40m QIL Cryo_Lab CTN SUS_Lab TCS_Lab OMC_Lab CRIME_Lab FEA ENG_Labs OptContFac Mariner WBEEShop
  PSL, Page 3 of 52  Not logged in ELOG logo
ID Date Author Type Categorydown Subject
  1291   Fri Aug 9 17:58:01 2013 taraNotesopticcoating optimization for AlGaAs

Better TO optimized coatings calculation is done. Now the Transmission, phase reflection, and TO noise are optimized.

From previous elog, these are explanation about the optimization codes.


The codes for optimizing Thermo-optic noise in coatings are up on svn.

I adopt some codes that have been on svn for awhile and modified them for AlGaAs coatings. There are two main codes


    2) optAlGaAs.m

        This file is the modification of optETM.m found in ../iscmodeling/coating/AlGaAs/optETM.m .It calculates the reflectivity and the TO coefficients from the given layer structure. The modifications are:

  • (Line41-45) Layer structure, the cap start with nH. The material for substrate is SiO2 with nsub = 1.45.
  • (Line60) Desired transmission, as a test, I chose 200 ppm.
  • (Line88) Calculation for TO coefficients (StoZ), I switched from getCoatThermoOptics.m to getCoatThermoOPticsAGS.m. Codes with AGS suffix in /GwincDev folder are fixed for AlGaAs coatings structure. This code calls many functions in /GwincDev folder.


 So optAlGaAs.m calculates a parameter y which is the cost function that is minimized in fmincon in doAlGaAs.m code.  Originally the cost function y includes the difference between the expected transmission and the transmission from the given layer, and the level of TO noise which are:

y = [(T - <T>) / <T>]^2   + sTO (f0).   The goal is to minimize y.   Where

  • T = transmission of the mirror with the optimized layers
  • <T> is the required Transmission
  • sTO(f0) is TO noise at f0
  • Each effect is weighted differently

This cost function does not care about the total phase of the reflected beam. T is the absolute value of the transmission, so the information about the phase is removed, and the optmized coatings calculated from this cost function won't have phase close to 180 degree. The previous result showed 180-1.2 degree.

So I added the phase of the reflection in the cost function, with appropriate weight, and ran the optimization.

==Phase calculation==

rCoat is the reflectivity of the coatings, by using atan(imag(rCoat)/real(rCoat)), we obtain the phase of the reflectivity. I tried to you atan2(y,x) to get the phase of 180, but it does not work well with the optimization. I'm not sure why. So I use atan function, and check the value of rCoat after the optimization to make sure that rCoat is close to -1 + 0i. The result is shown below.


above: the layer structure, optimized for 200ppm, y axis is in unit of lambda in the layer. The first layer is the 1/4 wave cap, the last layer is the layer just before the substrate.


above: noise budget for the optmized structure, the reflection phase is 180- 1e-6 degree.

 The layer structure is attached below in .mat format. Note: the structure does not include 1/4 cap on top.

== summary of the modifications of optAlGaAs.m==

  • (line 90 - 95) add calculation of the phase of the reflectivity
  • line 97 the cost function includes phase of the reflectivity that is close to 180 degree (r is close to -1 + 0i). The weigh functions  from TO noise/transmission/phase are chosen so that each factor are about the same, and the result looks reasonable ( coating thickness ~0.1 - 0.3 lamda, correct reflectivity, correct transmission).
Attachment 2: TOoptimized_2013_08_09.fig
Attachment 4: TO_opt_200ppm_layer.fig
Attachment 5: 2013_08_09_TOopt_200ppm.mat
  1315   Tue Aug 27 16:11:26 2013 taraNotesopticcoating optimization for AlGaAs:error analysis

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

evanB8.png[evan B8],

where alpha bar is

evanA1.png[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.



  • 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.
Attachment 2: error_analysis_0.5percent.fig
Attachment 6: yamamoto_TR_correction.png
  1318   Wed Aug 28 21:21:38 2013 taraNotesopticGWINC for TO calculation: recap

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.

  1320   Sun Sep 1 18:38:37 2013 taraNotesopticcoating optimization for AlGaAs:error analysis

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.

mu1 = 0;
sigma1 = 0.5;  % 2sigma is 1percent;
mu2 = 0;
sigma2 = 1;

run_num = 5e4; % how many test we want

errH = normrnd(mu1,sigma1,[run_num,1]);  %errH in percent unit
errL = normrnd(mu2,sigma2,[run_num,1]);  %errL in percent unit   
errL = abs(errL).*sign(errH);                        %make sure that errH and errL have the same sign

dOpt = xout;             % xout from doAlGaAs (optimized layer)
dOpt = [ 1/4 ; dOpt];    % got 54 layer no cap from doALGaAs, need to add the cap back

dOpt_e = zeros(length(dOpt),1);

  for ii = 1:run_num;

dOpt_e(1:2:end)= dOpt(1:2:end)*(1+ errH(ii)/100 );
dOpt_e(2:2:end)= dOpt(2:2:end)*(1+ errL(ii)/100 );




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.


Attachment 2: error_compare_opt0901v2.fig
Attachment 6: 2013_09_01_opt_nbv2.fig
Attachment 7: 2013_09_01_200ppm_54v2.mat
  1322   Mon Sep 2 18:31:46 2013 taraNotesopticcoating optimization for AlGaAs:error analysis

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

  1340   Wed Sep 18 21:55:11 2013 taraNotesopticcoating optimization for AlGaAs:error analysis


Optimized coatings structure.


Attachment 1: opt_coatings.mat
  1344   Thu Sep 19 20:38:17 2013 taraNotesopticcoating optimization for AlGaAs:error analysis

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.

  1345   Fri Sep 20 19:26:45 2013 taraNotesopticcoating optimization for AlGaAs:error analysis

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.

params +sigma -sigma Note
BetaL 1.02 1.12  
BetaH 1.03 1.15  
Young L 8.0 1.77  A
Young H 8.3 1.8  A
Young HL 28.3 4.7  B
alpha L 1.54 1.2  
alpha H 1.19 1.53  
kappa L 0.979 1.023  
kappa H 0.975 1.028  
CL 0.99 1.0143  
CH 0.99 1.0137  
sigmaL   20.6  C
sigmaH   21.7  C
sigmaHL   84.14  B
nH 1.168 1.004  
nL 11.15 6.507



  • 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.

Attachment 2: error_check_params.fig
Attachment 4: error_thick_params_compare.fig
  1346   Fri Sep 20 21:19:29 2013 Matt A.Notesopticcoating optimization for AlGaAs:error analysis

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:



Change: TO'/TO TO'/Br
No Change 1 0.015
C_c = CH 0.99 0.014
C_c = CL 1.01 0.015
k_c = kH 1.12 0.016
k_c = kL 0.89 0.013
alphaBar_c = aH 358 5.17
alphaBar_c = aL 384 5.55
alphaBar_k = alphas 372 5.37
alphaBar_k_TR = alphas 3.12 0.045
alphaBar_c = alphaBar_kH 2.88 0.042
alphaBar_c = alphaBar_kL 2.047 0.030
alphaBar_k_TR = alphaBar_k 5.775 0.084
alphaBar_k = alphaBar_k_TR 145 2.096

 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.


  1347   Sat Sep 21 23:49:29 2013 ranaNotesopticcoating optimization for AlGaAs:error analysis

 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.

  1348   Sun Sep 22 00:27:09 2013 some random goonNotesopticcoating optimization for AlGaAs:error analysis


 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.


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.


  1350   Mon Sep 23 18:07:22 2013 ranaNotesopticcoating optimization for AlGaAs:error analysis


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?

  1351   Mon Sep 23 18:50:05 2013 taraNotesopticcoating optimization for AlGaAs:error analysis



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?

 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.

Attachment 1: compare_indices.png
Attachment 2: compare_indices.fig
  1356   Thu Sep 26 23:25:40 2013 taraNotesopticcoating optimization for AlGaAs:error analysis

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.


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.

Attachment 2: compare_error_ana.fig
  1359   Thu Oct 3 10:34:32 2013 taraNotesopticcoating optimization for AlGaAs:error analysis

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

  1363   Thu Oct 10 01:59:24 2013 taraNotesopticcoating optimization for AlGaAs:error analysis

I recalculated the coatings properties, with the values of nH and nL to be 3.48 and 2.977. Note about each optimization is included here. Transmission plots are added in google spread sheet. I'll finish the calculation for E field in each layer soon.

Note about each optimized coating version: different versions were obtained from different cost functions, and different number of layers.


  • 55 Layers
  • T = 210 ppm
  • TO noise and transmission is too sensitive to the change in nH and nL
  • 1/4 cap of nH. I did not fix the cap thickness for other coatings. Since there is no reason to keep the thickness of the cap constant.
  • TO noise and transmission of this one changes a lot with uncertainty in nH/nL



  • 57 Laayers
  • T = 150 ppm
  • Transmission is still too sensitive to the change in nH and nL
  • TO noise/ transmission is less susceptible to change in nH/nL.
  • First layer is 0.1 lambda thick (~285 nm) I'm not sure if this will be a problem for a cap or not.



  • 57 Layers
  • T = 150 ppm
  • TO noise and Transmission are less sensitive to nH and nL
  • less amount of nL material, should be less sensitive to error in thickness control



  • 59Layers
  • T= 144 ppm
  • TO noise and Transmission are less sensitive to nH and nL
  • reflected phase is more sensitive compared to opt4
  • use less nL material
  • 0.1 lambda thick

Judging from TO noise level, Transmission and reflected phase, I think opt4 is the best choice for us. The structure consist of thick nH layers and thin nL layers. This is good for us in terms of thickness control.


  1365   Fri Oct 11 15:23:54 2013 taraNotesopticcoating optimization for AlGaAs:electric field in coating layer

Electric field in coating layer is calculated. This will be used in loss calculation in AlGaAs coatings.


  • In each coating layer, there are two E waves, transmitted and reflected  waves. The two interfere and become an effective field.
  • The averaged electric field will depend only on the transmitted beam inside each layer, see the calculation.
  • The effective transmissivity can be calculated, for coatings with N layers between air and substrate, there will be an N+1 vector representing the effective transmission, called tbar in the code. This tbar(n) is the transmissivity in the nth layer, similar to rbar in Evans etal calculation.
  • The ratio of E field/ E input in nth layer will be tbar(1)*tbar(2)*...tbar(n)
  •  |E field/ E input |^2 of the final transmitted beam is the transmission of the coatings.  The numbers from this calculation agrees to the calculation from before.

==supplementary information==

1) average E field in layer is the transmitted E field in the layer.


 I attached a short matlab file for a simulation of the combined field. Ein in each layer will be the transmitted beam through the layers. For a value of r close to 1, we get a standing wave. Try changing the value of r in test_refl.m to see the effect


2) Calculation for the transmitted field in each layer


I borrow the notation from Evns etal paper (rbar), the calculation code multidiel_rt.m is attached below. Note: the final transmission calculated in the code is the transmission from the coating to the substrate. To calculate the transmission to the air, multiply the last transmission by 2*n_sub/(n_sub + n_air) which is the transmission from sub to air. Since the thickness of the substrate is not known with the exact number, it will not be exact to the transmision calculated in GWINC or Matt A's code (which do not take the sub-air surface into account), but they will be close, because the reflected beam in the last interface will be small compare to those in the coatings.




The penetration of E field for QWL and different optimized coatings are shown here. The transmissions in the legend are calculated from MattA./GWINC and the values in the parenthesis are calculated from multidiel_rt.m which include the effect from the substrate-air surface. This makes the values in the parenthesis smaller (as more is reflected back and less is transmitted).

Attachment 3: test_refl.m.zip
Attachment 4: multidiel_rt.m.zip
Attachment 6: Efield.fig
  1367   Mon Oct 14 21:02:00 2013 taraNotesopticcoating optimization for AlGaAs:variation in x

I checked the dependent of coatings properties with the uncertainty in x (amount of Al in Al_x Ga_(1-x) As). The effect is already within the uncertainties in materials parameters we did before and will not be a problem.

G. Cole told us about the variations in Al contents in the coatings. Right now the values are 92% +/- 0.6%. 

(92.10, 91.43, 91.34, 91.57, 92.73, 92.67).  Although the deviation is small, the Al content does not always hit 92%, but 92+/- sigma%. So I decided to check the effect of x on the optimization.

The materials properties that change with x are heat capacity, alpha, beta, heat conductivity and n. The values of those as functions of x can be found on ioffee  except n. So I looked through a couple of sources ( rpi, sadao)  to get n as a function of x, (Note: E0 and D0 are in eV, they have to be converted to Joules when you calculate chi and chi_so).  GaAs (nH) has a well defined value ~ 3.48+-0.001, nL has a bit more uncertainty, but it is within the approximated standard deviation of 0.03 . The table below has numbers from the sources. For RPI, I use linear approximation to get nL for x = 0.92 @ 1064nm.

source nL(x=0.92) nH
G.Cole 2.977 3.48
RPI 3.00 3.48
Sadao 2.989 3.49

The dependent of n on x is about -0.578 *dx. The numbers from RPI and Sadao are about the same. This means that for the error of 0.6% in Al. nL can change by 0.578*0.006 = 0.0035. The number is almost a factor of ten smaller than the standard deviation of nL and nH I used in previous calculation (0.03). For examples,

  • x = 0.914, nL = 2.993,
  • x=0.92,     nL = 2.989
  • x=0.926    nL = 2.986  (From Sadao's fit)

This means that the uncertainty in nL/nH (+/- 0.03) we used are much larger than the effect coming from uncertainty in x. This is true for other parameters as well.

  1374   Sun Oct 27 20:12:25 2013 taraNotesoptic photothermal noise in AlGaAs

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


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

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

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

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

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

==calculation and a hand waving argument==

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



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

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

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

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


Attachment 2: Int_cotings.fig
  1376   Wed Oct 30 01:56:38 2013 taraDailyProgressoptictable work

I'm optimizing the setup, and clearing the table a little bit.

  • Self homodyne setup in ACAV path is removed. This is from Erica's setup and it is not used. The input part is left, since I might use it for fiber distribution system
  • optics on RCAV path, all polarization are optimized. This includes, the input and output polarization for EOAM, and quarter wave plate before the periscope. The input polarization for sideband EOM is left intact after the last adjustment, and it should be good. With+/- 4V input, I can change the power by +/-10%, (1.0 +-0.1 mW is the current setup). For Evan: Do not touch anything before discussing with me!!!
  • I replaced a new PBS for PDH locking in RCAV path. The old one is bad. The surface between the prisms is milky, see the pictures below for comparison. There is also beams from multiple reflection within the cube. The new one is much better. There is no ghost beam anymore.
  • I blocked all the scattered light I could find in RCAV path with Irises and beam dumps. For ACAV, I just blocked the scattered lights from the laser to the PMC. I will finish the whole setup later.
  • I rechecked the height of the beam through EOMs/EOAMs. Since it is a little tricky to center the beam through the openings. The EOMs in RCAV path are all checked. For ACAV, only those between the laser and the PMC are checked(BB for phase locking and 21.5 for PMC sideband). The 14.75Mhz sideband and EOAM will be done later. The EOAM and wave plates are removed temporarily.
  • I modified the TTFSS for RCAV to have a gain reduction switch to help locking the laser. I tried to lock RCAV, but I cannot turn up the gain. I'm not sure what I did wrong but this has to be investigated.

To do lists

  • put optics back in ACAV path and optimize them (alignment + polarization).
  • fix RCAV TTFSS . Check by measuring the TF of the modified stage/ scanning laser + checking error signal


above: old PBS, bad inter surface can be seen.


above: new PBS: all surfaces are clear

  1379   Fri Nov 1 00:22:40 2013 taraDailyProgressopticmore optimization

I'm putting EOAM back on ACAV path. The setup is roughly optimized.

(14.75 MHz) EOM , EOAM, quarter waveplate and PBS in ACAV path are put back together. I used a half waveplate in front of the EOM to adjust the beam to S- polarization. Right now all the polarizations optimization (to all EOMs, both ACAV/RCAV path) are adjusted to S-polarization with respect to the table. We may have to fine tune it later to match the E field in the EOMs.  The EOAM setup is optimized. With +/-4 V, the output power can be adjusted to 1mW +/- 0.09 mW (+/- 9%). The performance is comparable to RCAV EOAM. (10%) . I have not add another half waveplate before the EOAM yet. We can add it back later if we need to adjust the input polariztion to the EOAM.

I checked scattered light in the area between PMC and ACAV.  There is a reflection from EOAM back to EOM, but I cannot really block it with an iris. It probably bounces of the case of the EOM or going back to the crystal. Anyway I'll block the beam around this path later.

I have not aligned the beam to the cavity yet, since the temperature was changing because I removed the insulation  caps to patch them with black out material.

 I put black out material (R @1064 ~0.4-0.6%)on the vac tank insulation caps to minimize any possible scattered light source inside the tank that might leak out.  It also keep the surface cleaner from all the foam dust.



  1385   Fri Nov 8 03:36:44 2013 taraDailyProgressopticredo- PMC path

I'm re-arranging the optics in PMC path a bit. The work is in progress, so ACAV path is still down.

I'm investigating why ACAV TTFSS performance is worse than that of RCAV. One thing is that ACAV has the PMC. This area has not been optimized for awhile, so I'm checking everything.

  1386   Mon Nov 11 19:37:13 2013 taraDailyProgressopticredo- PMC path

PMC path is back, I aligned the polarization of the input beam to the BB EOM for TTFSS. The visibility of PMC is now ~ 80%.

  1392   Wed Dec 18 21:05:28 2013 taraNotesoptic photothermal noise in AlGaAs: thickness resolution

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

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

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



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




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


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

Attachment 5: 05Atrancate_err.fig
Attachment 6: 05Atruncate_err_ana.fig
Attachment 7: 05Atruncate_nb.fig
Attachment 8: 05Atruncate_T.fig
  1403   Mon Feb 3 23:56:07 2014 taraPhotosopticpacking mirror

 I"m packing the mirrors so that they are ready to be shipped to G. Cole. The mirrors are packed properly, see picasa.

  1425   Sat May 17 22:01:28 2014 taraNotesopticCoating TO opt for Adv LIGO: ETM

Here is a prelim result for AlGaAs TO opt for ETM coating.


The optimization is named opt_ETM5 in .mat file. The structure is in optical length unit ( the physical thickness = (opt length) * 1064e-9 / n). The first layer is the air-coating GaAs layer . For the current optimization (opt_ETM5.mat) the transmission is 5.4 ppm, the reflected phase is off by about 2 degrees. 




ETM parameters used in the optimization

  • Spot radius (1/e^2 power) = 6 cm
  • Substrate radius =19 cm (GWINC)
  • Substrate thickness = 20 cm (GWINC)
  • Target transmission = 5 ppm

Note about optimization:

  •  The current optimization is just a prelim result for demonstrating that it is possible to optimize coating structure for ETM.
  • I have not included any uncertainties in the result.
  • The cost function used for this optimization is a only for nH = 3.48, nL = 2.977. So the coating properties might change rapidly with the uncertainties of the refractive indices see PSL:1356. I have not used the cost function with multi-value refractive indicesbecause this optimization is intended for parameter configuration (adjusting the target TO noise level, weight functions for each parameters, numbers of layer). 
  • The optimization was done for room temperature (300 K) @1064nm.
  • All the codes are attached in the zip file.

 To run the code:

  • run optETM.m with the current parameters. The result structure will be called xout in matlab workspace.
  • use CoatingThermalNoiseCalcETM.m to plot the noise budget.
  • I might miss some functions in the zip file, one is multidiel_rt.m , those are available on svn directory
Attachment 1: ETM_TO_OTP.zip
Attachment 2: opt_ETM_2014_05_17.mat
Attachment 6: dOpt_ETM5.fig
Attachment 7: opt_ETM5_nb.fig
  1426   Sun May 18 10:45:42 2014 taraNotesopticCoating TO opt for Adv LIGO

I did an optimized structure for ITM and plotted the estimated noise budget of AdvLIGO using optimized AlGaAs coating on ETM and ITM. More details will be added later.



Above: Optimized structure of ITM



Above: AdvLIGO with Optimized AlGaAs coatings on SiO2 substrate, room temp. The plot is generated by GWINC.

Attachment 2: dOpt_ITM1.fig
Attachment 4: AdvLIGO_AlGaAs.fig
  1437   Thu Jun 26 12:07:17 2014 EvanDailyProgressopticHWP adjustments; south locking

I wanted enough power to accommodate both the fiber noise measurement and the south cavity locking. I moved the HWP after the PMC from 338 degrees to 79.5 degrees. Then I moved the HWP after the south EOAM from 249.5 degrees to 280.0 degrees. This gives 1.5 mW transmitted through the PBS toward the south refcav, and a few milliwatts reflecting off the PBS and going toward the fiber.

It looks like we still have good mode-maching into the south cavity; transmission is easily seen on the camera.

  1439   Sun Jun 29 19:04:13 2014 Emily, EvanNotesopticfiber phase noise measurement

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.






  1449   Tue Jul 15 18:26:20 2014 taraDailyProgressopticsetting up scattered light measurement

I'm setting up a scattered light measurement for AlGaAs samples. The methods are summarized below.


I discussed with Manasa about the setup and how to do the measurement. The goal is to measure  scattered losses from AlGaAs samples from a normal incident beam. The setup is shown below.



The setup is in the ATF lab, on the unused optical table. It is too crowded on CTN table. So I will need a to borrow a 1064 laser from somewhere. 

The incident beam will have to be slightly angle from the normal angle in order to dump the beam properly. 

The arm holds the camera, it can rotate to change the angle to cover the measurement from around 10 degrees to ~70 degrees.


==calibration method==

  • We can take a picture from a diffuser plate, make sure it is not saturated. 
  • Then use a power meter, measure the power fall on the camera.
  • compare the output of the camera and the measured power
  • I have to think about how to make sure the solid angle of the camera aperture and the power meter are the same.

==measurement and data analysis==

  • For each position, take one picture without the beam on the mirror and one with the beam on the mirror. The first one will be used for subtracting the ambient noise from a picture when the beam is on the mirror. 
  • Make sure that no pixel is saturated
  • For each pair of picture, we will use Matlab to count the output, then use the calibration to convert to power.
  • integrate over half the sphere. I have to think about this to make sure I get it right.


  1452   Thu Jul 17 18:57:54 2014 taraDailyProgressopticsetting up scattered light measurement

I'm testing the setup and a code for extracting scattered light from the images. 


I used a red laser pointer to test the scattered light setup. Then took a picture with no light (fig1) and a picture with the incident light (fig2). The scattered light can be extracted by subtract fig1(background) from fig2.

The snapshots saved by SampleViewer are in .bmp file. When it is read by MATLAB, the file will contain 480x752x3 matrix element, Each are varied between 0 and 255. The values are proportional to the brightness (how many photons hit the cell). 480x752 is the resolution of the image, x3 are for R G B color. In our case, the image is greyscale and the values are identical. The code can be found in the attached file.  


fig1: The test mirror without incident beam taken as a background image. The image is enhanced by a factor of 5 (by matlab).



fig2: The test mirror with a red incident beam around the center. The image is enhanced by a factor of 5.



fig3: the image is created by subtracting data of fig1 (background) from fig2 (scattered light) and enhanced by a factor of 100. The scattered light on both surfaces can be seen clearly around the center.

 ==To do next==

  • From fig 3, the background can be seen even after subtraction, so some black curtains and beam dumps should be added behind the mirror.
  •  A room light filter should be installed in front of the camera.
  • I'll see if we can find a sample with known scattering loss, so that we can compare how accurate the measurement is.
Attachment 4: scattered_.zip
  1455   Wed Jul 23 00:28:14 2014 taraDailyProgressopticsetting up scattered light measurement

I'm checking the linearity of power and exposure on the camera. The ccd counts are quite linear with the exposure setup, but I have to check the power again.


==ccd count vs exposure setup==

  The exposure time on the camera can be set to adjust the brightness of the image. Since we might have to adjust it to make sure that the images won't be saturated, it is necessary to check if the ccd count response linearly to the exposure setup or not.

I used a silver mirror as a test sample. The incident power is constant, and the camera position is fixed. Then adjust the exposure from 5k to 30k. I'm not sure if it is in nano second or microsecond unit. [Edit, 20140725: according to page 18 of the manual for the Prosilica GC750, the available exposure options are 30 µs to 60 s, in 1 µs increments. —Evan] But from fig1, the ccd count is quite linearly proportional to the exposure value.


It turns out that when I try to calibrate a sample, the incident power on the sample has to be more (so the power meter can measure some scattered power) and the camera can be saturated. The exposure value has to be around 1000, and I have not checked the response at this level. I might have to remeasure it.


==ccd count vs power== 

 This measurement is similar to the above. But this time the incident power (to the sample) is varied. The result is not linear. I check the images and see that the bright spot moves. The camera might move during the measurement. I'll repeat this again. It will be complicated for the calibration if the ccd count is not linear with the power.


== To do==

  • check the ccd count for exposure value down to lowest setting.
  • check the ccd count for different power incident.
  • check the ccd count with different ND filter in front of the camera.


  1456   Thu Jul 24 02:00:23 2014 taraDailyProgressopticsetting up scattered light measurement

I rechecked the CCD response vs exposure time and power. The results are linear.


After some adjustments (strain relief on the camera's cables, clamping down the camera properly), I made sure that the camera is more stable and repeated the measurement. The CCD response is linear with the incident power on the sample (this is under the assumption that the scattered power is directly proportional to the incident power). 


Fig1:  CCD response vs incident power. The camera response is linear.

== AlGaAs Samples==

I prepared the sample for measurements. All the samples are quite dirty, especially on the flat sides. So I wiped all of them. I still cannot get rid off some water marks on the annulus of the mirror. It might cause some problems when I optical contact the mirrors. I'll try to clean them later.


fig2: one of the AlGaAs mirrors before cleaning. 

I put one of the samples in the scattered light setup. The transmitted beam has a lot of diffused light behind the mirror. The amount of the diffused light changes with the beam direction. I'm not sure exactly why. I'll try to investigate it more. But the scattered light from the sample is very small. Most of the light is from debris on the surface, not the micro roughness of the sample. The amount of scattered light significantly changes with the beam position on the mirror.


fig3: diffused light behind the mirror. It might come from the reflection inside the substrate because the incident beam is not normal to the surface.

  1457   Thu Jul 24 17:11:18 2014 EvanDailyProgressopticCalibration for scattered light measurement

[Tara, Evan, Josh, et al.]

Today we did some characterization and calibration of the scattered light apparatus.

To start with, we examined an AlGaAs mirror (s/n 173). We found that there was a great deal of diffuse light transmitted through the mirror (as seen in fig. 3 of ctn:1456). On Josh's suggestion, we put down an iris about 5" in front of the mirror. We stopped it down just enough so that both the incident and reflected beams could clear the aperture. This made the diffuse stuff disappear.

Next, we swapped out the AlGaAs mirror for a Lambertian diffuser (the same one used in Magaña-Sandoval et al.). Tara affixed the power meter to the camera boom in such a way that it could be raised or lowered in front of the camera.

We adjusted the incident power on the diffuser to be 3.00(1) mW. We then swung the boom in 5° increments from 10° to 70° from normal incidence. At each angle, we took the following:

  1. Power incident on power meter with beam blocked
  2. Power incident on power meter with beam unblocked
  3. CCD image with beam blocked
  4. CCD image with beam unblocked.

The beam was blocked using a dump located immediately upstream of the steering mirror.

The first attachment is the BRDF of the diffuser based on the power data. The second is the inferred calibration between total CCD counts (with background counts subtracted) and scattered power. The correlation is not great. We may want to retake this data with the room lights off, and also we may want to take multiple exposures per angle setting (that way we can make some estimate of the uncertainty in the CCD counts). The third attachment shows the analyzed CCD region for the 10° images; I've restricted the analysis to a 200×200 pixel region around the diffuser.

The exposure time was 100 µs, and there was a 1 µm long-pass filter (RG1000) affixed to the camera lens.

Data, CCD images, and plot-generating code are on the SVN at CTNLab/measurements/2014_07_24.

Attachment 1: power.pdf
Attachment 2: ccdCal.pdf
Attachment 3: 10.pdf
  1458   Fri Jul 25 08:12:40 2014 EvanDailyProgressopticCalibration for scattered light measurement


The first attachment is the BRDF of the diffuser based on the power data. The second is the inferred calibration between total CCD counts (with background counts subtracted) and scattered power. The correlation is not great. We may want to retake this data with the room lights off, and also we may want to take multiple exposures per angle setting (that way we can make some estimate of the uncertainty in the CCD counts).

 I put the boom at 15° and took four sets of five exposures. Then I ran my image processing code again to get an uncertainty in the count values. I get the following:

  • Beam incident, room lights on: 546(31) × 103 cts
  • Beam blocked, room lights on: 417(9) × 103 cts
  • Beam incident, room lights off: 547(34) × 103 cts
  • Beam blocked, room lights off: 410(2) × 103 cts

For each set of five, the nominal value is the mean and the uncertainty is the standard deviation of the total counts within the 200×200 pixel region around the beam. Again the exposure time is 100 µs and there was an RG1000 filter in front of the camera lens.

Using a fractional uncertainty of 31/546 = 0.057 for yesterday's background-subtracted total counts, I reran the calibration code. The new plot is attached. The calibration slope (and its uncertainty) doesn't change much, but we can see that the uncertainties in the total counts are quite large. Do we need to improve this before moving on to the AlGaAs BRDF measurement?

Attachment 1: ccdCal.pdf
  1459   Fri Jul 25 14:21:34 2014 EvanDailyProgressopticCalibration for scattered light measurement


 Do we need to improve this before moving on to the AlGaAs BRDF measurement?


We added an OD1.5, an OD3.0, and an RG1000 in front of the camera lens (note that these ODs are probably specked for something other than 1064 nm). Then we increased the exposure time to 20 ms. For the AlGaAs measurement, we may need to increase it even further in order to get good statistics.

Then we fixed the boom at 25° and varied the power using the upstream HWP + PBS combo.

For each power level, we took a measurement with the power meter, then 10 CCD images, then another measurement with the power meter. From this we are able to extract nominal values and uncertanties for the power level and the counts. The result is attached. The calibration has about a 4% uncertainty.


Note (Tara): The power measurement includes the solid angle of 3.375 x10^-3 str ( detector diameter = 0.4 inch, distance from the sample = 15.5 cm)

Attachment 1: cal.pdf
  1460   Sun Jul 27 19:46:16 2014 EvanDailyProgressopticBRDF of AlGaAs mirror 137B1

[Tara, Evan]

We replaced the Lambertian diffuser with AlGaAs mirror 137B1. We intentionally induced a nonzero AOI of the incident beam, so that the reflected beam could be dumped cleanly. At a distance of 25.7(3) cm back from the mirror, the reflected and incident beams were separated by 1.3(1) cm, giving an AOI of 1.45(11)°.

  1. We measured the incident laser power as 9.94(2) mW.
  2. We set the exposure time of the camera to 250 ms.
  3. We swung the boom to 13°, 16°, 19°, 22°, 25°, 28°, 31°, and 34°. At each angle, we took 5 CCD images with the beam incident, and 1 CCD image with the beam blocked.
  4. We measured the incident laser power as 9.95(2) mW.
  5. Because the scattered power had fallen off sharply by 30°, we turned up the exposure time to 1.00 s.
  6. We swung the boom to 31°, 34°, 37°, 40°, and 43°. At each angle, we took 5 CCD images with the beam incident, and 1 CCD image with the beam blocked.
  7. We measured the incident laser power as 10.08(2) mW.
  8. We swung the boom to 46°, 49°, 52°, 55°, 58°, 61°, 64°, 67°, and 70°. At each angle, we took 5 CCD images with the beam incident, and 1 CCD image with the beam blocked.
  9. We measured the incident laser power as 10.06(2) mW.

For all of these measurements, the two ND filters (OD1.5+OD3.0) were not attached; just the RG1000. With the ThorLabs power meter, we measured the combined transmissivity of these two ND filters to be 1865(14) ppm.

The first attachment shows an example CCD image. The second attachment shows the raw counts, the inferred scattered power, and the BRDF.

Attachment 1: ccdImage.pdf
Attachment 2: 137brdf.pdf
  1461   Tue Jul 29 11:40:09 2014 EvanDailyProgressopticBRDF of AlGaAs mirror 143

[Tara, Evan]

Yesterday we took a scatter measurement of AlGaAs mirror #143. Instead of one bright scattering center, we saw 3.

The procedure is identical to the procedure used for mirror #137, although the exposure settings and choice of angles are a bit different (see the attached plot). Also, we used 20 mW of incident power instead of 10 mW.

Total integrated scatter from 14° to 82° is 80(8) ppm.

Data, images, and plot-generating code are on the SVN at CTNlab/measurements/2014_07_28.

Attachment 1: 143brdf.pdf
  1462   Wed Jul 30 17:47:56 2014 taraDailyProgressopticBRDF of AlGaAs mirror 143

 I used the setup to measure scattered loss from an REO mirror (mirror for iLIGO refcav, the one we measured coating thermal noise) and get 6 ppm. This number agrees quite well with the previous Finesse measurement.


  Finesse measurement from REO mirrors = 9700 , see PSL:424 The absorption loss in each mirror is ~ 5 ppm ( from photo thermal measurement, see PSL:1375). The measured finesse infers that the roundtrip loss is ~ 24 ppm, see here. So each mirror has ~ 12 ppm loss. With ~ 5ppm absorption loss, we can expect ~ 6-7 ppm loss for scattered loss.  So this measurement roughly says that our scattered light setup and calibration is ok.


  1463   Thu Jul 31 09:40:24 2014 EvanDailyProgressopticBRDF of AlGaAs mirror 114

[Tara, Evan]

Tara took a BRDF measurement yesterday of AlGaAs mirror #114.

In this measurement, the return beam is dumped using black anodized foil instead of a razor blade dump. This seems to make the peak at 20° disappear, and now we get a more or less monotonic falloff in scattered power.

TIS from 14° to 71° is 39(6) ppm.

Data and code are on the SVN at CTNlab/measurements/2014_07_30.

Attachment 1: 114brdf.pdf
  1465   Mon Aug 4 15:23:06 2014 EvanDailyProgressopticBRDF of AlGaAs mirror 114 after cleaning

[Tara, Evan]

Tara also took a BRDF measurement of #114 after cleaning it.

After cleaning, TIS from 14° to 71° is 2.7(5) ppm. Much improved.

Data and code are on the SVN at CTNlab/measurements/2014_07_31.

Attachment 1: 114_cleaned_brdf.pdf
  1466   Tue Aug 5 08:14:14 2014 EvanDailyProgressopticBRDF of AlGaAs mirror 141 after cleaning

Incident power: 20.0(1) mW

Exposure times used: 25 ms, 50 ms, 200 ms, 500 ms, 1000 ms

Transmitted power: 3.34(2) µW. This gives a transmission of 167(1) ppm for this mirror.

TIS from 16° to 73° is 18(1) ppm.

Data and code are on the SVN at CTNLab/measurements/2014_08_05.

Attachment 1: 141brdf.pdf
  1467   Tue Aug 5 14:54:36 2014 EvanDailyProgressopticBRDF of AlGaAs mirror 132 after cleaning


Incident power: 20.0(1) mW

Exposure times used: 25 ms, 50 ms, 200 ms, 500 ms, 1000 ms

Transmitted power: 3.34(2) µW. This gives a transmission of 167(1) ppm for this mirror.

TIS from 16° to 73° is 18(1) ppm.

Data and code are on the SVN at CTNLab/measurements/2014_08_05.

 Basically the same story with 132.

Attachment 1: 132brdf.pdf
  1468   Tue Aug 5 18:10:31 2014 EvanDailyProgressopticAlGaAs mirror transmissions; optical contacting

I used the ThorLabs power meter to get the transmission coefficients for the five AlGaAs mirrors.

For each measurement, I wrote down the incident power (20 mW nominal), the transmitted power (≈3.5 µW, depending on the mirror and background light level), and the transmitted power with the beam blocked (to get the dark power).

Transmission (ppm) Average (ppm)
#114 142(6) 142(6)
#132 162.4(1.4), 159.8(2.1), 163.0(2.1) 161.7(1.9)
#137 149.8(3.4), 149.5(2.0), 148.0(2.0) 149.1(2.5)

154.9(2.0), 155.4(2.1), 155.4(2.1)

#143 155.6(2.1), 154.7(2.1) 155.2(2.1)

In other news, Tara bonded mirror #114 to spacer #95. The contacting seems to be tough going because of some recalcitrant smudges on the substrate surfaces.

Attachment 1: almost.jpg
Attachment 2: done.jpg
  1471   Thu Aug 14 15:23:36 2014 Emily, EvanNotesopticAOM fiber noise cancellation

 New setup for fiber phase noise cancellation with one AOM

We re-did mode-matching calculations and replaced the lenses before the fiber input in order to optimize the amount of power that comes out of the fiber.  The waist coming out of the PMC is 370 microns.  Following the PMC are the following lenses: placed 7 inches away is a PLCX- with a focal length of 250mm, placed 29 inches away is a PLCX-25.4-64.4-C-1064 with a focal length of 125 mm, and placed 35 inches away is a KBX052 with a focal length of 50.2mm. This yields a waist of 69 microns going into the fiber.  Going into the fiber is about 1.1 mw and coming out is approximately 500 micro watts.  We replaced the VCO driver since it was not driving the AOM and had a deformed signal.  Now we are using a Marconi and low-noise amplifier to drive the AOM.  We also replaced the AOM with an Isomet AOM 1205c-843.  
We re-did mode-matching calculations into the AOM and to the mirror.  After the fiber output is a waist of 50 microns.  Placed 2 inches away is a: PLCX-25.4-33.7-UV-1064 with a focal length of 50mm, placed 10 inches away is a: PLCX-25.4-77.3-UV-1064 with a focal length of 150mm and placed 18 inches away is a: PLCX-25.4-36.1-UV-1064 with a focal length of 70mm.  The first two lenses before the AOM yield a was it of 150 microns going through the AOM (recommended waist from the Isomet AOM 1205c-843 manual) and the third lens yields a waist of 156 microns at the mirror.  We used a beam dump to block the zeroth order beam, so the only the first order beam is double passed through the fiber.  
We are using the same setup to beat the double passed beam with the original beam onto a new focus 1811 photodiode.  The original beam has a power of 850 micro-watts and the double-passed beam has a power of 10 micro-watts. While the efficiency can be improved, for now we will work with what we have in order to prove that our new setup with 1 AOM will cancel the noise in the system.  
In this setup, we lock the optical beat to the marconi in a PLL.  
The AC signal optical beat fluctuation was 198-428mV.
Once the optical beat was locked to the marconi, we measured the error signal and control signal.  We also measured the control signal without cancellation to make sure that this works.  In order to do the measurement without cancellation, we locked the marconi to the optical beat.  We also measured the open loop transfer function with and without cancellation.  The following data was obtained: 
  1472   Thu Aug 14 15:24:14 2014 Emily NotesopticTemporarily changed angle on half wave plate

(Laser going to ACAV) I changed the angle of the half-waveplate before the PBS in order to increase the amount of power going into the fiber that goes to gyro lab.  Its original position was at 277 degrees.  I put a beam dump behind the lens (PLCX-25.4-38.6-UV-1064) so the higher power does not reach the photodiode.  The new position is at 248 degrees.  I will move it back before I leave.

  1486   Wed Aug 27 03:21:53 2014 ranaSummaryopticoptimization for ETM with a-Si/SiO2 coatings

 I filled in more values for a-Si at 120 K into the wiki that Matt Abernathy set up. Then I ran the optimization code for Brownian noise only:


The above plot shows the comparison between the optimized aLIGO coating (silica:tantala at 300K) v. the a-Si coating at 120 K.


Then, finally, I compared the TO and Brownian noise of the two designs using the plotTO120.m script:


The dashed curves are silica:tantala and the solid lines are a-Si:silica. The Brownian noise improvement is a factor of ~6. A factor of ~1.6 comes from the temperature and the remaining factor of ~3.9 comes from the low loss and the lower number of layers.

I think this is not yet the global optimum, but just what I got with a couple hours of fmincon. On the next iteration, we should make sure that we minimize the sensitvity to coating thickness variations. As it turns out, there was no need to do the thermo optic cancellation since the thermo-elastic is so low and the thermo-refractive is below the Brownian almost at all frequencies.

  1488   Thu Aug 28 17:36:03 2014 EvanDailyProgressopticMode-matching solution for north cavity

Current configuration:

  • Target waist: 180 µm, z = 0 mm
  • Lens 1: 140 mm focal length, z = −711 mm (24″ from center of vacuum chamber + 4″ through periscope)
  • Lens 2: 84 mm focal length, z = −991 mm (11″ further behind lens 1)
  • Seed waist = ??

Since we know we were mode-matched fairly well into the 180 µm waist of the silica/tantala cavity (>93% visibility), I asked alm to propagate this waist backward through the lenses in order to find a seed waist. It reports a waist of 161 µm at z = −1373 mm.

I asked alm for a new configuration using the same two lenses. The best configuration (mode overlap = 1) is as follows:

  • Seed waist: 161 µm at z = −1373 mm
  • Lens 1: 140 mm focal length, z = −743 mm
  • Lens 2: 84 mm focal length, z = −1023 mm
  • Target waist: 215 µm, z = 0 mm

So we should move lens 1 back by 32 mm (=1.3″), and move lens 2 back by the same amount.

Attachment 1: ctn_algaas_alm.pdf
Attachment 2: ctn_algaas.zip
  1489   Thu Aug 28 19:10:40 2014 EvanDailyProgressopticMode-matching solution for north cavity


Current configuration:

  • Target waist: 180 µm, z = 0 mm
  • Lens 1: 140 mm focal length, z = −711 mm (24″ from center of vacuum chamber + 4″ through periscope)
  • Lens 2: 84 mm focal length, z = −991 mm (11″ further behind lens 1)
  • Seed waist = ??

Since we know we were mode-matched fairly well into the 180 µm waist of the silica/tantala cavity (>93% visibility), I asked alm to propagate this waist backward through the lenses in order to find a seed waist. It reports a waist of 161 µm at z = −1373 mm.

I asked alm for a new configuration using the same two lenses. The best configuration (mode overlap = 1) is as follows:

  • Seed waist: 161 µm at z = −1373 mm
  • Lens 1: 140 mm focal length, z = −743 mm
  • Lens 2: 84 mm focal length, z = −1023 mm
  • Target waist: 215 µm, z = 0 mm

So we should move lens 1 back by 32 mm (=1.3″), and move lens 2 back by the same amount.

I moved both lens mounts back by 1″, then adjusted the Vernier knobs and periscope mirrors to try to maximize the visibility as seen on north REFL DC.

The best I am able to do so far is a visibility of v = 1 − 0.57(1) V / 1.74(1) V = 0.672(6).

  1503   Sat Sep 6 12:54:05 2014 Tara, EvanDailyProgressopticNorth photothermal TF

Tara and I took an SR785 measurement of the north photothermal transfer function.

Clearly there's something wrong with the measurement above 1 kHz.

Attachment 1: nPT.pdf
Attachment 2: npttf.zip
ELOG V3.1.3-