Summary

- The breadboard has a resonance at 1.2kHz. The resonant freq may be chagned depending on the additional mass and the boundary condition.

- There is no forest of resonances at around 1kHz. A couple of resonances It mainly starts at 5kHz.

- The PZT mirrors (CM1/CM2) have the resonance at 10kHz as I saw in the past PZT test.

Motivation

- Zach's LLO OMC characterization revealed that the OMC length signals have forest of spikes at 400-500Hz and 1kHz regions.

- He tried to excite these peaks assuming they were coming from mechanical systems. It was hard to excite with the OMC PZT,
but actuating the OMCS slightly excited them. (This entry)

Because the OMC length control loop can't suppress these peaks due to their high frequency and high amplitude, they limit
the OMC residual RMS motion. This may cause the coupling of the OMC length noise into the intensity of the transmitted light.
We want to eventually suppress or eliminate these peaks.

By this vibration test we want to:

- confirm whether the peaks are coming from the OMC or not.
- identify what is causing the peaks if they are originated from the OMC
- correct experimental data for comparison with FEA

Method

- Place a NOLIAC PZT on the object to be excited.
- Look at the actuation signal for the OMC locking to find the excited peaks.

Results

Breadboard

- This configuration excited the modes between 800-1.2kHz most (red curve). As well as the others, the structures above 5kHz are also excited.

- The mode at 1.2kHz was suspected to be the bending mode of the breadboard. To confirm it, metal blocks (QPD housing and a 4" pedestal rod)
  were added on the breadboard to change the load. This actually moved (or damped) the mode (red curve).

- Note that the four corners of the breadboard were held with a PEEK pieces on the transport fixture.
  In addition, the installed OMC has additional counter balance mass on it.
  This means that the actual resonant frequency can be different from the one seen in this experiment. This should be confirmed with an FEA model.
  The breadboard should also exhibit higher Q on the OMCS due to its cleaner boundary condition. 

DCPD / QPD

- Vibration on the DCPDs and QPDs mainly excited the modes above 3kHz. The resonances between 3 to 5kHz are observed in addition to the ubiquitous peaks above 5kHz.
  So are these coming from the housing? This also can be confirmed with an FEA model.

- Some excitation of the breadboard mode at 1.2kHz is also seen.

CM1/CM2 (PZT mirrors)

- It is very obvious that there is a resonance at 10kHz. This was also seen in the past PZT test. This can be concluded that the serial resonance of the PZT and the curved mirror.
- There is another unknown mode at around 5~6kHz.

- Some excitation of the breadboard mode at 1.2kHz is also seen.

FM1/FM2 and Peripheral prism mirrors (BSs and SMs)

- They are all prism mirrors with the same bonding method.

- The excitation is concentrated above 5kHz. Small excitation of the breadboard mode at 1.2kHz is also seen. Some bump ~1.4kHz is also seen in some cases.

Beam dumps

- The excitation is quite similar to the case of the peripheral mirrors. Some bump at 1.3kHz.

Other tapping test of the non-OMC object on the table

- Transport fixture: long side 700Hz, short side 3k. This 3K is often seen in the above PZT excitation

- Fiber coupler: 200Hz and 350Hz.

- The beam splitter for the back scattering test: 900Hz

Improved vibration measurement of the OMC

Improvement

- Added some vibration isolation. Four 1/2" rubber legs were added between the OMC bread board and the transport fixture (via Al foils).
  In order to keep the beam height same, 1/2" pedestal legs were removed.

- The HEPA filter at the OMC side was stopped to reduce the excitation of the breadboard. It was confirmed that the particle level for 0.3um
  was still zero only with the other HEPA filter.

Method

- Same measurement method as the previous entry was used.

Results

Breadboard

- In this new setup, we could expect that the resonant frequency of the body modes were close to the free resonances, and thus the Q is higher.
  Noise is much more reduced and it is clear that the resonance seen 1.1kHz is definitely associated with the body mode of the breadboard (red curve).

  As a confirmation, some metal objects were placed on the breadboard as tried before. This indeed reduced the resonant frequency (blue curve).

DCPD / QPD

- Vibration on the DCPDs and QPDs mainly excited the modes above 2~3kHz.
  In order to check if they are coming from the housing, we should run FEA models.

- Some excitation of the breadboard mode at 1.1kHz was also seen.

CM1/CM2 (PZT mirrors)

- Baseically excitation was dominated by the PZT mode at 10kHz. Some spourious resonances are seen at 4~5kHz but I believe this is associated with the weight placed on the excitation PZT.

FM1/FM2 and peripheral prism mirrors (BSs and SMs)

- The modes of the FMs are seen ~8k or 12kHz. I believe they are lowered by the weight for the measurement. In any case, the mode frequency is quite high compared to our frequency region of interest.

- As the prism resonance is quite high, the excitation is directly transmitted to the breadboard. Therefore the excitation of the non-cavity caused similar effect to the excitation on the breadboard.
  In fact what we can see from the plot is excitation of the 1.1kHz body mode and many high frequency resonances.

Beam dumps

- This is also similar to the case of the peripheral mirrors.

Prisms

Fundamental: 12.3kHz Secondary: 16.9kHz

DCPDs

Fundamental: 2.9kHz Secondary: 4.1kHz

QPDs

Fundamental: 5.6kHz Secondary: 8.2kHz

Structural analysis of the PZT mirror with COMSOL.

Inline figures: Eigenmodes which involves large motion of the tombstone. In deed 10kHz mode is not the resonance of the PZT-mirror joint, but the resonance of the tombstone.

Attached PDF: Simulated transfer function of the PZT actuation. In order to simulate the PZT motion, boundary loads on the two sides of the PZT were applied with opposite signs.
10kHz peak appears as the resonance of the tombstone dominates the mirror motion. At 12kHz, the PZT extension and the backaction of the tombstone cancells each other and
the net displacement of the mirror becomes zero.

https://awiki.ligo-wa.caltech.edu/wiki/EOM_Mount_Stability

A simple COMSOL simulation was run to see how the PZT deforms as the voltage applied.

Use the geometry of the ring PZT which is used in the OMCs -  NAC2124 (OD 15mm, ID 9mm, H 2mm)
The material is PZT-5H (https://bostonpiezooptics.com/ceramic-materials-pzt) which is predefined in COMSOL and somewhat similar to the one used in NAC2124 (NCE51F - http://www.noliac.com/products/materials/nce51f/)
The bottom surface of the ring was electrically grounded (0V), and mechanically fixed.
Applied 100V between the top and bottom.

As performed in the ELOG 202, the PZTs of the OMC 002 were tested.

DC response was measured by sweeping each PZT with 0-150V triangular voltage at 11Hz. Acquire 0.2sec of the tie series using an oscilloscope to get the PDH error, cavity transmission, and the sweep signal.

The voltage where the tranmission peaks were observed were fitted were recorded. One fringe corresponds to the displacement of 532nm. So the displacement and the applied volatagewere fitted witha linear function.

This gave the PZT response for PZT1 and PZT2 to be 14.9nm/V and 14.4nm/V.

AC response was measured with SR785. The PZT was shaken with 1~50mVpp signal with the DC offset of 5V while the OMC was locked with the feedback to the laser fast PZT. The transfer function from the applied PZT voltage to the servo output were measured. The closed loop TF was also measured to remove the effect of the servo control.  The DC levels of the responses were calibrated using the values above.

[Koji Stephen]

The four PZT sub-assemblies were glued in the gluing fixtures. There were two original gluing fixtures and two additional modified fixtures for the in-situ bonding at the repair of OMC(002).

- Firstly, we checked the fitting and arrangements of the components without glue. The component combinations are described in ELOG 329.
- Turned on the oven toaster for the cure test (200F).
- Then prepared EP30-2 mixture (7g EP30-2 + 0.35g glass sphere).
- The test specimen of EP30-2 was baked in the toaster oven. (The result shows perfect curing (no stickyness, no finger print, crisp fracture when bent)
- Applied the bond to the subassemblies.
- FInally the fixtures were put in airbake Oven A. We needed to raise one of the tray with four HSTS balance weights (Attachment 2).

[Stephen, Koji]

As mentioned in eLOG 331, either increased thermal cycling or apparent improvements in cured EP30-2 strength led to fracture of curved mirrors at unintended locations of bonding to the PEEK fixture parts.

The issue and intended resolution is summarized in the attached images (2 different visualizations of the same item).

Redline has been posted to D1600336-v3.

Drawing update will be processed shortly, and parts will be modified to D1600336-v4.

I helped to complete the 5th OMC Transport Fixture. It was built at the 40m clean room and brought to the OMC lab. The fixture hardware (~screws) were also brought there.

The AL metal bracket was replaced with a PEEK version.

Attachments 1/2: Before the replacement. The photos show how the cables are arranged.

Attachment 3: How the replacement work is going. The 1/4-20 screws were super tight. Once the connectors were removed, an Allen key was inserted to a hole so that the 1/4-20 on the short sides were removed by closing Allen key arms. For the screws on the longer sides, the same technique can be applied by using three Allen keys. This time none of the screws/cable pegs were wasted. The clothes were used to protect the breadboard from any impact of the action.

Attachments 4/5: Final state.

OMC #1 repair has been 100% done

---------

We still have 4 correct cable pegs and many 1/4-20 BHSCs for OMC #4.

Yesterday, we noticed that we could not close the transport fixture for OMC #4. We could not fully rotate the knobs of the locks. Today, I took the hooks from the functioning locks of the spare transport fixture.

It turned out that the default dimension of the lock seemed too tight. The functioning one has the through holes elongated by a file or something. This modification will be necessary for future transport fixtures.

The transport fixture was brought to the 40m clean room to use as an assembly reference.

Inserted 4-40 and 2-56 helicoils into the DCPD/QPD housings for the 4th OMC. The retainer caps were also fastened to the housings.

EDIT (ZK): All the plots here were generated using my MATLAB cavity modeling tool, ArbCav. The utility description is below. The higher-order mode resonance plots are direct outputs of the function. The overlap plots were made by modifying the function to output a list of all HOM resonant frequencies, and then plotting the closest one as a function of cavity length. This was done for various values of highest mode order to consider, as described in the original entry.

Description:

This function calculates information about an arbitrary optical cavity. It can plot the cavity geometry, calculate the transmission/reflection spectrum, and generate the higher-order mode spectrum for the carrier and up to 2 sets of sidebands.

The code accepts any number of mirrors with any radius of curvature and transmission, and includes any astigmatic effects in its output.

As opposed to the previous version, which converted a limited number of cavity shapes into linear cavities before performing the calculation, this version explicitly propagates the gouy phase of the beam around each leg of the cavity, and is therefore truly able to handle an arbitrary geometry.

----------------Original Post----------------

I expressed concern that arbitrarily choosing some maximum HOM order above which not to consider makes us vulnerable to sitting directly on a slightly-higher-order mode. At first, I figured the best way around this is to apply an appropriate weighting function to the computed HOM frequency spacing. Since this will also have some arbitrariness to it, I have decided to do it in a more straightforward way. Namely, look at the spacing for different values of the maximum mode number, n_max, and then use this extra information to better select the length.

Assumptions:

• The curved mirror RoC is the design value of 2.50±0.025 m
• The ±9 MHz sidebands will have ~1% the power of the other fields at the dark port. Accordingly, as in Sam's note, their calculated spacing is artificially increased by 10 linewidths.
• The opening angle of 4º is FIXED, and the total length is scaled accordingly

Below are the spacing plots for the bowtie (flat-flat-curved-curved) and non-bowtie (flat-curved-flat-curved) configurations. Points on each line should be read out as "there are are no modes of order N or lower within [Y value] linewidths of the carrier TEM₀₀ transmission", where N is the n_max appropriate for that trace. Intuitively, as more orders are included, the maxima go down, because more orders are added to the calculation.

*All calculations are done using my cavity simulation function, ArbCav. The mode spacing is calculated for each particular geometry by explicitly propagating the gouy phase through each leg of the cavity, rather than by finding an equivalent linear cavity*

Since achievable HOM rejection is only one of the criteria that should be used to choose between the two topologies, the idea is to pick one length solution for EACH topology. Basically, one maximum should be chosen for each plot, based on how how high an order we care about.

Bowtie

For the bowtie, the n_max = 20 maximum at L = 1.145 m is attractive, because there are no n < 20 modes within 5 linewidths, and no n < 25 modes within ~4.5 linewidths. However, this means that there are also n < 10 modes within 5 linewidths, while they could be pushed (BLUE line) to ~8.5 linewidths at the expense of proximity to n > 15 modes.

Therefore, it's probably best to pick something between the red and green maxima: 1.145 m < L < 1.152 m.

By manually inspecting the HOM spectrum for n_max = 20, it seems that L = 1.150 m is the best choice. In the HOM zoom plot below and the one to follow, the legend is as follows

• BLUE: Carrier
• GREEN: +9 MHz
• RED: -9 MHz
• CYAN: +45 MHz
• BLACK: -45 MHz

Non-bowtie

Following the same logic as above, the most obvious choice for the non-bowtie is somewhere between the red maximum at 1.241 m and the magenta maximum at 1.248 m. This still allows for reasonable suppression of the n < 10 modes without sacrificing the n < 15 mode suppression completely.

Upon inspection, I suggest L = 1.246 m

I reiterate that these calculations are taking into account modes of up to n ~ 20. If there is a reason we really only care about a lower order than this, then we can do better. Otherwise, this is a nice compromise between full low-order mode isolation and not sitting directly on slightly higher modes.

RoC dependence

One complication that arises is that all of these are highly dependent on the actual RoC of the mirrors. Unfortunately, even the quoted tolerance of ±1% makes a difference. Below is a rendering of the RED traces (n_max = 20) in the first two plots, but for R varying by ±2% (i.e., for R = 2.45 m, 2.50 m, 2.55 m).

The case for the non-bowtie only superficially seems better; the important spacing is the large one between the three highest peaks centered around 1.24 m.

Also unfortunately, this strong dependence is also true for the lowest-order modes. Below is the same two plots, but for the BLUE (n_max = 10) lines in the first plots.

Therefore, it is prudent not to pick a specific length until the precise RoC of the mirrors is measured.

Conclusion

Assuming the validity of looking at modes between 10 < n < 20, and that the curved mirror RoC is the design value of 2.50 m, the recommended lengths for each case are:

• Bowtie: L_RT = 1.150 m
• Non-bowtie: L_RT = 1.246 m

 HOWEVER, variation within the design tolerance of the mirror RoC will change these numbers appreciably, and so the RoC should be measured before a length is firmly chosen.

EDIT 2 (ZK): As with the previous post, all plots and calculations here are done with my MATLAB cavity modeling utility, ArbCav.

EDIT (ZK): Added input q parameters for OMMT 

I found the nice result that the variation in the optimal length vs. variation in the mirror RoC is roughly linear within the ±1% RoC tolerance. So, we can choose two baseline mode definitions (one for each mirror topology) and then adjust as necessary following our RoC measurements.

Bowtie

For R = 2.5 m, the optimal length (see previous post) is L_RT = 1.150 m, and the variation in this is dL_RT/dR ~ +0.44 m/m.

Here is an illustration of the geometry:

The input q parameters, defined at the point over the edge of the OMC slab where the beam first crosses---(40mm, 150mm) on the OptoCad drawing---are, in meters:

• q_ix = - 0.2276 + 0.6955 i
• q_iy = - 0.2276 + 0.6980 i

Non-bowtie

For R = 2.5 m, the optimal length is L_RT = 1.246 m, and the variation in this is also dL_RT/dR ~ +0.44 m/m.

Geometry:

q parameters, defined as above:

• q_ix = - 0.0830 + 0.8245 i
• q_iy = - 0.0830 + 0.8268 i

Here is the proposed RoC measurement setup. Koji tells me that this is referred to as "Anderson's method".

We would like to use a linear cavity to measure the RoC of the curved mirrors independently (before forming the ring cavity), since the degeneracy of HOMs will make the fitting easier.

• An NPRO is PDH locked to a linear cavity formed of a high-quality flat mirror on one end, and the OMC curved optic on the other.
• A second, broadband EOM is placed after the first one, and its frequency is swept with a VCO to generate symmetric sidebands about the carrier
• A TRANS RFPD's signal is demodulated at the secondary EOM frequency, to give a DC signal proportional to HOM transmission
• This HOM scan is fit to a model, with RoC the free parameter. Since there are two sidebands, the HOM spectrum of the model must be folded about the carrier frequency.
• To get a good signal, we should slightly misalign the input beam, allowing for higher overlap with HOMs.

If we decided that the symmetric sidebands are too unwieldy, or that we have issues from sidebands on sidebands, we can accomplish the same style measurement using an AOM-shifted pickoff of the pre-PDH EOM beam. The advantage of the former method is that we don't have to use any polarization tricks.

Nic Smith sent me a bunch of elog lists where the results of the mode scan can be found.

From Nic:

There have been many mode scan analyses done at LLO:
http://ilog.ligo-la.caltech.edu/ilog/pub/ilog.cgi?group=detector&date_to_view=06/07/2008&anchor_to_scroll_to=2008:06:07:20:55:41-jrsmith
http://ilog.ligo-la.caltech.edu/ilog/pub/ilog.cgi?group=detector&date_to_view=06/16/2008&anchor_to_scroll_to=2008:06:16:17:47:11-waldman
http://ilog.ligo-la.caltech.edu/ilog/pub/ilog.cgi?group=detector&date_to_view=08/06/2009&anchor_to_scroll_to=2009:08:06:12:23:16-kissel
http://ilog.ligo-la.caltech.edu/ilog/pub/ilog.cgi?group=detector&date_to_view=09/25/2009&anchor_to_scroll_to=2009:09:25:20:57:47-kate

We didn't do as much of this at LHO. At some point we were trying to figure out how the arm cavity mode was different from the carrier mode:
http://ilog.ligo-wa.caltech.edu/ilog/pub/ilog.cgi?group=detector&date_to_view=04/17/2009&anchor_to_scroll_to=2009:04:17:23:15:05-kawabe
http://ilog.ligo-wa.caltech.edu/ilog/pub/ilog.cgi?group=detector&date_to_view=03/27/2009&anchor_to_scroll_to=2009:03:27:21:38:14-kawabe
http://ilog.ligo-wa.caltech.edu/ilog/pub/ilog.cgi?group=detector&date_to_view=02/18/2009&anchor_to_scroll_to=2009:02:18:20:15:00-kawabe

Here's a long mode scan that was done, and the data is attached to the elog, but none of the amplitudes are analyzed.
http://ilog.ligo-wa.caltech.edu/ilog/pub/ilog.cgi?group=detector&date_to_view=07/08/2009&anchor_to_scroll_to=2009:07:08:17:02:19-nicolas

Here is a more detailed version of the setup, so that we can gather the parts we will need.

Parts list:

• Optics, etc.:
  • 1 NPRO
  • 2 QWP
  • 3 HWP
  • 2 PBS
  • 2 EOM (at least one broadband)
  • 2 RFPD (at least one very-high-bandwidth for TRANS, e.g., 1611)
  • 1 CCD camera
  • OMC curved mirrors to be tested
  • 1 low-loss flat reference mirror with appropriate transmission (e.g., G&H, ATF, etc.)
  • ~3 long-ish lenses for MMT, EOM focusing
  • ~2 short lenses for PD focusing
  • 1 R ~ 80% power splitter for TRANS (can be more or less)
  • ~7 steering mirrors
  • ~3 beam dumps
  • Mounts, bases, clamps, hardware
• Electronics:
  • 1 fixed RF oscillator (e.g., DS345, etc.)
  • 1 VCO (e.g., Marconi, Tektronix, etc.)
  • 2 Minicircuits RF mixers
  • 2 Minicircuits RF splitters
  • 2 SMA inline LPFs
  • Locking servo (SR560? uPDH? PDH2?)
  • Some digital acquisition/FG system
  • Power supplies, wiring and cabling.

Based on Zach's experiment design, I wrote up a bit more detailed optical layout for the mirror test.

Item: Newfocus Fast PD
Qty.: 1
Mirror: Newfocus Fast PD
Mount: Post
Post: Post Holder (Newfocus)
Fork: Short Fork

Item: Thorlabs RF PD
Qty.: 1
Mirror: Thorlabs RF PD
Mount: Post
Post: Post Holder (Newfocus)
Fork: Short Fork

Item: Newfocus Broadband
Qty.: 1
Mirror: Newfocus EOM
Mount: Newfocus
Post: Custom Mount? or Pedestal X"?
Fork: Short Fork

Item: Newfocus Resonant
Qty.: 1
Mirror: Newfocus EOM
Mount: Newfocus
Post: Custom Mount? or Pedestal X"?
Fork: Short Fork

Item: ND Filter
Qty.: 2
Mirror: -
Mount: Thorlabs FIlter Holder
Post: Pedestal X"
Fork: Short Fork

Item: New Port Lens Kit 1"
Qty.: 1

Item: Thorlabs ND Kit
Qty.: 1

Item: Plano Convex Lens
Qty.: f=100, 100, 150, 200
Mirror: New Port (AR)
Mount: Thorlabs
Post: Post Holder (Newfocus)
Fork: Short Fork

Item: Bi-Convex Lens
Qty.: 75
Mirror: New Port (AR)
Mount: Post
Post: Post Holder (Newfocus)
Fork: Short Fork

Item: Flipper Mirror
Qty.: 1
Mirror: CVI Y1-10XX-45P
Mount: New Focus Flipper
Post: Pedestal X"
Fork: Short Fork

Item: Steering Mirror
Qty.: 8
Mirror: CVI Y1-10XX-45P
Mount: Suprema 1inch
Post: Pedestal X"
Fork: Short Fork

Item: PBS
Qty.: 3
Mirror: PBS 1inch BK7
Mount: Newport BS Mount
Post: Pedestal X"
Fork: Short Fork

Item: Knife Edge Beam Dump
Qty.: 4
Mirror: Thorlabs Knife Edge
Mount: Post
Post: Post Holder (Newfocus)
Fork: Short Fork

Item: Half Wave Plate
Qty.: 4
Mirror: CVI QWPO-
Mount: CVI
Post: Pedestal X"
Fork: Short Fork

Item: Quater Wave Plate
Qty.: 3
Mirror: CVI QWPO-
Mount: CVI
Post: Pedestal X"
Fork: Short Fork

Item: OMC Curved Mirror
Qty.: 2
Mirror: -
Mount: Suprema 0.5inch + Adapter
Post: Pedestal X"
Fork: Short Fork

Item: Prism Holder
Qty.: 1
Mirror: OMC Prism
Mount: Newport Prism Mount
Post: Pedestal X"
Fork: Short Fork

Item: CCD
Qty.: 1
Mirror: Thorlabs?
Mount: Thorlabs?
Post: Post Holder (Newfocus)
Fork: Short Fork

EGE&G 2mm photodiode angle response measured by Sam T1100564-v1

• HWP set
  
  • Optics: CVI QWPO-1064-08-2-R10
  • Mount: New Focus #9401
  • Post: Pedestal 2.5inch
  • Returned: Oct 19, 2012 by KA
• QWP set
  
  • Optics: CVI QWPO-1064-05-4-R10
  • Mount: New Focus #9401
  • Post: Pedestal 2.5inch
  • Returned: Jan 17, 2013 by KA
• Faraday set
  
  • Optics: OFR IO-2-YAG-HP Returned: Mar 21, 2013 by KA
  • Mount: New Focus #9701 Returned: Apr 17, 2013 by KA
  • Post: Pedestal (1.5+0.25inch)x2
• Steering Mirror 1
  
  • Optics: CVI Y1-1037-45S
  • Mount: Newport Ultima U100-AC
  • Post: Pedestal 3inch
  • Returned: Jan 17, 2013 by KA
• Steering Mirror 2
  
  • Optics: CVI Y1-1037-45P
  • Mount: Newport Ultima U100-AC
  • Post: Pedestal 3inch
  • Returned: Jan 17, 2013 by KA
• Steering Mirror 3
  • Optics: New Focus 5104
  • Mount: Newport Ultima U100-AC
  • Post: Pedestal 3inch
  • Returned: Jan 17, 2013 by KA
• Prism Mount
  
  • Mount: Thorlabs KM100P+PM1 2014/7/17
  • Post: Pedestal 1.5+1+1/8inch
• 0.5" Mirror Mount
  
  • Mount: Newport U50-AReturned: Apr 17, 2013 by KA
  • Mount: Newport U50-A 2014/7/17
  • Post: Pedestal 1.5+2inch
• Black Glass Beam Dump
  • Optics: 1" sq. schott glass x3
  • Mount: Custom Hexagonal 1"
  • Post: Pedestal 3inch
• PBS Set
  
  • 05BC16PC.9 (PBS 1064 1000:1)
    
  • Mount: Custom Aluminum
  • Returned: Jan 17, 2013 by KA
• Lenses
  
  • KBX067.AR33 f=125mm
  • KPX106 f=200mm, KPX109 f=250mm unknown-coat
  • KPX088.AR33 f=75mm
  • KPX094.AR33 f=100mm
  • PLCX-C (BK7) 3863 (f=7.5m), 2060 (f=4.0m), 1545 (f=3.0m), 1030 (f=2.0m) non-coat
  • PLCX-UV (FS) 30.9 non-coat(!) f=60mm
  • Returned: Jan 17, 2013 by KA
• Pedestals
  
  • 1/4" x5, 1/8" x3, Returned: Jan 17, 2013 by KA
  • 0.5" x1, 1.5" x1

Another loan from the 40m on Oct 17th, 2012

• Minicircuits
  
  • Splitter ZFSC-2-5 x2
  • Filter SLP-1.9 x2 / BLP-1.9 x1/2 / SLP-5 x1
  • Returned: Jan 17, 2013 by KA
• Connectors / Adaptors
  
  • SMA TEE x1 / SMA 50Ohm x 1 / BNC T x 10, Returned: Jan 17, 2013 by KA
  • SMA TEE x1 / SMA 50Ohm x 1Returned: May 20, 2013 by KA
• Pomona Box x1, Returned: Jan 17, 2013 by KA
• Pomona Box x1
• Power supply for New Focus Fast PD made by Jamie R Returned: Apr 17, 2013 by KA
• BS-1064-50-1037-45S / Newport U100-A mount / 1"+2" Pedestal, Returned: Jan 17, 2013 by KA
• BS-1064-50-1025-45P / Newport U100-A mount / 3/4" post + Base, Returned: Jan 17, 2013 by KA
• BNC cable 21ft x2, Returned: Jan 17, 2013 by KA
• SMA Cable 6ft

Another loan from the 40m on Nov 21th, 2012

• Mounting Base Thorlabs BA-2 x 17
• Mounting Posts (phi=3/4", L=2.65", normal x15, and 1/4"-20 variant x2)

Yet another loan from the 40m on Jan 16th, 2013

• V-groove Mounting Bases Custom. Qty.2Returned: Feb 25, 2013 by KA

Loan from ATF

32.7MHz EOM+Tilt aligner
Thorlabs Broadband EOM+Tilt aligner
Forks x 5Returned: Feb 25, 2013 by KA
JWIN Camera x 2

The RoC test setup has been built on the optical table at ATF.

The cavity formed by actual OMC mirrors have been locked.

The modulation frequency of the BB EOM was swept by the network analyzer.
A peak at ~30MHz was found in the transfer function when the input beam was misaligned and clipping was introduced at the transmission PD.
Without either the misalignment or the clipping, the peak disappears. Also the peak requires these imperfections to be directed in the same way
(like pitch and picth, or yaw and yaw). This strongly suggests that the peak is associated with the transverse mode.

The peak location was f_HOM = 29.79MHz. If we consider the length of the cavity is L=1.20m, the RoC is estimated as

RoC = L / (1 - Cos[f_HOM/(c/2/L) * PI]^2)

This formula gives us the RoC of 2.587 m.

I should have been able to find another peak at f_FSR-f_TMS. In deed, there was the structure found at 95MHz as expected.
However, the peak was really weak and the location was difficult to determine as it was coupled with the signal from residual RFAM.

The particle level in the clean booth was occasionally measured. Every measurement showed "zero".

To be improved:

• The trans PD is 1801 which was found in ATF with the label of the 40m. It turned out that it is a Si PD.
  I need to find an InGaAs PD (1811, 1611, or my BBPD) or increase the modulation, or increase the detected light level.
  (==> The incident power on 1810 increased. Oct 17)
• The BS at the transmission is actually Y1-45P with low incident angle. This can be replaced by 50% or 30% BS to increase the light on the fast PD.
  (==> 50% BS is placed. Oct 17)
• I forgot to put a 50ohm terminator for the BB EOM.
  (==> 50Ohm installed. Oct 17)
• A directional coupler could be used for the BBEOM signal to enhance the modulaiton by 3dB.
• The mode matching is shitty. I can see quite strong TEM20 mode.
• Use the longer cavity? L=1.8m is feasible on the table. This will move the peak at 27MHz and 56MHz (FSR=83MHz). Very promising.
  (==> L=1.8m, peak at 27MHz and 56MHz found. Oct.17)

Significant improvement has been achieved in the RoC measurement.

• The trans PD has much more power as the BS at the cavity trans was replaced by a 50% BS. This covers the disadvantage of using the a Si PD.
• The BB EOM has a 50Ohm terminator to ensure the 50Ohm termination at Low freq.
• The length of the cavity was changed from 1.2m to 1.8m in order to see the effect on the RoC measurement.

By these changes, dramatic increase of the signal to noise ratio was seen.

Now both of the peaks corresponds to the 1st-order higher-order modes are clearly seen.
The peak at around 26MHz are produced by the beat between the carrier TEM00 and the upper-sideband TEM01 (or 10).
The other peak at around 57MHz are produced by the lower-sideband TEM01 (or 10).

Peak fitting

From the peak fitting we can extract the following numbers:

• Cavity FSR (hence the cavity length)
• Cavity g-factor
• Approximate measure of the cavity bandwidth

Note that the cavity itself has not been touched during the measurement.
Only the laser frequency and the incident beam alignment were adjusted.

The results are calculated by the combination of MATLAB and Mathemaica. The fit results are listed in the PDF files.
In deed the fitting quality was not satisfactory if the single Lorentzian peak was assumed.
There for two peaks closely lining up with different height. This explained slight asymmetry of the side tails
This suggests that there is slight astigmatism on the mirrors (why not.)

The key points of the results:

- FSR and the cavity length: 83.28~83.31MHz / L=1.799~1.800 [m] (surprisingly good orecision of my optics placement!)

- Cavity g-factor: Considering the flatness of the flat mirror from the phase map, the measured g-factors were converted to the curvature of the curved mirror.
RoC = 2.583~4 [m] and 2.564~7 [m]. (Note: This fluctuation can not be explained by the statistical error.)
The mode split is an order of 10kHz. This number also agrees with the measurement taken yesterday.

If the curved mirror had the nominal curvature of 2.5m, the flat mirror should have the curvature of ~20m. This is very unlikely.

- Approximate cavity line width: FWHM = 70~80kHz. This corresponds to the finesse of ~500. The design value is ~780.
This means that the locking offset is not enough to explain the RoC discrepancy between the design and the measurement.

Wedge angle test

Result: Wedge angle of Prism A1: 0.497 deg +/- 0.004 deg

Principle:

o Attach a rail on the optical table. This is the reference of the beam.

o A CCD camera (Wincam D) is used for reading out spot positions along the rail.

o Align a beam path along the rail using the CCD.

o Measure the residual slope of the beam path. (Measurement A)

o Insert an optic under the test. Direct the first surface retroreflectively. (This means the first surface should be the HR side.)

o Measure the slope of the transmitted beam. (Measurement B)

o Deflection angle is derived from the difference between these two measurements.

Setup:

o An Al plate of 10" width was clamped on the table. Four other clamps are located along the rail to make the CCD positions reproducible.

o A prism (Coating A, SN: A1) is mounted on a prism mount. The first surface is aligned so that the reflected beam matches with the incident beam
with precision of +/-1mm at 1660mm away from the prism surface. ==> precision of +/- 0.6mrad

o In fact, the deflection angle of the transmission is not very sensitive to the alignment of the prism.
The effect of the misalignment on the measurement is negligible.

o Refractive index of Corning 7980 at 1064nm is 1.4496

Result:

Without Prism
Z (inch / mm), X (horiz [um] +/-4.7um), Y (vert [um] +/-4.7um)
0” / 0, -481.3, -165.1
1.375" / 34.925, -474.3, -162.8
3" / 76.2, -451.0, -186.0
4.375" / 111.125, -432.5, -181.4
6" / 152.4, -432.5, -181.4
7.375" / 187.325, -330.2, -204.6
9" / 228.6, -376.7, -209.3

With Prism / SN of the optic: A1
Z (inch / mm), X (horiz [um] +/-4.7um), Y (vert [um] +/-4.7um)
0” / 0, -658.3, -156.8
1.375" / 34.925, -744.0, -158.1
3" / 76.2, -930.0, -187.4
4.375" / 111.125, -962.6, -181.4
6" / 152.4, -1190.4, -218.6
7.375" / 187.325, -1250.9, -232.5
9" / 228.6, -1418.3, -232.5

Analysis:

Wedge angle of Prism A1: 0.497 deg +/- 0.004 deg

[Click for a sharper image]

A1
Horiz Wedge    0.497    +/-    0.004 deg
Vert Wedge      0.024    +/-    0.004 deg

A2
Horiz Wedge    0.549    +/-    0.004 deg
Vert Wedge      0.051    +/-    0.004 deg

A3
Horiz Wedge    0.463    +/-    0.004 deg
Vert Wedge      0.009    +/-    0.004 deg

A4
Horiz Wedge    0.471    +/-    0.004 deg
Vert Wedge      0.019    +/-    0.004 deg

A5
Horiz Wedge    0.458    +/-    0.004 deg
Vert Wedge      0.006    +/-    0.004 deg

KA's question:

Do you know how to apply this epoxy?
Do we need a plunger and a needle for this purpose?

Nic saids:

When we did it with Sam, I seem to remember just squirting some on some foil then dabbing it on with the needle.

Optical prisms 50pcs (A14+B12+C6+E18)
Curved Mirrors 25pcs (C13+D12)

Now it's enough for the first OMC (or even second one too).
Today's measurements all distributed in theta>0.5deg. Is this some systematic effect???
I should check some of the compeled mirrors again to see the reproducibility...

A1    Horiz Wedge    0.497039    +/-    0.00420005    deg / Vert Wedge     0.02405210    +/-    0.00420061    deg

A2    Horiz Wedge    0.548849    +/-    0.00419993    deg / Vert Wedge     0.05087730    +/-    0.00420061    deg
A3    Horiz Wedge    0.463261    +/-    0.00420013    deg / Vert Wedge     0.00874441    +/-    0.00420061    deg
A4    Horiz Wedge    0.471536    +/-    0.00420011    deg / Vert Wedge     0.01900840    +/-    0.00420061    deg
A5    Horiz Wedge    0.458305    +/-    0.00420014    deg / Vert Wedge     0.00628961    +/-    0.00420062    deg

B1    Horiz Wedge    0.568260    +/-    0.00419988    deg / Vert Wedge    -0.00442885    +/-    0.00420062    deg
B2    Horiz Wedge    0.556195    +/-    0.00419991    deg / Vert Wedge    -0.00136749    +/-    0.00420062    deg
B3    Horiz Wedge    0.571045    +/-    0.00419987    deg / Vert Wedge     0.00897185    +/-    0.00420061    deg
B4    Horiz Wedge    0.563724    +/-    0.00419989    deg / Vert Wedge    -0.01139000    +/-    0.00420061    deg
B5    Horiz Wedge    0.574745    +/-    0.00419986    deg / Vert Wedge     0.01718030    +/-    0.00420061    deg
E1    Horiz Wedge    0.600147    +/-    0.00419980    deg / Vert Wedge     0.00317778    +/-    0.00420062    deg
E2    Horiz Wedge    0.582597    +/-    0.00419984    deg / Vert Wedge    -0.00537131    +/-    0.00420062    deg
E3    Horiz Wedge    0.592933    +/-    0.00419982    deg / Vert Wedge    -0.01082830    +/-    0.00420061    deg

-------

To check the systematic effect, A1 and B1 were tested with different alignment setup.

A1    Horiz Wedge    0.547056    +/-    0.00419994    deg / Vert Wedge    0.0517442    +/-    0.00420061    deg
A1    Horiz Wedge    0.546993    +/-    0.00419994    deg / Vert Wedge    0.0469938    +/-    0.00420061    deg
A1    Horiz Wedge    0.509079    +/-    0.00420003    deg / Vert Wedge    0.0240255    +/-    0.00420061    deg

B1    Horiz Wedge    0.547139    +/-    0.00419994    deg / Vert Wedge    0.0191204    +/-    0.00420061    deg



 

Mirror T test

The mirror was misaligned to have ~2deg incident (mistakenly...) angle.

C1: Ptrans = 7.58uW, Pinc = 135.0mW => 56.1ppm

C1 (take2): Ptrans = 7.30uW, Pinc = 134.4mW => 54.3ppm

C2: Ptrans = 6.91uW, Pinc = 137.3mW => 50.3ppm

C3: Ptrans = 6.27uW, Pinc = 139.7mW => 44.9ppm

C4: Ptrans = 7.62uW, Pinc = 139.3mW => 54.7ppm

C5: Ptrans = 6.20uW, Pinc = 137.5mW => 45.1ppm

A1: Ptrans = 1.094mW, Pinc = 133.6mW => 8189ppm

In order to resume testing the curvatures of the mirrors, the same mirror as the previous one was tested.
The result looks consistent with the previous measurement.

It seems that there has been some locking offset. Actually, the split peaks in the TF@83MHz indicates
the existence of the offset. Next time, it should be adjusted at the beginning.

Curved mirror SN: C1
RoC: 2.5785 +/- 0.000042 [m]

Previous measurements
=> 2.5830, 2.5638 => sqrt(RoC1*RoC2) = 2.5734 m
=> 2.5844, 2.5666 => sqrt(RoC1*RoC2) = 2.5755 m

C1: RoC: 2.57845 +/− 4.2e−05m

C2: RoC: 2.54363 +/− 4.9e−05m

C3: RoC: 2.57130 +/− 6.3e−05m   

C4: RoC: 2.58176 +/− 6.8e−05m

C5: RoC 2.57369 +/− 9.1e−05m

==> 2.576 +/- 0.005 [m] (C2 excluded)

The thicknesses of the prism mirrors (A1-A5) were measured with micrometer thickness gauge.
Since the thickness of the thinner side (side1) depends on the depth used for the measurement,
it is not accurate. Unit in mm.

A1: Side1: 9.916, Side2: 10.066 => derived wedge angle: 0.43deg
A2: Side1: 9.883, Side2: 10.065 => 0.52
A3: Side1: 9.932, Side2: 10.062 => 0.38
A4: Side1: 9.919, Side2: 10.060 => 0.40
A5: Side1: 9.917, Side2: 10.058 => 0.40

Total (excluding C2, C7, C8): 2.575 +/- 0.005 [m]

New results

C6: RoC: 2.57321 +/− 4.2e-05m

C7: RoC: 2.56244 +/− 4.0e−05m ==> Polaris mount

C8: RoC: 2.56291 +/− 4.7e-05m ==> Ultima mount

C9: RoC: 2.57051 +/− 6.7e-05m

Previous results

C1: RoC: 2.57845 +/− 4.2e−05m

C2: RoC: 2.54363 +/− 4.9e−05m ==> Josh Smith @Fullerton for scattering measurement

C3: RoC: 2.57130 +/− 6.3e−05m   

C4: RoC: 2.58176 +/− 6.8e−05m

C5: RoC 2.57369 +/− 9.1e−05m

Measured the thickness of a curved mirror:

Took three points separated by 120 degree.

S/N: C2, (0.2478, 0.2477, 0.2477) in inch => (6.294, 6.292, 6.292) in mm

Conclusion: Good. First contact did not damage the coating surface, and reduced the loss

- Construct a cavity with A1 and C2

- Measure the transmission and FWHM (of TEM10 mode)

- Apply First Contact on both mirrors

- Measure the values again

Transmission:

2.66 +/- 0.01 V -> 2.83  +/- 0.01 V

==> 6.3% +/- 0.5 % increase

FWHM of TEM10:

Before: (66.1067, 65.4257, 66.1746) +/- (0.40178, 0.38366, 0.47213) [kHz]
After: (60.846, 63.4461, 63.7906) +/- (0.43905, 0.56538, 0.51756) [kHz]

==> 5.1% +/- 2.7% decrease

Question: What is the best way to measure the finesse of the cavity?

Yesterday I measured the thickness of the PZTs in order to get an idea how much the PZTs are wedged.

For each PZT, the thickness at six points along the ring was measured with a micrometer gauge.
The orientation of the PZT was recognized by the wire direction and a black marking to indicate the polarity.

A least square fitting of these six points determines the most likely PZT plane.
Note that the measured numbers are assumed to be the thickness at the inner rim of the ring
as the micrometer can only measure the maximum thickness of a region and the inner rim has the largest effect on the wedge angle.
The inner diameter of the ring is 9mm.



The measurements show all PZTs have thickness variation of 3um maximum.

The estimated wedge angles are distributed from 8 to 26 arcsec. The directions of the wedges seem to be random
(i.e. not associated with the wires)



As wedging of 30 arcsec causes at most ~0.3mm spot shift of the cavity (easy to remember),
the wedging of the PZTs is not critical by itself. Also, this number can be reduced by choosing the PZT orientations
based on the estimated wedge directions --- as long as we can believe the measurements.



Next step is to locate the minima of each curved mirror. Do you have any idea how to measure them?

The items:

- Autocollimator (AC) borrowed from Mike Smith (Nippon Kogaku model 305, phi=2.76", 67.8mm)

- Retroreflector (corner cube)

- Two V grooves borrowed from the 40m

Procedure:

- Autocollimator calibration

o Install the AC on a optical table

o Locate the corner cube in front of the AC.

o Adjust the focus of the AC so that the reflected reticle pattern can be seen.

o If the retroreflection and the AC are perfect, the reference reticle pattern will match with the reflected reticle pattern.

o Measure the deviation of the reflected reticle from the center.

o Rotate the retroreflector by 90 deg. Measure the deviation again.

o Repeat the process until total four coordinates are obtained.

o Analysis of the data separates two types of the error:
   The average of these four coordinates gives the systematic error of the AC itself.
   The vector from the center of the circle corresponds to the error of the retroreflector.

- Wedge angle measurement

To be continued

An autocollimator (AC) should show (0,0) if a retroreflector is placed in front of the AC.
However, the AC may have an offset. Also the retroreflector may not reflect the beam back with an exact parallelism.

To calibrate these two errors, the autocollimator is calibrated. The retroreflector was rotated by 0, 90, 180, 270 deg
while the reticle position are monitored. The images of the autocollimator were taken by my digital camera looking at the eyepiece of the AC.

Note that 1 div of the AC image corresponds to 1arcmin.

Basically the rotation of the retroreflector changed the vertical and horizontal positions of the reticle pattern by 0.6mdeg and 0.1mdeg
(2 and 0.4 arcsec). Therefore the parallelism of the retrorefrector is determined to be less than an arcsec. This is negligibly good for our purpose.

The offset changes by ~1div in a slanted direction if the knob of the AC, whose function is unknown, is touched.
So the knob should be locked, and the offset should be recorded before we start the actual work every time.

The wedge angle of the prism "A1" was measured with the autocollimator (AC).

The range of the AC is 40 arcmin. This means that the mirror tilt of 40arcmin can be measured with this AC.
This is just barely enough to detect the front side reflection and the back side reflection.

The measured wedge angle of the A1 prism was 0.478 deg.

Ideally a null measurement should be done with a rotation stage.

Method:

• Mount the tombstone prism on the prism mount. The mount is fixed on the rotation stage.
• Locate the prism in front of the autocollimator.
• Find the retroreflected reticle in the view. Adjust the focus if necessary.
• Confirm that the rotation of the stage does not change the height of the reticle in the view. 

  If it does, rotate the AC around its axis to realize it.
  This is to match the horizontal reticle to the rotation plane.
• Use the rotation stage and the alignment knobs to find the reticle at the center of the AC.
Make sure the reticle corresponds to the front surface.
• Record the micrometer reading.
• Rotate the micrometer of the rotation stage until the retroreflected reticle for the back surface.
• There maybe the vertical shift of the reticle due to the vertical wedging. Record the vertical shi
• Record the micrometer reading. Take a difference from the previous value.
   

Measurement:

• A1: α = 0.68 deg, β = 0 arcmin (0 div)
• A2: α = 0.80 deg, β = -6 arcmin (3 div down)
• A3: α = 0.635 deg, β = -1.6 arcmin (0.8 div down)
• A4: α = 0.650 deg, β = 0 arcmin (0div)
• A5: α = 0.655 deg, β = +2.4 arcmin (1.2 div up)

Analysis:

• \theta_H = ArcSin[Sin(α) / n]
• \theta_V = ArcSin[Sin(β) / n]/2
   
• A1: \theta_H = 0.465 deg, \theta_V = 0.000 deg
• A2: \theta_H = 0.547 deg, \theta_V = -0.034 deg
• A3: \theta_H = 0.434 deg, \theta_V = -0.009 deg
• A4: \theta_H = 0.445 deg, \theta_V = 0.000 deg
• A5: \theta_H = 0.448 deg, \theta_V = 0.014 deg

Measurement:

• A6:   α = 0.665 deg, β = +3.0 arcmin (1.5 div up)
• A7:   α = 0.635 deg, β =   0.0 arcmin (0.0 div up)
• A8:   α = 0.623 deg, β = - 0.4 arcmin (-0.2 div up)
• A9:   α = 0.670 deg, β = +2.4 arcmin (1.2 div up)
• A10: α = 0.605 deg, β = +0.4 arcmin (0.2 div up)
• A11: α = 0.640 deg, β = +0.8 arcmin (0.4 div up)
• A12: α = 0.625 deg, β = - 0.6 arcmin (-0.3 div up)
• A13: α = 0.630 deg, β = +2.2 arcmin (1.1 div up)
• A14: α = 0.678 deg, β =   0.0 arcmin (0.0 div up)
• B1:   α = 0.665 deg, β = +0.6 arcmin (0.3 div up)
• B2:   α = 0.615 deg, β = +0.2 arcmin (0.1 div up)
• B3:   α = 0.620 deg, β = +0.9 arcmin (0.45 div up)
• B4:   α = 0.595 deg, β = +2.4 arcmin (1.2 div up)
• B5:   α = 0.635 deg, β = - 1.8 arcmin (-0.9 div up)
• B6:   α = 0.640 deg, β = +1.6 arcmin (0.8 div up)
• B7:   α = 0.655 deg, β = +2.5 arcmin (1.25 div up)
• B8:   α = 0.630 deg, β = +2.8 arcmin (1.4 div up)
• B9:   α = 0.620 deg, β = - 4.0 arcmin (-2.0 div up)
• B10: α = 0.620 deg, β = +1.2 arcmin (0.6 div up)
• B11: α = 0.675 deg, β = +3.5 arcmin (1.75 div up)
• B12: α = 0.640 deg, β = +0.2 arcmin (0.1 div up)

Analysis:

• \theta_H = ArcSin[Sin(α) * n]
• \theta_V = ArcSin[Sin(β) / n]/2
   
• A6:   \theta_H = 0.490 deg, \theta_V =  0.017 deg
• A7:   \theta_H = 0.534 deg, \theta_V =  0.000 deg
• A8:   \theta_H = 0.551 deg, \theta_V = -0.0023 deg
• A9:   \theta_H = 0.482 deg, \theta_V =  0.014 deg
• A10: \theta_H = 0.577 deg, \theta_V =  0.0023 deg
• A11: \theta_H = 0.526 deg, \theta_V =  0.0046 deg
• A12: \theta_H = 0.548 deg, \theta_V = -0.0034 deg
• A13: \theta_H = 0.541 deg, \theta_V =  0.013 deg
• A14: \theta_H = 0.471 deg, \theta_V =  0.000 deg
• B1:   \theta_H = 0.490 deg, \theta_V =  0.0034 deg
• B2:   \theta_H = 0.563 deg, \theta_V =  0.0011 deg
• B3:   \theta_H = 0.556 deg, \theta_V =  0.0051 deg
• B4:   \theta_H = 0.592 deg, \theta_V =  0.014 deg
• B5:   \theta_H = 0.534 deg, \theta_V = -0.010 deg
• B6:   \theta_H = 0.526 deg, \theta_V =  0.0091 deg
• B7:   \theta_H = 0.504 deg, \theta_V =  0.014 deg
• B8:   \theta_H = 0.541 deg, \theta_V =  0.016 deg
• B9:   \theta_H = 0.556 deg, \theta_V = -0.023 deg
• B10: \theta_H = 0.556 deg, \theta_V =  0.0068 deg
• B11: \theta_H = 0.475 deg, \theta_V =  0.020 deg
• B12: \theta_H = 0.526 deg, \theta_V =  0.0011 deg

 [Jeff, Yuta, Koji]

Gluing test with UV-cure epoxy Optocast 3553-LV-UTF-HM

- This glue was bought in the end of October (~3.5 months ago).

- The glue was taken out from the freezer at 1:20pm.
- Al sheet was laid on the optical table. We made a boat with Al foil and pour the glue in it (@1:57pm)
- We brought two kinds of Cu wires from the 40m. The thicker one has the diameter of 1.62mm.
The thinner one has the diameter of 0.62mm. We decided to use thinner one being cut into 50mm in length.

- The OMC glass prisms have the footprint of 10mmx20mm = 200mm^2. We tested several combinations
of the substrates. Pairs of mirrors with 1/2" mm in dia. (127mm) and a pair of mirrors with 20mm in dia. (314mm).

- Firstly, a pair of 1/2" mirrors made of SF2 glass was used. A small dub on a thinner Cu wire was deposited on a mirror.
  We illuminated the glue for ~10sec. When the surfaces of the pair was matched, the glue did not spread on the entire
  surface. The glue was entirely spread once the pressure is applied by a finger. Glue was cured at 2:15pm. 12.873mm
  thickness after the gluing.

Some remark:
1. We should be careful not to shine the glue pot by the UV illuminator.
2. The gluing surface should be drag wiped to remove dusts on the surface.

- Secondly, we moved onto 20mm mirror pair taken from the remnant of the previous gluing test by the eLIGO people.
This time about 1.5 times more glue was applied.

- The third trial is to insert small piece of alminum foil to form a wedge. The thickness of the foil is 0.041mm.
The glue was applied to the pair of SF2 mirror (1/2" in dia.). A small dub (~1mm in dia) of the glue was applied.
The glue filled the wedge without any bubble although the glue tried to slide out the foil piece from the wedge.
So the handling was a bit difficult. After the gluing we measured the thickness of the wedge by a micrometer gauge.
The skinny side was 12.837mm, and the thicker side was 12.885mm. This is to be compared with the total thickness
12.823mm before the gluing. The wedge angle is 3.8mrad (0.22deg). The glue dub was applied at 2:43, and the UV
illumination was applied at 2:46.

- At the end we glued a pair of fused silica mirrors. The total thickness before the gluing was 12.658 mm.
The glue was applied at 2:59pm. The thickness after the gluing is 12.663 mm.
This indicates the glue thickess is 5um.

Perpendicularity test of the mounting prisms:

The perpendicularity of the prism pieces were measured with an autocollimator.

Two orthogonally jointed surfaces forms a part of a corner cube.
The deviation of the reflected image from retroreflection is the quantity measured by the device.

When the image is retroreflected, only one horizontal line is observed in the view.
If there is any deviation from the retroreflection, this horizontal line splits into two
as the upper and lower halves have the angled wavefront by 4x\theta. (see attached figure)

The actual reading of the autocollimator is half of the wavefront angle (as it assumes the optical lever).
Therefore the reading of the AC times 30 gives us the deviation from 90deg in the unit of arcsec.

SN / measured / spec

SN10: 12.0 arcsec (29 arcsec)

SN11: 6.6 arcsec (16 arcsec)

SN16: 5.7 arcsec (5 arcsec)

SN20: -17.7 arcsec (5 arcsec)

SN21: - 71.3 arcsec (15 arcsec)

Mounting Prisms:
(criteria: 30arcsec = 145urad => 0.36mm spot shift)
SN  Meas.(div) ArcSec Spec.
10   0.3989    11.97   29    good
11   0.2202     6.60   16    good
16   0.1907     5.72    5    good
20  -0.591    -17.73    5    good
21  -2.378    -71.34   15

21  -1.7      -51.     15
01  -0.5      -15.     52
02  -2.5      -75.     48
06  -1.0      -30.     15    good
07   1.7       51.     59
12  -2.2      -66.     40
13  -0.3      - 9.     12    good
14  -2.8      -84.     27
15  -2.5      -75.     50
17   0.7       21.     48
22   2.9       87.     63

Mirror A:
A1  -0.5      -15.     NA    good
A3   0.5       15.     NA    good
A4   0.9       27.     NA    good
A5   0.4       12.     NA    good
A6   0.1        3.     NA    good
A7   0.0        0.     NA    good
A8   0.0        0.     NA    good
A9   0.0        0.     NA    good
A10  1.0       30.     NA    good
A11  0.3        9.     NA    good
A12  0.1        3.     NA    good
A13  0.0        0.     NA    good
A14  0.6       18.     NA    good

Mirror B:
B1  -0.9      -27.     NA    good
B2  -0.6      -18.     NA    good
B3  -0.9      -27.     NA    good
B4   0.7       21.     NA    good
B5  -1.1      -33.     NA
B6  -0.6      -18.     NA    good
B7  -1.8      -54.     NA
B8  -1.1      -33.     NA
B9   1.8       54.     NA
B10  1.2       36.     NA   
B11 -1.7      -51.     NA
B12  1.1       33.     NA


Perpendicularity of the "E" mirror was measured.

Mounting Prisms:
(criteria: 30arcsec = 145urad => 0.36mm spot shift)
SN  Meas.(div) ArcSec Spec.
10   0.3989    11.97   29    good
11   0.2202     6.60   16    good
16   0.1907     5.72    5    good
20  -0.591    -17.73    5    good
21  -2.378    -71.34   15

21  -1.7      -51.     15
01  -0.5      -15.     52
02  -2.5      -75.     48
06  -1.0      -30.     15    good
07   1.7       51.     59
12  -2.2      -66.     40
13  -0.3      - 9.     12    good
14  -2.8      -84.     27
15  -2.5      -75.     50
17   0.7       21.     48
22   2.9       87.     63

Mirror A:
A1  -0.5      -15.     NA    good
A3   0.5       15.     NA    good
A4   0.9       27.     NA    good
A5   0.4       12.     NA    good
A6   0.1        3.     NA    good
A7   0.0        0.     NA    good
A8   0.0        0.     NA    good
A9   0.0        0.     NA    good
A10  1.0       30.     NA    good
A11  0.3        9.     NA    good
A12  0.1        3.     NA    good
A13  0.0        0.     NA    good
A14  0.6       18.     NA    good

Mirror B:
B1  -0.9      -27.     NA    good
B2  -0.6      -18.     NA    good
B3  -0.9      -27.     NA    good
B4   0.7       21.     NA    good
B5  -1.1      -33.     NA
B6  -0.6      -18.     NA    good
B7  -1.8      -54.     NA
B8  -1.1      -33.     NA
B9   1.8       54.     NA
B10  1.2       36.     NA   
B11 -1.7      -51.     NA
B12  1.1       33.     NA

Mirror E:
E1  -0.8      -24.     NA    good
E2  -0.8      -24.     NA    good
E3  -0.25     - 7.5    NA    good
E4  -0.5      -15.     NA    good
E5   0.8       24.     NA    good
E6  -1.0      -30.     NA    good
E7  -0.2      - 6.     NA    good
E8  -0.8      -24.     NA    good
E9  -1.0      -30.     NA    good
E10  0.0        0.     NA    good
E11 -1.0      -30.     NA    good
E12 -0.3      - 9.     NA    good
E13 -0.8      -24.     NA    good
E14 -1.0      -30.     NA    good
E15 -1.2      -36.     NA
E16 -0.7      -21.     NA    good
E17 -0.8      -24.     NA    good
E18 -1.0      -30.     NA    good