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ID Date Author Type Category Subject
1066   Wed Oct 24 20:22:01 2012 taraDailyProgressNoiseBudgetThermoelastic noise in spacer

I used COMSOL to estimated thermoelastic noise in 1.45" spacer.  The noise is not significant for our coating Brownian measurement. I still need to verify the model with some analytical estimation.

• The model is 1/8 of the spacer with symmetry boundary condition on each cut surface.
• The applied force is a quarter of an annulus, 2 mm width. This annulus represents the contact area between the substrate and the spacer.
• The deformation is simulated, and its gradient is calculated by COMSOL and integrated over the volume (1/8 of the cavity).
• I followed the calculation on Liu and Thorne, 2000, and get thermoelastic noise from spacer. It is lower than coating's Brownian noise at least 1 order of magnitude and will not be a limiting source for us. The plot below show spacer' TE in black dashed line.

Note:

• I should compare the simulation result with an analytical result, but I'll do that later in parallel with other work. This is not an urgent one. I'll also try to reproduce the result reported by Kessler et al. about Brownian noise in spacer as well. Then calculate the Brownian noise in our cavity.
• I'll check the spacer's TE noise for our previous 8" cavity to make sure that there is consistent with the result.
1073   Mon Nov 12 22:56:10 2012 taraNotesNoiseBudgetThermoelastic noise in spacer and substrate

I'm checking the calculation for TE noise in substrate and spacer. I'm comparing the results from analytic calculation and simulation. The results still do not agree. Comsol gives a result ~ a factor of 4 lower than its analytical counterpart.

Since the TE noise in substrate will be significant in AlAs/GaAs mirrors, the TE noise estimation should be correct. The TE calculation in substrate was done by (BGV, Liu and Thorne, and Cerdonio). The correction was noted in Numata 03 and Black 04 papers.  I think the calculation is well established because the calculations from all of the papers agree (with all corrections taken into account). So It will be nice if an FEA simulation predicts the similar result as well.

I followed the calculation done by Kessler etal paper where they calculated the Brownian noise in spacer. The mirror-spacer assembly is pushed by a static force with Gaussian profile, P = 2 F0 / (pi*w0^2) * exp(-2r^2/w0^2), where w0 is the spot radius = 182 um for 1.45" cavity with 0.5 mRoC mirrors, at r = w0, intensity drops by 1/e^2, F0 is the magnitude of the force (1N for my simulation) .

1.    I simulated 1/8 of the cavity which is cut by xy,yz, and zx planes.
2. Then I used COMSOL to calculated (gradient of expansion)^2,  (expansion = divergence of displacement in the body),
3. integrated over the calculated body. (get 4.18x10^-12)
4. Then multiplied by  8 to include all the sections of the cut cavity,
5. multiplied by 2 for double cavities,
6. divided by 2 for averaging the dissipated power over 1 period.
7. then followed the calculation given by Liu and Thorne. The result is still lower than the analytical model.

Note about COMSOL: I used extra fine mesh in a small volume where the beam hits the mirror, fine mesh in the rest of the substrate, and normal mesh in the spacer. This reduced the memory used in the calculation a lot and should not introduce a lot of error, since all the deformation will concentrate near the beam spot.

1074   Tue Nov 13 01:56:24 2012 taraNotesNoiseBudgetThermoelastic noise in spacer and substrate

I realized that the mesh size was too large, even with the finest mesh for default setting. So I reduced the mesh size around the beam area and the results got closer to the analytical prediction. It is still a factor of 2 below the prediction. I'll see if I can hunt down this problem . I think it will be a good idea to verify my model by using my model to calculate Brownian noise and comparing with the result reported by Braunschwig group.

When I defined mesh size in COMSOL, I used the predefined value provided by COMSOL. The finest mesh has maximum element size ~500 um, and minimum ~5um. Since the beam size is ~ 180 um, the maximum element size should be ~10 um. So I changed the values around, defined new area for smaller mesh until the results did not change much. I ran the simulation a few time to make sure that the solution converges. Right now my substrate has 3 regions

1. a cylinder at the center where the beam hits the mirror, Radius = 2x180um, depth=2x180um ,   Min/Max mesh size = 12.6/27 um
2. an outer region, radius = 5x180um, depth = 5x180 um, min/max mesh size = 10/50 um
3. The rest of the substrate, fine mesh

I tried to change the mesh size/boundary size a bit to get the result accurate enough without taking too much time. The TE estimation still a factor of 2 below the analytical estimate.

1076   Wed Nov 14 19:46:47 2012 taraNotesNoiseBudgetThermoelastic noise in spacer and substrate

Found the problem. My noise budget code was wrong. So after I fixed it, the TE noise in substrate result from COMSOL agrees pretty well with the analytical result (within 20%).

The result from COMSOL is plotted in dashed-black line. The result from Cerdonio is plotted in dashed pink.  Since my simulation uses the adiabatic assumption (used in BGV and Liu&Thorne paper), the results agree at high frequency. So I think the calculation is correct. I'll check some options (changing spot size, changing material) to see if TE noise can be made lower for AlAs/GaAs samples.

I attached my COMSOL file below. This is done in 3D model. It could have been done in 2-D axis symmetric setting, but I used 3-D for spacer sagging before, so I just used the same geometry I had.

 Quote: I realized that the mesh size was too large, even with the finest mesh for default setting. So I reduced the mesh size around the beam area and the results got closer to the analytical prediction. It is still a factor of 2 below the prediction. I'll see if I can hunt down this problem . I think it will be a good idea to verify my model by using my model to calculate Brownian noise and comparing with the result reported by Braunschwig group.  When I defined mesh size in COMSOL, I used the predefined value provided by COMSOL. The finest mesh has maximum element size ~500 um, and minimum ~5um. Since the beam size is ~ 180 um, the maximum element size should be ~10 um. So I changed the values around, defined new area for smaller mesh until the results did not change much. I ran the simulation a few time to make sure that the solution converges. Right now my substrate has 3 regions a cylinder at the center where the beam hits the mirror, Radius = 2x180um, depth=2x180um ,   Min/Max mesh size = 12.6/27 um an outer region, radius = 5x180um, depth = 5x180 um, min/max mesh size = 10/50 um The rest of the substrate, fine mesh I tried to change the mesh size/boundary size a bit to get the result accurate enough without taking too much time. The TE estimation still a factor of 2 below the analytical estimate.

1079   Tue Nov 20 11:50:29 2012 ranaNotesNoiseBudgetThermoelastic noise in spacer and substrate

What is the reason for the COMSOL TE noise to diverge from the analytic one at low frequencies?

Don't you have to consider the coherent TO noise between the coatings and the substrate?

1080   Wed Nov 21 20:16:55 2012 ranaNotesNoiseBudgetThermoelastic noise in spacer and substrate

 Quote: What is the reason for the COMSOL TE noise to diverge from the analytic one at low frequencies? Don't you have to consider the coherent TO noise between the coatings and the substrate?

At low frequency, the adiabatic approximation (used by BGV, Liu & Thorne) breaks down. Basically, it assumes that heat inside the material is not diffusive. The only place that heat flow must be considered is in the volume integral where gradient of expansion is non zero for the dissipation. (see Liu & Torne explanation just above eq 8). This is easier for COMSOL simulation. Since I just press the substrate with static force, and calculate the deformation of the body which, under adiabatic approximation, gives me the temperature change of the body.

If I want to take into account the heat flow, I have to (see Cerdonio)

• solve The stress balance with temperature dependent and
• solve heat equation with expansion dependent (these two equations are coupled).

Then for COMSOL simulation I have to use different setting and I'm not exactly sure how to do this yet.

1081   Mon Nov 26 15:36:46 2012 ranaNotesNoiseBudgetThermoelastic noise in spacer and substrate

If the Cerdonio paper is correct, then just use those equations instead of the Thorne ones.

1082   Tue Nov 27 05:30:03 2012 ranaNotesNoiseBudgetThermoelastic noise in spacer and substrate

 Quote: If the Cerdonio paper is correct, then just use those equations instead of the Thorne ones.

I usually use Cerdonio's in the noise budget. But I used Thorne's to compare with COMSOL result because of the same adiabatic assumption.

1083   Tue Nov 27 05:38:01 2012 taraNotesNoiseBudgetThermoelastic noise in spacer and substrate

I calculated brownian noise in AlAs/GaAs coatings, brownian noise and thermoelastic noise in fused silica substrate for different beam sizes. From the plot, we can see that a smaller spotsize might be better for us.

This is a quick study to see the how spotsize on a mirror affects Brownian noise and thermoelastic noise in coatings and substrate. The radii of the beam (where the beam intensity drops by 1/e^2) used in the calculation are 91, 182, 364 um. Loss in coatings is 10^-5, loss in substrate is 10^-7. Note for 1.45" cavity with 0.5m RoC mirrors, the beam radius is 182 um.

Reminders:

• The plot is shown in displacement noise, not frequency noise from cavity.
• The psd (m^2/Hz) of coating Brownian noise is proportional to 1/w^2 (w is the beam radius)
• The psd of substrate Brownian is proportional to 1/w
• The psd of substrate thermoelastic is proportional to 1/w^3 ,at high frequency where adiabatic assumption valids. But at low frequency, when heat diffusive flow rate is comparable to the beam radii, TE noise is reduced from that of adiabatic assumption.

The Brownian noise in the coatings is more comparable to TE noise in substrate with smaller beam size although the crossing between the two noises are at higher frequency. So it should be able to see the total noise from both effects. However, to get smaller beamsize, we probably have to use even shorter cavities, or smaller RoC mirrros. So it might not be practical for us.. Nevertheless, going to smaller beam size should  be a good idea.

Note:

• for 1.45" long cavity, no choices of RoC give w = 92 um,
• for mirror with RoC = 0.5m, cavity length of 0.1 inch(2.5 mm) gives w = 92 um
• I think I made a mistake in the proposal since Brownian noise in substrate was higher than coatings' noise. I double checked it for this calculation and Brownian noise in substrate is always lower than coating brownian.

2356   Fri Jun 7 17:42:06 2019 anchalDailyProgressBEATThree Corner Hat Method

A wise man told me to use three corner hat method to extract individual frequency noise information of Marconi, Moku and the Wenzel crystal. I updated my mokuReadFreqNoise.py to support frequency noise calculation for two channels and their difference.

I'm perplexed to see the result actually and I'm not sure if this is what was expected.

### Measurement details:

I did two identical runs (I wasn't sure if I was seeing the truth from my first run) with the following settings:

• Both Marconi and Moku are directly connected to Rb 10 MHz clock with equal length cables.
• Wenzel Crystal 500-13905 oscillating at 24.4835 MHz was connected to input 1 of Moku.
• Marconi with set to same frequency was connected to input 2 of Moku. Note that modulation feature was not on in this experiment so the expected noise is lower than CTN:2286 experiment.
• With two channels recording, the acquisition rate is 15.625 kSa/s only.

### Analysis:

• In the first plot, I just plotted the frequency noise of input 1 (Wenzel), input 2 (Marconi) and (input 2 - input 1) using mokuReadFreqNoise.py. Although I have checked this code multiple times, I really want a new set of eyes to go through it and confirm it is calculating this correctly.
• I assumed that the difference between two channels will have negligible frequency noise of Moku itself and is a good approximation of frequency noise between Wenzel and Marconi.
• In the second plot, I used the 3 corner hat method to calculate individual frequency noise ASDs of the three instruments. Some points are missing as the sum of two contributing PSDs was lower than non-contributing PSD at some points.
• In the third plot, to disregard the assumption I have made above, I used data from CTN:2286 experiment. Remember though that in this experiment, modulation was on at 500 Hz/V actuation slope.
• In the fourth plot, I used 3 corner hat method again but with CTN:2286 experiment data.

### Implications:

• Well clearly the 4th plot is useless. It is comparing two different versions of Marconi data, so it is essentially blurring out all data.
• From 2nd plot, if this experiment was meaningful, even though Moku seems an order of magnitude more noisy than Marcon (which is just freely running), Moku's frequency noise is less than 2 mHz/rtHz upto 400Hz and if we ignore the bump at 500 Hz as some experimental artifact, is less than 3 mHz/rtHz upto 1 kHz. Expected coating brownian noise is between 4-10 mHz/rtHz from 100Hz-400Hz region.
• Ideally, we would like an order of magnitude lower instrument noise than what we are trying to measure. So maybe Moku is not a good choice.
• But I still am not sure if I should take strong inferences from this experiment because when I do low acquisition and use Moku's inbuilt frequency noise ASD plotter, I get results as attachment 3 which is also a check of how good my code computes the ASD.
• This graph shows that the difference spectra is growing above 100 Hz contrary to previous results. This would mean that the frequency noise of moku is least above 100 Hz.  But that is not the case when I do a fast acquisition.
• So overall, after today's efforts, I'm back to square one. I'm not sure if Moku should be used for frequency noise measurement
1767   Wed Nov 9 17:43:59 2016 awadeSummaryTempCtrlThree wire temperature sensor circuit for shields

At some stage we will need to install new temperature sensors on the thermal shields.  Tara et al. had installed AD590s in vacuum (and did a similar thing for the pervious longer cavities), these are now broken. They give currents proportional to applied voltage in the forward direction (see: PSL:1173). One theory is that they were overheated during soldering. Another possibility is that that the ICs didn't fare well in vacuum.  Either way it would be best to have passive components that we know are vacuum compatible and low noise.

Previous rana post here on temperature sensor noise plots: PSL:1205

We need a robust low noise circuit to turn resistance into a ADC usable voltage.  I've attached a sketch below. It uses a IC dual current source regulator (REG200) and a low noise instrument amplifier (AD620) to convert resistance of a PT100 sensor (like the one used in the TCS, see PSL:1700 and subsequent posts) in a three wire scheme. I've yet to compute a noise budget, for now I've penciled in some specs for noise I've drawing from their data sheets. This scheme would require three wires per sensor (but it might be possible to double up the grounding line between sensors).

Note: the R1 resistor provides an offset so that the Vout is within a useable range for high gain. R_g sets gain, where G = 49.4kΩ/R_g +1.

edit: added not on function of R1 and R_g - awadeWed Nov 9 17:47:14 2016

1778   Tue Nov 29 23:17:14 2016 awadeDailyProgressTempCtrlThree wire temperature sensor circuit for shields

I've now built this circuit out onto a small breadboard patterned proto-board as a tester.  It is configured with a offset resistor of 7.31 kΩ and a AD620 gain resistor of 9.7kΩ (I would have liked 10kΩ but we're out). The intention is to intitially test its performance for 10kΩ thermister (I have one from the PSL lab), we may eventually go for the standard Pl 100Ω RTD. The only thing that will need to change is the offset resistor and the gain at the instrument amplifier stage. The board has +/- 15 V regulators and another step down to +5V with similar 0.1A regulators. Seems a bit crude to voltage adjust like this but the datasheet suggests it should still have good rejection and the REF200 chip offers a further stage of supply noise rejection.

I'm debating whether I should add a sallen-key style active LP filter. Maybe at 1 Hz.

 Quote: At some stage we will need to install new temperature sensors on the thermal shields.  Tara et al. had installed AD590s in vacuum (and did a similar thing for the pervious longer cavities), these are now broken. They give currents proportional to applied voltage in the forward direction (see: PSL:1173). One theory is that they were overheated during soldering. Another possibility is that that the ICs didn't fare well in vacuum.  Either way it would be best to have passive components that we know are vacuum compatible and low noise.   Previous rana post here on temperature sensor noise plots: PSL:1205 We need a robust low noise circuit to turn resistance into a ADC usable voltage.  I've attached a sketch below. It uses a IC dual current source regulator (REG200) and a low noise instrument amplifier (AD620) to convert resistance of a PT100 sensor (like the one used in the TCS, see PSL:1700 and subsequent posts) in a three wire scheme. I've yet to compute a noise budget, for now I've penciled in some specs for noise I've drawing from their data sheets. This scheme would require three wires per sensor (but it might be possible to double up the grounding line between sensors).    Note: the R1 resistor provides an offset so that the Vout is within a useable range for high gain. R_g sets gain, where G = 49.4kΩ/R_g +1.   edit: added not on function of R1 and R_g - awadeWed Nov 9 17:47:14 2016

2326   Wed Apr 24 16:01:55 2019 anchalDailyProgressFSSTime series and spectrum analysis of RFout of SCavReflRFPD near resonance

I took time series and spectrum of RF output of South Cavity Reflection RFPD through a 20 dB coupler.

### Time Series Measurement Setup:

• The RFout port of South Cavity Reflection RFPD SN010 was connected to IN port of ZFDC-20-5-S+. OUT port of the coupler is connected to TTFSS box's PD input port.
• The CPL port of the coupler was connected to CH3 in TDS3034C oscilloscope at 50 Ohm input impedance and probe set to 10x to compensate for 20 dB loss in coupling and have  a real estimate.
• CH1 of the oscilloscope is connected to the output of Cavity Transmission Photodiode.
• CH2 of the oscilloscope is connected to OUT1 port of TTFSS box, which is connector J1 in D040105. This is supposed to be 0.36 times the RF amplitude level measured with 50 Ohm termination (hence voltage divided after final RF opamp stage in RFPD).
• CH4 of the oscilloscope is connected to Mixer output port of FSS which is at the output of the first common amplification stage in D040105. This is supposed to be 3.16 times OUT1 value.
• I scan the laser pzt near resonance at 2 Hz with 2 V peak-to-peak sine wave. Incident light on the RFPD was measured as 2.95 mW.
• Except for first two measurements which were triggered by transmission peak, I triggered the rest of the measurements by PDH error signal peak.

### Analysis:

• First, I just triggered the data capture with a wide 400 ms capture (Sampling rate of 25 kSa/s). I found that RFout level is 210 mVpp instead of expected 1.495 Vpp. OUT1 level was 53 mVpp (which ideally should be 75 mVpp given 210 mVpp RFout level). Mixer out level is as expected so the first stage common amplification is definitely good.
• Next, I zoomed into 250 kSa/s because very clearly there were some oscillations. It seemed like there was a strong ~240Hz oscillation in RFout. This oscillation is quite big too, almost 100 mVpp. But at this point, I'm not really sure if this was an artifact of using a coupler.
• Next, I zoomed in further in time scale going to 250 MSa/s sampling rate. In a 40 us snap, I saw another amplitude modulation. This time it corresponded to 290 kHz.
• Next, wanting to see 37 MHz signal, I zoomed into 1 GSa/s where 10 us snap clearly shows this 290 kHz amplitude modulation.
• Zooming into this 1GSa/s data, I can see 37 MHz sine wave. I saw some sharp features near the edges.
• So to be sure, I zoomed into 5 GSa/s where I saw the sine wave better. Near the top, there are no sharp edges but still, it is not nicely curved. The bottom definitely looks sharper than top. But these minute defects in the RF signal could be due to oscilloscope quantization error or something else.

Clearly, I needed to see what other frequencies are there in this RFout signal. So I decided to take a spectrum of the signal.

### Spectrum measurement setup:

• I connected the transmission photodiode signal to the external trigger input of HP4395A (this is in the back). I couldn't get the analyzer to trigger with PDH error signal, so I had to use the transmission peak.
• I connected the CPL port form the coupler to the spectrum analyzer directly which always has 50 Ohm input impedance.
• Later I realized I do not need to do this as I am anyways not using down converted signal from FSS for triggering or anything. But I decided to keep going to keep the two measurements consistent.
• Hence, in the analysis, I added 20 dBm in the measured output to compensate for coupler loss.
• All measurements were taken with automatic IF bandwidth setting, so it changes according to span and is marked in the graphs. I took 100 averages in all the measurements which were triggered individually by transmission peak. So measurements were roughly taken over 100s.

### Spectrum analysis:

• First I took a wide scan to get a relative idea of important frequency peaks. I see that 37 MHz is the most dominant frequency (thankfully) at -30.71 dBm, which corresponds to 20 mVpp.
• The reason this value is so small is that the FFT is taken over 281.3 ms which is over a quarter cycle in PZT scanning. So triggering from transmission peak, this must be the spectrum of the region where the PDH error signal has died out mostly. I know this measurement sounds stupid at this point, but I realized this in hindsight only. Still, we get an idea of other frequencies present. I have a better plan too which is about to come in the next post.
• Second in the race is a peak at 36.72 MHz at -40.66 dBm. I think this is because the SN010 RFPD actually has its peak at 36.67 MHz and not 37 MHz and the EOM driver on the south path doesn't have a sharp resonance and has about 2-3 dB gain at 36.67 MHz, so that's why we are seeing this another peak (my guess).
• Third, in line is 29.5 MHz peak at -45.62 dBm. This is the second harmonic of RFAM (RAM for people who prefer this) of EOM behind South PMC used of PDH of PMC. This surprisingly leaks through the PMC and I have not been able to tune it down passively.
• Next, I took a board spectrum from 0-500 kHz to spot that 290kHz we saw in time series data. Indeed there is a peak at 281 kHz of -66.36 dBm. This looked like a bigger oscillation in time series (~50 mVpp => -22 dBm but again, this data taking method is not really good). There are other nearby peaks at ~269 kHz and 2~284 kHz. I'm not sure why these peaks are here. But they can not be some standing wave in the cable as it will require ~700m long cable.
• There is some more activity near 60 and 70 kHz of ~-60 dBm again.
• In the very low side, I took a broad spectrum up to 1 kHz and we see a horrifying comb of 60 Hz harmonics with 180Hz and 60 Hz being the dominant once. But the magnitudes in this measurement do not make much sense in my opinion.
• And then I realized, I forgot to take spectrum near 14.75 MHz (the frequency of PMC PDH lock) but then the triggering stopped working. I guess the temperature in the lab changed and the intensity of laser changed slightly enough to make transmission peak low. That's my theory, but I do not know for sure why triggering stopped working. It was a very clunky way of doing science anyways :(

### Some conclusions:

• Well, clearly the RF output is indeed not strong enough from this RFPD (7 times smaller actually).
• The shape of 37 MHz wave is also questionable. There are many dominant other frequencies in this signal. Need better measurements.
• The draconian 60 Hz harmonics family is here as well. However, I hope after down conversion, it doesn't matter much.

### Better measurements?

• To be honest, I wished I took the spectrum in a cleaner way, exactly knowing where I am triggering and what part of time series data is being Fourier transformed.
• So I started making a TTL triggering box for the same. See next post for details.
• Next, I'll reduce PZT scan frequency and maybe FFT points and take a quick FFT around the PDH error signal peak only using my new trigger box.

2328   Fri Apr 26 14:34:03 2019 anchalDailyProgressFSSTime series and spectrum analysis of RFout of SCavReflRFPD near resonance

I think I figured the source of this 281 kHz peak. 281 kHz  ≈ 37 MHz - 36.72 MHz, so it is the beat signal between 37 MHz and the 36.72 MHz signals. I think I should tune the RFPD more next time I open the cage to bring its resonance closer to 37 MHz.

 Quote: Next, I took a board spectrum from 0-500 kHz to spot that 290kHz we saw in time series data. Indeed there is a peak at 281 kHz of -66.36 dBm. This looked like a bigger oscillation in time series (~50 mVpp => -22 dBm but again, this data taking method is not really good). There are other nearby peaks at ~269 kHz and 2~284 kHz. I'm not sure why these peaks are here. But they can not be some standing wave in the cable as it will require ~700m long cable.
2380   Tue Jul 30 15:56:15 2019 ScottADailyProgressRFAMTime series for AC Port of RAM Measurement

This is the time series from the AC port of the 1811 new focus photodiode which is set up for RAM measurement. A strange waveform is present, it has a peak to peak voltage of around 2.9 V and a frequency of around 60 kHz.

2381   Wed Jul 31 17:53:20 2019 ranaDailyProgressRFAMTime series for AC Port of RAM Measurement

## to find out why

2273   Fri Jan 4 19:04:29 2019 awadeDailyProgressRFAMTime to look at RF AM and RIN

That roll up in the HF range to 3 kHz hump looks suspect.

## PLL?

We need to check that we're actually implementing the PLL properly and unwrapping the BN PSD properly from the actuation signal.  You could end up from a result like this if the UGF was, say, ~ 1 kHz: then the PSD * (marconi slope) approximation will no longer be true and would look more like PSD * (marconi slope + 1/Mix*SR560).  As demodulation for PLL frequency gives a 1/f in closed loop (from freq->V_out), this would give a roll up directly proportional to frequency around and above UGF when inverting. We should go back and check again that the transfer function measured yesterday of the PLL had a UGF of >60 kHz. You should remeasure the PLL open loop gain and post it on the elog. Make sure you use a small excitation signal and play around with the cycle averaging settings to smooth out noise for a nice clean trace. Also a schematic of exactly where signals are injected, values of gains, slopes and mixer conversion efficiencies (spec sheet value will do) and RF power from beat note detector.

You'll also way to check that you're not saturating the NF1811.  You don't want weird artifacts from not being linear in response at RF... slew rate limit etc. Details of internals of NF1811 can be found in the PSL Electronics Wiki.

## Just Marconi noise?

Also see figure 4.8 of Tara's thesis.  I'm having trouble making out the colours but there is peaking there in the marconi frequency noise at around 3 kHz. This plot places the 10 kHz/V modulation slope as being clear by at least an order of magnitude.  Always be suspicious. Are our macnoni's still performing?  Add this to the moderate-to-low-priorities list of things to check.

## RF AM again?

The BN PSD doesn't extend high enough to compare fully to all the others but if we find that the PLL -> BN is correct then maybe this is an old problem related to excess AM from the 36 MHz and 37 MHz EOMs producting AM and PM.  See PSL:2083 and related backlinks.  In particular we want to know if the laser RIN has some coherence with the BN.  See what Evan did in PSL:1524.  Before screwing around with optimizing the AM (maybe a 1-2 day task) figure out how you can use the transmission signals to get a RIN of both cavities and make a coherence plot.  This would be your smoking gun.  After that maybe look into whether you should sink time into optimizing RF AM and ISS.

Checking RIN and coherence with the beat note is maybe a 1/2 day task once everything is locked up and working.

Also, put those thermal hats back on those EOMs.  Its winter, have a heart.

2275   Wed Jan 9 17:25:38 2019 anchalDailyProgressRFAMTime to look at RF AM and RIN

I measured RIN of the two paths yesterday through taking spectrum of transmission PDs and measured cross-correlation with the Beatnote.

## Measurement conditions:

• Beatnote frequency was not temperature controlled and was arounf 127 MHz slowly increasing.
• Note, this is near the edge of the DC-125 MHz wideband RF detector used for BN measurement.\
• PLL Actuation slope was 5 kHz/V
• Cross-correlation was measured as a FFT group measurement by SR785 using Cross Spec measurement.
• Averaging was on and set to 50 with Linear averaging.

## Conclusions:

From the plots attached, it is clear that RIN of both paths have a peak near 3 kHz but the south path has excessive RIN in comparision to North parth and has much more coherence with BN. I'm looking into possible RF AM in south path.

Edit Wed Jan 16 14:08:03 2019 :

I forgot to convert the noise spectrum measured to laser power spectrum earlier. I am also realizing now that I should have measured the transmitted power to get the RIN. So this measurement only provides Intenisty (or Power) noise of transmitted lasers. I'm attaching the fixed plot now.

2276   Wed Jan 9 19:05:56 2019 anchalDailyProgressRFAMTime to look at RF AM and RIN

## Preliminary testing

I hooked up an HP8560E to RF port of the South FSS Refl RFPD. I unlocked laser from the cavity and brought it to a place which seemed far away from any mode of the cavity.

I was hoping to see a peak at 37 MHz which is PDH modulation frequency of FSS on this path. To my surprise, signal level was ~-80 dBm only at 37 MHz. On zooming out, I saw a 29.5 MHz peak instead of about ~-55dBm. @9.5 MHz is second harmonic of the modulation frequency for South PMC PDH loop. This seemed weird as sidebands of EOM before PMC should not reach after PMC. So I have taken noted some preliminary numbers for future. This isn't complete analysis:

Laser Slow Freq Offset (V) Peak Frequency (MHz) Peak Value (dBm)
-5.9975 0 -11
-5.9975 29.5 -55
-5.9975 37 -60
-5.9875 0 -11
-5.9875 29.5 -55
-5.9875 37 -60
-6.0275 0 -11
-6.0275 29.5 -55
-6.0275 37 -70

All data was taken with a span of 50 MHz. Note how on changing the frequency offset, I got a offset point where 37 MHz Peak almost disappears but the 29.5 MHz peak is present irrespective of the frequency. Need to investigate more.

Thu Jan 10 14:31:56 2019, in reply 2278

It is a resonant EOM.

2278   Thu Jan 10 11:38:53 2019 awadeDailyProgressRFAMTime to look at RF AM and RIN

Is this the resonant EOM or a BBEOM driven with an external circuit? The driving requirements are different, if you overdrive you'll get a bunch of higher harmonics.

Maybe check the modulation depth, make sure it isn't too excessive.  Beta=0.3 should be enough. Error signal Vpp = $\inline V_\textrm{pp} = G\times4\sqrt{P_cP_s} = G\times 2P_0\beta$ (where P0 is the incident power, and G is the PD + mixer gain. Just make sure beta it isn't excessive in producing significant higher order components.

You want to figure out if the 29.5 MHz harmonic feature is an electrical cross coupling or optical. Check your cable routing, are you getting any cross coupling pickup from collocated coaxial lines?  Pretty sure we got the mode cleaner PDH demodulation stuff right, but check mixer is right power level with 4th order LP filter + 50 ohm termination on input side of the LP filter with a RF compatible T-junction.

Also, looking back at the design documents for the PMC, it looks like the nominal design frequency considered was ~30 MHz modulation.  Have a look Evan's earlier​ calculations, especially with respect to HOM suppression.  It looks like for 30 MHz the 60 MHz harmonic is in a relatively low transmission point for HOM. If the issues are optical artifacts transmitted it might be HOM... you can always up the frequency to something closer to 30 MHz.

Take all of the above with a grain of salt.  Consider how much time to sink into it based on whether you think its actually driving a noise source in the system.  Eliminating this 14.75 MHz harmonic may be in the basket of diminishing returns for your time.  The 36 MHz and 37 Mhz AM components are a much bigger concern for FSS related coupling of RIN into frequency noise.

Quote:

## Preliminary testing

I hooked up an HP8560E to RF port of the South FSS Refl RFPD. I unlocked laser from the cavity and brought it to a place which seemed far away from any mode of the cavity.

I was hoping to see a peak at 37 MHz which is PDH modulation frequency of FSS on this path. To my surprise, signal level was ~-80 dBm only at 37 MHz. On zooming out, I saw a 29.5 MHz peak instead of about ~-55dBm. @9.5 MHz is second harmonic of the modulation frequency for South PMC PDH loop. This seemed weird as sidebands of EOM before PMC should not reach after PMC. So I have taken noted some preliminary numbers for future. This isn't complete analysis:

Freq Offset Peak Frequency (MHz) Peak Value (dBm)
-5.9975 0 -11
-5.9975 29.5 -55
-5.9975 37 -60
-5.9875 0 -11
-5.9875 29.5 -55
-5.9875 37 -60
-6.0275 0 -11
-6.0275 29.5 -55
-6.0275 37 -70

All data was taken with a span of 50 MHz. Note how on changing the frequency offset, I got a offset point where 37 MHz Peak almost disappears but the 29.5 MHz peak is present irrespective of the frequency. Need to investigate more.

2279   Thu Jan 10 14:19:46 2019 anchalDailyProgressRFAMTime to look at RF AM and RIN

I found this paper on OSA: Control of residual amplitude modulation in Lithium Niobate phase modulators. It suggests a control mechanism which does not require controlling the temperature. The main point in it is that if a DC offset is present in the RF signal going into the EOM, it is effectively the same as changing the temperature by some amount. So, in principle, by changing the DC bias of the RF signal with a bias-tee just before the EOM, one can minimize the RF AM modulation. The paper though doesn't suggest the feedback mechanism or what sensor would be good for this. If we think this is worth giving a shot, in my opinion, if we fork the output of EOM somehow, measure the RFAM through it and employ a feedback circuit to control the DC offset, we can actively suppress the RFAM. Just a thought at this moment.

Just after writing above, I realized people at JILA have done something similar (with more complexity though):
Reduction of residual amplitude modulation to 1 × 10-6 for frequency modulation and laser stabilization

2280   Thu Jan 10 17:30:24 2019 anchalDailyProgressRFAMTime to look at RF AM and RIN

We measured the modulation index of 0.142 rad when we installed the PMC (See PSL:2251). I checked both PMC loops, none of them are oscillating.

I think I understand now what is happening. The Amplitude modulation from EOM behind the PMC is about -21 dBm . From Evan's earlier calculations , this RF AM should be suppressed by 0.02 only since it is at 14.75 MHz. This corresponds to -34 dB and hence we are seeing a 29.5 MHz amplitude modulaion ahead of about -55 dBm. There is some mechanism which is frequency doubling this modulation and we are seeing it at 29.5 MHz after the PMC.

I think I will try reducing this RFAM with a combination of PBS and tuning both polarizer and EOM angles. But if we had an extra resonant 21.5 MHz EOM and RFPD, this problem would completely go away as PMC will be able to reduce the RFAM more effectively there.

2281   Thu Jan 10 18:52:20 2019 anchalDailyProgressRFAMTime to look at RF AM and RIN

I think I found the culprit. the polarizer behind the EOM (PMC loop EOM) was a multi-order one and hence was extremely sensitive to temperature. I replaced it with a zero order half wavepleate and realigned the EOM to minimise the RF AM to about -70 dBm. The PMC has got misaligned in this procedure, so tomorrow I'll align it back and see if our changes made a difference.

2282   Sat Jan 12 13:11:02 2019 awadeDailyProgressRFAMTime to look at beatnote after RF AM and RIN tuneup

Nice.

It would be a good time to retake the BN + cross spectrum with RIN to see if these improvements squash the 3 kHz hump.  You'll probably want to recheck the RFAM levels immediately before retaking the BN in case there has been any drift.  When plotting the RIN you should include a trace that quantifies the dark noise of the PDs and the shot noise. The traces are not much use if they are limited by either of these, the elog readers would benefit from having such traces as a bench mark.

A good thing to do, as well, would be to resurrect the AEOM power controls in both paths.  You can then use a swept sine to take a transfer function from intensity noise to beat note directly without just relying on the residual RIN of the laser*.  This will help you model the expected real TF from intensity noise to frequency noise (for the noise budget) and help justify the design choices of the ISS (how far along is the ISS BTW?).  It also lets you know the susceptibility of each path to RIN, regardless of the performance differences between the two laser.  Maybe its also possible to fine tune the offsetting on the FSS PDH controls by watching the transfer function live and adjusting the DC offset to minimize Intensity->FSS->Freq Noise conversion.  The offsets and gains on the FSS loop are now more or less arbitrary, this is something you can try next time you tweak up these loops.

THe AEOMs should be configured with s-polarized light (vertical) going into the modulator with a quarter-wave plate, followed by a PBS at the output.  Adjust the quarter-wave plate to get yourself to 50:50 splitting, this gives you the maximum W/V slope with close to linear response. You'll need to adjust upstream powers accordingly to give you 1.5 mW at the input of the RefCavs. Be aware of how hard you are driving the modulators so that you are sure that it is in the linear regime.  Terminate AEOMs when not in use.

* It would also be nice to have a tap off somewhere (<10%) to be able to sample the pre-cavity RIN.  Given that any BS/ wedge you insert will misaligned the beams it will be a 0.5 day exercise to realign cavities etc, thus mid-low priority.

 Quote: I think I found the culprit. the polarizer behind the EOM (PMC loop EOM) was a multi-order one and hence was extremely sensitive to temperature. I replaced it with a zero order half wavepleate and realigned the EOM to minimise the RF AM to about -70 dBm. The PMC has got misaligned in this procedure, so tomorrow I'll align it back and see if our changes made a difference.

2333   Wed May 1 18:45:47 2019 anchalNotesOtherTo scale complete optical layout of CTN

I have completed making an optical layout for CTN lab. From now onwards, I'll update this layout if I make any major changes in the path.

https://nodus.ligo.caltech.edu:30889/ATFWiki/lib/exe/fetch.php?media=main:experiments:psl:ctn_optical_layout.pdf

Please comment if you think I should represent something better.

1554   Wed Jun 24 16:24:32 2015 EvanNotesScheduleTo-do list

Compare with previous todo list.

To-do list (short term):

• Check health of PDH loops:
• Check centering on RFPDs
• Check slope and balancing of error signal
• Turn on chamber heating
• Re-establish beat
• Re-insert south EOAM

To-do list (medium term):

• Replace PBS/QWP reflection locking with Faraday isolators
• Need two Faraday isolators with large apertures
• Need four HWPs: one on each cavity input, one on each cavity output
• Fix power supply situation [Aidan already doing this]
• RFAM mitigation
• PMCs

To-do list (long term)

• Install crystal oscillators, retune RFPDs, retune EOMs
• Acromag
1435   Tue Jun 24 14:07:13 2014 EvanNotesPMCTodo list for PMC heater

Supplies

• Aluminum tape
• High-current buffer (maybe can use linear power supply with aux inputs on back)

Computing

• Set up or co-opt channel to output to heater
• Modify PMC MEDM screen to accommodate heater
1442   Wed Jul 2 09:56:18 2014 EvanNotesPMCTodo list for PMC heater

 Quote: Supplies Foam (already have) Aluminum tape Kapton heater (already have) High-current buffer (maybe can use linear power supply with aux inputs on back) Computing Set up or co-opt channel to output to heater Modify PMC MEDM screen to accommodate heater

Instead of using a power supply as a current buffer, we can use a mosfet like so:

This is based loosely on the aLIGO PMC heater (D1001618-v1, p. 10).

If we instead want to run off of a unipolar supply, we can replace the AD620 with a noninverting op-amp. We'll lose the common-mode rejection, though.

2591   Wed Sep 30 11:13:28 2020 anchalNotesEquipment loanTook home moku and wenzel crystal for characterization

I have brought home the following items from CTN Lab today:

1. Moku with SD Card inserted and charger.
2. Ipad pro with USB-C to USB-A charging cord
3. Wenzel 5001-13905 24.483 MHz Crystal Oscillator
4. HP E3630A triple output DC power supply
5. One small 5/16 spanner
6. 4 SMA-F to BNC-F adaptors
7. 4 SMA-M to BNC-F adaptors
8. 2 10 dB BNC Attenuators
9. 4 BNC cables

Additionally, I got 4 BNC-Tee and a few plastic boxes from EE shop. Apart from this, I got a box full of stuff with red pitaya and related accessories from Rana.

2609   Tue Feb 23 11:05:28 2021 anchalNotesEquipment loanTook home moku and wenzel crystal for characterization

Returned all remaining stuff to CTN:

1. Wenzel 5001-13905 24.483 MHz Crystal Oscillator
2. One small 5/16 spanner
3. 4 SMA-F to BNC-F adaptors
4. 4 SMA-M to BNC-F adaptors
5. 2 10 dB BNC Attenuators
6. 4 BNC cables

Also returned the Red Pitaya accessory box to CTN. I've kept Red Pitaya at home for more playing.

2115   Sun Mar 4 05:22:05 2018 ranaMiscPurchasesTorque spec for optical mounts

The case I was describing is with the BA-1, BA-2, or BA-3 from thorlabs, using a steel (18-8) screw and a SS washer. In this case, you want to go to ~75% before plastic deformation of the aluminum. In this situation, the screw and the base will be elasticly deformed. More tightness will make it plastic and then slowly drift. Less will just give you less stiffness against vibration.

For the case of the 1/4-20 screw with washer in a fork clamp, I expect it can go more, but probably not necessary. To test for drift, we would need an ultra stable Mach-Zender and a long term visibility test, as was done for the stability tests of the Japanese Super Duralumin mounts that Koji has.

Dennis Coyne has a formula to figure out these numbers. I'm going to get to the bottom of this and make it part of this summer's course on Lab Skills.

2132   Tue Mar 13 15:32:49 2018 CraigDailyProgressISSTrans DC jumpiness

When the cavities relock themselves, our Trans DC values change drastically.

I just noticed this when the North cavity lost lock while I was messing around with some optics.  The autolockers worked their magic, but upon relocking the NCAV_TRANS_DC value went from ~3 V to ~4 V.  It's been as low as 0.9 Volts as well, that's why I changed the thresholds for awade's NCAV autolocker .ini file.
What the heck?  We know they are locking to the same fringe, at least for the Fabry-Perot cavity.  The PMC is locked to a different fringe though, maybe this increased it's power output?  But that wouldn't explain the South path jumps.
Unclear why this would happen.

First plot: Last 30 minutes.
Second plot: Last 12 hours.  EVEN CRAZIER

2376   Wed Jul 24 16:14:42 2019 ScottADailyProgressRFAMTransfer Function of EOM Driver plus Bias Tee from RF Input to EOM
• I have calculated the expected transfer function from the RF input of the EOM Driver (DCC: https://dcc.ligo.org/D1200794-v3) to the direct short connection to the EOM (Graph 3).
• To do this I took the transfer function calculated in the previous post (Graph 2) which was from the RF input to the RF monitoring port and divided it by a calculated transfer function from the EOM Short to the RF Monitoring port (Graph 1).
• The gain at 37 MHz seen by the EOM is around 10, in order to get a modulation depth of 0.3 we need a signal with 40 Vpp. This means we need a 4 Vpp input signal to achieve the desired modulation depth. As mentioned in https://nodus.ligo.caltech.edu:8081/CTN/2242 "the frequency source is a preamplified OCXO crystal sources (see PSL:2235, for info and links) that outputs about ... +26 dBm out of the EOM driver SMA."
• +26 dBm is a voltage of 4.4 volts which is at the required level for the 0.3 modulation depth, so it seems this circuit will perform what we want.

### Summary of Results:

• The transfer function from the RF Input of the EOM Driver to the EOM has a resonant peak around 37 MHz with a max gain of around 10.
• This gain will be enough to get a 40 Vpp signal which equates to a 0.3 modulation depth.

Edit Thu Aug 1 16:11:12 2019 ScottA :

4 Vpp is actually 16 dBm, so we need to feed 16 dBm power from OCXO to the EOM. So we'll need ~10dB attenuation but everythign will still work.

2375   Tue Jul 23 18:59:40 2019 ScottADailyProgressRFAMTransfer Function of EOM driver with Bias Tee and Dummy EOM

Here is the result of taking the transfer function of the EOM Driver (DCC: D1200794-v3) with the bias tee and a dummy EOM from the RF input to the RF monitor output. A Black 143-10J12L tunable inductor (438 nH - 788 nH) was used to bring the peak over 37 MHz. The data was taken using an Agilent 4395A Analyzer which was controlled using the .py .yml and .ini files provided in the zip.

987   Wed Jun 13 19:00:26 2012 SarahDailyProgressLaserTransfer Functions

Today Tara and I measured the coherence between the intensity noise from RCAV and ACAV, as well as the transfer function between the power fluctuations and frequency. We used the following setup:

With a pda 100a photodiode behind ACAV, we looked at the intensity fluctuations, as well as the noise level of the pd. The noise of the sr758 in this case was low enough to consider negligible. The results for pd noise and intensity noise are plotted with respect to the left y-axis. The Relative Intensity Noise for ACAV, the intensity fluctuations divided by the DC voltage, is plotted with respect to the right y-axis.

We also measured the coherence between RCAV_TRANSPD and ACAV_TRANSPD, where we used about 2000 averages:

Next we measured the transfer function between power coupling and frequency. In order to do this, we reduced the power of RCAV to a minimum of 50uW and increased the power in ACAV to a maximum of 2.5mW. The gain in ACAV was too high, and we had to add an attenuator of 30dB to the servo input.

The transfer function is found by dividing the response function by the reference function. In this case, we let the response function be the AOM feedback signal, and the reference signal be the ACAV power fluctuations. The use of ACAV power fluctuations is optimal because ACAV is being operated a maximum power. Additionally, there was a 1kHZ input range to ACAV which will be used for calibration to absolute frequency later.

Using the swept sine measurement group, we measured the following transfer functions:

The blue transfer function was the first obtained. In order to confirm the accuracy of the transfer function, we changed both the excitation and the power level to ACAV. If the transfer function is accurate, we expect it to remain relatively constant in these cases.

Green Plot: After changing the DC power in ACAV to half its current value, to 1.25mW, the green transfer function was obtained. Because the power was decreased, the gain decreased, and we adjusted the attenuation to ACAV from 30dB to 13dB.

Red Plot: Next, we changed the excitation amplitude down to 1V, and the transfer function remained the same. However, after changing the attenuation back to 30dB, the transfer function did change slightly as shown in the red curve.

Black Plot: Increasing the power to ACAV to 1.9mW, the transfer function is portrayed as the black curve.

Yellow Plot: In an attempt to look for the common mode effect, we increased the power to RCAV to 1mW, a value relatively close to that of ACAV. The resulting transfer function, the yellow curve, does not indicate the presence of any common mode effect. One possible reason for this is that the coupling for the two cavities might not be the same.

To sum up, the transfer function measurements we have might not be the real coupling from RIN to frequency noise because:

• It does not stay at the same value when we change the power to ACAV. (Blue -> Green).
• TF changes with the attenuator we use from mixer out to ACAV servo in order to keep the loop stable (Green-> RED)
• TF does not change when the power to RCAV is changed, and power to ACAV is kept constant. It should become smaller as the power between the two cavities are about the same (assuming similar absorption) due to common mode effect (black and yellow) and become larger if the power difference between the two cavities increase.

== How does it show up in the noise budget?==

However, as a rough check, if we assume that the measured TF is valid, the coupling from RIN to frequency noise in beat signal is plotted below.

The measured TF (feedback to AOM/ ACAV_TRANSPD) used in this plot is taken from the red TF from the above plot which gives the maximum coupling.  I assume that the TF at low frequency has the same slope (1/f^0.15) from DC to around 1kHz and roll off with the same measured slope

.

[above, TF plotted with fit curve]

Then

Estimated Frequency Noise = [ACAV_TRANSPD_DC [v] ] x [measured RIN_ACAV [1/sqrtHz]] x [10  (TF/20)] x 2 x 710 [Hz/V] ,where

• TF is measured in dB, [V/V]
• a factor of 2 at the end is for double passed AOM,
• a factor of 710 [Hz/V] is the calibration for 1kHz input range on Marconi for AOM
• no common mode rejection is assumed (to get the upper bound). This should be valid, since the coherence between ACAV and RCAV_TRANS_PD is very tiny at low frequency, where the coupling and RIN are supposed to be large.
• assume 2mW input for ACAV

As it turns out, the measured TF is not totally wrong since the estimated effect is still below the measured beat signal. It is interesting to see that, from 10 to 100Hz, the shape of the RIN noise follows the trend of the measurement nicely.  Thus, developing ISS might improve our signal to certain level.

I'll add the contribution from RIN in the noise budget code and see if the sum total noise match the measurement or not.

1005   Wed Jun 27 18:51:56 2012 SarahDailyProgressLaserTransfer Functions

Tara and I performed additional measurements of the transfer function for the coupling between power fluctuations and frequency.

Setup:

This time we altered the setup and instead of attenuating the signal input to the ACAV servo, we added an optical attenuator before the pd. We attenuated before the pd this time because of the possibility of pd saturation in the previous setup. The setup we used today was:

Measurement and Data Analysis:

Consistent with the last measurements, the response function for the transfer function was the AOM Feedback and the reference function was the ACAV power fluctuations. We used the sine swept measurement group in the SR785 to get the data. We checked the TF by changing the power from 2.2mW to .22mW, and the data remained the same.

We calibrated the raw data from dB to the units of Hz/RIN using the following relationship:

TF [Hz/RIN] = 10(TF[dB]/20) *710[Hz/V] * 3.6[V] *2

where the factor of 2 accounts for the double passed AOM, the factor of 710 is the calibration for the Marconi, and the 3.6 is the DC level.

The results for the TF are plotted below:

For the magnitude, the data taken at different frequency intervals overlapped perfectly. For the phase, the data did not overlap perfectly, so the data was concatenated with a slight jump at 100Hz.

Application to Noise Budget:

Using the previously measured RIN, I estimated the frequency noise with the transfer function just measured. First I fit the transfer function as shown below:

Next I applied the following relationship to obtain the estimated frequency noise, and plotted it with the noise budget:

Frequency Noise: RIN * 3.6 [V] * 2 * 710 [Hz/V] * 10(TF[dB]/20)

Compared to the RIN induced frequency noise with the previously measured TF (refer to elog entry attached to this one), the noise is lower at higher frequencies, drops off with a slightly steeper slope in the center, and slightly higher at lower frequencies (this could be due to error in fit though). Note that this RIN induced noise is only an estimate, and the calculation may be slightly incorrect due to the fact that the DC level was slightly different (by ~ a factor of 2) for the measurement of the intensity noise (previous elog) and the current transfer function measurement.

Comparing the calculated TF from elog 989 (using RIN from previous setup), the following plot is obtained:

Thus, the transfer function still does not match the calculated curve perfectly, but its a better match shapewise than the previous TF. Additionally, there still might be an error in the calculated curve.

Conclusion:

The TF looks considerably better than before, perhaps because we optimized the phase for the EAOM two days ago, so we are driving the amplitude with more modulation.

== Note on the measurement ==

•       RCAV is locked with 100 uW input power, Common/Fast gains on the TTFSS are 950/750. The reason to use low power is that we want to make sure that the effect due to power modulation will not be common in both paths. However, we need enough power so that RCAV loop gain is still high enough so that the frequency noise in the laser is suppressed and does not cover the RIN induced noise in ACAV loop.
•       ACAV input power is 2.2 mW. To avoid having too much gain and unstable loop, we use an ND filter to reduce the power on RFPD down to the level it usually is at 1mW power (~200mV).
•       To check if the TF is real or not, we tried to lower the power down to 0.2 mW and see no change in the measured TF. This is good, since the TF should be independent of the power input.
•       The DC level from PDA100A @gain 20 is 3.6 V (the reference signal of our TF measurement). The modulation is 380mV pk-pk in sine wave form, so the TRANSPD_DC is ~ 3.6 +/- 0.19 V. We make sure that the PD is not saturated.
•  ***** The measurement is made possible because the drift is very small. For the past 5 Hrs, it has been less than 1kHz in 5 minutes. **
1014   Fri Jul 6 18:59:49 2012 taraDailyProgressLaserTransfer Functions

I have been thinking that the TF measurement (coupling from RIN to frequency noise) we plotted before has unusable unit [Frequency noise /RIN]. We have to correct it by converting it to [frequency noise/ watt]. With that we can compare the result to other experiment/ calculation or use it in the noise budget.  As an example, I plot the result calculated by Cerdonio etal 2003 here as well.

==we use wrong unit==

I am editing my noise budget code to incorporate the effect from RIN induced noise and find out that, the unit we have in Fnoise/RIN is not making sense. In order to get the noise due to RIN I have to multiply measured RIN to the measured TF, that is    Freq noise due to RIN = [measured TF] x [measured RIN behind CAV] = [Hz/RIN] x [RIN] = Hz. As we can see, it does not change with the input power level. In reality, it should depend on the power level as well.  That is why I think Hz/RIN unit is unusable.

==result from Cerdonio==

Braginsky etal calculated the noise from thermal expansion due to heat absorbed from shot noise. The result was later corrected for all frequency span by Cerdoniot etal in 2003. The result tells us the displacement noise due to shot noise. With some modification, we can apply the result to get the displacement noise due to RIN. This will be compared with the measurement later. [add calculation]

fig1: calculation for TF using Cerdonio etal's result.

fig2: calculated TF in unit of [Hz/Watt] (I convert the result from m/watt to Hz/watt). Frequency noise can be calculated by multipling the TF with RIN x Pin. [fig file, code]

==some thing about the measurement setup==

The nice thing from the measurement is that we can see the Cerdonio effect when the thermal diffusion length is comparable to the spot size (around 3Hz) nicely. However, the asymptotic behavior of our measurement does not agree well with the prediction. It has a slope of 1/f0.75 , while we expect 1/f.  I'll find out what's wrong with the setup (bad alignment on EAOM, PDH signal, etc) or other mechanism that might cause this effect.

1016   Tue Jul 10 02:55:37 2012 taraDailyProgressLaserTransfer Functions

I tried to remeasure the coupling from RIN to frequency noise (same setup as in psl:1005).  However I have not been able to reproduce the result yet.

The result we got in psl:1005 does not have the same TF shape as we expected from the calculation. The slope is off by 1/f^0.25. So There might be something wrong with the setup, for example bad alignment in EAOM that adds PM to the beam and effect the PDH signal. So in order to verify the problem I redo the measurement with the similar setup. This time, however, when I change the power into ACAV, the measured TF changes as well (this did not happen before), so I'm checking what's wrong with the setup.

Checking plan:Once I can remeasure the TF (ACAV AOM feedback/ ACAV TRANSPD). I want to check

1. effect of beam EAOM alignment to the TF
2. comparison between TF from (ACAV AOM feedback/ACAV TRANSPD) and (beat signal/ACAV TRANSPD). I tried this already and they are quite similar except some phase shift.
3. To verify that the measurement is valid, I'll make sure that the TF is independent of excitation level and power input to ACAV.
1017   Wed Jul 11 11:13:38 2012 SarahDailyProgressLaserTransfer Functions

Tara and I measured the correlation between Voltage and Power behind ACAV, and applied the found calibration to get the TF magnitude in the units of Hz/Watt.

Intro:

We wanted to convert the previously measured TF magnitude (elog 1005) into units of Hz/Watt, as opposed to the previously used Hz/RIN. See attached elog (1014) for an explanation of why these units have a more applicable meaning and application.

Setup/Data Obtained:

We measured the power immediately behind ACAV, the power immediately before the pd (there is a beam splitter between the first and second power measurements), and the corresponding voltage after the pd. The pd gain was set to 20dB. I plotted the results and fit each data set:

The fit equations are:

pd fit: y = 5680.4x + 0.036843

cavity fit: y = 2923.3x + 0.027703

Where y is the voltage (Volts) after the pd and x is the power (Watts) in front of the pd for the pd fit, and right behind the cavity for the cavity fit.

TF Magnitude in Hz/Watt:

Using the slope of the line relating the power behind the cavity to the voltage as the calibration, I was able to convert the previously measured TF magnitude into the units of Hz/Watt, and plot it against the calculated TF (elog 1014) magnitude in units of Hz/Watt (calculated using Cerdonio et al's results):

Application to Noise Budget:

I also plotted the RIN induced noise using the TF in units of Hz/Watt using :

Frequency Noise = TF[Hz/Watt] * RIN * Power_in

I used an input power of 2mW, and the RIN from 6/13 behind ACAV.

The frequency noise generated is a factor of 1.4 larger than that generated using the TF in units of Hz/RIN. Since the TF in Hz/RIN was measured, it is more reliable. This discrepancy indicates that the TF magnitude is also probably too high, and there is a possible error in the calibration constant used to convert voltage to power, or possibly an error in the power readings.

1020   Mon Jul 16 19:08:34 2012 taraDailyProgressNoiseBudgetTransfer Functions (RIN to Frequency noise via photothermal)

Sarah and I are trying to remeasure the coupling from RIN to frequency noise. Here we list the problems that might cause the error in the measurement.

Before measuring anything, we aligned the beam to ACAV and RCAV , adjusted the power so the power to ACAV is 2mW and RCAV has 0.2mW.

We found out that:

1. EAOM alignment does not change the measured TF. We misaligned the EAOM and measured the TF. There was no significant change in the measured TF.
2. The measured TF does not change with excitation level (from SR785). With output level of 1-5Vpkpk, the measured TF remains the same.
3. However, the TF changes if we change the power to ACAV. The measure TFs with different power level differ at high frequency and they converge at low frequency depend on the power level. For example, if we choose RFpower on Marconi to 12 dBm, the measured TF will be higher than the TF with 13dBm power ~ 2dB at 1kHz, and converge around 300Hz.

Since the TF remains the same at lower frequency, we thought that the gain of ACAV loop cannot keep up with the frequency noise and cause the deviation in the measure TF, so we checked the UGF of ACAV with different power level (*this is done roughly for a quick check, we will come up with more careful analysis later).

 RFpower[dBm] [P_acav mW] UGF 10  [0.4] 16kHz 12.2 [1.3] 39kHz 13 [2.0] 50kHz

The measurements above were done with an extra ND filter that reduce the power on RFPD by a factor of 2. The shape of the TF is roughly 1/f.  The UGF is significantly higher than the interested frequency (DC-1kHz), so we think it is not the insufficient gain in ACAV loop.

So we change the gain in RCAV loop, by increasing the power to 0.4 mW. With this level to RCAV, the TF does not change with power to ACAV that much, unless the power goes down to ~0.4mW.  On the other hands, the TF(RIN coupling) also changes if we reduce RCAV gain to certain level. We will investigate more about this.

 Quote: I tried to remeasure the coupling from RIN to frequency noise (same setup as in psl:1005).  However I have not been able to reproduce the result yet.   The result we got in psl:1005 does not have the same TF shape as we expected from the calculation. The slope is off by 1/f^0.25. So There might be something wrong with the setup, for example bad alignment in EAOM that adds PM to the beam and effect the PDH signal. So in order to verify the problem I redo the measurement with the similar setup. This time, however, when I change the power into ACAV, the measured TF changes as well (this did not happen before), so I'm checking what's wrong with the setup. Checking plan:Once I can remeasure the TF (ACAV AOM feedback/ ACAV TRANSPD). I want to check effect of beam EAOM alignment to the TF comparison between TF from (ACAV AOM feedback/ACAV TRANSPD) and (beat signal/ACAV TRANSPD). I tried this already and they are quite similar except some phase shift. To verify that the measurement is valid, I'll make sure that the TF is independent of excitation level and power input to ACAV.

1021   Tue Jul 17 19:05:32 2012 taraDailyProgressNoiseBudgetTransfer Functions (RIN to Frequency noise via photothermal)

Tara and I re-measured the transfer function coupling the RIN to frequency noise at five different power levels.

We were having problems with the ACAV gain at low powers, so we chose appropriate attenuation through an OD filter to compensate.

The following plot shows the TF's measured, with their corresponding ACAV power levels:

The transfer functions measured at 2.2mW, and 1.9mW were measured with a .15 OD filter. Those measured at 1.77mW, 1.6mW, and 1.42mW were measured with a .10 OD filter.

As shown in the plot, the magnitudes of the transfer functions measured at different power levels match up quite nicely, confirming the validity of the transfer function. The phase plots are pretty consistent, with slight variation up to 20 degrees at higher frequencies.

I converted the above transfer function magnitudes to units of [Hz/Watt] and plotted the results with the calculation using Cerdonio's result:

The main source of error between the calculated and measured transfer function is from the voltage to power calibration. We will re-measure this and see if a result closer to the calculation is achieved. Since the measured transfer functions are all fairly consistent with each other in magnitude, I used the transfer function measured at 2.2mW and calculated the residuals for the calculation w/ Cerdonio's results:

I attached the raw data, where the first column of each .mat variable is frequency and the second is dB for magnitude variables and degrees for phase variables.

1029   Tue Jul 24 17:02:35 2012 SarahDailyProgressNoiseBudgetTransfer Functions (RIN to Frequency noise via photothermal)

Tara and I measured the transfer function coupling RIN to Frequency noise over a wider range of power levels.

Setup and Measurements:

RCAV power was set to.3mW. We varied ACAV power, and added the rf amplifier mentioned in Elog 1022  after the rfpd to compensate for low power levels. We measured the visibility of the cavity to be 72%, and including this number should slightly  improve the accuracy of the input power level used in calculations. The TF was measured at the following power levels: 2.7mW, .84mW, .32mW, and the results plotted with the TFs measured last week at: 1.6mW, 1.4mW, 1.3mW, 1.2mW, 1.0mW. It should be noted that the visibility was not measured during data collection for the TFs measured last week, so in scaling the power I assumed a visibility of 72%. This may not be perfectly accurate, however as of now it only affects the labeling of the power, since the creation of the following plots does not depend on input power. The upper power limit for measurement was set by the saturation of the photodiode, which we found out saturates at about 10.2V. While inserting a filter after the photodiode would allow us to measure at higher powers, it would also mean we would need to recalibrate, so we just measured up to the saturation of the photodiode for these measurements.

Data and Results:

The following plot shows the raw data collected for all eight TFs, in dB and degrees:

The transfer functions appear quite consistent and thus don't seem to depend on the power level. We expected to see more of a common mode effect for the measurements where ACAV power was comparable to RCAV's .3mW power. This effect is apparently absent, and we plan to do further measurements to investigate it further. We also measured the coherence between the AOM feedback signal and intensity noise, as well as frequency responses for the three recently measured transfer functions, as shown below:

A white noise excitation was used for the frequency response and coherence measurements. The coherence was measured to be essentially zero without excitation. It is possible there was an error in measurement for the .32mW measurements, as the frequency response does not seem to follow the appropriate trend, which should be consistent with the magnitude of the transfer function.

I converted the 2.7mW transfer function magnitude to units of Hz/Watt and plotted it against the calculations using Cerdonio's and Farsi's results:

The voltage to power calibration factor is still a main source of error in this conversion.

1032   Fri Aug 3 02:46:15 2012 taraDailyProgressNoiseBudgetTransfer Functions (RIN to Frequency noise via photothermal)

I fixed the calculation for photothermal noise and compare it with the measured results. This time, they agree quite well.

I include Thermo expansion and Thermo refractive effects in coatings in to the calculation, and make sure that they are treated coherently. However I still use Farsi's calculation, not GWINC code (see below for why).  Now the calculated TF shape agrees well with the measurement. However, the magnitude is still off by a factor of ~5. This can come from the calibration from power to Volt on the PD_trans_dc (from PSL:xx), the measurement data is taken from PSL:1021.  The absorption I use for calculation is 5ppm, finesse is 7500. These numbers contribute to the magnitude of the calculated TF. I'll try to plot it with confidence interval to see if it will be close to the measured result or not.

==why not GWINC?==

Since GWINC code has a section(s) for thermo-optic noise (TO) calculation (following Evans 2008 paper), we should be able to modify it to produce the result for RIN induced noise in our case. However, there is one complication for this option. GWINC calculates (TO) by using the [ Power spectral of temperature fluctuation on surface] x [dphi/dT]. [dphi/dT] is derived from the coating structure and materials' properties. However, the temperature fluctuation on the surface is derived by fluctuation-dissipation theorem then averaged over a guassian beam profile(see Levin,2002).  Hence, to use GWINC code to calculate our result, we need to calculate the pwr spectral density of the surface temperature which is heated up by gaussian beam profile, and averaged over gaussian beam as well. I'll try to do this later when I have more free time.

I reviewed Farsi calculation carefully They follow the sign for TE and TR in the coating(practically following Evans' paper),so I think it is valid as well. Even though Farsi calculates the effect from the first few layers which, as they claim, contribute most to TR, their argument agrees with the result provided by Evans' paper where they compare TR effect between ITM(8doublets), and ETM(19doublets) which are almost the same.

Plus, the effect from coating becomes comparable to that of substrate around 100 Hz and higher frequency. This means the contribution from substrate and coating must be calculated together, which is nicely done by Farsi as well. (This means you cannot just calculate the effect from a bare substrate, ie. from cerdonio, and add the effect from the coating on top of one another) Since we are going to use the calculation from substrate with coating from them, why not the coating calculation as well?

1298   Tue Aug 13 21:45:51 2013 taraDailyProgressNoiseBudgetTransfer Functions (RIN to Frequency noise via photothermal)

I rechecked the TF between power fluctuation and frequency noise in beat measurement that I did last year. The estimated result agrees more with the measured result. This can be used to estimate the requirement for ISS for SiO2/Ta2O5 and AlGaAs coatings.

The calculation is taken from Farsi etal 2012 (J. Appl. Phys. 111, 043101), and compared with the measurement from 8" cavities, SiO2/Ta2O5 QWL with SiO2 1/2 wave cap. The code I wrote before has several mistakes, so I fixed them.

Mistakes in the original code:

1.  Beta effective was for 1/4 cap of nL: I changed it to the right one (1/2 cap of nL). This can be done by GWINC or an analytical result.
2.  Cut off frequency ws, wc in the paper, I divided by a factor of 2*pi make them in Hz.
3. Missing a factor of imaginary in thermoelastic in coatings calculation.
4. r0 in the paper is where the power is dropped by 1/e, so r0 = w0/sqrt(2) where w0 is the radius of the beam when the power is dropped by 1/e^2.

Above: Measurement(purple) from SiO2/Ta2O5 coatings and analytical result (cyan) in comparison. Finesse = 7500 (old ACAV), absorbtion = 5ppm.  The slope at high frequency seems to be real TO noise. Notice that phases from TE and TR have different sign and cancel one another.

==for TO optimized AlGaAs coatings==

Above: Calculation for RIN induced thermo noise for optimized AlGaAs coatings in Hz/Watt unit. The calculation is for 200 ppm transmission,-> Finesse ~14 000. 1.45" cavity. The cancellation in coatings will reduce the noise. The estimated effect is plot against the measurement from 8" cavity, T=300ppm, SiO2,Ta2O5 cavity.

We might have to make sure that RIN is small enough, since this time we will have no common mode rejection like what we had with just a single laser. I'll add the estimated requirement later.

1300   Fri Aug 16 04:35:58 2013 taraDailyProgressNoiseBudgetTransfer Functions (RIN to Frequency noise via photothermal)

I estimated the requirement for laser RIN for AlGaAs coatings. The result is a factor of 5 more stringent from what we need for SiO2/Ta2O5 cavity.

See some calculation about RIN requirement PSL:1270.

I estimated the RIN induced TO noise in AlGaAs cavities. Due to the TO optimization, the effect will be small and we will see only the effect from the substrate, see RIN induced noise estimate.

This will be quite serious, if we do not have a good ISS, since we will not have common mode rejection like what we had with the single laser setup anymore. I'll look up what was the RIN performance we had before.

1310   Thu Aug 22 13:36:19 2013 taraDailyProgressNoiseBudgetTransfer Functions (RIN to Frequency noise via photothermal)

I went through all the code with Evan and found another mistake. This time the code should be correct, and the result is close to what we measured a year ago.

The calculation in PSL:1014 is wrong. There should be no square root for the absorption power (Finesse/pi * absorption).  With that correction, and an assumption of absorption of 18ppm in the mirrors (9ppm on each) with Finesse of 7000, see PSL:425. The result matches with the calculation quite well.

The validity of this result depends on the absorption factor and cavity finesse. The finesse was measured, but the absorption measurement has never been done. So it might be good to think about how to measure that.

We did the same measurement with the current ACAV 1.45" cavity. Evan will post the result later.

1019   Sun Jul 15 23:20:32 2012 taraDailyProgressNoiseBudgetTransfer Functions (power fluctuation to Frequency noise via photothermal effect)

I calculated the photothermal noise following the method from Farsi etal 2012 paper. The results is plotted below. I think I did something wrong, by looking at the low frequency part, the results from Cerdonio and Farsi do not agree. I'm still checking on it.

==Cerdonio  vs Farsi==

Cerdonio calculated the displacement noise due to thermal expansion of substrate induced by shot noise. This can be modified to estimate the noise due to absorption of RIN (see PSL:). Farsi extended the calculation to take thermal expansion and thermo refractive effect from coating into account. Since our measurement does not match up with Cerdonio's calculation that well.  I check if the mismatch comes from coating expansion or not. (I did not expect much, since the spotsize is 291 um, and the coating thickness is ~4um. Heat diffusion length ( ~ sqrt(k/2piCf ) )tells us that the effect from coating will be ~ 1000 Hz and above)

==result==

There are a few things that make me uncertain about my calculation code:

1. The effect from substrate is going up with wrong slope while it should match the calculation from Cerdonio at low frequency because the thermal diffusion length is much longer than the coating thickness and most of the effect comes from substrate only.
2. With our parameters the effect from coating is not significant until ~ a few kHz while it is dominating around 100 Hz for their setup.Their spot size on the mirror is~ 100um, so I expect that for our setup, the effect from the coating should kick in before 1kHz.

I'll double check my calculation again.

1023   Thu Jul 19 03:01:26 2012 taraDailyProgressNoiseBudgetTransfer Functions (power fluctuation to Frequency noise via photothermal effect)

I fixed the code for photothermal effect (following Farsi), the calculation for substrate effect agrees with Cerdonio at low frequency. And both calculations (Cerdonio/ Farsi) agree if the coating thickness is zero.

I found a mistake in my code for photothermal noise calculation and fixed it. Now the result agrees well with that of Cerdonio's. However, the effect from thermal expansion of coating may be wrong. I try using the parameters in their setup and have not come up with the similar plot they have. So, I'll have to check my calculation again.

fig1: comparison between Cerdonio's and Farsi's calculation. The effect from coating(red) may be still incorrect.

Note: I use Riemann sum for the integral in both calculation. The step size has to be small enough for both calculations, otherwise the results won't match up nicely.

1025   Thu Jul 19 23:56:45 2012 ranaDailyProgressNoiseBudgetTransfer Functions (power fluctuation to Frequency noise via photothermal effect)

Does the coating term include the thermo-optic cancellation between thermo-refractive and thermo-elastic? I think you have to use the Evans/Ballmer paper for that (i.e. the GWINC code that I sent you before).

I am surprised if we can use these other papers without modification since the boundary conditions of our optic are fixed. The edge of the mirror doesn't move since its contacted to the spacer. How do you account for that?

1027   Fri Jul 20 01:32:45 2012 taraDailyProgressNoiseBudgetTransfer Functions (power fluctuation to Frequency noise via photothermal effect)

1) The coating term is account for thermal expansion only(TE), no thermo refractive has not been included yet.

Farsi treats the effect from TR by assuming that all the TR contribution comes from the first few layers with 180 degree phase different from TE. From their result, TR contribution is much smaller in our frequency band, so I haven't included it in the calculation yet.

2) I agree that our fixed spacer setup will have different result. I'll think about it. Since the coupling is high at low frequency, and the thermal diffusion length is large  ~sqrt(k/C/2pif), which is ~ 1.7 cm [sqrt(1Hz/f)],  (SiO2 material properties) This is certainly comparable to the radius of the mirrors, and any effect on the edge may not be negligible.

Mistake!!, the heat diffusion length is sqrt[ k/ (rho*C*2pif) ] ,  where k is heat conductivity (W/mK), rho is mass density, C is specific heat per kg. This gives 367 um x sqrt(1Hz/f) in fused silica, which is ~ 1.2 mm at 0.1 Hz, and it is still small compared to the mirror's size. Then the boundary condition of our optics might not be as bad as I thought.  I'm thinking about using COMSOL to estimate the effect due to heat escaping from the substrate to the spacer. However, I expect that the boundary effect will help us a bit. The contact area at the spacer will provide additional heat bath for the substrate and reduce the heat at the spot area, thus reducing the thermal expansion effect. Plus, the expansion of the spacer/the substrate at the contact area will be in the opposite direction of that on the spot area. The expansion at the spot area will make the cavity shorter, while the expansion of the spacer/contact area will make the cavity longer. So I think the calculation will still give us the upper bound level, the shape at low frequency ( around 0.5 Hz and below), may change due to the longer heat diffusion length and the boundary effect is not negligible.

 Quote: Does the coating term include the thermo-optic cancellation between thermo-refractive and thermo-elastic? I think you have to use the Evans/Ballmer paper for that (i.e. the GWINC code that I sent you before). I am surprised if we can use these other papers without modification since the boundary conditions of our optic are fixed. The edge of the mirror doesn't move since its contacted to the spacer. How do you account for that?

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