This is not such a bad base design, but remember that we have to get a couple of parts with the purple anodize to see if there is a difference between black and purple in terms of the 532 nm reflectivity.

[Kiwamu, Jenne]

We went this evening in search of a beat note signal between the Xarm transmitted green light and the PSL doubled green light. 

First, we removed our new ETMX camera (we left the mount so it should be easy to put back) from the other day.   We left the test masses exactly where they had been while flashing for IR, so even though we can no longer confirm, we expect that the IR beam axis hasn't changed.  We used the steering mirror on the end table to align the green beam to the cavity.  We turned on the loop to lock the end laser to the cavity, and achieved green lock of the arm.

Then we went to the PSL table to overlap the arm transmitted light with the PSL doubled light.  We made a few changes to the optics that take the arm transmitted light over to the PD.  We found that the arm transmitted light was very high, so we changed from having one steering mirror to having 3 (for table space / geometry reasons we needed 3, not just 2) in order to lower the beam axis.  We also found that the spot size of the arm transmitted beam was ~2x too small, so we changed the mode matching telescope from a 4x reducer to a 2x reducer by changing the 2nd lens from f=50mm to f=100mm (the first lens is f=200mm).  We made the arm transmitted beam and the PSL green beam overlap, but we saw no peak on the spectrum analyzer. 

We checked the temperature of the PSL and end lasers, and determined that we needed to adjust the set temp of the end laser.  However, we still didn't find any beat note.

We then tweaked the temperature of the doubling oven at the end station, to maximize the power transmitted, since Kiwamu said that that had worked in the past.  Alas, no success tonight.

We're stopping for the evening, with the success of reacquiring green lock of the Xarm.

 I summarized how we proceed our green locking in this month on the wiki.

Since step1 and 2 shown on the wiki are mostly done apparently, so we will move on to step 3-D and 3-E.

A short term target in the coming couple of days is to phase lock the VCO to the beat note.

 I connected the PLL signal to the ADC on c1ioo. 

So now we are able to take the data into the digital world, and will be able to feedback signals to the suspensions.

 The output signal from the VCO box goes to a black beakout board on 1X2 rack though a BNC cable.  

Then the signal comes out from the back side of the board with DB39 style, so I put a DB39 to SCSI adapter so that we can take it to the IO chasis.

Now the SCSI is connected to ADC_1 (the second ADC card) on the IO chasis at 1X1. 

  Additionally I modified the green locking simulink model, C1GCV, in order to pick the right ADC channels.

A medm screen for green locking is now under the construction. I put a link on the sitemap screen, so anyone can look at the half-baked green locking screen.

Any comments and suggestions are really welcome.

I realized that the black AA board I mentioned on the last entry has the same range issue as Valera reported before (see #3911). 

Basically our ADC card has +/- 10V input range, but on the other hand the AA board is already limited by approximately +/- 2V.

We have to fix it.

 [Suresh, Kiwamu]

  We did the following things:

     - installed a 1/10 voltage divider such that the signal won't be saturated at the AA board (see here)

     - put a Ithaco preamplifier 1201 as a whitening filter

     - checked the entire beat detection system without using the real beat note

Here are some items to be done before the sun goes down tomorrow:

       - calibration of ADC and the interfaces including the voltage divider and the whitening filter.

     - fine matching of unwhitening filter at the digital side

         - PLL response measurement ( freq to voltage response ) over the frequency range of interest

         - plotting an well calibrated spectrum of the PLL output 

(whitening filter)

The Ithaco 1201 was setup to have a zero at 0 Hz and two poles at 0.1 Hz and 10 Hz in order to emphasize the signal over the frequency range of interest.

Around 1Hz it is supposed to have a gain of 1000. These settings have done by tweaking the knobs on the front panel of the Ithaco 1201.

In addition to that, we made an unwhitening filter in digital filter banks. This filter was designed to cancel the analog whitening filter.

(system check) 

 To check the entire beat detection system, we phase-locked the VCO to a Marconi running at 80 MHz, which is the center frequency of the VCO.

Then we imposed a frequency modulation on the Marconi to see if the signal is acquired to ADC successfully or not. It's quite healthy.

According to the spectra corrected by the unwhitening filter, we confirmed that the noise floor at 1Hz is order of 1Hz/sqrt Hz, which is already quite good.

Then we took several spectra while putting a modulation on the Marconi at a different frequency in each measurement.

The peak due to the artificial modulation essentially works as a calibration peak in the spectra.

So in this way we briefly checked the flatness of the response of the system in the frequency domain.

As a result we found that the response is not perfectly flat in the range of 0.05 - 30Hz, probably due to a mismatch of the combination of the whitening and unwhitening filters.

We will check it tomorrow.

[Kiwamu, Suresh, Rana]

Our goal:

        We wished to determine the performance of the VCO PLL at low frequencies,. 

The procedure we followed:

        The scheme is to use the Marconi (locked to Rb Clock) as an 80MHz reference and lock to it using the PLL. 

        We set up the VCO PLL as in the diagram shown in the attachment and obtained the spectra shown below.

Results:

          We need to figure out the PLL servo gain profile in order to build the Inv PLL filter....

Damn. If this figure is true, we were looking at wrong signal. We should look at the feedback signal to the VCO.

[Rana, Suresh, Kiwanu]

 We did the following things:

   *  taking the VCO stability data from the error signal instead of the feedback

   *  tried calibrating the signal but confused

   *  increased the modulation depth of the green end PDH.

--

 We found that a cable coming out from the VCO box was quite touchy. This cable was used for taking the feedback signal.

When we touched the cable it made a big noise in the feedback. So we decided to remove the cable and take the signal from the error point (i.e. just after the mixer and the LPF.)

In order to correct that signal to the one in terms of the feedback signal, we put a digital filter which is exactly the same as that of the PLL (pole at 1.5 Hz, zero at 40 Hz, G=1) .

However for some reasons the signal shown in the digital side looked completely mis-calibrated by ~ 100. We have no idea what is going on.

Anyway we are taking the data over tonight because we can correct the signal later. The 2nd round data started from AM1:40

What is the point to use the error instead of the feedback? It does not make sense to me.

If the cable is flaky why we don't solder it on the circuit? Why we don't put a buffer just after the test point?

It does not make sense to obtain the error signal in order to estimate the freeruning noise without the precise loop characterization.
(i.e. THE FEEDBACK LOOP TRINITY: Spectrum, Openloop, Calibration)

RA: I agree that feedback would be better because we could use it without much calibration. But the only difference between the "error signal" and the "feedback signal" in this case is a 1.6:40 pole:zero stage with DC gain of 0 dB. So we can't actually use either one without calibration and the gain between these two places is almost the same so they are both equally bad for the SNR of the measurement. I think that Suresh and Kiwamu are diligently reading about PLLs and will have a more quantitative result on Monday afternoon.

I succeeded in green-locking the X arm by feeding back the beat signal to ETMX.

Here are some quick reports. Some more details will be posted tomorrow.

The below shows a time series data of the PLL feedback signal when the servo was acquiring the lock.

At t = -2 sec. I started feeding back the signal to ETMX with the gain 50 times smaller than its nominal.

Then at t = 0 sec.I switched on a low frequency boost (pole 0.1Hz and zero 1Hz) to make it more robust.

At t = 3 sec. I increased the gain to the nominal.

Finally the UGF became ~ 60 Hz according to my open loop measurement by diaggui.

However I couldn't make the UGF higher than 60Hz because the more gain caused a instability for some reasons.

Here is a diagram for the green locking.

I used the same VCO box as we setup on the last Friday (see #4189).

Very cool.

But the PLL seems very fishy to me. The ZP-3MH needs 13 dBm to operate correctly. You should change the MODLEVEL input of the VCO so as to make the LO input of the mixer go up to 13 dBm. Then the input from the PD should be ~0 dBm.

Also, the PLL diagram seems to show that you have a 1/f^2 loop: 1/f from the SR560 and 1/f from the Hz->rad conversion ??

Well... The ALS loop is engaged and the error was suppressed.
So, how is the IR error signal stabilized when the IR is brought in to the resonance?

I can see the linear trend of 0.1V/s from 5s to 10s.  This corresponds to 100kHz/s and 13nm
for the residual beat drift and the arm length motion, respectively. That sounds huge. The DC gain must be increased.

Well, the diagram I drew is true. I also have been confused by this 1/f^2 issue in our PLL.

As Rana pointed out, the open-loop TF should become 1/f^2 over most of the frequency range, but it still remains 1/f above 5kHz for some reasons. 

 Need more investigations.

 At the beginning I tried phase-locking the VCO to the beat note without any external filters (i.e. SR560 see here), but I never succeeded.

It was because the hold-in range of the PLL was not sufficiently wide, it could stay locked within frequency range of less than +/- 1MHz from the center frequency of 80 MHz.

This is obviously not good, because the beat note typically fluctuates by more than +/- 3MHz in time scale of 1 sec or so.

  So I decided to put an external filter, SR560,  in order to have a larger DC gain and a higher UGF.

Somehow I unconsciously tuned the SR560 to have a pole at 1Hz with the gain of 2000, which shouldn't work in principle because the open-loop will be 1/f^2.

However I found that the PLL became more robust, in fact it can track the input frequency range of +/- 5MHz.

The open-loop TF is shown above. For comparison I plotted also the open-loop TF wehn it's without the SR560.

I checked the frequency of the VCO output when it was phase-locked to a Marconi, it was healthy (i.e. the same frequency as the input signal from Marconi).

 I haven't yet taken any data for the IR fluctuation when the Xarm is locked by the green locking.

You are right, the DC drift was due to a lack of the DC gain. But don't worry about that, because this issue has been solved.

(DC gain issue)

  The lack of DC gain was because I put an IIR filter called ''DC block" that I made. It has 1/f shape below 30mHz and becomes flat above it.

The purpose of this filter was to avoid a DC kick when it starts feeding back to ETMX.

Usually the output signal from the PLL has an offset, typically ~5V, then this offset is also acquired into the ADC and eventually kicks ETMX through the feedback.

So when I took the time series data I enabled the 'DC block', that's why it drifts slowly.

 After taking the time series, I found that without this 'DC block' technique, the lock can be achieved by appropriately subtracting the offsets with epics numerical values.

This subtraction technique, of course, gave me more stable lock at DC.

(open loop transfer function)

Here is the open-loop TF of the arm locking I measured last night:

The IIR filter chain has the following poles and zeros:

     pole 0.1Hz, 1000Hz,

   zero 1Hz, 30Hz

For the fitting I assume that the ETMX pendulum has a resonance at 1Hz with Q of 5. Also I put the cavity pole at 24 kHz, assuming the finesse is 80 at 532 nm.

I just fitted the gain and the time delay by my eyes.

If I believe the result of the fitting, whole time delay is 330 usec, which sounds pretty large to me.

I scanned the X arm by changing an offset for the feedback to ETMX while the arm stayed locked by the green locking.

But the resultant plot is still far away from a beautiful one.

Changing the offset broke the lock frequently, so eventually I couldn't measure the stability of the IR-PDH signal at the resonance. 

 The plot above is a result of the scanning. You can see there is a clear resonance at the center of the plot.

However the lock frequently became unstable when I was changing the offset.

It looked like this unstability came from the end PDH lock. I guess there are two possible reasons:

  (1)  feedback range for the laser PZT is not wide enough. Right now the range is limited by a SR560, which has been used for a summing amplifier.

  (2)  Length to Alignment coupling. Pushing ETMX causes a misalignment.

The issue (1) can be easily solved by engaging the temperature feedback, which helps actuating the laser frequency a lot at DC.

The issue (2) will be also solved by well align the IR beam, the arm cavity and the green beam.

Here are some tasks that I want someone to work on during my absence.

1. Y-arm alignment for IR

 Basically we gradually have to move onto the Y-arm locking at some point.

Prior to it we need to align the Y arm for IR. Probably we have to touch PZT1 and PZT2.

It would be very nice if the X-arm alignment also gets improved together with this work. 

2. Temperature feedback with a digital control for X end PDH lock

  Need a temperature feedback not with an analog way but with a digital way because we want to put an offset and the feedback signal at the same time (#4198).

 Right now the temperature control input of the laser is connected to a slow DAC (#3850).

Probably we should plug the feedback signal from the PDH box to the fast ADC (i.e. c1iscex), and then connect a fast DAC to the laser temperature.

This entry maybe helpful.

3. Calibration of optical gain for IR arm locking

 In order to evaluate the performance of the green locking, one of the key points is the IR PDH signal.

Because it tells us how much the motion of the X arm is suppressed at IR when the green lock is engaged.

To get this information in m/sqrtHz, we need to know the optical gain.

4. MC servo characterization and PSL frequency noise measurement

 SInce the green beat note tells us the frequency difference between the MC and the arm in the current configuration, we should know how the MC servo is.

Along with this work, I need someone to measure the PSL frequency noise, when it is locked to the MC over the frequency range from 0.01Hz to 1kHz.

5. PLL characterization 

 Solve this issue (#4195) and make it reliable.

I implemented a slow servo for green laser thermal control on c1scx.mdl. Ch6,7 of ADC and ch6 of DAC are assigned for this servo as below;

Ch6 of ADC: PDH error signal

CH7 of ADC: PZT feedback signal

CH6 of DAC: feedback signal to thermal of green laser

Note that old EPICS themal control cable is not hooked anymore.

I made a simple MEDM screen(...medm/c1scx/master/C1SCX_BCX_SLOW.adl) linked from GREEN medm screen (C1GCV.adl) on sitemap.

During this work, I noticed that some of the epics switch is not recovered by autoburt. What I noticed is filter switch of SUSPOS, SUSPIT, SUSYAW, SDSEN, and all coil output for ETMX.

I had no idea to fix them, probably Joe knows. I guess other suspensitons has the same problems.

1. The dewhitening filter CH6 had no output. I disconnected the cable and put it to the monitor out of the AI filter.
So the dewhitening is not in the loop.

2. I have made a thermal control filter

BANK1: pole 0Hz, zero 1mHz / LF boost stage
BANK2: pole 1mHz, zero 30mHz / LPF stage
BANK3: pole 1Hz, zero 0.1Hz / phase compensation stage
Gain: 0.05

It seems working with the gain of 0.05. As the thermal is very strong, the output has less than 10.
This means the we are effectively only using ~4bit. We need external filter.

Note that output of 30000counts were about 3V at  CH6.

3. Measured End PZT feedback with and without the thermal control. The UGF seems to be 0.2Hz.
The suppression at 10mHz is ~100. This is so far OK.

Whether or not it's as clean as we'd like, it's really nice to see this result with real data.

Experiment in the night of Jan 26.

o The arm was locked for the IR beam and was aligned for it.
o The green was aligned to the arm
o The beat freq was observed with the RF analyzer and the webcam.
o Engaged the ALS servo
o Compared the fluctuation of the beat freq with and without ALS
o Scanned the beat freq in order to find an IR resonance

The beat freq was scanned. A resonance for IR was found.
However, the residual motion of the arm was not within the line width of the IR resonance.

 To Do
- Improve the ALS servo (==>Koji)
- VCO noise characterization (==>Suresh is on it)
- Calibrate the PLL feedback (i.e. ALS error) into Hz/rtHz (==>Suresh)
- Calibrate the end green PZT fb into Hz/rtHz (==>Osamu is on it)
- Tuning of the suspension filters to reduce the bounce mode coupling.

DETAILS

o How to lock the arm with IR

• Coarsely align the arm without lock. Transmittion was ~300 with MCTRANS ~40000
• REFL11I is the error signal. unWhiten filter (FM1) should be on.
• Unlock the MC and null the error and the arm trans offset by running the following commands

ezcaservo -g -0.1 -r C1:LSC-REFL11_I_OUTPUT C1:LSC-REFL11_I_OFFSET
ezcaservo -g -0.1 -r C1:LSC-REFL11_Q_OUTPUT C1:LSC-REFL11_Q_OFFSET
ezcaservo -g 0.1 -r C1:LSC-TRX_OUTPUT C1:LSC-TRX_OFFSET

• Confirm the input matrix to pass REFL11I to MC path (why don't we use XARM path...?)

ezcawrite C1:LSC-MTRX_81 1.0

• Servo configuration
  • For acquisition: Gain of 2. Only FM1 (1000:10) has to be on.
  • After the acquisition (TRX>200): The gain is to be changed to 1. FM2 and FM3 can be turned on for the LF boost.
• Actuator matrix: connect MC path to ETMX and MC2

ezcawrite C1:LSC-OM_MTRX_18 1.0
ezcawrite C1:LSC-OM_MTRX_78 1.0

o How to align the green beam

• After the alignment I went the end and aligned the last two steering mirrors.

o The beat freq monitor

• Put the RF analyzer at the RF splitter of the RFPD output.
• Used Zonet webcam (http://192.168.113.201:3037) for the remote monitoring

o How to engage the ALS servo

• Preparation:
  
  • VCO PLL feedback comes to X_FINE path.
  • Put an offset of -850 to cancel too big offset (when the VCO is unlocked)
  • Use Y_FINE channel for the offset addtion. FM1 is 10mHz LPF in order to make the offset smooth.
  • Add X_FINE and Y_FINE by the matrix.
• Control
  
  • Turn off X_FINE out. Leave Y_FINE output turned on.
  • Turn on ETMX ALS path.
  • Servo setting: FM1 1000:30 ON, others OFF, gain1
  • Wait for the beat comes in to the locking range at around 80MHz.
  • If the peak is too far, sweep Y_FINE offset in order to . Or change GCV slow thermal offset to let the beat freq jump.
  • You may have ambiguity of the feedback sign depending on which green has higher freq.
  • After the capture of the ALS lock, increse the gain up to 20. Turn on 0.1:boost at FM3.

o Comparison of the stability of the beat freq (Attachment3)

• The spectra of the VCO PLL feedback was measured.
• First of all, the signal was measured without ALS (blue).
  The PLL lost lock quite frequently, so the careful adjustment of the offset was necessary.Still I think there was slight saturation upconversion.
• Then, the ALS was turned on (red). The gain was 20. This is an in-loop evaluation of the servo. The suppression was ~1000 at 1Hz.

o Beat freq scanning

• The following command was used for the beat note scanning 

ezcastep -- "C1:GCV-YARM_FINE_OFFSET" "5,500"

• Once the IR transmission was found, the scan was stopped.
• Because the resultant rms stability of the arm was not within the line width of the cavity, the smooth resonant curve was not obtained.
• From the shape of the error signal the peak-to-peak displacement (f>1Hz) was estimated to be +/-0.7nm. The dominant displacement
  in the period is 16Hz component.

Joe and I built a very simple digital frequency to amplitude converter using the RCG. The input from an ADC channel goes through a filter bank (INPUT), is rectified and then split in two. One path is delayed by one DAQ cycle (1/16384 s) and then the two paths are multiplied together. Then the output from the mixer goes through a second filter bank (LP) where we can strip off twice the beat frequency. The DC output from the LP filter bank should be proportional to the input frequency.

Input Channel: C1:GFD-INPUT_xxx

Output Channel: C1:GFD-LP_xxx

Joe compiled the code and we tested it by injecting a swept sine [100, 500]Hz in the input filter bank. We confirmed that output of the LP filter bank changed linearly as a function of the input frequency.

The next thing we need to do is add a DAC output. Once that's in place we should inject the output from a 4kHz VCO into the ADC. Then we can measure the transfer function of the loop with an SR785 (driving the VCO input and looking at the output of the DAC) and play around with the LP filter to make sure the loop is fast enough.

The model is to be found here:

/opt/rtcds/caltech/c1/core/advLigoRTS/src/epics/simLink/c1gfd.mdl

The attached figures show the model file in Simulink and a realtime dataviewer session with injecting a swept sine (from 500Hz to 100Hz) into the INPUT EXC channel. We've had some frame builder issues so the excitation was not showing on the green trace and, for some reason, the names of the channels are back to front in dataviewer (WTF?), - the lower red trace in dataviewer is actually displaying C1:GFD-LP_OUT_DAQ, but it says it is displaying C1:GFD-INPUT_OUT_DAQ - which is very screwy.

However, the basic principle (frequency to amplitude) seems to work.

No signal is transmitted from C1:GCV-SCX_ETMX_ALS (on c1gcv) to C1:GCV-SCX_ETMX_ALS (on c1scx)

I can't find RFM definition for ALS channels in c1rfm. Where are they???

That's some pretty fast work! I thought we would be taking up to a week to get that happening. I wonder what's the right way to measure the inherent frequency noise of this thing?

Also, should the comparator part have some hysteresis (ala Schmidt trigger) or is it best to just let it twirl as is? Is it sensitive to DC offsets on the input or is there a high pass filter? What's the correct low pass filter to use here so that we can have a low phase lag feedback to the ETM?

We could try inputing a 4kHz carrier modulated width a depth of a few Hz at a modulation frequency of F1. Then we could take an FFT of the output of the discriminator and measure the width of the peak at F1 Hz. This seems like an arduous way to measure the frequency noise at a single frequency though.

It'll definitely be sensitive to DC offsets but there is already a filter bank on the INPUT filter so we can shape that as necessary. We could probably band-pass that from [4.5 - 5.3kHz] (which would correspond to a range of [73,87] MHz into a 2^14 frequency divider.

 One more thing ... we can calibrate the output of the LP filter to give a result in Hz with the following calibration:

LP_OUT = -1/(2*dt)*(LP_IN -1), where dt is 1/16384, the delay time of the delayed path.

Therefore LP_OUT = -8192*(LP_IN-1).

As you've correctly noted, the source of the C1:GCV-SCX_ETMX_ALS channels is in the c1gcv model. The first 3 letters of the channel name indicate this (GCV).

The destination of this channel is c1scx, the 2nd 3 letters indicate this (SCX). If it passed through the c1rfm model, it would be written like C1:GCV-RFM_ETMX_ALS.

This particular channel doesn't pass through the c1rfm model, because the computers these two run on (c1ioo and c1scx) are directly connected via our old VMIC 5565 RFM cards, and don't need to pass through the c1sus computer. This is in contrast to all communications going to or from the c1lsc machine, since that is only connected the c1sus machine by the Dolphin RFM. The c1rfm also handles a bunch of RFM reads from the mode cleaner WFS, since each eats up 3-4 microseconds and I didn't want to slow the c1mcs model by 24 microseconds (and ~50 microseconds before the c1sus/c1scx computer switch).

So basically c1rfm is only used for LSC communications and for some RFM reads for local suspensions on c1sus.

As for the reason we have no transmission, that looks to be a problem on c1ioo's end. I'm also noticing that MCL is not updating on the MC2 suspension screen as well as no changes to MC PIT and YAW channels, which suggests we're not transmitting properly.

I rebooted the c1ioo machine and then did a burt restore of the c1ioo and c1gcv models. These are now up and running, and I'm seeing both MCL and ALS data being transmitted now.

Its possible that when we were working on the c1gfd (green frequency divider model) on c1ioo machine we disturbed the RFM communication somehow. Although what exactly, I'm not sure.

I've had a go at trying to estimate the frequency noise of the digital frequency discriminator (DFD). I input a 234.5Hz (0.5Vpp) signal from a 30MHz function generator into the ADC. The LP output of the DFD measured 234.5Hz. However, this signal is clearly modulated by roughly +/- 0.2Hz at harmonics of 234.5Hz (as you can see in the top plot in the dataviewer screenshot below). So the frequency noise can be estimated as rms of approximately 0.2Hz.

This is supported by taking the spectra of the LP output and looking at the RMS. Most of the power in the RMS frequency noise (above the minimum frequency) comes from the harmonics of the input signal and the RMS is approximately 0.2Hz.

I believe this stems from the rather basic LP filter (three or four poles around 10Hz?) that is used in the LP filter to remove the higher frequency components that exist after the mixing stage. (The currently loaded LPF filter is not the same as the saved one in Foton - and that one won't load at the moment, so I'm forced to remember the shape of the current filter).

 The attached screen capture from data viewer shows the LP_OUT hovering around 234.5Hz.

A prototype freq divider has been made which works up to ~40MHz.

74HC4060 (14bit binary ripple counter) divides the freq of the input signal, which is comverted by the comparator LT1016
into the rectangular signal. The division rate is 2^14.

Attachment1: Circuit diagram

Attachment2: Photo, the prototype bread board

Attachment3: Photo, the spectrum of the freq divided output. The 40MHz input has been divided into 2.4k.
There are the 3rd and 5th harmonics seen. The peak was pretty sharp but the phase noise was not evaluated yet.

The circuit was made on the prototype bread board which is apparently unsuitable for RF purposes.
Indeed, it was surprising to see its working up to 40MHz...

In order to increase the maximum freq of the system we need the following considerations

• RF PCB board
• Input RF buffer (or amplifier) with a 50Ohm input impedance.
• Faster comparator. LT1016 has the response time of 10ns, which is not enough fast.
• Faster counter. Faster chip 74HC4020 has already been ordered.

 Here is the spectrum of the input into the DFD (a 234.5Hz sine wave, 0.5 Vpp) and the spectrum and RMS of the LP output. The linewidth of the input signal is clearly much less than 0.1Hz, where as the RMS noise (above 2mHz) is approximately 0.2Hz and the main contributions are clearly the harmonics of the 234.5Hz signal.

I added an MEDM screen for the DFD to the GREEN screen. It is displayed in the attached screen shot.

This screen is located in: /cvs/cds/rtcds/caltech/c1/medm/c1gfd/C1GFD_DFD.adl

This is a plot showing the old filters and the new ones we added this morning.

The new ones have a Cheby for AC coupling below 10 Hz and then a 500 Hz LP after the mixer. The LP frequency has been increased so that we can use this signal in a feedback loop to the ETM with a ~100 Hz UGF.

Joe injected a 234.567 etc. Hz sine wave into the excitation channel in the DFD INPUT filter. The spectrum of the output of the LP filter with the new filter is shown below with the RMS calculated from 300Hz down to 1mHz - see first attachment. The RMS is equal to about 2.5Hz. (Incidentally, the RMS is very much higher (slightly less than 400Hz - see second attachment) if you calculate it from 7kHz down to 1mHz). 

The freq divider was built and installed in the beat detection path.

Attachment 1: Circuit diagram

• Input stage:  Wideband RF amp with DC block at the input and the output. The gain is 10dB typ.
• 2nd stage: Ultra fast comparator AD9696. Note: AD9696 is an obsolete IC and there are only a few extra at Wilson house.
  The output is TTL/CMOS compatible.
• 3rd stage: 14bit binary ripple counter (fmax~100MHz.)

Note: I have added 7805/7905 regulators to the circuit as I could not find -5V supply on the 1X1/2 racks.

Attachment 2: Packaging

• The box is german made Eurocard size box from Techno-Isel Linear Motion http://www.techno-isel.com/lmc/Products/EnclosureProfiles11055.htm
  The box is excellent but I didn't like the fixing bolts as they are self-tapping type. I tapped the thread and used #6-32 screws.
   
• The prototyping board is BPS's (BusBoard Prototype System http://www.busboard.us/)  SP3UT. The card size is 160mm x 100mm.
  The other side is a ground plane and the small holes on the board are through holes to the ground plane.
  This particular card was not easy to use.
   
• The input is SMA. Unfortunately, it is not isolated. The output is an isolated BNC.
   
• The supply voltage of +/-15V is given by the 3pin D-connector. The supply voltages have been obtained from the cross connect of 1X1.

Attachment 3: Input specification

• The input frequency is 10MHz~85MHz. At lower frequency chattering of the comparator against the multiple zero crossing of the (relatively) slow sinusoidal waves.
• The input amplitude. There are no apparent degradation of the freq jitter when the input power was larger than -30dBm.

- The freq divider and Rana's PFD were hooked up to the ADCs. (Attachment 1)
(I leave the analog PFD not explained in this entry.)
For this purpose, the VCO feedback signal has been disconnected and the beat signal was moved from the VCO loop to the analog PFD.

The output level of the splitter was +12dBm and was too high for the freq divider.
So, I had to stupidly add an attenuator of 10dB before the box.

- Gain of the digital PFD LPF

The LPF of the digital PFD had the gain of -4096 to let the output signal indicate the direct frequency reading.

The gain has been changed to -67.108864
such that the output shows the direct reading of the beat freq in the unit of MHz

-4096*2^14/10^6 = -67.108864

- Attachment 2 shows the acquired beat note through the freq divider.
The blue is the beat note between "green locked" and "IR locked only to MC" (i.e. MC vs XARM)
The red is the beat note with the both beam locked to the arm

The freq divider is a bit flaky in some freq region as the divided output sometimes shows freq jumps or the captured at a freq.
I still don't know why it happens. We have to check why this happens.

The freq fluctuation of the beat note has been measured with the following condition

• The IR beam only locked to the MC. The green beam locked to the arm
• Both of the IR and green locked to the x-arm

Calibration
- The output of the freq divider is already calibrated to have the unit of MHz.

- The transfer function between the analog PFD channel and the digital PFD output was measured to be -23dB = 0.7.
  The gain of the XARM-FINE channel was changed to 0.7 such that the output is calibrated in MHz.

Results

- I have not checked the analog noise level of the analog PFD path. We may need more whitening gain (by icreasing the gain of SR560).

- The analog PFD is always better than the digital PFD above 20Hz.

- Both the digital and analog PFD showed good agreement below 20Hz.
  Note the measurement was not simultaneous.

- When the arm is locked with the ETMX being actuated , the fluctuation of the arm length must be stabilized by a huge factor
(~10^5 according to Kiwamu's entry) However, we only could see the stabilization factor of 30.

As this residual is the difference of the freq noise felt by the IR and the green,
this is a real issue to be tackled.

- The RMS fluctuations of the arm with and without the IR beam being locked are 2MHz and 0.1MHz,
which correcponds to the arm length motion of 250nm and 13nm, respectively.
Ed: I had to use 532nm in stead of 1064nm. The correct numbers are 130nm and 7nm.

- Without the IR locked, The typical peak-to-peak fluctuation of the beat freq was 10MHz.

I found that some flakiness of the beat signals comes from the RF components for the beat detection.
They are touching the racks in an indefinite way. If we move the components the output of the analog PFD
goes crazy.

Once Kiwamu is back I will ask him to clean up all of the green setting in an appropriate way.

This measurement pertains to the BL2002 VCO PLL unit.

Our goal is to measure the frequency fluctuations introduced by the VCO. 

First the VCO calibration was checked.  It is -1.75 MHz per volt.  The calibration data is below:

Next we measured the Transfer function between points A and B  in the diagram below using the Stanford Research System's SR785.  This measurement was done with loop opened just after the 1.9MHz LPF and with the loop closed.

The TF[open] / TF [closed ] gave the total gain in the loop.  As shown below:

Green curve is the Transfer Function with the loop open and the red with that of the loop closed.

Gain Shown below is the quotient TF[open]/TF[closed]

 c) As can be seen from the graph above the loop gain is >>1 over 0.1 to 300Hz.  And hence the frequency noise of the VCO is just the product of the voltage noise and the VCO calibration factor over this range,

d) the noise power at the point B was measured and multiplied by the VCO calibration  factor to yield dF(rms)/rtHz:

The green line with dots are the data

The blue line is the rms frequency fluctuation.

This corresponds to a arm length fluctuation of about 20pm.

Here's the reference for the self-reference frequency detection idea. See Figure 2.

http://www.phys.hawaii.edu/~anita/new/papers/militaryHandbook/mixers.pdf

 I did a quick back of the envelope calculation of the expected green phase change on reflection from the aLIGO ITM.

The phase change per nm, K1 = delta phi/delta Lambda, around 532nm is ~1.5 degrees/nm (from the LMA data) [this number is approximately 100x smaller at 1064nm]

I assumed that very small changes in the thickness of the coating appear equivalent to shifting the spectra for reflection/transmission/phase-change-on-reflection up or down by delta lambda, where

delta Lambda/Lambda = delta h/h

where h is the total thickness of the coating and delta h is the change in the thickness of the coating.

Assume that delta h/h = alpha deltaT, where alpha is the coefficient of thermal expansion and delta T is the change in temperature. (approximately 1K)

Then delta phi = K1* Lambda * alpha * delta T = 1.5 degrees/nm * 532nm * 10^-5 K^-1 * 1.0 K =  8 * 10^-3 degrees.

Assume that 360 degree phase change corresponds to one FSR.

Therefore, the frequency shift due to temperature change in the coating = 8*10^-3/360 * FSR = 2.2 *10^-5 * FSR.

Therefore, the expected frequency shift per degree temperature change = 2.2*10^-5 * FSR [Hz/K]

 Yesterday I moved the whole green electronics stuff, which had been sitting on the floor at the X end,  into a new electronics rack.

The rack now is placed under the cable rail close to the ETMX chamber.

Using a stray beam that is generated as the transmitted green beam from the Xarm goes through the viewport to the PSL table, I installed a fast lens (because I was constrained for space) and a Thorlabs PDA36 photodiode on the PSL table.

The BNC cable runs along the edge of the PSL table, up the corner hole with the huge bundle of cables, and over to IOO_ADC_0. It's channel 3 on the simulink model, which means that it is plugged into connector #4.

With the green resonating TEM00, I have ~1.4V output from the photodiode, as seen on a voltmeter. This corresponds to ~1500 counts on the MEDM screen.

Note to self:  Switch to a ~1cm diode with a boatload of gain (either from the 40m or Bridge), and use transmission through a steering mirror of the actual beat note path, not the jittery viewport pickoff.  Want RIN noise level to be about 1e-5, only care about below ~100Hz so don't need broadband.

 I repeated the same measurement as that Koji did before (see here) with the mixer-based frequency discriminator.

The frequency fluctuation of the beat note is now 50 kHz in rms integrated down to 0.1 Hz, which is a bit better than before.

However there still is the same undesired structure in the spectrum below 10 Hz.

Fig.1 power spectra of the green beat note fluctuation in terms of frequency fluctuation.

   Red curves were taken when the IR was locked to the MC, and the green was locked to the X arm.

Blue curves were taken when both the IR and the green were locked to the X arm.

Black curve was also the one taken when the IR and the green were locked to the X arm, but showing the lower noise level.

I have no idea what exactly was going on when I took the black curve, but this noise level sometimes showed up.

The discrepancy may come from a kind of calibration error although I kept using the same calibration factor to convert the data from count to frequency.

Need more investigations.

 Additionally Koji and I took the coherence between the beat fluctuation and the transmitted lights of both the IR and the green.

It showed a strong coherence at 1 Hz, which is one of the dominant noise of the beat note.

This probably indicates that the 1 Hz peak is produced by a coupling from amplitude fluctuation.

 For monitoring the green transmitted light, I used the Jenne's PD (see here)

The amounts of the X arm's beam off-centering have been measured by the A2L technique.

So now we are able to start aligning the IR beam axis in a quantitative way.

(motivation)

 Since we saw big residual motions at 1 Hz, 16 Hz on both the green beat note signal and the IR PDH signal (see #4268 and #4211),

we are suspecting that these noise come from an angle to length coupling.

In order to minimize the angle to length coupling, one thing we can do is to bring the beam spots to the center of ITMX and ETMX more precisely.

To do it, we have to quantitatively know how well the beam spots are on the center of the optics. Therefore I started measuring the amount of the beam off-centering.

(method)

 The A2L technique was used to measure the off-centering with the real-time lockin system, which has been recently embedded in the real-time code by Joe (see #4265).

The idea is the same as Yuta did before (see #3863).

But this time the excitation signal from the real-time oscillator was injected directly to the coil matrix on either ITMX or ETMX, at 18.13 Hz with the amplitude of about 400 cnt.

When the IR laser stays locked to the X arm, the LSC feedback signal is demodulated with the oscillator signal.

This demodulated signal gives the amount of the off-centering.

For this purpose I modified Yuta's A2L script such that we can use it also for the X arm.

(results)

 I obtained the following values:

     - ETMX

         PIT  = -1.61 mm

         YAW =  -0.918 mm

    - ITMX

         PIT = -3.76 mm

        YAW = -2.24 mm

I used the same calibration factor as that of Koji calculated (see #3020) for MC, in order to convert the results from the coil gain to the off-centering.

These values are consistent with the spots appearing on the CCD monitors.

[Koji and Kiwamu]

 We took transfer functions (TF) from the angle excitations at ETMX and ITMX to the green beat note signal (i.e. angle to length TF).

It turned out that the coupling from ETMX_PIT is quite large.

I wonder how f2p of the ETMX changes this coupling. We'll see.

The plot above shows a set of the transfer functions from the angle excitation to the green beat note.

Note that the y-axis has not been calibrated, it is just a unit of counts/counts.

You can see that the TF from ETMX_PIT to the beat (red cruve) is larger than the others by about a factor of 10 over most of the frequency range.

This means that any PIT motions on ETMX can be coupled into the green beat signal somewhat over the wide frequency range.

It looks having a resonance at 1.5 Hz, but we don't exactly know why.

At that time the coil gains on only ITMX were tuned by applying f2p filters, but ETMX wasn't because of a technical reason coming from epics.

- - - - measurement conditions

  * PSL laser was locked to X arm by feeding back the IR PDH signal to MC2.

  * the green laser was locked to Xarm as usual.

  * took the green beat note signal (approximately 0 dBm) into Rana's MFD with the cable length of about  6 m.

  * the output from the MFD was connected to XARM_COARSE channel without a whitening filter.

  * excitation signal was injected into either ASC_PIT or ASC_YAW. The excitation was Gaussian noise with frequency band of 10 Hz and amplitude of 300 counts.

  * only ITMY had the f2p filters, which balance the coil gains all over the frequency.

New noise spectra of the green locking have been updated.

The plot below shows the in-loop noise spectra when the beat signal was fedback to ETMX.

The rms noise integrated from 0.1 Hz to 100 Hz went down to approximately 2 kHz.

The red curve was taken when the beat was controlled only by a combination of some poles sand zeros on the digital filter banks. The UGF was at 40Hz.

This curve is basically the same as that Koji took few weeks ago (see here). Apparently the rms was dominated by the peaks at 16 Hz and 3 Hz.

The blue curve was taken when the same filter plus two resonant gain filters (at 16.5 Hz and 3.15 Hz) were applied. The UGF was also at 40Hz.

Due to the resonant gain filter at 16.5 Hz, the phase margin became less, and it started oscillating at the UGF as shown in the plot.

I did a quick calculation to determine the amount of sideband transmission through the FP cavity.

The modulation frequency of the end PDH is 216kHz. The FSR of the cavity is about 3.9MHz. So the sidebands pick up about 0.17 radians extra phase on one round trip in the cavity compared to the carrier.

The ITM reflectance is r_ITM^2 = 98.5% of power, the ETM reflection is r_ETM^2 = 95%.

So the percentage of sideband power reflected from the cavity is R_SB = r_ITM*r_ETM*(exp(i*0.17) - 1)^2 / (1 - r_ETM*r_ITM exp(i*0.17) )^2 = 0.85 = 85%

So about 15% of the sideband power is transmitted through the cavity. The ratio of the sideband and carrier amplitudes at the ETM is 0.05

So, on the vertex PD, the power of the 80MHz +/-200kHz sidebands should be around sqrt(0.15)*0.05 = 0.02 = 2% of the 80MHz beatnote.

Once we get the green and IR locked to the arm again, we're going to look for the sidebands around the beatnote.

Two different measurement have been performed for a test of the green locking last night.

Everything is getting better. yes. yes.

[ measurement 1 : IR locking]

The X arm was locked by using the IR PDH signal as usual (#4239,  #4268) .

The in-loop signal at from the IR path and the out-of-loop signal at from the green beat note path were measured.

Let us look at the purple curve. This is an out-of-loop measurement by looking at the green beat note fluctuation.

The rms down to 0.1 Hz used to be something like 60 kHz (see here), but now it went down to approximately 2 kHz. Good.

This rms corresponds to displacement of about 260 pm of the X arm. This is barely within the line width. The line width is about 1 nm.

[ measurement 2 : green locking]

The motion of the X arm was suppressed by using the green beat signal and feeding it back to ETMX.

After engaging the ALS servo, I brought the cavity length to the resonance by changing the feedback offset from epics.

Then took the spectra of the in-loop signal at the beat path and the out-of-loop signal at the IR PDH path.

 Here is a time series of TRX after I brought it to the resonance.

TRX was hovering around at the maximum power, which is 144 counts.

Since I put one more 10:1 filter to suppress the noise around 3 Hz, the rms of the in-loop beat spectrum went to about 1 kHz, which used to be 2 kHz (see #4341).

But the out-of-loop (IR PDH signal) showed bigger noise by a factor of 2 approximately over frequency range of from 2 Hz to 2 Hz. The resultant rms is 2.7 kHz.

The rms is primarily dominated by a peak at 22 Hz (roll mode ?).

I calibrated the IR PDH signal by taking the peak to peak signal assuming the finesse of the cavity is 450 for IR. May need a cooler calibration.

I forgot to mention about the whitening filter for the ALS digital control system.

As usual I used a whitening filter to have a good SNR against ADC noise, but this time our whitening scheme is little bit different from the usual our systems.

I used two ADC channels for one signal and put a digital summing point  and digital filters to keep good SNR over the frequency range of interest.

It's been working fine but it's still primitive, so I will study more about how to optimize this scheme.

     The diagram above shows our scheme for the signal whitening.

Basically the SNR at DC is bad when we use only a whitening filter as shown on the bottom part of the diagram because the signal is quite tiny at DC.

On the other hand if we take raw signal into ADC as 'DC path'  shown above, the SNR is better at DC but not good at intermediate frequencies (30 mHz - 1kHz).

So the idea to keep the good SNR over the frequency range of interest is to combine these 'DC path' and 'AC path' in a clever way.

     In our case, the 'DC path' signal is not as good as the 'AC path' signal above 30 mHz, so we cut off those high frequency signals by using a digital low pass filter.

In addition to it, I put a gain of 1000 in order to match the relative gain difference between 'DC path' and 'AC path'.

Then the resultant signal after the summing point keeps the good SNR with a flat transfer function up to 1 kHz. 

In this past weekend I replaced a summing amplifier for the end green PDH locking by a home-made summing circuit box in order to increase the control range.

It's been working well so far.

However due to this circuit box, the demodulation phase of the PDH locking is now somewhat different from the past, so we have to readjust it at some point.

(background)

    At the X end station, the voltage going to the NPRO PZT had been limited up +/- 4 V because of the summing amplifier : SR560.

Therefore the laser was following the cavity motion only up to ~ +/- 4 MHz, which is not wide enough. (it's okay for night time)

So we decided to put a passive circuit instead of SR560 to have a wider range.

(summing box)

   We made a passive summing circuit and put it into a Pomona box.

The circuit diagram is shown below. Note that we assume the capacitance of the 1W Innolight has the same capacitance as that of the PSL Innolight (see #3640).

The feedback signal from a PDH box goes into the feedback input of the circuit.

Then the signal will be low passed with the corner frequency of 200 kHz because of the combination of RC (where R is 681 Ohm and C is capacitance of the PZT).

Because of this low pass filter, we don't drive the PZT unnecessarily at high frequency.

On the other hand the modulation signal from a function generator goes into the other input and will be high passed by 50 pF mica capacitor with the corner frequency of 200 kHz.

This high pass filter will cut off noise coming from the function generator at low frequency.

In addition to it, the 50 pF capacitor gives a sufficient amount of attenuation for the modulation because we don't want have too big modulation depth.

Here is a plot for the expected transfer functions.

You can see that the modulation transfer function (blue curve) has non-zero phase at 216 kHz, which is our modulation frequency.