I guess it didn't make sense since f_beat can be arbitrarily moved, but the beat is taken around the PSL freq ~ 281.73 THz. Attachment #1 shows the overlapping tau allan deviation for the exact same dataset but using the python package allantools, where this time I used the PSL freq as the base frequency. This time, I can see the minimum fractional deviation of 1.33e-13 happening at ~ 20 seconds.

Another, more familiar interpretation

The allan variance is related to the beatnote spectral density as a mean-square integral (the deviation is then like the rms) with a sinc window.

[Paco]

In the morning I took some time to align the AUX beams in the XEND table. Later in the afternoon, I did the same on the YEND table. I then locked the AUX beams to the arm cavities while they were stabilized using POX/POY and turned off the PSL hepa off temporarily (this should be turned on after today's work).

After checking the the temperature slider sign on the spectrum analyzer of the control room I took some out-of-loop measurements of both ALS beatnotes (Attachment #1) by running diaggui /users/Templates/ALS/ALS_outOfLoop_Ref_DQ.xml and by comparing them against their old references (red vs magenta and blue vs cyan); it seems that YAUX is not doing too bad, but XAUX has increased residual noise around and above 100 Hz; perhaps as a result of the ongoing ALS SURF loop investigations? It does look like the OLTF UGF has dropped by half from ~ 11 kHz to ~ 5.5 kHz.

Anyways let this be a reference measurement for current locking tasks, as well as for ongoing SURF projects.

[Paco, Deeksha, rana]

Quick elog for this evening:

• Rana disabled MC servo .
• Slow loop also got disengaged.
• AUX PSL beatnote is best taken with *free running lasers* since their relative frequency fluctuations are lowest than when locked to cavities.
• DFD may be better to get PZT transfer funcs, or get higher bandwidth phase meter.
• Multi instrument to be done with updated moku
• Deeksha will take care of updated moku

The PZT sweeps that we've been making to characterize the ALS-X laser should probably be discarded - the DFD was not setup correctly for this during the past few months.

Since the DFD only had a peak-peak range of ~5 MHz, whenever the beat frequency drifts out of the linear range (~2-3 MHz), the data would have an arbitrary gain. Since the drift was actually more like 50 MHz, it meant that the different parts of a single sweep could have some arbitrary gain and sign !!! This is not a good way to measure things.

I used an ezcaservo to keep the beat frequency fixed. The attacehed screenshot shows the command line. We read back the unwrapped beat frequency from the phase tracker, and feedback on the PSL's NPRO temperature. During this the lasers were not locked to any cavities (shutters closed, but servos not disabled).

For the purposes of this measurement, I reduced the CAL factor in the phase tracker screen so that the reported FINE_PHASE_OUT is actually in kHz, rather than Hz on this plot. So the green plot is moving by 10's of MHz. When the servo is engaged, you can see the SLOWDC doing some action. We think the calibration of that channel is ~1 GHz/V, so 0.1 SLOWDC Volts should be ~100 MHz. I think there's a factor of 2 missing here, but its close.

As you can see in the top plot, even with the frequency stabilized by this slow feedback (-1000 to -600 seconds), the I & Q outputs are going through multiple cycles, and so they are unusable for even a non serious measurement.

The only way forward is to use less of a delay in the DFD: I think Anchal has been busily installing this shorter cable (hopefully, its ~3-5 m long so that the linear range is more. I think a 10 m cable is too long.), and the sweeps taken later today should be more useful.

[Anchal, Yehonathan]

I laid down another temporary cable from Xend to 1Y2 (LSC rack) for also measuring the Q output of the DFD box. Then to get a quick measurement of these long cable delays, we used Moku:GO in oscillator mode, sent 100 ns pulses at a 100 kHz rate from one end, and measured the difference between reflected pulses to get an estimate of time delay. The other end of long cables was shorted and left open for 2 sets of measurements.

I-Mon Cable delay: (955+/- 6) ns / 2 = 477 +/- 3 ns

Q-Mon Cable delay: (535 +/- 6) ns / 2 = 267 +/- 3 ns

Note: We were underestimating the delay in I-Mon cable by about a factor of 2.

I also took the opportunity to take a delay time measurement of DFD delayline. Since both ends of cable were present locally, it made more sense to simply take a transfer function to get a clean delay measurement. This measurement resulted with value of 197.7 +/- 0.1 ns. See attached plot. Data and analysis here.

[Paco, Anchal, Radhika]

We tried to debug why the XARM green laser isn't catching lock with the arm cavity. First I tried to improve alignment:

- Aligned the arm cavity axes by maximizing IR transmission.

- Adjusted M1 and M2 steering mirrors to align the X green beam into the arm. GTRX reached ~0.3.

     - At the vertex table, I adjusted the lens in the GTRX path to focus the beam onto the DCPD. This increased GTRX to ~0.7.

- Visually I confirmed that TEM00 of the green laser was flashing in the arm cavity, fairly centered. But it was not catching lock.

We suspected the XARM AUX PZT might be damaged/unresponsive. Paco, Anchal, and I fed several frequency signals to the PZT and looked for a peak in the AUX-PSL beatnote spectra at the expected frequency. We confirmed that the X-arm AUX PZT is responsive up to 12 kHz (limited by ADC samping rate). We have no reason to suspect the PZT wouldn't be responsive at the PDH modulation frequency of 231 kHz.

Next steps:

- Investigate PDH servo box / error signal.

I tested the mixer by feeding it a 300 kHz signal sourced from a Moku:Go. I kept the LO input the same - 231.25 kHz from the signal generator. The mixer output was a ~70 kHz waveform as expected, so demodulation is not the issue in green locking.

Next I'll align the arm cavities with IR and check to see if the green REFL signal looks as expected. If not, we'll have to invesitage the REFL PD. If the signal looks fine, and we now know it's being properly demodulated, the issue must lie further downstream.

I took a transfer function measurement of the XEND PDH servo box, from servo input to piezo output [Attachment 1]. The servo gain knob was set to 10. The swept sine input was 50 mVpp, as to not saturate the servo components. I toggled the local boost on/off for these measurements. With the boost on, coherence was lost from ~100Hz-10kHz, and the saturation light indicators were flashing. I will retake this measurement shortly.

Atachment 2 is from a previous measurement of this PDH servo TF, found here. For this measurement, boost was off and the gain knob was set to 2.0. (If there is a more recent measurement than 2010, please point me to it.)

[Radhika, JC]

We retook transfer function measurements of the XEND PDH servo box, this time setting the gain knob to 3.5 to avoid saturation. Once again I toggled the boost on/off. Attachment 1 shows the resulting bode plots, which now resemble the previous measurements circa 2010. This measurement along with the previous one suggest that setting the gain knob too high might affect the loop shape in an unpredictable way. With this accounted for, it seems the PDH servo box is functioning as expected.

[Radhika, Paco]

Paco suggested that alignment could still be the primary reason why the XEND green laser is not catching lock. With the xarm cavity aligned with IR, I adjusted the M1 and M2 steering mirrors for the green laser, looking at the REFL PD output in an oscilloscope. Paco joined and was able to achieve better mode matching by adjusting mirrors and rotating the half-wave plate. At this point, we could see TEM00 consistently flashing. Green transmission also reached a value of 3, from around 0.5 that I was able to achieve previously (this channel is not normalized).

We broke the loop to make sure the demodulated signal looked as expected, and indeed it resembled a PDH error signal. After reconnecting the loop (with the gain knob set to 3.5), Paco lowered the REFL PD gain by 3 stages and I was able to raise the gain knob to 8 without the servo saturating. I turned boost on and toggled the servo inversion until the laser started to hold lock for a few seconds. The piezo output signal looked reasonable at this point, without clipping on either end. 

After some final adjustments to the steering mirrors and the half-wave plate, the green laser can hold lock for around 5 seconds. However it's unclear why the loop isn't more stable, and more updates are to come. 

On Monday I aimed to measure the transfer function of the x-arm AUX PDH loop while momentarily locked, with a Moku:Go. I re-aligned the XEND green beam input to the arm cavity with M1 and M2 steering mirrors. I got GTRX to ~1.4 and the TEM00 mode nominally locked (back to ~5 seconds of lock, like last time). Previously Paco and I had achieved transmission of 3, so there was still a good way to go in mode matching. 

However I noticed the backwards-propagating beam started to drift relative to the opening of the Faraday isolator (located after the shutter). During manual alignment the backwards beam cleared through the aperture of the FI, but around 5 minutes later it had drifted too high and the beam spot was visible against the FI body, missing the aperture. At this point transmission had dropped to 0, and I realigned the beam to clear through the opening. I tried to further increase transmission but the drift continued to occur within a few minutes of re-alignment. I double checked that there was no dithering of ITMX or ETMX. It seemed there was high residual motion of the ETM, but I was not sure how to decrease this (damping filters were on). I moved on to setting up the TF measurement and decided to return to alignment once the loop excitation was configured.

I chose to inject an excitation from the Moku at the error point of the PDH servo box. I set up the measurement from 100 kHz to 100 Hz, zoomed in around the loop UGF. I passed the mixer output / error signal (alpha) to a T-splitter and sent one copy to input A of an SR560, and routed the Moku excitation to input B. The summed output of the SR560 was sent to the PDH servo input (beta). I passed the second copy of the error signal (alpha) to the Moku, along with the servo input monitor signal (beta) from the PDH box. The Moku measured the transfer function alpha/beta to obtain G_OLG. 

I returned to align the green beam and recovered flashing of the TEM00 mode. However when I closed the loop (with excitation), it didn't catch lock. I quickly reverted the loop back to its original state and confirmed that TEM00 locked for ~5 seconds. This made me think the excitation signal was too large relative to the error signal, so I reduced its amplitude to 500 mVpp. This still didn't recover the lock, and at this point the alignment had drifted again so I decided to wrap up. 

TODO:

I am working remotely for the next week, so I can carry out these steps in January.

[Paco, Anchal] Log from yesterday work around 1Y2 rack; note that while this work was ongoing, TT2 position drifted slowly and misaligned the IFO input over the course of less than an hour. I suspect the DB9 breakout board and temporarily present components noted below may have introduced a floating ground in 1Y2, making the TT coil drivers misbehave. To support this claim, we noted that after removing the breakout board the drift disappeared!

We calibrated the DFD discriminant as a function of RF input level. The configuration was as follows:

1. Break out IQ demod board RF output (in the rear chassis on 1Y2), looking at Ch1 board outputs (for BEATX). The two differential outputs were broken into two BNCs (pairs 1,6 and 2,7 for Q and I respectively), and fed into the Moku:Lab. A Marconi 2023A was used as a VCO, with FM ext mode enabled and a FreqDVN (modulation slope) of 200 kHZ / Vrms (1 Vrms = 1.41 Vp = 0.705 Vpp). The FM ext input on the Marconi was sourced by the OUT1 of Moku:Lab, and the IQ demod outputs were connected to IN1 and IN2 on Moku:Lab.
2. After measuring the TF using a swept sine, I verified that the frequency response was flat up to 150 kHz (Marconi cuts FM ext at 275 kHz), so I switched to the oscilloscope instrument and setup OUTPUT to a 211.1 Hz sine wave, 1.41 Vpp to dither the 40 MHz by +- 100 kHz.
3. Using the arbitrary math function in Moku:Lab Scope, I computed the DFD output magnitude = sqrt(I**2 + Q**2), and measured its mean over 3 seconds.

The results are summarized in Attachment #1.

[Radhika, Anchal, Paco]

AUX PDH Loop Stability

Today I tried aligning the XEND green beam into the arm cavity. Using M1 and M2 steering mirrors, I reached a max transmission ~1.2 of TEM00. In this configuration there was a "donut" mode also flashing, with transmission exceeding that of TEM00. Scanning all 4 degrees of freedom, I couldn't get TEM00 transmission to exceed 1.2, or significantly suppress the other modes. Not great mode matching. (PD gain: 20 dB; servo gain: 10.0.) 

In an earlier conversation Paco had recommended I preamplify the green REFL signal with an SR560 before feeding it to the RF mixer. (For yarm this is done with an SR560 gain of 1000.) I did so and raised the gain on the SR560 until it overloaded (PD: 0 dB; SR560: 100). This didn't immediately improve the lock quality, but because alignment still needed work I wasn't surprised. 

Anchal suggested the laser mode might be distorted by some lenses further upstream. We noticed some vertical spreading/distortion of the green beam by the first lens after SHG. I adjusted the pitch of an IR steering mirror until it disappeared. We then used the irises by the entrance to the arm cavity to coarsely align the input beam with M1 and M2. This time, fine alignment brought green transmission to just under 4. After slightly adjusting the half-wave plate, green transmission peaked at 4. (This is the highest I've seen it - previous max was 3.) The final combination of PD gain, SR560 gain, and servo gain that maximized transmission and duration of lock was (PD: 10 dB; SR560: 20; servo: 4.0). At its longest, lock on TEM00 was maintained for ~10 seconds.

AUX PDH Loop OLTF

In parallel with above, I was trying to take an OLTF of the loop whenever it was temporarily locked. I set up the measurement configuration like in the previous ELOG (injection at error point). Like last time, the loop would not lock when summing the PDH error signal with the excitation. I confirmed this was true even when I turned off the Moku excitation output. Checking the summed signal output, the Moku was adding an offset to the error signal. Buffering the excitation with an SR560 solved this issue.

The locked mode was switching pretty rapidly during the time I tried to measure the OLTF, and I ended up moving onto trying to improve lock. I might return today to try to take a measurement - I'll post it here.

[Anchal, Paco]

We measured DFD AM coupling; it seems to be minimum at higher RF input and low modulation depths as expected.

To do this, we set up Moku:Lab for AM ext with a spare DAC channel (C1:BAC-SPARE_CH14_OUT) which we send a swept sine excitation using diaggui. We vary the carrier level, and the modulation depth (every time we changed the level, we run the phaseUGF.py script to allow the phase tracker to adjust its loop gain properly). Attachment #1 shows the results, showing the finite bandwidth effect of the phase tracker as well as the mean magnitudes of the AM coupling below 100 Hz. This measurement and the script live in

What this means for ALS calibration:

It seems the residual AM coupling for a typical RF input level from our ALS beatnote corresponds to the couplings of ~ 2 Hz/V. This means that if the RF input level is fluctuating by 100mV, our residual beat frequency fluctuations only move by 200 mHz. This is not the case when the arms are locked... there the beat level stability is closer to 1 mV (so 2 mHz coupling to the phase tracker). Under previous SNR conditions, our lines are typically at a few 100 Hz of amplitude, with a noise floor comparable to a few 100 mHz (SNR ~ 100s), so AM coupling seems not to be statistically limiting for 0.1% calibration.

Next:

• To further reject this residual coupling, it may be worth balancing the demodulated IQ amplitudes, by using the digital gains "C1:ALS-BEATX_FINE_Q_GAIN, C1:ALS-BEATX_FINE_I_GAIN".
• For now, this effect (and its frequency dependence above 300 Hz) can probably be neglected for ALS calibration purposes.

I took transfer function measurement of DFD AM coupling using noise excitation.

Noise excitation setup

Noise is injected using C1:BAC-SPARE_CH14_EXC using awggui which is filtered by a foton filter to simulate the real beatnote RF amplitude noise measured by taking quadrature sum of C1:ALS-BEATY_FINE_I_OUT and C1:ALS-BEATY_FINE_Q_OUT. See attachment 1.

The DAC output is connected to MP1 at CH1. MP1 is set to run in waveform generation mode with following settings:

• Carrier frequency: 45 MHz
• Carrier Level: 500 mVpp
• No offset or phase offset
• Amplitude modulation ON
  • Modulation slope: 100%/V
  • Source Input: Ch1

The AWGUI is set to excite C1:BAC-SPARE_CH14_EXC using settings mentioned in attachment 2.

With this setup, the RF amplitude noise is simulated with MP1 and DAC excitation.

Transfer function measurement

With AWGGUI running as mentioned above, I simply used diaggui in spectrum mode for channels C1:BAC-SPARE_CH14_EXC and C1:ALS-BEATY_FINE_PHASE_OUT_HZ. The second channel is already calibrated into Hz, and the first channel is in counts. To convert it into voltage of amplitude fluctuation, I first converted DAC excitation to voltage by assuming 16 bit DAC with +/- 10 V range, this gives conversion constant of 10/2**15 V/cts. Then since MP1 is doing 100%/V AM modulation, for 500 mVpp RF level, this means 0.25 V/V AM modulation. Multiplying these two together gives, 7.6294e-5 V/cts. I put this number in teh diaggui calibration for C1:ALS-BEATY_FINE_PHASE_OUT_HZ.

This created the transfer function measurement attached in attachment 3.

The measurement resulted in roughly 2kHz/V AM to frequency coupling in DFD + phase tracker setup. The previous measurement with coherent sinusoidal excitation was exactly a factor of 1000 less than this, so I believe I might have made some error in calibrating or there could be an error in the previous elog. Please check my calculations. But a solid thing to note is the coherence measured below 1Hz. I'll do more sophisticated analysis on weekdays.

I also think that coherence was low because of low excitation. We should redo this test with more noise power to get good coherence in all frequency band to have good idea of what would happen to ebatnote RF amplitude noise at all frequencies.

Mon Jan 23 11:47:23 2023 Adding Attachment 4:

I realised that with the noise excitation setup set to mimic real beatnote amplitude noise with very low frequency noise as it is seeded with Moku:Pro, the measured frequency noise by the DFD+Phase Tracker setup at C1:ALS-BEATY_FINE_PHASE_OUT_HZ is an indicator of how much RF amplitude noise of beatnote contribute to the frequency noise measured by DFD+Phase tracker. Attachment 4 is the spectrum measured during this measurement.

Both the TF measurement and the noise measurements are useful, but the nosie measurement is much more meaningful. Since we expect the main coupling to be incoherent, what we really want is a noise budget style measurement:

1. Measure the FM noise spectrum with only a single sine wave into the Moku.
2. Same as #1, but with the AM noise added as you already did.
3. Estimate the noise budget contribution by doing PSD subtraction, and then scale that by the excitation magntiude. This will be the contribution of beat amplitude noise to the measured calibration.

I returned the half-wave plates on the XEND table back to their original angles, and restored the loop configuration with the PDH servo box. I returned the PD gain to 40 dB (original setting), and set the servo gain knob to 6. This was the region of highest loop stability, with the lock holding for a few seconds (as before). The control signal on the scope did not look intuitive - the peaks of the control signal corresponded with zero crossings of the error signal. 

Paco encouraged me to retake transfer function measurements of the PDH servo box. The main takeaway is the PDH servo (boost on) has the expected frequency response at a gain setting of 3 or under, up to 100 mVpp of input. Attachment 1 shows the frequency response at a servo gain of 2, for varying input amplitudes. 

The rest of the bode plots correspond to servo gain of 4, 6, 8, and 10 (boost on). The saturation LED would turn on above a gain value of ~3.25, so these results can't be analyzed or interpreted. But it does seem like a steep, low-frequency jump is a signature of the saturated servo. This jump doesn't appear with 10 mVpp input, at least at or above 1 Hz. 

Model changes and addition of Moku Phasemeter

Today I setup Moku:Pro MP1 with phasemeter app to replace DFD + Phase tracker.

Phasemeter settings:

• Both channels:
  • Frequency: Auto (Auto track frequency)
  • Bandwidth: 1 MHz
• Advanced:
  • Freewheeling: ON
  • Single input: ON (Used for now, later the two channels will use different inputs)
• Output for both outputs:
  • Signal: Freq offset
  • Scaling: 1.000 mV/Hz
  • Invert: off
  • Offset: 0.0000 V

Moku Input output settings:

• In 1 and In 2:
  • AC: 50 Ohm
  • -20 dB attenuation: 4 Vpp range
• Out1 and Out2:
  • +14 dB gain: 10 Vpp range

The phasemeter is set to autotrack the frequency with PLL bandwidth fo 1 MHz. The output of the phasemeter (frequency offset) is sent out through the output channels at 1mV/Hz rate. These are digitized at c1lsc ADC and are available as an alternative to phase tracker output channel. One can switch between the two ways of measurement by using C1:ALS-SEL_PHASE_SOURCE channel. See attachment 1 and 2 for the two mode options. For this, I modified c1lsc model today

Moku Phasemeter calibration

I used marconi to send 45 MHz RF output as -2 dBm level with internal FM modulation of peak 200 Hz at 211 Hz. This was used to calibrate the Moku Phasemeter outputs to set channels

C1:ALS-BEATX_MOKU_PHASE_OUTPUT_HZ and C1:ALS-BEATY_MOKU_PHASE_OUTPUT_HZ in units of Hz. This method is not very reliable as I do not know if marconi actually sent 200 Hz peak. The calculations from ADC conversion and moku slope of 1mV/Hz give similar numbers though. However, if we want to be accurate in our calibration project, more detailed calibration of these channels is required with a better technique. For now, I assumed that this value is good atleast to a 1% level.

AM coupling test and noise measurement

I followed the exact same setup as in 40m/17409 to create a RF signal using MP1 waveform generator which is AM modulated by awggui noise excitation to create similar AM noise as measured for BEATY RF output. The measurement can then take AM coupling transfer function measurements. Attachment 3 are the results of this measurement. In comparison to DFD + Phase tracker system, the transfer function is 2 orders of magnitude less. Even if my calibration of AM modulation is wrong, same calibration is sued for both transfer functions, so the difference measured is real. We are mostly measuring noise in this measurement as the coherence is also very low for all of the frequency range. See the 4th plot to see the inferred measurement noise of Moku phasemeter setup. Attachment 4 shows this data in comparison to data taken in 40m/17409 with DFD + Phase Tracker setup. Moku Phasemter setup provides roughly factor of 4 less noise in our calibration line frequency band.

Last week I captured the closed-loop error signal of the xend green PDH loop. Green transmission was around 2.5, and the laser was locking for about 3 seconds every couple minutes or so. The servo gain knob was set to 5.0. Repeating this with higher transmission/locking time is worthwhile.

Attachments 1 and 2 are two separate lock durations, with x-axes spanning 1 second each. The trace of interest (error signal out of mixer) is Channel 1. Channel 2 contains the control signal outputted by the PDH servo box.

The error signal is contained in a slow-moving envelope at ~4.5 Hz, zoomed in with time cursors in Attachments 3 and 4.

Zooming in further, the error signal has a fast component at ~150 Hz (Attachments 5, 6).

Before taking these traces, I captured the green REFL signal and open-loop PDH error signal shapes (Attachment 7). This error signal linear range spans ~500 mVpp. From looking at this signal it seems like the closed loop contains excess noise.

From considering the above traces and loop calculations I can start to infer the closed loop shape and/or UGF, and what direction we need to move in to recover good locking.

I wondered if Moku could have lied about its noise measurement since the RF source was the same Moku device. To avoid this bias, today I repeated this measurement with sendinf RF from Marconi. Marconi settings were:

• Carrier Frequency: 45 MHz
• RF Level: -2 dBm
• Mod AM ext DC: 90 %

The Marconi was fed noise from DAC output to match the measured BEATY RF amplitude like the previous posts: Attachment 1 shows AWGGUI settings required and attachment 2 shows the measured RF amplitude noise with the simulated source.

This source was then fed one by one to DFD + Phase tracker system (attachment 3) and then Moku Phasemeter setup (attachment 4). The phasemeter settigns were same as the previous post. Attachment 5 shows the two transfer functions of AM to frequency coupling on the same plot for comparison. Attachment 6 shows the comparison of frequency noise floor between the two methods on the same plot. In this measurement, I rechecked by DAC actuation calibration by measuring it directly. For Marconi AM modulation slope, I took into account the fact that the slope is in %/Vrms. I got it crosschecked with Paco this time. I think the calibration is correct. Moku phasemeter is indeed better by atleast 20 times in the frequency region of interest. The nosie floor is a factor of 3 less. I think this measurement clears Moku phasemter as the choice of frequency discriminator for calibration project. Any comments/opinions are welcome.

I reconnected the green REFL monitor channel and acquired its spectra when the laser was (mostly) locked. During the collection window, TEM00 would catch lock for a few seconds, drop, and catch again. As of today this is the longest the lock will hold. I'm uploading a screenshot for now but will replace with a proper .pdf spectra image.

There is a peak ~558 Hz and at its second harmonic. Additionally there is a less sharp peak at 760 Hz.

After seeing a 560 Hz peak in the XAUX REFL PD signal, I took spectra of the PDH error signal (post-demod) [Attachment 1]. The peak remained, warranting further investigation.

I disconnected the XAUX PDH loop (including PZT modulation) and looked at the beatnote between the PSL (locked to IMC) and the free-running XAUX laser. Attachment 2 shows the PSL-XAUX beatnote alongside the PSL-YAUX beatnote (both around 60 MHz). Note that the YAUX PDH loop was already disconnected, but I added a terminator to the PZT input BNC. Here the 560 Hz peak originating from the XAUX laser is clear. (It is also interesting that the BEATY signal has a significant comb structure compared to BEATX.)

Anchal suggested I tune the XAUX temperature for the frequency difference to switch signs (keeping magnitude at 60 MHz). The result is in Attachment 3 - the 560 Hz peak remained, showing it's not a local temperature-dependent feature.

From this is seems the 560 Hz noise is coming from the XAUX laser.

[Rana, Radhika]

Yesterday we looked at the out-of-loop PDH error signal of the AUX laser and determined that the LO phase needed significant adjustment. Previously I suspected that the LO phase knob was not actually connected to the circuitry, and we confirmed this looking inside the PDH servo box. Instead we shifted the modulation frequency towards a large PZT resonance in order to obtain a phase shift. (Original frequency: 231.25 kHz.) On a scope it looked like the PDH error signal was improving.

Today I manually swept across modulation frequency in increments of 5 kHz. Qualitatively the PDH signal looked the cleanest between 285 and 290 kHz [Attachment 1]. Here the linear region spans 2V, although it could still be larger in amplitude relative to the side peaks. More fine tuning is still remaining, and at this frequency I'll measure spectra + time series of the err and control signals. 

I retook the last spectrum measurement of ALS beatnote fluctuations, with the HEPA on and off. The top plot corresponds to BEATY, and the bottom plot corresponds to BEATX. The 560 Hz peak doesn't seem to be dependent on the status of the HEPA. The noise floor change in BEATY is probably due to drift of the beatnote frequency.

Stable lock of the X End green laser was recovered.

- The biggest issue was that the laser PZT input had been terminated with a 50ohm at the laser head. (See Attachment 1: The terminator has already been removed in the photo.) Since the PZT output of the servo box (output impedance 10Ohm) goes through 680Ohm at the summing node for the modulation, the PZT output was attenuated by a factor of 15. This made the required servo gain for locking more than the box could deliver. More importantly, the PZT range (in terms of the laser frequency) was also limited. Momentary locks were still possible with the reduced range and gain. However, the actuation signal hit the rail within a few seconds because of the pendulum motion.

Once the terminator was removed from the head, the Xarm was locked with the green laser like a charm.

- On the way to the resolution, I had to go through the full scrutinization of the loop components one by one. Here is the record of the findings:

• Inspected the green Refl PD (Thorlabs PFA36A). The gain setting of the PD was 40 dB, and the unlocked output voltage was 10.8 V. This is not only very close to saturation, but also the bandwidth drops below the modulation frequency (150 kHz according to Thorlabs' manual). The gain was changed to 20dB. This made the unlocked PD output to be 1.08V and the BW was expected to be 1MHz.
   
• Checked the LO setting. The box has a label saying "LO 7dBm". The function generator setting of "0.66 Vrms" resulted in 7.0dBm at the mixer LO input. So this number is used. Exactly the same amount goes to the PZT summing node.
   
• Checked the mod freq. The PDH error signal amplitude was maximized at 278.5kHz (mixer output observed with 50Ohm: 46.0mV), however, the signal looked distorted from the text-book shape of the PDF error. This means that the demod phase was not optimized.
  The mod freq of 287.5kHz made the PDH error signal look better while the response was weaker (mixer out: 31.2mV). It turned out that the cavity locking didn't like these mod freq between 280kHz~290kHz. The momentary lock stretches showed a lot of quasi-sinusoidal fluctuation ~600Hz in the error and transmission signals. Instead, the modulation of 210.5kHz was used. This made the error signal during lock stretches clean and tight. 
   
• Box inspection: Checked the signal ratio between the error in and the error mon. The monitor gain seemed x20~x21. The PZT output and the PZT mon had identical gains. The transfer function of the box was measured with the gain knob changed from 0.00 to 7.00 where the transfer function started to get distorted with the given input. The gain was increased by 5dB/turn (i.e., 1 turn increases the gain by 5dB). ? It does not match with the info on the schematic and the datasheet? Anyways, the gain knob is working fine.
   
• To resurrect the SLOW THERMAL servo, the monitor channels were connected to the DAQ interface. The existing slow channel servo/setting worked fine, wh
   
• Usual caution: a slight touch to the satellite amp caused the UR OSEM PD completely black out. It means that just your presence at the X end can make some changes to the suspension.
   

After the XAUX - XARM lock was recovered the C1:ALS-TRX_GAIN was set from 0.002 to 0.0006 to normalize the green transmission to 1 when the cavity is aligned. This situation was verified with YAUX as well. The green transmissions are now normalized to 1 when both arm cavities are aligned.

After this I took a reference ALS noise spectra (Attachment #1). The XALS rms noise is ~ 100 Hz (which is great compared to previous reference of > 250 Hz), while the YALS is slightly worse at high frequency but the rms is comparable to previous references (~ 250 Hz). This is somewhat encouraging for our future PRFPMI lock acquistions.

I measured the OLTF of the XAUX-PDH loop [Attachment 1] now that the green laser is stably locking. I injected an excitation (100mVpp) at the error point of the loop using a Moku:Go. The excitation was summed with the PDH error signal (alpha) using an SR560, and the summed signal (beta) was sent to the PDH servo. (The Moku excitation was buffered with another SR560.) The transfer function beta/alpha was measured on the Moku. 

The loop has a UGF of 26.3 kHz, and a phase margin of ~25º (using 1/1-OLG convention).

Next steps:

- Replace PDH servo demod + controller with Moku:Go lock-in amplifier (ensure loop shape is maintained)

- Deploy digital filters to further increase loop bandwidth/phase margin

I calibrated the moku phasemeter setup for reading beatnote fluctuations today. The calibration is referred to the DFD output (not including the phase tracker) channels by using the measurement made by gautam in 40m/14981.

Measurement setup

• Set marconi to 40 MHz carrier, FM1 sine deviation of amplitude 2000 kHz (we expect maximum beatnote fluctuation of ~1.8 kHz for 50 pm length modulation in the arm length) at 145 Hz.
• The output of amrconi is splitted, one half going to DFD for BEATY, one half going to Moku Phasemeter input 1.
• Moku phase meter is set with following settings:
  • Input1:
    • Frequency : Auto
    • Bandwidth: 1 MHz
    • Coupling: AC
    • Impedance: 50 Ohms
    • Range: 400 mVpp
  • Output1:
    • Signal Freq offset
    • Scaling: 1 mV/Hz
    • Invert: Off
    • Offset: 0
    • Range: 10 Vpp
• Measurement taken from 1365442502 to 1365444003

Analysis

• Read channels C1:ALS-BEATY_FINE_I_OUT C1:ALS-BEATY_FINE_Q_OUT C1:ALS-BEATY_MOKU_PHASE_IN1 for 500s.
• Used np.arctan2(Q, I) to read DFD phase output. Multiplied it by 1e6/70.973 to convert it into Hz using DFd calibration by Gautam in 40m/14981. This measurement brings in 340 ppm of uncertainty in the measurement.
• Demodulated the phase at 145 Hz to get the signal sent by Marconi. Blue trace in the attachment is this signal.
• Demodulated Moku phase output at 145 Hz and calculated the calibration constant required to match the ampltiude with 400second averaged DFD output.
  Calibration constant came out to be: 0.2953 +/- 0.0001
• Multiplied the calibration constant to moku phase output. This is the orange curve in the attachment.
• With this method, we get 0.035% uncertainty on phase calibration from Moku.
• We can now use moku phasemeter for calibration measurements as the pahse tracker gain is not high enough for calibration lines above 200 Hz.

Ditto of 40m/17543 but for XBEAT >> Calibrated to 0.3061 +/- 0.0001

An interesting thing to look at is the ALS out of loop spectra using our Moku DPLL. Attachment #1 shows the calibrated noise spectra in Hz/rtHz of both XBEAT and YBEAT as taken by the Moku phasemeter when the ARM cavities are locked to PSL using POX/POY. A great improvement is noted at lower frequencies (almost an order of magnitude for Y, over an order of magnitude for X) and some residual seismic noise (between ARMs and IMC) is noticeable! At higher frequencies, the suppressed laser frequency noises are close to their former references.

However this is only great news for our ALS calibration scheme, as the DPLL range is limited and may not be useful for the usual CARM offset reduction using ALS.

The rms fluctutations for the ALS beatnotes using the Moku Phasemeter have dropped below the 100 Hz floor! We now have 50-55 Hz (before we had 200 to 300 Hz)

Took some ITM/ETM single arm calibration data using Moku Phasemeter ALS>

• ITM gpstimes = [1365471104 to 1365471582]
• ETM gpstimes = [1365472286 to 1365473448]

I then took some ITM actuation calibration data using the Michelson fringe. For this I lock MICH and turn on all five lines using AS55_Q >

• ITMX gpstimes = [1365474355 to 1365474788]
• ITMY gpstimes = [1365474816 to 1365475268]
• Free swing = [1365475309 to 1365475535] (to get the fringe amplitude)

The ETM actuation calibration at these frequencies can be transferred using the POX/POY error signals and the ITM calibration from the gpstimes above. This should allow us a back to back cross-calibration comparison for arm cavities. Full analysis to follow this entry.

Finally, please take note of the area around the LSC rack! The temporary Moku phase meter calibration and setup referenced above are still a bit in the way. See Attachment #2

[Anchal, Paco]

We updated the LSC model to use the amplitude as a normalization (analogous to what happens in OpLevs). For reference Attachment #1 shows the previous model detail, and Attachment #2 shows the updated one. We then built, restarted and ran the model to realize the phase tracker gain can now be set once and for all assuming we still have a simple integrator and 2 kHz of phase tracker bandwidth. Doing this results in the ALS residual noise shown in Attachment #3. Compared against the reference spectra, the improvement is modest but not as great as what the moku had.

We ran ITMY actuation calibration using this infrastructure; to do this we lock arm cavities to PSL, lock AUX lasers to arm cavities, turn on our five lines and read back the demodulated signals from the beatnote as it goes through DFD + phase tracker. The results are summarized in Attachment #4. This time we correctly accounted for all known sources of statistical and systematic uncertainties (including a recently  measurement of the AUX loop gain),

how about the other idea of downloading the I & Q channels and doing the analysis offline? I'm curious if its better or worse. How could the Moku possibly be better?

Another idea is to use the frequency divider and then directly digitize. I believe someone tried that a few years ago, but not sure how good it was.

I did offline analysis with the available data. We were only saving signals at 2048 Hz rate, so analysis can not be done on 1.4 kHz line. See attached plot for the difference in the two analysis.

We are aiming to prepare a realtime system deployable calibration method, that's why we were using phase tracker. Note that the calibration results with phase tracker have been compensated for any lack of gain due to phase tracke limited bandwidth, open loop gain of aux loop or remaining suppression from YARM loop despite the notches.

About the moku, we think that something is wrong in connection of moku output to ADC. We see the same cal line heights in the moku app in ipad but after going through ADC, we see about 10 times less line heights and 10 time sles noise floor too. But when we stick a marconi split between DFD and moku, we see the same results, so we are not sure what is wrong with it but it is not trustworthy. Maybe the order of magnitude noise reduciton is because of this factor of 10 that happens when it reads beatnote. To be solved in future, we will carry on with DFD for now.

Last night I took ITMY calibration data using MICH with AS55_Q. Adding that to the same plot. The error bars are probably underestimate with the MICH calibration method due to systematics not taken into account. For this measurement, MICH was locked with low UGF of 20 Hz to avoid all lines in MICH loop. Notches at the line frequencies were also put in. MICH OLTF was measured and any possible suppression of lines has been compensated for (very small). Note that error bars are present for DFD method too, but they are too small in this scale.

MICH calibration did not independently verify the higher actuation strength found by DFD methods at higher frequencies. For an ideal pendulum, the calibration constants should ahve been freqeuncy independent. It does see higher calibration constant values at 500 Hz and 1.4 kHz lines, but with a lot of noise. See attachment 2 for the calibration in real time, but this plot is bit messy. For the three lower frequency lines, DFD+Phase tracker and DFD with offline analysis match in their estimates , there is a significant mismatch at 500 kHz line and we do not have data for doing this for 1.4 kHz line.

I modified the analysis to correct for any affects due to Anti-Aliasing or Anti-Imaging filters, and I also found a insignificant error on how I was undoing the suppression due to MICH loop in the MICH data. I also propagated the calibration in MICH method better. Attached are the updated results. The upward swing is still present.

Also, last night, Koji and I looked into any frequency dependent deviation in sensing arm length between POY11 and BEATY_PHASE (using DFD+Phase tracker) This was done by locked the YARM to the main laser and locking YAUX to the YARM, sending excitationa at C1:SUS-ETMY_POSCAL_EXC and taking transfer function between C1:LSC-YARM_IN1 and C1:ALS-BEAT_Y_FINE_PHASE_OUT. This transfer function was flat upto about 600 Hz and the deviation from there to 2000 Hz was expected based on limited bandwidth of the phase tracker. I don't have the plot to attach, someone should redo this quick measurement to save the data.
Interestingly, the same measurement when done with  C1:LSC-DARM_IN1 in FPMI configuration did not show a flat response. This is can mean that the DARM strain relationship with the beatnote frequency deviation is not a simple constant factor and/or depends on DARM or CARM OLTFs. I leave my remarks on this project here for the baton to be picked up by others in future. I unfortunately only have this much time to contribute to FPMI calibration.

Tl;dr: Tried to replace of XEND green PDH servo controller with Moku template IIR filter, designed to match PDH servo frequency response. The green laser did not catch lock with this filter.

Attachment 1 plots the measured TF of the PDH servo controller, with boost on and the gain knob set to 7.22 (the current lock configurations). It also plots an 8th order Chebyshev type II low-pass filter, with cutoff frequency and scale chosen to best match the data. (8 was the highest order filter that could be represented by 4 second-order-sections, the maximum allowed by the Moku.) I wanted to test if the XAUX PDH lock could be maintained using this filter as the controller.

The phase of the Chebyshev II filter does not seem to be a good fit to the data, but I wanted to see how far we could get using a template filter already designed for discrete time, and with a magnitude frequency response that approximates the servo. This would bypass having to perform a bilinear transform from the s-domain to the z-domain, which can raise more complications.

The PDH error signal (mixer output) was split and sent to the Moku (input 1) and to the PDH servo input. Closing the loop with the Moku filter output, the green laser was not able to catch lock. Attachment 2 shows the Moku:Go Digital Filter Box configurations, as well as the traces comparing output of the filter and the output of the PDH servo. The red trace is the output of Moku filter, and the blue trace is the output of the PDH servo (input 2) with the loop open (nothing feeding back to laser PZT). The input gain of the filter module was chosen to match the amplitudes of the two control signals. Qualitatively, the filter output contains higher frequency components and preserves the odd polarity of the PDH error signal, compared to the servo output. 

I then tried to directly fit the PDH servo TF data. I fit the (analog) poles and zeros of the TF using vectfit. In theory, using a bilinear transform can convert the analog zpk TF to digital zpk, with some frequency pre-warping required. However, vectfit did not return a "normal" transfer function, defined as having at least as many poles as zeros. This caused the bilinear transform to fail.

Next, I will need to use a different fitting package (perhaps IIRrational) to obtain a nicer TF fit, in normal form. Then I can attemp the bilinear transform, confirm it preserves the desired frequency response, and test it out with the Moku:Go.

[Mayank, Radhika]

I retook a transfer function measurement of the uPDH servo closed-loop (using the SR560 to simulate a cavity pole) [Attachment 1]. While some coherence is lost at low frequencies, the servo does not appear to be saturating. Moving forward this measurement is used to design a digital filter that can replicate the uPDH servo box response. *Note: for now the chosen sampling frequency for the discrete filters is 61.04 kHz, the lowest sampling frequency setting of the Moku:Go.

We performed a low-order fit of the TF using vectfit. Vectfit always seems to return 1 more zero than pole - this results in an "improper" transfer function that causes any transformation to the z-domain to fail. Mayank took the fitted zeros and poles from vectfit and manually removed one of the zeros. After transforming the zeros and poles to the z-domain (using control.matlab.c2d), we noticed multiple resonances around 100 kHz that reached 10-20 dB. We decided to estimate poles and zeros by eye instead of using vectfit. 

2 zeros and 2 poles were selected by eye to get an estimated fit in the s-domain. Using continous-to-discrete transforms (tried scipy.signal.bilinear and control.matlab.c2d) resulted in unstable controller responses. Attachment 2 shows the original TF measurement with the designed analog filter and the resulting digital filter. The orange 'x's and 'o's mark the poles and zeros used. The digital filter contains many high-frequencies resonances, the most significant at the sampling frequency, 61.04 kHz, reaching 20 dB. Next we tried to manually load the analog ZPK coefficients into Foton. This resulted in the same digital filter as the python s-domain to z-domain functions [Attachment 3].

**UPDATE** Now looking back it's clear that the high-frequency response is limited by the sampling rate. I will redo this for the highest Moku:Go sampling rate of 3.9 MHz.

XAUX laser locked with Moku:Go controller

The analog zeros and poles used to design this filter were:

Attachment 1 shows the resulting digital SOS filter (sampling rate: 3.9 MHz) compared to the measured uPDH servo transfer function (loop closed). The filter design was loaded on the Moku:Go.

Lock acquisition

I locked the AUX laser with the uPDH servo box and maximized its transmission to ~0.8. I then fed the Moku digital filter output to the PZT and the laser was able to catch lock. However, the max green transmission I could achieve using the Moku controller was 0.5. Attachment 2 is a screenshot of the green transmission ndscope during a lock sequence.

I measured the OLTF of the loop by injecting an excitation at the error point. An SR560 was used to sum the error signal with the excitation. The Moku multi-instrument mode was configured with the Frequency Response Analyzer and Digital Filter Box; it was able to source the excitation and take a transfer function measurement of error signal / (error signal + excitation), while keeping the loop closed.

The OLTF measurement [Attachment 3] points to a loop UGF of ~4 kHz, and phase margin of ~70 deg. An optimal controller would be able to boost the gain around the UGF without changing the phase too much (lag compensator)?

         f_fsr
dfmn =   ----- * (m+n) * acos(sqrt(g1*g2))
           pi

I pushed the "closed loop" button on PZT2 YAW around 3:40 pm today, then roughly recentered it using the DC Offset knob on the PiezoJena controller and the IP ANG QPD readbacks.  There was a large DC shift.    We'll watch and see how much it drifts in this state.

 Here's the trend.

The transient at ~22:40 is Rob switching to 'Open Loop' on the Piezo Jena PZTs. I don't see any qualitative change in the drift after this event.

At 05:55 UTC, I removed an iris that was blocking the IP POS beam (the sum goes up from 2 to 6.5) without disturbing the mirrors who's oplev beam are on that table. Steve has conceded one sugar Napoleon after betting against my ninja-like iris skills.

We should recenter the beam on IP POS now that its unclipped - I'll let it sit this way overnight just to get more drift data.

I wanted to see how long our IP POS beam has been badly clipped - turns out its since April 1, 2007.

Steve's April Fool's joke is chronicled then. The attached trend shows that the drop in IP POS is coincident with that event.

In trying to align IPPOS, I noticed that someone has placed a ND2.0 filter (factor of 100 attenuation) in front of it. This is kind of a waste - I have removed IPPOS to fix its resistors and avoid this bad optic. Also the beam coming onto the table is too big for the 1" diameter optics being used; we need to replace it with a 2" diamter optic (Y1-2037-45P).

IP ANG dropped by a factor of 2 back in early August of '08.

We need this guy on the investigation:

Tonight I aligned the IFO by running the scripts one by one.

SRC was far off and I had to align SRM by hand before the script could work. SPOB is still low when DRM is aligned.

I'm restoring the full IFO now that I'm taking off.