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  15380   Mon Jun 8 11:50:02 2020 HangUpdateBHDAstigmatism and scattering plots

We consider the astigmatism effects of the stock options. The conclusions are:

1. For the AS path, the stock should work fine for the phase-one of BHD, if we could tolerate a few percent MM loss. The window for length adjustment to achieve >99% MM for both s and t is only 1 mm for 1% RoC error (compared to ~ 1 cm in the customized case). 

2. The LO path seemed tricky. As LO3 & LO4 are both significantly curved (RoC<=0.5 m), the non-zero angle of incidence makes the astigmatism quite sever. For the t-plane the nominal MM can be 0.98, yet for the s-plane, the nominal MM is only 0.72. We could move things around to achieve a MM ~ 0.85, which is probably fine for the phase-one implementation but not long term. 

Details:

Attachments 1-3 are for the AS path; 4-6 are for the LO path. 

1 & 4. Marginalized MM distribution for the AS/LO paths. Here we assumed 5 mm positional error and 1% fractional RoC error. Due to the astigmatism, the nominal s-plane MM is only 0.72 for the LO path. 

2 & 5. Scattering plots for the AS/LO paths. We color coded the points as the following: pink: MM>0.99; olive: 0.98<MM<=0.99; grey: MM<=0.98. For the AS path, MM is mostly sensitive to the AS1 RoC and can be adjusted by changing AS1-AS3 distance. For the LO path, the LO3 RoC and LO3-LO4 distance are most critical for the MM. 

3 & 6. Assuming +- 1% AS1 (LO3) fractional RoC error, how much can we compensate for it using AS1-AS3 (LO3-LO4) distance. For the AS path, there exists a ~ 1 mm window where the MM for s and t can simultaneously > 99%. For the LO path, the best we can do is to make s and t both ~ 85%. 

Quote:

Summary

For the initial phase of BHD testing, we recently discussed whether the mode-matching telescopes could be built with 100% stock optics. This would allow the optical system to be assembled more quickly and cheaply at a stage when having ultra-low loss and scattering is less important. I've looked into this possibility and conclude that, yes, we do have a good stock optics option. It in fact achieves comprable performance to our optimized custom-curvature design [ELOG 15357]. I think it is certainly sufficient for the initial phase of BHD testing.

Vendor

It turns out our usual suppliers (e.g., CVI, Edmunds) do not have enough stock options to meet our requirements. This is for two reasons:

  • For sufficient LO1-LO2 (AS1-AS4) Gouy phase separation, we require a very particular ROC range for LO1 (AS1) of 5-6 m (2-3 m).
  • We also require a 2" diameter for the suspended optics, which is a larger size than most vendors stock for curved reflectors (for example, CVI has no stock 2" options).

However I found that Lambda Research Optics carries 1" and 2" super-polished mirror blanks in an impressive variety of stock curvatures. Even more, they're polished to comprable tolerances as I had specificied for the custom low-scatter optics [DCC E2000296]: irregularity < λ/10 PV, 10-5 scratch-dig, ROC tolerance ±0.5%. They can be coated in-house for 1064 nm to our specifications.

From modeling Lambda's stock curvature options, I find it still possible to achieve mode-matching of 99.9% for the AS beam and 98.6% for the LO beam, if the optics are allowed to move ±1" from their current positions. The sensitivity to the optic positions is slightly increased compared to the custom-curvature design (but by < 1.5x). I have not run the stock designs through Hang's full MC corner-plot analysis which also perturbs the ROCs [ELOG 15339]. However for the early BHD testing, the sensitivity is secondary to the goal of having a quick, cheap implementation.

Stock-Part Telescope Designs

The following tables show the best telescope designs using stock curvature options. It assumes the optics are free to move ±1" from their current positions. For comparison, the values from the custom-curvature design are also given in parentheses.

AS Path

The AS relay path is shown in Attachment 1:

  • AS1-AS4 Gouy phase separation: 71°
  • Mode-matching to OMC: 99.9%
Optic ROC (m) Distance from SRM AR (m)
AS1 2.00  (2.80) 0.727  (0.719)
AS2 Flat   (Flat) 1.260  (1.260)
AS3 0.20  (-2.00) 1.864  (1.866)
AS4 0.75  (0.60) 2.578  (2.582)

LO Path

The LO relay path is shown in Attachment 2:

  • LO1-LO2 Gouy phase separation: 67°
  • Mode-matching to OMC: 98.6%
Optic ROC (m) Distance from PR2 AR (m)
LO1 5.00  (6.00) 0.423  (0.403)
LO2 1000 (1000) 2.984  (2.984)
LO3 0.50  (0.75) 4.546  (4.596)
LO4 0.15  (-0.45) 4.912  (4.888)

Ordering Information

I've created a new tab in the BHD procurement spreadsheet ("Stock MM Optics Option") listing the part numbers for the above telescope designs, as well as their fabrication tolerances. The total cost is $2.8k + the cost of the coatings (I'm awaiting a quote from Lambda for the coatings). The good news is that all the curved substrates will receive the same HR/AR coatings, so I believe they can all be done in a single coating run.

 

Attachment 1: AS_MM_hist_stock.pdf
AS_MM_hist_stock.pdf
Attachment 2: AS_MM_t_scat_stock.pdf
AS_MM_t_scat_stock.pdf
Attachment 3: AS_MM_adj_stock.pdf
AS_MM_adj_stock.pdf
Attachment 4: LO_MM_hist_stock.pdf
LO_MM_hist_stock.pdf
Attachment 5: LO_MM_s_scat_stock.pdf
LO_MM_s_scat_stock.pdf
Attachment 6: LO_MM_adj_stock.pdf
LO_MM_adj_stock.pdf
  15503   Tue Jul 28 13:55:11 2020 HangUpdateBHDExploring bilinear SRCL->DARM coupling

We explore bilinear SRCL to DARM noise coupling mechanisms, and show two cases that by doing BHD readout the noise performance can be improved. In the first case, the bilinear piece is due to residual DHARD motion (see also LHO:45823), and it matters mostly for the low-frequency (<100 Hz) part, and in the second piece the bilinear piece is due to residual SRCL fluctuation and it matters mostly for the a few x 100 Hz part. Details are below:

=================================================

General Model:

We can write the SRCL to DARM transfer function as (Evan Hall's thesis, eq. 2.29)

Z_s2d(f) = C_lf(f) * F^2 * x_D + C_hf(f) * F * dphi_S * x_D    ---- (1)

where

C_lf ~ 1/f^2 and C_hf ~ f are constants at each frequency unless there are major upgrades to the IFO,

F is the finesse of the arm cavity which depends on the alignment, spot position on the TMs, etc., 

dphi_S is the SRCL detuning (wrt the nominal 90 deg value), 

x_D is the DC DARM offset. 

The linear part of this can be removed with feedforward subtractions and it is the bilinear piece that matters, which reads

dZ_s2d = C_lf * <F>^2 * dx_D + C_hf * <F> * <dphi_S> * dx_D

             + 2C_lf * <F> * <x_D>  * dF + C_hf * <dphi_S> * <x_D> * dF

             + C_hf  * <F> * <x_D> * d(dphi_S).     ---- (2)

The first term in (2) is due to residual DARM motion dx_D. This term does not depends on the DC value of DARM offset <x_D> and thus does not depend on doing BHD or DC readout. On the other hand, the typical residual DARM motion is 1 fm << 1 pm of DARM offset. Since the current feedforward reduction factor is about 10 (see both Den Martynov's thesis and Evan Hall's thesis), clearly we are not limited by the residual DARM motion. 

The second term is due to the change in the arm finesse, which can be affected by, e.g., the alignment fluctuation (both increasing the loss due to scattering into 01/10 modes and affecting the spot positon and hence changing the losses), and is likely to be the reason why we see the effect being modulated by DHARD. 

The last term in (2) is due to the residual SRCL fluctuation and is important for the ~ a few x 100 Hz band.

=================================================

DHARD effects. 

As argued above, the DHARD affects the SRCL -> DARM coupling as it changes the finesse in the arm cavity (through scattering into 01/10 modes; in finesse we cannot directly simulate the effects due to spot hitting a rougher location). 

Since in the second term of eq. (2) the LF part depends on the DARM DC offset <x_D>, this effect can be improved by going from DC readout to BHD. 

To simulate it in finesse, at a fixed DARM DC offset, we compute the SRCL->DARM transfer functions at different DHARD offsets, and then numerically compute the derivative \partial Z_s2d / \partial \theta_{DH}. Then multiplying this derivative with the rms value of DHARD fluctuation \theta_{DH} we then know the expected bilinear coupling piece. 

The result is shown in the first attached plot. Here we have assumed a flat SRCL noise of 5e-16 m/rtHz for simplicity (see PRD 93, 112004, 2016). We do not account for the loop effects which further reduces the high frequency components for now. The residual DHARD RMS is assumed to be 1 nrad. 

In the first plot, from top to bottom we show the SRCL noise projection at different DARM DC offsets of (0.1, 1, 10) pm. Since the DHARD alignment only affects the arm finesse starting at quadratic order, it thus matters what DC offset in DHARD we assume. In each pannel, the blue trace is for no DC offset in DHARD and the orange one for a 5 nrad DC offset. As a reference, the A+ sensitivity is shown in grey trace in each plot as a reference. 

We can see if there is a large DC offset in DHARD (a few nrad) and we still do DC readout with a few pm of DARM offset, then the bilinear piece of SRCL can still contaminate the sensitivity in the 10-100 Hz band (bottom panel; orange trace). On the other hand, if we do BHD, then the SRCL noise should be down by ~ x100  even compared to with the top panel. 

(A 5 nrad of DC offset in DHARD coupled with 1 nrad RMS would cause about 0.5% RIN in the arms. This is somewhat greater than the typically measured RIN which is more like <~ 0.2%. See the second plot). 

=================================================

SRCL effect. 

Similarly we can consider the SRCL->DARM coupling due to residual SRCL rms. The approach is very similar to what we did above for DHARD. I.e., we compute Z_s2d at fixed DARM offset and for different SRCL offsets, then we numerically evaluate \partial Z_s2d / \partial dphi_S. A residual SRCL rms of 0.1 nm is then used to generate the projection shown in the third figure. 

Unlike the DHARD effect, the bilinear SRCL piece does not depend on the DC SRCL detuning (for the 50-500 Hz part). It does still depends on the DARM DC offset and therefore could be improved by BHD.

Since we do not include the LP of the SRCL loop in this plot, the HF noise at 1 kHz is artifical as it can be easily filtered out. However, the LP will not be very strong around 100-300 Hz for a SRCL UGF ~ 30 Hz, and thus doing BHD could still have some small improvements for this effect. 

Attachment 1: SRCL_bilin_DHARD.pdf
SRCL_bilin_DHARD.pdf
Attachment 2: ARM_RIN.pdf
ARM_RIN.pdf
Attachment 3: SRCL_bilin_SRCL.pdf
SRCL_bilin_SRCL.pdf
  16373   Mon Oct 4 15:50:31 2021 HangUpdateCalibrationFisher matrix estimation on XARM parameters

[Anchal, Hang]

What: Anchal and I measured the XARM OLTF last Thursday.

Goal: 1. measure the 2 zeros and 2 poles in the analog whitening filter, and potentially constrain the cavity pole and an overall gain. 

          2. Compare the parameter distribution obtained from measurements and that estimated analytically from the Fisher matrix calculation.

          3. Obtain the optimized excitation spectrum for future measurements.   

How: we inject at C1:SUS-ETMX_LSC_EXC so that each digital count should be directly proportional to the force applied to the suspension. We read out the signal at C1:SUS-ETMX_LSC_OUT_DQ. We use an approximately white excitation in the 50-300 Hz band, and intentionally choose the coherence to be only slightly above 0.9 so that we can get some statistical error to be compared with the Fisher matrix's prediction. For each measurement, we use a bandwidth of 0.25 Hz and 10 averages (no overlapping between adjacent segments). 

The 2 zeros and 2 poles in the analog whitening filter and an overall gain are treated as free parameters to be fitted, while the rest are taken from the model by Anchal and Paco (elog:16363). The optical response of the arm cavity seems missing in that model, and thus we additionally include a real pole (for the cavity pole) in the model we fit. Thus in total, our model has 6 free parameters, 2 zeros, 3 poles, and 1 overall gain. 

The analysis codes are pushed to the 40m/sysID repo. 

===========================================================

Results:

Fig. 1 shows one measurement. The gray trace is the data and the olive one is the maximum likelihood estimation. The uncertainty for each frequency bin is shown in the shaded region. Note that the SNR is related to the coherence as 

        SNR^2 = [coherence / (1-coherence)] * (# of average), 

and for a complex TF written as G = A * exp[1j*Phi], one can show the uncertainty is given by 

        \Delta A / A = 1/SNR,  \Delta \Phi = 1/SNR [rad]. 

Fig. 2. The gray contours show the 1- and 2-sigma levels of the model parameters using the Fisher matrix calculation. We repeated the measurement shown in Fig. 1 three times, and the best-fit parameters for each measurement are indicated in the red-crosses. Although we only did a small number of experiments, the amount of scattering is consistent with the Fisher matrix's prediction, giving us some confidence in our analytical calculation. 

One thing to note though is that in order to fit the measured data, we would need an additional pole at around 1,500 Hz. This seems a bit low for the cavity pole frequency. For aLIGO w/ 4km arms, the single-arm pole is about 40-50 Hz. The arm is 100 times shorter here and I would naively expect the cavity pole to be at 3k-4k Hz if the test masses are similar. 

Fig. 3. We then follow the algorithm outlined in Pintelon & Schoukens, sec. 5.4.2.2, to calculate how we should change the excitation spectrum. Note that here we are fixing the rms of the force applied to the suspension constant. 

Fig. 4 then shows how the expected error changes as we optimize the excitation. It seems in this case a white-ish excitation is already decent (as the TF itself is quite flat in the range of interest), and we only get some mild improvement as we iterate the excitation spectra (note we use the color gray, olive, and purple for the results after the 0th, 1st, and 2nd iteration; same color-coding as in Fig. 3).   

 

 

 

Attachment 1: tf_meas.pdf
tf_meas.pdf
Attachment 2: fisher_est_vs_data.pdf
fisher_est_vs_data.pdf
Attachment 3: Pxx_evol.pdf
Pxx_evol.pdf
Attachment 4: fisher_evol.pdf
fisher_evol.pdf
  16384   Wed Oct 6 15:04:36 2021 HangUpdateSUSPRM L2P TF measurement & Fisher matrix analysis

[Paco, Hang]

Yesterday afternoon Paco and I measured the PRM L2P transfer function. We drove C1:SUS-PRM_LSC_EXC with a white noise in the 0-10 Hz band (effectively a white, longitudinal force applied to the suspension) and read out the pitch response in C1:SUS-PRM_OL_PIT_OUT. The local damping was left on during the measurement. Each FFT segment in our measurement is 32 sec and we used 8 non-overlapping segments for each measurement. The empirically determined results are also compared with the Fisher matrix estimation (similar to elog:16373).

Results:

Fig. 1 shows one example of the measured L2P transfer function. The gray traces are measurement data and shaded region the corresponding uncertainty. The olive trace is the best fit model. 

Note that for a single-stage suspension, the ideal L2P TF should have two zeros at DC and two pairs of complex poles for the length and pitch resonances, respectively. We found the two resonances at around 1 Hz from the fitting as expected. However, the zeros were not at DC as the ideal, theoretical model suggested. Instead, we found a pair of right-half plane zeros in order to explain the measurement results. If we cast such a pair of right-half plane zeros into (f, Q) pair, it means a negative value of Q. This means the system does not have the minimum phase delay and suggests some dirty cross-coupling exists, which might not be surprising. 

Fig. 2 compares the distribution of the fitting results for 4 different measurements (4 red crosses) and the analytical error estimation obtained using the Fisher matrix (the gray contours; the inner one is the 1-sigma region and the outer one the 3-sigma region). The Fisher matrix appears to underestimate the scattering from this experiment, yet it does capture the correlation between different parameters (the frequencies and quality factors of the two resonances).

One caveat though is that the fitting routine is not especially robust. We used the vectfit routine w/ human intervening to get some initial guesses of the model. We then used a standard scipy least-sq routine to find the maximal likelihood estimator of the restricted model (with fixed number of zeros and poles; here 2 complex zeros and 4 complex poles). The initial guess for the scipy routine was obtained from the vectfit model.  

Fig. 3 shows how we may shape our excitation PSD to maximize the Fisher information while keeping the RMS force applied to the PRM suspension fixed. In this case the result is very intuitive. We simply concentrate our drive around the resonance at ~ 1 Hz, focusing on locations where we initially have good SNR. So at least code is not suggesting something crazy... 

Fig. 4 then shows how the new uncertainty (3-sigma contours) should change as we optimize our excitation. Basically one iteration (from gray to olive) is sufficient here. 

We will find a time very recently to repeat the measurement with the optimized injection spectrum.

Attachment 1: prm_l2p_tf_meas.pdf
prm_l2p_tf_meas.pdf
Attachment 2: prm_l2p_fisher_vs_data.pdf
prm_l2p_fisher_vs_data.pdf
Attachment 3: prm_l2p_Pxx_evol.pdf
prm_l2p_Pxx_evol.pdf
Attachment 4: prm_l2p_fisher_evol.pdf
prm_l2p_fisher_evol.pdf
  16388   Fri Oct 8 17:33:13 2021 HangUpdateSUSMore PRM L2P measurements

[Raj, Hang]

We did some more measurements on the PRM L2P TF. 

We tried to compare the parameter estimation uncertainties of white vs. optimal excitation. We drove C1:SUS-PRM_LSC_EXC with "Normal" excitation and digital gain of 700.

For the white noise exciation, we simply put a butter("LowPass",4,10) filter to select out the <10 Hz band.

For the optimal exciation, we use butter("BandPass",6,0.3,1.6) gain(3) notch(1,20,8) to approximate the spectral shape reported in elog:16384. We tried to use awg.ArbitraryLoop yet this function seems to have some bugs and didn't run correctly; an issue has been submitted to the gitlab repo with more details. We also noticed that in elog:16384, the pitch motion should be read out from C1:SUS-PRM_OL_PIT_IN1 instead of the OUT channel, as there are some extra filters between IN1 and OUT. Consequently, the exact optimal exciation should be revisited, yet we think the main result should not be altered significantly.

While a more detail analysis will be done later offline, we post in the attached plot a comparison between the white (blue) vs optimal (red) excitation. Note in this case, we kept the total force applied to the PRM the same (as the RMS level matches).

Under this simple case, the optimal excitation appears reasonable in two folds.

First, the optimization tries to concentrate the power around the resonance. We would naturally expect that near the resonance, we would get more Fisher information, as the phase changes the fastest there (i.e., large derivatives in the TF).

Second, while we move the power in the >2 Hz band to the 0.3-2 Hz band, from the coherence plot we see that we don't lose any information in the > 2 Hz region. Indeed, even with the original white excitation, the coherence is low and the > 2 Hz region would not be informative. Therefore, it seems reasonable to give up this band so that we can gain more information from locations where we have meaningful coherence.

Attachment 1: Screenshot_2021-10-08_17-30-52.png
Screenshot_2021-10-08_17-30-52.png
  16390   Mon Oct 11 13:59:47 2021 HangUpdateSUSMore PRM L2P measurements

We report here the analysis results for the measurements done in elog:16388

Figs. 1 & 2 are respectively measurements of the white noise excitation and the optimized excitation. The shaded region corresponds to the 1-sigma uncertainty at each frequency bin. By eyes, one can already see that the constraints on the phase in the 0.6-1 Hz band are much tighter in the optimized case than in the white noise case. 

We found the transfer function was best described by two real poles + one pair of complex poles (i.e., resonance) + one pair of complex zeros in the right-half plane (non-minimum phase delay). The measurement in fact suggested a right-hand pole somewhere between 0.05-0.1 Hz which cannot be right. For now, I just manually flipped the sign of this lowest frequency pole to the left-hand side. However, this introduced some systematic deviation in the phase in the 0.3-0.5 Hz band where our coherence was still good. Therefore, a caveat is that our model with 7 free parameters (4 poles + 2 zeros + 1 gain as one would expect for an ideal signal-stage L2P TF) might not sufficiently capture the entire physics. 

In Fig. 3 we showed the comparison of the two sets of measurements together with the predictions based on the Fisher matrix. Here the color gray is for the white-noise excitation and olive is for the optimized excitation. The solid and dotted contours are respectively the 1-sigma and 3-sigma regions from the Fisher calculation, and crosses are maximum likelihood estimations of each measurement (though the scipy optimizer might not find the true maximum).

Note that the mean values don't match in the two sets of measurements, suggesting potential bias or other systematics exists in the current measurement. Moreover, there could be multiple local maxima in the likelihood in this high-D parameter space (not surprising). For example, one could reduce the resonant Q but enhance the overall gain to keep the shoulder of a resonance having the same amplitude. However, this correlation is not explicit in the Fisher matrix (first-order derivatives of the TF, i.e., local gradients) as it does not show up in the error ellipse. 

In Fig. 4 we show the further optimized excitation for the next round of measurements. Here the cyan and olive traces are obtained assuming different values of the "true" physical parameter, yet the overall shapes of the two are quite similar, and are close to the optimized excitation spectrum we already used in elog:16388

 

Attachment 1: prm_l2p_tf_meas_white.pdf
prm_l2p_tf_meas_white.pdf
Attachment 2: prm_l2p_tf_meas_opt.pdf
prm_l2p_tf_meas_opt.pdf
Attachment 3: prm_l2p_fisher_vs_data_white_vs_opt.pdf
prm_l2p_fisher_vs_data_white_vs_opt.pdf
Attachment 4: prm_l2p_Pxx_evol_v2.pdf
prm_l2p_Pxx_evol_v2.pdf
  16399   Wed Oct 13 15:36:38 2021 HangUpdateCalibrationXARM OLTF

We did a few quick XARM oltf measurements. We excited C1:LSC-ETMX_EXC with a broadband white noise upto 4 kHz. The timestamps for the measurements are: 1318199043 (start) - 1318199427 (end).

We will process the measurement to compute the cavity pole and analog filter poles & zeros later.

Attachment 1: Screenshot_2021-10-13_15-32-16.png
Screenshot_2021-10-13_15-32-16.png
  16467   Tue Nov 16 11:37:26 2021 HangHowToSUSFitting suspension model--large systematic errors

One goal of our sysID study is to improve the aLIGO L2A feedforward. Our algorithm currently improves only the statistical uncertainty and assumes the systematic errors are negligible. However, I am currently baffled by how to fit a (nearly) realistic suspension model...

My test study uses the damped aLIGO QUAD suspension model. From the Matlab model I extract the L2 drive in [N] to L3 pitch in [rad] transfer function (given by a SS model with the A matrix having a shape of 103x103). I then tried to use VectFIT to fit the noiseless TF. After removing nearby z-p pairs (defined by less than 0.2 times the lowest pole frequency) and high-frequency zeros, I got a model with 6 complex pole pairs and 4 complex zero pairs (21 free parameters in total). I also tried to fit the TF (again, noiseless) with an MCMC algorithm assuming the underlying model has the same number of parameters as the VectFIT results. 

Please see the first attached plots for a comparison between the fitted models and the true one. In the second plot, we show the fractional residual

    | TF_true - TF_fit | / | TF_true |,

and the inverse of this number gives the saturating SNR at each frequency. I.e., when the statistical SNR is more than the saturating value, we are then limited by systematic errors in the fitting. And so far, disappointingly I can only get an SNR of 10ish for the main resonances...

I wonder if people know better ways to reduce this fitting systematic... Help is greatly appreciated!

Attachment 1: L2L_L3P_fit.pdf
L2L_L3P_fit.pdf
Attachment 2: L2L_L3P_residual.pdf
L2L_L3P_residual.pdf
  16486   Mon Nov 29 15:24:53 2021 HangHowToGeneralFisher matrix vs length of each FFT segment

We have been discussing how does the parameter estimation depends on the length per FFT segment. In other words, after we collected a series of data, would it be better for us to divide it into many segments so that we have many averages, or should we use long FFT segments so that we have more frequency bins?

My conclusions are that:

1). We need to make sure that the segment length is long enough with T_seg > min[ Q_i / f_i ], where f_i is the resonant frequency of the i'th resonant peak and the Q_i its quality factor. 

2). Once 1) is satisfied, the result depends weakly on the FFT length. There might be a weak hint preferring a longer segment length (i.e., want more freq bins than more averages) though. 

=================================================================

To reach the conclusion, I performed the following numerical experiment.

I considered a simple pendulum with resonant frequency f_1 = 0.993 Hz and Q_1 = 6.23. The value of f_1 is chosen such that it is not too special to fall into a single freq bin. Additionally, I set an overall gain of k=20. I generated T_tot = 512 s of data in the time domain and then did the standard frequency domain TF estimation. I.e., I computed the CSD between excitation and response (with noise) over the PSD of the excitation. The spectra of excitation and noise in the readout channel are shown in the first plot. 

In the second plot, I showed the 1-sigma errors from the Fisher matrix calculation of the three parameters in this problem, as well as the determinant of the error matrix \Sigma = inv(Fisher matrix). All quantities are plotted as functions of the duration per FFT segment T_seg. The red dotted line is [Q_1/f_1], i.e., the time required to resolve the resonant peak. As one would expect, if T_seg <~ (Q_1/f_1), we cannot resolve the dynamics of the system and therefore we get nonsense PE results. However, once T_seg > (Q_1/f_1), the PE results seem to be just fluctuating (as f_1 does not fall exactly into a single bin). Maybe there is a small hint that longer T_seg is better. Potentially, this might be due to that we lose less information due to windowing? To be investigated further... 

I also showed the Fisher estimation vs. MCMC results in the last two plots. Here each dot is an MCMC posterior. The red crosses are the true values, and the purple contours are the results of the Fisher calculations (3-sigma contours). The MCMC results showed similar trends as the Fisher predictions and the results for T_seg = (32, 64, 128) s all have similar amounts of scattering << the scattering of the T_seg=8 s results. Though somehow it showed a biased result. In the third plot, I manually corrected the mean so that we could just compare the scattering. The fourth plot showed the original posterior distribution. 

 

Attachment 1: setup.pdf
setup.pdf
Attachment 2: Fisher_vs_Tperseg.pdf
Fisher_vs_Tperseg.pdf
Attachment 3: fisher_vs_mcmc_offset_removed.png
fisher_vs_mcmc_offset_removed.png
Attachment 4: fisher_vs_mcmc.png
fisher_vs_mcmc.png
  17011   Mon Jul 18 15:17:51 2022 HangUpdateCalibrationError propagation to astrophysical parameters from detector calibration uncertainty

1. In the error propogation equation, it should be \Delta \Theta = -H^{-1} M \Delta \Lambda, instead of the fractional error. 

2. For the astro parameters, in general you would need t_c for the time of coalescence and \phi_c for the phase. See, e.g., https://ui.adsabs.harvard.edu/abs/1994PhRvD..49.2658C/abstract.

3. Fig. 1 looks very nice to me, yet I don't understand Fig. 3... Why would phase or amplitude uncertainties at 30 Hz affect the tidal deformability? The tide should be visible only > 500 Hz. 

4. For BBH, we don't measure individual spin well but only their mass-weighted sum, \chi_eff = (m_1*a_1 + m_2*a_2)/(m_1 + m_2). If you treat S1z and S2z as free parameters, your matrix is likely degenerate. Might want to double-check. Also, for a BBH, you don't need to extend the signal much higher than \omega ~ 0.4/M_tot ~ 10^4 Hz * (Ms/M_tot). So if the total mass is ~ 100 Ms, then the highest frequency should be ~ 100 Hz. Above this number there is no signal. 

 

  17029   Sun Jul 24 08:56:01 2022 HangUpdateCalibrationError propagation to astrophysical parameters from detector calibration uncertainty

Sorry I forgot to put tc & phic in the example. 

I modified astroFisherLib.py to include these parameters. Please note that their meaning is that we don't know when the signal happens and at which phase it merges.

It does not mean the time & phase from a reference frequency to the merger. This part is not free to vary because it is fixed by the intrinsic parameters.  

It might be good to have a quick scan through the Cutler & Flanagan 94 paper to better understand their physical meanings.

 

  10083   Fri Jun 20 18:33:53 2014 HarryUpdateGeneralRazorblade Beam Analysis Setup

 Eric Q and I set up the optical configuration for razorblade beam analysis on SP table for future use.

It has been aligned, and will be in use on Monday.

The beam will be characterized for future characterization of optical fibers.

  10098   Wed Jun 25 09:16:52 2014 HarryUpdateGeneralRazorblade Measurements

Purpose

To use a razorblade to measure beam waist at multiple points along the optical axis, so as to later extrapolate the modal profile of the entire beam. This information will then be used to effectively couple AUX laser light to fibers for use in the frequency offset locking apparatus.

Data Acquisition

1) Step the micrometer-controlled razorblade across the beam at a given value of Z, along optical axis, in the plane orthogonal to it (arbitrarily called X).

2) At each value of X, record the corresponding output of a photodiode, (Thorlabs PD A55) here given in mV.

3) Repeat process at multiple points along Z

Analysis

Data from each iteration in the X were fitted to the error function shown below.

V(x) = A*(erf((x-m)/s)+c)

In the Y, they were fitted to:

V(x) = -A*(erf((x-m)/s)+c)

'A' corresponds to an amplitude, 'm' to a mean, 's' to a σ, and 'c' to an offset.

(Only because in Y measurements, the blade progressed toward eclipsing the beam, as opposed to in the X where it progressively revealed the beam.

These fits can be solved for x = (erf-1((V/A)-c)*s)+m1  which can be calculated at the points (Vmax/e2) and (Vmax*(1-1/e2)). The difference between these points will yield beam waist, w(z).

Conclusion

Calculations yielded waists of: X1=66.43um, X2=67.73um, X3=49.45um, Y1=61.20um, Y2=58.70, Y3=58.89

These data seem suspect, and shall be subjected to further analysis.

 

Attachment 1: 40m.zip
  10100   Wed Jun 25 09:30:44 2014 HarryUpdateGeneralWeekly Update

See attached weekly update

Attachment 1: Weekly_Update—June_25_thru_July_1.pdf
Weekly_Update—June_25_thru_July_1.pdf
  10103   Wed Jun 25 17:49:36 2014 HarryUpdateGeneralRazorblade Analysis Pt. 2

Reconfigured razorblade analysis setup on the PD table as per instructions. Used it to collect data to calculate beam waist with, analyses to follow.

See attached schematic for optical setup.

Attachment 1: RazorbladeSetup.pdf
RazorbladeSetup.pdf
  10106   Fri Jun 27 10:09:10 2014 HarryUpdateGeneralBeam Waist Measurement

Purpose

To use a razorblade to measure beam waist at four points along the optical axis, so as to later extrapolate the waist. This information will then be used to effectively couple AUX laser light to fibers for use in the frequency offset locking apparatus.

Data Acquisition

1) Step the micrometer-controlled razorblade across the beam at a given value of Z, along optical axis, in the plane orthogonal to it (arbitrarily called X).

2) At each value of X, record the corresponding output of a photodiode, (Thorlabs PD A55) here given in mV.

3) Repeat in Y plane at the same value of Z

4) Repeat process at multiple points along Z

Analysis

Data from each iteration were fitted to the error function shown below.

y(x) = (.5*P)*(1-erf((sqrt(2)*(x-x0))/wz))

'P' corresponds to peak power, 'x0' to the corresponding value of x (or y, as the case may be), and 'wz' to the spot size at the Z value in question.

The spot sizes from the four Z values were then fit to:

y(x) = w0*sqrt(1+((x*x)/(zr*zr)))

Where 'w0' corresponds to beam waist, and 'zr' to Rayleigh Range.

Conclusion

This yielded a Y-Waist of 783.5 um, and an X-Waist of 915.2 um.

The respective Rayleigh ranges were 2.965e+05 um (Y) and 3.145e+05  um (X).

Next

I will do the same analysis with light from the optical cables, which information I will then use to design a telescope to effectively couple the beams.

Attachment 1: BeamWaist.zip
  10139   Mon Jul 7 14:42:33 2014 HarryUpdateGeneralBeam Waists

I was finally able to get a reasonable measurement for the beam waist(s) of the spare NPRO.

Methods

I used a razorblade setup, pictured below, to characterize the beam waist of the spare 1064nm NPRO after a lens (PLCX-25.4-38.6-UV-1064) in order to subsequently calculate the overall waist of the beam. The setup is pictured below:

 

RzorbladeSetupFinal.pdf

After many failed attempts, this was the apparatus we (Manasa, Eric Q, Koji, and I) arrived with. The first lens after the laser was installed to focus the laser, because it's true waist was at an inaccessible location. Using the lens as the origin for the Z axis, I was able to determine the waist of the beam after the lens, and then calculate the beam waist of the laser itself using the equation wf = (lambda*f)/(pi*wo) where wf is the waist after the lens, lambda the wavelength of the laser, f the focal legth of the lens (75.0 mm in this case) and wo the waist before the lens.

We put the razorblade, second lens (to focus the beam onto the photodiode (Thorlabs PDA255)), and the PD with two attenuating filters with optical density of 1.0 and 3.0, all on a stage, so that they could be moved as a unit, in order to avoid errors caused by fringing effects caused by the razorblade.

I took measurements at six different locations along the optical axis, in orthogonal cross sections (referred to as X and Y) in case the beam turned to be elliptical, instead of perfectly circular in cross section. These measurements were carried out in 1" increments, starting at 2" from the lens, as measured by the holes in the optical table.

Analysis

Once I had the data, each cross section was fit to V(x) = (.5*Vmax)*(1-erf((sqrt(2)*(x-x0))/wz))+c, which corresponds to the voltage supplied to the PD at a particular location in x (or y, as the case may be). Vmax is the maximum voltage supplied, x0 is an offset in x from zero, wz is the spot size at that location in z, and c is a DC offset (ie the voltage on the PD when the laser is fully eclipsed.) These fits may all be viewed in the attached .zip file.

The spot sizes, extracted as parameters of the previous fits, were then fit to the equation which describes the propagation of the spot radius, w(z) = wo*sqrt(1+((z-b)/zr)^2)+c, w(z) = w0*sqrt(1+((((z-b)*.000001064)^2)/((pi*w0^2)^2))) where wo corresponds to beam waist, b is an offset in the z. Examples of these fits can be viewed in the attached .zip file.

Finally, since the waists given by the fits were the waists after a lens, I used the equation wf = (lambda*f)/(pi*wo), described above, to determine the waist of the beam before the lens.

Plots

 

note: I was not able to open the first measurement in the X plane (Z = 2in). The rest of the plots have been included in the body of the elog, as per Manasa's request.

Y_Waist_Fit.pngY_plane_measurement_6_(Z_7in).pngY_plane_measurement_5_(Z_6in).pngY_plane_measurement_4(Z_5in).pngY_plane_measurement_3_(Z_4in).pngY_plane_measurement_2_(Z_3in).png

 

Y_plane_measurement_1_(Z_2in).png X_plane_measurement_6_(Z_7in).pngX_plane_measurement_5_(Z_6in).pngX_plane_measurement_4_(Z_5in).pngX_plane_measurement_3_(Z_4in).pngX_plane_measurement_2_(Z_3in).pngX_plane_measurement_1_(Z_2in).pngX_Waist_fit.png

Conclusion

The X Waist after the lens (originally yielded from fit parameters) was 90.8 27.99 ± .14 um. The corresponding Y Waist was 106.2 30.22 ± .11 um.

After adjustment for the lens, the X Waist was 279.7 907.5 ± 4.5 um and the Y Waist was 239.2 840.5 ± 3.0 um.

edit: After making changes suggested by koji, these were the new results of the fits.

Attachments

Attached you should be able to find the razor blade schematic, all of the fits, along with code used to generate them, plus the matlab workspace containing all the necessary variables.

NOTE: Rana brought to my attention that my error bars need to be adjusted, which I will do as soon as possible.

Attachment 2: erFitFinal2.zip
  10158   Tue Jul 8 23:59:49 2014 HarryUpdateGeneralWeekly Plan (7.8.14)

 Last Week:

-I continued to struggle with the razorblade beam analysis, though after a sixth round of measurements, and a lot of fiddling around with fit parameters in matlab, there seems to be a light at the end of the tunnel.

 

Next Week:

-I plan to check my work with the beamscan tomorrow (wednesday) morning

-Further characterize the light from the fibers, and set up the collimator

-Design and hopefully construct the telescope that will focus the beam into the collimator

 

Materials:

- Razorblade setup or beamscan (preferably beamscan)

- Fiber Illuminator

- Collimator (soon to be ordered)

- Lenses for telescope (TBD)

 

  10170   Wed Jul 9 23:02:33 2014 HarryUpdateGeneralBeam Waists via Beamscan

 Today, I borrowed the beam profiler from Brian (another SURF) in order to double check my razor blade measurement figures, using the below setup:

beamscanSetup.png

Measurements are included in the a la mode code that is attached entitled beamfit.m. The beam fitting application yielded me waists (after the lens) of 35.44 um in the x plane, and 33.26 um in the y plane. These are both within 3 um of the measurements I found using the razor blade method. (I moved and resized the labels for the waists in the figure below for readability purposes.)

beamScanWaists.png

I then plugged these waists back into ALM, in addition to the lens specifications, to determine waist size and location of the NPRO, which turned out to be 543 um in the x located at Z = 1.160m, and 536 um in the y, located at 1.268m. These measurements are based upon zero at the waist after the lens, and the positive direction being back toward the NPRO.

beamProfileX.pngbeamProfileY.png

The only systemic difference between these measurement and my original razor blade measurements was that I had taken the focal length of the lens as 75mm, which is advertised on the manufacturer's site. However, the more detailed specs revealed that the focal length was 85.8mm at 1064nm, which made a difference of about 400 um for the final waist determination.

Attachment 4: beamScanWaist.zip
  10175   Thu Jul 10 15:27:09 2014 HarryUpdateGeneralCoupling telescope design

 I designed this telescope to couple the 1064 NPRO into the PM980 fiber, using lenses from the Thorlabs LSB04-C kit.

The collimator is a CFC-2X-C, which has a variable focus length (2.0, 4.6, 7.5, and 11.0 mm) which gives corresponding angles of divergence of 0.298, 0.130, 0.79, and 0.054 degrees by the formula theta = (180*MFD) / (pi*f).

Then, using these values I calculated the spot size of a beam collimated by the CFC-2X-C, using f = w / tan(theta) where w is the spot size. This gave a value of 10.4 um.

I used this value (10.4 um) as a target waist for the telescope system, with the NPRO waist as a seed, at the origin.

telescopeBeamProfile.png

It consists of two lenses, one located at Z = 77cm f = 50cm, and the second located at Z = 85.88 cm f = 2.54cm, which yields a waist of 13um at Z = 88.32cm, (which is where the collimator would go) for an overlap of .974.

Note that the telescope is so far "downrange" from the NPRO waist because it's a virtual waist, and the NPRO itself is located at about Z = 73cm.

Find attached the alm code used.

Attachment 2: telescope.zip
  10185   Fri Jul 11 15:29:26 2014 HarryUpdateGeneralTelescope With Collimator

 I used a la mode to make a design for the coupling telescope with a 3.3um target waist, that included the collimator in the overall design. The plot is below, and code is attached.

The components are as follows:

 label         z (m)     type    parameters         

   -----         -----     ----    ----------         

    lens1         0.7681    lens    focalLength: 0.5000

    lens2         0.8588    lens    focalLength: 0.0350

    collimator    0.8832    lens    focalLength: 0.0020

 

The z coordinates are as measured from the beam waist of the NPRO (the figure on the far left  of the plot).

Moving forward, this setup will be used to couple the NPRO (more specifically, the AUX lasers) light into the SM 980 fibers, as well as to help characterize the fibers themselves.

Ultimately, this will be a key component in the Frequency Offset Locking project that Akhil and I are working on, as it will transport the AUX light to the PSL, where the two beams will be beaten with each other to generate the input signal to the PID control loop, which will actuate the temperature servos of the AUX lasers.

Attachment 1: telescope_2.zip
Attachment 2: telescopeWCollimator.png
telescopeWCollimator.png
  10204   Tue Jul 15 18:26:40 2014 HarryUpdateGeneralBeam Waist, Telescope, and Fiber Coupling

 Goal

To design an optical setup (telescope / lens) to couple 1064nm NPRO light into PANDA PM980 fibers in order to characterize the fibers for further use in the frequency offset locking setup.

Design

 fiberTestingSetup.png

Calculations

 The beam waist of the NPRO was determined as 233um 6cm in front of the NPRO. This was used as the seed waist in ALM.

The numerical aperture of the fiber was given as 0.12, which allowed me to calculate the maximum angle of light it would accept, with respect to the optical axis, as NA = sin(theta) where theta is that angle.

Given that the coupler has a focal length of 2mm, I used the formula r = f * tan(theta), to yield a "target waist" for efficient coupling into the fiber. This ended up being 241.7um.

Since there was not a huge difference between the natural beam width of the NPRO and our target waist, I had no need for multiple lenses.

I used 230um as a target waist for a la mode, to leave myself some room for error while coupling. This process gave me a beam profile with a lens (f=0.25m), and a target waist of 231um, located 38.60cm from the coupling lens

I have attached ALM code, as well as the beam profile image. Note that the profile takes zero to be the location of the NPRO waist.

fiberTestingCouplingDesign.png

Next Steps

 

After this setup is assembled, and light is coupled into the fibers, we will use it to run various tests to the fiber, for further use in FOL. First of all, we wish to measure the coupling efficiency, which is the purpose of the powermeter in the above schematic. We will measure optical power before and after the fibers, hoping for at least ~%60 coupling. Next is the polarization extinction ratio measurement, for which we will control the input polarization to the fibers, and then measure what proportion of that polarization remains at the output of the fiber. 

Attachment 3: fiberTesting.zip
  10205   Tue Jul 15 18:39:04 2014 HarryUpdateGeneralWeekly Plan (7.16.14)

 The Past Week

 

Attempted to design coupling telescope, turned out waist measurement was still off. Took another waist measurement, this time more reasonable.

Used recent waist measurement to actually design a coupling system to couple NPRO light into Panda PM980 fibers (see recent elog)

The Next Week

Assemble fiber coupling system

Measure coupling efficiency, ensure it's at least 60%

Begin measuring Polarization Extinction ratio

Materials

 

PLCX lens with f = 0.25m ------> status: here

Fiber Coupled Powermeter//PD ------> status: unknown (have any laying around?)

Quarter Wave Plate, Polarizing Beamsplitter, Photodiodes ------> status: here

other components from original razorblade measurement  setup

  10218   Wed Jul 16 17:34:11 2014 HarryUpdateGeneralFiber Coupled

 Purpose

To couple the spare NPRO into our Panda PM980 fibers, in order to carry out tests to characterize the fibers, in order to use them in FOL.

Design

 Manasa and I spent this morning building the setup to couple NPRO light into the fibers. We used two steering mirrors to precisely guide the beam into the coupler (collimator).

We also attached the lens to a moveable stage (in the z axis), so the setup could be fine tuned to put the beam waist precisely at the photodiode.

The fiber was attached to a fiber-coupled powermeter, so I would be able to tell the coupling efficiency.

fiberTestCouplingSchematic.png

Methods 

During alignment, the NPRO was operating at 1.0 amps, roughly half of nominal current (2.1A).

I first placed the coupler at the distance that I believed the target waist of 231um to be.

Using the steering mirrors and the stage that holds the couple, I aligned the axes of the coupler and the beam.

Finally, I used the variable stage that the lens is attached to to fine tune the location of the target waist.

Results

Once I was getting readings on the powermeter (~0.5nW), the laser was turned up to nominal current of 2.1A.

At this point, I and getting 120nW through the fiber.

While far from "good" coupling, it is enough to start measuring some fiber characteristics.

Moving Forward

Tomorrow, I hope to borrow the beam profiler once again so as to measure the fiber mode.

Beyond this, I will be taking further measurements of the Polarization Extinction Ratio, the Frequency Noise within the fiber, and the effects of a temperature gradient upon the fiber.

Once these measurements are completed, the fiber will have been characterized, and will be ready for implementation in FOL.

  10230   Thu Jul 17 17:08:58 2014 HarryUpdateGeneral1X2 Rack Changes

 Purpose

 

Steve and I moved some things around in the 1X2 rack in order to make room (roughly 6") for the electronics box that will contain rf frequency counters, ADC, and Raspberry Pi's for use in the Frequency Offset Locking apparatus

Picture

1X2Changes.png

Occurrences

First, we killed power by removing the fuse that the boxes we were moving were running through.

Then, we moved the boxes. I dropped//lost a washer. It didn't seem to cause any problems, so no further attempts to locate it were made.

The fuse was reinstalled, and everything was reconnected.

Moving Forward

We are now working on putting together the electronics box, which will contain ADC, and raspberry pi's. The frequency counters will be mounted on the front of the box.

Once complete, it will be installed for use in FOL.

  10240   Sat Jul 19 01:59:34 2014 HarryUpdateGeneralFiber Mode Measurement

Purpose 

We wanted to measure the mode coming out of the fibers, so we can later couple it to experimental setups for measuring different noise sources within the fiber. i.e. Polarization Extinction Ratio, Frequency Noise, Temperature Effects.

Methods

I used the beamscan mounted on a micrometer stage in order to measure the spot sizes of the fiber coupled light at different points along the optical axis, in much the same way as in the razorblade setup I used earlier in the summer.

fiberModeMeasurement.png

Analysis

I entered my data (z coordinates, spot size in x, spot size in y) into a la mode to obtain the beam  profile (waist size, location)

 fiberModeMeasurement1.png 

Code is attached in .zip file.

Moving Forward

After I took these measurements, Manasa pointed out that I need points over a longer distance. (These were taken over the range of the micrometer stage, which is 0.5 inches.)

I will be coming in to the 40m early on Monday to make these measurements, since precious beamscan time is so elusive.

Eventually, we will use this measurement to design optical setups to characterize Polarization Extinction Ratio, Frequency Noise, and temperature effects of the fibers, for further use in FOL.

Attachment 3: fiberModeMeasurement1.zip
  10244   Mon Jul 21 10:30:38 2014 HarryUpdateGeneralFiber Mode Measurement

 Purpose

The idea was to measure the profile of the light coming out of the fiber, so we could have knowledge of it for further design of measurement apparatuses, for characterization of the fibers' properties.

Methods

The method was the same as the last time I tried to measure the fiber mode.

This time I moved the beam profiler in a wider range along the z-axis.

Additionally, I adjusted the coupling until it gave ~1mW through the fiber, so the signal was high enough to be reliably detectable.

Measurements were taken in both X and Y transections of the beam.

The range of movement was limited by the aperture of the beam profiler, which cuts off at 9mm. My measurements stop at 8.3mm, as the next possible measurement was beyond the beam profiler's range.

fiberModeMeasurement.png

Analysis

I entered my data into A La Mode, which gave me a waist of 5um, at a location of z = -0.0071 m, that is to say, 7.1mm inside the fiber.

Note that in the plot, data points and fits overlap, and so are sometimes hard to distinguish from each other.

Code is attached.

fiberModeFit2.png

Moving Forward

Using this data, I will begin designing setups to measure fiber characteristics, the first of which being Polarization Extinction Ratio.

Eventually, the data collected from these measurements will be put to use in the frequency offset locking setup.

Attachment 3: fiberModeMeasurement2.zip
  10249   Mon Jul 21 18:08:19 2014 HarryUpdateGeneralFiber Mode Measurement

Quote:

 Purpose

The idea was to measure the profile of the light coming out of the fiber, so we could have knowledge of it for further design of measurement apparatuses, for characterization of the fibers' properties.

Methods

The method was the same as the last time I tried to measure the fiber mode.

This time I moved the beam profiler in a wider range along the z-axis.

Additionally, I adjusted the coupling until it gave ~1mW through the fiber, so the signal was high enough to be reliably detectable.

Measurements were taken in both X and Y transections of the beam.

The range of movement was limited by the aperture of the beam profiler, which cuts off at 9mm. My measurements stop at 8.3mm, as the next possible measurement was beyond the beam profiler's range.

fiberModeMeasurement.png

Analysis

I entered my data into A La Mode, which gave me a waist of 5um, at a location of z = -0.0071 m, that is to say, 7.1mm inside the fiber.

Note that in the plot, data points and fits overlap, and so are sometimes hard to distinguish from each other.

Code is attached.

fiberModeFit2.png

Moving Forward

Using this data, I will begin designing setups to measure fiber characteristics, the first of which being Polarization Extinction Ratio.

Eventually, the data collected from these measurements will be put to use in the frequency offset locking setup.

 Edit

 

 

The previous data were flawed, in that they were taken in groups of three, as I had to move the micrometer stage which held the beamscan between holes in the optical table.

In order to correct for this, I clamped a straightedge (ruler) to the table, so I could more consistently align the profiler with the beam axis.

These data gave a waist w_o = 4um, located 6mm inside the fiber. While these figures are very close to what I would expect (3.3um at the end of the fiber) the fitting still isn't as good as I would like.

The fit given by ALM is below.

fiberModeMeasurement3.png

Moving Forward

I would like to get a stage//rail so I can align the axes of the beam and profiler more consistently.

I would also like to use an aperture the more precisely align the profiler aperture with the beam axis.

Once these measurements have been made, I can begin assembling the setup to measure the Polarization Extinction Ratio of the fiber.

  10255   Tue Jul 22 16:26:04 2014 HarryUpdateGeneralFiber Mode Measurement

I repeated this process once more, this time using the computer controlled stage that the beam profiler is designed to be mounted to.

These data//fitting appears to be within error bars. The range of my measurements was limited when the beam width was near the effective aperture of the profiler.

This latest trial yielded a waist of 4um, located 2.9 mm inside the fiber for the X profile, and 3.0mm inside the fiber for the Y profile.

fiberModeProfile3.png

Code is attached in fiberModeMeasurement4.zip. Note that the z=0 point is defined as the end of the fiber.

Attachment 2: fiberModeMeasurement4.zip
  10256   Tue Jul 22 17:45:11 2014 HarryUpdateGeneralWeekly Update

 The Past Week

 

I spent the past week coupling NPRO light into the fibers, and subsequently measuring the fiber mode profile using the beam profiler.

The Next Week

In the next week, I plan to at least do measurements of the Polarization Extinction Ratio of the fibers.

Materials

My current optical setup, plus an additional polarizing beam splitter (have it).

  10264   Wed Jul 23 17:54:51 2014 HarryUpdateGeneralCoupling Improvements plus PER Measurement Setup

 Purpose

We wanted to improve the coupling into the fibers, because it's very rarely good enough to take measurements with, as the beam is obscured by random noise.

Additionally, we want to add some things to the current setup in order to better measure Polarization Extinction Ratio.

What Was Done

After flailing for several hours, Koji helped me couple the NPRO light into the fiber, using the fiber illuminator for alignment. The coupled optical power immediately jumped from 0-1uW to 5.6mW (around 11% coupling).

Q and I discussed the setup for measuring PER. In addition to the current setup, we added a half wave plate to control the angle of the polarization, in addition to the existing quarter wave plate, which corrects the beam for ellipticity.

PERSetup.png

Once everything was coupled, I started minimizing S-Polarization coming out of the first polarizing beam splitter, and maximizing the P-Polarization entering the fibers.

I did this by first varying the Quarter Wave plate to eliminate as much S Polarization as possible, and then, maintaining a constant differential in angle between QWP and HWP, I rotated them both to maximize power coupled into the fibers.

I measured 0.2 mW of S-Polarization, and 54.3 mW of P-Polarization.

At this point, a locking effort started, and I had to leave the 40m.

Moving Forward

 

Tomorrow, I would like to finish the setup of the PER measurement design. That is to say, add a collimator to the other end of the fiber, and align it with the second PBS.

And, of course, take a measurement of the Polarization Extinction Ratio of the fiber.

To eventually be implemented in Frequency Offset Locking.

  10271   Thu Jul 24 17:37:19 2014 HarryUpdateGeneralCoupling Improvements plus PER Measurement Setup

Quote:

 Purpose

We wanted to improve the coupling into the fibers, because it's very rarely good enough to take measurements with, as the beam is obscured by random noise.

Additionally, we want to add some things to the current setup in order to better measure Polarization Extinction Ratio.

What Was Done

After flailing for several hours, Koji helped me couple the NPRO light into the fiber, using the fiber illuminator for alignment. The coupled optical power immediately jumped from 0-1uW to 5.6mW (around 11% coupling).

Q and I discussed the setup for measuring PER. In addition to the current setup, we added a half wave plate to control the angle of the polarization, in addition to the existing quarter wave plate, which corrects the beam for ellipticity.

PERSetup.png

Once everything was coupled, I started minimizing S-Polarization coming out of the first polarizing beam splitter, and maximizing the P-Polarization entering the fibers.

I did this by first varying the Quarter Wave plate to eliminate as much S Polarization as possible, and then, maintaining a constant differential in angle between QWP and HWP, I rotated them both to maximize power coupled into the fibers.

I measured 0.2 mW of S-Polarization, and 54.3 mW of P-Polarization.

At this point, a locking effort started, and I had to leave the 40m.

Moving Forward

 

Tomorrow, I would like to finish the setup of the PER measurement design. That is to say, add a collimator to the other end of the fiber, and align it with the second PBS.

And, of course, take a measurement of the Polarization Extinction Ratio of the fiber.

To eventually be implemented in Frequency Offset Locking. 

 

Today, I encountered a problem with the stage that holds the coupler, in that its ability to rotate unchecked causes coupling to degrade over time due to torsion in the fibers. Our solution was to stress-relieve the fiber with a clamp.

Unfortunately, this also meant losing coupling completely. It was re-coupled at up 72% efficiency. (Subsequent changes in the setup have decreased that to ~24%)

When I took preliminary measurements of the PER, it was significant, which was unexpected. Upon further discussion with Q, we concluded that since the fiber's fast axis hadn't been aligned with the light's polarization, I was getting multiple polarizations out the end of the fiber.

Subsequent measurements of the power contained in the two polarizations of the output light gave about 0.8% S-Polarization introduced by the fiber.

Tomorrow

I would like to find another collimator holder, to hold the output side of the fiber.

Also, I will spend more time aligning the fiber axes, and the second PBS in order to get a better (read: more reasonable) measurement of PER.

  10273   Fri Jul 25 17:28:31 2014 HarryUpdateGeneralFOL Box and PER Update

 Purpose

We're putting together a box to go into the 1X2 rack, to facilitate the frequency counters, and Raspberry Pi that will be used in FOL.

Separately, I am working on characterizing the Polarization Extinction Ratio of the PM980 fibers, for further use in FOL.

What's Been Done

The frequency counters have been mounted on the face of the box, and nylon spacers installed in the bottom, which will insulate the RPi in the future, once it's finally installed.

FOLBox.png

In regard to the PER setup, there is an issue, in that the mounts which hold the collimators rotate, so as to align the axes of the fibers with the polarization of the incoming light.

This rotational degree of freedom, however, isn't "sticky" enough, and rotates under the influence of the stress in the fiber. (It's not much, but enough.)

This causes wild fluctuations in coupled power, making it impossible to make accurate measurements of PER.

What's Next

In the FOL box's case, we've ordered a longer power cable for the raspberry pi (the current one is ~9 inches long).

Once it arrives, we will install the RPi, and move the box into its place in the rack.

In the case of the PER measurement, we've ordered more collimator mounts//adapters, which will hopefully give better control over rotation.

 

  10282   Mon Jul 28 17:25:32 2014 HarryUpdateGeneralFiber Mode With Collimators

 Purpose

We want a measurement of the fiber modes at either end, with the collimators, because these will be the modes that we'll be trying to match in order to couple light into the fibers, for FOL and/or future projects.

Measurement

In order to measure these modes, I used the beam profiler (Thorlabs BP 209-VIS) to take measurements of the beam diameter (cut off at 13.5% of the amplitude) along the optical axis, for each of the fiber ends.

The ends are arbitrarily labelled End 1 and End 2.

For each measurement, the fibers were coupled to roughly 30%, or 25mW at the output.

Regarding the issue of free rotation in the collimator stages: while End 1 was relatively stable, End 2 tended to move away from its optimal coupling position. In order to correct for this, I chose a position where coupling was good, and repositioned the stage to that coordinate (124 degrees) before taking each measurement.

The data were then entered into A La Mode, which gave waist measurements as follows:

End 1--- X Waist: 197um at Z = 4.8mm       Y Waist: 190um at Z = 13.6mm

End 2--- X Waist: 192um at Z = 7.4mm       Y Waist: 190um at Z = 6.0mm

end1Profiles.pngend2Profiles.png

A La Mode code is attached in .zip file

Moving Forward

These are the types of profiles that we will hopefully be matching the PSL and AUX lasers to, for use in frequency offset locking.

More characterization of the fibers is to follow, including Polarization Extinction Ratio.

We also hope to be testing the overall setup soon.

 

 

Attachment 3: FiberModeWCollimators.zip
  10287   Tue Jul 29 18:52:42 2014 HarryUpdateGeneralPSL and AUX Coupling Waist Measurement

//edit Manasa//  Harry will update this elog with before/after pictures of the table and power of the 1064nm rejected beam from the SHG.
While making these measurements, I reduced the Y end laser power (decreasing the current) so that we could use the beam profiler without burning anything and then brought it back up to the nominal power after the measurements were done.

Purpose

We wanted to take measurements of "waists" of the PSL and AUX (Y-Arm) so I can then design a telescope to couple both into fibers for use in FOL.

Measurements

For both lasers, PSL and AUX, I measured the profile of the dumped red (1064nm) beams coming out of the second harmonic generators, as this is the light that we will be using in FOL.

The power in the beam I measured from the PSL was 87.5 mW, and the power in the measured beam at the end table was 96 mW (when reduced from nominal power).

I used the beam profiler to take measurements of spot size at multiple points along the optical axis of both lasers.

An issue with these measurements was space constraints. In other words, there was no room on either table for a translation stage to hold the Profiler. I used a tape measure to determine Z-Coordinates. However, especially in the case of the AUX laser, parallax error caused uncertainty in my position measurements, which I would estimate at plus and minus 1.5cm.

I then fit these data using ALM to determine waist size and location for use in telescope design.

Z = 0 in the PSL graph is the face of the first mirror in the beam path, and in the AUX graph Z = 0 is the face of the SHG.

NPROProfileMeasurement.png

PSLProfile.pngAUXProfile.png

My measurement of the PSL gave:

X Waist = 43um at z = 6.8mm, as measured from the face of the SHG.

Y Waist = 44um at z = 6.8mm, as measured from the face of the SHG.

AUX Measurements gave:

X Waist = 44um at z = -3.1mm from the SHG face

Y Waist = 36um at z = -3.6mm from the SHG face

 

Find attached alm files in .zip

Movement on the Tables

In order to facilitate the measurements, we needed to move some things around, as pictured below.

On the PSL table, we installed a steering mirror after the Green filtering mirror, which is immediately after the SHG output, in addition to appropriate beam dumps.

before PSLBefore.png      after   PSLAfter.JPG

At the end table, we removed some unused optics, as well as a PD, which were in the way . //edit// manasa: We removed IPANG (which has no light on it) and the associated steering optics.

before    AUXBefore.JPG  after   AUXAfter.JPG

Moving Forward

Either tonight or tomorrow morning, I will use these data to design coupling telescopes for the PSL and AUX light.

Tomorrow, I will couple both lasers to fibers, and hopefully finish assembling the optics for FOL

Attachment 4: FOL.zip
Attachment 8: AUXBefore.JPG
AUXBefore.JPG
  10289   Tue Jul 29 19:00:40 2014 HarryUpdateGeneralWeekly Plan (7.29.14)

 The Past Week

In the past week, I have improved the coupling in the fiber testing setup on the SP table to up to ~45%

I also measured the input/output modes of the fiber with collimators.

Manasa, Q and I have designed, and redesigned a setup to measure Polarization Extinction Ratio introduced by fibers.

I have also partially assembled the box that will hold the frequency counters and RPi for FOL.

Today (Tuesday) I measured waists of PSL and AUX, at dumped light from the SHG's for use in designing coupling telescopes for FOL.

Next Week

In the next week, I will design and couple light from PSL and AUX (Y arm) into fibers for use in testing FOL.

Once that's done, I will continue testing fiber characteristics, starting with Polarization Extinction Ratio.

Items Needed

Power cord for Raspberry Pi (ordered)

AD9.5F collimator adapter (ordered)

 

  10299   Wed Jul 30 18:09:08 2014 HarryUpdateGeneralAUX and PSL Coupling Telescopes

 Purpose

These telescopes will be used to mode match//couple the dumped SHG light from both PSL and AUX (Y-Arm) lasers into PM fibers for use in FOL.

Methods

Using the waist measurements I made yesterday (29/7/14) as seed waists, I used a la mode to design coupling telescopes.

These are designed to match the output mode of the fibers with collimators.

AUXTelescope.m    PSLTelescope.png

 

 

ALM files are attached in .zip file.

AUXTelescopePlot.png PSLTelescopePlot.png

Moving Forward

Once the fibers are coupled, I will continue in assembling the Y-Arm FOL setup, using fiber coupled beam combiner and photodiodes.

I will also do the same procedure for the X-Arm, access permitting.

Attachment 2: AUXTelescope.png
AUXTelescope.png
Attachment 3: telescopes.zip
  10308   Thu Jul 31 15:25:51 2014 HarryUpdateGeneralPolarizationExtinction Ratio of Fibers

 Purpose

We wanted to measure the PER of the polarization maintaining fibers, so we could say to what extent they are truly polarization maintaining.

Setup

The experimental setup of this measurement includes: The NPRO, quarter and half wave plates for tuning ellipticity and orientation of the resultant polarization, attenuating optics, two steering mirrors for coupling, a polarizing beam splitter before and after the laser coupled fibers, the coupling assembly and fiber, and a powermeter.

PERSetup.png

I measured the beam power at all the pertinent locations, shown in the figure below. Note that dots represent S polarization, and orthogonal line segments represent P polarization.

PERBeamPower.png

 

Methods

I first assembled this, coupling the output to a fiber coupled powermeter, in order to adjust the coupling.

Then I needed to couple the fibers to the NPRO, which I did to 39.8%. This gave me enough output power to have a coherent, visible beam. (Visible to non-fiber coupled power meter, and on the viewer card). It was important to be sure that the fast axis of the fiber was aligned in some known orientation. Mine was aligned to the horizontal, using the key on the fiber as an indicator. This is to be certain that the output polarization is consistent with the input.

Once everything was coupled and collimated, I began tuning the polarization of the beam at different points.

Immediately after the NPRO, I used the quarter and half wave plates to first eliminate as much ellipticity as possible, and then turn the polarization to align it with the beam splitter and the fiber axis. I then tuned the first PBS to reflect as little as possible. At the output, I installed the second PBS. Since there was no fine adjustment for the angle of this one, I tuned it using the yaw controls of the 6-axis mount the collimator was held in.

Once all this tuning was done, I took power measurements (displayed above) using the unfiltered, Orion/PD power meter.

Results

From a theoretically completely P-polarized input, the Polarization Extinction Ratio, calculated at 10*log(P/S), was  -24.26 +/-  0.43 dB.

These results can be effected by environmental conditions, such as high tightly wound the cable it, its length, etc.

 

Moving Forward

The next measurement to make would be to characterize the frequency noise introduced by the fiber.

In addition to this measurement, the setup of the beat note system for FOL can be done as soon as we have more collimator adapters.

These measurements may be important in FOL, and in future experiments that may use these types of apparatuses.

  10336   Wed Aug 6 10:10:45 2014 HarryUpdateGeneralWeekly Plan 8.6.14

Last Week

 

Took first round of PER measurements after a long setup.

Started setting up to take measurement of the other polarization--ran into issues with mounts again. (Spinning of their own free will again.)

Devised a new scheme for taking more robust measurements of PER--still in progress.

Next Week

Finish data analysis of these latest PER measurements

Hopefully finally move on to frequency noise characterization

Materials Needed

None for PER

Unknown for frequency noise

 

  10347   Thu Aug 7 14:50:43 2014 HarryUpdateGeneralPER Measurement

 Purpose

I wanted to do a more robust measurement of PER of PM fibers for FOL, so I thought up this scheme.

Methods

I put together a setup as depicted below in order to take measurements of PER.

PERFinalSetup.png

The first thing to do was to calibrate the whole setup. In order to do so, I first used the quarter and half wave plates closest to the NPRO to eliminate as much ellipticity from the output beam as possible, and then rotate the newly linearized light to be in alignment with the transmittance of the first polarizing beam splitter (P-Polarization).

I then aligned the fiber's fast axis with the P-Polarization on both the input and output sides. This was important so that no virtual ellipticity would be measured in the final measurement of PER.

I then mode matched and fiber coupled the first PBS output into the fibers, to about 30 mW (~60% coupling).

Photodiode Calibration

I wanted to measure both intensity of P and S simultaneously, so as to minimize the random little time-varying changes that would affect the measurements, so I used a powermeter and a PD, calibrated with the aformentioned powermeter.

In order to be able to compare the photodiode (PDA520) output to the powermeter (Orion) output, I fixed them each in their positions, and varied the laser power to produce the type of linear relationship we expect to see between PD Voltage and Optical Power. In this case, the conversion was P = V*2.719.

PDCalibration.png

PER Measurement

As opposed to the first method, which took only one datum, this method records P and S simultaneously, at different points through rotation of a linearly polarized beam.

Using the second HWP, I rotated the linearly polarized beam before it entered the fiber, at each point, recording the outputs of the PD and the Powermeter.

These data were then converted to be the same units, and fit to a sine wave.

Polarization_Intensity_Variation.png

As you can see, the intensities vary nearly identically, at a half wavelength phase difference, which is what one expects in this case. The PER of each polarization can be calculated by dividing the maximum value of one by the minimum of the other, and vice versa. The fact that these oscillate as we expect shows that the beam is relatively well linearized, and essentially that everything is working as it is assumed to be.

By looking at these fits, however, it is visible that they do not overlap with the actual extrema of the data. So, in order to produce more realistic values of extrema, those particular regions were fit to second order polynomials.

Extrema.png

The values of these extrema yield the following measurements:

(SMin / PMax) = 0.007 +/- .004  --->  -21.54 +/- 2.48 dB

(PMin / SMax) = 0.022 +/- .009  --->  -16.58 +/- 1.78 dB

Conclusion

The problem I find with these measurements is that they're hard to reproduce.

Plus they seem high, since non-PM fibers advertise extinction ratios around -30 dB., plus I measured it at roughly -24 dB the first time I tried.

Moving Forward

 

The next thing to do in terms of fiber characterization is to measure the frequency noise they introduce.

With respect to FOL, I just need some time to work on the PSL table, and at the Y end to couple the dumped SHG light, and then we can start using 1064nm beat notes to test//implement the feedback control system.

Attachment 5: PEReport.zip
  10349   Thu Aug 7 17:09:53 2014 HarryUpdateGeneralAUX Coupling In Progress

 I'm currently in the process of coupling dumped SHG light from the Y arm end table into fibers for FOL.

The main point is that the NPRO at that end in shuttered, because I wasn't sure whether or not leaving it open would've set anything on fire.

  10360   Sun Aug 10 00:54:54 2014 HarryUpdateGeneralAUX Couping

The Y End laser dumped SHG light has been coupled into the yellow fiber that terminates at the PSL table.

It's not super stably coupled, and only at 5mW. I'll be interested to see what it is on monday.

  10371   Tue Aug 12 23:07:24 2014 HarryUpdateGeneralPSL Telescope

I put the PSL telescope in place, and started coupling to it.

Unfortunately, I was only able to couple about 55 uW into the "fiber coupler" (read: fiber coupled splitter). See picture below:

PSLTelescopePic.png

Additionally, I'm not sure why this is, but both of the splitters we ordered don't split equally, but to 90% and 10% in each output port.

We also found that, since we aren't using the fibers we originally intended to, the specs are a little different, and the waist we're trying to have at the collimator face is now 283 um.

  10373   Wed Aug 13 10:49:39 2014 HarryUpdateGeneralWeekly Update

 In the past week, I designed and assembled coupling telescopes for the PSL and Y Arm Lasers

The Y Arm was coupled to ~5mV, and the PSL remains uncoupled.

 

For the next week, I'm planning on working on things like my presentation and/or final report.

Though as of last night, my computer refuses to turn on, so there may be some further "troubleshooting" involved in that whole process.

  10376   Wed Aug 13 16:12:55 2014 HarryUpdateGeneralFOL Layout Diagram

Per Q's request, I've made up a diagram of the complete FOL layout for general reference.

FOLLayout2.png

  10389   Thu Aug 14 18:10:46 2014 HarryUpdateGeneralFiber Temperature Effects Setup

Purpose

We want to characterize the sort of response the fibers have to temperature gradients along them (potentially altering indices of refraction, etc.)

Experimental Setup

I have constructed a sort of two chambered "calorimeter" (by which I mean some coolers and other assorted pieces of recycling.)

The idea is that half of the length of PM fiber resides in one chamber, and the other in the other.

One chamber will remain at an uncontrolled, stable temperature (as measured by thermocouple probe) while the other's temperature is varied using a heat gun.

Using this setup, one can measure losses in power, and effects on polarization within the fiber.

Caveat

This is currently living on the electronics bench until tomorrow morning, and is a little fragile, just in case it needs to be moved.

Attachment 1: tempAffectsSetup.zip
  10403   Fri Aug 15 17:24:44 2014 HarryUpdateGeneralFiber Temp.

 Earlier today Q and I somewhat resurrected my old PER measurement setup so I could run the temperature characterization experiment.

Unfortunately, when I tried to use the fiber illuminator, no light came from the other end, causing me to fail my primary goal for the summer of "don't break anything." The fiber has been re-spooled and labeled appropriately. Also sorry.

In addition to this, Q and I scavenged parts from the telescopes on the PSL and Y End tables, which were either not functional, or needed to have their mode matching adjusted, since we're using the non-PM fibers for FOL, which have a different numerical aperture, and thus slightly different output modes.

Specifically, this is involved removing the rotational mounts, and appropriate beam dumping.

My "calorimeter" still remains intact, in case anyone wants to make this measurement in the future, as this is my last day in the lab.

It's also effective at keeping drinks cold, if you'd rather use it for that.

  10092   Tue Jun 24 13:04:49 2014 Harry, ManasaUpdateGeneralRazorblade Beam Analysis Setup

Harry will update this elog with details about his beam waist measurements for the old NPRO on the SP table.

  10099   Wed Jun 25 09:17:33 2014 Harry, ManasaUpdateGeneralRazorblade Beam Analysis Setup

Quote:

Harry will update this elog with details about his beam waist measurements for the old NPRO on the SP table.

 see http://nodus.ligo.caltech.edu:8080/40m/10098 for the update

  2708   Wed Mar 24 12:38:17 2010 HartmutConfigurationGreen LockingBroadband PD for green PLL

Modified one of the PD assemblies carrying a large SI-Diode (~10mm diameter).

Removed elements used for resonant operation and changed PD readout to transimpedance

configuration. The opamp is a CLC409 with 240 Ohm feedback (i.e. transimpedance) resistor.

To prevent noise peaking at very high frequencies and get some decoupling of the PD,

I added a small series resistor in line with the PD and the inverting opamp input.

It was chosen as 13 Ohm, and still allows for operation up to ~100MHz.

Perhaps it could be smaller, but much more bandwith seems not possible with this opamp anyway.

Changes are marked in the schematic, and I list affected components here.

(Numbers refer to version 'PD327.SCH' from 30-April-1997):

-removed L4

-connected L3 (now open pad) via 100 Ohm to RF opamp output. This restores the DC sognal output.

-removed c17

-connected pin 3 of opamp via 25 Ohm to GND

-connected kathode of PD via 13 Ohm to pin 2 of opamp

-removed L6, C26, L5, C18, and C27

-shorted C27 pad to get signal to the RF output

 

Measured the optical TF with the test laser setup.

(Note that this is at 1064nm, although the PD is meant to work with green light at 532nm!)

Essentially it looks usable out to 100MHz, where the gain dropped only by about

6dB compared to 10MHz.

Beyond 100MHz the TF falls pretty steeply then, probably dominated by the opamp.

 

The maximal bias used is -150V.

If the bias is 'reduced' from -150V to -50V, the response goes down by 4dB at 10MHz and

by 9dB at 100MHz.

 The average output was 30mV at the RF output, corresponding to 60mV at the opamp output (50Ohm divider chain).

With 240 Ohm transimpedance this yields 250µA photo-current used for these transfer functions.

SiAmpl.png

 

SiPhase.png

 

 

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