We swept the temperature of the ACAV laser and monitored the transmission through the cavity. In the attached image, the TEM00 modes (separated by 3GHz or 1 FSR) are located at C3:PSL-ACAV_SLOWOUT values of 0.5344V and 1.379V. There is a TEM20 mode at 1.52V.

current heater value is around 4.66. changed crate startup value to current value

re-aligned the ACAV once more, now about 91% are coupled into the cavity

I put most optics on ACAV path. I have not tried to lock the cavity yet. I'll install ACAV RFPD next.

summary of all changes made and more detailed plots will be posted soon, so check back later

writing in progress

• replaced New Focus power supply for RFPD with Agilent power supply (+/-15V)
• added isolation transformer between mixer LO and main splitter of 14.75MHz LO
• changed gain of input stage from PDH-box from 10 to 20
• replaced thickfilm resistors in input stage with thin film ones
• added offset potentiometer to input opamp
• added 25MHz HP-filter to AOM driver/amplfier

ACAV loop is now completely free from line harmonics and the in-loop level dropped to ~10nV/rtHz (includes 7nV/rtHz from analyzer). Mixer dark noise is ~25nV/rtHz.

I updated the schematic for ACAV RFPD.

I'll update the schematic for RCAV servo, ACAV servo as well.

The ACAV RFPD stopped working this afternoon. It had high current consumption on the +15V supply, causing the supply to drop down to 2.3V.
I turned out that the logic IC (U8, see schematic) was broken and so the +5V (internally regulated) caused the high current flow which is supplied from the +15V.
I removed U8 entirely as we don't need it. Pin7 of U2 can be left open according to the datasheet in order to enable the device. Diode is now working again.

Already yesterday we made several changes in order to make the RFPDs for both cavities the same. Basically more DC and AC gain.
Attached the modified schematic (only page 1) for ACAV RFPD. Changes are in red.

PID process running on the Sun workstation stopped at lunch time with error "couldn't read process variable ...bla bla bla "
Turned it on again.

 after rebooting yesterday the ACAV heater was railing over night.
Today i figured out that the integrater value in the startup skript had the wrong sign!
Changed the entry according to Tara's post last week. Now temp controller is working again.

I'm aligning the AOM. The R=0.5m mirror's position crosses the insulation border by 1.5" (see attached picture.) The black line on the table shows the border of the insulator. The mirror is on a translational stage.

I'm thinking of 2 choices to solve this,

 1)using a mirror to turn the beam to the side of the table. The mirror will be placed after the AOM, around the edge the border.

2) using 2 mirrors (after the beam is split to RefCav and ACav's paths) to shift the beam path to the side of the table.

The first choice will be better, since I won't have to recalculate the mode matching, but there might be unexpected problems.

The VCO is working fine, I can see +/- 1st order beams coming out.

A few more changes to the PMC north board. Hopefully this is the last.

Changing series resistance at the output

There was some limit to the gain before the PMC loop became unstable.  I realized that I hadn't implemented the 10 Hz pole at the output, that could be the reason.  The resistor in series with the output was only 1 kΩ.  The Noliac NAC2124 PZT on the PMC cavity has a specified capacitance of 510 nF and about 5 meters of BNC cabling should have a capacitance of 0.5 nF (for 101pF/m).  This should give a pole of about 312 Hz, we want to bring this down.  I replaced the 1 kΩ series resistance at the HV output with a 30.9 kΩ to bring to pole down to 10 Hz.  

Schematic is updated below.

Removing short from PD RF input

For whatever reason the AC coupling resistor had been deliberately shorted on the PD RF input to the board (C3).  I removed the short.  It is AC coupled again.

Altering the Acromag excitation voltage and divider resistors

I realized running the Acromags off 6 V is a little awkward.  Most power supplies come in other standard values like 5 V, 7.5 V, 9V etc.  I've raised the excitation of the binary channels to 9 V and made some changes to the divider resistors. Resistors on SW1 and SW2 binary engages were changed to equal values of 1790 Ω for R1 and R2 (see option D, attachment, PSL:2058). On the blanking pin used to activate the AD602, equal values for R1 and R2 of 154 Ω were used.  These resistor choices give a high voltage of 4.5 V and a low of 0.66 V.  There is also a margin of error if the power supply used goes a little over voltage.

I've ordered standard barrel 2.1x5.5 mm panel Jacks so that the unit can be powered from a standard 9V plug pack.

I used the 633 nm fiber illuminator and the ThorLabs power meter (set to 633 nm) to test the 60 m polarization-maintaining fiber that we have.

Power right out of the illuminator was 1.25(2) mW, and the power out of the fiber was 0.45(1) mW. Since this fiber is only specked to work above 980 nm, I'm not sure how to interpret this number.

I'd like to compare to the 35 m PX980-XP fiber we have strung from CTN to Crackle.

I performed the same test with the 1060XP fiber (50 m, not polarization maintaining). I got 0.12(1) mW transmission.

found the box with the beam splitters Dmass bought almost 2 years ago but never unpacked or used. They are super-polished 50:50 beam splitters for 532&1064nm but optimized for 1064nm.There are 16pcs total, so i don't see why we can't use 3 of them for our beat setup. We now have only SP optics in the critical beam paths except for the windows of the vacuum can, all lenses and wave plates where required. I hope this will reduce the amount of scattered light a little bit. The new setup only uses a minimum of components.

If you look at our beatnote ASD you can see a broad dirty hump at 500 Hz.
awade played a pure 500 Hz tone through our lab speakers, and you could see the resonance peak being driven.  Blue are the driven spectra, orange are the non-driven spectra.
If we turn up the speakers it causes our North path to lose lock.

Some sort of mechanical resonance in the North path is causing this.  Buzzing is underway.
 

After buzzing the table with a probe at 500 Hz, the source of the 500 Hz resonance is the first steering mirror after the PMC.  The PMC itself also exhibits a smaller 500 Hz resonance, unclear how much of that is actually the PMC mount vs. coupling through the PMC to the first steering mirror.

Checkout the latest noisebudget. 500 Hz peak is gone now. This could be because of any of the changes I made in past 2 days:

1) NPMC servo gain increased. I changed R8 from 9.09k to 51 Ohms. That increased the gain by a factor of 200 which is equivalent to 46 dB. The slider for AD602 gain decreased by 23 dB to remain below oscillations wiht a 1dB gain margin. So maybe this reduced the noise a lot more (even though it is still present)

2) I did replace a normal beam dump (91,45) on the reflection path from North PMC with a triangular black glass cavity and I oriented another one (94,30) just before NPMC blocking rejection from a PBS as it was oriented horribly wrong.

3) We also changed the detector to NF1811, but that hasn't resulted in changing this feature in the past.

Note that the expected noise has now decreased roughly by 3 times in the range 200 Hz to 500 Hz. See CTN: 2423

[awade, Craig]

As a side note to this diagnostic oscilloscope probing I noticed the other day that there were 50 MHz oscillations at TP14 and TP15 in the fast path of both field boxes. These points are probing the two active LP filters in the fast stage, an OP27 and AD797 respectively.  Values are as follows:

North (2009:005) 21.6 mVpp @ TP14, 203 mVpp @ TP15, 42 mVpp @ TP16, too small to see at subsequent stages.

South (2009:007) 32 mVpp @TP14, 189 mVpp @ TP15, 40 mVpp @ TP16, too small to see at subsequent stages.

I'm guessing the oscillations are a stability artifact of the OP27 stage one circuit (U8) which is then amplified by the stage two AD797 (U9). After this point in the path the 50 MHz is attenuated by the subsequent stages as they are essentially in buffering G = 1 mode, I'm guessing it sits outside their bandwidth. The size isn't so small but its at very high frequency and quickly filtered out by the circuit: so maybe its not really a problem.  

When I zoomed out a little in the time scale and adjusted the trigger threshold up it seemed like some of these 50 MHz oscillations were being excited by glitches. In the time domain these ring down to the stead state levels listed above.

On another thing, I'm not sure why there are two different types of op amps here.  I guess I find it strange that the OP27 is first, the AD797 spec sheet seems to suggest it has a lower noise than the OP27. Maybe its because the GBW of the OP27 is higher? 

Anyway, just a note for future reference. I have no conspiracy theories that this is an actual issue for us, yet.

If you have an oscillation in a circuit, it is no longer linear!

Sounds like a typical AD797 oscillation. GBWs of OP27 and AD797 are 8MHz and 110MHz, respectively. OP27 can't make such high freq oscillation.
I didn't check the circuit diagram. Usually AD797 has ~5pF feedback capacitance to increase the stability. You may be able to stop the oscillation by adding/replacing a mica capacitor  from 10~470pF. But 50% of the time the oscillation is not fixed with this kind of modification. You need a cut-and-try.

Ok. Doesn't sound great, but is common to both the units we have.

The AD797 is configured with a feedback capacitor of 1.5 nF parrallel to to a 3.08 kΩ.  This is for a 34 kHz pole.  Could it be an issue with the choise of capacitor type?  I'll try switching out the one that is in there for another mica one, I would have thought the one that is there would be enough (unless it has bad HF impedance).  

I'll try some things.

I have a set of two Wenzel OCXO added to the electronics chassis, courtesy of the gentry from the Cryo Lab. The chassis has outputs for 36MHz and 37MHz.

We can use these temporarily and exchange the oscillators in future when we select a new sideband wavelengh.

There is a 35 MHz pick up from cables to the crate. Right now there are ACAV and RCAV_RCTRANSPD that cause the pick up.

When I unplug the cable to the crate and just measure directly at the PD output, the signal is fine.

I took the transfer function through our two 35.5 MHz RFPDs.

RFPD B, labeled "Low Q" on top, has lived up to it's name.  It is the orange curve below.  We opened up the two PDs to see if there were obvious differences, and there were.  We also discovered these differences were documented.

On the PSL wiki, there is an altered schematic of the 35.5 MHz RFPD.  Here is the original schematic on the DCC.  In order to produce a PD with a lower Q, it seems that some inductors were shorted or replaced by tunable coilcraft inductors.  A resistor and capacitor to ground were also removed.

Now we wonder if we should lower the Q of RFPD A or increase the Q of RFPD B.  Andrew says that the higher the Q, the lower the bandwidth of our controller.  I can barely understand him sometimes, but he's always right about these things.  We've decided to seek out Koji the PD master and ask his opinion.  Remember that the purpose of these PDs is to read out sidebands for PDH locking to the PMCs.

I also attached a tar containing the data, python script which makes this plot, and the plot itself.  It is located in the git repo CTN_noisebudget/RFPDTFs.

No, we don't want low Q for the PMC RFPDs. We want Q ~10 for the RefCav RFPDs, and whatever high Q we can get for the PMCs, so that the SNR can be high with low light. The PMCs should have a low modulation index, so the more SNR, the better. But the PMC RFPD noise requirement is not stringent, so don't spend more than a day on these.

The two PMCs craig measured are for the RefCav RFPDs.  I don't recall if we had a second 21.5 MHz resonant RFPD for the south path MC, I'll check again around the lab. If not we could lock one or both PMCs at 14.75 MHz using the PDs currently used for RefCav locking.

Point taken about the Q~10. So we're looking to ensure both circuits have a bandwidth of 3.5 MHz? Also it looks like the overall gain of the RFPD-B is 10 dB less than that of RFPD-A, I guess we should make these the same as well...

Craig: probably a good idea to zip and attach data with working plotting script to posts in addition to putting in shared syncing folder. Takes an extra minute, but worth it in 6 months when you can't work out which data goes with which post. Data has a half-life of 2 weeks sitting on your computer hard drive, after a while you won't remember what goes with what.

agreed; should do for all labs

the 3123 card (16bit input) seems to be broken. That's the card which also samples the PMC transmitted light which fluctuates periodically since a couple of days...
I changed the database to read the temp sensors for both cavities and when testing the inputs i figured out that it's reading only 8.97V of the 10 i put in, same for other values...
soft and hard resetting the crate doesn't change anything...

gonna replace the card...

UPS supply 30A plug is installed in the PSL lab in the corner by the rack.  Port 058B/38.

The supply came with a rack mounting kit but it only attaches at the front; all the load of the ~40 kg unit is held on four screws which is not good.

TODO: order 2x extruded aluminum L pieces (90 degree angle) to support weight (dimensions 2ft x 2" x 2").

I couldn't find what I was looking for on the computer/enterprise punch outs on Techmart but McMaster sells 90 degree angle 2"x2"x2' lengths that are pretty much what we have now: 

https://www.mcmaster.com/#8982k14/=18dvdxq just need to drill some holes in the right place for our rack.

I've bought a UPS to help the lasers + computer ride out the frequenent power outages in Bridge West.  Its needs a 30A plug.  

A job is booked in the AiM's system (#24141) work will take place 0800 Tuesday 27 June. They may need to power down adjacent power while routing cables.  

I ran another Comsol simulation with a simplified version of the PMC spacer. This time I put fixed constraints on two circular regions on the sides of the PMC near where it was clamped for the ringdown measurement. Comsol says the spacer has a mode where it twists about these clamp points, and the frequency of the mode is 270 Hz.

Here is our first trans spectrum in Vrms/rtHz.  We haven't had time to fully calibrate the PLL actuation to get the spectrum into Hz/rtHz, that will come tomorrow.

The beatnote is around 100 MHz.  We demodulated the beatnote with a PLL, using the Marconi as local oscillator with a 800 kHz FM modulation range.

The North cavity temperature voltage was set to 10.6 V by me at around noon today, and the beatnote frequency is just now settling down, still drifting by a little but not so bad as earlier where we had to retune the Marconi carrier frequency every five minutes.

Ocassionally the South path will start ringing at the PZT starts railing.  I turned the common and fast gains way down so this doesn't happen so much, this had a marked effect on this spectrum.  Further investigation is needed for why the South path is ringing, Andrew suspects our negative power supply is not outputting any current, which could make the PZT suseptible to railing somehow.

So  1-2 kHz feature has popped up from time to time in previous beats.  It seems to be mostly arise from changes to the AEOM (installing) and poor polarization alignment of the RF EOMs and BB EOMS.  I can't find in the elog anywhere where it was explicitly pined down by tara optimized it out with fine tuning alignment of RF EOM (see PSL:1311).  Evan also made a measurement of the coherence between the RFAM (PSL:1524) and the beat, this looks like a pretty credible source of the hump.

My suspicion is that this noise hump is too high to be seismic (unless its unconverted).  RIN coupling in through photo thermal effects should dominate at lower frequencies unless the power spectrum of intensity noise is strongly skewed to  higher frequency components.  I've attached the Photo thermal transfer function from the noise budget notebook below for reference.  This has a trace with previous RIN measured in the old setup. We need  to measure RIN again, however, unless its very different its unlikely the source. 

Hypothesis #1:

The the RFAM out of the resonant modulation EOMs is poorly optimized.  The stationary component of this residual AM creates a DC offset in the error signal that isn't wholly nulled by the FSS offset adjust. This lock point error means that the actual lock point of the FSS is slightly down the cavity fringe and that any small fluctuations in intensity vary the slope of the error signal are directly coupled to first order as if they were frequency noise.  If the error signal is properly zeroed on the resonance we would be immune to this effect to first order.  Slow temperature variations may slightly change the polarizations so optimizing the voltage offset in the FSS may not hold true after a room temperature change.  In the past (PSL:1994) we had suppressed the AM component 80 dBm/sqrtHz when measuring on the reflection PD using a flipper mirror in front of the cavity.  It had been better that this in the past and is worse in the north path by an order of magnitude. This has not been checked in the last few months.

Hypothesis #2:

We are not just looking at a stationary lock point error from RFAM but also a component that originates from the FSS EOM path or is coupled back through it.  The BBEOM in the FSS loop can induce intensity changes if it not a optimal polarization alignment.  This may convert what is supposed to be a phase correction to the light into an intensity change.  If there is noise in the EOM path of the FSS this can convert into noise through hypothesis #1.  There could also be a feed back where the RIN is made worse by dynamically feeding back through the FSS making more RIN from the BBEOM.  

One possibility here to test this hypothesis is to inject a signal in the BBEOM path to see if we can induce a narrow peak (or possible band passed noise component) that couples all the way through to the BN and the FSS error spectrum. 

Not that the ISS is not currently turned on.  The optics need a quick tune up and the loops should be switched back on. The ISS was inducing some phase as part of the AEOMs operation.  You can see this in the actuation signal of the FSS as it fights to compensate the ISS.  Between the two of them they should suppress intensity noise and the higher frequency discrepancy with the reference cavity frequency: but, they are not entirely orthogonal in practice.  The ISS definitly make the FSS EOM work harder.

Some measurements to make

• Free running RIN of both the north and south paths
• RIN when ISS activated and comparison of BN spectrum change
• RFAM residual and why it isn't lower
• Signal injection test in the FSS EOM path to see bad conversion of phase actuation in to intensity
• AEOM phase conversion

Need to make thermal hats for all the remaining Lithium Niobate based modulators and maybe even the wave plates.

Attempting to identify the source of the 200-3000kHz hump.  

Optimizing polarization into north BBEOM and AEOM

I made a number of optimizations of polarization into the modulating optics over the weekend.  The BBEOM used for fast actuation of the north FSS loop was optimized by driving the BBEOM with a 20 Vpp @ 101 Hz sin wave and minimizing the residual AM (as seen on the PMC reflection PD).

For the amplitude modulator used for the ISS RIN suppression, I deactivated this optically.  The polarization was aligned horizontal going into the AEOM and the following quarter-wave plate was set for maximum throughput.  In this configuration applied voltage to the AEOM results in little to no actuation.  I did this to remove the AEOM from consideration in diagnosing the 14.75 MHz RFAM residual.  

Attempting to improve the north AM residual from the 14.75 MHz modulation

I found that the residual AM, as see by the FSS Relf PD, was considerably higher than it could or should be. The initial level of AM was about -30 dBm.  With some adjustment of the two wave plates before the EOM I found I could reduce this level to -37 dBm. However, this was still a long way from the previous <-70 dBm achieved in the past.

After checking I was actually using a lambda/2 + lambda/4 pair I found that the pointing through the EOM (NP 4004) itself had an impact on the degree of AM reduction. It turns out that the strait shoot through the center of the aperture had a higher minimum RFAM residual compared to aligning the beam a little to the left on the output aperture (looking along the axis of the device). The beam is still well clear of the aperture but I was able to get to -72 dBm of residual AM.

What I found was that the AM would reduce for a minute or two and then creep back up to ~-40 dBm.  I suspected that this was temperature related. I pointed a heat gun at the EOM+ wave plates area at a distance of 1.5 meter for 5 seconds: it blew the AM reduction back up to -30 dBm.  It didn't seem to matter if the thermal hat was on the EOM or not.  I'm pretty sure these wave plates are zero-order but not sure how to tell just by looking at the optic, its possible that the label on the mount doesn't tell the truth.  

When I tried this optimization again today I had a lot of trouble finding an and optimal input polarization.  Eventually I've identified a source of polarization drift that is occurring somewhere between the 21.5 MHz PMC modulator and just before the wave plates into the 14.75 MHz oscillator.  This path is basically a two steering mirrors and the PMC.  I put a PBS in transmission between the PMC and the input to the north 14.75 MHz EOM. I found that the stability of the polarization alignment into that EOM improved significantly.  It was possible to get the residual AM to dip down to the -80 dBm noise floor of the analyzer (for that BW setting). There is, however, still a strong thermal dependence somewhere there which leads to the residual RFAM rising again.  

Side note: the orders for PMC mirrors indicate that p-pol mirrors were used.  Evan's notes don't seem justify this choice. I am working on the assumption that the PMCs should be operated using p- polarized light.

Following up on the last optimization of RFAM (see PSL:2087), I tried to obtain the -80 dBm RFAM at the north FSS refl PD with the flipper mirror up.  For some reason I am unable to reproduce the previous achieved RFAM lower bound (-80 dBm). 

We seem to be limited to -50 dBm with the flipper up.  I'm not sure what is going on here. Its possible that the large unfocused beam of the flipper reflection is givening secondary beams going through the Faraday isolator and we are actually looking at RF components mixed down with itself on a secondary reflection.  Also even after installing a PBS before the PMC there is still significant polarization drift.  The RFAM stays optimal for only 15 minutes or less. The EOM has an insulated hat, the waveplates and PMC do not. I don't know if we need to attempt a temperature control of these critical components.

Below I have attached a few ASDs taken with Criag's new live calibrated ASD generator (see PSL:2090).  One is taken before optimization of the RFAM on the north path, the next is imediatly after at 19:34 pm yesterday and the third is from this morning.  The system stopped logging BN spectra some time after 7 pm yesterday. When I checked early this morning at about 1 am it hump had returned.  I don't have the csv data files handy, so I am unable to complie them into a single plot, but you can see that the hump was greatly reduced with polarization optimization into the north 14.75 MHz EOM. 

It seems like this hump that pops up is a 14.75 MHz residual AM issue.  I'm guessing that the mechanism is that the lock point error offset is allowing intensity noise to couple into our measurement.  However, in the past Evan implemented an ISS only to find that it didn't improve the BN noise. A good test would be to inject an AM modulation line or swept sine and see how it propagates to the BN above what we would expect from photo thermal noise.   We need to address how to stabilize or remove this polarization drift. Active control sounds like a massive pain. Passive temperature stabilization might buy us an 30 to 60  minutes of good measurement but is not a good permanent solution.  Ideally we would locate the worst offending optic that is causing drift and deal with that.

Edit awade Fri Feb 16 13:07:12 2018: staring at the second attachment Beatnote_ASD_20180215_193422.pdf, something doesn't seem quite right. We definitely saw 0.3-0.6 Hz/sqrtHz on the SR785 last night. However, the roll up below 100 Hz in the auto generated ASD doesn't seem to have the same characteristic shape for scatter that we were looking at before.  Craig was working on scatter in the transmission table but the scatter shelf was back this morning so not likely that we really found the worst offending scatter.  Also, not sure if we are limited by the ADC noise above a 1 kHz there.  We need to go back an measure this with the SR785 and also check the PLL loop gain.  

One of my DAQs (18bit, 1V range, NI 6289) in the seismo lab is recording data from a T240 broadband seismometer on the PSL table. Here, I am going to present plots for the first two days of data taking. I think that there are a couple of interesting features that should eventually be explained using additional seismometers.

The first datum is taken shortly after 2010-12-18 00:00 UTC. The seismometer is oriented along the sides of the table. If I am not mistaken, then the long side of the table should be approximately parallel to the East-West cardinal.

2010-12-18 (Saturday UTC, Friday/Saturday PT)

The plot that I like to look at first is my "hourline" plot. It is inspired by ancient seismology print-out styles. It shows 24h of displacement. Each hour is represented by 200 data points per channel properly filtered. The absolute value of the plot has no information. Different normalizations are chosen at different days to make the largest displacement of the day still fit without intersecting other hour lines. What you can see here is that the vertical channel is very stationary and weaker than the horizontals. The disturbances within the first hours is Tara working at or near the table and causing strong tilts. We will see more detail in this plot at the next day.

The next step is usually to look at the spectra. I like to produce quiet-time and total-time averages. I need to apologize about the labeling. I just noticed that there is still "ASD" on the y-axis. An amplitude spectral density would have different units (m/s/Hz). So these are root power spectral densities (sometimes also called linear spectral densities). In any case, the quiet-time spectrum is just barely below the global NHNM (new high-noise model) of Peterson. This is scary. If your measurement depends on seismic noise, then look for another lab. Characteristic for near coast sites is the double peak at oceanic microseismic frequencies (also seen at the Virgo site). Now, the higher-freq one is not easy to explain. I can only imagine that there is evanescent coupling of ocean wind waves (which do not produce significant microseisms far from the coast) to ocean bottom near the coast. The lower-freq peak is the usual ocean swell, freq doubled peak. You can also see Tara's low-freq tilts comparing the two plots. We will be able to understand more about the >1Hz spectrum in following plots.

The H/V ratio is the ratio of horizontal spectra to the vertical spectrum. It can tell you a lot if you know the seismic speed. If you don't know seismic speeds, then it can still be helpful to identify local anthropogenic sources. A seismic field "randomizes" over large propagation distances, which means that it loses its inital polarization (elliptical for Rayleigh and linear for body waves in many cases). The PSL ratios are not much different for the two horizontal directions. It is difficult to say what it means, but my first guess would be that all structures in the ratios are not due to source characteristics, but due to site characteristics (layers that cause resonances, the table itself,...). But it could also be related to sources.Only a seismic array can help here.

I am only showing two of the three spectral histograms. The level of spectral variation is actually lower than expected (low-freq tilts are the exception). The fact that you don't see much blue in the two plots tells you that the seismic field is quite stationary (well, at least in relation to its high absolute value). I have absolutely no explanation for this. I am very curious to observe the variations over longer periods of time. Especially the vertical displacement is surprisingly stationary. We will see this better in the time frequency plots.

I usually look at normalized time-frequency plots, but the unnormalized versions seem more exciting to people who don't look at them very often. Again, only two out of three channels. You can see many of the features that we also found in earlier plots (tilts, ocean microseisms, high-freq disturbances). Aparently, the near-coastal wind must have lost some strength during these 24h. Its peak was losing power at evening (keep in mind the 8h time difference). I don't understant part of the >10Hz vertical spectrum. What disturbance (small bandwidth) is losing power over night?

Finally, I plotted a few particle trajectories. There is a low-freq plot with horizontal data <1Hz. It was taking during night when Tara had already left. So the polarization is natural. Although together with the other three plots (>20Hz, all three channels combinations) I get the idea that this polarization could be because of the table. One should eventually compare with data taken from the ground. I intend to program a trajectory histogram since there is more informaition in the high-freq plots than can be represented in these plots. So stay tuned. It requires a serious effort (a seismic array) to understand seismic polarization if you don't have any other site-specific information. Anyway, polarization is already interesting and can be used to give you a factor 2 in (seismic-noise limited) sensitivity if you orient your suspension system along the right direction! On the PSL table, you should avoid alignment parallel to the short side.

As we decided to use lower sideband frequency (14.75MHz, instead of 35.5MHz), I replaced the Broadband EOM with 14.75MHz EOM.

==Motivation==

   The current broadband EOM give only small modulation depth (~0.06 rad with maximum power from the LO, seepsl:745) With a resonant EOM, we can get higher modulation depth with the same amount of power.

   Plus, in general, the RFPD's Q will be also higher at lower frequency, so we should get higher gain to suppress more frequency noise (the exact number of Q has not been measured yet).

==To Do/ Problems==

  We no longer use LIGO's old LO cards. All of the spares in the lab are also broken. We will use a function generator and adjust the cable length to change phase between LO and PD. 

 After I added the resonant EOM to the setup the beam path changed quite a lot, I need to re-aligned the beam before I can see the error signal and lock the cavity.

The 14.75 MHz EOM we have is for visible light, so we went to TNI and borrowed a 14.75 MHz EOM for IR and an 14.75 Mhz resonant RFPD.  I will re-aligned the beam and measure the error signal tomorrow.

 The current function generator can provide power up to 23dBm. So the EOM can be driven around ~ 19 dBm(~2V@ 50Ohm) (-3 dBm for a splitter, -1 dBm for loss in the cable). So we can expect the modulation index to be 0.2*2 = 0.4 rad.

Peter gave me the hint that the default values are stored in an eeprom in the laser head. So connecting the head to a driver not used before shows the default values for the head. For this head it's 0.86A. So i measured the slope of the NPRO up to that value, reaching the 100mW at the default value stored in the head without tuning the diode temperature. So the head seems to be refurbished and not dead...

we still have serious problems with the 100mW laser head. I traced it down to the connection between the PCB and the hermetically sealed optical part. There is a really loose connection somewhere. The connector seems to be OK, the PCB and all solder points are OK too (visually). But if you slightly touch the PCB you can see the yellow LED flickering, if you touch it a bit more the laser goes off and on. This happens too if you touch the D-SUB cable on the back. I added some little stress to the PCB when putting the thing back together, now the situation seems to be better, but is far away from being gone. In order to get started we are using it now as long as we can and think about a solution in the meantime. One option would be to fix the busted NPRO Peter has. This would probably take about a week or so. We have to align the laser diode and focusing lens and solder (!)  the focusing lens in place. The problem is that you can't align in vertical direction, so you have to remove the laser diode, put some more or less indium foil below and start again from zero. But it's an option. Peter had it already back to 550mW (out of 700mW) or so (for a couple of minutes, simply holding all parts in place. So the difficult part is to keep it permanent in the right place...

I'm working on the new mount for 1.45" refcav. I 'll discuss the design with Eric G and some mech engineers (Mike Smith, Ken Mailand) later.

Here is the assembly of the mount, with only one cavity shown.

copper thermal shield around the cavity is 1.75" OD, 1.686" ID, wll thickness = 0.064", 3" long. (I'll order the tube from McMaster-Carr.

bottom mount will be a single piece, holding both cavities together.

I'll add a top plate to hold the shield and cavity later.

Note: I'm thinking about using teflon to make all the mounting pieces (top and bottom) so the mount will act as heat insulation between the shield and the platform.

modification of the previous mount, work in progress.

I finished the design for dual cavity mount. The assembly looks fine, all parts fit together. I'll make sure that the mount can be screwed down to the current seismic stack before I submit the drawing.

After finding the optimum support points using COMSOL, I redid my cavity support design. The picture below shows the assembly of a metal base, peek pieces for support points, and copper shield. The picture shows only half of the mount.

Personal note: 

The current design, the beam height is 1.32 inch above the top seismic stack, ~5.5 inch measured from the table.

With the new cavity mount design, the beam height will be 1.5 inch above the top seismic stack.

I finished the drawing for refcav mount and the top plate. Everything fits together, so I'll submit the drawing tomorrow.

New things I added:

• Top plate for holding the thermal shields, and the cavities with screws.
• wall between the cavities for radiation shield.
• new top plate for the seismic stack, the dimension is similar to the one we have now, but the hole pattern is modified to fit the refcav mount
• cap for thermal shield (not shown).

The refcav mount is a bit wider than the top seismic stack plate, but it fits inside the chamber, see the assembly. So I don't think it will be a problem.

 I used COMSOL model to calculated Brownian noise in substrate. This was done for cross checking my model simulation. The result from model is within 2% compared to half infinite model calculation.

I followed Levin's Direct approach to calculate Brownian noise in substrate, basically, to calculate the elastic energy inside the substrate under the applied test force. This can be done using COMSOL and analytical calculation. The comparison between the two is shown below.

U is the stored energy in substrate.

Note: I used the same COMSOL model for TE noise calculation. I just asked it to produce the strain energy in the substrate (no spacer).

The simulation is very close to the analytical result. So I think my spacer-cavity model and all the factors in the calculation are correct. The TE calculation is a little more complicated, since I have to calculate the gradient of expansion in COMSOL and it might be wrong somewhere. I'll check that. 

current settings for the slow actuator to bring the cavities on resonance are:

• refcav 1 : 0.6836V
• refcav 2 : 0.7350V

df~54MHz

We heard back from G. Cole about the thickness resolution in the AlGaAs coating manufacturing process will be around 0.5 A. So I'm checking how the noise budget will change by rounding up the physical thickness in opt V4 to the next 0.5A. The design will still work. The round up thickness is added in the google document (for opt v4 only).

The estimated growth rate of the crystal is 4.8A/s and shutter speed is assumed to have 0.1 sec time step. This means the smallest step of the thickness control is ~0.5A. So I round up the physical thickness to the next 0.5 A and calculate the coating properties.

1) Rounding up to the next 0.5 Angstrom. The truncating process acts like a random thickness variation in the optimized coatings with maximum error ~ 0.25 Angstrom. The averaged layer thickness is ~ 800 Angstrom.

2)Results when the layers physical thickness are round up to the closest 0.5 A. The noise budget does not change much.

The coatings properties still hold, even with random error in parameters, thickness.

Note: For the error calculation I did before I used 1 sigma to be 1% for AlGaAs, and 0.5% for GaAs. The thinnest layer is AlGaAs at 35 A, so its sigma is about 0.35 A. The average thickness is 90 Angstrom, so the average error is about 0.9 A. The estimated error in the calibration process is already larger than the error from the truncation(0.25A). That's why the error analysis results are still valid.

I revised the calculation for photo-thermal noise in AlGaAs coatings, the photo thermal noise should not be a limiting source.

==review==

photothermal noise arises from the fluctuation in the absorbed laser power (RIN + shot noise, mostly from RIN) on the mirror. The absorbed power heats up the coatings and the mirror. The expansion coefficient and refractive coefficients  convert thermal change into phase change in the reflected beam which is the same effect as the change of the position of the mirror surface.

Farsi etal 2012, calculate the displacement noise from the effect. The methods are

• Solving heat equation to get temperature profile in the mirror.
• Use elastic equation to calculate the displacement noise due to the temperature change (thermoelastic)
• For TR, the effect is estimated from effective beta (from QWL stack) and the temperature at the surface ,as most of the TR effect comes from only the first few layers

When they solve the heat equation, the assume that all the heat is absorbed on the surface of the mirror. This assumption is ok for their case ( SiO2/Ta2O5) with Ta2O5 at the top surface, all QWL, as 74% of the power is absorbed in the first four layers (with the assumption that the absorbed power is proportional to the intensity of the beam, and all absorption in both materials are similar).

However, for AlGaAs coatings with (nH/nL) = (3.48/2.977) The E field goes in the coatings more that it does in SiO2/Ta2O5, see the previous entry. So we might want to look deeper in the calculation and make sure that photo thermal noise will not be a dominating noise source.

==calculation and a hand waving argument==

 The plot below shows the intensity of the beam in AlGaAs Coatings, opt4, and the estimated intensity that decreases with exponential square A exp(-z^2/z0^2). X axis is plotted in nm (distance from surface into coatings). The thickness of opt4 is about 4500 nm. To simplify the problem, I use the exponential decay function as the heat source in the diff equation. But I have not been able to solve this differential equation yet. Finding particular solution is impossible.  So I tried to solve it numerically with newton's method, see PSL:284. But the solution does not converge. I'm trying green function approach, but i'm still in the middle of it.

However, the coatings optimized for TO noise should still be working. Evans etal 2008 discuss about how the cancellation works because the thermal length is longer than the coating thickness. The calculation (TE and TR)  treat that the temperature is coherent in all the coatings ( they also do the thick coatings correction where the heat is not all coherent, and the cancellation starts to fail at several kHz). So the clue here is that the cancellation works if the heat (temperature) in the coatings change coherently.

For photothermal calculation, if we follow the assumption that all heat is absorbed at the surface (as in Farsi etal), we get the result as shown in psl:1298, where most of the effect comes from substrate TE . In reality, where heat is absorbed inside the coatings as shown in the above plot, heat distribution in the coatings will be even more coherent, and the effect from TE and TR should be able to cancel each other better. Plus, higher thermal conductivity of AlGaAs will help distribute the heat through the coatings better.

This means that  the whole coatings should see the temperature change more coherently, thus allowing the TO cancellation in the coatings to work. The assumption that heat is absorbed on the surface should put us on an upper limit of the photothermal noise.

This means that photothermal noise in the optimized coatings should be small and will not be a dominating source for the measurement.

I use COMSOL to simulate the mirror of RefCav.

I tried only DC heating from the beam. The mirror has finite size, absorbed power is radiated outside.

Next step will be using DC power + small fluctuation.

 The information about dT will be used to calculate phase shift due to thermoelastic and thermorefractive noise.

note about heat3.mph file

 COMSOL 4.0

MIRROR model for PSL
This is a note about file heat3.mph

1) Global definition
     1.1) parameters: most of them are self explanatory. Some that might need
                     clarification are
             a)  p0 is the total power absorbed on the surface
                  which is Power input x absorption x finess/pi 

                  = 10mW x 5ppm x 10^4/pi ~ 1.6 x10^-4 watt

             b) I0, (p0/2pi w^2) Intensity factor of the Gaussian beam, when integrated the
                   intensity over  the area, the total power will be p0

              c) Qin, gaussian beam profile on the mirror

2) Model 1

   2.1) Geometry 1
           a) a substrate with thickness, radius as specified in (1.1)
           b, and so on) multiple coating layers*
              *note: I tried both 3 doublets with 1 cap and effective 5 um coating, but when I mesh the geometry, it's out of memory.
              So I disabled all coatings, and use only substrate. Frank suggested I can reduce the
              mirror's size if the temperature across the surface drops fast enough. I haven't tried that
              *effective coating is a single layer, 5 um thick. Thermal expansion coeff and heat capacity is
               calculated from multiple layers of Ta2O5 and SiO2.
 
          c) Form Union-> choose Form a union then, click "Build All"  

  2.2) Materials
        a) SiO2 (fused quartz): from COMSOL library
             surface emissivity is 0.75 (taken from  <http://www.optotherm.com/emiss-table.htm> and

<http://www.google.com/url?sa=t&source=web&cd=2&ved=0CCIQFjAB&url=http%3A%2F%2Fwww.holanengineering.com%2Fsitebuildercontent%2Fsitebuilderfiles%2Femissivity_1.pdf&ei=JGBgTKr9IIL2tgOPj-ipCw&usg=AFQjCNHFASfDeyG6yvq-FNXuEUShtmH_2Q>

    b) Ta2O5, all parameters are from Evans etal paper.
            Note that the value from Evans' paper,
           the specific heat capacity for Ta2O5 is  2.1 X10^9 [Joule/m^3 kelvin]
             in comsol I defined
                specific heat capacity to be 2.1 x10^9[Joule/kg Kelvin] and,
                 mass density to be     1.0   [kg/ m^3] , so heat capacity per volume is the same.
     c) effective coating's properties from multiple layers of SiO2 and Ta2O5
   thermal conductivity
 
2.3) Heat Transfer(ht)
         a) heat transfer in solid: all domains
         b) thermal insulation : only coatings' edge
        c) initial values: all domains are set at 310 K
         d) boundary heat source: at the topmost surface, Qin is defined in (1.1) (gaussian beam)
         e) surface to ambient radiation: all surfaces except coatings' side
              *for surface emissivity value, I have to choose User difined to be 0.75. I tried "from material"
                but it didn't work even though I add the surface emissivity in material property already, see (2.2)
2.4) Mesh
       - choose free tetrahedral, and specify size as you want, click build all.

3) study
    a) right click on study, select compute. Sit back, relax and enjoy the result.

4) Results
    a) 3d plot group1 shows a 3D picture
    b) 3dplot Group2 shows a slice
    c) 1D temp center axis shows a temperature plot along the center axis

I tried to separately mesh the geometry.

Only the small part (1/2 radius, 1/3 thickness) is extremely fine mesh, the rest is regular mesh, see fig1.

The result looks similar, with shorter time for calculation.

Also, the contact area between the mirror and the spacer

is modeled as a constant temperature (@ 35 C)boundary condition.

 The temperature profile across the surface,

nd the temperature difference along the depth due to RIN is plotted below.

The area under the curve for T,Z is 6.1e-9 [meter.Kelvin]

 Expansion coeff for SIO2 is 5.1e-7. Thus, dL = 3.1e-15m.

Use df/f = dL/L, L =0.2035m, we get df = 4.5 Hz.

As for thin coatings, I tried swept mesh, which creates prisms of quadrilateral surface.

However, when I ran the simulation, there are warnings about

ill-precondition from the size of the coatings.

After a talk with Greg's SURF student, he wrote a code similar to what I'm doing.

I'll try MATLAB code this time.

The configuration run:

I ran overnight PIDAutoTune with following parameters:
RelayAmplitude = 0.75 W
Offset = 0.25 W (So Differential Heater switches between -0.5W to 1W)
Setpoint = 34 MHz
Initial Differential Heater (Actuator) = 0 W
Common Heater = 0.5 W
Runtime = 15 hrs
This gave the following results:
Critical Gain, Kc = -12.27416
Critical Time Period = 84.3s (Note the reduction in time from the last measurement)
PID constants: Kp = -2.4548, Ki = -0.05824, Kd = -68.98078

Conclusions and next steps over the long weekend:

Today, I manually brought the frequency to near 27.3 MHz and switched on the PID with the estimated parameters. It looked like it was doing a good job except for momentary jumps in the actuation. This might be readout error or simply that we need some sort of LPF on the actuation calculation. Even 0.1s actuation on South heater causes a big problem because of huge change in current and because the south heater is a much more effective heater than north.

Just to check my hypothesis, I modified the PIDLocker_beta.py code to create a condition that actuation will be changed only if it is changing by less than 0.5 or if it has been asked to change in last two timesteps. I see that this successful in avoiding the harsh jumps. Now I'm running it to see how it works with an initial error of about 5 MHz. It is much more than I would like to start this PID (for reasons stated below) but I need to go for the weekend now.

Thoughts:

• In my opinion, since the PID parameters turned out to be so huge, they will properly work in small deviation from setpoint only. Definitely within ~50 MHz of setpoint which was maximum amplitude during Relay tuning.
• This also suggests that we probably cannot create an all regime working PID with our actuators. We simply need more ability to actuate if current cooling times are going to be constant for a faster convergence to the desired setpoint from far off place.
• I and Awade were discussing this yesterday. If we ant convergence to 27.34 MHz from initial points as far away as ~500-900 MHz, we need some artificially intelligent code.
• Not too intelligent though. In awade's words "we need something dumber than neural networks (because of the time involved in making and training them) and smarter than a PID".
• I'm thinking of a code which looks at higher derivatives than first, maybe up to the third derivative.
• If we get a code like this, which we can train during night times it might be a good thing to have to save about (6hrs to a day) while bringing the frequency to the desired point. I'll keep this at a lower priority for now though as we have other pressing issues to work on.