The new 2x2 fiber couplers arrived today so Eric gave me an overview on the changes to be made to the existing configuration of the FOL fiber box. I removed the box from the table after ensuring that the PDs were powered OFF and removing and capping all fiber leads on the front panel. Here is a summary of the changes made.

• On-Off positions for the rocker switches corrected - these switches for the power to the PDs were installed such that the "1" position was OFF. I flipped both the switches such that the "1" position now corresponds to ON (see Attachment #1).
• All the couplers/beam combiners/splitters were initially removed. 
• I then re-configured the layout as per the schematic (Attachment #2). I only needed to use one of the 4 new 2x2 couplers ordered. I think the 1x2 couplers are appropriate for mixing the PSL and AUX beams, as if we use a 2x2 coupler, half of the mixed light goes nowhere? Indeed, if we had one more such coupler, we could do away with the 2x2 coupler I am now using to divide the PSL light into two. 
• The spec-sheets on the inside of the top cover were updated to reflect the new hardware (Attachment #3).
• The old hardware from the box that was not used, along with their spec-sheets, are stored temporarily in a Thorlabs lab snacks box (all the fibers have been capped).
• The finished layout is shown in Attachment #4.

I then ran a quick check to see what the power levels were at the input to the PDs, using the fiber coupled power meter. However, I found that there was no light in the fiber marked "PSL light in" (the power meter read out "Sig. Low"). The X arm Aux light had an input power of 1.12 mW, which after the various coupling losses etc went down to 63 uW just before the PD. The corresponding figures for the Y arm are 200 uW and 2.2 uW. I am not too sure of how the AUX light is coupled into fibers so I am not trying to tweak the alignment to see if I get more power. 

Eric pointed out that the 1x2 couplers that were used in the previous arrangement and which I recycled, were in fact NOT appropriate - they are not 50-50 couplers but 90-10 couplers, which explains the measured power levels I quoted here.

I switched out these for a pair of the newly arrived 2x2 couplers, and have also replaced the datasheets on the inside of the top cover. I then redid the power level measurements, and got some sensible values this time (see Attachment #1 for revised layout and measured power levels, numbers in red are powers for PSL light, numbers in green are for AUX laser light, and all numbers are in mW). I did find that the 90-10 splitter in the PSL+Y path was not working (though the one in the PSL+X path seems to be working fine), and hence, have not quoted power levels at the output of these splitters. For now, I guess we can bypass the splitters and take the PSL+AUX light from the 2x2 couplers directly to the PDs.

[gautam, ericq]

We had a look at the IR beat (PSL+Xarm) today using the new FOL fiber box, and compared it to the green beat signal for the same combination. We first switched out the green Y beat input into the RF amplifiers on the PSL table with the PSL+Xarm IR beat input (so in all the plots, the BEATY channels really correspond to the IR beat for PSL+X). The IR and green beat notes were found without much difficulty, and we compared the beat signal PSDs for the green and IR signals (see Attachment #1 - arms were locked to green and the X slow control was turned on). The pink trace (labeled REF1) corresponds to the green beat signal, and was in good agreement with an earlier reference trace Eric had saved for the same signal. The teal trace (labeled REF0) corresponds to the the IR beat signal monitored simultaneously. 

We then went back to the PSL table to check the amplitude of the signal from the broadband fiber PDs using the Agilent network analyzer. An initial measurement yielded a beat note (@~50MHz) at ~-22dbm (17mV rms). We figured that by bypassing the 90-10 splitter in this path, we could get a stronger signal. But after switching out the fiber connections we found that the signal amplitude had fallen to ~-27dbm (10mV rms). As per my earlier measurements here, we expect ~600uW of light on the PD, and a quick calculation suggested the signal should be more like 60mV, so we used the fiber power meter to check the power levels after each of the couplers again. We then found that the fiber connector on the front panel of the box for the PSL input wasnt ideal (the laser power after the first 50-50 coupler was only ~250 uW, though the input was ~1.2  mW). The power after the first coupler also fluctuated unpredictably (<100 uW to 350 uW) in response to slightly tightening/loosening the fiber connections on the front panel. I then switched the PSL input to one of the two unused fiber connectors on the front panel (meant for the 10% of the beat signal for the DC readout), and found that this input behaved much better, with ~450 uW of power available after the first 50-50 coupler. The power going into the beat PD was also measured to be ~550uW, closer to what was expected. The beat signal peak now was ~-14dbm (~30mV rms).

We then once again repeated the comparison between green and IR beat signals - but while in the control room, I noticed that the beat signal amplitude on the network analyzer in the control room was fluctuating by nearly 1.5 divisions on the vertical scale - not sure what the reason for this is. A look at the PSD of the IR beat with higher power incident on the PD was also not encouraging (see blue trace in Attachment #1), it seems to have gotten worse in the 10-30 Hz range. We also looked at the coherence between the beat spectrum and the beat note amplitude in order to look for any linear coupling between the two, but from Attachment #2, we cannot explain the disparity between the green and IR beat spectra. This warrants further investigation.

Everything on the PSL table has now been restored to the configurations before these investigations (i.e. the Y+PSL green beat cable has been reconnected to the RF amplifier, and both green beat PDs have been powered back ON. The fiber PDs are powered OFF) 

The new ZKL-1R5 RF amplifier that Steve ordered arrived yesterday. I installed this in the frequency divider box and did a quick check using the Fluke RF signal generator and an oscilloscope to verify that both the X and Y paths were working. 

I've now installed the box in the 1X2 rack where the olf "RF amplifiers for ALS and FOL" box used to sit (I swapped that out as I needed the L brackets on that chassis to mount mine, see Attachment #1 for the new layout). The power cable that used to power the old chassis was available, but the connector was of the wrong gender, so I had to switch this out. After verifying that I was getting the correct voltage (+15V), I connected it to the chassis.

I then did a quick check with the Fluke generator to make sure that all was working as expected - Eric had set up some ADC channels for me earlier today in the C1ALS model, and I copied over my frequency counting module from C1TST into C1ALS, and recompiled the model. The RF generator was set to generate a 25MHz signal at -20dBm, which I then split using an RF power splitter between the X and Y arms. I then checked the output using dataviewer - I recovered an output frequency of ~27.64 MHz with a jitter of ~0.02 MHz with a 20Hz low-pass filter in place (see Attachment #2), which looks consistent with the systematic error inherent in the zero-crossing counting algorithm and random fluctuations I had observed in my earlier trials, discussed here. But a more systematic investigation needs to be carried out in this regard. The interfacing between the hardware and software seems to be working alright though. I've left the RF generator near the 1x2 rack for now, though its powered off. 

The mode cleaner unlocked quite a few times while I was working but looks stable now. 

I carried out some more tests on the digital frequency counting system today, mainly to see if the actual performance mirrors the expected systematic errors I had calculated here. 

Setup and measurement details:

I used the Fluke 6061A RF signal generator to output an RF signal at various frequencies, one at a time, between 10 and 70 MHz. I split the signal (at -15 dBm) into two parts, one for the X-channel and one for the Y-channel using a mini-circuits splitter. I then looked at the input signal using testpoints I had set up within the model, to decide what thresholds to set for the Scmitt trigger. Finally, I averaged the outputs of the X and Y channels using z avg -s 10 C1:ALS-FC_X_FREQUENCY_OUT and also looked at the standard deviation as a measure of the fluctuations in the output (these averages were taken after a low-pass filter stage with two poles at 20Hz, chosen arbitrarily).

Results:

• Attachment #1 shows a plot of the measured RF frequency as a function of the frequency set on the Fluke 6061A. The errorbars on this plot are the standard deviations mentioned above. 
• Attachment #2 shows a plot of the systematic error (mean measured value - expected value) for the two channels. It is consistent with the predictions of Attachments #3 and #4 in elog 11628 (although I need to change the plots there to a frequency-frequency comparison). This error is due to the inherent limitations of frequency counting using zero crossings, I can't think of a way to get around this).
• I found that a lower threshold of 1800 and an upper threshold of 2200 worked well over this range of frequencies (the output of the Wenzel dividers goes between 0V and 2.5V, and the "zero" level for the digitized signal corresponds to ~2000, as determined by looking at a dataviewer plot of a tetspoint I had set up in my model). Koji suggested taking a look at the raw ADC input signal sampled at 64 kHz but this is not available for c1x03, the machine that c1als runs on. 

Summary:

I carried out some further diagnostics and found some ways in which I could optimize the zero-crossing-counting algorithm, such that the error in the measured frequency is now entirely within the expected range (due to a +-1 clock cycle error in the counting). We can now determine frequencies up to ~60 MHz with less than 1 MHz systematic error and <10 kHz statistical error (fluctuations after the 20 Hz lowpass). This should be sufficient for slow control of the end-laser temperatures.

Details: 

The conclusion from my earleir tests was that there was possibly an improvement that could be made to setting the thresholds for the Schmitt trigger stage in the model. In order to investigate this, I wanted to have a look at the 64K sampled raw input to the ADCs. Yesterday Eric helped me edit the appropriate .par file for viewing these channels for c1x03, and for an input frequency of 70MHz (after division, ~4.3 kHz square wave), the signal looked as expected (top left plot, attachment #1). This prompted me to check the counting algorithm again with the help of various test points I had setup within the model. I found that there was a tendency to under-count the number of clock-cycles between zero-crossings by more than 1 clock cycle, due to the way my code was organized. I fixed this and found that the performance improved dramatically, compared to my previous trials. With the revised counting algortihm, there was at most a +-1 clock cycle error in the counting, and the systematic error between the measured and requested RF frequencies is now completely accounted for taking this consideration into account. The origin of this residual error can be understood by looking at the top right plot in Attachment #1 - presumably because of the effects of some downsampling filter, the input signal to the Schmitt trigger isnt a clean square wave (even at 4kHz) - specifically, the time spent in the LOW and HIGH states of the Schmitt trigger can vary between successive zero crossings because of the shape of the input waveform. As a result, there can be a +-1 clock cycle error in the counting process. Attachment #2 shows this - the red and blue lines envelope the measured frequency for the whole range investigated: 10-70MHz. Attachment #3 shows the systematic error as a function of the requested frequency.

If there was some way to bypass the downsampling filter, perhaps the high-frequency performance could be improved a little. 

Steve pointed out that in the aftermath of the Nitrogen running out a couple of times last week, the RGA had shut itself off thinking that there was a leak and so it was not performing the scheduled scans once a day. So the data files from the scheduled scans were empty in the /opt/rtcds/caltech/c1/scripts/RGA/logs directory. The wiki page for getting it up and running again is up-to-date, but the script RGAset.py did not exist on the c0rga machine, which the RGA is communicating with via serial port. I copied over the script RGAset.py from rossa to c0rga and ran the script on that machine - but the error flags it returned were not all 0 (indicating some error according to the manual) - so I edited the script to send just the initialize command ('IN0') and commented out the other commands, after which I got error flags which were all 0. After this, I ran a manual scan using 'RGAlogger.py', and it appears that the RGA is now able to take scans again - I'm attaching a plot of the scan results. We've saved this scan as a reference to compare against after a few days. 

I'm working on setting up a moving-average in the custom C code block that counts the zero crossings to see if this approach is able to mitigate the glitchy frequency readout due to mis-counting by one clock cycle between successive zero crossings. I'm storing an array the size of the moving average window of frequency readouts at each clock cycle, and then taking the arithmetic mean over the window. By keeping a summing variable that updates itself each clock cycle, the actual moving average process isnt very intensive in terms of computational time. The array does take up some memory, but even if I perform the moving average over 1 second with 16384 double precision numbers stored in the array, its still only 130 kB so I don't think it is a concern. Some tests I've been doing while tuning the code suggest that with a moving average over 16384 samples (i.e. 1 second), I can eliminate glitches at the 1Hz level in the frequency readout for frequencies up to 5 kHz (generated digitally using an oscillator block). Some tuning still needs to be done, and the window could possibly be shortened. I also need to take a look at the systematic errors in this revised counting scheme, preferably with an analog source, but this is overall, I think, an improvement.

On a side note, I noticed some strange behaviour while running the cds average command - even though my signal had zero fluctuations, using z avg 10 -s C1:TST-FC_FREQUENCY_OUT gave me a standard deviation of ~1 kHz. I'm not sure what the problem is here, but all the calibration data I took in earlier trials were obtained using this so it would be useful to perform the calibration again. 

I've made quite a few changes in the software as well as the hardware of the digital frequency counting setup.

• The main change on the software side is that the custom C code that counts intervals between successive zero crossings and updates the frequency output now has a moving average capability - the window size is readily changable (by a macro in the first line of the code, which resides at /opt/rtcds/userapps/release/cds/c1/src/countZeroCrossingWindowed.c - however, changing the window size requires that the model be recompiled and restarted), and is currently set to 4096 because based on some empirical trials I did, this seemed to give me the frequency output with the least jitter, and also smaller systematic errors than in my earlier trials described here.
• The filter modules for both the X and Y channels now have 2 pole butterworth low pass filters with poles at 64Hz, 32Hz, 16Hz, 8Hz, 4Hz, 2Hz and 1Hz loaded. Again, based on my empirical trials, a combination of a moving average filter in the C code and the IIR filters after that worked best in terms of reducing the jitter in the frequency readout. I think the fact that the moving average 'spreads' the impulse caused by a glitch in the counting algorithm improves the response of the combination as compared to having only the IIR filters in place. 
• The Frequency Counting SIMULINK block has been cleaned up a little - I have removed unnecessary test points I had set up for debugging, and is now a library part called "FC".
• After the experience of having C1ALS crash as noted here, I was doing all my testing in the C1TST model. Having made all the changes above, I reverted to the C1ALS model, which compiled and ran successfully this time.
• On the hardware side, I interchanged the couplers mentioned here - so the 20dB coupler now sits on the X green beat PD, while the 10dB coupler sits on the Y green beat PD. This change was motivated by wanting to test out the digital frequency counting setup by performing an arm scan through an IR resonance using ALS, and we found that the PSL+Y green beat frequency was better behaved than the X+PSL combination.

Arm scan

Eric helped me test the new setup by doing an arm scan through an IR resonance by ramping the ALS offset from -3 to +3 with a ramp time of 45 seconds. The data was acquired with the window size of the moving average set to 4096 clock cycles, and a 2 Hz low pass IIR filter before the frequency readout. Attachment 1 shows a plot of the data, and a fit with a function of the form trans = a/(1+((x-b)/c)^2), where a = normalization, b = center of lorentzian, and c = linewidth (FWHM) of the peak (the fitted parameter values, along with 95% confidence bounds are also quoted on the plot). In terms of the data acquisition, comparing this dataset to one from an earlier scan Eric did (elog11111) suggests that the frequency counting setup is working reasonably well - at any rate, I think the data is a lot cleaner than before implementing the moving average and having a 20Hz lowpass IIR filter. In any case, we plan to repeat this measurement sometime next week during a nighttime locking session. It remains to calculate the arm loss from these numbers analogous to what was done earlier for the X arm.

Calculation of loss:

Fitted linewidth = 10.884 kHz +/- 11Hz (95% C.I.)

FSR of Y arm (from elog 9804) = 3.9468 MHz +/- 1.1 kHz

=> Y arm Finesse = FSR/fitted linewidth =  362.6 +/- 0.5

Total round trip loss = 2*pi/Finesse = 0.0173

Sorry for the confusion - I did mean Green beat frequency, and I had neglected the factor of 2 in my earlier calculations. However, the fit parameter "c" in my fit was actually the half-width at half maximum and not the full width at half maximum. After correcting for both these errors (new fit is Attachment #1, where I have now accounted for the factor of 2, and the X axis is the IR beat frequency), I don't think the numbers change too much. It could be that the frequency counter wasn't reading out the frequency correctly, but looking at a time series plot of the frequency counter readout (Attachment #2), and my earlier trials, I don't think this is the case (38 MHz is a frequency at which I don't expect much systematic error - also, the offset was stepped from -3 to 3 over 45 seconds). 

The revised numbers:

Fitted linewidth = 2*c = 10.884 kHz +/- 2 Hz (95% C.I.)

FSR of Y arm (from elog 9804) = 3.9468 MHz +/- 1.1 kHz

=> Y arm Finesse = FSR/fitted linewidth =  362.6 +/- 0.5

Total round trip loss = 2*pi/Finesse = 0.0173

I found (an old) 10 dB coupler in the RF component shelves near MC2 - it has BNC connectors and not SMA connectors, but I thought it would be worth it to switch out the 20dB coupler currently on the X green beat PD on the PSL table with it. I used some BNC to SMA adaptors for this purpose. It appears that the coupler works, because I am now able to register an input signal on the X arm channel of the digital frequency counter (i.e. the coupled output from the green beat PD). I thought it may be useful to have this in place and do an IR transmissions arm scan using ALS for the X arm as well, in order to compare the results with those discussed here. However, the beat note amplitude on the analyzer in the control room looks noticeably lower - I am not sure if the coupler is responsible for this or if it has to do with the problems we have been having with the X end laser (the green transmission doesn't look glitchy on striptool though, and the transmission itself is ~0.45). In any case, we could always remove the coupler if this is hindering locking efforts tonight. 

I began my attempts to characterize the PDH loops at the X end today. My goal was to make the following measurements:

• Dark noise and shot noise of the PD
• Mixer noise
• Servo electronics noise 

which I can then put into my simulink noise-budget scheme for the proposed IR beat setup.

I've made an Optickle model of a simple FP cavity and intend to match the measured PDH error signal from the X end to the simulated error signal to get the Hz/V calibration. I'll put the plots up for these shortly.

With regards to the other measurements, I was slowed down by remote data-acquisition from the SR785 - I've only managed to collect the analyzer noise floor data, and I plan to continue these measurements during the day tomorrow. 

Over the course of my investigations into the systematic errors in the frequency readout using digital frequency counting, I noticed that my counter variable that keeps track of the number of clock cycles between successive zero crossings was NOT oscillating between 2 values as I would have expected (because of there being a +/- 1 clock cycle difference between successive zero crossings due to the fixed sampling time of 1/16384 seconds), but that there were occassional excursions to values that were +/- 3 clock cycles away. I then checked the output of the SCHMITTTRIGGER CDS library part (which I was using to provide some noise immunity), and noticed that it wasn't triggering on every zero crossing at higher frequencies. I tested this by hooking up a digital oscillator to the SCHMITTTRIGGER part, and looked at its output for different frequencies. The parameters used were as follows:

CLKGAIN: 10000

SCHMITTTRIGGER lower threshold: -1.0

SCHMITTTRIGGER upper threshold: +1.0

I am attaching plots for two frequencies, 3000Hz and 4628Hz (Attachments #1 and #2) . I would have expected a flip in the state of the output of the schmitt trigger between every pair of horizontal red lines in this plot, but at 4628 Hz, it looks like the schmitt trigger isn't catching some of the zero crossings? Come to think of it, I am not even sure why the output of the schmitt trigger takes on any values other than 0 or 1 (could this be an artefact of some sort of interpolation in the visualization of these plots? But this would not affect the conclusion about the schmitt trigger missing some of the zero crossings?)

As an interim measure, I implemented a Schmitt trigger in my C code block - it was just a couple of extra lines anyways - I have designated the schmitt trigger output as a static variable that should hold its value in successive execution cycles, unless it is updated by comparing the input value to the thresholds (code attached for reference). Attachments #3 and #4 show the output of this implementation of a Schmitt trigger at the same two frequencies, and I am seeing the expected flip in the state between successive zero crossings as expected (though I'm still not sure why it takes on values other than 0 and 1?). Anyways this warrants further investigation. An elog regarding the implications of this on the systematic error in the frequency counter readout to follow.

I was trying to take a few more IR transmission scans with ALS when the ETMX got kicked again. I'm not sure how to fix this, so for the time being, I'm leaving the Oplev servo and the LSC turned off. The oplev spot looks really far off center especially in yaw, the yaw error is ~ -80.

While the ETMx issues are being investigated - with Eric's help, I took some data from arm scans of the Y arm through ~2FSRs using ALS. I've also collected the data from the frequency counter readout during these scans but since they were done rather fast (over 60seconds), I am not sure how accurate this data will be. The idea however is to use the frequency readout from the phase tracker - this has to be linearized though, which I will do during the daytime tomorrow. The plan is to use our GPS timing unit to synchronize the following chain :

GPS timing unit 1PPS out --> FS725 Rb Clock 1PPS in (I recovered one which was borrowed from the 40m some time ago from the ATF lab yesterday evening, waiting for it to lock to the Rb clock now)

FS725 Rb Clock 10 MHz out --> Fluke 6061A 10MHz reference in

FS725 Rb Clock 10 MHz out-->agilent network analyzer 10MHz reference in (for measurement of the frequency of the signal output from the Fluke RF signal generator independent of its front panel display)

Then I plan to look at the phase tracker output as a function of the driving frequency (which will also be measured, offline, using the digital frequency counter setup) over a range of 20 MHz - 50 MHz in steps of 1 MHz. Results to follow.

Earlier tonight, Eric and I tweaked the PMC alignment (the mode cleaner was not staying locked for more than a couple of minutes, for almost an hour). 

I've made a few more changes to the frequency counting code - these are mostly details and the algorithm is essentially unchanged.

• The C-code block in the simulink model now outputs the number of clock cycles (=1/16384 seconds) rather than the frequency itself. I've kept converting this period to frequency step by taking the reciprocal as the last step of the signal chain, i.e. after the LP filter.
• In the current version of the FC library block, I've disabled the moving average in the custom C code - I've left the functionality in the code, but the window length at the moment is set to 1, which in effect means that there is no moving average. I found that comparable jitters in the output are obtained by using no moving average, and having two 2-pole IIR low-pass filters in series (at 4Hz and 2Hz) as by doing a moving average over 4096 clock cycles and then passing that through a 2Hz IIR lowpass filter (as is to be expected).

Systematic error

The other thing that came up in the meeting last week was this issue of the systematic errors in the measured frequency, and how it was always over-estimating the 'actual' frequency. I've been investigating the origin of this over the last few days, and think I've found an explanation. But first, Attachment #1 shows why there is a systematic error in the first place - because we are counting the period of the input signal in terms of clock cycles, which can only take on discrete, integer values, we expect this number to fluctuate between the two integers bounding the 'true value'. So, if I'm trying to measure an input signal of 3000Hz, I would measure its period as either 5 or 6 clock cycles, while the "true"  value should be 5.4613 clock cycles. In attachment #1, I've plotted the actual measured frequency and the measured frequency if we always undercounted/overcounted to the nearest integer clock cycles, as functions of the requested frequency. So the observed systematic error is consistent with what is to be expected.

The reason why this doesn't average out to zero is shown in Attachment #2. In order to investigate this further, I recorded some additional diagnostic variables. If I were to average the period (in terms of clock cycles - i.e. I look for the peaks in the blue cuve, add them up, and divide by the number of peaks), I find that I can recover the expected period in terms of clock cycles pretty accurately. However, the way the code is set up at the moment, the c code block outputs a value every 1/16384 seconds (red curve) - but this is only updated each time I detect a zero crossing - and as a result, if I average this, I am in effect performing some sort of weighted average that distorts the true ratio of the number of times each integer clock-cycle-period is observed. This is the origin on the systematic error, and is a function of the relative frequency each of the two integer values of the clock-cycle-period occurs, which explains why the systematic error was a function of the requested frequency as seen in Attachment #1, and not a constant offset. 

At the frequencies I investigated (10-70MHz in 5MHz steps), the maximum systematic error was ~1%.

Is there a fix?

I've been reading up a bit on the two approaches to frequency counting - direct and reciprocal. My algorithm is the latter, which is generally regarded as the more precise of the two. However, in both these approaches, there is a parameter known as the 'gate-time': this is effectively how long a frequency counter measures for before outputting a value. In the current approach, the gate time is effectively 1/16384 seconds. I would think that it is perhaps possible to eliminate the systematic error by setting the gate time to something like 0.25 seconds, and within the gate time, do an average of the total number of periods measured. Something like 0.25 seconds should be long enough that if, within the window, we do the averaging, and between windows, we hold the averaged value, the systematic error could be eliminated. I will give this a try tomorrow. This would be different from the moving average approach already explored in that within the gate-time, I would perform the average only using those datapoints where the 'running counter variable' shown in Attachment #2 is reset to zero - this way, I avoid the artificial weighting that is an artefact of spitting out a value every clock cycle. 

Summary:

I performed a preliminary calibration of the X and Y phase trackers, and found that the slopes of a linear fit of phase tracker output as a function of driven frequency (as measured with digital frequency counter) are 0.7886 +/- 0.0016 and 0.9630 +/- 0.0012 respectively (see Attachments #1 and #2). Based on this, the EPICS calibration constants have been updated. The data used for calibration has also been uploaded (Attachment #4).

Details:

I found that by adopting the approach I suggested as a fix in elog 11736, and setting a gate time of 1second, I could eliminate the systematic bias in measured frequency I had been seeing, the origin of which is also discussed in elog 11736. This was verified by using a digital oscillator to supply the input to the frequency counting block, and verifying that I could recover the driving frequency without any systematic bias. Therefore, I used this as a measure of the driving frequency independent of the front panel display of the Fluke 6061A. 

The actual calibration was done as follows:

1. Close PSL green and end green shutters. Turned off the power to the green transmission PDs on the PSL table and disconnected the couplers from their outputs.
2. Connected the output of the Fluke 6061A RF signal generator to a splitter, and to the inputs of the couplers for the X and Y signal chains.
3. Adjusted the amplitude of the RF signal output until the Q readout of the rotated X and Y outputs were between 1000 and 3000. The final value used was -17dBm. As a qualitative check, I also looked at the beat signal on the spectrum analyzer in the control room and judged the peak height to be roughly the same as that seen when a real beat note was being measured. The phase tracker gains after setting the UGF were ~83 and 40 for the X and Y arms respectively.
4. Step through the frequency from 20MHz to 70MHz in steps of 1MHz, and record the outputs of (i) Digital frequency counter readout, and (ii) Phase tracker phase readout for the X and Y arms. I used the z avg -s utility to take an average for 10 seconds, and the standard deviation thus obtained correspond to the errorbars plotted. 
5. Restore the connections to the green beat PDs and power them on again.

Y-arm transmission scan

I used the information from Attachment #2 to calibrate the X-axis of the Y-arm transmission data I collected on Wednesday evening. Looking at the beat frequency on the analyzer in the control room, between 24 and 47 MHz (green beat frequency, within the range the calibration was done over), we saw three IR resonances. I've marked these peaks, and also the 11MHz sideband resonances, in Attachment #3. It remains to fit the various peaks. I did a quick calculation of the FSR, and the number I got using these 3 peaks is 3.9703 +/- 0.0049 MHz. This value is ~23 kHz greater than that reported in elog 9804, but the error is also ~4 times greater (6 IR resonances were scanned in elog 9804) so I think these measurements are consistent.

Rubidium clock

I had brought an FS725 Rubidium clock back from W Bridge - the idea was to hook this up to the GPS 1PPS output, and use the 10MHz output from the FS725 as the reference for the fluke 6061A. However, the FS725 has not locked to the Rb frequency even though it has been left powered on for ~2days now. Do I have to do something else to get it to lock? The manual says that it should lock within 7 minutes of being powered on. Once this is locked, I can repeat the calibration with an 'absolute' frequency source...

Summary:

As an update to Yutaro's earlier post - I've done an independent study of this data, doing the fitting with MATLAB, and trying to estimate (i) the FSR, (ii) the mode matching efficienct, and (iii) the modulation depths at 11MHz and 55MHz.

The values I've obtained are as follows:

FSR = 3.9704 MHz +/- 17 kHz 

Mode matching efficiency = 92.59 % (TEM00 = 1, TEM10 = 0.0325, TEM20 = 0.0475)

Modulation depth at 11MHz = 0.179

Modulation depth at 55MHz = 0.131

Details:

• To approximately locate the TEM10 and TEM20 resonances, I followed the methodology listed here (though confining myself to (m+n) = 1,2). 
• To approximately locate the 11 MHz and 55 MHz sidebands, I used the mod command in MATLAB to locate approximately how far they should be from a carrier resonance. 
• The results of these first two steps are demonstrated pictorially in Attachment #1. Red = carrier resonance, grey = 55MHz sideband resonance, cyan = 11MHz sideband resonance, green = TEM20 resonance, and yellow = TEM10 resonance. 
• The FSR was calculated by fitting the center frequencies of fits to the three carrier resonances with a lorentzian shape, vs their index. The quoted error is the 95% C.I.s generated by MATLAB
• The mode-matching efficiency was calculated by taking the fitted height of Lorentzian shapes to the TEM00, TEM10 and TEM20 shapes. The ratio of the peak heights was taken as a measure of the fraction of total power coupled into the TEM10 and TEM20 modes relative to TEM00. In calculating the final value, I took the average of the 3 available values for each peak to calculate the ratios.
• The modulation depth was calculated by approximating that the ratio   , and solving for . Attachment #2 shows a plot of the RHS of this equation as a function of  - the two datatips mark the location of the ratios on the LHS of the equation - both P_c and P_s were averaged over the 3 and 6 values available, respectively. The values I have obtained are different from those cited here - not sure why? The real red flag I guess is that I get the modulation depth at 11MHz to be larger than at 55MHz, whereas elog10211 reports the reverse... Do we expect a resonance for a 44MHz sideband as well? If so, it could be that the two peaks close to the carrier resonance is in fact the 55.30 MHz sideband resonance, and the peaks I've identified as 55MHz sideband resonances are in fact 44MHz sidebands.. If this were true, I would recover the modulation depth for 55.30 MHz sidebands to be approximately 0.22...

Misc Remarks and Conclusions:

• The y-scale in Attachment #1 is log(transmission) - the semilogy command in MATLAB messed up the rendering of the overlaid semi-transparent rectangles, hence the need for adopting this scale...
• I've attached the code used to split the entire scan into smaller datasets centered around each peak, and the actual fitting routine, in Attachment #3. I've not done the error analysis for the mode matching efficiency and the modulation depths, I will update this entry with those numbers as soon as I do. 
• In my earlier elog11738, I had mislabelled some peaks as being sideband peaks - attachment #1 in this entry is (I think) a correct interpretation of the various peaks. 
• There are two peaks on either side of every carrier resonance, spaced, on average, about 177kHz away from the resonance on either side. I am not sure what the interpretation of this peak should be - are they the 55.30 MHz resonances? 
• These values should allow us to carry out alternative measurements of the round trip arm loss as estimating this from the cavity finesse seems to not be the best way to go about this. 

After thinking about the interpretation of the various peaks seen in the scan through 2 FSRs, I have revised the information presented in the previous elog. Yutaro pointed out that the modulation frequency isn't exactly 11MHz, but according to this elog, is 11.066209 MHz. So instead of using mod(11e6,FSR), I really should have been using mod(11.066209,FSR) and mod(5*11.066209,FSR) to locate the positions of the 11MHz and 55MHz sidebands relative to the carrier resonances. With this correction, the 'unknown' peaks identified in Attachment #1 in elog 11743 are in fact the 55MHz sideband resonances. 

However, this means that the peaks which were previously identified as 55MHz sideband resonances have to be interpreted now - I'm having trouble identifying these. If we assume that the types of peaks present in the scan are 11 MHz sideband, 55MHz sideband, and the TEM00, TEM10, TEM20, TEM30, and TEM40 mode resonances, then the peaks marked in grey in Attachment #1 to this elog can be interpreted as TEM30 (right of a carrier resonance) and TEM40 (left of a carrier resonance) mode resonances - however, the fitted center frequencies differ from the expected center frequencies (determined using the same method as elog 469) by ~3% (for TEM30) and ~20% (for TEM40) - therefore I am skeptical about these peaks, particularly the 4th HOM resonances. In any case, they are the smallest of all the peaks, and any correction due to them will be small. 

The updated modulation depths are as follows (computed using the same method as described in elog 11743, the updated plot showing the ratio of bessel functions as a function of the modulation depth is Attachment #2 in this elog):

@11.066209 MHz ---- 0.179

@5*11.066209 MHz --- 0.226

These numbers are now reasonably consistent with those reported in elog10211.

As for the mode-matching efficiency, the overall number is almost unchanged if I assume the TEM30 peaks are accurately interpreted: 92.11%. But the dominant HOM contribution comes from the first HOM resonance: (TEM00 = 1, TEM20 = 0.0325, TEM10 = 0.0475, TEM30 =  0.0056). These numbers may change slightly if the 4th HOM resonances are also correctly identified.

ETMx is still not well behaved and the mode cleaner isnt too happy either, so I think we will save the measurement of the round trip arm loss for daytime tomorrow.  

In the last few days, with Koji's help, I have recovered both the FS725 Rubidium references from W. Bridge, one from the ATF lab, and one from the CTN lab. Both are back at the 40m at the moment.

However, the one that was recovered from the ATF lab is no longer locking to the Rubidium reference frequency, although it was locked at the time we disconnected it from the ATF lab. I emailed the support staff at SRS, who seem to think that either the internal oscillator has drifted too far, or the Rb lamp is dead. Either ways, it needs to be repaired. They suggested that I run a check by issuing some serial commands to the unit to determine which of these is actually the problem, but I've been having some trouble setting up the serial link - I will try this again tomorrow. I'm also having trouble generating an RMA number that is needed to start the repair/maintenance process, but I've emailed SRS support again and hope to hear back from them soon. 

The other FS725, recovered from the CTN lab earlier today, seems to work fine and is locked to the Rb reference at the moment. I plan to redo the calibration of the phase tracker with an 'absolute' frequency reference with the help of the FS725 and out GPS timing unit tomorrow. Once that is done, the working unit can be returned to the CTN lab. 

In order to synchronise the FS725 Rb clock with our GPS timing signals, I laid out a longish cable running from 1X7 to the IOO rack via the overhead cable guide. There was a T-connector attached to the 1pps output of the GPS timing unit, with one of the outputs unused - I have connected one end of the cable I laid out to this output, with the other end going to the 1pps input of the FS725. I am now waiting for the FS725 to sync to the external reference, before running the calibration of the phase tracker once again using the same method detailed here, using the 10MHz output from the FS725 to serve as a reference for the Fluke RF signal generator...

[yutaro, gautam]

Summary:

Having obtained a working FS725 Rubidium standard and syncing it to out GPS timing unit, I wanted to have one more pass at calibrating the phase tracker output, with the RF signal generator calibrated relative to an 'absolute' source. I also extended the range of frequencies swept over to 15MHz to 110MHz. We found that the phase tracker output appears linear over the entire range scanned, but taking a closer look at the residuals suggested some quadratic structure. Restricting the fitted range to [31MHz 89MHz] yields the following calibration constants for the X and Y arm respectively: 0.9904 +/- 0.0008 and 0.9984 +/- 0.0005. This suggests that out previous calibration was pretty accurate, and that it is valid over a wider range of frequencies, so we could plausibly fit in more FSRs in future scans if necessary. I have not updated these values on the EPICS screens (though judging by how close they are to 1, I wonder if this is even necessary)...

Details:

The principle change in the setup compared to that used to collect the data presented in elog 11738 was the addition of the FS725 rubidium standard. As detailed here, I synced the Rubidium standard to our GPS timing unit (this took a while - the manual suggests it should only take minutes, but it took about 10 hours - the two photos in Attachment #1 show the status of the front panel before and after it synced to the external 1PPS input). I then took 10 MHz outputs from the FS725, and ran one to the Fluke 6061A, and the other to the AG4395A. The Fluke 6061 A has a small switch at the back which has to be set to "EXT" in order for it to use the external reference (it has now been returned to the "INT" state). We then connected the output of the signal generator via a 3-way minicircuits splitter to the AG4395A, and the two beat channels. 

I cleared the phase history on the MEDM screen, and set the phase tracker UGF. We then swept through frequencies from 15MHz to 110MHz (using the AG4395 to verify the frequency at each step). I used the following command to record the average value (over 10 seconds) and the standard deviation: z avg 10 -s C1:ALS-BEATX_FINE_PHASE_OUT_HZ >> 20151113_PT_X.dat and so on.. The amplitude of the signal generated (i.e. before the splitter) was -18dBm (chosen such that the Q outputs of either phase tracker was between 1000 and 3000), while the gains were ~100 (X) and 50 (Y). I then downloaded the data and fitted it.

Fitting details:

The output of the phase tracker looks roughly linear over the entire range of frequencies scanned - but looking at the residuals, one could say there was some quadratic structure to it (see residual plots in Attachment #2). By looking at the shapes of the residuals, I judged that if we fit in the range [31MHz   89MHz] (for both X and Y), we should see negligible structure in the residuals. Attachment #3 contains the fits and residuals for these fits. One could argue that there is still some structure in the residuals, but is markedly less than over the entire range, and, I think, small enough to be neglected. The calibration constants quoted at the beginning of the elog are from the fits over this range. In principle, we could always break this down into smaller pieces and do a linear fit over that range. But this should allow us to scan through >5 FSRs.

Other remarks:

Since the beat signal also goes to the frequency counter via the couplers, I was also collecting the readouts of the frequency counter. Attachment #5 contains the data collected. It is interesting to note that the FCs fail at ~101 MHz (corresponding to ~6146 Hz after the dividers).

Also, we had taken another dataset last night, but found that there was an anomalous kink in the X phase tracker output at (coincidentally?) 89 MHz (I've attached the data in Attachment #6). I'm not sure why this happened, but this is what led me to take another dataset earlier today (Attachment #4).

Summary of Attachments:

1. Attachment #1: Photos showing the front panel of the FS725 before and after syncing to the external 1PPS input.
2. Attachment #2: Fits and residuals over the entire range scanned.
3. Attachment #3: Fits and residuals over restricted range [31 89] MHz
4. Attachment #4: Data used for phase tracker calibration.
5. Attachment #5: Frequency counter data.

Summary:

I followed a slightly different fitting approach to Yutaro's in an attempt to determine the g-factor of the Y arm cavity (details of which are below), from which I determined the FSR to be 3.932 +/- 0.005 MHz (which would mean the cavity length is 38.12 +/- 0.05 m) and the RoC of ETMY to be 60.5 +/- 0.2 m. This is roughly consistent (within 2 error bars) of the ATF measurement of the RoC of ETMY quoted here.

Details:

I set up the problem as follows: we have a bunch of peaks that have been identified as TEM00, TEM10... etc, and from the fitting, we have a bunch of central frequencies for the Lorentzian shapes. The equation governing the spacing of the HOM's from the TEM00 peaks is:

The main differences in my approach are the following:

1. I attempt to simultaneously find the optimal value of FSR, g1 and g2, by leaving all these as free parameters and defining an objective function that is the norm of the difference between the observed and expected values of  (code in Attachment #1). I then use fminsearch in MATLAB to obtain the optimal set of parameters.
2. I do not assume that the "unknown" peak alluded to in my previous elog is a TEM40 resonance - so I just use the TEM10, TEM20 and TEM30 peaks. I did so because in my calculations, the separation of these peaks from the TEM00 modes are not consistent with (m+n) = 4 in the above equation. As an aside, if I do impose that the "unknown" peak is a TEM40 peak, I get an RoC of 59.6 +/- 0.3 m.

Notes:

1. The error in the optimal set of parameters is just the error in the central positions of the peaks, which is in turn due to (i) error in the calibration of the frequency axis and (ii) error in the fit to each peak. The second of these are negligible, the error in my fits are on the order of Hz, while the peaks themselves are of order MHz, meaning the fractional uncertainty is a few ppm - so (i) dominates.
2. I am not sure if leaving the FSR as a free parameter like this is the best idea (?) - the FSR and arm length I obtain is substantially different from those reported in elog 9804 - by almost 30cm! However: the RoC estimate does not change appreciably if I do the fitting in a 2 step process: first find the FSR by fitting a line to to the 3 TEM00 peaks (I get FSR = 3.970 +/- 0.017 MHz) and then using this value in the above equation. The fminsearch approach then gives me an RoC of 60.7 +/- 0.3 m. 

A Caltech maintenance staff dropped by at around noon today, and told me that he had seen a small puddle of water on the other side of the door along the Y-arm that is kept locked (about 10m from the end-table, on the south side of the arm). He suspected a leak in the lab. Koji and I went down to the said door and observed that there was indeed a small puddle of water accumulated there. There isn't any obvious source of a leak on our side of the door, although the walls tiles in the area suggest that there could be a leak in one of the pipes running through the wall/under the floor. In any case, the leak doesn't seem too dramatic, and we have decided to consult Steve as to what is to be done about this once he is back on Wednesday.

I noticed that all the models running on C1LSC had crashed when I came in earlier today. I restarted all of them by ssh-ing into C1LSC and running rtcds restart all. The models seem to be running fine now.

We've been talking about putting in BLRMS filters for several channels - it would be a pain to manually copy over the correct bandpass and lowpass filter coefficients into the newly created filter banks, and so I've set up a script (attached) that can do the job. As template filters, I'vm using the filters rana detailed here. Essentially, what the script does is identify the (empty on creation) block of text for a given filter: e.g. RMS_STS1Z_BP_0p01_0p03 for STS1Z), and appends the template filter coefficients. To test my script, I first backed up the original C1PEM.txt file from /opt/rtcds/caltech/c1/chans, removed all the filter coefficients for the STS1Z BLRMS filters, and then replaced it with one generated using my script. I then loaded the coefficients for all the filters in the C1PEM modules, without any obvious error messages being generated. I also checked that foton could read the new file, and checked tmake sure that sensible filter shapes were seen for some channels. Since this seems to be working, I'm going to start putting in BLRMS blocks into the models tomorrow.

Summary:

I've made several changes to the C1MCS model and C1PEM model, and have installed BLRMS filters for the MC mirror coils, which are now running. The main idea behind this test was to see how much CPU time was added as a result of setting up IPC channels to take the signals from C1MCS to C1PEM (where the BLRMS filtering happens) - I checked the average CPU time before and after installing the BLRMS filters, and saw that the increase was about 1 usec for 15 IPC channels installed (it increased from ~27usec to 28usec). A direct scaling would suggest that setting up the BLRMS for the vertex optics might push the c1sus model close to timing out - it is at ~50usec right now, and I would need, per optic, 12 IPC channels, and so for the 5 vertex optics, this would suggest that the CPU timing would be ~55usec. I have not committed either of the changed models to the SVN just yet. 

Details:

1. On Eric's suggestion, I edited the C1_SUS_SINGLE_CONTROL library part to tap the signal at the input to the output filters to the coils, as this is what we want the BLRMS of. I essentially added 5 more outputs to this part, one for each of the coils, and they are named ULIn etc to differentiate it from the signal after the output filters. I have not committed the changed library part to the SVN just yet. 
2. I used the cdsIPCx_SHMEM part to pipe the signals from C1MCS to C1PEM - a total of 15 such channels were required for the three IMC mirrors.
3. I added the same cdsIPCx_SHMEM parts to the C1PEM model in the receiving configuration, and connected their outputs to BLRMS blocks. The BLRMS blocks themselves are named as RMS_MC2_UL_COIL_IN and so on.
4. I shutdown the watchdogs to MC1, MC2 and MC3, and restarted the C1PEM and C1MCS models on C1SUS. Yutaro pointed out that on restarting C1MCS, the IMC autolocker was disabled by default - I have enabled it again manually.
5. I was under the impression that each time a BLRMS block is added, a filter bank is automatically added to the C1PEM.txt file in /opt/rtcds/caltech/c1/chans - turns out, it doesn't and my script for copying the template bandpass and lowpass filtes into the .txt files was needlessly complicated. It suffices to change the filter names in the template file, and append the template file to C1PEM.txt using the cat command: i.e. cat template.txt > C1PEM.txt. The computer generated file seems to organize the filters in alphabetical order, and my approach obviously does not do so, but the coefficients are loaded correctlty and the filters seem to be functioning correctly so I don't think this is a problem (I measured the transfer function of one of the filters with DTT, it seems to match up well with the Foton bode plot). 
6. I added a few lines to the script to also turn on the filter switches after loading the filter coefficients.

Next steps:

Now that I have a procedure in place to install the BLRMS filters, we can do so for other channels as well, such as for the coils and Oplevs of the vertex optics, and the remaining PEM channels (SEIS, accelerometers, microphones?). For the vertex optics though, I am not sure if we need to do some rearrangement to the c1sus model to make sure it does not time out...

[ericq, gautam]

While trying to resolve the strange SRCL loop shape seen yesterday (which has been resolved, eric will elog about it later), we got a chance to put in the correct filters to the "CINV" branch in the C1CAL model for MICH, PRCL, and SRCL - so we have some calibrated spectra now (Attachment #1). The procedure followed was as follows:

1. Turn on the LO gain for the relevant channel (we used 50 for MICH and SRCL, 5 for PRCL)
2. Look at the power spectra of the outputs of the "A" and "CINV" filter banks - the former has some calibrated filters in place already (though I believe they have not accounted for everything).
3. Find the peak height at the LO excitation frequency for the two spectra, and calculate their ratio. Use this to install a gain filter in the CINV filter module for that channel. 
4. Look at the spectrum of the output of the "W" filter bank for that channel - the plot attached shows this information.

The final set of gains used were:

MICH: -247 dB

PRCL: -256 dB

SRCL: -212 dB

and the gain-only filters in the CINV filter banks are all called "DRMI1f".

Once we are able to lock the DRFPMI again, we can do the same for CARM and DARM as well...

In order to be consistent with the naming conventions for the new BLRMS filters, I made a library block that takes all the input signals of interest (i.e. for a generic optic, the coil signals, the local damping shadow sensors, and the Oplev Pitch and Yaw signals - so a total of 12 signals, unused ones can be grounded). The block is called "sus_single_BLRMS". Inside the block, I've put in 12 BLRMS library blocks, with each input signal going to one of them. All the 7 outputs of the BLRMS block are terminated (I got a compiling error if I did not do this). The idea is to identify the optic using this block, e.g. MC2_BLRMS. The BLRMS filters inside are called UL_COIL, UR_COIL etc, so the BLRMS channels will end up being called C1:SUS-MC2_BLRMS_UL_COIL_0p01_0p03 and so on. I tried implementing this in C1PEM, but immediately after compiling and restarting the model, I noticed some strange behaviour in the seismic rainbow STS strip in the control room - this was right after the model was restarted, before I attempted to make any changes to the C1PEM.txt file and add filters. I then manually opened up the filter bank screens for the RMS_STS1Z bandpass and lowpass filters, and saw that the filter switches were OFF - I wonder if this has something to do with these settings not being updated in the SDF tables? So I manually turned them on and cleared the filter hitsory for all 7 low pass and band pass filter banks, but the traces on the seismic striptool did not return to their nominal levels. I manually checked the filter shapes with Foton and they seem alright. Anyways, for now, I've reverted to the C1PEM model before I made any changes, and the seismic strip looks to be back at its normal level - when I recompiled and restarted the model with the changes I made removed, the STS1Z BLRMS bandpass and lowpass filters were ON by default again! I'm not sure what I'm doing wrong here, I will investigate this further. 

[ericq, gautam]

BLRMS filters have been set up for the coil outputs and shadow sensor signals. The signals are sent to the C1PEM model from C1MCS, where I use the library block mentioned in the previous elog to put the filters in place. Some preliminary observations:

1. The entire operation seems to be computationally quite expensive - just for the 3 IMC mirrors, the average CPU time for C1PEM increased from ~50 usec (before any changes were made to C1PEM) to ~105 usec just as a result of installing 420 filter modules with no filter coefficients loaded (3 optics x 10 channels x 14 filter banks) to ~120 usec when all the BP and LP filters for the BLRMS blocks have been loaded and turned on (Attachment #1). Eric suggested that it may be computationally more efficient to do this without using the BLRMS library part - i.e. rather than having so many filter modules, do the RMS-ing using a piece of C code that essentially just implements the same SOS filters that FOTON generates, I will work on setting this up and checking if it makes a difference. The fact that just having empty filter modules in the model almost doubled the computation time suggests that this approach may help, but I have to think about how to implement some of the automatic checks that having a filter bank in place gives us, or if these are strictly necessary at all...
2. While restarting the C1PEM model, we noticed that some of the optics were shaking - looking at the CPU timing signals for all the models on C1SUS revealed that both the C1SUS model and the C1MCS model were geting overclocked when C1PEM was killed (see the sharp spikes in the red and green traces in Attachment #2 - the Y scale in this plot is poor and doesnt put numbers to the overclocking, I will upload a better screenshot that Eric took once I find it). The cause is unknown.
3. Yesterday, I noticed that when C1PEM was restarted, the states of the filter bank switches were not reverted to their states in the SDF tables. They are showing up as changes, but it is unclear why we have to manually revert them. I have also not yet added the states of the newly installed filters (BPs and LPs for the MC BLRMS blocks) to the SDF tables. 

Unrelated to this work: we cleaned up the correspondence between the accelerometer numbers and channels in the C1PEM model. Also, the 3 unused ADC blocks in C1PEM (ADC0, ADC1 and ADC2) are required and cannot be removed as the ADC blocks have to be numbered sequentially and the signals needed in C1PEM come from ADC3 (as we found out when we tried recompiling the model after deleting these blocks).

Summary:

I measured the PZT actuator gain for the Lightwave NPRO at the Y-end to be 3.6 +/- 0.3 MHz/V. This is somewhat lower than the value of 5 MHz/V reported here, but I think is consistent with that measurement. 

Details:

In order to calibrate the Y-axis of my Aux PDH loop noise budget plots, I wanted a measurement of the end laser actuator gain. I proceeded to measure this as follows:

1. Use a function generator to add a DC offset to the error point - I did this by taking the output of the RF mixer -> Input A of an SR560, output of the function generator -> input B of the SR560 (via a 20 Ohm attenuator, and with a 50ohm T-eed to the input for impedance matching), and setting the output to A-B, and feeding that to the "Servo Input" on the PDH box.
2. I then locked the arm to IR, ran the dither to maximize the green transmission, and set up a beat note at ~39 MHz with the help of the analyzer in the control room.
3. Set phase tracker UGF, clear phase history.
4. Vary the DC offset to the error point by using the offset on the function generator. I varied the offset until the green TEM00 lock was lost, in steps of 0.1 V. At each step, I averaged the output of the phase tracker for 15 seconds.
5. Convert the applied DC offset to the DC offset appearing at the servo output using the transfer function of the servo box (DC gain measured to be ~65 dB), taking into account the 20dB attenuator also.

The attached plot shows the measured data. The X-axis is shown after the conversion mentioned in the last bullet point. The error bars are the standard deviations of the averaging at each DC offset. 

To do:

1. The value of the DC gain of the servo, 65 dB, is an approximate one based on a rough measurement I did earlier today. I'll take a TF measurement with an SR785 tomorrow, but I think this shouldn't change the number too much.
2. Upload the noise budget measurements for the Y-end PDH loop.

Summary:

After the discussions at the Wednesday meeting, I redid this measurement using a sinusoidal excitation summed at the error-point of the PDH servo as opposed to a DC offset. From the data I collected, I measured the actuator gain to be 2.43 +/- 0.04 MHz/V. This is almost half the value we expect, I'm not sure if I'm missing something obvious.

Details:

1. Attachment #1 is a sketch of the measurement setup and points at which signals are measured/calculated. Some important changes:
   • I am now using the channel C1:ALS-Y_ERR_MON_OUT to directly measure the input signal to the servo. In order to get the calibration constant for this channel from counts to volts, I simply hooked up the input to the channel to an oscilloscope and noted the amplitude of the signal seen on the scope in volts. The number I have used is 52uV/count (note that the signal to the ADC is amplified by a factor of 10 by an SR560).
   • I measured the transfer function from the input to the servo (marked "A" in the sketch) to the output of the Pomona box going to the laser PZT (marked "B" on the sketch) using an SR785 - see Attachment #2. This allowed me to convert the amplitude of excitation at A to an amplitude at B, which is what we need, as we want to measure C/B.
2. The measurement itself was done by locking the arms to IR, running ASS to maximize IR transmission, setting up a green beat note, and then measuring the two channels of interest with the excitation to the error-point on. 
3. I was initially trying to use time-series plots to measure these amplitudes - Koji suggested I use the Fourier domain instead, and so I took FFTs of the two channels we are interested in (using a flat-top window with 0.1 Hz BW) and estimated the RMS values at the frequency at which I had injected an excitation. Data+code used is in Attachment #3. In particular, I was integrating the PSD over 1Hz centered at the excitation frequency in order to calculate the RMS power at the excitation frequency - it could be that for C1:ALS-BEATY_FINE_PHASE_OUT_HZ, the spectral leakage into neighbouring bins is more significant than for C1:ALS-Y_ERR_MON_OUT (see Attachment #4)?
4. With the amplitudes thus obtained, I took the ratio C/B (see sketch) to determine the MHz/V actuator gain. I had injected excitations at 5 frequencies (916Hz, 933Hz, 977Hz, 1030Hz and 1067Hz, choses in relatively "quiet" parts of the spectrum of C1:ALS-Y_ERR_MON_OUT with no excitations), and the result reported is the average from these five measurements, while the error is the standard deviation in the 5 measurements.
5. Unrelated to this meaurement - while I had the SR560 hooked up to the input of the PDH box, I inverted the mixer output to the servo input, as I thought I could use this method to estimate the modulation depth. I did so by locking the Y arm green to the sideband TEM00 mode, and comparing the green transmission in this state to that when the Y arm is locked to a carrier TEM00 mode. I averaged C1:ALS-TRY_OUT for 10 seconds in 3 cases: (i) Carrier TEM00, (ii)sideband TEM00, and (iii) shutter closed - from this measurement, I estimate the modulation depth to be 0.209 +/- 0.006 (errors used to calculate the total error were the standard deviations of the measured transmission). 

Next steps:

1. Check that I have not missed out anything obvious in estimating the actuator gain - particularly the spectral leakage bit I mentioned above.
2. If this methodology and measurement is legitimate, repeat for the X end, and complete the noise budgeting for both AUX PDH loops.

Summary:

I've attached the results from my measurements of the noise characteristics of the Y-end auxiliary PDH system.

Details:

The following spectra were measured, in the range DC-1MHz:

1. Analyzer noise floor (measured with input terminated)
2. Green REFL PD dark noise (measured with the Y-end green shutter closed)
3. Mixer noise (measured with input to mixer terminated - measured with an SR560 with a gain of 100)
4. Servo noise (measured with input to servo terminated)
5. In loop error signal (measured with green locked to Y-arm, LSC off - using monitor point on PDH box)
6. In loop control signal (measured with green locked to Y-arm, LSC off - using monitor point on PDH box)

In order to have good spectral resolution, the frequency range was divided into 5 subsections: DC-200Hz, 200Hz-3.4kHz, 3.4kHz-16.2kHz, 10kHz-100kHz, 100kHz-1MHz. The first three are measured using the SR785, while the last two ranges are measured with the Agilent network analyzer. The spectrum of the mixer output with its input terminated was quite close to the analyzer noise floor - hence, this was measured with an S560 preamplifier set to a gain of 100, and subsequently dividing the ASD by 100. To convert the Y-axis from V/rtHz to Hz/rtHz, I used two conversion factors: for the analyzer noise floor, PD dark noise, mixer noise and in-loop error signal, I made an Optickle simulation of a simple FP cavity (all parameters taken from the wiki optics page, except that I put in Yutaro's measured values for the arm loss and a modulation depth of 0.21 which I estimated as detailed here), and played around with the demodulation phase until I got an error signal that had the same qualitative shape as what I observed on an oscilloscope with the arms freely swinging (feedback to the laser PZT disabled). The number I finally used is 45.648 kHz/V (the main horns were 800mV peak-to-peak on an oscilloscope trace, results of the Optickle FP cavity simulation shown in Attachment #2 used to calibrate the X-axis). For the servo noise spectrum and in-loop control signal, I used the value of 2.43 MHz/V as determined here. 

I'm not sure what to make of the strong peaks in the mixer noise spectrum between ~60Hz and 10kHz - some of the more prominent peaks are 60Hz harmonics, but there are several peaks in between as well (these have been confusing me for some time now, they were present even when I made the measurement in this frequency range using the Agilent network analyzer. My plan is to repeat these measurements for the Xend now. 

I noticed what I thought was excessive movement of the beam spot on ITMX and ETMX on the control room monitors, and when I checked the CDS FE status overview MEDM screen, I saw that c1scx and c1asx had crashed. I ssh-ed into c1iscex and restarted both models, and then restarted fb as well. However, the DAQ-DCO_C1SCX_STATUS indicator remains red even after restarting fb (see attached screenshot). I am not sure how to fix this so I am leaving it as is for now, and the X arm looks to have settled down.

[ericq,gautam]

Forgot to submit this yesterday...

While we were trying to get the X-arm locked to IR using MC2, frame-builder mysteriously crashed, necessitating us having to go down to the computer and perform a hard reboot (after having closed the PSL shutter and turning all the watchdogs to "shutdown"). All the models restarted by themselves, and everything seems back to normal now..

Since there are a few hours to go before the locking efforts tonight, I've temporarily borrowed the channels used to read out the green beat frequency, and have hooked them up to the broadband IR PDs in the FOL box on the PSL table. I've used the network analyzer in the control room to roughly position the two beatnotes. I've also turned the green beat PDs back on (since the PSL shutter has to be open for the IR beat, and there is some green light falling on these PDs, but I've terminated the outputs).

So this needs to be switched back before locking efforts tonight...

I've set up two IPC channels that take the output from the digital frequency counters and send them to the end front-ends (via the RFM model). A summary of the steps I followed:

1. Set up two Dolphin channels in C1ALS to send the output of the frequency counter blocks to C1RFM (I initially used RFM blocks for these, but eric suggested using Dolphin IPC for the ALS->RFM branch, as they're faster.. Eric's removed the redundant channel names)
2. Set up two RFM channels in C1RFM to send the out put of the frequency counter blocks to C1SCX/Y (along with CDS monitor points to monitor the error rate and a filter module between the ALS->RFM and RFM->SCX/Y IPC blocks - I just followed what seemed to be the convention in the RFM model).
3. Set up the receiving channels in C1SCX and C1SCY
4. Re-compiled and re-started the models in the order C1ALS, C1RFM, C1SCX and C1SCY.

I've set things up such that we can select either the "PZT IN" or the frequency counter as the input to the slow servo, via means of a EPICS variable called "FC_SWITCH" (so C1:ALS-X_FC_SWITCH or C1:ALS-Y_FC_SWITCH). If this is 0, we use the default "PZT IN" signal, while setting it to 1 will change the input to the slow servo to be the frequency readout from the digital frequency counter. I've not updated the MEDM screens to reflect the two new paths yet, but will do so soon. It also remains to install appropriate filters for the servo path that takes the frequency readout as the input.

Tangentially related to this work: I've modified the FC library block so that it outputs frequency in MHz as opposed to Hz, just for convenience..

A few more related changes:

1. The couplers that used to sit on the green beat PDs on the PSL table have now been shifted to the IR broadband PDs in the FOL box so that I can get the IR beat frequency over to the frequency counters. The FOL box itself, along with the fibers that bring IR light to the PSL table, have been relocated to the corner of the PSL table where the green beat PDs sit because of cable length constraints.
2. I've updated the ALS slow control MEDM screen to allow for slow control of the beat frequency. The servo shape for now is essentially just an integrator with a zero at 1 Hz. The idea is to set an offset in the new filter module, which is the desired beat frequency, and let the integrator maintain this beat frequency. One thing I've not taken care of yet is automatically turning this loop off when the IMC loses lock. Screenshot of the modified MEDM screen is attached. 
3. I checked the performance by using the temperature sliders to introduce an offset. The integrator is able to bring the beat frequency back to the setpoint in a few seconds, provided the step I introduced was not two big (~20 counts, but this is a pretty large shift in beat frequency, nearly 20MHz).

To do:

1. Figure out how to deal with the IMC losing lock. I guess this is important if we want to use the IR beatnote as a diagnostic for the state of the X AUX laser.
2. Optimize the servo gains a little - I still see some ringing when I introduce an offset, this could be avoided...

When I came in this afternoon, I saw that the PZT voltage to the PMC had railed. Following the usual procedure of turning the servo gain to zero and adjusting the DC offset, I got the PMC to relock, but the PMCR level was high and the alignment looked poor on the control room monitor. So I tweaked the input alignment on the PSL till I felt it was more reasonable. The view on the control room monitor now looks more like the usual state, and the "REFL (V)" field on the PMC MEDM screen now reads 0.02-0.03 which is the range I remember it being in nominally. 

The Rubidium standard we had sent in for repair and recalibration has come back. I checked the following:

• Powered the unit on - it was locked to the internal rubidium reference within a few minutes as prescribed in the manual.
• After it had locked to the internal reference, I checked that it was able to lock to an external 1pps reference from our GPS timing unit- this too was achieved within a few minutes as prescribed in the manual. 

However, I am still having trouble setting up a serial communications link with the FS725 with a USB-serial adaptor - I've tried with a Raspberry Pi and my Mac (using screen to try and connect), and also using one of the old Windows laptops lying around on which I was able to install the native software supplied by SRS (still using the USB-serial adaptor to establish connection though). Could it be that the unit is incompatible with the USB-serial adaptor? I had specifically indicated in the repair request that this was also a problem. In any case, this doesn't seem to be crucial, though it would have been nice for diagnostics purposes in the future...

I've stored the repaired FS725 inside the electronics cabinet (marked "Eletronics Modules") for now (the other unit was returned to Antonio in W. Bridge some weeks ago). 

Summary:

I redid this measurement and have now determined the actuator gain to be 4.61 +/- 0.10 MHz/V. This is now pretty consistent with the expected value of ~5MHz/V as reported here.

Details:

I made the following changes to the old methodology:

1. Instead of integrating around the excitation frequency, I am now just taking the ratio of peak heights (phase tracker output / error signal monitor) to determine the actuator gain.
2. I had wrongly assumed that the phase tracker output was calibrated to green Hz and not IR Hz, so I was dividing by two where this was not necessary. I think this explains why my previous measurement yielded an answer approximately half the expected value.

I also took spectra of the phase tracker output and error signal to make sure I was choosing my excitation frequencies in regions where there were no peaks already present (Attachment #1).

The scatter of measured actuator gains at various excitation frequencies is shown in Attachment #2.

Summary:

I've re-measured the noise breakdown for the Y-end AUX PDH system. Spectra are attached. I've also measured the OLTF of the PDH loop, from which the UGF appears to be ~8.5kHz. 

Discussion:

As Eric and Koji pointed out, the spectra uploaded here were clearly wrong as there were breaks in the spectra between decades of frequency. I redid the measurements, this time being extra careful about impedance mismatch effects. All measurements were made from the monitor points on the PDH box, which according to the schematic found here, have an output impedance of 49.9 ohms. So for all measurements made using the SR785 which has an input impedance of 1Mohm, or those which had an SR560 in the measurement chain (also high input impedance), I terminated the input with a 50ohm terminator so as to be able to directly match up spectra measured using the two different analyzers. I'm also using my more recent measurement of the actuator gain of the AUX laser to convert the control signal from V/rtHz to Hz/rtHz in the plotted spectra. 

As a further check, I locked the IR to the Y-arm by actuating on MC2, and took the spectrum of the Y-arm mirror motion using the C1CAL model. We expect this to match up well with the in-loop control signal at low frequencies. However, though the shapes seem consistent in Attachment #2 (light orange and brown curves), I seem to be off by a factor of 5- not sure why. In converting the Y-arm mirror motion spectrum from m/rtHz to Hz/rtHz, I multiplied the measured spectrum by , which I think is the correct conversion factor (FSR/(0.5*wavelength))?

In preparation for tonight's work, I did the following:

On the PSL table:

• Powered the RF amplifiers for the green beat signal on
• Reconnected the outputs of the Green beat PDs to the RF amplifiers
• Restored wiring in the fiber box such that both IR beats go to the frequency counter.

At the IOO Rack area:

• Restored wiring to the frequency counter module such that the IR beats from both arms go to the respective channels
• Partially cleaned up the setup used for measuring AUX laser frequency noise - moved the SR785 to the X end along with one SR560 so that we can measure the end PDH OLTF
• Brought the HP network analyzer back to the control room so that we can view the green beatnotes.

At the X-end:

• Turned the function generator used for PDH locking back on
• Checked that the AUX laser diode current is 1.90 A, and the crystal temperature is ~47.5 degrees, both of which I think are "good" values from our AUX laser frequency noise measurements
• Did some minor manual alignment of the PZT mirrors

At the Y-end:

• Restored the BNC connection from the PDH box to the laser's "FAST" control input. The long BNC cable used for the PLL is still running along the Y-arm, I will clean this up later.

Having done all this, I checked the green transmission levels for both arms (PSL green shutter closed, after running ASS to maximize IR transmission). GTRY is close to what I remember (~0.40) while the best I could get GTRX to is ~0.12 (I seem to remember it being almost double this value - maybe the alignment onto the beat PD has to be improved?). Also, the amplitudes of the beatnotes on the network analyzer are ~-50dBm, and I seem to remember it being more like -25dBm, so maybe the alignment on the PD is the issue? I will investigate further in the evening. It remains to measure the OLTF of the X-end PDH as well.

Last week, Eric and I noticed that the green transmission levels at the PSL table seem much lower now than they did a month or two ago. To investigate this, I attempted to reproduce a power budget for the X endtable setup - see the attached figure (IR powers measured with calorimeter, green powers measured with Ophir power meter). A summary of my observations:

• The measurements were all made at an AUX-X laser diode current of 1.90A, and laser crystal temperature of 47.41 degrees. The current was chosen on the basis of the AUX-X frequency noise investigations. The temperature was chosen as this is the middle of three end-laser temperatures at wich a beat-note can be found now. Why should this temperature have changed by almost 5 degrees from the value reported here? I checked on the PSL laser controller that the PSL temperature is 33.43 degrees. Turning up the diode current to 2A does not change the situation significantly. Also, on the Innolight datasheet, the tuning geometry graphs' X-axes only runs to 45 degrees. Not sure of what to make of this. I tried looking at the trend of the offset to the slow temperature servo to see if there has been some sort of long-term drift, but was unable to do so...
• The IR power from the laser seems to have halved, compared to the value in Feb 2014. Is this normal deterioration over two years? Changing the laser diode current to 2A and the laser crystal temperature to ~42 degrees (the conditions under which the Feb 2014 measurements were taken) do not alter these numbers radically.
• The green power seems to have become 1/4 its value in Feb 2014, which seems to be consistent with the fact that the IR power has halved.

It is worth noting that two years ago, the IR power from the AUX-Y laser was ~280 mW, so we should still be getting "enough" green power for ALS?

While carrying out my end-table power investigations, I decided to take a quick look at the out-of-loop ALSX noise - see the attached plot. The feature at ~1kHz seems less prominent (factor of 2?) now, though its still present, and the overall noise above a few tens of Hz is still much higher than the reference. The green transmission was maximized to ~0.19 before this spectrum was taken.

EDIT 1130pm: 

We managed to access the trends for the green reflected and transmitted powers from a couple of months back when things were in their nominal state - see Attachment #2 for the situation then. For the X arm, the green reflected power has gone down from ~1300 counts (November 2015) to ~600 counts (january 2016) when locked to the arm and alignment is optimized. The corresponding numbers for the green transmitted powers (PSL + End Laser) are 0.47 (November 2015) and ~0.18 (January 2016). This seems to be a pretty dramatic change over just two months. For the Y-arm, the numbers are: ~3500 counts (Green REFL, Nov 2015), ~3500 counts (Green REFL, Jan 2016) ~1.3 (Green Trans, Nov 2015), ~1 (Green Trans, Jan 2016). So it definitely looks like something has changed dramatically with the X-end setup, while the Y-end seems consistent with what we had a couple of months ago...

I was trying to characterize the AM/PM response of the X end laser. I tried to measure the AM response first, as follows:

• I used the Thorlabs PDA 55, whose datasheet says it has 10MHz bandwidth - I chose it because it has a larger active area than the PDA 255, but has sufficient bandwidth for this measurement. 
• My earlier measurement suggested the IR power coming out of the laser is ~300mW. As per the datasheet of the PDA 55, I expect its output to be (1.5 x 10^4 V/A) * (~0.25 A/W) ~ 4000 V/W => I expect the PD output (driving the 50ohm input of the Agilent NA) to saturate at ~1.3mW. So I decided to use a (non-absorptive) ND 3.0 filter in front of the PD (i.e. incident power on the PD ~0.3 mW).
• I measured the AM response (inputA/inputR) by using the RF output from the Agilent analyzer (divided using a mini-circuits splitter half to input R and half to the laser PZT), and the PD output to input A. I set the power of the RF output on the analyzer to 0 dBm. 
• Attachment #1 shows the measured AM response. It differs qualitatively in shape from the earlier measurements reported in this elog and on the wiki below the 100kHz region. 
• I also took a measurement of the RIN with no drive to the laser PZT (terminated with a 50ohm terminator) - see Attachment #2. Qualitatively, this looks like the "free-running" RIN curve on the Innolight datasheet (see Attachment #3, the peak seems slightly shifted to the left though), even though the Noise Eater switch on the laser controller front panel is set to "ON". I neglected taking a spectrum with it OFF, I will update this elog once I do (actually I guess I have to take both spectra again as the laser diode and crystal temperatures have since been changed - this data was taken at T_diode = 28.5deg, I_diode = 1.90A, and T_crystal = 47.5 deg). But does this point to something being broken?
• I was unable to lock the PLL yesterday to measure the PM response, I will try again today.

There were a number of directories in /users/OLD/mott/PZT/2NPRO, I've used the data in Innolight_AM_New. Also, I am unsure as to what their "calibration" factor is to convert the measured data into RIN, so I've just used a value of 0.8, with which I got the plot to match up as close as possible to the plot in this elog. I also redid the measurement today, given that the laser parameters have changed. The main difference was that I used an excitation amplitude of +15dBm, and an "IF Bandwidth" of 30Hz in the parameter files for making these measurements, which I chose to match the parameters Mott used. There does seem to be a shift in some of the features, but the <100kHz area seems similar to the old measurement now. 

Having put the PD back in, I also took measurements of the RIN with the input to the laser PZT terminated. There is no difference with the Noise Eater On or OFF! 

I attempted to measure the frequency noise of the extra Lightwave NPRO we have that is currently sitting on the PSL table. I did the following:

1. Turn the Lightwave NPRO back on.
2. Disable MC autolocker and close the PSL shutter.
3. Checked the alignment of the pick off from the PSL beam and the beam from the Lightwave NPRO onto the PDA10CF. These seemed okay, and I didn't really have to tweak any of the steering optics. I was getting a DC signal level of ~7V (the PD should drive a 1Mohm load up to 10V so it wasn't saturated).
4. Swept the crystal temperature on the Lightwave using the dial on the front panel of the controller. I found beatnotes at 48.1831 degrees and 45.3002 degrees. However, the amplitude of the beatnote was pretty small (approx. -40dBm on the Agilent NA). I tried playing around with the beam alignment and laser power on the Lightwave NPRO to see if I could increase the beatnote amplitude, but was unsuccessful - turning up the laser power (from the nominal level of 55mW as per the front panel display) caused the PD to saturate at 10V, while as far as I could tell, the alignment of the two beams onto the PD is reasonably good. This seems inconsistent with the numbers Koji has reported in this elog, where he was able to get a beatnote of ~1Vpp for a DC of 2.5 V. 
5. I tried locking the PLL (in roughly the same configuration as reported here) with this small amplitude beatnote but was unsuccessful. 

I've turned the Lightwave NPRO back to standby for now, in anticipation of further trials later today. I've also restored the IMC. 

After adjusting the alignment of the two beams onto the PD, I managed to recover a stronger beatnote of ~ -10dBm. I managed to take some measurements with the PLL locked, and will put up a more detailed post later in the evening. I turned the IMC autolocker off, turned the 11MHz Marconi output off, and closed the PSL shutter for the duration of my work, but have reverted these to their nominal state now. The are a few extra cables running from the PSL table to the area near the IOO rack where I was doing the measurements from, I've left these as is for now in case I need to take some more data later in the evening...

Unfortunately I had closed all the DTT windows that Steve had used for the earlier plots. So I took the spectra again - there may be minor differences given that this measurement was taken at ~11pm at night. Anyways, plots and the xml data file are attached.