[ericq,Gabriele]

So, we want an relatively quick measurement of the PRC length error (with sign!) at the order of .5 centimeter or so. Rana suggested the "demodulation phase method," i.e. lock the simple Michelson, measure what demodulation phase brings the 1F signal entirely within the phase quadrature, then lock the PRMI and measure the demodulation phase again. This tells you something about the length of the PRC. 

Gabriele and I worked through a simulation using MIST to determine how to actually do this. We simulated the case of injecting a line at 1kHz in the laser frequency via the laser's PZT and looking at the transfer function of the 1kHz signal to the I and Q at the 1F AS demodulated signal when locked. (Michelson locked on the dark fringe, PRC locked on 11MHz sideband) With the I and Q in hand, we can measure some demodulation phase angle that would bring everything into I. 

When the PRC length is in the ideal location, the demodulation phases in the two cases are the just about the same. Sweeping the length of the PRC around the ideal length gives us a monotonic function in the difference in the demodulation phases:

So, with this simulation, we should be able to calibrate a measured difference in demod phase into the length error of the cavity! We will proceed and report...

[ericq, Gabriele, Manasa]

 We wanted to perform the PRC length measurement today with an AS11 signal, but such a signal didn't exist. So, we have temporarily connected the AS110 PD signal (which is some Thorlabs PD, and not a resonant one) into the REFL11 demod board. 

We then proceeded with the goal of locking the PRC with REFL165. A few parameters that were changed along the way as we aligned and locked things:

• the XARM gain was increased from 0.4 to 0.5 to help it acquire lock
• the MICH gain was decreased from -10 to -5 since there was some gain peaking in its servo output
• the REFL165 demodulation phase was changed from 155 to 122, to place a PRCL excitation entirely within I (we did this while locked on the carrier)

Sadly, in the end, we couldn't lock the PRC on a sideband in a stable manner. The alignment would drift faster than we could optimize the alignment and gains for the PRC. I.e. we would lock the PRC on the carrier, align PRM (and maybe touch ITMX) to maximize POPDC, switch to sideband locking, try to lock, and things would start looking misaligned. Switching back to carrier locking, the beam spots on REFL (for example) would have moved.

Manasa noted the MC_TRANS_Y has been substantially drifting along with small drift in MC_TRANS_P as well. So we need to fix the source of the mode cleaner beam drifting if we want to make this measurement. 

[ericq,Jenne]

Since we don't have agreement between the measurements we made the other day and the earlier estimations, I wanted to repeat the demodulation angle measurement. We had to do a few things to keep the PRMI locked, since in the last few days, it hasn't been stable enough.

The mode cleaner had been very fussy lately; the WFS were pushing in a way that caused fast oscillations of the transmission and reflection powers. I turned off the servos, manually aligned the mode cleaner to transmission of about 15k and refl of about .4, centered the beams on the WFS QPDs, and turned the loops back on. Things were much stable after that. Also, Jenne noticed that the PMC loop had walked the laser PZT temperature to a bad place, and fixed it.

After aligning the carrier locked PRMI, the last piece needed to get things stable enough for sideband locking was turning off the angular damping on the PRM suspension screen (this was turned back on when we were done). Waiting until evening noise levels probably helped too. We used a 1000 count MICH excitation in the PRMI case, and recorded data for about a minute in one degree steps around the demodulation phase that looked to put the excitation entirely within the Q of the PD. Also, we notched out the excitation frequency in the MICH servo bank for today's measurement; I think it's outside of the loop bandwidth anyways, but it's good to be sure. 

Jenne and I pondered a bit whether changing the AS55 demodulation phase while it (AS55 Q) is being used as the MICH control signal introduces subtleties that we haven't anticipated, but couldn't come up with anything concrete. Changing the angle from the what maximizes the Q just looks like a slight change in MICH gain, and shouldn't affect the phase of the excitation signal on the PD...

In any case, the data have been recorded, and the results will follow soon. 

I replaced the stupid broken fancy button with a simple sturdy switch. I had to file out the hole in the chassis a bit, but the switch is pressed in tightly and securely. I put the box back in the rack, but the power cable was coming directly from the power supplies with no fuses. The box was drawing ~.9 and 1.5 Amps from two supplies, so I put 2A fuses on both. Plugged everything back in, and the mode cleaner locks, so it looks like all is well.

RXA: When its so close, I prefer to size it up by 1 step. Please change to 5A fuses. Otherwise, we may blow them from power glitches.

Q: 5A fuses have been swapped in

[Manasa, ericq]

Both arms have been aligned via ASS. PRC locked on carrier.

SB locking hasn't happened yet...

Details:

• Aligned MC at low power, measured spots
• Found ITMX AS, REFL spots on cameras. Couldn't find ITMY spot. Found x-arm flashes with PRM aligned.
• MC Refl Y1 mirror was replaced with the 90:10 BS; blocked WFS path until MC was aligned
• PMC power was increased (~1.4W directly before PSL shutter)
• Touched up MC alignment, reactivated high power autolocker, measured spots.
• Locked x-arm on IR, ran ASS
• Found ITMY spot on AS camera, locked y-arm, ran ASS on both arms
• Checked green beams. Y-arm locks at around .6, X-arm at around .2 (input steering needs adjustment)
• Centered beams on WFS, reset filter bank offsets, turned on WFS
• Aligned PRM, locked PRC on carrier.
• Tried locking PRC on sideband, had troubles. Looks like there is some increased seismic activity; might be the culprit.

[ericq]

PRC Locked on Sidebands

Jenne reminded me that if we change a cavity, phases can change... So, first, I locked the PRC on the carrier, and then gave it MICH and PRCL excitations to optimize the AS55 and REFL55 phase rotation angles by looking at the excitation demodulated outputs of the unused quadrature (i.e. we want all of MICH to be in AS55 Q, so I rotated the phase until C1:CAL-SENSMAT_MICH_AS55_I_I_OUTPUT was zero on average).

This resulted in:

• AS55: 7 -> -5.5
• REFL55: 73 -> 86.9

I then used the same settings as in ELOG 9554, except I used -1s instead of +1s for the POP110I trigger matrix elements. (I'm not sure why this is different, but I noticed that the PRC would lock on carrier with positive entries here, so I figured we wanted the peaks with opposite sign).

So far, it seems more stable than when we were doing the demodulation phase measurements, it's been locked for >15 minutes without me having to tweak the gains or the alignment from the carrier locked case.

Adjusted the angles as Jenne suggested:

• POP22: 105 -> 163
• POP110: 150 -> -83

[ericq]

Today, I kicked the PRM to see the sideband splitting in POP110. 

First, we can qualitatively see we moved in the right direction! (See ELOG 9490)

I fit the middle three peaks to a sum of two Lorentzian profiles ( I couldn't get Airy peaks to work... but maybe this is ok since I'm just going to use the location parameter?), and looked at the sideband splitting as a fraction of the FSR, in the same way as in Gabriele's ELOG linked above.

This gave: c / (4 * f55) * (dPhi / FSR) = 0.014 +- .001 

Since the PRC length with simultaneous resonance (to 1mm) is given by c / (4 * f11) = 6.773, this means our length is either 6.759m or 6.787m (+- .001). Given the measurement in ELOG 9588, I assume that we are on the short side of the simultaneous resonance. Thus

The sideband splitting observed from this kick indicates a PRC length of 6.759m +- 1mm

 [ericq]

Steve fixed the PRM oplev pointing. I turned on the loops and measured the OLG, then set the pitch and yaw gains such that the upper UGF was ~8Hz (motivated by Jenne's loop design in ELOG 9401)

• Pitch gain: +7
• Yaw Gain: -5

I then measured the oplev spectra of the optics as they were aligned for PRMI. (OSEMs on, oplevs on, LSC off, and ASC off)

Next, Jenne and I need to fix the ASC loop such that it properly accounts for the oplev loop. 

 [Quick post, will follow up with further detail later. Excuse my sleepy ELOG writing]

Goal: Check out the transmon QPD signal chain; see if whitening works. Assess noise for 1/sqrt(TRX/Y) use. 

First impression: Whitening would not switch on when toggling the de-whitening. The front monitors on the whitening boards are misleading; they are taken a few stages before the real output. ADC noise was by far the limiting noise source. 

I updated the binary logic in the c1scx and c1scy to actually make the binary IO module output some bits. 

After consulting a secret wiring diagram on the wiki, not linked on the rack information page (here), I worked out which bits correspond to the bypass switches in the whitening board ( a fairly modified D990399, with some notes here)

Now, FM1 and FM2 (dewhitening filters on the ETM QPD quadrants) trigger the corresponding whitening in the boards. Here's a quick TF I took of the quadrant 1 board at ETMY. (I should take a whitening+dewhitening TF too, and post it here...)

Seems to roughly work. Some features may be due to non-accounted for elements in the anti-imaging of the DAC channels I used for the excitation, or such things. The board likely needs some attention, and at least a survey of what is there. 

I also need to take dark noise data, and convert into the equivalent displacement noise in the 1/sqrt(TRX/Y) error signals. For the no-whitening ADC noise, I estimated ~1pm RMS noise on a 38pm linewidth of PRFPMI arms. 

My apologies for all of that crap I left at the Y-end... I cleaned the rest of it up today. 

I took transfer functions of the four ETMY QPD whitening channels today. (Attempted the ETMX ones too, but had troubles driving the board; detailed below). I've attached a zip with the DTT xml files for the cases of no whitening / 1 whitening stage / both whitening stages engaged. Here's a plot of both whitening stages engaged. 

Given the way I measured, the DAC output anti-imaging is in the TFs as well. ( This is a D000186 board; with something like a 4th order elliptic LP, but I need to look at the board / fit the TF to see the parameters, there are different revisions with different filter shapes.) 

The c1scy model had excitation blocks on some of the unused DAC channels (C1:SCY-XXX_CHAN9 etc.), but these were in the second DAC output connection, and not cabled up. However, the 8th channel on the DAC had no connection in the simulink model, so I added another excitation block there (C1:SCY-XXX_CHAN8), and used the anti-imaging front panel lemo connector to drive the input of the whitening board. 

I also added a similar channel to the SCX model, but no data would show up in the channel as viewed by data viewer (though the channel name was black), or in analog world. There's the additional weirdness that the SCY excitation channels show up under SCX in DTT and awggui... I'm not entirely sure what's going on here.

I still need to look at the noise, and peek inside the boards, to check for homemade modifications and see if there are bad things like thick film resistors that may be spoiling the noise performance...

 Q EDIT: THIS IS WRONG. I LOCKED PRC ON THE CARRIER

 As Koji measured the other day: MICH and PRCL seem very degenerate in the 3f REFL PDs. 

I'm using this as a motivation to do some simulation in MIST and try to understand the best way to implement the 3F locking scheme. Hopefully my thinking below isn't nonsense...

First, I modeled the PRC with no arm cavities and the estimated cavity length I got with the PRM kick measurement, and looked at the REFL sensing matrix.

This agrees with the observed degeneracy. I then modeled the case of the PRC length that gives coincident SB resonance, again with no arm cavities.

Now there is good separation in REFL165. (REFL33 still looks pretty degenerate, however). This raised the question, "What does the angle between MICH and PRCL in REFL165 do as a function of macroscopic PRC length?" 

• We see ~90 degrees at coincident resonance
• Shortening the cavity, which we did to account for the arms, quickly shrinks the angle
• Presuming we moved to make the cavity 4cm shorter implies we had ~45 degrees between MICH and PRCL in REFL165 before the move. (Is this consistent with earlier observations?)

To me, this implies that locking the PRC on 3F from scratch won't be simple. However, the whole point of the PRC length choice is to have coincident SB resonance when the arms are resonating.

So: even if we're not spot on, we should be relatively close to the PRC length where having arms resonant gives us simultaneously resonant upper and lower sidebands, where MICH and PRCL should be orthogonal-ish. I.e. building up a little bit of IR power in the arms may start to break the degeneracy, perhaps allowing us to switch from 1F to 3F locking, and then continue reducing the CARM offset. 

So, I ultimately want to model the effect of arm power buildup on the angle between MICH and PRCL in the 3f PDs. This is what I'm currently working on. 

So far, I have reproduced some of the RC modeling results on the wiki to make sure I model the arms correctly. (I get 37.7949 m as the ideal arm length for a modulation freq of 11.066134 MHz vs. 37.7974m for 11.065399 MHz as stated on the wiki). Next, I will confirm the desired PRC length that accounts for the arms, and then look at the MICH vs PRCL angle in the REFL PDs as a function of arm power or detuning. 

 Q EDIT: THIS IS WRONG. I LOCKED PRC ON THE CARRIER

Koji noted oddities in the sensing matrix results I had gotten; namely that the plots showed REFL33 not changing at all, when we know for a fact that this should not be the case. 

Gabriele lent his eyes to my code, and came up with the idea that the modulation depths I was using were maybe not ideal (.1 for both 11 and 55). This affects REFL33 in that it is not simply Carrier * 33Mhz + 11Mhz * -22Mhz but also 22MHz * 55MHz, etc. 

I got more realistic values from Jenne (0.19 for 11MHz and .26 for 55Mhz) and re-ran the code, with more realistic results. The behavior for 165 has remained the same, but the other signals are more well behaved. 

Moral of the story: the modulation depths affect the 3f signals in a complicated way.

Disregard previous ELOGs, I had the PRC locked on carrier 

Locked on the sideband, the MICH / PRCL angle is much less sensitive to the PRC length, and shouldn't in fact be as degenerate as we've seen in reality. 

So, my simulations no longer provide any reason for the 3F signals to be so degenerate. 

EQ UPDATE: Measured it wrong the first time, fixed now.

I measured the spectra of the SQRTINV channels from dark QPDs, with offsets adjusted to imitate various transmission levels. (While the dark noise stays constant in terms of, say, TRX counts, 1/sqrt(TRX) isn't linear, and so the noise coupling depends on the TRX offset). 

I did some calculations to turn this into the equivalent displacement noise when using SQRTINV as an error signal. This depends on where on the fringe you are locking, since the slope of SQRTINV vs. position is not constant, and can only really be treated as linear down to about 1/3 of a line width away from full resonance. In my calculations, I assumed a coupled arm line width of 38pm, and a full transmission of 700 counts in TRX/Y. 

The QPD dark noise RMS when two line widths away (TR = 40) is about 5fm, and only goes down from there. 

After speaking with Jenne and Gabriele, I did a little bit of simulating based on my earlier code that looked at the angle of MICH vs. PRCL, just with cavity detuning instead of macroscopic length change.

The zero point in the following plots is with the PRC locked on the sideband. The PRC detuning was done by changing the PRM-BS microscopic length (in terms of phase), and the MICH detuning was done by adding half of the detuning to the BS-ITMY distance, and subtracting half of it from the BS-ITMX distance. 

This plot is in terms of radians, so to roughly relate it to line width, here's a plot of the POP powers as a function of the PRC detuning. 

 And glossing over the MICH offset, here's the PRC offset plots in displacement, rather than radians.

The simulation is actually slightly different now. I now use nominal ITM T values (T=.014) instead of the random R=.99 I had in place. 

(correction: Field Power should be Field Amplitude in the first plot)

I measured the arm cavity losses as Kiwamu did way back in ELOG 5074.

I used the same logic as the ../scripts/LSC/armloss script, but did it manually. This meant:

1. Lock and ASS-Align both arms. 
2. Misalign the ITM of the arm that I'm not measuring, to get its spot off of AS
3. Take 10 seconds of ASDC_OUT data while the arm is locked. 
4. Unlock, misalign ETM of arm of interest, take another 10 seconds of ASDC_OUT
5. Relock, run ASS, goto #3

Analysis was done similar to ../scripts/LSC/armloss.m. This uses the nominal T values (.014 and 15e-6) to estimate the input power from the unlocked ASDC data, and the cavity reflectivity from the locked ASDC / input power. Then, loss is calculated by:

• Pin = ASDC(unlocked) / R1
• Rc = ASDC(locked) / Pin
• rc=sqrt(Rc), etc.
• Loss = 1 - (( 1 / r1r2)) * ( 1 - t1^2 r2 / (r1 - rc)) ^2

I did this for pairs of locked / unlocked data stretches. (Subsequent pairs maybe have slightly different things going on, but each pair was taken within a minute or so of each other)

Unfortunately, during the X Arm measurements, the MC was misbehaving with large REFL fluctuations, so I don't have confidence the results.

The Y Arm data seems fine, however. 

The Y arm loss is 123.91 +/- 10.47 ppm 

(Trial-to-Trial fluctuations dominate the fluctuations within each trial by far, and their standard deviation is what I report as the random error above)

This seems roughly in agreement with old values I've seen in the ELOG. I'll remeasure the x arm tomorrow during the day. Here's a plot showing the ASDC values of the Y Arm measurements. 

At today's meeting, it was suspected that these noise levels were far too low. (ELOG 9660)

I've attached the math I did to get the conversions, as well as the dark noise SQRTINV spectra at various imitated transmission values and the python script that does the converting. 

I've gone over my calculations, and think they're self-consistent. However, a potential source of misestimation is the treatment of the Lorentzian profile simply existing with the coupled arm line width (38pm). The conversion to m/rtHz is directly proportional to the line width of the transmission peak, so if it is much broader in practice (because of imperfect PRC buildup or something), the noise will be that much worse.

I'm open to any other feedback about what I may have done wrong!

Using Koji's mathematica notebook, and Nic's python work, I set out to run a time domain simulation of the error signal, with band-limited white noise added in. 

Basically, I sweep the displacement of the cavity (with no noise), and pass it to the analytical formulae with the coefficients Koji used, with some noise added in. I also included some 1/0 protection for the linearized PDH signal. I ran a sweep, and then compared it to an ALS sweep that Jenne ran on Monday; reconstructing what the CESAR signal would have looked like in the sweep. 

The noise amounts were totally made up. 

They matched up very well, qualitatively! [Since the real sweep was done by a (relatively) noisy ALS, the lower noise of the real pdh signal was obscured.]

Given this good match, we were motivated to start trying to implement it on Monday. 

At this point, since we've gotten it working on the actual IFO, I don't plan on doing much more with this simulation right now, but it may come in handy in the future...

Two weeks ago (Feb 26) I took the "Q MON" output of the demodulator that sends its Q output to the MC servo board as the error signal, and connected it to an SR785, so we can occasionally monitor the error signal noise. (Also, I did not appropriately ELOG the fact I touched things...)

I'm working on an automated script to do the monitoring, but the wireless router that the SR785 is connected is wicked slow. I should run an ethernet cable to it...

I'm just figuring I'll look at the full span (~100kHz) spectrum every ten minutes, and compare it to some nominal spectrum from a known-good time, and the last few hours.

Speaking of the whitening board, I had neglected to post details showing the the whitening was at least having a positive effect on the transmon QPD noise. So, here is a spectrum showing the effects that the whitening stages have on a QPD dark noise measurement like I did in ELOG 9660, at a simulated transmission level of 40 counts. 

The first whitening stages gives us a full 20dB of noise reduction, while the second stage brings us down to either the dark noise of the QPD or the noise of the whitening board. We should figure out which it is, and fix up the board if necessary. 

The DTT xml file is attached in a zip, if anyone wants it.

 I've been getting a simulation going with the eventual goal of simulating CESAR-type signals for CARM. So for I've only been using MIST, though I'm still thinking about what to do for a fully time domain approach. (For example, maybe a mixture of simulink and analytical equations? We'll see how painful that gets...)

Anyways, with the parameters I have for the 40m, I've set up a simulation, where I can do things like a "static" CARM scan.

(i.e. PRMI perfectly locked. Ask what different PDs see if the arms were just statically sitting at some CARM offset)

PDH signals are there in the REFL diodes. The coupled line width here looks smaller than the ~40pm number I've heard before, so I should check my parameters. (Likely culprit, I'm using nominal R and T for the arm cavities)

I've also done the slightly more sophisticated thing of looking at the transfer function from CARM motion to different PDs, at different CARM offsets. For TRX and REFLDC, these seem to match up qualitatively to some plots that Kiwamu has done for aLIGO, with frequencies shifted by the relative arm length factor of 100. (Q's left, K's right, Y-axis on mine are W/m with 1W input the IFO)

We can also look at the PDH diodes (revised from my initial post. Had an error in my code): 

That's where I've gotten so far!

Extending the previous model, I've closed a rudimentary CESAR loop in simulink. Error signals with varying noise levels are combined to bring a "cavity" to lock.  

There are many things that are flat out arbitrary at this point, but it qualitatively works. The main components of this model are:

• The "Plant": A pendulum with f0 = 2Hz, Q = 10
• Some white force noise, low passed at 1Hz before input to the plant.
• The Controller: A very rough servo design that is stable...
• ALS signal: Infinite range Linear signal, with a bunch of noise
• Transmission and PDH signals are computed with some compiled C code containing analytic functions (which can be a total pain to get working), have less noise than ALS
• Some logic for computing linearized PDH and SqrtInv signals
• A C code block for doing the CESAR mixing, and feeding to the servo

And it can lock! 

Right now, all of the functions and noise levels are similar to the previous simulation, and therefore don't tell us anything about anything real...

However, at this point, I can tune the parameters and noise levels to make it more like our interferometer, and thus maybe actually useful. 

Incidentally, while messing around with transfer functions and sensing matrix elements this evening, I was able to sideband lock straight onto REFL33 I&Q.  The settings were all identical to Koji's ELOG, with the following differences:

Input ports:
REFL33   WHTN: 30dB demod phase +125.5deg (tweaked from 135.5 to minimize MICH in I)

Input matrix:

REFL33I x +1.0 -> PRCL
REFL33Q x +3.0 -> MICH

Servo:
MICH OFS 0 / Gain 1/ Limitter ON (Oscillations occurred at 1.3)
PRCL OFS 0 / Gain -0.04 / Limitter ON

Output matrix:

MICH ITMX -1.0 / ITMY 1.0
PRCL PRM 1.0

ETMX ASC output was turned off for whatever reason. Switched it on, ASS is fine.

Last week, while I had the PRMI locked on REFL33, I did some poking around with mirror excitation to RFPD quadrature transfer functions. I got some indication of weird things with sensing MICH with the 3F REFL signals, but it should be explored more before taken as a real thing. I just figured I would show what I saw. 

With that disclaimer out of the way, here's what I did:

• Locked PRMI on PRCL:REFL33_I and MICH:REFL33_Q, as detailed in my earlier ELOG
• Created PRCL and MICH excitations at two different frequencies, notched said frequencies out of the control filters
• Took transfer functions from mirror LSC output signals to 33 I, 33 Q, 165 I, 165 Q in DTT
• For each DOF, look at the measured transfer functions only at the excitation frequency. (Assuming good coherence, which was there)

The basic idea was, some PRCL motion (for instance), has a transfer function to both the I and Q quadratures at a given PD. As the PRCL excitation sine wave goes through one cycle, the REFL signals at the excitation frequency go through some coherent cycle. Thus, the excitation traces out some trajectory in the I vs. Q plane. I believe this is analogous to the typical "radar plot" that we make for sensing matrix elements. 

However, the straight line that we normally plot in the radar plots assumes a certain phase relationship between the DOF-> I and DOF->Q transfer functions that results in a straight line. Here are the trajectories I actually measured, normalized by the excitation amplitudes.

The plotted traces are (x,y) = (H_prcl->I * prcl, H_prcl->Q * prcl) and  (x,y) = (H_mich->I * mich, H_mich->Q * mich) where H_prcl->I is the measured complex transfer function from prcl to REFL I, for instance, and prcl and mich are the excitation signals, normalized to unit amplitude.

PRCL looks like a nice straight line in both of these, and pretty well phased, but not only is MICH not very orthogonal to PRCL, there is quite a bit of ellipticity present, which means we can't fully decouple the two DOFs, even if they were nominally orthogonal. 

I'm not sure what may cause this. To back up this measurement/interpretation, I tried to take measurements of these transfer functions across different excitation frequencies via swept sine DTT, but seismic activity kept me from staying locked long enough...

So, here's the basic: "We reduced the CARM offset and saw more TRY" plot. 

As Jenne mentioned, we suspected that we were seeing real displacement information in the sqrtInv signals. (We had incidentally hard switched to the transmon QPDs for all of this)

Here's a 2d-histogram of the ALS CARM error signal vs. the sqrtInv CARM signal (i.e. 1/sqrt(TRX) + 1/sqrt(TRY))

This is exactly the shape we expect, which is cool. You can see where we stepped the offsets, too. It looks like the signal gets into it's good linear range when ALS CARM was about -20, which is when TRY was a little under 0.1, which seems pretty early and potentially useful. 

Also, here are snapshots of what REFL11_I and sqrtInv CARM were doing in the last five seconds of time in the above plot, which was shortly before we made the offset push that broke the PRMI lock. If you look really closely, maybe you can convince yourself that there is some common information in them...? It's hard to say. In any case, there is definitely CARM pdh action happening.

 The other day, Jenne and I were comparing my MIST simulation to her Optickle simulation for the CARM transfer functions I posted some days ago. She told me that the arms are not exactly where they should be for the whole "PRC length tuning to account for sideband reflection phase off resonant cavity" deal. 

Specifically, as in the wiki (but with newer modulation frequencies), I calculated the ideal arm length to be 37.795 m some time ago, when doing PRC length simulations, and Jenne has told me that the X arm is more like 37.6m, and Y is 37.9. So, I updated my simulations, and found the following:

This does weird things to the f2 sideband buildup on resonance in the PRFPMI configuration:

(POP is way huger than than the TR's, because the POP pd's are artificially "inside" the cavity, whereas TRX/Y is actually transmitted through an ETM)

This is not necessarily directly something to worry about, but I think the following may be. It looks like this arm length mismatch actually causes the PRCL demodulation phase in REFL 165 to change dramatically with the CARM offset. (REFL33 seems fine, though. 5 degrees causes less than a 1% effective gain change.) 

My simulations don't include any signal recycling yet, so I don't have anything to show if there is a similar effect for SRCL, but it wouldn't surprise me... 

In today's ISC call, Kiwamu was comparing two ways to approach resonance: 

• "C-Type": The scheme we currently think about; zero DARM offset and slowly reduce the CARM offset
• "D-Type": Start with no CARM offset, but a DARM offset and reduce that. 

D-type might be interesting to check out, since things change a little less dramatically when you reduce the DARM offset. Maybe this makes signal hopping easier? Signal recycling may complicate things, though. 

So, I've simulated CARM and DARM offset effects on CARM and DARM signals. (As with the previous plots, this is for the PRFPMI configuration.) From moving both offsets around, it looks like the resonance peak is about 5x wider in DARM than in CARM, so I simulated a 50pm offset range for CARM and a 250pm offset range for DARM. 

Here are some CARM signal transfer functions subject to CARM offsets in the top plot, and DARM offsets in the bottom plot. 

It's looks like the DARM offset changes cause much less dramatic changes in the CARM plant features. It's conceivable that this would make CARM locking easier. 

Here are some DARM plant transfer functions. 

In these plots, I did something kind of artificial: when we move the CARM offset, it changes the proper demodulation phase to get DARM in the Q of the AS 1F RFPDS. So, at each CARM offset, I re-phased the AS 1F demodulators, to show the total DARM information available at the AS RFPDs at each offset, rather than what one would actually see in them with a static demod phase. 

 21 dB. We played with the whitening gain a little bit; at around 30dB with the signal levels at TRX = .1ish, we were consistently saturating the ADC. 

For future reference:

As we were poking around with the common mode servo in an FPMI configuration, we locked CARM/DARM with ALS as in recent ELOGs.

MICH was locked on ASDC: ASDC -> MICH = 10.0 in the DCPD DoF Matrix (I couldn't easily get AS55Q working, ASDC worked quickly and good enough)

MICH gain +25, FM4 FM5 On, FM2 switched on once locked. Offset was manually adjusted to get closer to dark fringe.

Actuated on BS: MICH->BS = 0.5 in Output Matrix.

 As Jenne mentioned, we took OLTF transfer functions, and determined that we had more than enough phase margin to switch on the LSC boosts in FM4. This improved the error signal noise spectra quite a lot, and noticeably reduced the TRX/TRY fluctuations, and actuation output. 

Here's the CARM OLTF (FM4 boost on in red, boost off in black)

Here's what happened to the CARM and DARM spectra when we turned on the boosts. (ALS only in black, initial IR signal transitions in mid-color, boosted IR signals in bright color)

Jenne made some suggestions for some plots that would be useful on our CARM offset reduction adventures, so I made some with my MIST model. 

First, here's a plot showing the transfer function of CARM to TRX, with logarithmically spaced offsets out to 3nm. While not a control signal, it shows us where the optical plant resonance stuff is happening. The peaks in this TF correspond to peaks in REFL11, REFL55, AS11, etc., as in the close-to-resonance TFs in ELOG 9785. 

[more to come, had a MATLAB issue]

Came in, and the PMC and MC needed aligning. 

PMC Trans .74->.83

I wasn't able to move the MC1&3 the right way in pitch without having a terrible MC2 position... using the move MC2 scripts to bring it back threw off the other spots.

In an effort to familiarize myself with the analog CM servo, I've begun to replicate Koji and Den's work from the ELOG post that this is a reply to.

I hooked POX11Q into the IN1 of the CM board. (POX is rotated by ~86 degrees in the CDS, meaning analog Q is almost perfect.)

While there, I took out the too-long delay cables Jenne introduced for REFLs 11 and 55. (Also note: when we do cable-based analog phasing in the future, we should do it on the LO side, instead of the PD input side.) I also heard a dangerously crinkly sound from the short SMA cable for REFL11, so I replaced it with a beefy looking new one I found on the SP table.

I messed with the gain and offset in the CM_SLOW input filter to get it to look just like POX11_I_ERR, and was able to lock the arm on it without an issue. I then put the SR560 between the CM and MC (30k pole, but also AC coupled, because I figure the digital loop should be doing the work down there, and don't want to kick the AO with an offset), and was able to turn on the AO path with a gain of 8dB on the CM board and 10dB on the MC board, as detailed in Koji's procedures.

I wasn't able to increase the AO gain to 9dB without breaking lock, but maybe this is ok, because by judging by the LSC filter gains, POX11 might be about 3 times bigger than POY, so maybe 8dB AO gain on POX ~ =18dB AO gain on POY? I was able to put the CM servo offset at 0, but turning on boosts promptly kicked the MC out of lock.

I'm stopping for the night; but tomorrow I'll bust out a spectrum analyzer to see if I actually have won some bandwidth with the CM servo, and check out the situation with the offsets and boosts.

I added ~1m of cable to the LO side of the REFL11 Demodulator, which brought its PRCL demod phase to about 8 degrees. According to my simulations, PRCL and CARM have the same angle (but opposite sign) at resonance. There seems to be a severe lack of SMA cables in the lab, so I didn't tune it to be any closer. Cos(8 degrees)=.99, so I think it should be fine to use it for the CARM servo, since none of the other signals are going to be nearly as big. I plugged analog REFL 11 I back into the CARM servo IN1. 

As for IN2, I threw together a temporary setup for using REFLDC as a complementary signal. I T'd off the REFLDC signal (which is the DC signal out of REFL55), and sent it into an SR560 to subtract an offset. The offset comes from a 1Hz-passive-pomona-box-low-passed C1:IOO-TT4_LR output, since there are 8 DAC channels set up for the nonexistent tip tilts 3 and 4 actively running. The output of the SR560 is sent to the CARM servo IN2. 

I adjusted the offset by turning on only IN2 in the CARM servo MEDM screen, and looking at the CM_SLOW signal in data viewer. I adjusted gains and such to get it to look just like REFLDC with the PRC locked. There was good coherence and no appreciable phase difference from DC out to some kHz, albeit a dip in coherence to about .8-.9 from ~40 to 300Hz, for some reason. (This included turning on the unWhite FM in the REFLDC filter bank)

If this signal turns out to be useful, it will be relatively straightforward to put together a little box that does the offset subtraction nicely, but this should do for our immediate needs.

Lastly, I hung up this plot in the control room to give us information about the DC values of different signals as the CARM offset changes. This is helpful to see what our CARM offset is, based on the transmission we se, when different signals start to have length dependence, where they start/stop being linear, etc. The TRX curve is scaled to a maximum of 600, REFLDC is normalized to input power = 1, and all the rest are arbitrarily scaled to fit on the plot. I've assumed 75ppm loss on all mirrors in my simulation (PRM, BS, 2xITM, 2xETM), mostly to get some realistic profile of REFLDC. 

[ericq, Jenne, Zach]

We spent some time tonight trying to push our CARM locking further, to little avail. DARM/CARM loop oscillations kept sneaking up on us. We measured some MC2 motion -> REFL11 Transfer Functions to see if we could see CARM plant features; plots will come in the near future...

I should've included this in my Thursday night ELOG... That evening, I aligned the mode cleaner with reasonable MC1/3 spot positions, and the MC2 spots very close to centered, and recentered the WFS and MC2 Trans QPDs. The mode cleaner held up very well over the course of that evening, even when actuating CARM on MC2 with WFS engaged (which previously wasn't very stable when the WFS weren't well aligned).

Inspired by a comment by Koji the other day, I spent some time yesterday and today working on locking a (very lossy) power recycled Y-arm. ITMX was misaligned, to save myself the headache of dealing with ITMY getting a sign flip and ITMX staying the same when the arm resonates. 

My main goal was to achieve high bandwidth control with the analog CARM servo. 

TL,DR: Transisitoned 90% to REFLDC through CM_SLOW at TRY = 2.1 twice. Couldn't make it all the way over. 

PRCL settings:

• Input: REFL165 I.
• Actuate on PRM +1
• Control: G=-.32 (~100Hz UGF); Acq on FM 4,5; Trig 1,2,3,6,9 (I modified the +10dB in FM1 to a 1kHz ELP)
• Trig: POP 110 I: 1.5 up, 0 down (max was around 4 counts, very weak PRC!)

The PRC was very stable in this configuration, which doesn't surprise me due to its simplicity. I was honestly a little surprised there was enough light to lock on 3f. REFL33 didn't work. 

My efforts to bring the Y-arm into lock were very similar to the CARM procedure we've been using recently. (Which is the motivation for this exercise)

At first I was actuating on ETMY, and got to the point where I wanted to start bringing in the CARM servo slow output, then realized that I didn't want to actuate both on the ETM and MC AO. (Maybe this would be doable, but in the end, not what I'm interested in learning about in terms of overlap with CARM locking)

From then on, I only actuated YARM on MC2. (Heads up, my lock-losses will show up in the trends of the MC2 Trans addition to the WFS.)

Transitioning the arm to SqrtInv TRY control was just as straightforward as it has been for CARM. However, engaging the LSCLock FM (FM4), would sometimes work beautifully, and sometimes kick the hell out of MC2. Keeping an eye on the error signal spectrum and UGF gave no indication which outcome would happen. Once FM4 could be engaged, the transmitted power was very stable. Without FM4, reducing the offset didn't get very far without losing lock. 

I tried a few times to bring in CM_slow (set to just IN2, i.e. offset adjusted REFLDC), at arbitrary arm powers, with little success. I didn't know how much arm power to expect at resonance, and thus didn't really know where on the line width I was.

I knew I was mostly outside of the linear regime of the PDH signals, since, even though I had good coherence between, say, REFL11 I and SqrtInvTry, with an ETMY excitation on; when I would turn TRY normalization on/off, I would see the sign of the TF change. 

I then realized that I could actively keep an eye on the trend of POY11, to see when I got to the PDH "hump", which is where REFLDC starts being usable, and SqrtInv is reaching its limit. 

This brought me to a YARM offset of .115, with a steady TRY of about 2.1. I adjusted the analog offset of the REFLDC input to the CARM board, and the digital gain of the CMSLOW input filter to get 1:1 correspondence between CMSLOW and the SQRTINVY channels. Their spectra were neigh identical, with CMSLOW having slightly more high frequency noise. 

I started stepping SQRTINV down by .1, and upping CMSLOW by .1. This shifted the offset around, so I opted for taking away gain before bringing it back, because I didn't want to get so close to resonance that SQRTINV would freak out. I got to .1*SQRTINVY + .9*CMSLOW, and lost lock. TRY was getting noisier as I made the transition. 

I'm not sure what exactly was the reason for failure. I'm going to go back over some of the data to try to get an idea.. Maybe I should've loosened up some of the gain/boosts during the transition. 

So, no great success story yet, but this configuration is a lot simpler than the full PRFPMI, and I feel that I should soon be able to get it fully controlled, and figure out a systematic way to make the digital to analog transition for this PRFP cavity, and thus have a much more informed basis for doing the same for CARM control. 

Just to be clear, the normal POY signals are not currently present, so the restore POY script will not result in the arm locking. POY11_I is turned off, POY11_Q is the output of the CM board, which can be used to lock the arm, as we did tonight. 

The POY digital demos angle went -56 -> 90, to get all of POY11_Q_IN1 to POY11_I_ERR

Miscellaneous things:

• Right now, the cable from CM board ->MC board is a BNC. There appeared to be a differential 2-pin lemo hanging around for this purpose, but it didn't seem to be transmitting the signal. However, we will want something better than a BNC to keep this signal clean. 
• I took SR785 TFs of the CM board from IN to the slow and fast outs. They looked reasonable, and will be posted in time. 
• We enabled the 79:1.6k filter in the CM screen (though it is unclear if these are the actual values...), and put in its inverse in the digital path. I.e. we only want this shape in the AO path, to give it 1/f shape in the vicinity of the crossover. This is only necessary in the uncoupled cavity case. 

 (Edited this post; Forgot to account for the FMs other than 4 and 5... it now agrees better!)

I did some quick MATLAB simulation of the relevant loops to try and understand what was going on. I put the digital UGF around 200Hz, and then brought in the AO path with both signs. 

In these plots, blue is digital only, green is AO+digital with the crossover happening at the UGF, and red is the AO gain set to five times of what it was in the green curve. 

Based on the phase curves in the loop measurements, I would be inclined to say the pink -AO case corresponds to the opposite sign plot, and the +AO case to the same sign plot. 

This correspondence also holds for the appearance of the peaks in the noise curves, the Opposite sign case has a dip in loop gain at ~50Hz (pink curve, -AO), same sign around ~30Hz (brown curve, +AO). 

However, both of these look like they become unstable at some point in the transition! This agrees with our experience last night...

I'll fiddle around and try to come up with some compensating digital filter that will make the Opposite sign scenario work. 

The MATLAB code I used to make these plots is attached. 

The PMC has been unlocked for ~23 hours. FSS slow was at ~-1.5 V. I zeroed it, and relocked the PMC, transmission is ~0.81V. MC with WFS came back fine.

 [Rana, ericq]

Today, we got a ~2kHz bandwidth lock of the YARM with the AO path. We weren't able to turn any boosts on, due to POY noise. 

Rana and Koji have written scripts (/scripts/PRFPMI/cm_step and cm_down) that work very reliably. 

Here is an OLTF. (Violin filter was off, the crap around 600Hz goes away with them on)

My MATLAB modeling was useful is predicting the features of the loop shape, and the dependence on AO gain/crossover. Still, I need to check it out, because there is nonzero discrepancy between reality and my model (this may be hiding in the non flat MC AO response, i.e. the bump at ~35kHz. Alternatively, the crossover frequency is a free parameter...)

In any case, we have confidence that the CM board is mostly working predictably. We presume that our current obstacle is the very noisy nature of POY, and thus it's not worth spending more time in this configuration. 

Upcoming plans:

• Use the CM board to control the Y arm coupled with the PRM. ("PRY"?)
• Determine the game plane for high BW control of CARM. 

Next steps:

• Check CM board boosts turn on politely (Transients, TFs)
• Use fast spectrum analyzer to check MC loop gain out to a few MHz. (The bump in the tens of kHz should be fixed / moved higher)
• Think about noise performance of, say, REFLDC, ASDC, RF AS signals, etc. in the PRY case, figure out which one to use first. 
• We may want to first focus on directly locking the arm on an RF signal, figure out gains etc. and then figure out how to do DC->RF handoff nicely, or if high bandwidth DC signal control is even feasible. 

RXA: we should also use AS45 instead of POY11. It has better SNR and I think our whole problem is too little light on POY.

 I took a look at the MC OLTF and AO path TFs with the fast agilent analyzer. 

I played with the relative gain of the EOM and PZT, but couldn't really change the MC OLTF shape much without making the PC Drive RMS angry. 

However, it turns out we have plenty of phase headroom to up the MC UGF from ~100kHz to ~180, with about 40 degrees of phase margin and ~7dB of gain margin. As I write this, PC drive RMS is around 1.1, and FSS Fast at 5.6, so I think the extra gain is fine for now. 

This pushes up and smoothens out the gain peaking in the AO path; see this figure:

(why does ELOG hate my python plots?! argggg)

Rana's rule of thumb was "We need at least +3dB MC loop gain at our CM servo UGF," so it looks like high tens of kHz bandwidth may be doable from the AO standpoint.

RXA: No, no, no, no, no, noooo. Rana said we need a gain of 3-10 at the CM UGF, not +3 dB.

 I've checked that the 2pin lemo connector that was run some time ago from the LSC rack to the MC board does indeed transmit signals. To try and evaluate its suitability I did the following:

• Generated a 5mVpp 1.3kHz signal with an SR785 and fed that into CM board In1, all boosts off, 0dB AO gain. 
• Both BNC and LEMO connected to CM servo out
• One of BNC or LEMO connected to IN2 of MC servo, input gain of 30dB but disabled, OUT2 switched to AO and fed to Agilent spectrum analyzer. 
• Terminated MC IN2 for comparison. 

No real difference was seen between the two cases. The signal peak was the same height, width. 60Hz and harmonics were of the same amplitude. Here are the spectra out to 200k, they are very similar. 

Mode cleaner was locked during this whole thing. This may interfere with the measurement, but is similar to the use case for the AO path. If ground loop / spurious noise issues keep occurring, it will be worthwhile to examine the noise of the CM and MC servo paths, inputs and outputs more carefully. 

On pianosa: The ezca.Ezca class somehow initializes with its prefix set to "C1:", even though the docstring says the default is None. This makes existing scripts act wonky, because they're looking for channels like "C1:C1:FO-BLAH".

In ligo/apps/linux-x86_64, I ran ln -sfn cdsutils-old cdsutils to get the old version back for now, so I don't have to edit all of our up/down scripts.

Also, Chiara can't find the epics package when I try to load Ezca. It exists in '/usr/lib/pymodules/python2.6/epics/__init__.pyc' on pianosa, but there is no corresponding 2.7 folder on chiara.

 Still no success tonight

• We took CARM OLTFs at various CARM offsets and could clearly see the peak in the optical TF (in once case ~2.5kHz), which gave us an indication of our offset (~200pm)
• REFLDC effectively sees the same plant TF as the transmission signals plus a zero at ~110 Hz, at all offsets under 1nm, from my simulations; this pushes up the optical resonance and causes a loop instability when we try to handoff. 
• We need to make the CARM OLTF steeper to suppress this instability, but also to make a good crossover with the AO path, which otherwise has too similar of a slope around the UGF, as we saw with our one arm test. 
• We're thinking of trying to turn the AO path on with REFLDC while keeping the arms on SQRTINV signals. This may be tricky, but if we can get the loop bandwidth above the optical peak, it'll be a lot easier to deal with, and transfer digital control to REFLDC as well. 

 I have redone the SPSR785 (spectrum measurement) and TFSR785 (TF measurement) commands in scripts/general/netgpibdata. This was mostly motivated by my frustration with typing out either a ton of command line arguments, or rooting around in the script itself; I'd rather just have a static file where I define the measurement, and can keep track of easier. 

They currently take one argument: a parameter file where all the measurement details are specified. (i.e. IP address, frequencies, etc.) There are a few template files in the same directory that they use as default. (Such as TFSR785template.yml)

If you call the functions with the option '--template', it will copy a template file into your working directory for you to modify as you wish. "SPSR785 -h" gives you some information as well (currently minimal, but I'll be adding more)

In the parameter file, you can also ask for the data to be plotted (and saved as pdf) when the measurement is finished. In SPSR785, and soon TFSR785, you can specify a directory where the script will look for reference traces to plot along with the results, presuming they were taken with the same measurement parameters and have the same filename stem. 

I've tested both on Pianosa, and they seem to work as expected. 

Todo:

• Add support for modifying some parameters at the command line 
• Extend to the Agilent analyzer
• Maybe the analyzer settings written to the output file should be verified by GPIB query, instead of writing out the intended settings. (I've never seen them go wrong, though)
• Make sure that the analyzer has PSD units off when taking a TF. (Thought I could use resetSR785 for this, but there's some funkiness happening with that script currently.)
• Possibly unify into one script that sees what kind of analyzer you're requesting, and then passes of to the device/measurement type specific script, so we don't have to remember many commands. 

Comments, criticism, and requests are very welcome. 

(P.S. all the random measurement files and plots that were in netgpibdata are now in netgpibdata/junk. I feel like this isn't really a good place to be keeping data. Old versions of the scripts I changed are in netgpibdata/oldScripts)

 It's taken a lot of trial and error, but I've found a path through MATLAB loops that seems like it may be stable at all points.

CAVEAT: This doesn't give any indication as to why we weren't able to turn up the AO gain more last night, as far as I can tell, so it's not all good news. 

However, it's still ok to at least have a plan that works in simulation... 

Based on the location of the optical resonance peak in the CARM plant, we estimate our CARM offset to be 200pm. I haven't simulated TFs there exactly, but do have 100pm and 300pm TFs. This procedure works in MATLAB starting at either, though 100pm is a little nicer than 300. MATLAB data and code is attached in a zip. 

The steps below correspond to the attached figures: Bode plots and step response of the Loop at each step. 

0. [Not Plotted] DCTrans sensing, MCL actuation on CARM. FMs1,2,3,5,8; UGF = 120. (DARM not considered at all)

1. AO path just turned on. Crossover with MCL path ~ 3.5kHz. 
2. AO gain increased. Crossover ~ 500 Hz. There are now multiple UGFs! Handling all of these in a stable manner is tricky. 
3. AO gain increased. Crossover = 150Hz. [No simulations with a higher crossover survived the next steps]
4. Compensation filter applied to MCL path; 1 real Zero at 105Hz and a pole at 1k. From a TF point of view, this is sort of like switching to REFLDC, but the SNR at low frequencies is probably better in TR signals at this point. 
5. CARM offset reduced to 30pm. (This smoothens out the optical plant resonance.)
6. Overall gain increased by factor of 3. There is now just one UGF at a few kHz, above the optical resonance. From here, gain can be further increased, boosts can go on, offset can go way down. In reality, we should switch to a single error signal once we're back to one UGF, and go from there. 

#4 Seems like the most sticky part. While both sides of this look stable as far as I can tell. I feel that flipping from the red phase curve to the teal might not actually be ok, since they are on either side of the bad phase of 0 degrees. It isn't immediately evident to me how to easily model the transitions between steps, rather than just the stability of of each step in the steady state.