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General (General)
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SatoruIkeda - 16:44, Thursday 13 March 2025 (3963)Get code to link to this report
Modified the display of the attached image of this elog

Changed so that Image files Attached to comments also appear in the original thread.

BIGFOOT (Cavity)
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MarcEisenmann - 11:24, Thursday 13 March 2025 (3962)Get code to link to this report
birefringence of Shinkosha (30*50) #3

Sample measured with input HWP rotation.

However, it seems that with the current situation only nearby polarization states can be generated that affects how many polarization states combination can be used (only 1 pair in below measurement).

 

sample = 'SHINKOSHA_30_50_3'

input_filenames = [
'Wed, Mar 12, 2025 12-00-10 PM.txt',
'Wed, Mar 12, 2025 12-14-14 PM.txt',
'Wed, Mar 12, 2025 1-18-31 PM.txt',
'Wed, Mar 12, 2025 4-39-58 PM.txt',
'Wed, Mar 12, 2025 4-45-39 PM.txt',
'Wed, Mar 12, 2025 4-59-45 PM.txt',
'Wed, Mar 12, 2025 5-05-32 PM.txt',
'Wed, Mar 12, 2025 5-19-36 PM.txt'
]

output_filenames = [
'Wed, Mar 12, 2025 12-06-17 PM.txt',
'Wed, Mar 12, 2025 12-18-40 PM.txt',
'Wed, Mar 12, 2025 1-24-16 PM.txt',
'Wed, Mar 12, 2025 4-35-22 PM.txt',
'Wed, Mar 12, 2025 4-50-50 PM.txt',
'Wed, Mar 12, 2025 4-55-12 PM.txt',
'Wed, Mar 12, 2025 5-10-00 PM.txt',
'Wed, Mar 12, 2025 5-14-37 PM.txt'
]



thickness = 0.05

Images attached to this report
3962_20250313032443_shinkosha30503.png
R&D (FilterCavity)
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MichaelPage - 04:01, Thursday 13 March 2025 (3961)Get code to link to this report
Restart of FIS systems

I restarted the squeezer electronics and did some checks. While turning on stuff in the FC room I clumsily dropped an oscilloscope on the floor. It still works but has some 45 kHz 4 mV noise when unplugged. Well it doesn't get used for critical measurements anyway so maybe ok. It has the yellow sticker "RM alignment feedback". I tested it using GRMC DEMOD (which was moved now to DDS2 DAC0) in both input channels and it gives basically the same result as the other oscilloscope.

SHG

The SHG was very misaligned, which was a bit strange considering that it usually maintains its alignment for quite a long time. It started out at about 40% mode matching. I used the steering mirrors and XY lens mount and realigned it to (1960 mV, 280 mV, 80 mV -> 84.5%), which is a little bit less than the reference alignment from 2024-12-25 (1840 mV, 200 mV, 140 mV -> 86.8%). I tried also the waveplate to correct the polarization but it had no effect. I also checked the input IR which reads 805 mW on the stick sensor vs 800 mW on 2024-12-25. I locked it and optimized the green output power to 296 mW (temperature controller 3.191) before the green FI. 

GRMC

I checkced the GRMC alignment, it was ok, basically where I left it, so I didn't tweak it. I checked the error signal and optimized the demodulation phase to i-phase, then locked. I could see that it stably outputs 25.3 mW (316 mV on oscilloscope) of green power, checked at the OPO steering mirror 1 using the ring sensor, which is stable at the third decimal place on the power meter. I tweaked the servo gain to bring it to the threshold of oscillation (1.1) then reduced it (0.75). Also at one point the power meter randomly spiked to 44 mW, I'm not sure if this was due to the actual green power or just the power meter electronics being weird.

As presented in the research meeting there was an issue with GRMC unlock caused by the demodulation phase seemingly flipping from i-phase to q-phase. By switching channels to DDS2 DAC0, I can see that the problem is fixed. GRMC can maintain lock for > 90 min with the same output power and power stability (at least as seen on the power meter). In other words, the previously used channel DDS2 DAC2 is drifting in phase with respect to other channels. There is a bit of an annoying problem where when the GRMC/MZ assembly is manually unlocked it can sometimes kick one of the PZTs along the green path and requires the MZ to be realigned.

The PDH signal has about 100 mV DC offset as well which is a bit strange. But the error signal is 2.08 Vpk so it doesn't cause any immediately apparent problems.

IRMC

Mode matching was checked (1210 mV, 72 mV -> 94.4%) and was good. PDH signal is the same size as last time I checked (400 mVpk). I locked and saw it transmits 2.30 mV, same as normal.

Homodyne

Homodyne balance was quite bad, about -17 mV. I realigned it to zero, making sure to check the lenses in front of the homodyne PDs to confirm that there is no clipping of the beam. I checked the homodyne spectrum which gives the usual ~ -132 dBVrms/rtHz at high frequencies > 5 kHz. It seems to be about -131.8 dBVrms/rtHz at low frequencies, I feel it is maybe a bit noisy but I guess the squeezing measurement will determine the real performance.

 

to do: PLLs, OPO, nonlinear gain, squeezing

General (General)
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MarcEisenmann - 18:26, Tuesday 11 March 2025 (3960)Get code to link to this report
finalizing TAMA re-organization

[Marc, Shalika, Takahashi]

We moved the dessicator containing TAMA main laser spare parts close to TAMA main laser bench.

We moved a table, 4 small dessicators 2 shelves and an electronic rack at the bottom of the stairs where the bigfoot table was previously located.

It needs some setup but it can be useful for testing and assembling components.

BIGFOOT (Characterization)
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MarcEisenmann - 17:39, Tuesday 11 March 2025 (3959)Get code to link to this report
birefirngence of HWP

In order to measure large sample or measure birefringence at high power density we should remvove the polarizer placed right before the sample.

For all previous measurement, various input linear polarization from 0 to 90deg with 15deg increment rotation were used.

As our measurement technique is compatible with any polarization states, it should be fine.

The polarizer was removed and the HWP was installed in the motorized rotator mount.

 

To test this technique, we measured birefringence of a commercial HWP as below.

The measurement is working fine but at the given QWP orientation, several polarization pairs were failing our realizability condition.

 

 

input_filenames = [
    'Tue, Mar 4, 2025 7-07-08 PM.txt',
    'Tue, Mar 4, 2025 7-32-13 PM.txt',
    'Tue, Mar 4, 2025 8-12-45 PM.txt',
    'Tue, Mar 4, 2025 8-53-59 PM.txt']

output_filenames = [
    'Tue, Mar 4, 2025 7-26-03 PM.txt',
    'Tue, Mar 4, 2025 7-38-51 PM.txt',
    'Tue, Mar 4, 2025 8-22-31 PM.txt',
    'Tue, Mar 4, 2025 9-00-23 PM.txt'
    ]
thickness = 0

Images attached to this report
3959_20250311093916_hwp.png
BIGFOOT (Readout)
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ShalikaSingh - 17:28, Tuesday 11 March 2025 (3952)Get code to link to this report
EOM characterization with respect to input polarization

The EOM characteristics were noted in cross polarizer configuration. I rotate the input polarization, by rotating the input polarizer. The output polarizer was also rotated by the same amount in the same direction. At last, I obtain a sinusoidal response of transmission for different rotation of input polarization. In order to maximize the transmission, i.e optimize the input polarization to be 45 degree relative to the crystal axis, I move the polarizer to the maximum transnmission position. The polarizer was at the end rotated by -12deg.

Images attached to this report
3952_20250311092946_polarizationrotvstransmissionrotcharacteristics20250310.png
BIGFOOT (Characterization)
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MarcEisenmann - 14:58, Tuesday 11 March 2025 (3958)Get code to link to this report
birefringence of shinkosha (30 * 50) #2

This sample is shinkosha 1623047-2 (4/6).

white dot at top towards laser,

 

sample = 'SHINKOSHA_30_50_2'

input_filenames = [
    'Mon, Mar 10, 2025 4-33-24 PM.txt',
    'Mon, Mar 10, 2025 3-54-38 PM.txt',
    'Mon, Mar 10, 2025 4-10-45 PM.txt',
    'Mon, Mar 10, 2025 5-05-32 PM.txt',
    'Mon, Mar 10, 2025 5-10-14 PM.txt',
    'Mon, Mar 10, 2025 5-28-08 PM.txt',
    'Mon, Mar 10, 2025 5-34-31 PM.txt'    
    ]

# centered at X=304, Y=156
output_filenames = [
    'Mon, Mar 10, 2025 4-38-05 PM.txt',
    'Mon, Mar 10, 2025 3-54-38 PM.txt',
    'Mon, Mar 10, 2025 4-04-05 PM.txt',
    'Mon, Mar 10, 2025 4-42-34 PM.txt',
    'Mon, Mar 10, 2025 5-18-28 PM.txt',
    'Mon, Mar 10, 2025 5-22-55 PM.txt',
    'Mon, Mar 10, 2025 5-40-41 PM.txt'
    ]
thickness = 0.05
 

Images attached to this report
3958_20250311112342_shinkosha30502.png
BIGFOOT (Characterization)
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MarcEisenmann - 14:55, Tuesday 11 March 2025 (3957)Get code to link to this report
birefringence of shinkosha (30 * 50) #1

This sample is shinkosha 1623047-2 (5/6)

white dot at the top towards laser.

 

sample = 'SHINKOSHA_30_50_1'

input_filenames = [
    'Wed, Feb 26, 2025 6-57-14 PM.txt',
    'Thu, Feb 27, 2025 12-51-50 PM.txt',
    'Thu, Feb 27, 2025 1-29-04 PM.txt',
    'Thu, Feb 27, 2025 1-49-28 PM.txt',
    'Thu, Feb 27, 2025 2-18-11 PM.txt',
    'Thu, Feb 27, 2025 2-40-41 PM.txt',
    'Thu, Feb 27, 2025 3-10-32 PM.txt'    
    ]

output_filenames = [
    'Thu, Feb 27, 2025 12-06-40 PM.txt',
    'Thu, Feb 27, 2025 1-13-41 PM.txt',
    'Thu, Feb 27, 2025 1-39-08 PM.txt',
    'Thu, Feb 27, 2025 2-02-35 PM.txt',
    'Thu, Feb 27, 2025 2-30-26 PM.txt',
    'Thu, Feb 27, 2025 2-57-31 PM.txt',
    'Thu, Feb 27, 2025 6-02-58 PM.txt'
    ]
thickness = 0.05

Images attached to this report
3957_20250311070355_shinkosha30501.png
BIGFOOT (Characterization)
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MarcEisenmann - 14:53, Tuesday 11 March 2025 (3956)Get code to link to this report
birefringence of aztec (30 * 20) #3

white dot at the top towards laser.

 

sample = 'AZTEC_30_20_3'

input_filenames = [
    'Tue, Feb 25, 2025 7-11-55 PM.txt',
    'Wed, Feb 26, 2025 12-03-06 PM.txt',
    'Wed, Feb 26, 2025 1-24-42 PM.txt',
    'Wed, Feb 26, 2025 2-09-13 PM.txt',
    'Wed, Feb 26, 2025 2-43-35 PM.txt',
    'Wed, Feb 26, 2025 3-36-07 PM.txt',
    'Wed, Feb 26, 2025 5-26-21 PM.txt'    
    ]

output_filenames = [
    'Tue, Feb 25, 2025 7-26-18 PM.txt',
    'Wed, Feb 26, 2025 12-28-13 PM.txt',
    'Wed, Feb 26, 2025 2-09-13 PM.txt',
    'Wed, Feb 26, 2025 2-32-59 PM.txt',
    'Wed, Feb 26, 2025 2-53-52 PM.txt',
    'Wed, Feb 26, 2025 4-17-25 PM.txt',
    'Wed, Feb 26, 2025 5-36-24 PM.txt'
    ]
thickness = 0.02

Images attached to this report
3956_20250311070455_aztec30203.png
BIGFOOT (Characterization)
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MarcEisenmann - 14:52, Tuesday 11 March 2025 (3955)Get code to link to this report
birefringence of aztec (30 * 20) #2

[Marc, Michael M.]

white dot at the top towards laser.

 

sample = 'AZTEC_30_20_2'

input_filenames = [
    'Fri, Feb 21, 2025 5-49-13 PM.txt',
    'Fri, Feb 21, 2025 6-15-32 PM.txt',
    'Fri, Feb 21, 2025 6-36-09 PM.txt',
    'Fri, Feb 21, 2025 7-03-06 PM.txt',
    'Tue, Feb 25, 2025 4-50-36 PM.txt',
    'Tue, Feb 25, 2025 5-19-28 PM.txt',
    'Tue, Feb 25, 2025 5-42-55 PM.txt'    
    ]

output_filenames = [
    'Fri, Feb 21, 2025 6-01-01 PM.txt',
    'Fri, Feb 21, 2025 6-25-32 PM.txt',
    'Fri, Feb 21, 2025 6-51-49 PM.txt',
    'Tue, Feb 25, 2025 4-37-00 PM.txt',
    'Tue, Feb 25, 2025 5-04-45 PM.txt',
    'Tue, Feb 25, 2025 5-31-45 PM.txt',
    'Tue, Feb 25, 2025 5-55-36 PM.txt'
    ]
thickness = 0.02

Images attached to this report
3955_20250311070525_aztec30202.png
BIGFOOT (Characterization)
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MarcEisenmann - 14:51, Tuesday 11 March 2025 (3954)Get code to link to this report
birefringence of AZTEC (30 * 20) #1

[Marc, Michael M.]

This sample corresponds to the previously measured sample which showed increase in birefringence due the stress of the fixing screw.

The sample is mounted using the 3D printed holder.

white dot at the top towards laser.

sample = 'AZTEC_30_20_1'
input_filenames = [
    'Thu, Feb 20, 2025 5-12-04 PM.txt',
    'Fri, Feb 21, 2025 10-45-33 AM.txt',
    'Fri, Feb 21, 2025 11-13-00 AM.txt',
    'Fri, Feb 21, 2025 3-03-40 PM.txt',
    'Fri, Feb 21, 2025 3-40-19 PM.txt',
    'Thu, Feb 20, 2025 2-50-39 PM.txt'
    ]

output_filenames = [
    'Thu, Feb 20, 2025 5-42-37 PM.txt',
    'Fri, Feb 21, 2025 10-57-50 AM.txt',
    'Fri, Feb 21, 2025 11-27-17 AM.txt',
    'Fri, Feb 21, 2025 3-26-59 PM.txt',
    'Fri, Feb 21, 2025 3-53-44 PM.txt',
    'Thu, Feb 20, 2025 2-54-18 PM.txt'
    ]
thickness = 0.02

Images attached to this report
3954_20250311065107_aztec30201.png
General (General)
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MarcEisenmann - 22:39, Monday 10 March 2025 (3953)Get code to link to this report
restart after shutdown

[Marc, Takahashi]

I restarted PCI and BIGFOOT area, West end, old/new DGS without issues.

It seems the FC fan was on but could be restarted aswell.

FInally, we moved back the 2 shelves + large dessicator nearby IMC tube.

R&D (FilterCavity)
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MichaelPage - 22:18, Friday 07 March 2025 (3951)Get code to link to this report
Filter cavity RF synthesis (particularly green lock)
As I presented in the research meeting on 25-03-05, there was some issues with the green control RF electronics. Lately the limiting factor to long term squeezing operation is green lock stability. It seems to be coming from the unlock of the green mode cleaner, and when the error signal is inspected it is found to be in Q-phase, despite optimizing for I-phase during the daily activities. I decided to check the RF signals to see if it was an electronics issue. The relevant signals to compare are modulation (SHG EOM from DDS1 DAC0) and demodulation (GRMC DEMOD from DDS2 DAC2). Both of these signals are sent to ~ +14 dB RF amplification on the amplifier rack, though SHG EOM is annoying to unplug from the amplifier so I just measured it straight from the synthesizer box. I looked at the spectra of the signals. Modulation SHG EOM (first image) is fine, although the amplitude of the modulation is quite low due to the ongoing master clock issue. Demodulation GRMC demod has many noise peaks including a rather concerning one at ~ 250 MHz, about -20 dB below the main signal (shown below before sending to +14 dB RF amp).

Fig-1

Fig-1

I then looked at the signals in the oscilloscope to see if the phase difference stays stable over a long time. I found that GRMC demod drifts with respect to SHG EOM. The separation changes from 3.8 ns to 2.8 ns after about 40 minutes of waiting. I checked SHG EOM vs SHG DEMOD and in that case it works fine, no significant change.

Fig-1

Fig-1

Looking at the PDH signal, I locked the SHG and then checked GRMC error signal. It seems to noticeably change in shape over roughly the same timescale. So it looks like the RF signal is not very good. There was some discussion in the research meeting that the frequencies are not exactly the same and this may lead to some slight phase error. There could also be a possibility that the PLL of the DDS board is broken leading to desync between boards. I checked an unused port on DDS2 DAC0. In this case, the spectrum looks better than DAC2. The main peak has +4 dB signal and there is only a faint noise peak at -60 dBm. After sending through the RF amplifier I see some 2f and 3f spurious peaks but these are not as large.

Fig-1

Fig-1

I then looked at SHG EOM vs DDS2 DAC0 on the oscilloscope and there was no significant change in phase delay after 40 min of waiting. So it looks like DDS2 DAC2 is emitting a dirty signal.

Fig-1

Fig-1

I changed the GRMC DEMOD channel to DDS2 DAC0.

Also, someone took my wiper bucket and the other one next to the IMC vacuum tube had a broken seal so couldn't be used. I took one from on top of a toolbox near the end of the West tunnel.
Images attached to this report
3951_20250307141520_img1253dac2noisenoamp.jpg 3951_20250307141528_img1257shgeom.jpg 3951_20250307141538_img1260init.jpg 3951_20250307141546_img1264wait.jpg 3951_20250307141554_img1275dac0noamp.jpg 3951_20250307141606_img1277dac0amp.jpg 3951_20250307141612_img1282init.jpg 3951_20250307141617_img1284wait.jpg
General (General)
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MarcEisenmann - 19:01, Friday 07 March 2025 (3949)Get code to link to this report
moving table from ATC to BIGFOOT lab

[Marc, Shalika, Takahashi]

We moved the 2000*1200 table from ATC to BIGFOOT lab.

This table was used to store bulk scattering measurement, FC spare laser and some components of the RObert's linkage experiment.

They are all placed on a nearby empty optical table.

After moving the table, we reinstalled the IMC vacuum pipe close to the IMC end vacuum tank.

BIGFOOT (Thermal Compensation)
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ShalikaSingh - 23:25, Wednesday 05 March 2025 (3940)Get code to link to this report
Thermal simulation

The material of YVO4 was simulated using comsol. The heat distribution pattern was obtained. I then computed the retardation of each point in 3D and then multplied the Jones matrix of each data point along the depth of the plate. This resulted in a cumulative retardation of the plate. The Fig 1 shows the heat distribution of the plate, and Fig 2 is the retardation map obtained. The relevant specs are mentioned on the image.

The retardation was calculated assuming beam propagation along c axis of the crystal. Also, during retardation calculation I consider both the change in retardation due to heat and thermal expansion.

Images attached to this report
3940_20250305124424_yvo4heatmap.png 3940_20250305124429_yvo42dretardationmap.png
General (Test)
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SatoruIkeda - 22:34, Wednesday 05 March 2025 (3941)Get code to link to this report
Embedded Image Testing

If you want to embed images, you can do so by following these steps

1. Upload the image.

2. Select Plane text in the Choose editor menu.

3. Copy and paste the following line and change alt, src, height, and width.

Fig-1

4. Finally, select CKEditor (HTML) to embed the image.

Comments related to this report
ShalikaSingh - 22:31, Wednesday 05 March 2025 (3943)

The line to add is

<img alt="Fig-1" src="https://gw-elog.mtk.nao.ac.jp/osl/uploads/3931_20250304153753_noninvopamplcseries.png" style="height:300px; width:400px" />

where this 'https://gw-elog.mtk.nao.ac.jp/osl/uplods/3931_20250304153753_noninvopamplcseries.png' is the address you get on opening the image in new tab

The purpose is that pictures in comments should be visible in the main entry.

 

 

 

 

 

 

General (Test)
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ShalikaSingh - 22:31, Wednesday 05 March 2025 (3943)Get code to link to this report
Comment to Embedded Image Testing (Click here to view original report: 3941)

The line to add is

<img alt="Fig-1" src="https://gw-elog.mtk.nao.ac.jp/osl/uploads/3931_20250304153753_noninvopamplcseries.png" style="height:300px; width:400px" />

where this 'https://gw-elog.mtk.nao.ac.jp/osl/uplods/3931_20250304153753_noninvopamplcseries.png' is the address you get on opening the image in new tab

The purpose is that pictures in comments should be visible in the main entry.

 

 

 

 

 

 

BIGFOOT (Readout)
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ShalikaSingh - 22:28, Wednesday 05 March 2025 (3937)Get code to link to this report
Comment to Modulation depth of EOM at 45 degree relative to input polarization (Click here to view original report: 3931)

The spectrum of laser modulation at 2.5Vp-p from moku, with harmonics.

Fig-1

Images attached to this comment
3937_20250305090356_sa20250305.png
BIGFOOT (Readout)
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ShalikaSingh - 22:22, Wednesday 05 March 2025 (3938)Get code to link to this report
Comment to Modulation depth of EOM at 45 degree relative to input polarization (Click here to view original report: 3931)


Yesterday, I had noted the PSD units of voltage. As the ratio power is Outputpower/Input power, I redid measurements to take into account only Vp-p. In the following plot you can see the saturation after 2.5V or so. ]

Fig-1


Images attached to this comment
3938_20250305094839_transmissioncharacteristics20250305.png
BIGFOOT (Cavity)
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MarcEisenmann - 20:03, Wednesday 05 March 2025 (3939)Get code to link to this report
Characterization of Radius of curvature of unknown SignmaKoki mirrors

[Kohara-san, Marc]

The mirrors initially planned to be used for this cavity disappeared...

I found some other possible ones in the large dessicators : PSCM99.99Q25.4C08-r300-Y1-1D-2.8D and PSCM98Q25.4C08-r300-Y1-1D-2.8D

It is custom made by Sigma Koki who refuses to tell me their parameters if I can not guess the purchaser...

After some times, I found also some partial information about them. They were purchased around 2013 and characterized in october 2013.

They have HR reflectivity of either 99.99% and 98% (to be checked) and AR reflectivity of 0.1%.

With Kohara-san, we used the motorized microscope MITAKA NH-3SP to measure their radius of curvature.

We measureed HR RoC of about 0.3m and AR RoC flat with a wedge.

HR side is where the arrow on the barrel is pointing towards.

The arrow itself seems to be aligned with the wedge and minimal thickness of the wedge is close to the arrow.

There are also some characterization sheets that I will upload to the wiki.

Detailled measurement are below.

The second line of the japanese characters is the RoC in um.

For each component, except if indicated otherwise, the first measurement is HR side (arrow pointing up) and second one AR side (arrow pointing down)

__________________________________

XY cross measurement
1000um pitch
XY 10000um range


99_1
  ���S���W:  X=5832.79  Y=8090.89  Z=325044.694
  ���̔��a�i�ʂ��j: 300974.56
  �^���x�i�ʂ��j: 3.47

  ���S���W:  X=574928.39  Y=486026.38  Z=-2147483.648
  ���̔��a�i�ʂ��j: -2147483.65
  �^���x�i�ʂ��j: 1.41


99_2
  ���S���W:  X=9413.71  Y=3922.84  Z=324641.935
  ���̔��a�i�ʂ��j: 300517.78
  �^���x�i�ʂ��j: 3.73

  ���S���W:  X=343179.78  Y=-88975.30  Z=-2147483.648
  ���̔��a�i�ʂ��j: -2147483.65
  �^���x�i�ʂ��j: 2.80

98_1
  ���S���W:  X=9824.51  Y=5359.10  Z=327495.068
  ���̔��a�i�ʂ��j: 303392.40
  �^���x�i�ʂ��j: 6.60

  ���S���W:  X=11790.56  Y=810305.67  Z=-2147483.648
  ���̔��a�i�ʂ��j: -2147483.65
  �^���x�i�ʂ��j: 1.32

98_2
spherical surface
1000um pitch
  ���S���W:  X=8820.63  Y=11065.34  Z=328849.728
  ���̔��a�i�ʂ��j: 304724.39
  �^���x�i�ʂ��j: 9.54
pitch 100um
  ���S���W:  X=8810.48  Y=11089.98  Z=329527.916
  ���̔��a�i�ʂ��j: 305403.18
  �^���x�i�ʂ��j: 29.23
45degree rotation
  ���S���W:  X=11973.85  Y=15667.13  Z=326057.078
  ���̔��a�i�ʂ��j: 301946.05
  �^���x�i�ʂ��j: 3.99
1000um pitch
  ���S���W:  X=48816.30  Y=278499.69  Z=-2147483.648
  ���̔��a�i�ʂ��j: -2147483.65
  �^���x�i�ʂ��j: 4.06