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ID Date Author Type Category Subject
  996   Fri Jun 22 11:27:40 2012 FrankDailyProgressPDPD responsivity scans

Background: We would like to measure the spatial distribution of the responsivity of photodiodes - for characterization of the size of the damaged area due to the pulse testing  - and in general for determining the sensitivity to beam pointing (coupling from beam pointing into RIN).

Status: I have started building a PD scanning setup using the transmitted beam through the curved mirror of the PMC focusing on a PD mounted on a motorized XY-translation stage with manual Z adjustments. The whole scanning control and DAQ is done in Labview. I have now finished the first set of tools for

  1. Finding the focus of the beam on the PD - This is done by scanning across the PD along one axis near the metal contact ring around the PD which serves as a knife edge. While scanning one has to manually adjust Z to find the focus., but it is very easy. Picture of the GUI below.
  2. Finding the geometric center of the PD - This is still under development. The idea is to automatically scan in X and Y and calculate the geometric center of the PD using the scan. This information is required for the final 2D-surface scan to optimize the measurement time. Due to the high resolution of the scans (typically 10um) the total scan time for a 2mm diode is about 6.5h, for 25um it is still ~2h.
  3. Raster the surface, grab the data using the Keithley Ampmeter at the moment and plotting it in real time as 2D surface plot and 3D plot. Also saving the data as ASCI and as 8-bit PNG grayscale image. User has fully control about the bias voltage, scanning area, resolution etc. Sample picture of a shitty PD with glass window and crossed-out window using black marker below.

FindFocus_Frontpanel.jpg testdiode_screen.jpg

Attachment 3: testdiode_10um.png
testdiode_10um.png
  995   Fri Jun 22 03:35:54 2012 taraDailyProgressBEATfrequency noise of demodulated beat

I added the result from the I-Q measurement method in PSL:993.

  994   Thu Jun 21 16:04:39 2012 taraDailyProgressBEATlow frequency beat with 32kHz ADC

Quote:

 This is overdoing it. Please just post the existing beat data somewhere and I can show you how to do it easily with a few lines of matlab code. Then you can go back to your usual noise hunting.

 Here is the demodulated beat signal, with 32kHz sampling rate, 120 second time strecth. I used SR560 to amplify the demod signal so that pk-pk value is ~10 000 counts. The data is store in demod.data with a signal column .

Attachment 1: demod_2012_06_21.mat
  993   Wed Jun 20 20:48:16 2012 SarahDailyProgressBEATfrequency noise of demodulated beat

 To avoid doing PLL with Simulink, Tara and I measured the Q and I signals for the demodulated beat frequency to measure the frequency noise. We used the following setup:

6_20_setup.png

The measured demodulated signal was around 1kHz. From the visio, the signal was split, and thus the power went from 13 dBm to 10dBm. The mixers used were intended for a power of 13dBm, not 10dBm, but since we were not worried about the signal to noise ratio it was okay. The function generator was set at 172MHz, because that is the frequency corresponding to a 90 degree phase shift. Additionally, the SR560 was set to a gain of 20 to avoid saturating the ADC. I am currently processing the data, which includes plotting Q vs I, finding delta_phi/delta_t to get the instantaneous frequency, and taking a FFT to get the frequency noise.

== the cable==

we calculated the length of the cable for 90degree phase shift around 170MHz to be ~0.3m (speed of the signal in the cable is 2e8 m/s), so we picked a cable with the length close to our estimation and measured the TF to check the phase delay. The chosen one has the following TF, so we chose the frequency around 170 MHz for 90degree delay.

TF_delay.png

 

== explanation for this method==

IMG_1415.jpg

 

== demodulated beat frequency ==

After evaluating the instantaneous demodulated beat frequency by dphi/dT, I plotted the result of demod freq vs time to check if it agrees with what we saw on the scope or not(~1kHz). The result looks good, the frequency fluctuates around 1khz as intended.

freq_drift.png

 

== FFT of the demodulated frequency==

 Then I tried to find the PSD of the above plot, and compare with the measured frequency noise from a Marconi with 100kHz input range. The results are not in good agreement. The result from ADC is about a factor of 10 lower than the measured frequency noise. The result from ADC agrees more with Marconi frequency noise with10kHz input range It might be possible that I made a mistake by choosing 10kHz instead of 100kHz when I setup the input range for the marconi.  The shape of the signal from ADC drops at higher frequency probably because of the anti aliasing filter in ADC.

compare.png

  992   Wed Jun 20 17:50:59 2012 ranaDailyProgressBEATlow frequency beat with 32kHz ADC

 This is overdoing it. Please just post the existing beat data somewhere and I can show you how to do it easily with a few lines of matlab code. Then you can go back to your usual noise hunting.

  991   Wed Jun 20 16:06:50 2012 taraDailyProgressBEATlow frequency beat with 32kHz ADC

Koji suggested I try to measure the frequency noise of the demodulated beat this way. By using I and Q signals of the demodulated beat signal, I can plot the signal of I and Q, which should be a circle. From that I can get dphi/dt which is the instantaeneous frequency, then FFT to get the beat noise. 

To do that I need:

  • Power splitter with 90 degree phase shift - ZMSCQ-2-180, datasheet.
  • another cable for DAQ (one for I, one for Q)
  990   Tue Jun 19 00:08:19 2012 taraDailyProgressBEATlow frequency beat with 32kHz ADC

I'm using simulink to do software PLL. 

As Zach suggested that using simulink to do the PLL might be easier than using his codes, I looked up this  example and trying to build a model for PLL. It's not working yet, I'm still trying to get FFT from the feedback signal to the vco.

Quote:

Quote:

==comments==

     The FFT results from the fix demodulated signal are not very stable. Thus, the line width is quite large and depends on the number of average and time of the measurement we choose. The plot shows the FFT results from two different average, 200 and 100, (and one more 100 from different time).  We might need a code to track the center frequency of the time series data and then FFT it to get a valid result for this technique.

 Yes, absolutely. If the frequency has some low frequency wander, there's certainly no way to measure the frequency noise with a straight FFT. Instead, you make sure that the beat frequency is up at ~5-10 kHz and then record a long time series (100 - 1000 s). You then use a software PLL to estimate the frequency noise.

Make sure the beat shows up as at least 10000 counts peak.

 

  989   Mon Jun 18 19:04:08 2012 SarahNotesLaserMeasured vs. Theoretical Transfer Functions

Today I plotted the transfer function measured last week against a calculated transfer function. First, I plotted the transfer function obtained last week with the physical units of Hz/RIN [Hz/sqrt(Hz)]. Then I used the code from elog entry PSL:372 to calculate a theoretical transfer function. The code calculates delta_f using a 1D heat equation solution, due to a change in power. I modified the code to find delta_f at each frequency, and divide it by the RIN at that frequency. The results are plotted below, with the calculated curve in red and the measured curve in blue:

TF_calculated_vs_measured.png 

The slope of the calculated curve appears to be somewhat correct, at ~1/f. The observed differences could be due to non idealities in the actual experiment, or using an imperfect model when calculating the delta_f.

Attachment 2: theoretical_tf.zip
  988   Fri Jun 15 21:41:16 2012 frank, taraNotesDAQTemperature control updated

We switched the temperature readout channels used for temp feedback control to improve the signal. The new signal is significantly smoother.

      The signals from 4 thermostats around the vacuum chamber were acquired through 4 channels, C3:PSL-RCAV_SENSE(1-4). These channels were then connected to DAQ. This made the signal noisy because the resolution of analog to digital converter was low. In order to fix that we use an analog circuit to sum and average the signals from 4 sensors then amplify it before sending to DAQ,C3:PSL-RCAV_TEMP, then calibrated it to C3:PSL-VAC_CHAMBERTEMP by comparing RCAV_TEMP [V] to RCAV_TEMPAVG[C] which is calibrated to deg C already. 

      CHAMBERTEMP = (RCAV_TEMPx-0.495) + 34.957

     

     We corrected the perl script (in SUN machine) used for thermal feedback on the heater jacket. Now the script is named rcav_PID_2012_06_15.pl, see wiki. The servo is now back on.

  987   Wed Jun 13 19:00:26 2012 SarahDailyProgressLaserTransfer Functions

Today Tara and I measured the coherence between the intensity noise from RCAV and ACAV, as well as the transfer function between the power fluctuations and frequency. We used the following setup:

 photo_(5).JPG

With a pda 100a photodiode behind ACAV, we looked at the intensity fluctuations, as well as the noise level of the pd. The noise of the sr758 in this case was low enough to consider negligible. The results for pd noise and intensity noise are plotted with respect to the left y-axis. The Relative Intensity Noise for ACAV, the intensity fluctuations divided by the DC voltage, is plotted with respect to the right y-axis.

 PD_and_RIN.png

 

We also measured the coherence between RCAV_TRANSPD and ACAV_TRANSPD, where we used about 2000 averages:

 Coherence.png

Next we measured the transfer function between power coupling and frequency. In order to do this, we reduced the power of RCAV to a minimum of 50uW and increased the power in ACAV to a maximum of 2.5mW. The gain in ACAV was too high, and we had to add an attenuator of 30dB to the servo input.

The transfer function is found by dividing the response function by the reference function. In this case, we let the response function be the AOM feedback signal, and the reference signal be the ACAV power fluctuations. The use of ACAV power fluctuations is optimal because ACAV is being operated a maximum power. Additionally, there was a 1kHZ input range to ACAV which will be used for calibration to absolute frequency later.

Using the swept sine measurement group, we measured the following transfer functions:

 TFs.png

The blue transfer function was the first obtained. In order to confirm the accuracy of the transfer function, we changed both the excitation and the power level to ACAV. If the transfer function is accurate, we expect it to remain relatively constant in these cases.

Green Plot: After changing the DC power in ACAV to half its current value, to 1.25mW, the green transfer function was obtained. Because the power was decreased, the gain decreased, and we adjusted the attenuation to ACAV from 30dB to 13dB. 

Red Plot: Next, we changed the excitation amplitude down to 1V, and the transfer function remained the same. However, after changing the attenuation back to 30dB, the transfer function did change slightly as shown in the red curve.

Black Plot: Increasing the power to ACAV to 1.9mW, the transfer function is portrayed as the black curve.

Yellow Plot: In an attempt to look for the common mode effect, we increased the power to RCAV to 1mW, a value relatively close to that of ACAV. The resulting transfer function, the yellow curve, does not indicate the presence of any common mode effect. One possible reason for this is that the coupling for the two cavities might not be the same. 

 

   ==comments==

    To sum up, the transfer function measurements we have might not be the real coupling from RIN to frequency noise because:

  • It does not stay at the same value when we change the power to ACAV. (Blue -> Green).
  • TF changes with the attenuator we use from mixer out to ACAV servo in order to keep the loop stable (Green-> RED)
  • TF does not change when the power to RCAV is changed, and power to ACAV is kept constant. It should become smaller as the power between the two cavities are about the same (assuming similar absorption) due to common mode effect (black and yellow) and become larger if the power difference between the two cavities increase.

   == How does it show up in the noise budget?==

    However, as a rough check, if we assume that the measured TF is valid, the coupling from RIN to frequency noise in beat signal is plotted below.

RIN_beat_2012_05_18.png

 The measured TF (feedback to AOM/ ACAV_TRANSPD) used in this plot is taken from the red TF from the above plot which gives the maximum coupling.  I assume that the TF at low frequency has the same slope (1/f^0.15) from DC to around 1kHz and roll off with the same measured slope

coupling.png .

[above, TF plotted with fit curve]

Then

Estimated Frequency Noise = [ACAV_TRANSPD_DC [v] ] x [measured RIN_ACAV [1/sqrtHz]] x [10  (TF/20)] x 2 x 710 [Hz/V] ,where

  • TF is measured in dB, [V/V]
  • a factor of 2 at the end is for double passed AOM,
  • a factor of 710 [Hz/V] is the calibration for 1kHz input range on Marconi for AOM 
  • no common mode rejection is assumed (to get the upper bound). This should be valid, since the coherence between ACAV and RCAV_TRANS_PD is very tiny at low frequency, where the coupling and RIN are supposed to be large.
  • assume 2mW input for ACAV

As it turns out, the measured TF is not totally wrong since the estimated effect is still below the measured beat signal. It is interesting to see that, from 10 to 100Hz, the shape of the RIN noise follows the trend of the measurement nicely.  Thus, developing ISS might improve our signal to certain level. 

I'll add the contribution from RIN in the noise budget code and see if the sum total noise match the measurement or not.

Attachment 2: PD_and_Intensity_noise.png
PD_and_Intensity_noise.png
Attachment 3: RIN_ACAV.png
RIN_ACAV.png
Attachment 4: Coherence.png
Coherence.png
Attachment 5: transfer_functions.png
transfer_functions.png
Attachment 6: RIN_beat_2012_05_18.png
RIN_beat_2012_05_18.png
Attachment 11: TFs.png
TFs.png
  986   Wed Jun 13 11:45:12 2012 SarahDailyProgressLaserRelative Intensity Noise

 Yesterday Tara and I measured the relative intensity noise behind the cavity. We placed two pda 10Cs behind the cavity, one for the in loop sensor, and one for the out of loop sensor. Since the same source was split on the two photodiodes, the two signals were similar.

After centering the beams on the photodiodes, we measured the noise from the photodiode itself, the noise from the SR758, as well as the intensity noise. The noise from the pd was measured at a -50dB range, while the noise from the sr758 was measured at a -20dB range. At the -50dB range, the sr758 would have 7nN of noise, which is much lower than the pd noise level. Thus, the measurement of the pd noise is valid.The results were processed in MATLAB and are plotted below. 

PD_SR758_Intensity_Noise.png 

The following graph shows the relative intensity noise of the laser as measured behind the cavity, obtained by dividing the intensity noise by the DC voltage:

 Relative_Intensity_Noise_.png

With the above information, the next step will be to measure the transfer function between the power fluctuations and the beat signal.

Attachment 1: PD_and_intensity_noise.fig
Attachment 2: PD_and_intensity_noise.jpg
PD_and_intensity_noise.jpg
Attachment 3: relative_intensity_noise.jpg
relative_intensity_noise.jpg
Attachment 4: PD_and_Intensity_Noise.png
PD_and_Intensity_Noise.png
Attachment 5: Relative_Intensity_Noise.png
Relative_Intensity_Noise.png
  985   Wed Jun 13 11:12:55 2012 taraNotesopticcavity mirrors

Frank showed me where we keep the spare cavity mirrors. They are in a cardboard box labeled REO in the left cabinet. There are 7 substrates with the coatings similar to what we use in the current setup. They are specified as polished annulus, and wedge (details are added in the proposal). So, if we have short spacers, we can assemble the cavities asap. The coatings profile is not written anywhere(# of layers, transmissivity), I'll ask peter if he has the information about this.

IMG_1357.jpgIMG_1358.jpg

IMG_1359.jpg

 

  984   Tue Jun 12 16:04:33 2012 SarahNotesDocumentationcomsol progress

 Attached is the file with the latest progress I have made in modeling the change in cavity length due to acceleration. I ran a time dependent simulation using the beam physics under the structural mechanics catagory. The deformation results are plotted in a 3D plot in the attached file. The results attached were obtained with the cavity supported at .25 inches from both ends of the spacer. I still have yet to determine how to get comsol to give me the actual change in length as a result. Additionally this is only a rough model, because the acceleration only applies to the points on the cavity as opposed to the entire cavity itself. I plan to introduce more physics to correct this, as well as plot change in length versus support points to find the optimal points of support for the cavity.

Attachment 1: cavity_.25in.mph
  983   Mon Jun 11 12:02:39 2012 SarahDailyProgressDocumentationcomsol

 I am trying to model the change in cavity length due to acceleration using COMSOL. After obtaining the software I am attempting to first model a simple beam bending under acceleration. Using the Structural Mechanics physics for a beam and a stationary study, I first fixed the beam at one end and added a prescribed acceleration. Currently the results are not as expected, and the beam is not bending under acceleration. Adding a force instead of acceleration gives the expected results of beam bending. Additionally working in a time dependent study as opposed to a stationary study produces expected results of beam bending under acceleration. However, it should work with a stationary study, so I am still trying to figure out how to use the software and get this model working.

I have already constructed the model for the cavity with the 1.45in x 1.5in spacer, and once I get the beam simulation working, I should be able to apply a similar study to this model. 

  982   Sat Jun 9 01:49:52 2012 taraNotesPMCPMC servo was acting strange

 Today when Sarah and I tried to align the beam to PMC,  we lost PMC lock and could not bring it back. So we investigated it. The cause of the lost lock is not yet exactly concluded, but we can lock pmc back at ~ 40mW with usual stability.

 What we did before we lost lock:

  • We realigned EAOM in front of PMC. Since we replaced the laser head, the beam misaligned a bit and clipped/ scattered at EAOM. This turns out to be irrelevant with the problem (see details below).

What we did to check what was wrong with the PMC servo:

  • Made sure that the power input to PMC did not exceed  80 mW, so the RFPD for PMC was not destroyed (It was not saturated either).
  • Check the PZT response, by scanning the DC offset. By doing this we still see HOMs showing up on ccd behind the PMC, so the PZT is working fine.
  • Measured error signal from mixer out while scanning the cavity. The error signal had sine wave around 30 Hz added into it, so the signal was error signal + sine wave (30Hz) with amplitude larger than of pk-pk level of error signal (when the alignment was still bad).
  • So I disconnected RF signal, terminated the input with 50ohm, the fluctuation was still there. It was gone after I disconnected LO singal.
  • I checked the signal from LO, nothing was wrong with it.
  • Then I tried to align the beam as best I could without locking the PMC. Once the alignment was good enough, the 30 Hz fluctuation amplitude was smaller than pk-pk signal of the error signal. However when I locked the PMC, it was not very stable. A light tap on the table could kick the PMC out of lock.
  • I tried to reverse all the setup back to original and measured the error signal. With 20mW power input, the error signal was totally fine.IMG_1343.JPG
  • Then I increased more power to PMC, by adjusting the half wave plate in front of the first Faraday Isolator. The shape of the error signal changed as the power increase, but I could still optimize it by adjusting the phase shift (I don't know why would the phase change with the power it should be independent from each other). However, at 60mW input power to PMC(this corresponds to ~110+ mW at the 21.5 MHz EOM) the error signal turned bad. It was distorted, and the peaks from sidebands were gone. It could not be adjusted by changing RF power to EOM or phase shift.     So it has to do with the power. I'm not sure if the alignment of the EOM will be the cause of this behavior, but I aligned it quite well. There was no obvious beam clipped or scattered light on the EOM openings.

IMG_1345.JPG

Current status:

  • PMC is locked with 40mW input, gain 15 dB.
  • The origin of 30 Hz modulation at mixer out is not yet verified, but it disappeared after I investigated the problem.
  • PMC lock is stable, tapping on the table won't kick it out of lock
  981   Wed Jun 6 16:53:12 2012 SarahDailyProgressLaserBeam Alignment

Today Tara and I aligned the beam of the new NPRO laser, so that it passed through all elements of the setup.

The hole patterns of the laser and aluminum block did not match up: 

photo_(4).JPG

Two screws were used in front, and a clamp in back to hold down the laser:

photo_(3).JPG

Before locking the Pre-mode cleaner, we measured the photodiode saturation at 684mV, corresponding to an input power to the pre-mode cleaner of 50mW. Thus, a voltage from the photodiode above 684mV would yield incorrect results.

We locked the Pre-mode Cleaner to the TM00 mode and optimized visibility by adjusting the mirrors. The maximized visibility through the pre-mode cleaner was 70%. The beam was attenuated between the laser and the input of the pre-mode cleaner to 28% of its power. So with the laser operating at its maximum power of 466mW, the output power from the pre-mode cleaner would be 91mW.

In an attempt to measure the effect of changing DC power in one cavity to the beat signal, we shifted the DC power for the Rcavity only, adjusting the half wave plate to keep the Acavity power constant, and measured the resulting change in the beat frequency.

Attachment 1: photo_(4).JPG
photo_(4).JPG
  980   Tue Jun 5 23:30:47 2012 ranaDailyProgressBEATlow frequency beat with 32kHz ADC

Quote:

==comments==

     The FFT results from the fix demodulated signal are not very stable. Thus, the line width is quite large and depends on the number of average and time of the measurement we choose. The plot shows the FFT results from two different average, 200 and 100, (and one more 100 from different time).  We might need a code to track the center frequency of the time series data and then FFT it to get a valid result for this technique.

 Yes, absolutely. If the frequency has some low frequency wander, there's certainly no way to measure the frequency noise with a straight FFT. Instead, you make sure that the beat frequency is up at ~5-10 kHz and then record a long time series (100 - 1000 s). You then use a software PLL to estimate the frequency noise.

Make sure the beat shows up as at least 10000 counts peak.

  979   Tue Jun 5 15:27:33 2012 SarahDailyProgressLaserPower Measurements

Tara and I measured the power of the currently used NPRO Laser to be 51mW. Previously the power of this laser was measured at 100mW, so this measurement indicates an irregular performance.

The beam is attenuated by 53% in between the laser output and pre-mode cleaner input. For the Pre-mode Cleaner, we tried to optimize the beam alignment by turning the mirrors in front of the Pre-mode cleaner to get maximum visibility. The input power was 26.9 mW and transmitted power was 21.2mW, yielding a 79% visibility.

 

Using the following setup with the higher power NPRO laser previously used in the TNI experiment we conducted the following measurements:

photo_(2).JPG

Directly from the laser, we measured a maximum power of 380mW. We were worried that the high power might burn through the power stick, so we decided to use a mirror to attenuate the beam. We placed the power stick away from the laser in order to get a larger beam size to avoid high intensities, which might destroy the diode as well.

With the mirror we measured the incident and transmitted power of the transmitted beam to calculate 47% power transmitted.

Then we increased the power by turning up the knob on the control box, until maximum power was reached. With the mirror the maximum power read 219mW on the power stick (on the control box it read ~700mW), which corresponds to 466mW directly from the laser. With the maximum power of 466mW, and an attenuation of 53%, we would have 247mW for the pre-mode cleaner input. With a visibility of 79% we would have 195mW from the output of the pre-mode cleaner, assuming the lasers have similar profiles, spot size, and waist position. In reality the power would be lower than 195mW.

 

We then replaced the currently used lower power NPRO laser with the higher power NPRO laser, using the current setup, to prepare to measure beam properties. We added a silicon heat sink between the laser and its aluminum heat block in order to avoid overheating. Additionally, we still need to finish aligning the beam so that it passes through all elements of the setup.

  978   Mon Jun 4 22:38:44 2012 taraDailyProgressBEATlow frequency beat with 32kHz ADC

I tried to measure beat signal without using PLL, the FFT of the demodulated signal does not look good. We probably need to do a code for software PLL to improve the signal for this method.

==Why not PLL?== ,

     as we can see in the previous beat measurement with PLL readout technique, frquency noise of the oscillator dominates the signal at high frequency (500Hz and above. Its frequency noise is dependent on the setup (carrier frequency and f modulation range). By turning off the modulation range, and demodulating the beat signal with a fixed frequency signal, we hope to reduce the frequency noise of the oscillator a by little bit.

==what I did==   

     We have a cable from PSL to ATF that goes to DAQ. The channel name is C2:ATF-PSL2_DAQ_OUT. 

  • Check DAQ: By sending in a sinewave signal, I can check that DAQ is working properly. [fig1, FFT of sinewave 15 Hz]. 
  • To calibrate the signal, I used DAQ to measure the signal at V feedback to VCO, then get the plot from diaggui in fb0, and scale it so that it is comparable with the calibrated beat measurement.The calibration is ~0.45  times the result from FFT, see the figure below.

beat_2012_06_04_b.png

  • Turn off the frequency modulation on the vco, then measure the demodulated signal at mixer out, use the calibration from (2) to convert to absolute frequency

demod.png

==comments==

     The FFT results from the fix demodulated signal are not very stable. Thus, the line width is quite large and depends on the number of average and time of the measurement we choose. The plot shows the FFT results from two different average, 200 and 100, (and one more 100 from different time).  We might need a code to track the center frequency of the time series data and then FFT it to get a valid result for this technique.

   

 

 

  977   Mon Jun 4 11:08:37 2012 Sarah NotesScheduleTest Page

Quote:

 Orientation June 19th 9am

 40m Wikipage

PSL Wikipage

  976   Mon Jun 4 11:06:10 2012 Sarah NotesScheduleTest Page

 Orientation June 19th 9am

  975   Fri Jun 1 01:00:30 2012 frank, taraDailyProgressAcousticsacoustic enclosure for input beam

The beat signal is measured with an adhoc lid covering the enclosure on the beat part. There are no significant improvement in the acoustic region of the beat signal yet.

     The closing lid is the only missing piece for our acoustic box, so I just use smaller pieces of acrylic planes I can find to cover the top, and measure the beat signal. There is not much improvement in the acoustic region, see fig2 below for a closer look.

     There might  be dust on the optics somewhere, because the signal at low frequency is not as stable as it used to be. I could see scattered light bump coming up when I averaged for too long (this did not happen last time). I'll check all optics and make sure that they are clean.

     NOTE: The temperature servo is back on. We had to disconnect it in order to install the acoustic box. I set C3:PSL-RCAV_TEMPAVG to 32.5 ( the previous value was 35.03). I changed it because I noticed that as the temperature reached up to the set point, the beat frequency went up as well.  I'll check if this set point will reduce beat frequency down to ~ 160 MHz or not.

    

 

beat_2012_05_31.png

beat_2012_05_31_b.png

  974   Thu May 31 15:10:57 2012 taraNotesPurchasesquote from Coastline

I called Coastline about the lead time for the substrates and asked if we could speed up the process by changing the specs to be less demanding (coarser roughness/ sphericity). The answer is no, all the main features of the substrate (curve surface with polished annulus, wedge surface) are the main driving factors, not the roughness or how flat it is. Additionally, they told me that, from their experience, the width of the annulus of 2-3 mm is enough for optical contact. 5mm width would be too large and it causes the surface near the annulus to deform, and it takes longer time (he could not tell exactly how longer). I put the quotes on CTN wiki.

  973   Wed May 30 23:39:41 2012 frank, taraDailyProgressAcousticsacoustic enclosure for input beam

We started installing the new acoustic enclosure box for the beat path. It covers the whole beat setup and the part for power detection. The walls are installed. The lid will be made later.

 

IMG_1300.jpg

The mirror mount in front of new focus 1811 PD has long knobs which extend into the wall, so I replace it with another mount that has no knobs, and the panel can fit without obstruction.

The current box has only three holes, 2 for input beams, one for output beam at the beam splitter. Windows might be installed in these holes for better acoustic enclosure.

  972   Wed May 30 23:39:15 2012 frank, taraDailyProgressAcousticsacoustic enclosure for input beam

We started installing the new acoustic enclosure box for the beat path. It covers the whole beat setup and the part for power detection. The walls are installed. The lid will be made later.

 

IMG_1300.jpg

  971   Wed May 23 15:04:53 2012 steveNotesopticwindows for vacuum chamber

 

 2"  optics with 2 degrees of wedge will have 0.375" thickness as std - get optics specification now

I thought about the design after talking to you yesterday:

a, use standard 3 3/8" od  flange for your windows

b, the 2 degrees of off- set into the 10" cf design will have to be assembled in horizontal position so the teflon gaskit would stay in place

c, the vertical assembly requires that you put the 2 degrees off-set into the 3.37" flange ( one side CF - the other o-ring groove) and delrin cover plate on top of it

  970   Mon May 21 21:11:16 2012 taraNotesNoiseBudgetthermo optic noise added to noise budget

Frank corrected me that the acoustic coupling was not improved with the legs changing around 500 Hz. The measurement in comparison was not equipped with acoustic box yet. So I compared the measurement with the result from psl:955 , and there is no improvement around acoustic frequency. This means that these peaks are really from acoustic coupling through air, not legs.

beat_2012_05_18_compare_lid.png

  969   Mon May 21 16:53:38 2012 taraNotesopticwindows for vacuum chamber

 I edited the drawing for 10" flange. The wedge surfaces for 2" windows are tilted by 2 degrees sideway.

 

I tried to assemble the pieces with 2" OD window, 0.25" thickness (without Oring). I think the clearance for the window might be too tight. I'll fix it.

 

window_assembly.PDF

window_assembly2.PDF

 

Attachment 1: edit_blank_10_wedge.PDF
edit_blank_10_wedge.PDF
  968   Mon May 21 02:38:48 2012 taraNotesNoiseBudgetthermo optic noise added to noise budget

Thermo optic noise (coating) calculation has been added to the noise budget code.

      The previous result (for example, see psl:901) was not done properly. What I did was calculated the TO noise using GWINC code independently then plotted the result on top of the noise budget. Now the calculation is included in the main noise budget file (by calling function from GWINC). The noise budget for shorter cavity can be done easily by changing the length of the cavity only. For 1.45" long cavity, the TO noise in coating will not be the dominant noise source.

 

nb_short_cav.png

  967   Fri May 18 18:44:38 2012 taraDailyProgressBEATbeat measurement update

I'm trying to fix the mechanical peaks in the beat signal. The work is still in progress.

There are several mechanical peaks around our most sensitive band (60 Hz - 600 Hz). It is important that we damp these to improve the beat signal. 

One of unidentified peaks are around 240 Hz , which might be originated inside the vacuum chamber. I tried tapping the chamber, and saw the peaks went up, but I could not pinpoint to where(stack/heat shield/ cavity motion) exactly.

There are peaks around 500Hz that come from QWPs behind the cavities. I checked their components individually to pinpoint where was the part that produced 500 Hz peak.  Each QWP was mounted on a rotatable square mount that are screwed down to a solid aluminum block.

  1. I inserted a sheet of rubber between the two mounts to damp any possible motion from the structure, but there was no improvement.
  2. I replaced the Al block with a steel 1" post.-> The peaks still there. So,
  3. I replaced the rotatable square mounts to the circular desing, on a steel post, and made sure that the QWPs were secured. -> The peaks still there
  4. I tilted the wave plates a little bit to prevent any possible back reflection, still no improvements.

It might be the motion of the plate itself. If this is the case, we have to have a better acoustic insulation box. The current one for the beat path has to many holes.

  966   Fri May 18 03:56:22 2012 taraDailyProgressBEATbeat measurement update

The beat signal is getting better at lower frequency, there is no obvious scattering bump around 80 Hz anymore. It is possible that the previous legs + leveling valves were bad and caused extra vibration.

After legs and leveling valves replacement,  the beat signal has better stability at low frequency. There is no bump due to scattered light around 80 Hz anymore. Plus, acoustic coupling (400-600Hz)f is significantly reduce without any improvement on the acoustic shield. Thus, it is very likely that acoustic coupling is related to legs' isolation performance.,Wrong statement, see PSL:970.(Mon May 21 21:13:11 2012 )

 Mechanical peaks around 25-50 Hz are probably from horizontal, or tip/tilt motion of the seismic stacks.

beat_2012_05_18.png

fig1: beat measurement. floated table, floated air spring. 1mW input power for each cavity, 1kHz input range on PLL.

 The result around 80-200 Hz has slope  f^(-0.5). Alas the span is only ~100 Hz bandwidth, with hideous unidentified peaks around 240 Hz. Otherwise we can be more certain that we reach thermal noise of something even though it is ~ a factor of 1.5 above the upper limit.

zoom.png

fig2: close up plot of the above figure, around 80-300 Hz. The measurement result is about a factor of 1.5 above the upper estimated level.

compare.png

fig3: comparison with f^-0.5 line (cyan).

 

 

  965   Thu May 17 17:35:17 2012 taraNotesPurchasesquote from ATF for substrate and spacer

I got the quote for substrates from ATF (AR coated on flat-wedge, blank on concave, R=0.5m side) quantity of 10 and 20. They also offer the cavity assembly as well, so I sent them the drawing of our cavity to ask for the quote.

For the spacer, I asked two other companies,cidra, and tecoptics, for the quote, but they have not replied back yet. So, I just asked another company,aiceramics.com, in hope of getting it done soon.

  964   Wed May 16 22:27:13 2012 taraNotesopticwindows for vacuum chamber

I finished the drawing for new vacuum windows. The o-ring for the windows will be #223 (1/8" thickness). I'll consult with Steve one more time before I submit the drawings.

A few comments about this desing:

  •  The design is intend for 2" OD, 0.25" thickness window. The blank has 2 degree wedge surface for the window.
  •   The grooves for the o rings are based on the instruction on previous entry.
  •  The material for the small window, and the 10" window will be stainless steel.
  •   I feel that the drawing is a bit unclear, I'll try to draw it properly.

2_small_window.PDF

blank_10_wedge.PDF

Quote:

Nice reference for O-ring + groove design. I'll put it on CTN wiki as well.

 

The o-ring I plan to use for 2" OD window is #223, 0.139" thickness, ID = 1.609", OD = 1.887". McMasterCarr.

 

  963   Wed May 16 22:25:06 2012 frank, taraDailyProgressSeismicreplacing table legs

We check the leak. There are no obvious leak on the hose or connectors. It appears that the current leveling valves are more sensitive than the previous sets. That explains why the compressor is activated every 30 minutes while the beam alignment is still quite good.

  962   Tue May 15 21:57:49 2012 frank, taraDailyProgressSeismicreplacing table legs

The leveling valve for table legs are installed. With the new legs, the beam can maintain its alignment better than before (from 30 minutes observation period).

      Three leveling valves are installed, all of them have T connectors for linking two legs together, so we use a short tube, filled with epoxy to blind the unused side of the T for two legs. The compressor works every 30 mins. Although the period is shorter than before (~1 hr), but  it takes only ~ 2 minutes to compress the air, and the beam alignment is stable before and during the air compression, see fig 2. 

IMG_0930.JPG

fig1: new legs with new leveling valve.

IMG_0931.jpg

fig2: RCAV_RFPD_DC, over 100 seconds while the compressor is working. Generally, the reflected power on the RFPD increases if the alignment changes. The stable DC level indicates good stability. For this setup, the DC level is 1.7V. when the beam is off resonance. The previous setup had bad stability, it drifted from ~ 100mV to ~400mV.

We will use soap water to check for any possible leak tomorrow to make sure that there is no obvious leak in the setup.

  960   Fri May 11 17:52:17 2012 taraNotesopticwindows for vacuum chamber

Nice reference for O-ring + groove design. I'll put it on CTN wiki as well.

 

The o-ring I plan to use for 2" OD window is #223, 0.139" thickness, ID = 1.609", OD = 1.887". McMasterCarr.

Attachment 1: O-Rings.pdf.zip
  959   Fri May 11 01:00:42 2012 taraNotesPurchasesreplacing table legs

Frank told me to get the leveling pressure from Cryo table. Now I have enough for the table (a set of three), so I don't need to buy the new set. All CTN table legs are replaced. I'll connect the pressure tube to the legs tomorrow.

Quote:

There are no spare leveling valve at 40m, I'll buy a set of new one from Newport. It costs ~ $ 800. I asked Eric and he said to go ahead and buy it.

leveling valve set of 3 

It should be able to mount on the leg with an adapter piece easily.

This is how it looks like when it is mounted on the leg

http://search.newport.com/?q=*&x2=sku&q2=S-2000A-819.5

 

 

 

  958   Thu May 10 16:04:24 2012 taraNotesPurchasesreplacing table legs

There are no spare leveling valve at 40m, I'll buy a set of new one from Newport. It costs ~ $ 800. I asked Eric and he said to go ahead and buy it.

leveling valve set of 3 

It should be able to mount on the leg with an adapter piece easily.

This is how it looks like when it is mounted on the leg

http://search.newport.com/?q=*&x2=sku&q2=S-2000A-819.5

Quote:

I'm replacing our table legs with the ones from Jan's lab.  Those should be a little newer than the one we are using. However, the regulators we have are not compatible with those new legs.

 The pressure regulator for the old legs (which we are using) need a plate with a slot for holding it lever (in red square). However, the legs I took from Jan's lab do not have such the structure because it has different regulator style (in green square) and there is only one.  Basically, we don't have enough regulators for the new legs (need 3, have 1). I'll look around, check the 40m if they have some unused regulator.

IMG_0893.jpgIMG_0894_1.jpg

Above, left) the structure for the regulator for the current legs. Right) the regulator for the new leg.

 

 

 

 

 

 

  957   Wed May 9 22:26:26 2012 taraNotesLaserexternal cavity laser diode

I just asked Aki a few more questions about the ecd laser. If we do not require the performance to be rival to that of the NPRO, making one is possible in a few weeks time scale.

Q1) The setup of the Littrow style laser you showed me had one mirror
behind the grating. Is the setup similar to this
<
http://rsi.aip.org/resource/1/rsinak/v72/i12/p4477_s1>? Where the
mirror is used so that the alignment does not change when the laser is
tuned.

A1) Actually, Yes, for the laser you took the photo. But, most of the lasers we use in the lab don't have a mirror, only diode and grating in the box. In our case, we only scan the frequency by ~1GHz and the pointing vector drift is negligible.

 

Q2) Did you remove the glass window of the diode laser when you assemble
 the laser? If so, how do you keep the diode clean, or it does not matter
for your requirement.

A2) We didn't remove the glass window. What we did is very simple. We mounted the bare diode on the thorlabs mount: http://www.thorlabs.com/thorProduct.cfm?partNumber=LT230220P-B

 

 Q3) You mentioned that the line width of the laser when locked to CS cell
is ~300kHz. Is it because of gain limited of the servo or the CS cell's
intrinsic noise?

A3) We haven't measure the linewidth with locking and without locking independently. It's possible that our laser linewidth (without frequency lock) might be ~300kHz. So I don't know what limits our linewidth.

One thing you may want to consider is that a diode laser is infamous for the broad background incoherent light, compared to the solid state lasers. We typically observe ~30nm-wide incoherent light around the carrier with 30-40dB suppression compared to the carrier. If your experiment is sensitive to the spectral purity, this might be an issue.

Aki

 

 So the question is do we want to try to build one similar to what they have? We know that with the time scale and experience we have it will not be as good as the performance of the ecd laser reported in Numata etal paper, but it might be a fun project for the SURF student.

Quote:

I'm looking into how to make external cavity diode laser (ecd).

Here is the list of what we need.

 

  • Laser diode 1064nm, diode (+AR coating)
  • Grating
  • Current driver for locking the laser (home made)

I ask Akihisa who works in Kimble's group about their home made 850 nm ecl. The performance is not as good as NPRO yet (300kHz line width when locked to CS cell), but it is certainly interesting.

  • They use Littrow configuration ( 1 grating to form a cavity). The mirror behind the grating is for adjusting the output beam.
  • The PD is not AR coated, a slight power (10 uW) that transmits inside the diode is enough for the feedback.
  • The linewidth is ~ 300kHz when locked to CS cell, the free running noise is not measured.
  • They use both PZT and current to actuate on the frequency stabilization, the bandwidth is 50kHz.
  • Temperature feedback is employed to keep the stability of the laser
  • Time for putting everything in the box (once all components are ready) is ~ 1wk

 (IMG_0887.jpg IMG_0888.jpg

 

  956   Wed May 9 19:59:44 2012 taraNotesSeismicreplacing table legs

I'm replacing our table legs with the ones from Jan's lab.  Those should be a little newer than the one we are using. However, the regulators we have are not compatible with those new legs.

 The pressure regulator for the old legs (which we are using) need a plate with a slot for holding it lever (in red square). However, the legs I took from Jan's lab do not have such the structure because it has different regulator style (in green square) and there is only one.  Basically, we don't have enough regulators for the new legs (need 3, have 1). I'll look around, check the 40m if they have some unused regulator.

IMG_0893.jpgIMG_0894_1.jpg

Above, left) the structure for the regulator for the current legs. Right) the regulator for the new leg.

 

 

 

 

 

  955   Wed May 9 03:11:33 2012 frank, taraDailyProgressAcousticsacoustic enclosure for input beam

I check the performance of the enclosure box for input optics. It neither improves the beat signal that much.

   ==Is the acoustic box good?  No==

   To check how good the acoustic shield can be, I measured the beat signal and feedback signal to ACAV AOM when the lid were on and off. There were no much improvement in both signals, see fig1 below.

IO_lid_compare.png

fig1, beat signal and ACAV feedback, converted to frequency noise. Beat signals between the lid close and open (red, purple) are very similar. Feedback signal to AOM are also the same (blue, cyan). I plot the 4 traces together to see if there are any coincided peak, so I can know where it happens (beat path or input optics). Note the peak at 280 Hz in Cyan trace is not real, it pops up after ~50Avg. I could not find its origin yet.

    ==Is it really acoustic coupling?  Yeah, kind of==

    The results were so similar between the lid open and close, so I wondered if those were really acoustic. To test this, I turned off the two computer (PC and fb2) and remeasured the beat. Those computers' fans are quite loud when they are on. For fb2, the fans still work even when it is shut down, but definitely much quieter. The beat signal was improved a bit, see figure 2. The results were real, I repeated them twice. Note that the room are still not totally quiet with the two computers off, sounds from sun machine and electronic rack are still there, and they are as loud as the two computer and closer to the beat setup as well. 

computer_compare.png

fig2: beat signals when the computer are on (blue) and off (red), several peaks are obviously reduced when the computers are off.

  ==discussion and plan==

    Since the computer are sitting on the floor, it is not certain if the peaks due to the computers are from acoustic transferred through air or vibration transferred through the ground. But the peaks in question are at high frequency (almost 1kHz), and we have 3 stage seismic isolation on (except floating table). It is very likely that these peaks are caused by acoustic. To make sure that they are really acoustic, I'll float the table and repeat the measurement again.

  954   Tue May 8 16:28:30 2012 taraNotesLaserexternal cavity laser diode

I'm looking into how to make external cavity diode laser (ecd).

Here is the list of what we need.

 

  • Laser diode 1064nm, diode (+AR coating)
  • Grating
  • Current driver for locking the laser (home made)

I ask Akihisa who works in Kimble's group about their home made 850 nm ecl. The performance is not as good as NPRO yet (300kHz line width when locked to CS cell), but it is certainly interesting.

  • They use Littrow configuration ( 1 grating to form a cavity). The mirror behind the grating is for adjusting the output beam.
  • The PD is not AR coated, a slight power (10 uW) that transmits inside the diode is enough for the feedback.
  • The linewidth is ~ 300kHz when locked to CS cell, the free running noise is not measured.
  • They use both PZT and current to actuate on the frequency stabilization, the bandwidth is 50kHz.
  • Temperature feedback is employed to keep the stability of the laser
  • Time for putting everything in the box (once all components are ready) is ~ 1wk

 (IMG_0887.jpg IMG_0888.jpg

  953   Fri May 4 20:19:58 2012 frank, taraDailyProgressAcousticsacoustic enclosure for input beam

The enclosure box for input optics are done. We still need to order more of the nuts for one panel, but the box should provide certain acoustic shielding for now.

We will measure the beat signal once the temperature stable.

IMG_0863.JPG

IMG_0864.jpg

    The box has four 1-inch diameter holes, 2 for periscope, one for input beam, another one is for the beam to RCAV curve mirror which we cannot fit in the box.

    We had to rearrange the cable for ACAV AOM to have fewer cables going in and out the box. The cable for driving the AOM was remade so that it did not block the panel.

  952   Thu May 3 22:26:14 2012 frank, taraDailyProgressAcousticsacoustic enclosure for input beam

We are still working on the acoustic shielding panels. The work should be done by tomorrow.

IMG_0855.JPGIMG_0856.jpg

Fig1: Left, one panel with damping foam + black pad on top( to prevent scattered light). Right,a panel with two layers of good damping material with a damping pad under it. This type can damp acoustic noise pretty well.

We prepared all sides of the acoustic box. However, we don't have enough damping materials, so all the panels are not similar, but they all have some soft foam to provide acoustic damping. All the holes for cables/ beam are marked and will be drilled tomorrow. 

  951   Wed May 2 19:48:32 2012 frank, taraDailyProgressAcousticsacoustic enclosure for input beam

      We measured the frequency response(microphone out/signal to speaker) to see how well we can shield the outside acoustic.  The test panel did help reducing the acoustic coupling, but there is still room for improvement.

     Den lend me a blue bird microphone from 40m.  So we setup a measurement to compare two panels we have. The first one was what we made yesterday (plastic with damping pad), the second one was the aluminum panel(1/8" thick) with soft foam on the inside and foam strip on the edge where the panel met the frame.

     ==setup==

     We measured the frequency response between the microphone signal and the speaker driving signal. The source was white noise (band limit) 100Hz - 6.5kHz, 1.4V. The output has a T so that one was sent to the speaker, another one was for chA.  The SR785 chB input for microphone signal was floated  since the mic gave differential output. This should prevent the pre-amp output to see "ground" at the output and break the opamp.The measurement was average over 5000 samples.

      We measured with the speaker on and off (but the white noise ref to chA was still connected) to check we have a good SNR for every setup. Three setups were:

  • 1) wihout panel (see fig1),
  • 2) with plastic panel + damping pad (see fig2,left),
  • 3) with aluminum panel + soft foam (fig3, right).

.IMG_0853.jpg

fig1: setup, with the panel remove.

IMG_0854.JPG

fig2: two panels for testing. Left, a plastic piece with damping pad attached on (from yesterday). Right, an aluminum panel with soft foam

IMG_0852.jpg

fig3: panel under test.

 

result.png

fig4: result.

  ==conclusion + plan==

    From the plot, it is not very clear if the aluminum panel (panel2) is better than the plastic one (panel1). It might be that noise coming from other panels(which we have not changed) is the dominating signal. We will put the mic in a smaller container surrounded by acoustic damping with an opening for the material/structure to be tested. Then we can test a sample easily without removing/installing the panel all the time.

     For now, we are planing to use another kind of foam to put inside the box. We check by ears and found that it is better than the current foam we use with the aluminum panel.

  950   Tue May 1 23:58:21 2012 frank, taraDailyProgressAcousticsacoustic enclosure for input beam

We added the lid on top of the enclosure. More work is needed to complete the box.

    We made the closing lids by cutting a 1/8" acrylic panel. A strip of soft foam was added between the frame and the lids to form a seal.

    We did a qualitative test by placing a white noise source inside the box and listening. The aluminum bubble wrap we used did not provide good noise reduction. So we replaced one side by a plastic piece (~1/8" thick) with a damping pad on. It could damp the noise pretty well. I'll borrow a blue bird microphone from Den tomorrow, so we can measure the TF or just the relative noise signal to check how much attenuation we get from our structure.

 

IMG_0851.jpg

  949   Tue May 1 20:37:16 2012 taraNotesopticwindows for vacuum chamber

I got the reply from Thorlab the flange can't accept the thicker optical windows. So I think we have to make our own custom small flanges. I'll check TCS small windows design and make a drawing and consult with Steve again.

 

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

Hi Tara,

Thank you very much for your response.  It looks like our flanges can only fit
windows 0.1 mm thicker, with a tolerance of +0.0/-0.2 mm, so these flanges would not
be cross-compatible with existing windows.  I apologize for any inconvenience this
may cause.  Please let me know if you have additional inquiries, as I am very happy
to help.
-------------
  948   Tue May 1 03:12:58 2012 frank, taraDailyProgressAcousticsacoustic enclosure for input beam

We started making the acoustic enclosure around the input beam area (second half of the table, before the chamber). The frame is done. We haven't received all items for the panels yet, so we just tried to use the aluminum bubble wrap as test panels. And we just used a piece of plastic planes to cover the top. There is no improvement in acoustic coupling yet.

 

IMG_0849.jpg

  947   Mon Apr 30 01:41:18 2012 taraDailyProgressBEATnoise due to air leaking from legs

I suspected that the air leaking from the legs might cause  noise in acoustic bandwidth, so I measured the beat signal with unfloated /floated table. The beat signals from the two look similar. Air leaking from legs does not cause any extra acoustic coupling from 100Hz - 3kHz in the beat signal. 

 

 beat_2012_04_29_compare.png

fig1: Beat signal between floated and unfloated table. There is no significant difference between the two.

       On Friday evening, I turned off the air compressor. When I came back on Sunday night, the table was not floated. I measured the beat signal, then turned on the compressor, realigned the beam, then measured the beat again. The results were similar in 100Hz- 6 kHz band. Floating the table with these leaking legs will not add any extra acoustic noise to our signal (at least, at this level).

      Since the result looked nice with fewer mechanical peaks at night, I took a chance to check if it was limited by frequency noise of marconi in PLL loop or not. I changed the input range from 1kHz to 200Hz (their frequency noise level should be different and observable at 100-1kHz bandwidth, see here), but there was not different between the two input range, see fig2 below.

beat_inputrange.png

fig2: beat with different input range. There is no significant change in the results.

    It is likely that the flat level we are sitting on are detection noise + shot noise. This will be carefully checked next.

  946   Fri Apr 27 22:37:54 2012 taraDailyProgressBEATreplacing one mirror mount in beat path

One of the mirror mount in beat path was not properly mounted on the board because of the limited space. I changed that mirror mount with a block mount (similar to the one we use for the beam recombining beam splitter). The acoustic coupling is getting better.

 

IMG_0842.jpg

fig1: the mirror with the mount similar to that of the BS, see psl:818.

beat_2012_04_27.png

fig2: beat signal, comparison between before and after the mount replacement.

I'm not sure why the beat signal at 2kHz and above does not match. It might be that I did not align the beat well enough, or the alignment in front of the cavities changed. However, there is a significant improvement in beat signal, except the new mechanical peak around 1.2kHz, it might be from the new mirror mount.

 

Note: I turned off the air compressor switch after I measured the beat before the mount replacement to make sure that the seismic isolation for both measurements will be similar.

 

 

Attachment 1: IMG_0841.jpg
IMG_0841.jpg
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