Here are my thoughts on calibration errors. This applies to the single arm actuation calibration, but may easily be extended to calibrate the DARM residual noise for example.

According to the math in this post, there are four parameters whose estimates build the total calibration uncertainty: arm length, wavelength, loop gain, and beatnote fluctuation. Below is a table for how each is measured, what the sources of statistical versus systematic error are, how large each relative contribution roughly is, and how we may improve on them.

Arm length

Statistical

The arm length has been estimated before by locking the arm with the ALS beat, scanning the arm length and looking at the IR resonances. From the statistical uncertainty standpoint the limit seems to be number of measurable FSRs. Using these numbers, the statistical uncertainty comes to ~ 0.6%. Other attempts claim to have improved on this by almost an order of magnitude giving ~ 0.02%. Simply scanning over more FSRs should improve this as the usual square root number of measurements statistical error reduction.

Systematic

Systematic error comes from the frequency referenced on this measurement (the Marconi 11 MHz sideband oscillator), nonlinearities in the mostly linear scan (e.g. POS to PIT coupling). I think it's safe to neglect frequency offsets > 1 Hz because of the Rb clock reference and the Marconi's own calibration. I'm not sure about the POS to PIT coupling magnitude and whether F2A filters are helping here, but offset scan nonlinearities should distort the FSR nonuniformly and this error may have sneaked into the statistical estimate above. From the posts referenced above,  the scan result seems extremely linear, but repeating the measurement and plotting the residuals may give an accurate estimate of the nonlinearity. I think either of the systematic errors discussed here should be below or around the ppm (0.0001%) level, but this should be confirmed.

Wavelength

Statistical

If we use the NPRO specification Mephisto's wavelength is 1064 nm and there is no statistical error.

If on the other hand we do iodine absorption spectroscopy, we may be able to see ~ 4 lines throughout the 30 GHz tuning range of the NPRO. Fun fact: 30 GHz correspond to 1 cm-1 (inverse centimeter). Assuming we can scan our laser with a 0.01 cm-1 resolution, it may be possible to estimate the absolute wavelength to 10 better than any line center. The ATLAS of iodine spectroscopy gives strong absorption lines around 532 nm to 0.001 cm-1, or 0.00001% accuracy. A simple Doppler broadened absorption should improve this further.

Systematic

If we use the NPRO specification the systematic error comes from the number of known significant figures ~ 0.047 %. A slightly better estimate comes from the Prometheus model with a frequency doubled output hitting near the P 83(33-0) line of iodine, at 18787.814 cm-1. This gives a nominal wavelength of 532.259 nm, or 1064.518 nm on the seed. Because the tuning range is 30 GHz, our systematic error may be +0.03 nm - 0.07 nm from 1064.52 nm. Taking the median of 0.05 nm, the relative systematic error from the Nd:YAG specification is 46.9 ppm = 0.0047%.

If on the other hand we do iodine spectroscopy, the systematic error will be dominated by the residual shifts on the iodine vapor, which are negligibly small compared to the Doppler broadened lines. They might add sub-ppm uncertainty to the absolute calibration.

Beat fluctuations

Statistical

The error in estimating beatnote fluctuations is statistically dominated if our beat detection is shot noise limited for example. Other stationary noises with power law spectra decaying faster than 1/f are subject to this effect. The allan deviation discriminates the timescales at which our measurement is dominated by statistical error. Currently our calibration lines have SNR of 10 to 100. Averaging seems to be limited to ~ 100 second timescales, so the statistical error on these measurements is ~ 0.1 to 1.0 %.

Systematic

As suggested in the above, the allan deviation discriminates the statistical dominated timescales for this measurement. There is a correspondence between noise spectra and allan deviation, so we should be able to point out what noises contribute to systematic drift in our ALS noise budget.

Loop gain

Statistical

Invoking Bendat and Piersol, Table 9.6 gives the statistical estimate of loop gain estimate with coherence gamma, and n_avg number of averages. Because of our resonant OL gain filters, assuming G ~ 100 there, and high coherence on the OLTF measurement so gamma ~ 0.9, with 12 averages we should get a relative loop gain error of 9.8%.

Systematic

Also from B&P, we should estimate how biased our TF is. This depends on delays, bandwidths, measurement device noises, etc. Furthermore, the analog electronics in the AUX servo should drift, but we neglect this contribution for now. A simple bias estimate (eq 9.75) tells us that the coherence is biased by the number of averages such that in our estimate above the unbiased coherence is roughly 0.897. This means our systematic contribution from TF bias is ~ 0.17 %.

We should remember that in the case of loop gain, the total error (systematic + statistical) gets an extra suppression factor of the order of the loop gain itself. Radhika's resonant digital gain filters should easily allocate 40 dB (or ~ 100) on every calibration line such that our total calibration error drops to the 0.1% level.

Conclusions

• The main calibration error (at the 1% level) seems to be from the ALS beat frequency. We can simply crank the SNR up, but we should work on the ALS relative stability. I think the low frequency end of the ALS residual frequency noise is currently limited by DFD... I wonder if we can improve on this by implementing a digital PLL (e.g. using a Moku)

Calibrated ETMY actuation strength using ALS. Attachment #1 shows the result, in close agreement with this previous measurement and a combined uncertainty estimate of 0.88%. The data was taken with 5 oscillators on, at slightly different strengths than with the ITMY run, and the actuation was on ETMY.

The ETMY actuation strength is

10.843e-9 / f^2 +- (0.88)% [m/count]

Note: gpstimes for raw data are 1356490036 to 1356495400 (a little bit over an hour and a half).

1. how much frequency dependent variation in the transfer function do we expect? Are there resonances in the mechanical suspension cage or the violin modes?
2. it would be interesting to make the same TF, but from counts to coil current, and see if the variation is there. I don't expect to see much variation in the electronics, but there might be something. In principle, we can just measure the voltage at the satellite box, but the coil cable's capacitance and the coil inductance make for some wiggle. I think the resonant frequency ought to be ~ 100 kHz, but perhaps there are some wiggles due to frequency response in the AI filter or something.

[Paco, Anchal]

One of the crucial and currently limiting calibration errors is in the ALS beat. We think a major driver of calibration uncertainty may be the DFD TF calibration since it depends on the RF beat power.

The RF beat power as monitored by C1:ALS-BEATY_RF_POW shows relative fluctuations of 0.02% at the 16 Hz sampling rate (actually 0.09% rms from Attachment #1) once the single arm and YAUX laser are both locked. This sounds ok, but that's just a statistical estimate. The beat frequency changes every time we break and reacquire the lock, making the BEAT PD frequency response and DFD overall calibration change their nominal TF. This changes can be significantly larger than 0.02% (e.g 4.9% = observed change in the RF power after breaking and reacquiring the YAUX lock this morning). This is far more significant than the contribution from the RIN on the two lasers.

This kind of systematic error could be addressed by either/all:

• Stabilizing the ALS BEAT absolute frequency (offset locking using freq counter and simple integrator or equivalent)
• Rejecting RF beat amplitude fluctuations by mixing a stable DC voltage in the DFD, or using a comparator. 
  • Our plan this afternoon is to quickly measure the RF AM rejection level from a simple mixer and a stable voltage reference and plan ahead.
• ISS on both lasers

The callibration constants were updated for the oplev pitch and yaw. The values were changed as denoted in 17471 were:

     PITH: 175.7→ 155 cts/urad

     YAW: 193 → 241 cts/urad

To make these changes for the oplev callibration constants I went to ETMY - SELECTED OPLEV SERVO BOX

I then opened OLMATRIX and turned off PITCH and YAW servos in the ETMY SUSPENSION SCREEN such that the system does not attempt to actively make corrections while values are being changed. 

Then I adjusted the matrix to include our updated calibration constants and reinitiated the oplev ptich and yaw servo's

This updated the calibration constants for everything

The next change that was made was the addition of the calibration filters for position, pitch, yaw and side into the sitemap view for the suspension systems.

Adding calibration filters will allow us to callibrate the pos, pitch, yaw, and side to true values of urad and umeters (see 17459)

The final screen may be seen bellow (the updated area is outlined in red):

When each of the filter buttons is clicked, the following screen will now appear (circled in yellow is the calibration constant gain we will be calculating and entering into the system):

To create the edits to the controls screen we must complete the following process

We can edit the original screen - right click > evaluate > edit this screen

Then I adjusted the width of the overall screen, and moved the right half of the modules over to the right so I could fit in some filter buttons. I then Navigated to the c1ioo wfs master screen using the open feature to copy a pre existing filter module

I then adjusted the filter module and its contents to correspond to the features and autogenerated model files from RTCDS

There was some rearranging and adjusting needed to get these files in place first. The autogenerated files from the RTCDS can be found in dir = "/opt/rtcds/caltech/c1/medm/c1sus/"

They were autogenerated with names "C1SUS_BS_PITCAL.adl", "C1SUS_BS_POSCAL.adl", "C1SUS_BS_YAWCAL.adl","C1SUS_BS_SIDECAL.adl" 

We copied these files to dir = "/opt/rtcds/userapps/trunk/sus/c1/medm/templates/NEW_SUS_SCREENS/"

The file names were changed to "SUS_PITCAL.adl", "SUS_POSCAL.adl", "SUS_YAWCAL.adl", "SUS_SIDECAL.adl" 

The directory we placed them in is where the models for c1 sus can be found that are referenced by the sitemap suspension monitor screen

Each file was then opened in Vscode and a few changes were made such that the specific naming values referenced by the different screens of the sitemap and different optics, are replaced by the overarching values seen in each instance of the screens.

There are approximately 50 referenced file names of "C1:SUS-BS_PITCAL" etc. In each instance we made the following changes:

"-BS" was changed to "-$(OPTIC)"

"C1:" was changed to "$(IFO):"

The new strings should read "$(IFO):SUS-$(OPTIC)_PITCAL"

Once this change was made we can now right click on the filter module box, click on "Label/Name/Args" button

In the display file, we must add the path name for the calibration directory "/opt/rtcds/userapps/trunk/sus/c1/medm/templates/NEW_SUS_SCREENS/SUS_POSCAL.adl"

And for the arguments box we will enter OPTIC=$(OPTIC), IFO=$(IFO)

You can also copy and paste the directory names in the file boxes using right click copy from the file manager and paste into the box using a single click of the mouse scroller wheel

Lastly, the PV limits were changed for each number output right click value box > PV limits > Precision > Source changed to "Default" with a value of 1.

The shown value of the position, pitch, yaw, and side was then changed to show the output from the newly added filter. This is done also by right clicking the value box and adjusting the "Readback Channel".

Value changed from "$(IFO):SUS-$(OPTIC)_TO_COIL_1_#_INMON" to the outputs from the filters which are

       "$(IFO):SUS-$(OPTIC)_POSCAL_OUTMON" (for others changing POSCAL to the appropriate variable)

This is how to edit and add the Medm screens for single suspension optics into the sitemap IFO SUS screen

Lastly, Tomohiro and I worked on acquiring 6 data sets from DC stepping through adjustments in pitch and yaw for MC1, MC2 and MC3. These datasets will be fit quadratically and combined with more tests dine by AC driving the stepper motors tomorrow to find the calibration constants for the mirrors.

Locked FPMI, measured DARM and CARM OLTFs, locked YAUX and measured the analog loop TF at the cal line frequencies. Turned the cal lines on with the new filters Anchal added on MC2 (ResGain within and Notches outside the CARM bandwidth which is set to 200 Hz), and hope to get 3600 seconds of data this evening. Log and measurement data are saved under /opt/rtcds/caltech/c1/Git/40m/scripts/CAL/FPMI

On rossa in tmux session name FPMI_DARM_Cal, a script is running to take FPMI DARM calibration data at 1:00 am on March 9th. Please do not disturb the experiment untill 6 am. To stop the script do following on rossa:

The script will lock both arms, run ASS, then lock FPMI, then tune beatnote frequency with Y AUX laser to around 40 MHz, set phase tracked UGF to 2 kHz, clear phase history, take OLTF of DARM from 2 kHz to 10 Hz, take OLTF of CARM and AUX loop at calibration line frequencies, turn on the calibration lines, and wait for FPMI to unlock or 5 hours to pass, whatever happens first. At the end it will turn off the calibration lines.

Running this test again tonight. Will probably run it every night now.

SN 46,795 of 2003 is back.

Just a quick note for now: I've repopulated C1CAL with a limited set of lockin oscillators/demodulators, informed by the aLIGO common LSC model. Screens are updated too. 

Rather than trying to do the whole magnitude phase decompostion, it just does the demodulation of the RFPD signals online; everything beyond that is up to the user to do offline. 

Briefly testing with PRMI, it seems to work as expected. There is some beating evident from the fact that the MICH and PRCL oscillation frequencies are only 2Hz apart; the demod low pass is currently at an arbitrary 1Hz, so it doesn't filter the beat much. 

Screens, models, etc. all svn'd.

Diagnoses from Glasglow:

“So far we have analyzed the laser. The pump diode is degraded. Next we would replace it with a new diode. We would realign the diode output beam into the laser crystal. We check all the relevant laser parameters over the whole tuning range. Parameters include single direction operation of the ring resonator, single frequency operation, beam profile and others. If one of them is out of spec, then we would take actions accordingly. We would also monitor the output power stability over one night. Then we repackage and ship the laser.”

1W Innolight is NOT getting Noise Eater as it was decided yesterday at the 40m meeting. Corrected 3-25-2016

Repair quote with adding noise eater is in 40m wiki

The laser is back. Test report is in the 40m wiki as New Pump Diode Mephisto 1000

It will go on the PSL table.

I brought a bunch of SR560s over for repair from Bridge labs. This unit, picture attached (SN 49698), appears to still not be retaining charge. I’ve brought it back. 

I made some rough measurements, using the setup I had used for CCD calibration, to get an idea of how good of a Lambertian scatterer the white paper is. Following are the values I got:

Note: All the measurements are just rough ones and are prone to larger errors than estimated.

I also measured the transmittance of the white paper sample being used (it consists of 2 white papers wrapped together). It was around 0.002

Summary:  I calibrated MC2 pitch and yaw offsets to spot position in mm. Here's what I did:

1. Changed the MC2 pitch and yaw offset values using  ezca.Ezca().write('IOO-MC2_TRANS_PIT_OFFSET', <pitch offset value> ) and ezca.Ezca().write('IOO-MC2_TRANS_YAW_OFFSET', <yaw offset value> )
2. Waited for ~ 700-800 sec for system to adjust to the assigned values
3. Took snapshots with the 2 GigEs I had installed - zoomed in and zoomed out. (I'll be using these to make a scatter loss map, verify the calibration results, etc)
4. Ran the mcassDecenter script, which can be found in /scripts/ASS/MC. This enters the spot position in mm in the specified text file.

Results:  In the pitch/yaw vs pitch_offset/yaw_offset graph attached,

• intercept_pitch = 6.63 (in mm) ,  slope_pitch = -0.6055 (mm/counts) 
• intercept_yaw = -4.12 (in mm) ,  slope_yaw = 4.958 (mm/counts) 

Summary : 

I have been working on analyzing the seismic data obtained from the 3 seismometers present in the lab. I noticed while looking at the combined time series and the gain plots of the 3 seismometers that there is some error in the calibration of the BS seismometer. The EX and the EY seismometers seem to be well-calibrated as opposed to the BS seismometer.

The calibration factors have been determined to be :

BS-X Channel: 

BS-Y Channel: 

BS-Z Channel:

Details :

The seismometers each have 3 channels i.e X, Y, and Z for measuring the displacements in all the 3 directions. The X channels of the three seismometers should more or less be coherent in the absence of any seismic excitation with the gain amongst all the similar channels being 1. So is the case with the Y and Z channels. After analyzing multiple datasets, it was observed that the values of all the three channels of the BS seismometer differed very significantly from their corresponding channels in the EX and the EY seismometers and they were not calibrated in the region that they were found to be coherent as well. 

Method :

Note: All the frequency domain plots that have been calculated are for a sampling rate of 32 Hz. The plots were found to be extremely coherent in a certain frequency range i.e ~0.1 Hz to 2 Hz so this frequency range is used to understand the relative calibration errors. The spread around the function is because of the error caused by coherence values differing from unity and the averages performed for the Welch function. 9 averages have been performed for the following analysis keeping in mind the needed frequency resolution(~0.01Hz) and the accuracy of the power calculated at every frequency. 

1. I first analyzed the regions in which the similar channels were found to be coherent to have a proper gain analysis. The EY seismometer was found to be the most stable one so it has been used as a reference. I saw the coherence between similar channels of the 2 seismometers and the bode plots together. A transfer function estimator was used to analyze the relative calibration in between all 3 pairs of seismometers. In the given frequency range EX and EY have a gain of 1 so their relative calibration is proper. The relative calibration in between the BS and the EY seismometers is not proper as the resultant gain is not 1. The attached plots show the discrepancies clearly : 

• BS-X & EY-X Transfer Function : Attachment #1
• BS-Y & EY-Y Transfer Function : Attachment #2

          The gain in the given frequency range is ~3. The phase plotting also shows a 180-degree phase as opposed to 0 so a negative sign would also be required in the calibration factor. Thus the calibration factor for the Y channel of the BS seismometer should be around ~3. 

• BS-Z & EY-Z Transfer Function : Attachment #3

The mean value of the gain in the given frequency range is the desired calibration factor and the error would be the mean of the error for the gain dataset chosen which is caused due to factors mentioned above.

Note: The standard error envelope plotted in the attached graphs is calculated as follows :

         1. Divide the data into n segments according to the resolution wanted for the Welch averaging to be performed later. 

         2. Calculate PSD for every segment (no averaging).

         3. Calculate the standard error for every value in the data segment by looking at distribution formed by the n number values we obtain by taking that respective value from every segment.

Discussions :

The BS seismometer is a different model than the EX and the EY seismometers which might be a major cause as to why we need special calibration for the BS seismometer while EX and EY are fine. The sign flip in the BS-Y seismometer may cause a lot of errors in future data acquisitions. The time series plots in Attachment #4 shows an evident DC offset present in the data. All of the information mentioned above indicates that there is some electrical or mechanical defect present in the seismometer and may require a reset. Kindly let me know if and when the seismometer is reset so that I can calibrate it again.