We've been thinking about putting in a blade spring / wire based aluminum breadboard on top of the ETM & ITM stacks to get an extra factor of 10 in seismic attenuation.

Today Koji and I wondered about whether we could instead put something on the outside of the chambers. We have frozen the STACIS system because it produces a lot of excess noise below 1 Hz while isolating in the 5-50 Hz band.

But there is a small gap between the STACIS and the blue crossbeams that attache to the beams that go into the vacuum to support the stack. One possibility is to put in a small compliant piece in there to gives us some isolation in the 10-30 Hz band where we are using up a lot of the control range. The SLM series mounts from Barry Controls seems to do the trick. Depending on the load, we can get a 3-4 Hz resonant frequency.

Steve, can you please figure out how to measure what the vertical load is on each of the STACIS?

Today Ishwita, Sonali, and I completed basic laser safety training with Peter King. I completed the Laser Safety Quiz and have turned in my certificate sheet.

I just need to turn in a signed copy of the Lab Safety Checklist to SFP (which I can now have signed by Koji after completing the course).

Steve and I have removed the TT mirror from the clean box. It is now on the small optical table in the lab that I have been working on.  Thanks to Steve, all of the mechanical components for the horizontal displacement measurement experiment are compiled and on the small optical table. Here is a photo of the small optical table with the gathered components.

The plan is to attach the slider and the shaker directly to the black mounting plate. On the slider, we we then place the smaller black mounting plate (with the lip). The lip will attach to the shaker. We know exactly where to drill and everything is lined up. The shaker will be placed on the smaller black mounting plate (with the lip).  The assembly will begin on Monday.

Here is a photo of the planned set-up for the shaker and the horizontal slider + mounting base.

I setup a basic MEDM screen for remote control of the PLL.

The Slow control voltage slider allows the frequency of the laser to be moved around via the front panel slow control BNC.

The TTL signal slider provides 0/5V to allow triggering of the servo. Eventually this functionality will be transferred to the buttons (which do not work for now).

The screen can be accessed from the PSL dropdown menu in sitemap. We can make this better eventually, but this should suffice for initial setup.

Motivation

• Getting myself familiar with Python.
• Characterize statistical errors in the loss measurement.

Summary

​The precision of the measurement is excellent. We should move on to look for systematic errors. 

In Detail

According to Johannes and Gautam (see T1700117_ReflectionLoss .pdf in Attachment 1), the loss in the cavity mirror is obtained by measuring the light reflected from the cavity when it is locked and when it is misaligned. From these two measurements and by using the known transmissions of the cavity mirrors, the roundtrip loss is extracted.

I write a Python notebook (AnalyzeLossData.ipynb in Attachment 1) extracting the raw data from the measurement file (data20190216.hdf5 in Attachment 1) analyzing the statistics of the measurement and its PSD.

Attachment 2 shows the raw data. 

Attachment 3 shows the histogram of the measurement. It can be seen that the distribution is very close to being Gaussian.

The loss in the cavity pre roundtrip is measured to be 73.7+/-0.2 parts per million. The error is only due to the deviation in the PD measurement. Considering the uncertainty of the transmissions of the cavity mirrors should give a much bigger error.

Attachment 4 shows noise PSD of the PD readings. It can be seen that the noise spectrum is quite constant and there would be no big improvement by chopping the signal.

The situation might be different when the measurement is taken from the cavity lock PD where the signal is much weaker.

Disclaimer: Wrong calibration factors! See https://nodus.ligo.caltech.edu:8081/40m/13391

The two acA640-120gm Basler GigE-Cams have been calibrated. I used the collimated output of a fiber that carried the auxiliary laser light from the PSL table. With a non-polarizing beam splitter some of the light was picked off onto a PD, and I modified the RF amplitude of the AOM drive signal to vary the power coming out of the fiber. The fiber output was directed at a white paper, which was placed 1.06m from the front of the lens tube assembly, which is where the focal plane is. Using the Pylon Viewer App I made sure that the entirety of the beam spot was imaged onto the CCD. Since the camera sensor is 1/4" across, I removed the camera from the lens tube and instead placed the Ophir power meter head at the position of the sensor and measured the power reported versus PD voltage, which turned out to be 1.5 V/uW.

The camera was put back in place and I used the Pypylon package Gautam had stumbled upon to sweep the exposure time from 100us to 10ms at different light power settings including no laser light at all for background subtraction, and rather than keeping the full bitmap data for O(100s) of images I recorded only the quantities

1. Pixel Max
2. Pixel Sum
3. Pixel Mean
4. Pixel Standard Deviation
5. Pixel Median

I performed this procedure for both the 152 and 153 cameras and plotted the pixel sum and the pixel max vs the exposure time. All the exposures were taken at a gain setting of 100, which is the smallest possible setting (out of 100-600). To obtain the calibration factor I use the input power Pin=75nW in the 'safe' region 1ms to 10ms where the pixel sum looks smooth and the CCD is reportedly not saturated.

The incident power can be calculated as Pin =CF*Total(Counts-DarkCounts)/ExposureTime.

I powered up the existing ace100gm GigE cam with the PoE injector and tried to interface with it as described in elog 4163. After a few initial problems with IP assignment and interfacing I connected it to one of the gigabit hubs and installed the most recent pre-compiled software suite on /opt/pylon5 on optimus, after which I was able to find it with the configuration software. I named it "c1gige_bas100-1" and gave it the static IP address 192.168.113.151.

Afterwards the image acquisition worked without problems.

It may be a good idea to leave the gigecam interfacing up to a dedicated machine. I was thinking I could use Mafalda for this, and also for developing the code for framegrabbing and imager settings, but found that it was dead, burnt at the stake so to say. I guess it wasn't running anything critical, since it wasn't even connected to the network and smelled like burnt electronics. I'll get a replacement desktop for it.

Indeed. I suggest discussing with Joe B. I believe we should use a dedicated cam network to get the camera signals from the ends and corner all into one machine. Do not use the main CDS FE network for this since it might produce weird collissions. How about make a diagram, post it to elog, and send link to Joe?

As part of an ongoing effort to improve airflow in workspaces/bathrooms on campus, I have installed an air scrubber unit in each of the bathrooms at the 40m lab.

Just in case we want to retrofit the Tip/Tils with Beryllium Copper wire, here are links to a few sources which have a supply of the right composition and temper:

http://www.lfa-wire.com/Tempered-Alloy-25_C17200.htm

http://www.alloywire.com/beryllium_copper_CB_101.html

http://www.ngk.co.jp/english/products/electronics/berylliumcopper/wire/index.html

http://www.goodfellow.com/E/Copper-Beryllium-Wire.html

I don't think its worth it to do something to modify them unless we get a real reduction in the hysteresis - need a benchtop test setup ASAP.

 Be Copper in the lab is from Ca Fine Wire :  alloy 10 CDA 17 in sizes .008"  &  0.002"  There are other sus wire choices in the Drever lab

I fit the data from the beam profile that Jenne measured on 5/21/2010. The distances are measured from halfway between MC1 and MC3 to the beam scanner. The fits give the following where w0 is the waist size and z0 is the distance from the waist to halfway between MC1 and MC3.

For the horizontal profile:

reduced chi^2 = 0.88

z0 = (1 ± 29) mm

w0 = (1.51 ± 0.01) mm

For the vertical profile:

reduced chi^2 = 0.94

z0 = (673 ± 28) mm

w0 = (1.59 ± 0.01) mm

I calculated the radius of curvature of MC2 using these values of w0:

horizontal: (16.89 ± 0.06) m

vertical:   (17.66 ± 0.07) m

For this calculation, I used the value of (13.546 ± .0005) m for the length of the mode cleaner measured on 6/10/2009. The specification for the radius of curvature of MC2 is (18.4 ± 0.1) m.

In the following plots, the blue curve is the fit to the vertical beam radius, the purple curve is the fit to the horizontal beam radius, * denotes a data point from the vertical data, and + denotes a data point from the horizontal data.

Very nice as usual. Can you add the curve to show the ideal mode of the MC on the profile plot?

[Keiko, Suresh]

   Keiko and I measured the IPPOS beam profile.  The fit parameters  are :

The data files are attached. 

If we assume the nominal wavelength of the IR light to be 1064nm and constrain the Rayleigh length to be zr = (pi w0^2)/lambda we obtain the following fit parameters: (these are compared with the beam profile measurements of June/18/2010 available in the wiki )

* I updated the waist waist location coz because I missed-out the distance in air from the vacuum port to the optic on the IPPOS table.

Keiko, Rana, Suresh

Related to the beam profile of IPPOS today, we tried to measure the beam size at the ETMY point in order to estimate the input beam mode. We measured the beam size hitting at the suspension frame by a camera image, with two situations to see two "z" for beam profile.

(1) Input beam is slightly misaligned and the injected beam hits the end mirror frame. Assuming z=0 at the input mirror, this should be z=40m.

(2) Input beam hits the centre of the end mirror, and ITMY is slightly misaligned and the beam hits the end mirror frame after the one-round trip. Assuming z=0 at the ITM, this position should be z=120m.

The injected beam at the end point and the one round trip ligt at the end point should be the same size, if the input mode matches to the cavity mode. You can see if your injected light is good for the cavity or not. We compared and assumed the above two beam sizes by looking at the photo of the beam spot.

(1)  (2) 

 Assuming the zoom factor difference by the part below the beam (shown with allow in the photos. Arbitrary unit.), the beam in (2) is smaller than expected (roughly 40%?).

However this is a very rough estimation of the beam sizes! It is difficult to assume the beam size shown on the photos! It looks smaller only because the power of (2) is smaller than of (1). I don't think we can say anything from this rough estimation. One may be able to estimate better with CCD camera instead of this normal camera. 

I'd like to know what we expect for these numbers.  I've added to Kiwamu's drawing some more distances, so I can calculate the expected beam size at the IPPOS port.

I changed the ETMY CCD camera angle so that we can see the suspension frame in order to repeat the same thing as yesterday. The ETMY camera is not looking at the beam or mirror right now.

The mode looks quite terrible in the plot, but in reality it is an illusion of the plot.

The actual TEM00 content in this beam is ~99.7%

mode_coupling.pdf

Based on the above document, you can calculate power coupling between two elliptic gaussian modes.

Give the parameters of one beam as

zRy1 = pi*(2.77e-3)^2 / 1064e-9
z1y = 3.37
zRx1 = pi*(2.47e-3)^2 / 1064e-9
z1x = 4.15

Then, assume a round beam for the other.

zRx2 = zRy2 = zR
z2x = z2y = z0

Then run the optimizer to find the maximum for the quantity |C|^2

|C|^2 max: 0.9967
zR = 20.19
z0 = 3.804

This is wrong!  See following elog for corrected plot (and explanation)

I'm not done meditating on what's going on, but here's what I've got right now:

This is a beam profile, using the distances from the combined Kiwamu / Jenne sketch earlier today. 

0 meters along the horizontal axis is meters from the Mode Cleaner waist. (Yes, I was bad and forgot to label it.  Get over it.)

The pink and green dots to the left of the plot are the MC fitted waist measurements that we made in May 2010.

The pink and green dots in the ~center of the plot are the fitted waist measurements that Suresh and Keiko took yesterday, of the IPPOS path, so after the MMT.

The black dot is where we would like our non-astigmatic beam to be.  This is the calculated waist size of the cavity mode, using the new ~37.76m distance, after we moved the ETMs to their current positions.  The black dot indicates 3.036 mm at the ITM (averaged between the BS-ITMX and BS-ITMY distances).

The moral of the story that I'm getting from this plot:  something funny is going on.

The distances Kiwamu quoted on the sketch are very close to the ones that I used for designing and checking the MMT in the first place, which were based off of measurements using rulers etc to measure distances.  Steve said he looked at photos today, and agreed that Kiwamu's numbers looked reasonable also.

Something that we haven't done lately is measure the position of each optic from every other optic, along the beam path.  I propose we come up with a clever way to put a target on top of / next to mirrors, and then a way to hold the laser distance measure-er at an optic, so that we can go thorough systematically and measure the actual path that our beam is seeing.  Maybe this is too much work, and not worth it, but it would make me happier.  In my head, these 'fixtures' are just small pieces of cleaned aluminum, one that can sit on a mirror mount, and one which we can use to align the laser ruler to approximately the front of an optic.  Nothing fancy.

 Yup, something funny was going on.  Nic's MM code that I used, "a la mode", calls for the focal length of the optics, whereas the code that I wrote and used for ages called for the radius of curvature.  f = R/2.  Fixing that factor of 2 I get something more like:

This is obviously much better, in that the beam profile goes through (within some error) both of the measured sets of points - the MC waist measured in May 2010, and after the MMT measured yesterday.

So, what does it all mean?  That I'm not sure of yet.

 In an attempt to estimate the errors on the fit parameters I upgraded my Mathematica code to use the function 'NonlinearModelFit', which allows us to define weights and also reports the errors on the fit parameters.   The plots have been upgraded to show the error bars and residuals.

The parameters determined are given below and compared to the earlier measurements of 06/18/2010

Vertical Profile:

Horizontal Profile:

There is a significant change in the beam waist location (as compared to previous report) because I corrected a mistake in the sign convention that I was using in measuring the distances to the waist from the zero-reference.
 

As I was a little dissatisfied with the inaccuracy in the distance numbers in Kiwamu's sketch, I went back to the 18 Dec 2010 table layout drawing for more accurate numbers.  These are now included in this round of plots.

Also, I include astigmatism due to the incident angles on MMT1 (~3.5 deg) and MMT2 (~1 deg).

First plot, IPPOS path, using the recent (fixed) measurements from Suresh to fix the beam width.  Note that the old 2010 measurements of the MC waist are consistent with this measurement.

Second plot, Main IFO path all the way to the ITM (average) position, using the 2010 MC waist measurements to fix the beam width.

Third plot, Main IFO path all the way to the ITM position, but with PRM flipped (negative RoC), using the 2010 MC measurement to fix beam width.

With the PRM correctly oriented (2nd plot), I get beam waists of (x = 2.529 mm, y = 2.646 mm), which corresponds to a mode matching to the arm cavity of (eta = 97.43%, PRM correct).

With the PRM flipped (3rd plot), I get beam waists of (x = 3.176 mm, y = 3.3 mm), which corresponds to a mode matching to the arm cavity of (eta = 99.55%, PRM flipped).

First plot:

Second plot (this is how the MMT was designed to be, before the ETMs were moved, which made the ideal waist larger):

Third plot:

For both the 2nd and 3rd plot, we can't look at the post-MMT waist measurements, since that distance on the plots is after the PRM, which is a curved optic.  So the fact that the post-MMT measurements match the correct-PRM plot better than the flipped-PRM plot can't be taken to be meaningful.

Moral of the story:  I'm not sure how to interpret any of this to tell us if the PRM is flipped or not, since the measurements are all of the beam profile before the beam sees the PRM.  We'd have to measure the profile after the PRM somehow in order to get that information.  We have okay but not great mode matching to the arm if the PRM is correct, but I don't know that we readjusted the MMT after we moved the ETMs.  I don't remember recalculating any optimal telescope lengths after the arm length change.  If we need better mode matching, I can do that calculation, although given how much space we don't have, it would be hard in practice to move the MMT mirrors by much at all.

More calculations....

Game Plan:  Using MC waist measured beam as the starting point of beam propagation, move MMT mirrors around until the beam profile fits with the IPPOS measurements from Monday.

Plot 1:  Allow MMT mirrors to move as much as they want to.  Note that the Y-beam goes through the IPPOS measured point. (This implies we put the MMT in the wrong place by ~half a meter.  Unlikely)

Plot 2: Using MMT locations from plot 1, what does the beam look like at the ITMs? 

Plot 3:  Allow MMT mirrors to move as much as 2cm.  Note that the Y-beam doesn't quite go through IPPOS measured point.

Plot 4: Using MMT locations from plot 3, what does the beam look like at the ITMs?

For all of the above, I was optimizing the propagation of the Y-beam profile.  Since the X-beam profile measurement is so different, if I want to optimize to X and let the MMT mirrors move as much as they want, MMT1 ends up inside the MC.  Unlikely.  So I'm just looking at Y for now, and maybe Suresh or someone needs to rethink the error bars on their measurements or just remeasure.

Plot 1:

Plot 2:

Plot 3:

Plot 4:

I fitzed by hand with the numbers for the incident angles on MMT1 and MMT2, and then let the code optimize the position of MMT1 and MMT2.

Here I have set the incident angle for MMT1 = 25deg, and MMT2 = 12deg (should be 3.5deg, 1deg by design).  The length of the telescope doesn't want to change by more than 7mm, but the position of the telescope wants to change by 1.3meters.  Is it possible that the distances on the Monday IPPOS measurements aren't actually correct?

Suresh noted that I never wrote down the waist positions of the beam propagated through the MMT (based on where we think it is from ruler-based measurements).  This uses the MC waist measured beam as the starting point, and just propagates through the MMT, out to the IPPOS port.

Yq:

  Properties:
                    q: 2.2488 +23.8777i
               lambda: 1.0640e-06
            waistSize: 0.0028  (at z = 13.2676 meters)
               waistZ: 2.2488    (relative to z = 13.2676 meters)
      divergenceAngle: 1.1910e-04
    radiusOfCurvature: 255.7849
            beamWidth: 0.0029
        rayleighRange: 23.8777

So, to sum up, the vertical beam waist is 2.8438 mm at 11.0188 meters from the MC waist.

Xq:

  Properties:
                    q: 5.1953 +24.7342i
               lambda: 1.0640e-06
            waistSize: 0.0029   (at z = 13.2676 meters)
               waistZ: 5.1953    (relative to z = 13.2676 meters)
      divergenceAngle: 1.1702e-04
    radiusOfCurvature: 122.9525
            beamWidth: 0.0030
        rayleighRange: 24.7342

So, to sum up, the horizontal beam waist is 2.8943 mm at 8.0723 meters from the MC waist.

In pictorial form,

I am trying to track down possible errors in our measurements. 

So as a first step I am recomputing the IPPOS waist location with respect to the MC waist, using the same optical layout diagram as the one used by Jenne in her calculations.  Pic of Jenne's lab notebook showing location of optics is attached.  

 Let us compare it with the old measurement of the IPPOS beam from June/18/2010.

Note that there is a discrepancy of about 3.2 m in the waist location for the vertical profile and about 3.5 m for the horizontal profile between these two measurements. 

Let us compare these measurements with what is expected from calculations.  Jenne uses the known parameters of MC waist and the locations of the MMT optics to compute the parameters for the IPPOS beam:

 As the 2010 measurements are reported wrt to MMT2 and calculations are wrt MCwaist, I have used the distance between the MCwaist to MMT2 = 3.910 m to shift the reference from MMT2 to MC waist. Refer to the attached diagram from Jenne's notes for this MMT2 <--> MC waist distance.

There is a discrepancy of 1.5 meters between the calculations and recently measured waist location.  The discrepancy with the 18Jun2010 measurement is much larger, about 3 meters in both v and h.

Are such variations to be expected between two successive measurements?  I looked at another case where we have two measurements of a beam to see what to expect.

I looked at the REFL (Reflection from PRM) case, where we repeated a measurement, to see how much variation could happen in w0 and zr, between repeated measurements. This was a particularly bad case as our first attempt had problems due to OL servo loop oscillations in the PRM suspension damping.  We fixed that later and measurement 2 has smaller residuals. And I think we are doing okay in IPPOS case as seen by the reduced scatter of the residuals.

 These are the fits from the REFL beam measurement 1

 I have also recomputed the fits to the data from REFL beam measurement 2.  They match the earlier fits reported by kiwamu in his elog 6446

Note that between these two measurements the beam waist location has shifted by 0.5 m for the vertical and about 1.3 m for the horizontal cases.  So variations of 1.5 m in the waist locations are possible if we are not careful.  But this is a particularly extreme example, I think we are doing better now and the measurement is unlikely to change significantly if we repeat it.

Some notes:

Fits for IPPOS and both REFL measurements 1 and 2 are attached. 

The zero reference for the z axis of the IPPOS beam plot is at a distance of 6.719 m from MC waist for a beam propagating towards the IPPOS QPD.

The zero reference for the z axis of the REFL beam plots is at a distance of 5.741 m from the MMT2 in the direction of a beam reflected by PRM and propagating towards the REFL port.

[Suresh, Jenne]

  The input beam is most probably being clipped at the Faraday Isolator.  

Evidence: 

a)  The beam scan of the IPPOS beam showed a nongaussian beam in the horizontal direction.  This was visible in the beam scan since it overlays a gaussian-fit over the data.

b)  I was able to remove this departure from gaussian profile by introducing an offset of 5 into the C1:IOO-WFS2_YAW_OFFSET.  

c)   We made a few measurements of the beam diameter as a function of distance at an offset of 7.  At a distance of beyond 3 m the deviation from gaussian profile was once again apparent. 

d)  We increased the offset to 14 to remove this deviation. 

e)  When we measured the beam diameter again with this new offset the horizontal diameter and vertical diameters dropped by 2.sigma.  Indicating there the beam was clipped till then.

f)   We increased the offset to 16 and the beam diameter did not change further (within 1.sigma). Implying no more clipping, hopefully. 

And then the earthquake stopped us from proceeding further. 

We plan to investigate this further to be sure..  Data attached.

Subsidiary effects to keep track of:

1) Introducing an offset into the WFS loops decreases the coupling from PSL into MC. 

2) If the beam is being clipped at the Faraday Isolator then the REFL beam would also show lesser clipping with WFS offsets.

I tried to determine an optimal WFS2YAW offset to be used so that we may avoid clipping.

Initially, I just measured the beam diameter as a function of offset.  If the beam diameter would become independent of offset if it is not clipped.  However a systematic effect became apparent when I shifted the beam on the detector to a slightly different location.  So I repeated the measurements while recentering the beam to the same location everytime  (centered at -1650+/- 50 for both H and V directions).

I have attached plots of the scans for both cases, with recentering and without.    I have not been able to figure out what is going on since the beam diameter does not become independent of the offset.  While the beam profile becomes more gaussian beyond offsets of about 7 or so, the beam diameter does not seem to follow a clear pattern.  The measurements are repeatable (within one sigma) so the experimental errors are smaller than 1 sigma.

The photographs below show the improvement of Horizontal beam profile with WFS2Yaw offset.  These seem to indicate a good gaussian beam for offsets beyond 7 or so.  At offsets more than 12 the MC unlocks.

Offset = -2	Offset = 0	Offset = 2	Offset = 8

This seems to indicate that the beam diameter does not vary for WFS2Yaw offset > 8	But if we recenter the beam for each measurement this effect seems to vanish

 Will continue tomorrow.   Jenne wants to do some IFO locking now.

 From the mode measurement I and Suresh have done yesterday, I calculated what beam size we expect at ETM ((1) upper Fig.1)  and at ETM after one bounce ((2) lower Fig.1).

Fig.1 (Yarm)

In case of (1), we expect approximately w=6300 um (radius), and w=4800 um for one-bounce spot (2) from the measured mode, see Fig.2.

Fig.2

This roughly agree with what we observed on CCD camera. See, pic1 for (1) and pic2 for (2). The spot at the ETMY (1) is larger than the one-bounced spot (2). From the monitor it is difficult to assume the radius ratio. The observed spot of (2) is a bit smaller than the prediction. It could happnen when (A) the ETMY (as a lens) is slightly back of the ideal position (= the distance between the ITM and ETM is longer than 40m) (B) the real waist is farer than ITM position toward MC (I assumed roughly 5 m from Jenne's plot, but could be longer than that).

pic1 (left): beam spot hitting on the suspension frame. pic 2 (right): the one-bounced beam spot hitting on the suspension frame.

[Kiwamu, Suresh]

   Today we attempted to measure the beam profile of the REFL beam under two conditions:

              (a) with PRM aligned and ITMs misaligned 

              (b) with PRM misaligned and ITMs aligned

The raw data is shown below.  In each of the above conditions we measured in both the vertical (v) and horizontal (h) directions.   The measurements in the vertical direction were better than the ones in the horizontal direction because the optics had a horizontal oscillation which gave larger errors in measurement.

Looking at the general trend of these lines it is clear that modes are not matched since the beam reflected by the PRM has a different divergence than that reflected from ITMs.  The beam is also astigmatic as the vertical and horizontal directions have different divergences.

I could find beam parameters only for the Blue line above (Profile in the vertical direction while PRM was aligned).   The fit is quite sensitive to the data points close to the waist, so we need to make better (lower St.Dev.) measurements near the AP table closer to the beam waist.  The intensity with only one ITM aligned is too low and also contributes to the errors.   The beam size is close to 6mm in the horizontal direction, this coupled with yaw oscillations give large errors in this measurement.

Here is the only reliable fit that could be obtained, which is for the prompt reflection from the PRM in the vertical direction

The fit function I used is  Beam Dia = Waist { Sqrt [ 1+  ((z + z0)/zr)^2). The fit parameters we get for this data are

z0 = 7.7 m 

Waist = 2.4 mm

zr = 6.9 m

Will make another attempt later today...

Gabriele left the DataRay beam profiler + peripherals (see Attachment #1) in his office. I picked them up just now and brought them over to the 40m.

I had measured the y-profile of the beam of Friday at 5 axial locations and fit them to an erfc function using the lsqcurvefit function of MATLAB. 

The results were as follows - 

z(cm)    w (in)

4          0.0131

10        0.0132

15        0.0137

20       0.0139

25        0.0147

I left w in inches in the intensity plots as MATLAB gave more accurate fits for those values.

I converted these to S.I while making the spot-size vs z plot and the corresponding values in microns were 

332.74, 335.28, 347.98, 353.06, 373.38.

On fitting these values to the formula for the spot size of a Gaussian beam, the beam waist came out to be 330.54 microns and the location of the beam waist was at z=-2cm, where z=0 marks the head of the laser. 

TO-DO : Measure the spot size of the beam at more axial points to obtain a better fit. 

              Measure the x-profile of the beam. 

              Analyse the error in the spot sizes and corresponding error in the beam waist. 

I have attempted to calculate the instrument error (micrometer least count) using the values of the spot size obtained by the least squares fitting method. This error is large towards the centre of the beam as the power varies significantly between adjecent markings of the micrometer. Using the new values of error obtained, I used the chi-square fitting minimisation method to further optimise the waist size. 

The modified values are - 

z(cm)    w (in)

4         0.0134

10        0.0135

15        0.0140

20        0.0142

25        0.0150

And the revised values for the beam waist and location are 338.63 microns and -2.65 cm respectively. 

I will now try to use the chi-square stastitic to estimate the error in spot size. 

1. Include several sources of error. Micrometer error is one, but you should be able to think of at least 3 more.
2. There should be an error bar for the x and y axis.
3. Also, use pdftk to put the PDFs all into a single file. Remove so much whitespace.
4. Google 'beautiful plots python' and try to make your plots for the elog be more like publication quality for PRL or Nature.

You may compare your results with this.

RXA: please no, that's not the right way

​Updates in the He-Ne beam profiling experiment. 

1. I've made intensity profile plots at two more points on the z-axis. The additition of this plots hasn't affected the earlier obtained beam waist significantly. 
2. I have added other sources of error, such as the statisitical fluctuations on the oscilloscope(which is small compared to the least count error of the micrometer) and the least count of the z-axis scale.
3. I have also calculated the error in the parameters obtained by fiiting by calculating the covariance matrix using the jacobian returned by the lsqcurvefit function in MATLAB. 
4. I have also added horizontal error bars to all plots. 
5. All plots are now in S.I. units 

New and improved plots for the He-Ne profiling experiment 

Font size has been increased to 30. 

The plots are maximum size (Following Rana's advice, I saved the plots as eps files(maximized) and converted them to pdf later).

There is a shaded region around the trendline that represents the parameter error. 

Function that I fit my data to (should have mentioned this in my earlier elog entries) 

Description of my error analysis -

1. I have assumed a 20% deviation from markings in the micrometer error. 

2. Using the error in the micrometer, I have calculated the propogated error in the beam power :

I added this error to the stastistical error due to the fluctuation of the oscilloscope reading to obtain the total error in power. 

3. I found the Fisher Matrix by numerically differentiating the function at different data points  with respect to the parameters    and .

I then found the covariance matrix by inverting the Fisher Matrix and found the error in spot size estimation. 

EDIT : Residuals added to plots and all axes made equal 

Andrew and I set up the razor blade beam profiling experiment for He-Ne lasers on the "SP" table.  Once I receive the laser safety training, I will make power measurements and fit it to an erfc curve from which I will calculate the gaussian profile of the beam. I'm attaching some pictures of the setup. 

Least count of the micrometer - 2 microns 

Laser  : Lumentum 22037130:1103P

Photodetector : Thor Labs PDA100A

The beam scan (which has been living in the bridge subbasement for a bit now) is in a state of imperfection.

I noticed that:

• The waist reading seems to change by not insignificant amounts as you move the spot across the head, even for just small perturbations about the center.
• None of the features which require two slits seem to be working (unsure if this is software or hardware related)

I took some pictures to try and illuminate the situation - The inverted images are included to make it easier to see the flecks (?) in the slits

I am not sure how to figure out if any bit of the scan is/has been fried.

Pending further investigation, enjoy large error bars in your scan measurements!

PICTURES OF BOTH SLITS ON THE BEAMSCAN HEAD:

There was something wrong with the Beam Scan PC.  The  mouse and screen were not responding and the PC was asking for drivers for any new hardware that we plugged in.  We called in the services of Junaid and co. since we do not have a Win98 Second Edition installation disk in the lab.   Junaid came with the disk, we changed the screen and the mouse and installed everything. 

We tried to get the network going on the PC so that we could update stuff easily over the net.  This didnt succeed. For now, we still have to depend on a Win98se CD to get drivers if any new hardware is connected to this machine. 

For future reference, some notes:

1)  We will get a copy of Win98SE for the lab from Junaid

2) We have to use a USB mouse from Dell. We have several spares of this. The drivers for these are present in the machine. 

The Beam Scan is working okay now.  We will proceed with the beam profile measurements.  

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.

 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

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.

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. 

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:

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.

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.

- Plots should be directly attached on the elog. (Attaching codes in a zip is OK.)

- Plot legends should not touch or hide any data points.

- Don't exclude data points.

- The model for the beam profile fitting is incorrect: zr and w0 are dependent

- The code needs to be reviewed by someone for refinement.
  (EricQ, or possibly Jamie, Jenne while he is absent).

 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.

After yesterday's changes in the MC cavity state today it was necessary to optimize the alignment to the Faraday.

The way I did it was by tuning the PSL periscope in pitch and yaw trying to maximize TRX with the arm locked. After a small change in either one of the two directions I first maximized the MC transmitted power and then I ran the alignment script for the X arm.

I explored the space for both pitch and yaw and the max that I could get from TRX was 0.91. I'm not sure whether the increase in TRX is entirely due to a better alignment to the Farady rather than to a higher MC transmitted power.

Also I'm not sure I'm well interpreting the image from the camera pointing at the Farady. I guess I need someone more familiar with it to tell me if it shows any sign of clipping.

Anyway, last week, even before the MC got misaligned, TRX didn't go above 0.90. So now I wonder whether it's the MC's fault or something else's if we have that value..

[Jenne, Raji (before dinner)]

We put the beam attenuation optics in place.  Before putting any optics down, I centered the IOO QPDs, then adjusted the HWPs and PBS such that we remained centered on those QPDs.

Now, I'm about to unblock the beam and let ~100mW into the vacuum so I can lock the MC.  Steve and Manasa were putting on the light access connector when I left earlier, so I'm excited to use it!

1. With TRX and TRY maximized using ASS, I centered the Oplev spots on the respective QPDs for the four test masses and the BS. I also centered the spot onto the IPPOS QPD by moving the available steering mirror.
2. At EX, I tweaked the input pointing of the green beam into the arm by manually twiddling with the PZT mirrors. I was able to get GTRX~0.4.
3. On the AS table - Koji and I found that there was a steering mirror placed in the AS beam path such that there was no light reaching the AS110 or AS55 PDs. Please - when you are done with your measurement, return the optical configuration to the state it was in before so that the usual locking activity isn't disturbed by a needless few hours troubleshooting electronics.

Once Koji is done with his checkout of the whitening electronics, I will try and lock the PRMI.

[yutaro, ericq]

We made the beam spot on QPD for the oplev of ETMY centered by changing the orientation of the mirror just before the QPD.

Before doing this, we ran dithering for Y arm and froze the output of ASS for Y arm.