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.
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. 126.96.36.199, 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).
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).
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.
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.
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.
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.
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!
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.
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.
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.
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
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).
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.
See attached weekly update
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.
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.
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).
3) Repeat in Y plane at the same value of Z
4) Repeat process at multiple points along Z
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.
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).
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.
I was finally able to get a reasonable measurement for the beam waist(s) of the spare NPRO.
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:
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.
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.
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.
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.
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.
-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.
-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
- Razorblade setup or beamscan (preferably beamscan)
- Fiber Illuminator
- Collimator (soon to be ordered)
- Lenses for telescope (TBD)
Today, I borrowed the beam profiler from Brian (another SURF) in order to double check my razor blade measurement figures, using the below setup:
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.)
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.
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.
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.
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.
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.
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.
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.
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.
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
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
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.
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.
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.
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.
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.
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
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.
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.
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.
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.
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)
Code is attached in .zip file.
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.
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.
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.
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.
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.
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.
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.
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.
Code is attached in fiberModeMeasurement4.zip. Note that the z=0 point is defined as the end of the fiber.
I spent the past week coupling NPRO light into the fibers, and subsequently measuring the fiber mode profile using the beam profiler.
In the next week, I plan to at least do measurements of the Polarization Extinction Ratio of the fibers.
My current optical setup, plus an additional polarizing beam splitter (have it).
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.
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.
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.
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.
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.
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.
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.
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.
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.
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
A La Mode code is attached in .zip file
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.
//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.
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.
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.
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.
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.
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
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.
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.
Power cord for Raspberry Pi (ordered)
AD9.5F collimator adapter (ordered)
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.
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.
ALM files are attached in .zip file.
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.
We wanted to measure the PER of the polarization maintaining fibers, so we could say to what extent they are truly polarization maintaining.
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.
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.
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.
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.
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.
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.
Finish data analysis of these latest PER measurements
Hopefully finally move on to frequency noise characterization
None for PER
Unknown for frequency noise
I wanted to do a more robust measurement of PER of PM fibers for FOL, so I thought up this scheme.
I put together a setup as depicted below in order to take measurements of PER.
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).
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.
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.
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.
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
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.
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.
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.
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.
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:
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.
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.
Per Q's request, I've made up a diagram of the complete FOL layout for general reference.
We want to characterize the sort of response the fibers have to temperature gradients along them (potentially altering indices of refraction, etc.)
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.
This is currently living on the electronics bench until tomorrow morning, and is a little fragile, just in case it needs to be moved.
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.
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
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):
-connected L3 (now open pad) via 100 Ohm to RF opamp output. This restores the DC sognal output.
-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.
Recorded transfer functions for the 1cm Si-PD as described on p. 2708
for different biases. I put the plots in there, to keep the info in one place,
where the label on the PD case (which Steve made without asking him) points
I talked to some people recently about the fact that the responsivity (A/W) of the PD
changes even at DC for different biases. I tested this again and should be more precise about this:
The first time I observed this was in the transfer functions as shown on p. 2708.
With 'DC' I meant 'low frequency' there, as you can still see an effect of the bias as low as 100kHz.
Then at one point I saw the responsivity changing with bias also at true DC.
However, it turned out that this is only the case if the photocurrent is too high.
If the photocurrent is 4mA, you need 400mV bias to get the max. responsivity.
For 2mA photocurrent, the responsivity is already maximal for 0V bias.
An effect for relative low frequencies remains however.
The DC check of responsivity was done with white light from a bulb.
just a few infos on Silicon PDs I looked up.
If you want to go beyond the 100MHz achievable with the device I worked on,
the one thing to improve is the opamp, where Steve is trying to find OPA657.
This is a FET with 1.6GHz BWP, minimum stable gain of 7, and 4.8nV/rt(Hz) noise.
Should be ok with 750-1000 Ohm transimpedance.
The other thing you might want to change is the PD
(although it might be the 1cm PD with high bias is as fast as smaller ones with lower bias).
There are two types of other Si diodes at the 40m right now (~3mm):
-Rana and I found a Centronic OSD 15-5T in the old equipment
-Frank gave me a Hamamatsu S1223-01 on a Thorlabs pre-amp device (could be taken out).
The Centronic OSD 15-5T has up to 80pF with 12 V bias according to the datasheet.
The Hamamatsu S1223-01 is stated with 20pF only, but stated to have a max. frequency resp. of 20MHz ('-3db point').
I dont know what this means, as the corner freq. of 10pF into 50Ohm is still 160MHz.
In any case there are faster 3mm types to start with, as for example Hamamatsu S3399 (~ 90$),
which is stated to have the corner at 100MHz with 50 Ohm load.
For this type the stated capacity (20pF) looks consistent with ~100MHz corner into 50 Ohm.
So probably you can get higher BW with this one using much smaller load, as in transimpedance stage.
I made a simple PD test circuit which may allow to test PD response up to few 100MHz.
Its not for low noise, only for characterising PD response.
Here is the circuit:
The 2 capacitor values (for bypassing) are kind of arbitrary, just what I found around
(one medium, one small capacity). Could be improved by better RF types (e.g. Mica).
The PD type has no meaning. I put in the Centronic 15-T5 for a start.
The bias can be up to 20V for this diode.
The signal appears across R1. It is small, to make a large bandwidth.
R2 is just for slightly decoupling the signal from the following RF amplifier.
The wire into the RF amplifier is short (~cm). And the amplifier is supposed to have 50 Ohm
I use a mini circuits ZFL 500 here.
power supply for this is 15V.
Restarted the C1sim machine at about 12:30 to help diagnose a network problem. Everything is back up and running