[Marc Shalika]

For all these measurements we set up HWP and QWP at the input beam to have as linear as possible light from our polarization camera.

Then, we placed the input polarizer aligned with this linear polarizer as in fig1. We got aximuth angle ~ - 0.05+/-0.05 deg and ellipticity ~ -0.23+/-0.02 deg.

After installing the output cross polarizer we got azimuth angle ~ -0.025+/-0.05 deg and ellipticity ~ 0.06 +/-0.02 deg as in fig 2.

• Extinction ratio

Before installing the output polarizer we installed each LC successively. We rotated the LC to find the minimum and maximum transmission. Then we swept the LC voltage from 0 to 25V and computed the extinction ratio from the transmitted power normalized by the input power.

For LC2, we found the max and min positions were matching well the principal axes but it was not the case for LC1...

• Fast axis direction

As pointed out by Shalika, our previous estimations of the LC fast axis where really dependent on the fitting parameters range. It could come from the fact that using several sine harmonics in our fit biased our estimation. We decided to use a different formula : P_trans = a * sin(2(theta-theta0))^2 with theta the rotation angle of the LC.

We swept the LC voltages at various rotation angles covering more than 90 deg as in fig4 for LC2. From the fit we could extract the fast axis direction of 12.18 deg. This is in really good agreement with our 'by hand' estimation of 11.43deg.

All the swept results are reported in fig5. It can be seen that we get the usual retardance varying from 17nm to 989 nm as a function of applied voltage for every rotation angle except when the LC fast axis is close to the input polarization direction. In that case the maximum retardance is only ~650 nm while smallest one is increased to ~ 60 nm.

We simulated a rotating LC inside cross polarizers. Input polarization and polarizers are assumed perfect but we added by hand a backgroud power of 22.12 nW as measured in cross polarizers without LC. The LC voltage response is coming from the fit of the value at 45deg rotation wrt input polarization direction and takes into account measured extinction ratio. Results are reported in fig6 and agree really well with our measurement (especially at low voltage). An offset of 0.75 deg creates a maximum retardance of 657nm!

For LC1, we repeated the same measurement and measured fast axis direction of 145.05 deg.

• Temperature effect

All these measurements are performed at 30 degC nominal value and we typically see variation of less than 0.1 degC.

We measured the retardance at 0V while changing the LC temperature and results are attached in fig 7.

For LC2 we measured a change of 9.81 nm / degC while for LC1 7.84 nm/degC.

I looked at the CC PLL again. It still seems to be quite unstable. There was one occasion where I could get it to lock for more than 10 minutes. During phase noise measurement I saw that the noise was glitch type rather than stationary, where the noise floor could be at the level of previous measurements but quickly gets pushed up by an impulse excitation.

This time I measured the phase noise by providing 7 MHz as the local oscillator from DDS3 DAC0 (PPol LO @ 9 dBm), which corresponds to the usual operation frequency of the CC PLL beat note (7MHz at "-23.5" dBm on the "17dB more is measured " spectrum analyser,  DDS signal to CC LO is 21 MHz). Changing the LO offset to both 6.9990 MHz and 7.0001 MHz (+/-100 Hz offset) resulted in a corresponding 100 Hz signal output from the mixer. On the oscilloscope I can still quite frequently see the signal glitches.

I tried twice to get the phase noise spectrum but it seems the signal is not cooperating. The noise floor gets raised quite high by random noise impulses (figure 1). Qualitatively, the noise floor should be about at the level of the other measurements.

Figure 2 shows the Apk calibration to go from Vrms to rad/rtHz. Last time it was 0.0086 mV, now it is 0.0078.
Figure 3 and 4 show some feedback on the CC spectrum analyser at 14 and 28 MHz. The CC PLL is going to a T attached on the spectrum analyser. The other exit of the T then goes to the RF port of a mixer. When disconnect the mixer the 14/28... peaks go away.
Figure 5 shows the period of 2 wavelengths when the local oscillator frequency is offset to 7.000 100 MHz in DDS3 DAC3. So a 100 Hz difference between DDS and beatnote produces the 100 Hz signal as expected.

The humidity in the west side of the tunnel is increasing (85%). I set the fan in the tunnel (photo). It is working during this rain season.

A parameter for a phase shifted voltage waveform between the two LCs has also been added. 

The VI is completely ready for use. The speed of VI (with all data saving) is 40Hz. 

The retardance of the second LC (oriented along its fast axis) was observed 

We were able to align LC perfectly to its axis.

Fast axis measurement of LC2. 

Investigating issues mentioned in 3269, I removed the LC and found that somehow the hwp and qwp before lc were not transmitting linear polarization. The beam was displaced in the yaw before even entering the box. This was corrected. This explains the absurd measurement of elog 3262. 

Seeing Fig 3 from elog 3269 (where the initial position was 13.58) I moved the LC by 15.41 degrees in antiCW and so the initial position was 358.17 deg. The measurement was done with this and the fast axis orientation obtained is as shown in Fig 1. This was done by 9deg resolution for rotation.

Since the beam changed its obvious that we can't compare this present results with past one. Rotating by 12.15 degree now should align LC to the fast axis. 

This fast axis measurement is becoming Mission Impossible. 

folder_name = r'C:\Users\atama\OneDrive\LC-Experiment\Measurement Data\LC2_calibration data\fast axis 12'

Summary

I measured the phase noise of the P-Pol PLL at 50 MHz (normal operation ~200 MHz) and of the CC PLL at 20 MHz (normal operation 7 MHz). Despite the CC PLL instability, the phase noise measurement is not so bad and basically consistent with previous measurements of PLL phase noise. I am guesing that there is an issue of glitches at the normal CC operation frequency because it is much more unstable at 7 MHz than the test frequency of 20 MHz.

Details

I measured the PLL phase noise of both the CC and PPol controls using the method outlined previously. Normally, these loops operate at 7 MHz and ~ 200 MHz, respectively, but this is for the output of the PLL control loop. In the digital system, we input 3x F for CC into DDS3 DAC0, i.e. 21 MHz -> 7 MHz, and (1/5)x F for PPol into DDS3 DAC1, i.e. 35 MHz -> 175 MHz (currently). However, the DDS3 board is mis-wired so DAC3 controls the PPol LO while DAC1 controls the homodyne. For measuring the PLL phase noise, the DDS system is cleanest below 100 MHz, so instead I measured the PPol phase noise using at 50 MHz and the CC at 20 MHz.

The principle behind the PLL phase noise measurement is described in Yuhang's thesis, pg 102. When we input a PLL beatnote and a local oscillator to a mixer at the same frequency we will be left with PLL phase noise. The power spectrum is measured in Vrms/rtHz, so to convert to rad/rtHz we must divide by a calibration factor Apk^2, where Apk is the peak to peak amplitude of the oscillating output of the mixer when the beatnote and LO are offset by some small frequency ~ 100 Hz. I use a small mixer MiniCircuits ZX05-1L-S+ which has a damage threshold of 17 dBm (50 mW at 50 Ohm). A local oscillator (either DAC0 or DAC3) goes into the LO port while the PLL [name] MON signal goes into the RF port. An SMA screw-on low pass filter is used at the output.

For the measurements I have the following inputs into the mixer:
CC 50 MHz LO 8.0 dBm, 50.000000 MHz on DDS and spectrum analyzer
PPol 50 MHz beatnote -17 dBm, 10.000000 MHz on DDS, 50.000000 MHz on spectrum analyzer
PPol 20 MHz LO 9.0 dBm, 20.000000 MHz on DDS, 19.913043 MHz on spectrum analyzer
CC 20 MHz beatnote -6 dBm, 60.000000 MHz on DDS, 20.030000 MHz on spectrum analyzer

The spectrum analyzer seems to be a bit inaccurate on peak finding. Oscillatory behaviour at the output of the mixer depends on frequency offset as set on the computer to the DDS and can be seen on the oscilloscope, rather than "as measured" on the spectrum analyzer peak finder.

For the spectral measurement I use PSD units Vrms/rtHz. I then convert to rad/rtHz using the Apk calibration factor, 0.0568 mVpk for the PPol and 0.0086 mVpk for the CC. The phase noise spectrum is shown in figure 1. They are compared with a previous measurement in September last year. It seems the CC phase noise at 20 MHz is not too bad. Both the PPol and CC loops remained locked for a long time during the test. However, the PLL lock for the CC was seen to be quite unstable at its normal operating frequency. Perhaps it is glitch noise rather than stationary noise, or maybe there is some cross coupling when operating at 7 MHz. PPol has about 50% extra noise in the range 500-2000 Hz. The difference at the lowest frequency is due to the frequency resolution of the measurement rather than the system.

Angle correction in analysis

The problem for angles is happening maybe because we were considering the start position of rotation as 0° (instead of the actual angle of rotator). This was removed and we consider initial angle as 0° for all measurements now to understand what's going on

1. Fig 1 from elog 3256 where measured angle is 191.43° (start point) at Temp=25°

2. Fig 2 from elog 3256 where measured angle is 193.54° (after CW rotation by 11.43°) at Temp=30°

3. Fig 3 from elog 3260 where measured angle is 195.41° (after CW rotation by 2.15°) at Temp=30°

4. Fig 4 from elog 3262 where measured angle is 183.3° (after CW rotation by 1.83°) at Temp=30°

I computed potential well and resonant frequency of Roberts Linkage.

Both results were made by material point model.
Potential well of Roberts Linkage of which depth is 250mm was only attached. Beacuse relationship between COM position and depth are same.

Resonant frequency of Roberts Linkage of which depth are 108mm and 250mm wrere attached.
Some measuremet results of which depth is 108mm are far from material point model's ones.
Actually, I don't know certain reasons. I just wrote down some suspicious points I thought.

• When I computed COM position,  there were mistakes.  I think it is most suspicious.
• Material point model was made by some approximation.  That maked some gaps?!
• I confused frequency for angular frequency.
• Basically, results' resonant frequency are wrong.
• Basically, material point model are wrong.

I measured the transfer function and Q factor of Roberts Linkage of which depth is 250mm.

The results were as follows.

I measured the resonant frequency by fitting transfer function. The results were attached.

I measured Q factor by ring down curve.
I can't measured Q factor of which COM position is 37mm, because ring down curve is affected by the another axis' motion.
I tryed doing FFT to ring down curve of which COM position is 37mm. 
The result related to ring down curve were also attaced.

Measured Fast axis orientation of second LC

Issue solved:

1. see elog 3242 for LC 1 fast axis. It was continuous (done in the PP(Parallel Polarizer) configuration)

2. see elog 3254 for LC 2 fast axis it was discontinuous.

3. We did LC 2 measurements and found Fig 1 and Fig 2 using the CP(Cross Polarizer) technique. But we used the cos function to fit it and other mistakes that are addressed below. We see that even if we moved our LC(by -11.62deg ) it seems that the LC didn't rotate at all. 

Mistakes we made

1. When using the fit equation the bounds of phase were given from -4 to 4. I have changed it from 0 to 2*pi. 

2. We should use the sine function to fit cross-polarizer data and cos for Parallel polarizer. This arises from the fact that we use power to understand the position of the fast axis. So if you observe data from these two techniques like power vs. rotation. It will be shifted. 

3. Now, let's compare Fig 1 and Fig 3 where CP data was fit using right parameters.

4. we also need to consider the initial angle where we start measurement both when observing power vs rotation and analyzing fast axis orientation. When I incorporated this we could exactly see how much were we rotating the fast axis or if we rotated in the wrong direction

5. So when we first did a measurement with CP (shown in Fig 1) (we had a lot of data points because we did it with a 10-degree resolution). But because we were using the wrong function to fit no matter how many times we did the measurement our data looked strange

6. When we shifted to PP after 4 sets of measurements, we did measure with less resolution and so it looked strange. 

7. We can see from Fig 3 that we are supposed to move LC by 11.43 degree. so I moved LC and measured again to obtain Fig 4, Fig 5 and Fig 6.

8. Just to be sure that our new analysis is correct you can compare Fig 7 from elog 3242 for LC 1's fast axis.  

9. As a matter of fact, it's better to use CP for such measurements to see small changes too (because of small retardance range of LC at high voltage). See Fig 8 and Fig 9 for measurement done using PP. Although these measurements entailed the corrections during analysis, the data seemed strange enough to be considered. 

Miscellanous:

1. some angles were omitted during analysis (likely because the LC cable caused disruption in beam and hence strange data). Also, this won't matter because we won't use these omitted orientations during characterization. Preferably the LC will be fixed along the fast axis

2. Moving on, the issue of temperature rising in LC was completely unrelated to the box or laser. It was due to us using tape to fix the wire so that it doesn't move and block the beam. This tension caused an elevated temperature of 26 deg even when the laser was off, the temperature controller was off and the box was lifted. The temperature was relieved as soon as I removed the tape!

for PP folder_name = r'C:\Users\atama\OneDrive\LC-Experiment\Measurement Data\LC2_calibration data\fast axis 8'

for CP folder_name = r'C:\Users\atama\OneDrive\LC-Experiment\Measurement Data\LC2_calibration data\fast axis 9'

Summary

When we were working with Yuhang in April, we noticed that the CC loop was very glitchy. I attempted to measure the CC PLL phase noise but got no signal.

Details

I attempted to measure PLL phase noise using the same method I did previously. To recap:

• The PLL outputs a sine wave
• If this is mixed with some local oscillator at the same frequency, then the output of the mixing will just be zero signal + phase noise
• The procedure is to put [name] PLL MON into RF and a local oscillator directly from the DDS3 into LO (last time I used 7.6 dBm).
• DDS3 outputs: Ch0 - CC LO 21 MHz, Ch1 - CC2, Ch2 - CC1, Ch3 - PPol LO 35 MHz - note that Ch1 and Ch3 are reversed compared to wiki/theses.
• Offsetting the PLL by 100 Hz should give a signal visible on the oscilloscope at about 0.08 V

I could see that the LO was generated from the DDS board (Ch3 - 50 MHz, 9 dBm), and that the CC PLL could lock. However, no signal came out of the mixer - the spectrum analyser just showed the same as when unplugged, and putting the signal into the oscilloscope gave nothing when the RF and LO were offset by 100 Hz.

Next time I will check the mixer and cables 

The measurement was repeated. First, I moved the LC to the new position of 337.78 degrees. Then I repeated the measurement with the angle of rotation incremented by 30 degrees. 

The issue with fast axis orientation continues. see Fig 1 and 2. It seems that there is a discontinuity at some points. This has been observed in almost all the 7 times that we did measurements. 

PS:

The data is stored in foldername= 'C:\Users\atama\OneDrive\LC-Experiment\Measurement Data\LC2_calibration data\fast axis 7'

[Shalika, Marc]

This measurement aims to find the fast axis orientation of our second LC so that we can align it correspondingly for future measurements. 

1. The fast axis orientation was measured using the method mentioned in elog 3242.

2. Our setup is inside a box and so (sometimes the laser hits the box or because of lack of air circulation) the temperature gets unstable and affects the LC. So we decide to use LC at 30 degrees. This helps us avoid any temperature fluctuations. 

3. The LC was rotated from 0 to 360 deg with increments of 45 degrees. 

4. To understand our fast axis position our data (where power is observed for the LC rotation) was fitted properly to the equations. (see Fig 1) . This fit is then used to get fast axis orientation.

5. The axis was found to be at -22.3 degrees (see Fig 2) and so the LC has been rotated to this position. The LC position is now 337.8 degrees. 

6. The measurement will be taken again to avoid any deviations from the best position, with 10 degree increments.

[we have tried taking this measurement 6 times as of now. We are a bit baffled by the mysterious nature of fast axis discontinuity. We will try to do this measurement with more points. ]

PS:

The data is stored in foldername= 'C:\Users\atama\OneDrive\LC-Experiment\Measurement Data\LC2_calibration data\fast axis 6'

To measure the fast axis orientation we shuold have the 2 polarizers parallels and not crossed.