loss angle.

Analysis Code

Attachment 1: CTN_Best_Measurement_Result.pdf
2587   Wed Jun 24 21:14:58 2020 AnchalDailyProgressNoiseBudgetBetter measurement on June 24th

### Final result of CTN experiment as of June 24  9 pm:

$\huge \Phi_B = (7.75 \pm 1.35) \times 10^{-4} \quad rad$

with shear loss angle taken from Penn et al. which is 5.2 x 10-7. The limits are 90% confidence interval.

The analysis is attached.

### Adding Effecting Coating Loss Angle (Edit Fri Jun 5 18:23:32 2020 ):

If all layers have an effective coating loss angle, then using gwinc's calculation (Yam et al. Eq.1), we would have an effective coating loss angle of:

$\huge \Phi_c = (4.39 \pm 0.76) \times 10^{-4} \quad rad$

This is worse than both Tantala (3.6e-4) and Silica (0.4e-4) currently in use at AdvLIGO.

Also, I'm unsure now if our definition of Bulk and Shear loss angle is truly the same as the definitions of Penn et al. because they seem to get an order of magnitude lower coating loss angle from their bulk loss angle.

Analysis Code

Automatically updating results from now on:

2588   Fri Jun 26 12:38:34 2020 AnchalDailyProgressNoiseBudgetBayesian Analysis Finalized, Adding Slope of Bulk Loss Angle as variable

I added the possibility of having a power-law dependence of bulk loss angle on frequency. This model of course matches better with our experimental results but I am honestly not sure if this much slope makes any sense.

Auto-updating Best Measurement analyzed with allowing a power-law slope on Bulk Loss Angle:

RXA: I deleted this inline image since it seemed to be slowing down ELOG (2020-July-02)

## Major Questions:

• What are the known reasons for the frequency dependence of the loss angle?
• Do we have any prior knowledge about such frequency dependence which we can put in the analysis as prior distribution?
• Is this method just overfitting our measurement data?

Analysis Code

Attachment 1: CTN_Bayesian_Inference_Final_Analysis_with_Slope.pdf
2608   Thu Feb 11 18:01:39 2021 AnchalDailyProgressInstrumentCharacterizationSR560 Intermodulation Test

I added script SRIMD.py in 40m/labutils/netgpibdata which allows one to measure second order intermodulation product while sweeping modulation strength, modulation frequency or the intermodulation frequency. I used this to measure the non-linearity of SR560 in DC coupling mode with gain of 1 (so just a buffer).

### IP2 Characterization

• Generally the second order intercept product increases in strength proportional to the strength of modulation frequency with some power between 1 and 2.
• The modulation frequency strength where the intermodulation product is as strong as the original modulation frequency signal is known as intercept point 2 or IP2.
• For SR560 characterization, I sent modulation signal at 50 kHz and set intermodulation frequency to 96 Hz.
• The script sends two tones at 50 kHz and 50khz -96 Hz at increasing amplitudes and measured the FFT bin around 96  Hz with dinwidth set by user. I used 32 Hz bin width.
• In attachment 1, you could see that beyond 0.1 V amplitude of modulation signal, the intermodulation product rises above the instrument noise floor.
• But it weirdly dips near 0.8 V value, which I'm not sure why?
• Maybe the modulation signal itself is too fast at this amplitude and causes some slew rate limitation at the input stage of SR560, reducing the non-linear effect downstream.
• Usually one sees a straight curve otherwise and use that to calculate the IP2 which I have not done here.

### IMD2TF Characterization

• First of all, this is a made up name as I couldn't think of what else to call it.
• Here, we keep the amplitude constant to some known value for which intermodulation signal is observable above the noise floor.
• Then we sweep the modulation frequency and intermodulation frequency both, to get a 2-dimensional "transfer function" of signal/noise from higher frequencies to lower frequencies.
• Here I kept the source amplitude to 0.4V and swept the modulation frequency from 10kHz to 100kHz and swept the intermodulation frequency from 96 Hz to 1408 Hz, with integration bandwidth set to 32 Hz.
• I'm not completely sure how to utilize this information right now, but it gives us an idea of how much noise from a higher frequency band can jump to a lower frequency band due to the 2nd order intermodulation effect.

Edit Wed Feb 17 15:34:40 2021:

Adding self-measurement of SR785 for self-induced intermodulation in Attachment 3 and Attachment 4. From these measurements at least, it doesn't seem like SR785 overloaded the intermodulation presented by SR560 anywhere.

Attachment 1: IP2SR560_11-02-2021_175029.pdf
Attachment 2: IMD2TFSR560s_11-02-2021_180005.pdf
Attachment 3: SR785_SelfIP2_12-02-2021_145140.pdf
Attachment 4: SR785_SelfIMD2TF_12-02-2021_145733.pdf
Attachment 5: SR560.zip
6   Thu Nov 12 17:39:49 2009 FrankElectronicsVCOtuning range

tuning range of the 80MHz VCO used for the frequency stabilization:

21   Mon Nov 30 15:01:40 2009 FrankElectronicsVCOVCO tuning

measured frequency tuning vs wideband input of VCO for calibration of measured spectra. graph coming soon...

Rana: measured spectra? Has there actually been a beat frequency measured after all these years???

22   Sun Dec 6 13:20:52 2009 FrankElectronicsVCOVCO tuning

 measured frequency tuning vs wideband input of VCO for calibration of measured spectra. graph coming soon... Rana: measured spectra? Has there actually been a beat frequency measured after all these years???

no, i mean i re-measured the slope of the frequency modulation input of the VCO with a lot more points. The  coefficient (MHz/V) changes a lot over the input range from -5V to 5V (internal gain of 2). We need this to calibrate the spectrum of the feedback-signal (into the VCO) for the 2nd cavity.

Attachment 2: vco-tuning.ps
27   Thu Dec 17 18:13:01 2009 FrankElectronicsRefCavpower supply remote programming

pictures taken from the existing power supply.

.

42   Tue Feb 2 16:36:46 2010 FrankElectronicsDAQDAQ pinouts

3123-card (16bit input), 25pin d-sub connector

 channel LO HI 0 2 14 1 16 3 2 5 17 3 19 6 4 8 20 5 22 9 6 11 23 7 25 12

4116-card (16bit output), 50-pin connector

 channel LO HI 0 3 4 1 5 6 2 7 8 3 9 10 4 11 12 5 13 14 6 15 16 7 17 18

43   Tue Feb 2 18:22:38 2010 FrankElectronicsDAQQPD channels

QPD channels for RefCav beam pointing measurements:

C3:PSL-RCAV_QPDX : X

C3:PSL-RCAV_QPDY : Y

C3:PSL-RCAV_QPDSUM : SUM

107   Tue Apr 13 18:23:41 2010 Tara ChalermsongsakElectronics TF of PDH Box

I measured TF of PDH box, D0901351, (The one we have was modified). This box sends the signal to VCO.

SR785 measures at low frequency ( 1 Hz to 100kHz)

4935A measures at high frequency (10Hz to 1Mhz)

The integrator switch of the PDH box is turned off. This will be calculate later. The gain is set at 10.

The magnitude as mesured by 4935A is corrected for impedence match by x1.2.( 4935A and the PDH box have 50 ohm impedence for both inputs and outputs.)

This data will be used for control loop model later.

Blue, data from sr785

Green, Data from 4395A, I didnot use the power splitter to split the signal from source.

Red, Data from 4395A, with power splitter to divide power from source. (The power has to be increased to -30dB)

The first plot is magnitude of the TF, the second plot is phase shift, as usual Bode plot.

Attachment 1: tf_PDH_04_09.png
Attachment 2: tf_PDH_04_09_phi.png

in order to gain more s/n ratio i modified the existing AD590 readout-box a little bit. I assumed that we wanna operate the cavity at 35C (which is not too high but well above RT or the temp of an additional temp stabilized box around both cavities) The required range for shifting the cavities is ~ 1 FSR, better would be a little bit more for each cavity as we can shift both independent.
As

df~156MHz /K    and     1 FSR~740MHz

this corresponds to ~4.75K/FSR we have to shift.

For testing purposes it might be helpful to have more than that as e.g. if we limit the total range to lets say 6K we might end up at the end of the range and run into trouble as soon some disturbance from outside (e.g we remove part of the insulation, lets say an end cap) might shift the whole thing at the end of the range. As soon as this happens the servo would go crazy.

So i think we should go for 10K range, centered around 35C, so from 30C to 40C. I modified the box for that, so the transimpedance resistors have now a value of 29.4K, which gives us ~9.21V for 40C at the output of this stage.

In order to supply it from an independed power supply to reduce our current ground loops, i've chosen a WM071, the same as we use for the PDH boxes. As they come only in +/-15V, i had to change the voltage regulators in the box to +/-12V instead of =/-15V.
This results in a maximum output voltage of the LT1125 of a couple of 100mV more than 10V, depending on the current they have to source/sink. So 9.2V is still well below the max.

I added a filtered 5V reference, (AD586, 4.7uF filter cap) for the dc offset @35C. The corresponding resistor for the summing amp is 1379.76 which can be implemented almost exact using 2k05 and 4k22 in parallel (1379.7) or 1k54 and 13k3 (1380.2). The feedback resistor of the last stage can then be calculated to be 170k45 in order to match 30C to 40C to -10V to 10V. Paralleling can be used here as well to get an almost exact value.

The matching is not that critical as we don't wanna measure absolut temp, but if can do it that easy why not.

---  new schematic following soon   ---

109   Fri Apr 16 10:45:04 2010 Tara ChalermsongsakElectronics Control Loop for PSL

This is the control loop for the current PSL setup.

There are still components to be added.

1) TF of the PDH box, the one we have is a modified D0901351, so I measured the TF of this box when the integrator is off (April13,2010 entry.)

This will be added in the model later. It is set to 1 for now.

2) TF of the photodiodes, I assume they are  Newfocus 1811 and choose the same value as used in linfss6.m.

3) I will verified the value of TF of the RefCav path (both Fast and PC paths are calculated from D980536) to see if they agree.

4) The TF of actuators will be added later.

Attachment 1: psl5_fig.png
Attachment 2: linpsl5.m
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%	UPDATED APRIL 15, 2010, Tara Chalermsongsak
%    linearize the Simulink block diagram of	 the     %
%	      FREQUENCY STABILIZATION SERVO       	 %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% This gets the linearized model from the simulink model
% "psl5.mdl"
deg = 180/pi;
... 219 more lines ...
110   Wed Apr 21 15:21:52 2010 Tara ChalermsongsakElectronics TF of PDH Box

I calculated the TF of the modified PDH box and fit it with the measurement. The comparison does not match perfectly. I'll take a look and check if all Rs and Cs in the circuit are actually the same as those in the box.

The circuit can be found at:

https://dcc.ligo.org/DocDB/0003/D0901351/002/pdh_b_v2.pdf

I checked only U7 and U4

R28 is 360 ohms

C18 is 3300 pF

C6 is 0.66 (2x0.33uF) uF

R30,R31, R23,R16,R24 have the same resistance as specified

C20,C28, C29, C14,C15, R25, C11 are removed.

The calculation assumes that the integrator switch is off (R16 is connected parallel to R24 and C6)

If this works, the TF for PDH will be used in the simulink model.

Attachment 1: 2010_04_20_bode_com.png
111   Wed Apr 21 15:39:46 2010 ranaElectronics TF of PDH Box

Use LISO for circuit simulation.

113   Mon May 3 15:47:58 2010 Tara ChalermsongsakElectronics TF of PDH Box

The values of some r and c in the circuit are corrected, I used wrong values last time ( details will be added later.)

The measured TF and calculated TF using LISO are plotted below. The measurement and calculated data agree well from 1 to 10^5 Hz using SR785.

The correction factor due to mismatch impedance when using 4395A will be checked again.

Attachment 1: TF_5_3.png
159   Sat Jun 12 17:11:26 2010 KojiElectronicsVCOPSL VCO removed and sent to LLO

As per the request from LLO, the PSL VCO was sent to the site.

We have to figure out how we continue the work.

161   Tue Jun 15 09:44:56 2010 taracElectronics PMC servo TF

The weird TF result from PMC seems to be the result of the insufficient voltage input. When I increased the swept sine voltage from 2mV to 500 mV, the result of the TF becomes as expected. See fig 1.

Before the signal is fed back to PMC, there is a PMC notch box. It is a low pass filter. It's TF looks fine (fig.2.)

However, when the TF of the servo and the notch is measured together, they look shaky.

I just read Frank's comment. I'll check the schematic of the PMC servo again.

Attachment 1: PMC2_bode.png
Attachment 2: notch_bode.png
Attachment 3: PMC2_bode.png
162   Tue Jun 15 10:14:32 2010 FrankElectronics PMC servo TF

that's not the TF of the PMC servo, it's something else. look at the gain level: -100dB. that's not more than some crosscoupling. Never trust a flat response, always think if the measured form and values make sense at all !

Take a minute and think about the form and values of the TF you expect from a servo like this. Have a look into the schematic and draw the TF shape of the individual gain stages and add them to an overall TF or use LISO to simulate it.  Then measure parts of the servo step by step in order to verify that the individual parts are working as expected.

 Quote: The weird TF result from PMC seems to be the result of the insufficient voltage input. When I increased the swept sine voltage from 2mV to 500 mV, the result of the TF becomes as expected. See fig 1.     Before the signal is fed back to PMC, there is a PZT notch box. It is a low pass filter. It's TF looks fine (I'll update it.) However when the TF of the servo and the notch is measured together.

163   Tue Jun 15 13:36:18 2010 taracElectronics debugging PMC servo

From the bode plot, something is not quite right. I'll debug the PMC servo. My plan is

1) Measure the TF from FP1 test to FP4 (output mon), change gain setting and see if the TF change as expected.

*note the real TF is 20log (Vpzt/ Vin) but Vpzt ~ 50 Vmon.  Vmon is connected to Vpzt with divider circuit. To get the real TF, 20log(Vpzt/Vin), the magnitude from out TF between FP1 and out mon will be added by 20log50 = 34 dB.

2) Compare it with the calculated TF from PMC schematic

169   Sun Jun 20 02:17:06 2010 ranaElectronicsRefCavphase noise of IFR + Rubidium

see this entry

179   Tue Jun 29 11:45:47 2010 FrankHowToNoiseBudgetunit converter

http://www.matweb.com/tools/unitconverter.aspx

188   Wed Jun 30 00:37:49 2010 ranaHowToComputersPMC servo debugging

 Quote: I was going to check the TF on each stage of PMC's servo. Unfortunately, I couldn't find the floppy disc drive, so I slide the sliders (gain, RF power) around. When I add more RF power (from 1V to 7V) to 21.5 MHz EOM, the oscilaltion subsides*.

How sad. Stop using the floppies and get one of the GPIB-Ethernet converters from Dmass. You can download the python scripts from the 40m wiki.

189   Wed Jun 30 00:59:13 2010 FrankHowToComputersPMC servo debugging

Quote:

 Quote: I was going to check the TF on each stage of PMC's servo. Unfortunately, I couldn't find the floppy disc drive, so I slide the sliders (gain, RF power) around. When I add more RF power (from 1V to 7V) to 21.5 MHz EOM, the oscilaltion subsides*.

How sad. Stop using the floppies and get one of the GPIB-Ethernet converters from Dmass. You can download the python scripts from the 40m wiki.

we already have one but i was waiting for one the wireless bridge devices someone wanted to buy to make it wireless.

But why do you need a floppy to measure a TF?

190   Wed Jun 30 11:34:37 2010 FrankHowToPMCPMC fixed

the reason why you had this flickering problem was that you had too much power on the RFPD in reflection of the PMC. You already saturated it.
I also reduced the RF power as the error signals were not signals anymore, just spikes.

my new settings are:

RF power : 3.0
Phase : 2.5
PMC Gain: 14dB

reduced laser power to 40mW. Transmitted power is 32mW .You have to exchange the output coupler mirror in front of the RFPD in order to increase the power. I think 32mW is enough, it's something like 13mW per cavity.

ELOG V3.1.3-