Mama mia!

Per favore, utilizzare solo PDF.

Scusami :-(. D'ora in poi usero' solo PDF :-)!!!

This fragility of MM is one of those things we ought to develop a MCMC for. Jenne did something like this for the 40m input mode matching a long time ago, but that was before I understood what corner plots were for.

I wonder if JamMT or alaMode have the ability to be run to generate corner plots. If so, we could find out the sensitivity to lens positions and lens focal length errors in a visually useful way for each mode matching solution (generated from the discrete set of available focal lengths in the CVI catalog).

Might be a project to give to the CTN SURF this summer.

Today I altered beamPath.m in alamode to support gwmcmc.m, which is pretty much emcee for matlab.  (The gw in gwmcmc stands for Goodman-Weare MCMC algorithm, not gravitational waves). 

It's capabilities are pretty limited, all it can do is move around optics.  It cannot set hard limits on where an optic can be placed yet, and it cannot vary a lens' focal length.  It would be easy to add these capabilities for the future.

My log likelihood for the MCMC algorithm is -0.5 * [ weight1 * (1 - overlap)^2 + weight2 * positionSensitivity^2 ], where weight1 = 100 and weight2 = 1.  The user can choose how much to weight each metric which quantifies the quality of the mode match.  Overlap and positionSensitivity were already calculated for me by alamode.

I ran the MCMC on our North path mode matching, allowing two of our lens to move around by about 20 cm for our old lens focal lengths.  Initially, Lens1 was 0.9625 m from the PMC and Lens2 was 1.3717 m.
I get two peaks of different mode matching, which I thought was pretty cool.  My final results for the Lens2 position ended up pretty far away from where I started, which is not physically possible in our setup.  Need to add hard limits to this. 

Not sure how to distribute this.  It's in the tar in this ELOG.  Will also copy this to Git/labutils/alm.  Once it's cleaned up, our future person could make a pull request on github/alm.

also Haocun at MIT started to convert alamode to python a few years ago. I don't know if anyone has gone further: https://github.com/Haocun/alm

And Lee@MIT also has a python alamode as part of his ultimate ('simulate everything') package:

https://github.com/nicolassmith/alm/issues/15

Perl scripts for controlling the vacuum tank and slow feedback to the two lasers are acting weird. Usually we can run three scripts simultaneously, but I just notice that only two can be run at the same time. When I restarted the script for acav feedback, the vac temp control stopped. When I restarted the vac temp control, acav slow feedback stopped.  I'll check this later.

Craig helped me with the epics channel calibration. I made a conversion formula for voltage to Celcius by setting the room temperature to the measured voltage of -8.63V which is what the channel had as its output. I used a linear conversion of , similar to the one I had for my initial sensor. T is temp in C and V is voltage in V. Since the AD590 outputs a current proportional to the temperature, we can just have a direct relationship between the temperature (in K) and voltage since the resistance in the circuit remains constant, and subtract off 273 to get Celcius. The output of this when applying it to sensor 4 was about 20C, which means this is working properly.

Spacer in BR noise

== COMSOL vs result from Kessler etal 2012==

     The analytical result from kessler2012, assume the force acts on whole surface of the spacer (with bore hole), I check this with COMSOL by comparing the result, similar to what I did in PSL:1075. The result agrees well within 2%. This verifies that COMSOL model is correct

==thermal noise level vs annulus thickness==

Typically, the contact surface between the spacer and the mirror is only a thin annulus, see psl:1199  . And the noise level is dependent on the actual area of contact. So I run the simulation to see the dependent of the stored energy (U) vs the annulus thickness. The annulus thickness is about 2 mm +/- 0.2 mm. The displacement noise is proportional to sqrt(U).

fig1: The stored energy as calculated by COMSOL, fitted with cubic polynomial.

The error from the contact area, the simulation result are small ~3% and 2%. These are smaller than the uncertainty of loss in bulk fused silica (can be from 10^-6 to 10^-7). The effect is still small in the total noise.

I measured the slope of the error signal from ACAV and RCAV loop. The values are 0.11MHz/V for ACAV and 0.275 MHz/V for RCAV.

I also obtained the calibration for Vapplied to the laser's fast channel to frequency change to be 3.09 MHz/V.

This will be a note on how to measure error signal slope for PDH locking technique.

The slope of the error signal will allow us to project the noise from RFPD, or anything before the frequency discriminator to frequency noise.

The slope will also depend on the input power, modulation depth, so these are the parameters of the setup when I measured the data.

Power input to each cavity :1mW input

Modulation depth: 10V

Phase adj: 4.75 V.

We have two cavities, ACAV and RCAV, here I illustrate the plots from ACAV data only.

I scanned the laser by sending  triangular signal, 18V pk-pk (+/- 9V), 5Hz. to fast modulation input on the laser's controller.

I used the 35.5 MHz sideband peak to convert time on the oscilloscope to frequency change due to voltage applied.

fig1) screen on the oscilloscope, blue is error signal x 100 , green is voltage applied to scan the laser on the laser controller.

dT between the carrier and the sideband on the oscilloscope is 0.01059 - -0.05239 = 0.0630 [sec].

Thus the conversion is 35.5 MHz/0.0630 = 563.7 MHz/ sec. This will be used to convert the slope of the error signal from V/sec to V/Hz or Hz/V.

Note that we can also learn the calibration for applied V at fast channel to frequncy shift from green plot. dV = 6.3 - -5.2 = 11.5 V.

So the calibration for frequency shift due to the applied V is 35.5 MHz/11.5V =  is 3.09 MHz/V. 

Then, I measured the slope of the error signal, twice for different time spans on the scope, no big difference.

fig2) error signal from ACAV. The center slope in the plot is 5200 V/ sec. Use the calibration before to get

563.7 [MHz/sec] / 5200 [V/sec]= 0.11 [MHz/V] for ACAV.

The center slope for ACAV = 0.11 MHz/V (with x30 pre amp for RFPD signal)

                             for RCAV = 0.275 MHz/V (measured from mixer mon channel)

I checked the pk-pk  of the error signal to, the separation is

RCAV = 63.9 kHz

ACAV = 100.4 kHz 

which are supposed to be cavities' FWHM.

On saturday a qualitative effect of the modulation produced by the EOM located in the PDH-north loop has been checked.

The goal was to have a look at the error signal of the PDH-north while the laser PZT was scanning frequecies around the two s-p TEM00 resonances. Because a that time I did not find the right error-signal connections on the FSS board (next elog will clarify where it is) I have demodulated the signal with an external mixer (and with a low pass filter) and monitored it. The picture shows the error-signal that we have with this setup: 

At current temperature, the estimated beat frequency will be ~ 60-100MHz. This is not so bad, since we can use 1811 to measure the beat signal and use PLL to extract the beat noise.

We will need to use thermal expansion to tune the beat frequency. So, as a start, I try to figure out the beat frequency, and how much we have to heat up the cavity. The heaters on each cavity is off, only the heater around the vac chamber is on (but the servo is off). 

Right now we have one laser locked to one cavity, but the beam path to the first cavity has a beam splitter that we can borrow the beam and direct it to the 2nd cavity. I realigned the beam to have both beams into both cavities. By adjusting the temperature control on the NPRO (slow signal), I can bring the beam to resonant in each cavity.

1st cav is resonant @ (334/398) and (150/398). The numbers correspond to coarse and fine knobs of the slow feedback to the laser.

2nd cav is resonant @ (154/398). (I'll come up with a better name to call the cavities)

The FSR is 4.07 GHz (for 1.45" long cavity). This means 334-154 = 184 clicks on the coarse knob equals to 4.07 GHz, or 22MHz per coarse click. Both cavities resonant at ~3-5 clicks apart. So the beat frequency is ~ 60-100MHz. This is quite good, at least we are not close to half FSR apart. The power required to tune the cavity length should not be that high.

The next thing to do is try to see which cavity we need to heat up in order to bring both cavities resonant frequency closer together.

Note:A test to check which cavity needs to be heated up.

1) when heaters (on the shields) are off, C3:PSL-VAC_CHMBRTMP =31.2

• CAV1 is locked @ (slow out Coarse/fine) = 774/500
• CAV2                 @ 769/500

2 when heater on CAV2(4V), C3:PSL-VAC_CHMBRTMP = 31.2

• CAV1             @ 775/500
• CAV2              @ 756/500

So to bring both cavity to be resonant at the same time, the heater on cav1 should be on.

I'm not sure if the thermometers on the shields are working or not, I'll check them.

I would have guessed that you heat both cavities. Unless they are both at an elevated temperature, how can you control their individual temperatures?

The cooling rate (and thus the bandwidth for control) is determined by the steady state temperature. I would guess that each cavity needs to be at least 35 C in order to have some headroom.

Isn't heating up one cavity enough? The goal is to keep the beat frequency constant, so we need to control the differential length between the two cavities. The first cavity can sit still, the second one can be heated up (for enough cooling rate). We plan to use a frequency counter to change beat frequency to the servo's error signal for feedback to the second cavity. 

Anyway, I still have to check if both heaters are working or not.

 No, both have to be stabilized to reduce the control signals sent to the lasers.

I did this analysis to calculate how much of Seismic noise couples to the cavity resonance frequency due to the birefringence of the mirror.

Short version:

The seismic noise can twist the cavity if the support points are not exactly symmetric which is highly possible. The twist in the cavity will change the relative angle between the fast axes of the mirrors (which should be close to 90 degrees normally). This twist changes the resonant frequency of the cavity as the phase shift due to the mirrors fluctuate.

Edit Tue May 5 11:09:53 2020 :

I added an estimate of this coupling by using some numbers from Cole et al . "Tenfold reduction of Brownian noise in high-reflectivity optical coatings" Supplementary Information. The worst worst-case scenario gives a vertical seismic acceleration coupling to cavity strain of 5x10^-13 s²/m (when the end mirros are at near 90 degrees to each other and the supports are misaligned differentially to cause normal force misalignment of 5 degrees). For comparison, the seismic coupling to cavity longitudinal strain is 6x10^-12 (from Tara's thesis). Note, that Tara took into account common-mode rejection of this coupling between the two cavities while in my estimate, I didn't assume that. So it is truly the worst worst worst-case scenario and even then an order of magnitude less than the usual seismic coupling we use in our noise budget calculations where Seismic noise is not dominating the experiment anywhere.

So the conclusion is that this effect is negligible in comparison to the seismic coupling through bending of the cavity.

measured a couple of times today with everything re-aligned and different gain settings for the FSS stuff. Measured also to lower frequencies. The problem here is that the frequency band of interest can not be measured with epics (to slow) and the measurement using the SR785 takes so long that the operating point of the VCO and therefore the coefficient changes during the measurement and different spectra don't fit together quite well. so we have to measure a couple of times to get some measurements fitting together when the changes are so small that we don't see it with our eyes. this gives us a new upper limit of:

maximum gain settings:
CG : 24dB
FG : 13dB

Looking better. I'm curious about what the existing loop shapes are. The old FSS hardware is designed to drive an NPRO + 1 EOM. Is that the existing layout?

However, I think its not designed to drive an EOM. The PDH box should be able to drive the VCO if we replace the output OP27 with a TLE2027. The main point is that the refcav only provides a pole @ 40 kHz and we need the electronics to be 1/f below there. The old FSS board used to do this by the combination of the series resistor and the NPRO PZT capacitance. The VCO is not a capacitive load. I guess that Tara is working on a Simulink model of this whole setup?

I kind of doubt that we will have success without using resonant RFPDs. In most of the PSLs we use a pretty large modulation depth and its necessary to really tune the 2f trap to get rid of the J1^2 term.

------

Different idea: why not just use the VCO/AOM to lock to the ACAV? Then if we pick off the beam for the RCAV after the AOM, the feedback to the NPRO can be used as the differential cavity signal. In this way, we are not sensitive to the VCO calibration issues since its squashed by the ACAV loop.

Idea #2: Just use the transmitted light from the cavities and beat them. Its only phase detection, but in principle, this is easily good enough to detect what we want. Also RF sidebands are gone and all we need is an 1811 or such to detect the beat signal.

we spent the whole night to re-align everything. By now everything is back online, both cavities were locked.for a short time. We still have the pointing problem. It's different now, seems to be smaller but is now almost the same for x and y. Will do this later today ....

The 10kHz peak in the old spectrum seems to be related to the crossover frequency of the fast actuator and the pc of the fss loop.

The PDH box is modified, all filter stages now have socket adapter boards to easily change the filter frequencies by changing the capacitor value within seconds to optimize everything. A zero for compensating the cavity pole is also installed.  A modulation input too.

I'm looking into how to make external cavity diode laser (ecd).

Here is the list of what we need.

• Laser diode 1064nm, diode (+AR coating)
• Grating
• Current driver for locking the laser (home made)

I ask Akihisa who works in Kimble's group about their home made 850 nm ecl. The performance is not as good as NPRO yet (300kHz line width when locked to CS cell), but it is certainly interesting.

• They use Littrow configuration ( 1 grating to form a cavity). The mirror behind the grating is for adjusting the output beam.
• The PD is not AR coated, a slight power (10 uW) that transmits inside the diode is enough for the feedback.
• The linewidth is ~ 300kHz when locked to CS cell, the free running noise is not measured.
• They use both PZT and current to actuate on the frequency stabilization, the bandwidth is 50kHz.
• Temperature feedback is employed to keep the stability of the laser
• Time for putting everything in the box (once all components are ready) is ~ 1wk

 (

I just asked Aki a few more questions about the ecd laser. If we do not require the performance to be rival to that of the NPRO, making one is possible in a few weeks time scale.

Q1) The setup of the Littrow style laser you showed me had one mirror
behind the grating. Is the setup similar to this
<http://rsi.aip.org/resource/1/rsinak/v72/i12/p4477_s1>? Where the
mirror is used so that the alignment does not change when the laser is
tuned.
A1) Actually, Yes, for the laser you took the photo. But, most of the lasers we use in the lab don't have a mirror, only diode and grating in the box. In our case, we only scan the frequency by ~1GHz and the pointing vector drift is negligible.

Q2) Did you remove the glass window of the diode laser when you assemble
 the laser? If so, how do you keep the diode clean, or it does not matter
for your requirement.
A2) We didn't remove the glass window. What we did is very simple. We mounted the bare diode on the thorlabs mount: http://www.thorlabs.com/thorProduct.cfm?partNumber=LT230220P-B

 Q3) You mentioned that the line width of the laser when locked to CS cell
is ~300kHz. Is it because of gain limited of the servo or the CS cell's
intrinsic noise?
A3) We haven't measure the linewidth with locking and without locking independently. It's possible that our laser linewidth (without frequency lock) might be ~300kHz. So I don't know what limits our linewidth.

One thing you may want to consider is that a diode laser is infamous for the broad background incoherent light, compared to the solid state lasers. We typically observe ~30nm-wide incoherent light around the carrier with 30-40dB suppression compared to the carrier. If your experiment is sensitive to the spectral purity, this might be an issue.

Aki

 So the question is do we want to try to build one similar to what they have? We know that with the time scale and experience we have it will not be as good as the performance of the ecd laser reported in Numata etal paper, but it might be a fun project for the SURF student.

Some notes about external cavity diode laser. I investigated in this about a year ago.  I think it might be a good time to work on it, since I'm modifying the  ctn layout and we can use a frequency stabilized laser (although locked to a short cavity) via fiber optic to test with a home made ecdl. 

 Since we measured thermal noise from the coating(QWL, SiO2/Ta2O5), we want to extract loss angles of each materials.  The losses are about a factor of 2 higher than the numbers reported in the literature.

So far, there are 3 calculations we have been using for coating noise estimation.

• Nakagawa , this calculation assumes Young’s moduli , Poisson ratio of the coating and the substrate are the same. The coating is s a single thin layer.  Sx ~ phiC . If we fit this calculation to our result, the coating loss is about 4.15e-4. This number agrees with the result from Numata2003, and agree with both our measurement from short and long cavities.
• Harry2002:  Sx is function of ( phi_perp, phi_para), both phi_perp and phi_para are functions of( Y,Yc,sigma,sumac, phiL, phiH)
• Hong2013,  Sx is function of phi_bulk and phi_shear. If we assume that phi bulk and shear are the same for each material phi bulk L = phi shear L = phi L, Sx ~ const1 phi L  + const2 * phi H,,  

In essence, both Harry's and Hong's result can be written as a linear combination of phiL and phiH.  I used Harry result to compare with Hong to see if there is any differences in the result or not, but both gave me the same answer.

==calculation==

The calculation is attached below. I made sure that the calculation from Hong and Harry are correct by choosing the elastic properties of the coatings to be the same as that of substrate and checking the the results agree with Nakagawa's. So the code should be correct.

Then, I varied phiL and phiH to match the measurement. The measurement is represented by the prediction by Nakagawa with the fitted loss (phiC = 4.15e-4).

Both calculations gave the similar relation between phiH (phi tantala) and phiL (phi silica) to match the measurement: 

 phiH = -1.4 phiL + 9.7  (Hong)

 phiH = -1.44 phi L + 9.77 (Harry) (assume sigma1 = sigma 2 = 0) 

The problem is if we use the nominal numbers from various reports, phiL ~ 1e-4, phiH ~ 4e-4.  The result will be off by almost a factor of 2. For example, for phiL = 1e-4, this means phi H has to be 8.4e-4.  Or if phi H is chosen to be 4e-4, phi L will be ~4e-4 as well. It seems that our result is higher than the predictions (under some assumptions).

Table1 below shows some possible values of phiL and phiH extracted from our result and the calculation.

 But we have good evidences from Numata and short/long cavities (spot size dependent) to believe that the measurement is real coating thermal noise . The reason why the prediction is smaller than the measurement could be that the losses is actually higher in our coating. Most ring down measurements were done after 2002 while our coatings were fabricated around 1997. Coating vendors might become more careful about loss and improved their process. But the result from Numata was out in 2003, and it is about the same as ours, so I'm really not sure what can we say about this.

==numbers from literature==

Penn2003: (disc ring down)  phiL = (0.5 +/- 0.3) x10^-4 ,  phiH = (4.4 +/- 0.2) x10^-4

Numata2003 (direct measurement)    phiC = 4.4e-4;

Crooks2004(disc ring down)    phiL = 0.4+/-0.3  x10^-4,   phiH = (4.2+/-0.4)x10^-4   (the frequency dependent part is ignored)

Crooks2006: (disc ring down)   phiL = (1.0 +/- 0.2) x10^-4     phiH = (3.8 +/- 0.2) x10^-4    (small change in TE calculation from previous paper)

Martin2009 : (blade)                                                      phiH = 3+/- 0.5 x10^-4  (at 300K)

Martin2010: (blade)                                                       phiH = (2.5-5) x10^-4  ( heat treated at 600C, several frequencies)

 LMA2014: (blade)   phiL = (0.43+/-0.02) x10^-4        phiH = (2.28 +/- 0.2) x10^-4 

 I independently computed the Hong result using the same assumptions (bulk and shear loss angles are equal, and no light penetration). I find

where I have included uncertainties for the Penn and Crooks measurements.

 I checked Brownian coating noise level with uncertainties in coating parameters. The measured result is barely at the edge of the confident interval. 

Hong2013 look into coating noise level when materials' parameters are changed. One example is the Young's modulus of Ta2O5. With the assumption phi bulk = phi shear, if Y_Ta2O5 is varied between 70e9 to 280e9 (nominal value = 140e9), coating thermal noise can be changed by a factor of 0.9 to 1.5 from the nominal value (in PSD m^2/Hz unit). It seems that the range is quite large compared to the numbers measured by various groups, (see PSL895 for error in material parameters). I used a smaller range, but I varied other parameters as well.

==Note about uncertainties in calculation==

I used rand command in Matlab to generate random values. The reasons are 1) for reported loss angles, say 4+/- 2e-4, if I use Gaussian dist, with sigma =2, mean = 4, sometimes the generated value will be negative, and 2) since we are only trying to see the possible range of the estimated noise level, not the real statistic value, rand should be ok at this point.

==1:fixed loss angles==

  First I checked how much the parameters effect the calculation if the loss angles are fixed (phi silica = 1e-4, phi tantala = 4e-4). Y tantala is chosen between (70-280 GPa), Y silica is varied between72e9 +/- 10%,  Poisson's ratio are varied between 10percent for coating materials. All substrate parameters are fixed, since they should be relatively well measured compared to that of the coatings.  The result is around 0.5-0.85 of the measurement (in PSD m^2/Hz).

  For a more conservative value of Ta2O5 ( 140+/-40 GPa), the result is a factor of 0.5-0.64 of the measurement.

 ==2:varied loss angles==

In this study, I varied loss angles of phi_silica = [0.8-1.2] x10^-4, phi_ta2O5 = [3,5]x10^-4, these numbers are reported from several measurement. Then I change the uncertainties range of Y_Ta2O5 in my calculation

•  Y_ta2o5 = [100,180] GPa, the result is around [0.4,0.88] of the measurement.
•  Y_ta2o5 = [70,280] GPa, the result is around [0.4,1.09] of the measurement. A histogram of the ratio between noise level and the measurement is shown below (from 1e4 runs). The measurement value (Sx/Smeasured = 1) is barely at the edge of the confident interval (and not from Gaussian distribution either).
• 

==note and comment==

 Both Hong's and Harry's calculation provide quite the same value (within 3%). So I show only histogram obtained from Hong's calculation. I don't know why the study shown in Hong paper choose the value of Y tantala between 70-280 GPa, most of the measurements report smaller uncertainty. But with that higher value of Y_Ta2O5, it can explain the measured noise level from our measurement. However, I doubt that this argument is valid, since most of the ring down measurements to evaluate phi_Ta2O5 assume Y_tantala ~ 140GPa. Then the loss angle of Ta2O5 should carry some information about Y_Ta2O5 in it and cannot be treated as an independent parameter like this calculation. I'll look into the ring down papers to see how much Y_Ta2O5 affects the extraction of its loss angle.

I'm checking how loss angle of Ta2O5 is related to its Young's modulus (as used in ring down measurements), then I use that relation in error calculation for BR noise in coating. The uncertainties in Young's moduli of SiO2/Ta2O5 might lead to errors in loss angles and BR noise in coating.

==Background==

Many ring down measurements (see Penn2003, Crooks2004, Crooks2006), observed loss from a disc substrate with multilayer coatings of Ta2O5/SiO2. The loss in the coating (ring down mode) is written as  

phi_c = (phi1*Y1*d1 + phi2*Y2*d2 )/ (Y1*d1 + Y2*d2)    --------(1)

Where phi_c is determined from the measurement. Y is the young's modulus, phi is loss angle of material, d is physical thickness of the material.

Then phi1 and phi2 is determined with the assumption that Y1 and Y2 are known.  

So, the reported value of phi Ta2O5 is directly related to its Young's modulus. The uncertainty calculation of BR noise where Y, phi are varied independently might not reflect the real situation.

For example, I recalculated phi_c (of QWL structure) using phiH phiL of  4e-4, 1e-4. YH = 140 Gpa, YL = 72GPa. Then I rearranged eq(1) so that phiH can be written as a function of YH to see how the loss angle of Ta2O5 (H) will change with its Young's modulus assuming that YL and phiL are fixed.

fig1: How phi Ta2O5 changes with Young's modulus.

==BR calculation with loss parametrized by Young's modulus==

With the loss angles parametrized by the Young's modulus, I calculate the estimated thermal noise compared to our measurement (using Hong2013) 

fig2: ratio of BR calculated and our result. 

It is interesting that, even with the lower phiH as YH increases, the total BR noise increases. And the nominal value that we have been using (YTa2O5 = 140 GPa) yields almost the minimum value of BR noise calculation. 

==next step== 

  So far, the calculation is done assuming phiL = 1e-4, YL = 72e9.  The next step is to varied phiL, YL, phiH, YH all together ( with the constraint given by eq1) and see how BR noise changes.

  I'm also checking how large the errors are in the measurements for Young's modulus (both SiO2/Ta2O5). Crooks2006 reports the value of Young's modulus of Ta2O5 with the assumption that Y_SiO2 is 72e9. This might give another constraint. 

 Ta2O5 Young's modulus is quoted to be 140 GPa from this paper Martin1993,  but that is the value of Ta2O5 deposited on Silicon substrate cf fig5, top plot. The deposition technique is IAD. I'm not sure if it is the same as ion beam sputtering or not. I'm looking into it.

Anyway, the Young's modlus of Ta2O5 can be down to 70 GPa for IAD technique on glass substrate, as the paper says in the conclusion section. 

 Note that Crooks2006 mentions other papers measure YTa2O5 to be around 100-110 GPa as well. I'm looking into it.

 I just talked to Matt and learned that:

• The measurement from the above paper (that everybody quotes) is wrong, they just measured the Young's moduli of the substrate. However, the actual value of Y_Ta2O5 is ~ 140 GPa (use +/- 30% for conventional uncertainty) (Abernathy's from 500 nm sample) and the measurement for Y_SiO2  is ~ 70 GPa ( from 2 um sample)
• The term ion beam sputter (IBS) for our coating is actually IAD.
•  Note about coating loss in Penn2003
• T

The measurement from Penn extracts phi1 and phi2 from

 phi_c = (Y1 *d1*phi1 + Y2*d2*phi2) / (d1*Y1 + d2*Y2).

Phi_c is calculated from the total phi of the ring down system.

The dissipated energy comes from two part, the substrate and the coating. With the assumption that phi sub is much smaller than phi coat, we can write 

phi_total (measured from ring down) =  |energy in coating| / |Energy in substrate|  * coating loss, and the ratio Ec/Es can be obtained from FEA.  For drum head mode it is ~ 1500 (From Penn paper), see the picture, top panel.

This Ec/Es also depends on the Young's moduli, so the calculated phi_c also has Y as a parameter.  The calculation I did before takes phi_c from the reported values, so it is not correct.

To get the correct phi_c, the ratio of Ec/Es has to be changed with Y. Crooks PDH thesis has an analytical expression for the drum head mode of a cylindrical substrate. The analytical result is comparable to the FEA result used in Penn2003 within 5%. Note that the young's modulus of the coating is the volume average (Yc tc = y1*t1 +y2*t2) where tc is the total thickness, tx = thickness of material x. See the middle panel in the picture above. 

For the next step, instead of using the report value of phi1,phi2 and Y1,Y2 to reconstruct phi_c (Penn2003). I will use the measured phi_tot (for drum mode) then use that as a constraint on Y1, Y2, phi1, and Phi2 instead, see bottom panel in the picture. This should give a correct dependent among these variables.

This formula is only sensitive to the ratio YL/YH (which I've called E1/E2).

I took the parameters from Penn, chose two fiducial coating thicknesses (a λ/4 + λ/4 coating, and a 3λ/8 + λ/8 coating), and used this (along with Penn's reported values for E₁, E₂, φ₁, and φ₂) to compute two fiducial values for φ_c. Then I solved these two equations for φ₁ and φ₂, and allowed them to vary parametrically with the ratio E₁/E₂.

 I used results from ring down measurement in Penn 2003, without assuming the values of YL,YH. If the actual Young's moduli of both materials are about 60% of their nominal values, the calculation of BR noise will match our measurement within 3%. 

I used ring down drumhead mode from sample C2 and F2 since the phi_coating as reported in the paper is about the same as the phi_coating obtained from the analytical result (see previous entry). With these two eqs, I can write

Ysub * D/3 * phitot_1  = phiL*YL*dL_1 + phiH*YH*dH_1-------(1)  (see previous entry, last eq).

Ysub * D/3 * phitot_2  = phiL*YL*dL_2 + phiH*YH*dH_2-------(2)  .

phi tot_1 and _2 are 1/Qtot from the two samples. D is the thickness of the substrate (0.25 cm). dL and dH are the physical thickness of siO2 and Ta2O5 in each sample.

For any fixed values of YH and YL, the two eqs will solve for a pair of phiL and phiH.

First, I checked the validity of these two ring down measurements by using YL = 72 GPa, YH= 140GPa. The results are 

PhiL = 1.29e-4, phiH = 4.13e-4. These numbers agree with the reported values.

Then, I varied YH from 0.5*YH_0 to 2*YH_0 and YL from 0.5*YL_0 to 2*YL_0 ( YH_0 = 140GPa, YL_0 = 72GPa), and solved for the corresponding phiL and phiH. Then with all 4 parameters, BR noise can be calculated.

Below is a plot of ratio of BR calculation and our measurement, vs YH. Each trace represents different value of YL.

Each point on the plot will have information about phiL and phiH. If YL = 43 GPa (0.6*72GPa) and YH = 84 GPa (0.6*140GPa), the loss angles extracted from the ring down measurements are phiL = 2.15e-4 and phiH = 6.9 e-4. All these four parameters give the estimated BR noise comparable to our measurement to 2% (in PSD unit). 

==Conclusion==

 I'm trying to explain why our measurement is larger than the estimated calculation using numbers from literature. But we have good reasons to believe that the measurement is really BR coating since 

• The data has a correct slope, 1/f in PSD
• Scale with 1/w^2 in PSD, (BR noise from substrate/ spacer will have different scaling)
• Agree with Numata2003.

It is possible that loss angles in our coating is lossier than usual. But there are still other possible explanations. The results from ring down measurements rely on the values of Young's moduli of the coating materials. If the actual values divert from the nominal values, the losses will be changed as well. So I used the result from the ring down measurement, without assuming any values of YH and YL, then extracted values of phiH and phiL using different combinations of YH and YL and  calculated the coating noise according to each set of parameters.  If YL and YH have lower Young's moduli than their nominal values, coating BR noise will be higher and agree with our measurement. 

One might argue that 0.6 YL and 0.6 YH are too low.  Ta2O5 was measured with nano indentation to be ~ 140 GPa (Abernathy). Other references measured Ta2O5 ~ 100 GPa (see ref 16, 20 in Crooks2006 paper). So, uncertainty around 40% might be possible.  

In addition, this calculation also assume phi_bulk = phi_shear.  But the different value of phiB/phiS can also change the calculation between 0.5*S_0 to 1.6*S_0, for different values of phi bulk/phi shear ratio is varied by a factor of 5(see Hong2013). These values also change the noise level significantly.

So with the uncertainties in Young's moduli, the loss angles from ring down measurements can be changed significantly.  If the Young's moduli of the coatings are smaller than the nominal values, the loss angles calculated from a ring down result will be higher, and  it resuls in a higher level of coating BR noise calculation.

==Note== 

I'm surprised that for the value of 0.6*YL_0 and 0.6*YH_0 used above, with the loss angles of phiH = 6.89e-4 and phiL = 2.15 e-4, the calculated BR noise is almost the same as when I use the nominal value of YH,YL with the same loss (2.15 and 6.89e-4) see, PSL:1408.  I double checked the result, but I did not see anything wrong in the calculation. It turns out that the BR calculation is not very sensitive to YL, YH, but it is directly proportional to phiH, phiL. However, the values of phiH, phiL obtained from a ring down measurement are very sensitive to YL and YH  as we can see from the plot above.  

Heat treatment after coating changes loss angles of both SiO2 and Ta2O5. Our coating might really have higher loss (maybe because of the low temp annealing), regardless of the actual values of coatings Young's moduli.

I went through the paper by LMA2014 that measured loss in SiO2 and Ta2O5 using interferometry on a cantilever blade. They could also extract Young's moduli from thin film SiO2 and Ta2O5, their results are ~ 70GPa and 118 GPa respectively.

One interesting result is that losses are reduced with heat treatment after coating process.

SiO2 loss before heat treatment is ~ 6e-4,  and it goes down to ~ 0.6e-4 after the annealing (from broadband measurement).

From ring down measurement, SiO2 before heat treatment is ~ 4e-4. no result for the measurement after annealing.

For Ta2O5,from broadband measurement, the loss after heat treatment is ~ 4.7e-4, no result from the before heat treatment is reported.

From ring down, the loss is ~ 11.4e-4 before annealing, and down to ~ 4.9e-4 after annealing. 

Their annealing process is described in the paper.  I should find out more how losses of both materials change with different heat treatment i.e. time/ temperature/cooling, then see if any information about our mirrors can be retrieved from REO or not.

Right now, we have only the information about phiH and phiL as phiH = a*phiL + b. I still need another relation to get phiH and phiL individually. My plan is finding information about heat treatment vs loss, like the picture below (I still need to find for Ta2O5). Otherwise, it is hard to say anything about the loss from each material.

Most reports have different annealing temp, (I'm not considering time/ heating rate/ cooling rate right now, but they might be important) So I can compare loss vs annealing temp.

• LMA2014 without annealing and annealing @ 500C, for SiO2 and Ta2O5, thin film.
•  G1000356: Thin SiO2 at 300C, 600C 800C, 900C. This shows that loss decreases as annealing temp increases, see the picture below. Notice that loss at 600C is comparable to what report in LMA (0.6e-4, @500C).

It is hard to extract the similar plot as above for Ta2O5 from Martin2010 paper. I'll try to ask Ian Martin if he can give me the raw data. 

From the loss vs annealing temp I found out below, it seems that the annealing temp for our mirrors will be less than 300C. Since at 300C, silica loss is ~ 1.5e-4, tantala loss is ~ 4e-4. These numbers give the estimated BR noise below our measurement. 

Note:

•  find out if Young's moduli change with annealing process. 
• Coating layer thickness increases after heat treatment effect. This directly increases thermal noise. Find out how much it could be.

ref: silica loss with vs different heat treatment temperature. https://dcc.ligo.org/DocDB/0010/G1000356/001/PennCoatingMarch10.pdf

Martin2010: Class. Quantum Grav. 27 (2010) 225020 (13pp): Tantala loss with different heat treatment temperature

awade & Craig

Craig and I tried to get the experiment back up yesterday but found everything in the lab had been power cycled.  The fb2 computer had to do a harddrive check that wasn't finished within ~3 hours. This doesn't bode well for the condition of the drives.  Its running Debian 2007: might be time for an upgrade of HDs and a rebuild.

fb2 is only being used for the front end user interface tools but its the only computer in the lab that has them.  In the next week I'm going to try and install EPICS tools on acromag1 (Ubuntu machine also running acromag modbus stuff) so we are not critically reliant on a single somputer for this stuff.  

Just double checked on the lab, I was going to see if individual machines need to pointed to an IP address of a modbus server to get access to channels.  However, issue with fb2 not being able to see channels and report/put values with caget and caput seems to have resolved itself.  Only change on the network is that fb0 and fb1 have been powered up.  

Not sure what has happened here. Problem solved for now.

Rebooted the framebuilder fb4 on Tuesday May 29.  I didn't realize that it had hung on reboot.  There was a period of 24 hour after this in which no data was logged for the lab.

Also the framebuilder clock has reset back to 1980.  I can't really find documentation on the wiki or elogs on how this was configured sans ADCs.  I guess we'll just have to go Back to The Future and just use 80's dates for now. 

Installation of optics for fiber phase noise measurement

Following the fiber output, which has a waist of ~50 microns, we calculated the proper lens to use as well as the proper distance to place the objects so that we would have a waist of approximately 150 microns going into the AOM.  Roughly 3.5 inches from the fiber output, we placed a lens: KBX052 with a focal length of 50.2 mm, followed by an AOM: 3080-194, as well as the AOM driver(1080AF-AIF0-2.0) 3 inches away from the AOM to the right. After the light passes through the AOM, we placed another lens: PLCX-24.5-36.1-C-1064, which gives another waist at the mirror placed at the end of this setup.  After the light passes through this lens, we placed a quarter wave plate: Z-17.5-A-.25-B-1064, which is followed by a mirror: PR1-1064-98-1037.

Installation of optics for fiber phase noise measurement

After light passes through the AOM, it is reflected back through the AOM and into the fiber.  We installed a 50/50 beamsplitter, quarter wave plate, mirror, lens and photodiode to do the beat measurement.  It is required that the beam spot size is 1/3 the diameter of the photodetector.  We installed a lens at the appropriate distance to obtain a waist that is roughly 50 microns.  We hooked up the photodiode to an oscilloscope and found that the voltage fluctuates between 100-500 mV.  We are not sure why the voltage is fluctuating, but we will continue to investigate the cause.  

started with some simple calculations for replacing the PLL with a delay line. Started with modeling the loss in the cable depending on frequency and length (separate matlab-function for different cables).
Below some first plots for our current "situation" (which probably changes in the near future but that's what it is right now)  having a beat note @ 160MHz , 5dBm from the PD and an ZHL-1A amplifier (16dB gain) and a 4-way splitter (for two delay lines with different cable length):

• loss in cable vs length
• delay vs length
• detection range (180deg phase shift) vs cable length
• signal strength at mixer output vs cable length in dBm and Vpp
• signal size at mixer output for two different power levels going into the cable
   - the first one using the ZHL-1A amplifier (16dB gain)
   - a second situation where we have 27dBm (0.5W) going into the cable (1W max for a single 2-way power splitter)
• frequency noise sensitivity for the current situation using the ZHL-1A amplifier and assuming a 1nV/rtHz amplifier at the mixer output (no other noise sources so far!) or an SR560 with 4nV/rtHz.

files are on the svn in "CTNLab\simulations\noise_budget\delay_line_readout".

The optimum sensitivity is reached when the decrease in output signal is compensated by the increase in 2*pi*tau, which happens with a total loss of 8.68dB (factor 1/e) of the cable.

We don't win with adding delay if we make the cable longer, even if we increase the power going into the cable! That also explains why i had such a poor sensitivity with the 500ft of RG58 (which had 33dB of loss). Using 15ft of cable instead would have given the same sensitivity!

UPDATE 2/14/2012@8pm- files on the SVN contain now also data for RG405 and LMR-400 !

still having trouble with the drift of the laser power but here a first result. Nice to see that there is actually a damaged area showing less sensitivity where i hit it with the high power beam 50k-times :-) The scale on the 3D-plot is the top 2% from min to max, so the damage is probably ~1% or less. However the dark current and noise is 6 orders of magnitude higher than normal.

I fitted the measured transfer functions for the EOM and PZT using LISO. Here are the results:

And here is the LISO file that fitted the data to the measured data:

Likewise, for the PZT actuator

Likewise for the EOM

I would really appreciate help in improving these models. I particularly need help improving the EOM fit, as LISO didn't even perform the fit. I just eyeballed it since LISO would do something crazy whenever I told it to fit the parameters. I think the chosen quality factors need to be improved before I can get a decent fit.

fixed some errors in our channel database for the framebuilder and restarted the daqd process

I use time dependent option to simulate temperature change inside the mirror. The power input is DC + fluctuation.

Assuming RIN = 10^-4 @ 10 Hz, no coatings layer.

The plot below shows the absolute value of temperature fluctuation |(T - <T>)| on y-axis, and depth from the surface on x-axis.

Different lines (data 1 to 11) are different times in the substrate, from 20.0 to 20.1 sec with 0.01 time step.

It seems that the thermal length is quite large ~0.26 mm compared to what we got from half infinite model (~5 um).

dT from 1-D model is ~0.32 uK, while the result from COMSOL is ~1.8 uK.

If we use dT = 1.8 uK the frequency noise at 10 Hz will be (a factor of 6 larger) ~0.009 Hz/ rtHz. Still too low to see.

we've cut the rest of the foam parts to fit on the smaller diameter (the main tube with the heaters). We already started to glue them together and have two halfs by now with a length of about 20". We have to make two thinner slices tomorrow to finish this inner part. We also have to glue the end caps together.

The current plan is to make 3 parts:

- one main section including the endcap parts divided into two parts which you put on the chamber from the sides

- one full endcap, which you put on the window from the end next to the edge of the table for easier access if we want to open the chamber

The current plan is to add one layer of aluminum foil and tie the three parts with aluminum tape together. We only need little force to put them together without any gap as we decided to use a 0.1" thick intermediate layer of foam which is typically used for wrapping stuff (its soft, flexible and Rod has plenty of it for packing things). This intermediate layer on top of the heater helps us to fill the gap between the heater, sensors and free space and the really stiff yellow foam. If we want to change things in vacuum we simple cut the aluminum tape along the junction and remove the endcap. This gives us full access to all the screws to open the chamber.

The new insulated legs should be finished by tomorrow morning...

in order to build a custom fit insulation for the cavities i've built some hot wire foam cutting machines to cut the 2" thick polyurethane thermal insulation. The wire i use is a .010 piano wire typically used for suspensions (thats what we had i the lab). Nominal current is about 1.5A at a couple of volts, so any simple power supply does the job.

Here are some pictures of the large foam cutter to cut the 48" x 48" boards into smaller peaces and the circle cutting device:

original panel size

pre-cut parts:

cutting into smaller segments:

surface comparison before and after hot wire cutting:

circle cutter:

some cut parts:

ready to cut the rest...

some more photos for Koji and Tara about the foam insulation and temp sensor location

physical properties for the new yellow foam used for insulation (Certifoam 25):

thermal conductivity k (Btu/h ft² °F):
@ 75° F mean :  0.200
6-Month Aged Values @ 75° F mean : 0.192
fresh (As Manufactured) : 0.11

assuming ~0.2 Btu/h ft² °F the calculated k-value in Si units is 1.136 W/m²-K which matches the R-value given below

density  : 29 kg/m³

thermal resistance (R-value, 1in thickness)  : 0.88 K-m²/W

The conversion between SI and US units of R-value is 1 h·ft²·°F/Btu = 0.176110 K·m²/W, or 1 K·m²/W = 5.678263 h·ft²·°F/Btu.

I vented the vacuum chamber and forgot to turn of the ion pump. It was on for ~ 5-10 minutes. I'm not sure if it is broken or not. I talked to Alastair and he said the metal plate might be contaminated and needed to be repair. I'll keep this in mind and see what happen when I pump down the chamber.

 I aligned the beam to ACAV and RCAV and measured the frequency difference between the two cavities to be 289 MHz.

I used SLOWDC for calibration, the beam resonates in ACAV and RCAV at

 DClevel                                  RCAV                 ACAV

     1st resonance       -0.0520 [V]                0.0088  [V]

      2nd resonance       0.1046                      0.1661

     dV                           0.1566                        0.1573

 For a quick calculation, I used nominal FSR = 737 MHz. The calibration is then FSR/dV = 4700 MHz/V.

The frequency different between the two cavities give (0.1661 - 0.1048)*4700MHz/V = 289 MHz.

(I think the frequency might be too high for the beat PD, we may need to have thermal control before we can measure the beat)

 use df/f = dL/L, the differential length between the two cavities is   dL =  df * L * lambda / c ~ 0.2 micron.

So common mode suppression for thermo-elastic or cavity sagging due to seismic can be approximated to be ~ dL/L = 0.2 micron / 0.2 m =  1e-6.

we can borrow the 2GHz PD from the cryo experiment for a quick measurement. Will get the shields/heaters next week and have the sensors. So we might be able to add those before the meeting, but i would do the test at 289MHz first to see what the noise looks like. If it's terrible we might have to work on other things as well. e.g. the cavity support.

dL~200nm + n*532nm, so you can't say what the common mode suppression really is. The only thing we know is that the length are not off by 1mm or so (which you would see and easily be able to measure), but it could be anything below that. Next time we open it we should use a good digital caliper and measure the actual lengths. But we don't have one which is long enough.