[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.

[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.

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. 

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 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.

[Paco, Anchal]

- Upon arrival, MC is locked, and we can see light in MON5 (PRM) (usually dark).

# XARM locking
- Read through "XARM POX" script (path='/cvs/cds/rtcds/caltech/c1/burt/c1configure/c1configureXarm')
- Before running the script, we noticed the PRM watchdog is down, so we manually repeat the procedure from last time, but see more swinging even though the watchdog is active.
- Run a reEnablePRMWatchdogs.py script (a copy of reEnableWatchdogs.py with optics=['PRM']), which had the same effect. 
- We manually disable the watchdog to recover the state we first encountered, and wait for the beam in MON5 to come to rest.
    - The question is; is it fine to lock Xarm with PRM watchdog down?
    - To investigate this, we look at the effect of the offset on the unwatchdog-PRM.
    - Manually change 'PRM_POS_OFFSET' to 200, and -800 (which is the value used in the script) with no effect on the PRM swinging.
- Moving on, run IFO > CONFIGURE > ! (X Arm) > RESTORE XARM (XARM POX), and ... success.

# MC-POX noise spectra
- With XARM locked, open diaggui and take spectra for C1:LSC-POX11_I_ERR_DQ, C1:LSC-POX11_Q_ERR_DQ, C1:IOO-MC_F_DQ
- Lost XARM lock while we were figuring out unit conversions...
    - Assuming 2.631e-13 m/counts (6941) and using 37.79 m (arm length), 1064.1 nm wavelength, we get a calibration factor of 2.631e-13 * c / (2*L*lambda) ~ 0.9809 Hz/count 
    - (FAQ?, how to find/compute/measure the correct calibration factors?)
- Relock XARM, retake spectra. Attachment 1 has plots for POX11_I/Q_ERR_DQ spectrum (cts/rtHz, we couldn't find relevant calibration) and MC_F_DQ in (Hz/rtHz from referring to 15576, we couldn't get the units to show on y scale.)

# MC-POY noise spectra (attempt)
- Now, run IFO > CONFIGURE > ! (Y Arm) > RESTORE YARM (YARM POY), and XARM locks (why?)
    - Could PRM watchdog being down be the cause? 
- Try C1ASS > (YARM) ! More Scripts > ON, and looked at YARM PIT/YAW striptool. 
- C1ASS > (YARM) ! Freeze Outputs, then OFF
- Go back to IFO > CONFIGURE > ! (Y Arm) > Align YARM  (ASS ON: Unfreeze), try running this then Freeze, then OFF Zero Outputs.
- Try RESTORE YARM (POY) again, still not working.
- Try RESTORE YARM ALS, then try again after opening the shutter, but also fail to lock AUX.
    - Is the PRM WD behind some evil misalignment? Will move forward with XARM bc it is happy.

# ARM locking
- Attempted the IFO > CONFIGURE > ! (X Arm) > RESTORE Xarm (XARM ALS) but green failed to lock and we lost XARM lock.
- Try to recover XARM lock... success. It's nice to have a (repeatable) checkpoint.
- Attempt YARM lock. Not successful. It just seems like the lock Triggers are not raised (misalignment?)
    - From C1SUS_ETMY, try changing the bias "C1:SUS-ETMY_YAW_OFFSET" manually to reduce the OPLEV_YERROR. Changed from -47 to -57.
    - Retry YARM lock script... no luck
    - From C1SUS_PRM, try changing the bias "C1:SUS-PRM_PIT_OFFSET" manually to reduce OPLEV errors. Changed from 34 to 22 with no effect, then realized the coil outputs are disabled because the WD is down...
    - So we do the following BIAS changes "C1:SUS-PRM_PIT_OFFSET" = 34 > 770 and "C1:SUS-PRM_YAW_OFFSET" = 134 > -6
    - Enable all Coil Outputs, turn WD to Normal, turn OPLEVs ON, (this time the beam does not swing like crazy).
    - Fine tune BIASes "C1:SUS-PRM_PIT_OFFSET" = 770 > 805  and "C1:SUS-PRM_YAW_OFFSET" = -6 > 65
        - Saw YARM locking briefly, then unlocking, but we stopped once the OPLEV_ERRs no longer overloaded (from magnitudes > 50 to ~ 40).
- Retry YARM lock... no luck
    - From C1SUS_ETMY, try changing the bias "C1:SUS-ETMY_PIT_OFFSET" from -1 to 6. 

Stop for the day. Leave XARM locked, MC locked. 

To avoid the strange kicking of ETMX, I locked XARM with ITMX actuated instead of ETMX so that I changed elements of C1LSC_OUTPUT_MTRX; before: XARM=ETMX, after: XARM=ITMX.

And I change C1:LSC-XARM_GAIN from 0.007 to 0.022.

With this setup, I ran dither but then error signals of dithering oscillated as shown in the figure below.

Then I found that if C1:ASS-XARM_ETM_PIT_L_DEMOD_SIG_GAIN / C1:ASS-XARM_ETM_YAW_L_DEMOD_SIG_GAIN in C1ASS_LOCKINS_XARM.adl are changed as 0.200 -> 0.100 and 0.200 -> 0.100, respectively, the dithering works well.

But the burt file that is loaded when you let dithering "ON" is not changed, because now I don't know how to update a burt file. So, if you let dithering "ON", the dithering will run with the condition that C1:ASS-XARM_ETM_PIT_L_DEMOD_SIG_GAIN / C1:ASS-XARM_ETM_YAW_L_DEMOD_SIG_GAIN are not 0.100 but 0.200.

I changed the snapshot file for ASS, /opt/rtcds/caltech/c1/scripts/ASS_DITHER_ON.snap as follows:

L124 >  C1:ASS-XARM_ETM_PIT_GAIN 1 -5.000000000000000e-02

        => C1:ASS-XARM_ETM_PIT_GAIN 1 -1.500000000000000e-02

L128>   C1:ASS-XARM_ETM_YAW_GAIN 1 5.000000000000000e-02

        => C1:ASS-XARM_ETM_YAW_GAIN 1 1.500000000000000e-02

The purpose of this change is to avoid the oscillation when the dithering of X arm is running.

XARM lock was achieved by POX11_I

Summary:

- The  whitening gains of POX11_I and Q are 42dB so that POX11_I have the same amplitude as AS55_I

- The demod phase of POX11 was adjusted to eliminate the PDH signal from the Q phase. The phase is  -100.5deg.

- In order to lock the XARM with POX11_I_ERR, I had to increase the trigger threshold from 0.1 to 0.2 as the arm was
kicked with the threshold of 0.1.

Method

- Lock the X arm with AS55_I at the XARM configuration.

- Adjusted POX11 demod phase so that POX11_Q is minimized.

- POX I&Q whitening gains were adjusted. When they are 42dB, POX11_I_ERR and AS55_I_ERR have almost the same signal amplitude.
(In reality, POX11_I_ERR has +1dB larger amplitude.)

- Adjusted POX11 demod phase again with better precision.

- Measured transfer function between AS55_I_ERR and POX11_I_ERR. As the sign was opposite, the demod phase was -180deg flipped.

- Tried to lock the arm with POX11_I_ERR. It did not acquire the lock. The arm looked kicked by the servo.

- Increased the trigger threshold from 0.1 to 0.2. Now the arm is locked with POX11_I_ERR.

[gautam, johannes]

I started a script on Friday night to collect some data for a reflection armloss measurement of the XARM. Unfortunately there seemed to have been a hickup in some data transfer and some errors were produced, so we couldn't really trust the numbers.

Instead, we took a series of manual measurements today and made sure the interferometer is well behaved during the averaging process. I wrote up the math behind the measurement in the attached pdf.

The numbers we used for the calculations are the following:

• alpha = 91.2% from elog 6859 
• m1=0.179  and  m2=0.226 from elog 11745

While we average about 50 ppm +/-15 ppm for the XARM loss with a handful of samples, in a few instances the calculations actually yielded negative numbers, so there's a flaw in the way I'm collecting the data. There seems to be a ~3% drift in the signal level on the PO port on the order of minutes that does not show in the modecleaner transmission. The signals are somewhat small so we're closing the shutter over night to see if it could be an offset and will investigate further tomorrow. I went back and checked my data for the YARM, but that doesn't seem to be affected by it.

[Anchal, Paco, Rana]

We locked the XARM using POX11 and made a noise budget for the single arm displacement; see Attachment #1. The noise budget is rough in that we use simple calibrations to get it going; for example we calibrate the measured error point C1:LSC-XARM_IN1_DQ using the single cavity pole and some dc gain to match the UGF point. The control point C1:LSC-XARM_OUT_DQ is calibrated using the actuator gain measured recently by Yuta. We also overlay an estimate of the seismic motion using C1:PEM-SEIS_BS_X_OUT_DQ (calibrated using a few poles to account for stack and pendulum), and finally the laser frequency noise as proxied by the mode cleaner C1:IOO-MC_F_DQ.

A couple of points are taken with this noise budget, apart from it needing a better calibration;

1. Overall the inferred residual displacement noise is high, even for our single arm cavity.
   1. By looking at the sim OLTF in foton, it seemed that the single arm cavity loop TF could easily become unstable due to some near-UGF-funkiness likely from FM3 (higher freq boost), so we disabled the automatic triggering on it; the arm stayed locked and we changed the error signal (light blue vs gold (REF1) trace)
2. The arm cavity is potentially seeing too much noise from the IMC in the 1 to 30 Hz band in the form of laser frequency noise.
   1. Need IMC noise budget to properly debug.
3. At high frequency (>UGF), there seem to be a bunch of "wiggles" which remain unidentified.
   1. We actually tried to investigate a bit into these features, thinking they might have something to do with misalignment, but we couldn't really find significant correlation.

RXA edit:

1. we also noticed some weirdness in the calibration of MC_F v. Arm. We think MC_F should be in units of Hz, and Paco calculated the resulting motion as seen by the arm, but there was a factor of several between these two. Need to calibrate MC_F and check. In principle, MC_F will show up directly in ALS_BEATX (with the green PDH lock off), and I assume that one is accurately calibrated. Somehow we should get MC_F, XARM, and ALS_BEAT to all agree. JC is working on calibrating the Mini-Circuits frequency counter, so once that is done we will be in good shape.
2. we may need to turn on some MC_L feedback for the IMC, so that the MC length follows the NPRO frequency below ~20 Hz.
3. Need to estimate where the IMC WFS noise is in all of this. Does it limit the MC length stability in any frequency band? How do we determine this?
4. Also, we want to redo this noise budget today, whilst using AS55 instead of POX. Please measure the Schnupp asymmetry by checking the optimum demod phase in AS55 for locking Xarm v Yarm.

[JC, Paco]

We took the long BNC cable that ran from ETMX to ETMY and ran it from ETMX into the control room instead. This way Cici and Deeksha can send small voltage signals to the AUX PZT and read back using the beatnote pickoff that is usually connected to the spectrum analyzer.

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)?

We now have two 80-foot, female-to-female XLR cables for our pretty new microphones, one yellow and one purple. They have been tested and appropriately labeled.

Also, here is a very helpful pdf for how to properly attach the XLR connectors to a raw quad cable, as well as one for how to put the actual connectors together (ignore the cable instructions on the connector page... the cable depicted is not a quad cable).

[Gautam Koji]

XLR(F)-XLR(M) cable for the blue microphone is missing. Steve ordered one.

We found one in the fibox setup. As we don't use it during the vent, we use this cable for the microphone.
Once we get the new one, it will go to the fibox setup.

We tweaked the mirror on the AP table to go through the center of the lens in order to get a more circular beam, but it seemed ineffective. So we put an IR card in front of the lens and behind the lens to see if the beam was circular or ovacular, but could not tell. We also moved the camera to see, but still couldn't see a distinct circle or oval. So Mike and Q will do a beam scan tomorrow in both the X and Y directions to see if the beam is circular or not.

Measured frequency noise is ~10Hz/rtHz @100Hz. 

Measure the out-of-loop noise of Xarm ALS:

1. The X-arm was locked for IR using PDH error signal.

2. 'CLEAR HISTORY' of the phase tracker filters.

3. Measured the power spectrum of the phase tracker output. I have used the newly created calibrated channel "PHASE_OUT_DQ. So the phase tracker output now reads in Hz.

Discussion:

The measurement was done with beat note frequency at ~40MHz. The flat noise level of 10Hz/rtHz from 20-100Hz (in plot 2) is not good. We should investigate as to what sets this noise level. The spike at 60Hz is because the 60Hz frequency comb filter was not enabled.

I plan to the following to get a clearer outlook
1. Connecting the beat box to an RF source and measure the noise levels for a range of frequency inputs to the beatbox.
2. Measure the noise at C1:ALS-BEATX_FINE_I_IN1 (before the antiwhitening filters) and check whether the new whitening filters has done anything good with respect to minimizing the DAQ noise.

X-Arm ASS was fixed.
ASS_DITHER_ON.snap was updated so that the new setting can be loaded from the ASS screen.

The input and output matrices and the servo gains were adjusted as found in the attached image.
The output matrix was adjusted by looking at the static response of the error signals when a DC offset
was applied to each actuator.

The servo was tested with misalignment of the ITM, ETM, and BS. In fact, the servo restored transmission
from 0.15 to 1.

The resulting contrast after ASSing was ~99% level. (I forgot to record the measurement but the dark fringe level of ASDC was 4~5count.)

Please remember that Xarm ASS needs FM6 (Bounce filters) to be ON in order to work properly.

While Gautam is working the restoration of Yarm ASS, I worked on Xarm.

Basically, I have changed the oscillator freqs and amps so as to have linear signals to the misalignment of the mirrors.
Also reduced the complexity of the input/output matrices to avoid any confusion.

Now the ITM dither takes care of the ITM alignment, and the ETM dither takes care of the ETM alignment.
The cavity alignment servos (4dofs) are running fine although the control band widths are still low (<0.1Hz).
The ETM spot positions should be controlled by the BS alignment, but it seems that these loops have suspicion about the signal quality.

While Gautam wa stouching the input TTs, we occasionally saw anomalously high transmission of the arm cavities (~1.2).
We decided to use this beam as this could have indicated partial clipping of the beam somewhere in the input optics chain.

Then the arm cavity was aligned to have reasonably high transmission for the green beam. i.e. Use the green power mon PD as a part of the alignment reference.

This resulted very stable transmission of both the IR and green beams. We liked them. We decide to use this a reference beam at least for now.

Attachment1: GTRX image at the end of the work.

Attachment2: ASSX screen shot

Attachment3: ASSX servo screen shot

Attachment4: Green ASX servo screen shot

Attachment 5: Screen shot of the ASS X strip tool

Attachment 6: Screen shot of the ASS X input matrix

Attachment 7: Screen shot of the ASS X output matrix

I've made a whole bunch of measurements on the Xarm green situation.

TL;DRs:

• GTRX was around 0.55 for all of the measurements tonight. 
• Based on where I saw gain peaking in the CLG, it looked like UGF was 1-2kHz. I cranked the gain to 10kHz, ~20dB gain peaking followed, making it hard to measure. Currently sitting at 5kHz-ish. 
• Measured CLG with AG4395A, calibrated for injection point response, inferred OLG. 
• Took various PSDs, still need to calibrate into physically meaningful units. 

Reasonable amounts of time were spent bending the AG4395 to my will; i.e. figuring out the calibration things Jenne and Rana did, finding the right excitation amplitude and profile that would leave the light steadily locked, and finding the right GPIB incantation for getting spectra in PSD units instead of power units. I'm nearing completion of a newer version of AG4395 scripts that have proper units, and pseudo-log spectra (i.e. logarithmically spaced linear sweeps)

Transfer functions

Here is too many traces on one plot showing parts of the OLTF for the x green PDH. One notable omission is the PD response (note to self:check model and bandwidth). The servo oddly seems to have a notch around 100k. My calibration for the CLG injection may not have been perfect, instead of flattening out at 0dB, I had 2dB residual. I tried to correct for it after the fact, assuming that certain regions were truly flat at 0dB, but I want to revisit it to be thorough. I found some old measurements of the Innolight PZT PM response, which claims to be in rad/V, and have included that on the plot. 

In the end, the mixer and PZT response make it look like getting over 10kHz bandwidth may be tough. Even finding a good higher modulation frequency to be able to scoot the LP up would leave us with the sharp slope in the PZT phase loss, and could cause bad gain peaking. Maybe it's worth thinking about a faster way of modulating the green light?

Noise Spectra

Tomorrow morning, I'll calibrate all the noise spectra I have into real units. These include:

• In loop error signal and control signal spectra
• Mixer output spectrum when PD is dark, and when mixer input is terminated
• Servo out spectrum when PD is dark, and when servo input is terminated

However, looking at the floors, it occurs to me that I may have left the attenuation on the input too high, in an effort to protect the input the PDH box, which rails all the time when not locked to a 00 mode, sometimes even with the input terminated or open. It's kind of a pain that the agilent makes it really hard to see the data when you're in V/rtHz mode, because I should've caught this while measuring :/

I used a scope to capture a pdh signal happening, which will let me transform the mixer output into cavity motion. The control signal goes to the innolight PZT with a ~1MHz/V factor. Here are the uncalibrated plots, for now. 

A MIST simulation tells me that the green pdh horn-to-horn displacement is about 1.2nm, or ~18kHz. I used this, along with the scope trace attached to the previous post, to calibrate the mixer output at 193419 Hz per V. (EDIT: I was a little too hasty here. What I'm really after is the slope of the zero crossing, which turns out to be almost exactly twice my earlier naïve estimate. See later post for correct spectra)

For the control signal, I assumed a flat Innolight PZT PM response of 1MHz/V. ( Under 10kHz, it is indeed flat, and this is the region where the control signal is above the servo output noise in yesterday's measurements)

Here are all of the same spectra from last night, with the above calibrations. 

Going off Jenne's earlier plot, it looks like the in-loop error signal RMS is ten times bigger than the CARM linewidth. 

I remeasured all of the noise spectra again today, making sure the input attenuation was as low as it could safely be. I also got a snap of the y green PDH signal; it's fairly larger than I saw the other day, which is good. I used this to calibrate the error signal voltage spectra. 

Here are the noise traces for each arm. During these measurements GTRX was about .6, GTRY about 1.0 The Yarm noise doesn't look so good: the error signal is just barely above the mixer+lowpass output noise, and the RMS is plauged by 60Hz lines. (Is this related to what we see in IR TRY sometimes?)

Here are the arms error signals compared directly:

 Xarm Green Steering Mirror Upgrade

Nick and I did the upgrade for the green steering mirror today. We locked in the TEM00 mode.
We placed the shutter and everything. We move the OL, but we placed it back. Tonight, I'll be doing a more complete elog with more details.

That was super fast! Great job, Andres and Nic!

[Rana, Jenne, EricQ]

We did several things tonight.  First, a list (so I can remember them all), and then some details.

(1) Jiggled ETMY SUS cables, removed kicks.

(2) Locked X and Y ALS, looked at POX, POY as out of loop sensors.

(3) Measured stuff (?) at the Yend.

(4) Reconnected REFL DC to SR560.

(5) Attempted CARM offset reduction.

Item 1:

When Rana and I started locking this evening, we saw (as Q has been witnessing for a while now) the ETMY kick a lot.  However, it seemed to be kicking even more than usual.  Since Q had been down at the end station recabling things, we wondered if a SUS-related cable got bumped.  Rana went down to the end and pushed all the cables into their receptacles.  One of the last sets that he pushed was the satellite box.  We didn't have walkie-talkie communication, but the DC offset of the ETMY oplevs changed just a minute or two before he returned to the control room.  So, we guess that it was the satellite box cables that were loose.  Unfortunately, there is no clear way to strain relieve them, which is why they can so often be troublesome.  Anyhow, the ETMY hasn't kicked since.

Item 2:

We locked the arms with ALS.  We saw that the POX signal was about 20% of the full pk-pk height of the PDH signal, so it's mostly within the linear range, but not entirely.  It is what it is, however, and we took measurements assuming that it's okay.  I calibrated POX by putting an excitation onto ETMX, and matching the height of the peak in POX and BEATX_FINE_PHASE_OUT_HZ.

Q and Rana had also [remembered / put in / something] a digital readback for the end green PDH error point.  Q went down to the end and gave me a number of 2600 Hz/V for the err mon port of the PDH board, which is what is connected to the ADC.  With that and 20/2^16 V/cts, I had a calibration of 0.8 Hz/ct. 

What we see in this plot is that the green end PDH is not the limiting noise for the POX out of loop measurement of the residual arm motion.  Also, in the multi-color metrology paper, Fig 7 (which is posted in the control room), we see at about a little over 1 Hz a ratio of about 4.5 between the residual motion and the AUX PDH error signal.  In today's plot, I see a ratio of about 20.  I infer from this that the green PDH for the Xarm is fine, and that we may want to re-look at the ALS digital loop, but we should leave the X PDH alone.

Here is the Xarm plot:

Q took the data for the Yarm plot, so hopefully he can give it to us in the morning.  What we did notice was that the noise was much worse for the Yarm.  This prompted Item 3, measuring the loop.

Item 3:

Q and Rana went down to the Yend and measured some things.  They came back, and said that they hadn't changed anything in analog while they were down there.  One thing that Q did note was that we have almost 90 degrees of phase margin (since it's a 1/f loop), and about 10 dB of gain margin, above the UGF.  So, we're in good shape for being able to try triggering the boost on the PDH box.  Q will give us more notes on this work, as well as plots, in the morning.

Item 4:

At some point, I remembered that Q and Gabriele had repurposed the SR560 that we had been using for the REFLDC input to the common mode board.  So, Q went and put it back, so that REFL DC goes into the SR560, and so does a DAC channel so that we can remotely set the offset.  The A-B output goes to the REFL11I whitening channel, since real REFL11I goes into the input of the CM board.  I think that today, the SR 560 was left at a gain of 1.

Item 5:

We decided to carry on and try to reduce the CARM offset some.  An annoyance is that the Yarm still has pretty significant low-frequency noise, but the idea is that if we can get over to the sqrtInvTrans signals, it will be fine.

So, we didn't get much farther than we had in the past, but it was nice to get there at all again.  I ran the carm_cm_up script (many times).  One of the times, all I wanted to do was see how much I could reduce the CARM offset.  CARM was on sqrtInvTrans, DARM was on ALS diff, and I was able to get the arm powers up to about 2.5.  I don't know why I lost lock.  The sqrtInv signals should be good until at least arm powers of 20 or so. 

I was able to see the REFL DC dip, but only a teensy tiny bit.  It went down by maybe 1 count.  Q suggested looking at how deep it could get while leaving CARM and DARM both on ALS, and setting both offsets to 0.  We were seeing arm flashes of about 50 counts, and REFL DC went from 0 to -800.  So, I wasn't seeing much of a REFL dip, but it was definitely there when I went to arm powers of 2ish.

We tried looking at different sqrtInv options for DARM, and haven't come to any real conclusion.  In the plot below, we are looking at a swept sine between DARM_IN1 (ALSdiff) and either MC_IN1 0.3*(sqrtInvX - sqrtInvY) or SRCL_IN1 (TRX - TRY / sqrt(TRX + TRY) ):

We have a few things to add to the to-do list:

* Put UGF servos for LSC loops in place.

* Implement UGF "servos" (per Koji's suggested method) for phase trackers.

* Write a lockloss script that is run by the ALS watch scripts - print a PDF of error and control signals for every lockloss, and save it somewhere.

* Fix up Ygreen modematching on the PSL table.  The X green spot is quite similar on the camera to the corresponding PSL green spot.  However the Y green spot is not at all the same as its PSL green spot. 

 Current Mode Matching and Gouy Phase Between Steering Mirrors

We found in 40m elog ID 3330 ( http://nodus.ligo.caltech.edu:8080/40m/3330) a documentation done by Kiwamu, where he measured the waist of the green. The waist of the green is about 35µm. Using a la mode, I was able to calculate the current mode matching, and the Gouy phase between the steering mirrors. In a la mode, I used the optical distances,which is just the distance measured times its index of refraction. I contacted someone from ThorLabs (which is the company that bought Optics For Research), and that person told that the Faraday IO-5-532-LP has a Terbium Gallium Garnet crystal of a length of 7mm and its index of refraction is 1.95. The current mode matching is 0.9343, and the current Gouy phase between steering mirrors is 0.2023 degrees. On Monday, Nick and I are planning to measure the actual mode matching. The attached below is the current X-arm optical layout. 

Calculation For the New Optical Layout

Since the current Gouy phase between the steering mirror is essentially zero, we need to find a way how to increase the Gouy Phase. We tried to add two more lenses after the second steering mirror, and we found that increasing the Gouy phase result in a dramatically decrease in mode matching. For instance, a Gouy phase of about 50 degrees results in a mode matching of about .2, which is awful. We removed the first lens after the faraday, and we added two more mirrors and two more lenses after the second steering mirror. I modified the photo that I took and I place where the new lenses and new mirrors should go as shown in the second pictures attached below. Using a la mode, we found the following solution:

 label                         z (m)            type                       parameters         

 -----                          -----              ----                        ----------         

 lens 1                       0.0800          lens                      focalLength: 0.1000

 First mirror              0.1550          flat mirror            none:            

 Second mirror         0.2800          flat mirror            none:            

 lens 2                      0.4275           lens                      focalLength: Inf   

 lens 3                     0.6549            lens                      focalLength: 0.3000

lens 4                      0.8968            lens                      focalLength: -0.250

Third mirror           1.0675            flat mirror            none:            

Fourth mirror         1.4183            flat mirror            none:            

lens 5                      1.6384            lens                     focalLength: -0.100

Fifth mirror            1.7351            flat mirror           none:            

Sixth mirror           2.0859            flat mirror           none:            

lens 6                     2.1621            lens                     focalLength: 0.6000

ETM                      2.7407            lens                    focalLength: -129.7

ITM                       40.5307          flat mirror          none:             

The mode matching is 0.9786. The different Gouy phase different between Third Mirror and Fourth Mirror is 69.59 degrees, Gouy Phase between Fourth and Fifth 18.80 degrees, Gouy phase between Fifth and Sixth mirrors is 1.28 degrees, Gouy phase between Third and Fifth 88.38 degrees, and the Gouy phase between Fourth and Sixth is 20.08 degrees. Bellow attached the a la Mode code and the Plots.

Plan for this week

I don't  think we have the lenses that we need for this new setup. Mostly, we will need to order the lenses on Monday. As I mention, Nick and I are going to measure the actual mode matching on Monday. If everything look good, then we will move on and do the Upgrade.

Towards finding the x-arm beat note:

The green would not lock to a maximum GTRX this morning. In the course of aligning the green stably to the X arm, somewhere down the line, the input pointing got messed up (reasons unknown). To set this right, Koji tried to lock the Yarm with POY DC but it wouldn't work. The transmon for Y had to be set up temporarily and the Y arm was locked with TRY. This restored the input pointing and the arms locked with transmission TRX/TRY > 0.9 counts. The transmon path along the Y arm was then re-configured as mentioned in Annalisa's elog.

I still had trouble getting the X-green locked in TEM00 (similar situation mentioned by Jenne in elog). The arm cavity mirrors were tweaked to get the green to resonate in TEM00 but it wouldn't stay locked when the temperature of the x-end NPRO was changed. Koji helped recover missing links to filters for the ALS_X_SLOW servo from the archives. Enabling the filters helped keep the green locking stable for laser temperature changes (which corresponds to 'offset' change in ALS_X_SLOW servo screen).

PSL green alignment was checked once again and the X-end laser temperature was scanned trying to find the beatnote. RFMON from the beatbox was connected to the spectrum analyzer. I have scanned through the whole range of offset but have not been able to find the beat note yet.

The search will continue tomorrow

We should consider to hook up the temperature monitors of the NPROs to the ADCs.

Squishing cables at the ITMX satellite box seems to have fixed the wandering ITM that I observed yesterday - the sooner we are rid of these evil connectors the better.

I had changed the input pointing of the green injection from EX to mark a "good" alignment of the cavity axis, so I used the green beam to try and recover the X arm alignment. After some tweaking of the ITM and ETM angle bias voltages, I was able to get good GTRX values [Attachment #1], and also see clear evidence of (admittedly weak) IR resonances in TRX [Attachment #2]. I can't see the reflection from ITMX on the AS camera, but I suspect this is because the ITMY cage is in the way. This will likely have to be redone tomorrow after setting the input pointing for the Y arm cavity axis, but hopefully things will converge faster and we can close up sooner. Closing the PSL shutter for now...

I also rebooted the unresponsive c1susaux to facilitate the alignment work tomorrow.

I don't know who left the X arm locked, but I just ran the Align Full IFO script, so everything is good in case Yoichi/someone comes in to lock the IFO this weekend.

There is an oscillation in the Xarm at 631Hz, which is not in the Yarm.  There is a small peak in POY11_I at this frequency, but only when the Xarm is locked.  If the Xarm unlocks, the peak disappears from POY.  The peak is 3 orders of magnitude larger in POX than in POY, and 4 orders of magnitude larger than the POY noise when this peak is not present.  In the plot, I have turned off the POY whitening, so that its situation is the same as POX (we still need to fix POX whitening switching).  Dark noise (MC unlocked) is the same for both PDs.

POX11 oscillation at 630 Hz was stopped by installing 630 Hz resonant gain to LSC_XARM.
After few hours, oscillation stopped. So I removed the resonant gain.
Our guess is that 630 Hz peak is some violin mode or something, and it was excited somehow, and didn't stopped for very long time because of its high Q. It coupled into POY11 somehow (scattering, electronics, etc).

  Don't use resonant gain - it can lead to a loop instability since it makes the loop have 3 UGFs.

Just use a elliptic bandstop filter at this harmonic frequency separately for each test mass. There are many detailed examples of this in elog entries from Rob and I over the past ~10 years. This bandstop should get clicked on automatically after lock acquisition.

I aligned the Xgreen and PSL green to overlap on the X beat PD, and reconnected the splitter which combines the X and Y beat signals and sends them to the control room.

I've been stepping the Xend laser temperature offset in steps of 20 counts, making sure the cavity unlocks and relocks on TEM00.  So far I have not seen any beat signals for the Xarm.  I've gone from 0 to 840.

I'll be back in a few hours to keep trying, although interested parties are invited to give it a whirl. 

We measured the Xend green laser PDH Open loop transfer function by following method:

• We first measured the feedback transfer function 'K' directly.
  • See attachment 2 for this measurement. We measured Out2/exc here.
• Then, we closed the loop as shown in attachment 1with SR560 as a summing juntion at error point.
  • We injected excitation through B channel in SR560 and measured transfer function Out1/Out2.
  • This measurement should give us by loop alegbra.
• Then we multiplied the two transfer function measurements to get open loop transfer function.

Result:

• Our measurement gives the same UGF of 10kHz and phase margin of 53.5 degrees as reported in 13238.
• The shape of measurement also follows 1/f above 10 Hz atleast.
• Our measurement might not be correct below 10 Hz but we did not see any saturation or loss of lock in 1Hz to 10 Hz measurement.
• This OLTF is different from the modelled OLTF here even though the UGF matches.
• The feedback gain is supposed to roll-off faster than 1/f in 30Hz to 1kHz region but it does not seem to in our measurement.
• This suggests that the actual uPDH box is shaping the loop different from what schematic suggests. This might mean that the gain is much lower in the low frequency region than we would like it to be.
• We will investigate the reason of difference between model and measurement unless someone has a better explaination for the descripancy.

Attachment 1 shows the closed loop of Xend Green laser Arm PDH lock loop. Free running laser noise gets injected at laser head after the PZT actuation as . The PDH error signal at output of miser is fed to a gain 1 SR560 used as summing junction here. Used in 'A-B mode', the B port is used for sending in excitation where .

We have access to three ports for measurement, marked at output of mixer, at output of SR560, and at PZT out monitor port in uPDH box. From loop algebra, we get following:

, where is the open loop transfer function of the loop.

So measurement of can be done in following two ways (not a complete set):

1. , if excitation amplitude is large enough such that over all frequencies.
   • In this method however, note that SR785 would be taking ratio of unsuppresed excitation at with suppressed excitation at
   • If the closed loop gain (suppression) is too much, the excitation signal might drop below noise floor of SR785 while measuring .
   • This would then appear as a flat response in the transfer function.
   • This happened with us when we tried to measure this transfer function using this method. Below few hundered Hz, the measurement will become flat at around 40 dB.
   • Increasing the excitation amplitude where suppression is large should ideally work. We even tried to use Auto level reference option in SR785.
   • But the PDH loop gets unlocked as soon as we put exciation above 35 mV at this point in this loop.
2. , if excitation amplitude is large enough such that over all frequencies.
   • In this method, channel 1 (denominator) on SR785 would remain high in amplitude throughout the measurement avoiding the above issue of suppression below noise floor.
   • We can easily measure the feedback transfer funciton with the loop open. Then multiplying the two measurements should give us estimate of open loop transfer function.
   • This is waht we did in 16194. But we still could not increase the excitation amplitude beyond 35 mV at injection point and got a noisy measurement.
   • We checked yesterday coherence of excitation signal with the three measurment points and it was 1 throughout the frequency region of measurement for excitation amplitudes above 20 mV.
   • So as of now, we are not sure why our signal to noise was so poor in lower frequency measurement.

Attachment 1 shows the case when excitation is sent at control point i.e. the PZT output. As before, free running laser noise  in units of Hz/rtHz is added after the actuator and I've also shown shot noise being added just before the detector.

Again, we have a access to three output points for measurement. right at the output of mixer (the PDH error signal), the feedback signal to be applied by uPDH box (PZT Mon) and the output of the summing box SR560.

Doing loop algebra as before, we get:

So measurement of can be done by

• For frequencies, where is large enough, to have an SNR of 100, we need that ratio of to integrated noise is 100.
• Assuming you are averaging for 'm' number of cycles in your swept sine measurement, time of integration for the noise signal would be where f is the frequency point of the seeping sine wave.
  • This means, the amplitude of integrated laser frequency noise at either or would be
  • Therefore, signal to laser free running noise ratio at f would be .
  • This means to keep a constant SNR of S, we need to shape the excitation amplitude as
  • Putting in numbers for X end Green PDH loop, laser free-running frequency noise ASD is 1e4/f Hz/rtHz, laser PZT actuation is 1MHz/V, then for 10 integration cycles and SNR of 100, we get:
• Assuming you are averaging for a constant time  in swept sine measurement, then the amplitude of integrated laser free noise would be
  • In this case, signal to laser free-running noise ratio at f would be
  • This means to keep a constant SNR of S, we need to shape the excitation amplitude as
  • Again putting in numbers as above and integration time of 1s, we need an excitation amplitude shape

This means at 100 Hz, with 10 integration cycles, we should have needed only 3 mV of excitation signal to get an SNR of 100. However, we have been unable to get good measurements with even 25 mV of excitation. We tried increasing the cycles, that did not work either.

This post is to summarize this analysis. We need more tests to get any conclusions.

We did the measurement of OLTF for Xend green laser PDH loop with excitation added at control point using a SR560 as shown in attachment 1 of 16202. We also measured coherence in our measurement, see attachment 1.

Measurement details:

• We took the measurement as per 16202.
• We did measurement in two pieces. First in High frequency region, from 1 kHz to 100 kHz.
  • In this setup, the excitation amplitude was kept constant to 5 mV.
  • In this region, the OLTF is small enough that signal to noise ratio is maintained in (SR560 sum output, measured on CH1). The coherence can be seen to be constant 1 throughout for CH1 in this region.
  • But for (PZT Mon, measured on CH2), the low OLTF actually starts damping both signal and noise and to elevate it above SR785 noise floor, we had a high pass (z:0Hz, p:100kHz, k:1000) SR560 amplifying before measurement (see attachment 2). This amplification has been corrected in Attachment 1. This allowed us to improve the coherence on CH2 to above 0.5 mostly.
• Second region is from 3 Hz to 1 kHz.
  • In this setup, the excitation was shaped with a low pass (p: 1Hz, k:5) SR560 filter with SR785 source amplitude as 1V.
  • We took 40 averaging cycles in this measurement to improve the coherence further.
  • In this freqeuency region, is mostly coherent as we shaped the excitation as  and due to constant cycle number averaging, the integrated noise goes as (see 16202 for math).
  • We still lost coherence in (CH1) for frequencyes below 100 Hz. the reason is that the excitation is suppressed by OLTF while the noise is not for this channel. So the shaping of excitation only helps fight against the suppression of OLTF somewhat and not against the noise.
    
  • We need shaping for this purpose but we were loosing lock with that shaping so we shifted back to shaping and captured whatever we could.
  • It is clear that the noise takes over below 100 Hz and coherence in CH1 is lost there.

Inferences:

• Yes, the OLTF does not look how it should look but:
• The green region in attachment 1 shows the data points where coherence on both CH1 and CH2 was higher than 0.75.  So the saturation measured below 1 kHz, particularly in 100 Hz to 500 Hz (where coherence on both channels is almost 1) is real.
• This brings the question, what is saturating. As has been suggested before, our excitation signal is probably saturating some internal stage in the uPDH box. We need to investigate this next.
  • It is however very non-intuitive to why this saturation is so non-uniform (zig-zaggy) in both magnitude and phase.
  • In past experiences, whenever I saw somehting saturating, it would cause a flat top response in transfer function.
• Another interesting thing to note is the reduced UGF in this measurement.
• UGF is about 40-45 kHz. This we believe is due to reduced mode matching of the green light to the XARM when temperature of the end increases too much. We took the measurement at 6 pm and Koji posted the Xend's temperature to be 30 C at 7 pm in 16206. It certainly becomes harder to lock at hot temperatures, probably due to reduced phase margin and loop gain.