New legs were installed.  The table is floated. The cables for signals/ power supplies will be reconnected later

 Evan and I replaced the old legs. I made sure that the leak was not in the connections and the tube. After the legs replacement, the air pump can reach 25 psi within ~25 minutes and the table can be floated.

The regulating valves are adjusted and the table is leveled.

The new optimization is less sensitive to the values of refractive indices, but the overall error will not change much if other material parameters have the uncertainties as we estimate.

Summary: see update of error analysis in PSL:1356. The issues from the previous entry are cleared

• I made sure that the monte carlo tests were correct
• The new optimization (called opt4, and opt5) will make the TO noise level/Transmission less sensitive to nH and nL values. But with the current estimate of uncertainties in other parameters, the performance will be about the same to that of the original optimization (called opt1).

1) show error analysis

 Today Tara showed me where to find isopropanol in order to clean the Peltier element. After cleaning it carefully, the TEC controller worked fine again! I am going to avoid using the silicone thermal paste for now in order to avoid this same problem, but if it becomes necessary I will add small amounts very carefully. I'm not sure how safe it is to clean the Peltier element often. The thermistor is being held onto the diode mount with aluminum tape. 

I worked on tuning the PID gain on the TEC controller. It seems a lot less stable than before, having a hard time settling on one temperature. Perhaps this is because I am not using the silicone thermal paste. I want to continue tweaking these settings, although I have them at something reasonably workable right now. It takes a minute or two for temperatures to settle, but they seem stable once a temperature has been reached. 

I cleared off a shelf in the ATF lab to keep my things. The collimating lens and lens adapter arrived, and Tara and I had to search for awhile to figure out where he put it (since they arrived while I was away). I put the lens into the lens adapter, and put this into the lens mount. Immediately, I noticed 2 problems which need to be fixed immediately:

1. The optic height of the lens (even with adjustment from the lens mount) is about 3-4 mm too low to work with the diode mount. I'm going to sketch something in Solidworks to hopefully get machined by the machine shop for next week so that we can fix this discrepancy. 
2. The collimating lens needs to be able to get closer to the diode mount, which means I need to modify the base. I will also sketch this in Solidworks and try to get it machined before next week. 

 Today I tried to calibrate the PID gain for the TEC controller. I noticed some connections needed repairing to I resoldered them, and checked every single connection.

However, the TEC controller still couldn't turn the Peltier element on, citing a "OPEN" problem (I believe according to the manual this means that something about the TEC connections are wrong). I checked these several times with my past notes and the instruction manual, but could not fix the problem. Then I tried cleaning the silicone thermal paste off of the Peltier element and was able to briefly make the Peltier element turn on. As soon as I tried reinstalling this in the ECDL setup, it stopped working. I was able to get the element working again briefly, but it was never stable (would stop working after a minute). I believe that I can use isopropyl alcohol without damaging any parts, but I want to do more reading online before I try this so that I am sure. It seems that trying to wipe the silicone paste out is insufficient, as I spent awhile trying this to recreate my results. 

I'm trying to find another optimization that is less sensitive to change in nH and nL. Here is a few thought and a few examples.

 ==problem==

We have seen that uncertainties (withing +/- 1%)in nH and nL result in higher TO noise (up to 10 time as much) in the coating. So we are trying to see if there is another possible optimized structure that is less sensitive to the values of n. We estimate the value of nH to be 3.51 +/- 0.03, and nL to be 3.0 +/-0.03. (The numbers we have used so far are nH/nL = 3.51/3.0,  while G.Cole etal use nH/nL = 3.48/2.977.

==Optimization method==

The algorithm is similar to what I did before[PSL]. But this time the cost function is taken from different values of refractive indices. The values of nH and nL used in this optimization are

• nH = 3.48, 3.51, 3.54
• nL = 2.97, 3.00, 3.03.

The cost function is the sum of the TO noise level at 100Hz, Transmission, and reflected phase, calculated from 9 possible pairs of nH and nL values. The weight number from each parameters (which parameter is more important) are chosen to be 1, as a test run. I have not had time to try other values yet, but the prelim result seems to be ok.

[Details about the codes, attached codes]

Note about the calculation,

The calculation follows these facts:

• The nominal values of nH/nL are 3.51/3.00
• The optical thickness is designed based on the above nH and nL
• The optimized design is reported in optical thickness which is converted to physical thickness with the nominal values of nH/nL
• The procurement of coatings control the physical thickness (with error in thickness discussed before PSL:)
• If the values of nH/nL changes from the nominal values, this will affect in the coatings properties because of the change in optical thickness.

 ==results from  QWL (55layers) and 4 other optimized coatings.==

1. Left plot shows  TO noise at 100Hz in m^2/Hz unit,
2. Middle plot:Transmission [ppm]
3. Right plot: reflection phase away from 180 degree.

Each plot has three traces (blue, black, red) for different values of nH (3.48, 3.51, 3.54). nL is varied on x-axis from 2.97 to 3.03. The first result is from QWL coating, with 55 layers. This serves as a reference, to see how much each property changes with the uncertainty in nH and nL.

   I tried to change the cost function in the optimization code and numbers of layer to see if better optimized structure can be done. The optimized structure (V3,4,5) seems to be less sensitive to the values of n, see below.

Above: from QWL coatings, 55 layers. nominal transmission = 100ppm.  We can see that the transmission of QWL coatings is still quite sensitive to uncertainties in nH and nL.

Above: First optimization reported before, TO noise is larger by a factor of 10 in certain case, and transmission can be up to 500 ppm. This coating is very sensitive to the change in refractive indices.

Above: opt3, obtained from the code using the new cost function discussed above.  55 layers, nominal transmission = 150ppm. The TO noise is less dependent on nH and nL, but the transmission is still quite high.

Above: opt4, the weight parameter for transmission is changed to 3, 57 layers.

above opt5,the weight parameter for transmission is changed to 50, Lower/Upper thickness bound = 0.1/0.5 lambda, 59 layers

 Above: Opt6, the weight parameter for transmission is changed to 500, Lower/Upper thickness bound = 0.1/1.2 lambda, 59 layers

From the results, optimized structure # 3,4,5 seem to be good candidates. So I ran another monte carlo error analysis on opt1 (as a reference), opt3, opt4, and opt5, assuming errors in both material properties and coating thickness. Each one has 5e4 runs. Surprisingly, the results from all designs are very similar (see the plot below). It is possible that, by making the coatings less sensitive to changes in nH/nL, it is more sensitive to other parameters (which I have to check like I did before). Or the properties are more dependent on coating thickness, not material parameters (this is not likely, see psl:1345). Or perhaps, there might be a mistake in the monte carlo run. I'll check this too.

I'll update the coating structure and forward it in google doc soon.

OK, I borrowed a Watec from the ATF. It is more sensitive than the jWin I was using, but judging by the graininess we appear to be close to the camera's noise floor. For the attached pictures I turned up the power on the RFPD from 1.0 mW to 1.5 mW, and that seemed to help a little.

 No (as I already told Tara).

The PD reflection is distorted and must be dumped in razor dump or black glass.

The mirror leakthrough can be detected easily by a CCD. CCD can easily see uW beams, but you have to use something beyond the $10 ones that Frank bought.

I placed a CCD camera behind the steering mirror directly before the south RFPD in the hopes of getting a handle on the shape of the refl beam while the refcav is locked or unlocked. Unfortunately I think the transmission through the mirror is too low; you can barely make out the refl spot when the cavity is unlocked, and it disappears when the cavity is locked.

Previously (PSL:798), Frank and Tara used a CCD camera to monitor the reflection off the RFPD itself. This reflection has enough power to be seen on an IR card, so perhaps this is the way to go (if we trust the face of the RFPD to not distort the beam).

Last week I talked to an engineer at Newport, and he agreed that the discrepancy (1 µW/V versus 30 µW/V) seemed unusual. Tara and I are sending this EOAM back to Newport for inspection; it should ship out today. We await Newport's diagnosis with bated breath.

I also mentioned to Newport that this EOAM has a minor annoyance with the two hex screws on the bottom of the case: the screw heads jut out slightly from the case rather than sitting inside the countersink (didn't think to take a picture, sorry). This causes the EOAM to have a slight roll when sitting on its kinematic mount. Tara was able to add a washer to the 1/4-20 screw holding the EOAM in order to mostly cancel this roll, but it would be nice to not have to deal with it in the first place.

 That surprises me too, but, that's what the calculation gives me. It is also strange that deviation in nH has smaller effect on to TO noise than nL does. I'm checking it. I ran the code one more time, and still got the same result.

Note: when I calculate the error in refractive indices, I assume that the physical thickness is constant = x * lambda/ n_0. Where x is the optical thicknesss. But if the the actual refractive index is not n_0, it means the optical length is not x, but x*n/n_0. I think this is a valid assumption, if they control the physical thickness during the manufacturing process.

update:Tue Sep 24 02:09:28 2013

The TO noise level does really change a lot when nL is nL + sigma (nL=3.0+ 0.03), dark green trace. Most of the change comes from TR noise level (not shown in the plot). TE noise remains about the same level.  It might be worth a try to find another optimization that is less sensitive to the change in value of n. I'll spend sometime working on it.

If that's true, then it means that a 1% deviation in the index of refraction of the low index material can by a 10x increase in the TO noise. Is this really true?

I removed 29 cm of SMA cable between the south RFPD RF output and the south TTFSS PD input in order to make the PDH error signal more symmetric. Relevant oscilloscope traces attached.

 The numbers in the table are the ratio between the TO noise when the parameter is changed by 1sigma and the TO noise calculated form the nominal value.

About the Poisson's ratios, Matt asked me to check for the values between 0.024 to 0.32, and the TO cancellation becomes much worse. I looked up papers about AlGaAs' Poisson's ratios. Most of the literature report the value ~0.32. I think we don't have to worry about it that much.

See

Krieger etal 1995 Table2, and ref 16 17 thereof.

Wasilewski et al1997 page 6, also discuss about the calculation and the measurement of poisson value in GaAs and AlAs, the value is still in the range of 0.27-0.33, not 0.024. The value of 0.27 is already considered very low.

zhou and usher has a calculation for poisson's ratio of AlAs. they report ~0.32, see table 2. and there references.

So I don't think Poisson's ratios of the materials will be a problem for us, since the reported numbers agree quite well.

 I don't understand these values for n.  

How can nH be 3 or 11? Isn't just that nL is ~1.45 and nH is ~2 ?  I would guess that the sigma for these is only ~1% of the mean values.

In our meeting, Eric mentioned that there might be some uncertainty in how the average coating properties are calculated.

To see how much it matters, I set the average properties to either that of the high-index (H) or low-index (L) material, and calculated the ratio of the new thermo-optic noise to the original calculation (TO'/TO) and the ratio of the new thermo-optic noise to the unchanged Brownian noise (TO'/Br) for Tara's optimized coating structure. The results are in the table below:

 C = Heat Capacity/Volume, k = thermal conductivity, alpha/a = thermal expansion

alphaBar_c and alphaBar_k are more complicated, since they take into account the Poisson ratio and Young's modulus of the coating materials, and may be wildly different from the thermal expansion coefficient. alphaBar_c is an average of alphaBar_k values, and when I use "alphaBar_k = alphas", I'm indicating that alphaBar_k is an array, and I have replaced that array with an array of the corresponding thermal expansion coefficients. As we can see in the final four rows of the table, alphaBar_c has a much smaller affect if we use an alphaBar_k value with all its added moduli and ratios instead of just regular thermal expansion. alphaBar_k_TR is the array of values used in the "Yamamoto Correction" to calculate the appropriate alphaBar for the thremo-refractive noise.

This all indicates to me that while most of the averages won't have much effect on our cancellation, a mistake in the calculation of alphaBar_k will.

The difference between alphaB_k and alphaBar_k_TR (in the last two rows of the table) is also interesting. Kazuhiro Yamamoto tells us this equation is correct, and explains the correction here. It's apparently because there is no added strain in the substrate due to the change in the refractive index, while there is strain for the thermal expansion.

I'm using Matt's code to do error analysis for AlGaAs coatings. This time I vary materials' parameters and compare the thermo optic noise, reflected phase and transmission. There is no alarming parameter that will be critical in TO optimization, but the values of refractive indices will change the transmission considerably.

Eric, Matt and I discussed about this to make sure that even with the errors in some parameters, the optimization will still work.

Parameters in calculation and one sigma estimated from Matt

% Coating stuff
betaL = 1.7924e-4 +/- 0.07e-4; %dn/dT
betaH = 3.66e-4  +/-0.07e-4 ;
CL = 1.6982e6   +/- 5%  ; % Heat Capacity per volume
CH = 1.754445e6   +/- 5%;
kL = 69.8672   +/- 5%   ; % Thermal Conductivity
kH = 55           +/- 5%;
alphaL = 5.2424e-6 +/- 5%; % Thermal expansion
alphaH = (5.73e-6 ) +/- 5%;
sigmaL = 0.32      +/- 10%; % Poisson Ratio
sigmaH = 0.32     +/- 10% ;
EL = 100e9    +/-20e9; % Young's modulus
EH = 100e9    +/-20e9;
nH = 3.51  +/-0.03   ; % Index of refraction
nL = 3.0     +/-0.03 ;

* Note: when I change nH and nL value, I keep the physical thickness of the layers constant. This is done under the assumption that the manufacturing process controls the physical thickness. The optical thickness in the calculation will be changed, as the actual dOpt = physical thickness * actual n / lambda.  And averaged values of coatings will depend on physical thickness.

 This is fixed in Line 120-180

== Effect on TO cancellation from each parameters==

 First, I calculate the TO cancellation when one of the parameter changes. Some parameters, for examples, Poisson ratios, Young's moduli, are chosen to be the same for both AlAs and GaAs. In this test, I vary only one of them individually, to see which parameters are important. The numbers indicate the ratio between the PSD of TO noise with change in the parameter and the optimized TO noise . Not the standard deviation of the parameters.

• A) + value for Young modulus is 142 Gpa, and - value is 83 Gpa, the value in the section below is 100 +/- 20 GPa
• B) Young's moduli and Poisson's ratios for the two materials are the same value in the calculation, Young HL row calculate the TO noise when both materials have the same value of Young's modulus, while YoungH and Young L row calculate the TO noise under the assumption that only nH material or nL material has different Young's mod.
• C) + value for Poisson is the nominal value, and - value is 0.024  the value in the section below is 0.32 +/- 10%

 Turns out that the change in Young's moduli and Poisson's ratios are quite important.

==Effect on TO cancellation, from all paramerters==

 Then, I calculate the TO noise when all parameters vary in Gaussian distribution, similar to what I did before,all parameters are uncorrelated. The histograms from 1000 runs are shown below.

1. Top, ratio of PSD of TO noise at 100Hz. The cancellation should still work well.
2. Bottom left, reflected phase. It is still close to 180 degree.
3. Bottom fight, transmission. The design is 200ppm, the result spread out in a big range from  10-500ppm.

I'll try more run overnight. Each run takes about 1 second.

== combined effect from errors in layer thickness and material parameters==

Since the comparison does not need to calculate the thermal fluctuations and finite size correction all the time, I cut that calculation out and save some computation time.  Now I compare errors from

1. Error in both layer thickness and materials parameters (red)
2. Error in layer thickness only (green)
3. Error in materials parameters only (blue)
4.  Error in refractive indices only (cyan)

Each simulation contains 5e4 runs.   The Transmission varies a lot depending on the material parameters ( mostly refractive indices,  see the cyan plot).

The cancellation seems still ok. Most of the time it will not be 10 times larger than the optimized one. Only the transmission that seems to be a problem, but this is highly depends on refractive indices. It's weird that the error makes the mean of the transmission smaller.

Details for AlGaAs coatings order

• Coating structure can be found in http://nodus.ligo.caltech.edu:8080/PSL_Lab/1340, 55 layers, T = 197ppm.
• Coatings for 4 mirrors plane/concave, 1” diameter, 1/4” thick, with radius of curvature = 1.0m.
• AlGaAs coatings will be applied on the concave side of the mirror.
• Flat side is already AR coated
• absorption loss 6-10ppm / scattered loss 3-4ppm
• Spot radius (1/e^2 power) will be 215 um.
• The mirrors have an annulus on the rim for optical contact with thickness ~ 3mm. This area should be kept clean.
• The coating wafer should be inside the mirror sagitta to make sure that it will not obstruct the optical bond area. By calculation, the wafer with 8mm diameter, 4.5um thick should be ok. The maximum diameter that makes the coating to be above the sagitta is about 16mm, for 4 um thickness.

• Required coating diameter = 5-8mm, Power loss due to clipping is less than 0.1 ppm, see below figure.

Above, plot of ratio of power due to finite size mirror P(r) / P0,  P(r) is the power of the beam at radius r from the center. G Cole said that the wafer can be made to 8mm diameter. diameter between 5-8 mm should be good for us.

 I discussed the calculation with Matt. The error in TO noise is large because it is a fraction of something small. Mostly it comes from TE part. The error in TO noise appears large (10%-20%) because the TO level is small.  Otherwise, the rests are in good agreement, and I think we should be able to order soon. 

 Below, summary of the calculation, dTE is alpha_effective * coating thickness, dTO is beta effective * lambda. 0.2% difference in dTE and 0% difference in dTR can cause error upto 40% in dTO when dTE and dTR cancel each other really well. But this will be insignificant, since the final TO levels are still in the same magnitude.

The summary of the TO cancellation is in wiki page AlGaAs

Tara noticed an accidental re-definition in my old code. I fixed it, and updated the svn. This fixes most of the discrepancies, but shifts the difference in thermo-optic to the low-frequency region.

Attachment 1 is the comparison from case 3 between mine and Tara's calculations of his optimized coating structure.

Attachment 2 is the comparison from case 2 between mine and Tara's calculations of a 55-layer 1/4-wavelength stack.

Yesterday I measured the noise of the refcav PDH loops. Because of RFAM effects, possible nonlinearity in the RFPD response, etc., the correct way to measure the loop noise is to take the PSD of the error signal (Common OUT1 on the TTFSS) while the cavity is unlocked but light is still incident on the cavity and on the RFPD.

For these measurements, the south TTFSS gain was 642 common and 702 fast, and the north TTFSS gain was 802 common and 835 fast; these are the highest gain settings I could achieve before the loops started to oscillate when locked. There was 1 mW of light incident on each cavity.

Plots and data are attached. I've converted from voltage to frequency using the slopes I found in PSL:1339. Current thoughts:

• These plots seem to say that at high TTFSS gain, we're actuating on sensing noise rather than cavity frequency noise. I'm not sure I believe this yet.
• We're dominated by (what is probably) seismic noise below a few hundred hertz.
• There's something goofy with the north TTFSS; I would say it's a grounding issue, but the fundamental peak looks more like 75 Hz than 60 Hz.

Optimized coatings structure.

I took measurements of the carrier and sideband power transmitted through each cavity in order to get the modulation depth Γ of the EOMs. The modulation depth is related to the transmitted powers by Γ²/4 = P_SB/P_car. [Edit: I checked last night in Mathematica, and it seems the approximation Γ ≈ J₁(Γ)/J₀(Γ) is good to about 1% for Γ < 0.3.]

First I aligned the cavities to get good refl visibility (about 90%). Then I aligned the transmitted beams onto the ISS transmission PDs. Then I unplugged the EOM HV actuation on the TTFSS.

To get the transmitted carrier power, I locked each cavity as usual and then wrote down the voltage on the ISS PD. To get the sideband power, I flipped the sign of the fast actuation on the TTFSS, thereby making the servo lock on the sideband. I then wrote down the voltage on the ISS PD. I also blocked each transmitted beam to get the dark voltage on the ISS PDs.

For posterity, I also took triangle-wave sweeps of the ISS transmission, the refl DC, and the error signal. The oscilloscope traces are attached. [Edit: from a quick look at the error signal traces, I get slopes of (164±10) kHz/V for the south cavity and (199±12) kHz/V for the north cavity.]

In other news, the south PDH error signal looks a bit asymmetric; I think it might need a phase adjustment.

 I checked the calculation. I think most of the discrepancies are from the thick coating correction calculation (from Evans etal paper). The error is frequency dependent, and the calculations that involve frequency dependence are temperature fluctuation and thick coating correction. The temperature fluctuations are the same from our results. So it is most likely the thick coating correction. I checked and the corrections did differ at high frequency.

 I need to take a closer look to tell exactly where the errors are. Since the error is small and only at high frequency (around the shot noise limit, 10kHz),  I don't think it will be a problem for us.

 combined PDFs with pdftk:

pdftk *.pdf cat output MattThermal.pdf

and saved as PDF-X for thumbnail compatibility

Neither Tara nor I can get the north New Focus 4104 to put out a significant amount of power modulation, despite going through (what we think is) the biasing procedure several times. We're getting modulation on the order of 1 µW/V, compared to 30 µW/V when we first installed the south EOAM (PSL:1287).

To review, these New Focus EOAMs consist of two lithium niobate crystals mounted with their fast and slow axes orthogonal to each other. If the crystals are the same length, then with zero applied voltage the EOAM should have no birefringence. Any applied voltage causes the EOAM to become birefringent; the voltage required to produce a λ/4 retardation between the two optical axes is called the quarter- wave voltage, and the voltage required to produce a λ/2 retardation is called the half-wave voltage (V_π).

To use the EOAM for intensity modulation, we put down a HWP before the EOAM to make sure the input beam is either p- or s-polarized relative to the optics on the table. The EOAM crystals are mounted at 45 deg., so the input beam therefore is projected in equal parts onto the EOAM's two optical axes. After the EOAM there is a QWP with its fast and slow axes aligned to the EOAM's optical axes [Edit: actually the manual says to align the QWP axes to be horizontal and vertical wrt the table, which I don't understand. At any rate, neither configuration makes the EOAM work.], and following that there is a PBS which passes only p-polarized light. The intensity of the light transmitted through the PBS is a linear function of the EOAM birefringence only when the beam entering the PBS is nearly circularly polarized, so the purpose of the QWP is to optically bias the beam so that we can actuate around zero volts on the EOAM. (The alternative is to have no QWP and instead electrically bias the EOAM to its quarter-wave voltage.)

Anywho, the procedure that Tara and I have gone through is

1. Remove the EOAM and QWP. Adjust the HWP preceding the EOAM so that the intensity through the PBS is at a minimum.
2. Put down the QWP and adjust it so that the intensity transmitted through the PBS is equal to the intensity reflected from the PBS. This should mean that the beam into the PBS is circularly polarized.
3. Put down the EOAM and align it so that the beam passes through.

After this, the setup should now give linear intensity modulation when a few volts are applied to the EOAM. For the south EOAM this procedure worked fine—by applying a few volts to the EOAM we could see the power change on the ThorLabs power meter. But with the north EOAM the power changes are much, much smaller.

[Tara, Evan]

In preparation for tomorrow's sprinkler installation, we have removed any extraneous optics, cables, and electronic equipment on and around the table. Everything on the table is now covered by a drop cloth.

I changed the values so that the feedback is 13 kΩ in series with 1.2 nF, and the inverting input is 1.3 kΩ. This puts the zero at 10 kHz.

I duplicated this with a second OP27 on the same circuit board, so now there is an integrator for each cavity.

Last night the best results seemed to be achieved with the SR560s set to G = 100 with a pole at 10 kHz.

The cause of the peaks around 1kHz in RIN is solved, PMC is the reason. After damping it, the peaks disappears.

Short notes from tonight measurement:

• RIN in ACAV is better after PMC is damped, no peaks around 1kHz anymore.
• The peaks in the beat measurement also disappear, so we really see photo thermal noise.
• PD for RIN measurement behind RCAV is added, RIN is measured.
• I Will add the effect from RIN and compare with beat measurement soon.

need to buy:

•    new PBS for PDH locking. the one for RCAV is not good because there is an unwanted reflected beam going to the RFPD.
•  other optics for EOAM for RCAV

I'm trying to understand the measured RIN in the setup. The evidence suggests that the measured RIN in 100Hz- 6kHz, is real intensity noise and not associated with alignment + jitter.

==Problem==

As seen in PSL:1329 that we might be limited by RIN at high frequency, I tried to figure out what cause the shape of the RIN around kHz to be mechanical -like peaks. So the problem can be minimized, and does not have to rely on ISS that much.

==Assumption==

My assumption was that they were from mirror mounts, because

1. the frequencies were close to mechanical resonances of the mounts, see PSL:818, PSL:824 for examples. The power coupled into the cavity would reduce, and thus causing the peaks in the RIN measured behind the cavity. And
2. the shape changes during the time of measurement. During the day, the shape is like a big bumb, while during the night, around 2-3am, the level is smaller and the individual peaks shows up instead (may be because of the lower seismic)

==Measurement==

So to test this, I measured RIN before and after ACAV (NOTE:ACAV path has PMC in it),  when

1. The beam was well aligned to the cavity (DC from REFL PD =94mV, total level ~ 1.6V)
2. The beam was misaligned a bit (DC from REFL PD = 175mV)

above, beam path in front of ACAV, before the beam enters ACAV. The PD for RIN measurement is circled in blue.

above, beam path behind ACAV.

If the measured RIN was from the jitter, RIN after the cavity should change with the alignment, and RIN before the cavity should not change much. I made sure that the spotsize on both PDs are significantly smaller than the PD to make sure that any jitter in front of the cavity should not change the power level that much.

==comments about the result==

• The result agrees with the assumption at low frequency (DC - 30Hz),
  
• However, from 100Hz and above, the measured RIN from four cases are very similar.
• The measured coherence between the two PDs are similar in both cases (aligned and misaligned), I plotted the one from the misaligned beam. It shows that at low frequency, RIN behind and after the cavity are not caused by the same mechanism, the one behind PD might suffer more from jitter. However, at 100Hz and above, anything observed before the cavity is seen behind the cavity as well. This rules out the assumption that the alignment change due to the motions(resonant peaks) from optics.
  
• As a comparison, I plotted RIN measured around 3am in brown trace, see PSL:1329, the level is smaller than those measured in the evening. It still makes me think that it is related to seismic but not alignment. I have to think about what other seismic driven mechanism might cause this intensity noise.
• The level of RIN seems to change as well, I looked at Evan's measurement, earlier today[/PSL:1330]. The bump around 1kHz is ~ 2e-6 1/rtHz, while for my measurement, it is close to 1e-5.  I'll try to investigate more to find out what change the level of RIN.

==To do next==

• Pick up the beam some where before PMC to check the RIN level and see where the peaks occur
• Install PD behind RCAV, see RIN from RCAV
• update noise budget: add RIN induced noise from ACAV and RCAV.

I made a quick inverting op-amp integrator which kicks in at 860 Hz at has gain 10 at infinity. The feedback is a 5.6 kΩ resistor in series with a 33 nF capacitor. On the inverting input there is a 560 Ω resistor.

I put this after the SR560 with gain set to 100 and bandwidth set to 30 kHz. It seems like this gives good RIN suppression.

The measured RIN is measured and converted to frequency noise via photo thermal effect then compared to beat. The effect seems to be significant now since we lost the common mode rejection.

I measured RIN after ACAV (there is only one PD behind ACAV right now. we will add another one for RCAV soon). The magnitude is comparable from what we measured before but the peaks seem to change, see PSLPSL:1326, :PSL:1308,  (8"cavity) PSL:742 .

The peaks around kHz  are more clear. I'm not sure where they are from, but I think it is associated with vibration on mirror mounts that causes beam jitter. Because the peaks look like mechanical peaks, and this time the cavities are shorter, the beamsize is smaller from 8" cavities, the same beam misalignment will cause the power coupled into the cavities to change more compared to that of 8" cavity. We can check that by mis-aligning the input beam a bit, and see if RIN becomes larger or not.

The coupling from RIN to frequency noise is discussed in PSL:1328

I applied that to the measurement and here is the result. Note, only the effect from one cavity (ACAV) is taken into account.

The peaks seems to match up, especially around 20-30Hz and around 1kHz, see the zoomed in picture below. This makes me think that we might be limited by RIN noise now.

To Do next:

• Install ISS system on RCAV (PD behind the cavity / EOAM)
• Re-measure the coupling from RIN to frequency noise of the cavity
• Measure RIN and apply it to the noise budget.
• Find out what causes RIN to change

I've taken the above RIN data and combined it with the intensity-to-frequency TF in PSL:1316 to arrive at an estimate of the RIN-induced frequency noise.

By eye, I fitted the magnitude of the transfer function from Tara's farsi.m code to the following model:

The first attachment shows this fit compared to the original TF.

I used this TF (along with the dc power 0.74 mW incident on the cavity) to convert the measured RIN (suppressed and unsuppressed) into frequency noise. I multiplied the result by a fudge factor of 3 to account for the fact that the TF we measured was a factor of 3 higher than the expectation.

The result is shown in the second attachment. Since this only with G = 500, Chas's high-gain ISS board should crush the RIN well below the expected Brownian noise.

Short note from tonight measurement:

1) scattered bump from dc to 100Hz is mostly from seismic. It is worse during the day. It gets smaller at around 3-4 am. Unless we have a better seismic isolation, we might not be able to see anything below 100Hz.

2) RIN shape from RCAV changes, reasons still unknown. (DC level 0.7 V)

3) I might see the effect from RIN induced TO noise at frequency ~ 1-3 kHz. (compare RIN and beat).

I'll get into details tomorrow.

At Tara's suggestion, I implemented a simple ISS by feeding the output of the PDA10CS into an SR560 (ac-coupled) with some gain, and then the output of the SR560 into the EOAM.

I found that by turning on a 6 dB, 30 kHz low-pass filter on the SR560, I could put the gain at 500 without saturating the SR560 output. No inversion is necessary because positive voltage on the EOAM decreases the beam power (so there is already a minus sign in the loop).

I monitored the RIN by feeding the output of the PDA10CS into the SR785. The in-loop RIN is suppressed by a factor of 6 or so. Once Chas's board is here, the suppression should be much greater (since the gain will be 10⁶ at low frequencies).

The shape of the RIN spectrum has changed compared to the previous RIN measurement. The 2 kHz peak is gone, and the shelf from 100 Hz to 1 kHz has dropped. Maybe it's because Tara has damped a lot of the mechanical resonances of the table optics with rubber stoppers. The low-frequency RIN remains at a few times 10⁻⁴/rtHz. According to Tara, this is probably induced by seismic coupling (not by fluctuations from the laser), and so the right way to make it go away is to float the table.

There is a minor mystery here. Based on the previous RIN measurement, I expect the dark noise of the PDA10CS to be at 7×10⁻⁷/rtHz or so abve 1 kHz. Why have I apparently been able to measure below this noise floor in the attached plot?

I used the black voltage calibrator to give the south EOAM a DC voltage, and then used the ThorLabs power meter to read off the DC power level before the PBS that used for picking off the RFPD path.

I find the volts-to-watts conversion is (5.93±0.12)×10⁻⁶ W/V. This will, of course, change if we change the input power level into the EOAM. I guess if there's a more lasting message here, it's that we've got the orientation of the QWP after the EOAM in a pretty good place, since there's no visible nonlinearity in the attached plot.

 The estimated seismic noise in the plot uses the coupling calculated by COMSOL model, see PSL:1060 and PSLL1065. It is the coupling between acceleration to the cavity displacement noise. It is just an upper bound of the seismic noise, no common mode rejection is used in the calculation.  (I have to check if the seismic noise data in the noise budget is from floated or unfloated table).  So far, only displacement noise from vertical seismic motion is calculated in the noise budget.

 I'm certain that the noise bump below 100 Hz is mostly scattered light induced by any vibration on the chamber. The reasons are:

1. The behavior of the noise. It slouches back and forth when I slightly tap on the vacuum chamber.
2. We have seen this before and after the table was floated. See the measurement from unfloated table, psl:878, and floated tablePSL:966. The hugh bump from DC to 100Hz disappears and the mehcanical peaks around 20-50 Hz show up after being buried by the big bump. The causes of these mechanical peaks are not known. I never found out where they came from. I thought they might be some modes of the seismic stacks, but the previous measurements do not have the peaks around 20-50Hz. See PSL:1314.

 So I don't think we really hit the actual seismic-driven displacement noise yet ,and what we see is mostly from seismic-driven scattered light which I don't know how to calculate. I ordered a new set of table leg to replace the current ones that leak. They should be here next month.

 Can you please explain how the seismic noise coupling is estimated for the noise budget?

Since the cavities are now on the same stack it seems tricky. I guess that some stack tilts produce differential vertical accelerations on the cavities. How much of the noise below 100 Hz is from scattered light?

Coating optimization and error analysis are updated, see PSL:1320.

It's a quiet night, so I went down the lab to measure the beat signal. We are getting close. I think I have to review my noise budget calculation and estimate the error in the measurement carefully.

So after a few things Evan and I did a few days ago:

1. rotate the stack to get rid off the reflected beam from the window
2. fix the insulation so the beam is not clipped on the opening.
3. add more modulation depth to RCAV path with the EOM driver (tuned to 14.75MHz)
4. Minimize some RFAM, by rotating the half wave plate in front of the sideband EOM

Then I measured the beat signal.

We reduce some noise from scattered light at frequency below 100 Hz, we are limited by some white noise at high frequency ~ above 1 kHz.

fig1: measurement vs noise budget

fig2: zoom in. The slope of the measured signal agrees well with the slope of thermal noise.

ToDo

• Estimate/measure shot noise PD noise and electronic noise in the setup. See if they match up with the measurement.
• Review the noise budget calculation. Looking at the slope of the signal around 1kHz, I think the calculated brownian noise is lower than what it should be.
• noise hunting, seems like scattered light at frequency below 100Hz. There are many mechanical peaks, and harmonic lines at higher frequency.
• add the contribution from RIN induced TO noise in the nb.

I updated the optimization and error analysis. The error in optimized structure is comparable to that of a standard quarter wave length structure.

      After a discussion with Rana, Garrett, and Matt, I fixed the thermo-optic calculation, and the error analysis done in PSL:PSL:1315.  The modifications are

       1)  fix the TO calculation (Yamamoto TR correction): There is a modification for TR correction that is not in Evans etal 2008, paper. I contacted M. Evans to ask about the details of this correction which is done in GWINC.  

       2)  Try another optimized coatings with the correct TO calculation:  After the correction, I ran doAlGaAs.m code, cf PSL:1269  using fmincon function , to find another optimized structure. The result is shown below.

above) layer structure in optical thickness, the .fig and .mat file are attached below. Note .mat file contains 54 layers, you need to add 1/4 cap to the first entry to calculate the noise budget.

above) noise budget of the optimized coating.

       3)  Repeat the error analysis : This time I used the following assumptions (from G Cole)

• the error is not random among each layer
• the error is constant in each layer type, ie all the layers from the same material (nH or nL) have the same percentage of error,
• error from nH and nL have the same sign. If one is thicker, another one is thicker, but the magnitude are uncorrelated.
• nH (GaAs) has better thickness control with 2sigma = 1percent, while nL(AlGaAs), has 2sigma = 2 percent.

Fig1: Above, percentage of error distribution between the two materials used in the calculation. nH(red) has 2 sigma = 1% and nL(blue) has 2sigma=1%.The same error distributions are used for both optimized layers and QWL layers in comparion, see fig2.

The section below is the algorithm used to distribute the error, this one makes the error between the two materials to be the same sign. The whole code can be found on svn.

===Result==

This time I calculated the change in reflection phase (TOP left), the ratio between TO noise from the coatings with error and the coatings with no error(top right), transmission (bottom left), and ratio of BR noise ( bottom right). The result from the optimized coating(blue) is compared with the QWL coating (black).

Fig2: Error analysis, in 5e4 run. Blue: from optimized coatings Black:from 55 QWL coatings, from 5x10^4 runs.

Reflection phase: The reflection phase can be away up to ~6 degree. The power at the surface will be ~Finesse/pi * Power input * sin^2 (6degree) ~ 50mW. Seems high, but this is about a regular power used in the lab.

Ratio of PSD TO/TO_0 : At worse, it seems the PSD TO noise will be ~ a factor of 10 higher than the design. However, this will be still lower than BR noise. I plotted only the error distribution for optimized coatings because for QWL coatings, the ratio will be about the same, since TO is dominated by TE.

Transmission: Most of the results are within 197-200 ppm. The optimized coating has transmission ~ 197ppm. The QWL with 55 layers has transmission ~100ppm.

Ratio of BR: not much change here.

The turbo pump is removed, and the ion pump is on. The initial value is ~7mA.

I removed the turbo pump and turn on the ion pump, see the procedure on wiki page. The initial value on the ion pump is ~ 7mA, similar to the last time we opened the chamber although this time I left the turbo pump on 4 days instead of 2 days. So I think this is the limit of this turbo pump.

Here is a summary for how I verify the codes for TO calculation.

So far, we have been using a set of modified GWINC codes to calculate TO noise, but I have not mentioned how did I make sure that the codes were reliable. So I'll try to explain how I check the codes here.

==What do we compute?==

  For the TO nosie calculation and the optimization, we are interested in:

• effective dn/dT (TR coefficient) of the coatings
• effective alpha (TE coefficient) of the coatings
• total reflectivity of the coatings (including the phase), and transmissivity

==Beta calculation check==

For TR coefficient we can compare GWINC with an analytical result (see Gorodetsky,2008, and Evans 2008) (when # of layers ~ 50 or more), see psl:1181. I tried the solution with nH, 1/4 cap and nL, 1/4 and 1/2 cap. All results agree.

==Alpha calculation check==

 There is no complication in this calculation. The effective alpha is just the sum of all layers. This calculation is quite straight forward.

==reflectivity check==

   This was done by reducing the coating layers to one or two layers and comparing with an analytical solution by hand. I checked this and the results agreed.

So I think the calculations for TO noise is valid, the noise estimated from the optimized coatings is done with some error check (previous entry). I think we should be ready to order.

We modified the EOM driver, so that the resonant frequency is now~ 14.75MHz. The full test will be done later.

As mentioned in PSL:1311, the resonant frequency on the EOM driver was not at 14.75MHz. Evan and I discussed about how to modify it and decided tof change L4 from 1.4uH to 3 uH, see the schematic here.

above, the driver after the inductor was replaced. The new one has a shield to reduce any magnetic field leakage. The legs are not fit with the footprint on the PCB, so I had to solder it to another wire to reach the footprint.

above: the TF of the driver measured between the drive and the mon output. Red trace shows the TF before the modification. Yellow  trace shows the TF after the modification, notice the peak is at 14.75MHz, the Q is about the same.

[Tara, Evan]

Last week we tried measuring a transfer function which takes intensity fluctuation induced at the south EOAM and returns frequency fluctuation as read out by Tara's beat setup. This is therefore meant to be the measurement corresponding to Tara's code farsi.m (on the SVN at CTNLab/simulations/misc).

We used the SR785 in swept-sine mode. As measured previously, the EOAM response is 3×10⁻⁵ W/V (although I think this number should be rechecked, since we've fooled around with the EOAM in the meantime). The beat PLL readout is 7.1 kHz/V (when the Marconi is set to its 10 kHz setting). [Edit, 2013–10–18: by comparing with the newer measurement in PSL:1368, I think the Marconi must have actually been at the 1 kHz setting, so the conversion factor is 710 Hz/V and the transfer function measurement below is a factor of 10 too high.] These two numbers give the conversion factor necessary to convert from V/V into Hz/W.

The attached plot shows the measurement and the expectation from Tara's code. Here I'm using the version of the code as checked out last night, and in my local copy of the code I changed the cavity length to 1.45″ and the input power to 1 mW. Below 200 Hz, the agreement in magnitude is good: the overall shapes agree the values are within a factor of 3 of each other. The phase also appears to be good below 40 Hz or so. Above 200 Hz the transfer function is apparently dominated by some other effect.

Since the optimized layer structure is designed, I'm checking how the coatings properties change with error in layer thickness.

G.Cole said that they can control each layer thickness within 0.3%. So I tested the optimized coatings properties by adding some random number within +/- 0.5% on each layer thickness. The results are shown below for 10 000 test.

The error check does the following:

• start from the optimized coating structure reported in PSL:1291.
• add random thickness to each layer, within 0.5% of each layer
• calculate the values of interest, then histogram them.

The figure below is an example of the varying layer thickness added by rand command. They are confined within 0.5%.

 1) result from the error in thickness control

Above: histograms of the important values. top left, reflected phase. top right, ratio between PSD of Brownian noise and Thermo optic noise at 100 Hz. Bottom left, transmission. Bottom right, total coating thickness error.

 comments: this test is chosen for 0.5% error which is almost a factor of 2 worse than what they claimed (0.3%), so the actual result should be better. I assumed 0.5% errof because of the irregular layer structure of the optimized coatings, there might be some more error in the manufacturing process.

• Reflected phase: we want the reflected phase to be close to 180, so that the E-field at the coating surface is close to 0. more than 50% of the results are within 179.5degree, this means that the power build up will be ~ Finesse/pi * Power input * sin^2 (0.5degree)  ~ less than 0.4 mW, so there should be no problem about burning at the surface.
• ratio between PSD of Brownian/Thermo optic noise. This plot imply how well the cancellation works. Since Brownian noise will almost not change (both materials have the same loss, total thickness varies less than 1%), the ratio of Br/TO noise (at 100Hz) tells how much TO cancellation is. From the histogram we are quite sure that cancellation will work most of the time.
• Transmission is good around 200+/- 10ppm this is ok with the requirement.
• total physical error is ~5nm while the coatings thickness is ~ 4um. so the total error is <0.1% Brownian noise calculation will not change much.

2) result from different calculated Beta values:

Here I checked what happen if the beta calculation was wrong, and the error is still within 0.5% in each layer.

In Evans paper, the effect from "Thermo-refractive" comes from the phase changes of the wave travels in each layer. So it includes the effect from dn/dT and dz. The effective beta for each layer is given as

[evan B8],

where alpha bar is

[evans A1]

Where s denotes substrate, k denotes the material in each layer (high or low indices).

So my, calculation & optimization have been using these equations.

However, in the original GWINC code for TO calculation, the calculation [B8], alphabark( used in dTR) is not the same as A1, but rather.

alphaH * (1 + sigH) / (1 - sigH)

see getCoatLayerAGS.m.  Line 16-17.

This is used in the calculation for beta effective in getCoatTOphase. Line73-74. Notice that for dTE, the alpha_bar_k is the same as used in Evans. (line 77).

the comment says "Yamamoto thermo-refractive correction". I emailed kazuhiro yamamoto, but never got a response back. So I keep using the same formula as in Evans because I don't see the reason why the expansion contribution should be different between TE and TR.

So this is the nb plot for TO noise from the optimized coating, if using yamamoto TR correction.

Above: nb from the optimized coatings, using Yamamoto TR correction. The cancellation becomes worse, but TO is still lower than other noise.

Finally, I repeat the same error analysis for random noise in the thickness (+/- 0.5%).

Most of the parameters behave similarly, except the cancellation (upper right plot). Now BR is only ~ x12 larger than TO noise because of the worse cancellation. Good news is, it still below Brownian noise, the cancellation still somehow works.

=summary=

• From the optimized coating structure (T=200ppm), thickness control within 0.5% in each layer will make the coating work as expected.
• The yamamoto TR correction is still an unresolved issue, but the optimized coating will still work.
• we should be ready to order soon.

[Tara, Koji, Evan]

On Friday when the vacuum chamber was open, we took some impulse response measurements of the seismic isolation stack. We used a HeNe laser and a PDA100A as a shadow sensor for recording the responses.

The measurement setups were as follows:

1. With the shadow sensor positioned so as to register vertical motion of the top surface of the seismic stack, Tara poked the top of the cavity mount.
2. With the shadow sensor positioned so as to register vertical motion of the top surface of the seismic stack, Tara poked the top surface of the seismic stack near the end of the stack.
3. With the shadow sensor positioned so as to register vertical motion of the top surface of the seismic stack, Tara poked the right side of the seismic stack near the end of the stack.
4. With the shadow sensor positioned so as to register horizontal motion of the transmission corner of the seismic stack, Tara poked the left side of the seismic stack near the end of the stack.
5. With the shadow sensor positioned so as to register horizontal motion of the transmission corner of the seismic stack, Tara poked the front of the seismic stack near the end of the stack.

For each setup, two ringdows were taken with the scope AC coupled (we'll call them measurements A and B).

I used scipy.optimize.curve_fit to fit each ringdown to the sum of two damped harmonic oscillators:

where θ is the Heaviside step function. In the table below I've collected the fitted frequencies and Q factors. In the first attachment I've plotted the ringdowns, their Fourier transforms (with no windowing—very crude, but it is only intended as a very rough guide), and the fits (in red).

I haven't assigned error bars here because I think I may be overfitting; the amplitude and phase parameters and the offset parameter have huge uncertainties (many times the nominal value). However, by eye the fits of the ringdowns appear to be pretty good, and so I am inclined to believe the fitted frequency values.

I closed the chamber. The turbo pump is on and pumping down.

 I realigned the beams so the visibilities for both cavities were 80% or more. This made sure that the beams' path would be close to the optimized path.

Now, the window reflection won't overlap with the cavity reflection, and can be dumped properly.

Note about a few things to do:

• The beam holes on the foam might have to be fixed, the beams slightly clip at the openings. I have to check if the beams are clipped at the periscope or not.
• modification of the seismic stack as suggested by Koji. The teflon pieces at the bottom plate are not screwed down to the stack making it hard to put the stack in the chamber. I think this should be fixed after the SiO2/Ta2O5 measurement is done and we have to reopen/ installed AlGaAs cavities.
• There is some strayed beam from the PBS in RCAV path. This is from left over beam in S-light that reflected off, and bounced back at the PBS surface before going to the PD. This might have to be fixed too.

FYI for torque wrench setting for CTN cavity:

 The CTN cavity is 10" OD,  the Torque required is 190 InchPound.

 [Tara, Evan]

Tara and I opened the CTN vacuum can this afternoon. Previously, the reflection from the vacuum window was overlapping with the reflection from the south refca, so Tara repositioned the seismic isolation stack in order to get rid of this overlap. We have now realigned into the two refcavs, and neither show any reflection overlap. The attached picture shows the two reflections at the PBS pickoff for the RFPD path for the south cavity. The large spot is the refcav reflection. Slightly to the left of it you can kind of make out a much smaller spot, which is the reflection from the vacuum window.

For the north cavity, the refcav reflection is currently clipping on the QWP nearest to the vacuum can, while the vacuum window reflection makes it through the QWP and onto the RFPD path. So evidently there's no overlap here either.

We also took some measurements of the impulse response of the seismic isolation stack, but that will be covered in a subsequent elog post.

The bump at 2kHz in the beat signal that I saw before was also from RFAM. By adjusting the 1/2 waveplate in front of the sideband EOM, the bump disappears. I still don't understand why adjusting the EOAM can reduce the bump from RFAM.

 As I planned to add the eom driver to the BB EOM for sideband in RCAV path, I wanted to see the improvement without worrying about the EOAM optimzation. So I removed the EOAM, but I still saw the bump I observed before. This time it came from the RFAM. By adjusting the wave plate to match the polarization of the input beam to the EOM axis, the bump is gone.

above: From right to left, 1) laser for RCAV, 2)&3) 1/2 and 1/4 wave plates, 4) lense, 5) Faraday isolator, 6) 1/2 wave plate, 7)BB EOM for frequency locking, 8) BB EOM for side band, the EOM driver is attached to the side (in aluminum foil wrapped box). RFAM is minimized by adjusting (6) 1/2 wave plate.

I added the EOM driver, however it was not yet modified for 14.75 MHz, so the amplification is small, see PSL:1234 . After adjusting the phase of the demodulated sigmal, the error signal slope is increased by a factor of 2. Then I remeasured the beat signal, and the beat was better by ~ a factor of 2 at high frequency. So I think now the signal is gain limited (in RCAV loop) at high frequency. This makes me confused why the error noise from RCAV loop does not match the beat signal in PSL:1307. I have to re check my work.

The next few things to do are:

• minimize RFAM (by temp control on both EOMs )
• re-install EOAM in RCAV path, think about alignment
• now scattered light at low frequency might come from seismic noise as well. I'll order the new floating table legs soon.
• check other noise limit to make sure that it will not be dominating (shot noise, electronic noise)
• modify the EOM driver, so that we have more gain in RCAV path.