40m QIL Cryo_Lab CTN SUS_Lab TCS_Lab OMC_Lab CRIME_Lab FEA ENG_Labs OptContFac Mariner WBEEShop
  OMC elog, Page 9 of 10  Not logged in ELOG logo
ID Date Author Type Category Subjectup
  284   Sat Jul 1 21:33:18 2017 KojiGeneralGeneralSome purchase notes

- Forgot to close the cylinder valve...

v HEPA prefilter (20"x20"x1" MERV 7)

- Replace the filter for the air conditioning

v Texwipe TX715 SWAB http://www.texwipe.com/store/p-817-tx715.aspx

v Gloves ~3 bags
VWR GLOVE ACCTCH NR-LTX SZ7.0 PK25 79999-304 x3
VWR GLOVE ACCTCH NR-LTX SZ7.5 PK25 79999-306 x1

v Vectra IPA soaked cloths

v Sticky mats

  • GLOVE ACCTCH NR-LTX SZ7 PK25 / 79999-304 / PK4
  • GLOVE ACCTCH NR-LTX SZ7.5 PK25 / 79999-306 / PK1
  • WIPER 100% IPA 23X23CM PK50. / TWTX8410 / PK2
  • MAT CLEAN ROOM 18X36IN BLUE / 89021-748 / CS1 (Qty4)
  • FILTER PLET AIR MERV8 20X20X1 / 78002-422 / EA4 / Direct from Supplier


  138   Wed Jun 5 18:19:51 2013 KojiGeneralGeneralSome recent photos from the OMC final test at CIT

Applying First Contact for the optics cleaning

PD alignment / scattering photos


Cabling (final) 

  213   Mon Jul 21 01:02:43 2014 KojiMechanicsCharacterizationSome structual mode analysis


Fundamental: 12.3kHz Secondary: 16.9kHz

PRISM_12_3kHz.png PRISM_16_9kHz.png


Fundamental: 2.9kHz Secondary: 4.1kHz

DCPD_2_9kHz.png DCPD_4_1kHz.png


Fundamental: 5.6kHz Secondary: 8.2kHz

QPD_6_0kHz.png QPD_8_2kHz.png

  120   Mon May 6 19:31:51 2013 KojiOpticsCharacterizationSpot position measurement on the diode mounts

Measurement Order: DCPD2->DCPD1->QPD1->QPD2

DCPD1: 1.50mm+0.085mm => Beam 0.027mm too low

DCPD2: 1.75mm+0.085mm => Beam 0.051mm too high (...less confident)

QPD1:   1.25mm+0.085mm => Beam 0.077mm too low

QPD2:   1.25mm+0.085mm => Beam 0.134mm too low
          or 1.00mm+0.085mm => Beam 0.116mm too high

  121   Wed May 8 15:08:57 2013 KojiOpticsCharacterizationSpot position measurement on the diode mounts

Remeasured the spot positions:

DCPD1: 1.50mm+0.085mm => Beam 0.084mm too high

DCPD2: 1.50mm+0.085mm => Beam 0.023mm too high

QPD1:   1.25mm+0.085mm => Beam 0.001mm too low

QPD2:   1.25mm+0.085mm => Beam 0.155mm too low

  158   Tue Aug 27 17:02:31 2013 KojiMechanicsCharacterizationSpot position measurement on the diode mounts

After the PZT test, the curved mirrors were aligned to the cavity again.

In order to check the height of the cavity beam, the test DCPD mount was assembled with 2mm shim (D1201467-3)
The spot position was checked with a CCD camera.

According to the analysis of the picture, the spot height is about 0.71mm lower than the center of the mount.

  180   Mon Mar 3 02:46:21 2014 KojiGeneralCharacterizationSpot positions scanned

Spot positions on CM1 and CM2 scanned according to the recipes provided by the previous entry.

The best result obtained was:

Transmission from FM2: 32.7mW
Incident on BS1: 34.4mW

Reflection (Unlocked): 5.99V
Reflection (Locked): 104mV
Reflection (Dark): -7.5mV

to accomodate the spot on BS1 it had to be about a mm moved from the template.

This gives us:
- Portion of the TEM00 carrier: R = 1-(104+7.5)/(5990+7.5) = 0.981
- Raw transmission: 32.7/34.4 = 0.950
- TEM00 transmission 0.950/R = 0.969
- Excluding the transmission of BS1: 0.969/0.9926 = 0.976
  => loss per mirror ~40ppm


  168   Fri Sep 13 15:09:20 2013 KojiGeneralGeneralSprinkler installation: done

A sprinkler head was installed on the HEPA enclosure. The head is covered with a plastic cap.

  218   Tue Sep 9 20:59:19 2014 KojiMechanicsCharacterizationStructural mode analysis for the PZT mirror

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.

PZT_10.0kHz.png PZT_14.6kHz.png PZT_18.0kHz.png

PZT_22.5kHz.png PZT_29.7kHz.png

  315   Sat Feb 2 16:17:13 2019 KojiOpticsCharacterizationSummary: OMC(001) HOM structure recalculation

Each peak of the transfer function measurement was fitted again with a complex function:

\begin{align} h(f;a_{\rm r}, a_{\rm i}, f_0, dT, \Gamma, a_0, b_0, a_1, b_1) & \nonumber\\ = (a_{\rm r} + i a_{\rm i}) e^{-i 2 \pi f dT} \frac{1}{1 + i (f - f_0)/\Gamma} &+ (a_0 + i b_0) + (a_1 + i b_1)f \nonumber \end{align}

OMC (001)
Measurement date 2013/5/31, Installed to L1 2013/6/10~

  316   Sat Feb 2 20:03:19 2019 KojiOpticsCharacterizationSummary: OMC(002) HOM structure recalculation (before mirror replacement)

OMC (002)
Measurement date 2013/10/11, Installed to L1 2013/XX

  317   Sat Feb 2 20:28:21 2019 KojiOpticsCharacterizationSummary: OMC(003) HOM structure recalculation

OMC (003)
Measurement date 2014/7/5, Stored for I1, Installed to H1 2016/8 upon damage on 002

  192   Fri Jun 27 18:51:33 2014 KojiGeneralGeneralSupply

PTOUCH TAPE (12mm white) x 2

9V batteries

  453   Fri Nov 11 19:07:48 2022 KojiSupplyGeneralSupply Order

Clean Supply Ordered

  • TexWipe TX8410 AlphaSat Vectra Alpha 10 50 sheets x 12 pk  (VWR TWTX8410)
  • Mask KIMTECH PURE® M3 Pleat-Style Face Masks 50 masks x 10 pk (VWR 15628-213)
  • Stainless Pan x3 (VWR 10193-562)
  • Ansell Accutech Latex Gloves 6.5 25*8pk (Fisher 19162026)
  • Ansell Accutech Latex Gloves 7.0 25*8pk (Fisher 19162027)
  396   Fri Oct 9 01:01:01 2020 KojiGeneralGeneralTFT Monitor mounting

To spare some room on the optical table, I wanted to mount the two TFT monitor units on the HEPA enclosure frame.
I found some Bosch Rexroth parts (# 3842539840) in the lab, so the bracket was taken for the mount. This swivel head works very well. It's rigid and still the angle is adjustable.


BTW, this TFT display (Triplett HDCM2) is also very nice. It has HDMI/VGA/Video/BNC inputs (wow perfect) and the LCD is Full-HD LED TFT.



The only issue is that one unit (I have two) shows the image horizontally flipped. I believe that I used the unit with out this problem before, I'm asking the company how to fix this.


  397   Fri Oct 16 00:53:29 2020 KojiGeneralGeneralTFT Monitor mounting

The image flipping of the display unit was fixed. The vendor told me how to fix it.

- Open the chassis by the four screws at the side.
- Look at the pass-through PCB board between the mother and display boards.
- Disconnect the flat flex cables from the pass-through PCB (both sides) and reconnect them (i.e. reseat the cables)

That's it and it actually fixed the image flipping issue.


  470   Mon Dec 19 18:51:50 2022 KojiOpticsCharacterizationTMS measurement with the PZT voltages altered

[Camille, Koji] Log of the work on Dec 15, 2023

The vertical and horizontal TMSs for OMC #4 were measured with the PZT voltages scanned from 0V to 200V.

We concluded that this alignment nicely avoids the higher-order mode structure up to ~19th order. We are ready for the cavity mirror bonding.

The RF transfer functions to the trans RF PD from the modulation on the BB EOM were taken with the presence of the vertical misalignment of the incident beam and the vertical clipping of the beam on the RFPD.

The typical measurement results and the fitting results are shown in Attachments 1/2.

The TFs were taken with the voltage 0, 50, 100, 150, and 200V applied to PZT1 while PZT2 were left open. The measurement was repeated with the role of PZT1 and PZT2 swapped.

The ratio between the TMS and FSR was evaluated for each PZT voltage setting. (Attachment 3)

When the PZTs are open, the first coincident resonance is the 19th-order mode of the 45MHz lower sideband. (Attachment 4)

When the PZT2 voltage is scanned with PZT1 kept at ~0V, no low-order sidebands come into the resonance (Attachment 5) until the PZT1 voltage is above 100V.

We found that the high voltage on PZT1 misaligns the cavity in yaw and the spot (presumably) moves to an undesirable area regarding the cavity loss.
This does not happen to PZT2. Therefore the recommendation here is that the PZT2 is used as the high voltage PTZ, while PZT1 is for the low voltage actuation.


  10   Mon Jul 23 17:15:14 2012 KojiCleanGeneralTalking with Margot

I consulted with Margot about the cleaning of the optics

  • Optics are considered as a clean object. Large dusts can be removed by ionized N2 flow etc.
  • Barrel of optics can be wiped with Acetone.
  • Optical surfaces are best to be cleaned by First Contact.
  • A peek mesh should be embedded in the first contact so that the First Contact sheet can be easily removed.
  • When peeling a F.C. sheet from a mirror surface, ionized N2 should be brown for discharging.
  • If there are residuals visible on the mirror surface, it should be removed by Acetone. Don't use alchols.
  • Use paper lens tissue for wiping as the lint free wipe can be eaten by Acetone.
  • In fact, All of the procedure is described in a certain document.
  • For a small amount, Margot can provide us a bottle of F.C. and some PEEK meshes.

Details of the Ionized N2 system

  • This N2 should have higher purity than 4N (UHP - Ultra High Purity). This means we should use 4N - UHP or 5N - Research Grade.
  • The ionized gun used in the clean room at Downs: made by Terra Universal.com
  • Flow path: N2 cylinder - Filter - Gun
  86   Thu Mar 28 03:37:07 2013 ZachOpticsConfigurationTest setup input optics progress

[Lisa, Zach]

Last night (Tuesday), I finished setting up and aligning most of the input optics for the OMC characterization setup. See the diagram below, but the setup consists of:

  • Faraday isolator/polarization definition
  • HWP+PBS for power splitting into two paths:
    • EOM path
      • Resonant EOM for PDH sideband generation
      • Broadband EOM for frequency scanning
    • AOM path
      • Double-passed ~200-MHz Isomet AOM for subcarrier generation. NOTE: in this case, I have chosen the m = -1 diffraction order due to the space constraints on the table.
  • Recombination of paths on a 50/50 beam splitter---half of the power is lost through the unused port into a black glass dump
  • Coupler for launching dual-field beam into a fiber (to OMC)

OMC_test_setup_IO.jpg 2013-03-27_05.48.20.jpg

Today, we placed some lenses into the setup, in two places:

  1. In the roundabout section of the AOM path that leads to the recombination, to re-match the AOM-path beam to that of the EOM path
  2. After the recombination beam splitter, to match the combined beam mode into the fiber

We (Koji, Lisa, and myself) had significant trouble getting more than ~0.1% coupling through the fiber, and after a while we decided to go to the 40m to get the red-light fiber illuminator to help with the alignment.

Using the illuminator, we realigned the input to the coupler and eventually got much better---but still bad---coupling of ~1.2% (0.12 mW out / 10 mW in). Due to the multi-mode nature of the illuminator beam, the output cannot be used to judge the collimation of the IR beam; it can only be used to verify the alignment of the beam.

With 0.12 mW emerging from the other end of the fiber, we could see the output quite clearly on a card (see photo below). This can tell us about the required input mode. From the looks of it, our beam is actually focused too strongly. We should probably replace the 75mm lens again with a slightly longer one.

Lisa and I concurred that it felt like we had converged to the optimum alignment and polarization, which would mean that the lack of coupling is all from mode mismatch. Since the input mode is well collimated, it seems unlikely that we could be off enough to only get ~1% coupling. One possibility is that the collimator is not well attached to the fiber itself. Since the Rayleigh range within it is very small, any looseness here can be critical.


I think there are several people around here who have worked pretty extensively with fibers. So, I propose that we ask them to take a look at what we have done and see if we're doing something totally wrong. There is no reason to reinvent the wheel.

  212   Sun Jul 20 17:20:39 2014 KojiGeneralGeneralThe 3rd (LIO) OMC was shipped out to LHO

The 3rd (LIO) OMC was shipped out to LHO on Friday (Jul 18) Morning.


- All of the on-breadboard cables should be attached and tied down.

- Peel First Contact paint and pack the OMC for storage.


  285   Wed Jul 5 16:59:44 2017 KojiGeneralGeneralThe OMC #002 was packed

[Stephen Koji]

The OMC #002 was packed for the transportation to Downs.

===> And transported to Downs 227 on Jul 6th.

  404   Mon Nov 23 23:17:19 2020 KojiElectronicsCharacterizationThe dark noise of the Q3000 QPDs

The dark noise levels of the four Q3000 QPDs were measured with FEMTO DLPCA200 low noise transimpedance amp.

The measurement has been done in the audio frequency band. The amp gain was 10^7 V/A. The reverse bias was set to be 5V and the DC output of the amplifier was ~40mV which corresponds to the dark current of 4nA. It is consistent with the dark current measurement.

The measured floor level of the dark current was below the shot noise level for the DC current of 0.1mA (i.e. 6pA/rtHz).
No anomalous behavior was found with the QPDs.

Note that there is a difference in the level of the power line noise between the QPDs. The large part of the line noises was due to the noise coupling from a soldering iron right next to the measurement setup, although the switch of the iron was off. I've noticed this noise during the measurement sets for QPD #83. Then the iron was disconnected from the AC tap.

  405   Tue Nov 24 10:45:07 2020 gautamElectronicsCharacterizationThe dark noise of the Q3000 QPDs

I see that these measurements are done out to 100 kHz - I guess there is no reason to suspect anything at 55 MHz which is where this QPD will be reading out photocurrent given the low frequency behavior looks fine? The broad feature at ~80 kHz is the usual SR785 feature I guess, IIRC it's got to do with the display scanning rate.


The measured floor level of the dark current was below the shot noise level for the DC current of 0.1mA (i.e. 6pA/rtHz).

  406   Tue Nov 24 12:27:18 2020 KojiElectronicsCharacterizationThe dark noise of the Q3000 QPDs

The amplifier BW was 400kHz at the gain of 1e7 V/A. And the max BW is 500kHz even at a lower gain. I have to setup something special to see the RF band dark noise.
With this situation, I stated "the RF dark noise should be characterized by the actual WFS head circuit." in the 40m ELOG.

  473   Wed Jan 25 23:51:04 2023 KojiGeneralGeneralThe items packed for Downs

Qty1 1/2 mounts
Qty2 prism mounts
Qty6 gluing fixures
Qty1 Rotary stage
Qty1 2" AL mirror
Qty1 Base for the AL mirror

=> Handed to Stephen -> Camille on Jan 27, 2023.

  421   Thu Jul 21 17:47:00 2022 KojiGeneralGeneralThe profile of the beam incident on the fiber input coupler

The profile of the beam incident on the fiber input

The fiber input was deflected by a 45deg mirror. The beam profile was measured with WincamD. The beam was too strong (~60mW) even at the smallest pump power (ADJ -50) of the NPRO. So the two ND20 filters were added to the lens right before the 45 deg mirror and the camera.

The measured profile had some deviation from the nice TEM00 particularly around the waist. This could be a problem of the too small beam on the ND filter and the CCD.
This is not an issue as we just want to know the approximate shape of the beam.

For the fiber coupling, if we have the beam waist radius of ~200um it is sufficient for decent coupling.

  413   Tue Jun 28 16:13:34 2022 KojiGeneralGeneralThe small optical table not small enough to get out

The table width was an inch too large compared to the door width. We need to tilt the table and it seemed too much for us. Let's ask the transportation for handling.

Photo courtesy by Juan

  50   Wed Jan 2 07:35:55 2013 KojiOpticsCharacterizationThickness of a curved mirror

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

  177   Tue Dec 10 16:41:51 2013 KojiGeneralGeneralTo Buy

Masks / Wipes => done

  200   Mon Jul 7 01:36:03 2014 KojiGeneralGeneralTo Do

Optical tests

  • Cleaning
  • Power Budget
  • FSR measurement
  • TMS measurement
  • TMS measurement (with DC voltage on PZTs)
  • PZT DC response
  • PZT AC response
  • QPD alignment
  • DCPD alignment

Backscattering test

Cabling / Wiring

  • Attaching cable/mass platforms
  • PZT cabling
  • DCPD cabling
  • QPD cabling

Vibration test


First Contact

Packing / Shipping

  204   Thu Jul 10 08:34:57 2014 KojiGeneralGeneralTo Do

Optical tests

  • Cleaning
  • Power Budget
  • FSR measurement
  • TMS measurement
  • TMS measurement (with DC voltage on PZTs)
  • PZT DC response
  • PZT AC response
  • QPD alignment
  • DCPD alignment

Backscattering test

Cabling / Wiring

  • Attaching cable/mass platforms
  • PZT cabling
  • DCPD cabling (to be done at LHO)
  • QPD cabling (to be done at LHO)

Vibration test


First Contact

Packing / Shipping

  2   Sat Jun 16 08:53:09 2012 KojiGeneralGeneralTo Do List



  • Work 
  • Design
    • How do we hold the PDs, QPDs, and black glass - we put 2 PDs and 2 QPDs on the PD mounting blacket.
  • Test
  • Things to be tested
    • New suspension scheme (cup & cone design)
    • Balancing the plates
    • Dummy metal payload?
  • => Suspending test with a suspension cage for a Faraday isolator@CIT
    • Supporting block for the suspension cage (to mimic the OMC suspension)
  • Things to be designed
    • Wire end (cone)
    • Diode holding structures
      PD/QPD/PZT holding structure
  • PZT alignment
  • Prototyping with metal parts?
  • UV glue? (heat) / gluing test
  • Balance / ballast
  • Solid works


  • Mirrors to be delivered ~Aug
  • Design down select
    • Between "Single output & BS" vs "Two outputs & no BS"
  • Mode design
  • Finalization of scattering paths / PD angles etc
  • Things to be decided / confirmed:
    • How to handle optics / assemblies (Talk to the prev people)
    • First contact? (Margot: applicable to a short Rc of ~2.5m)
    • Gluing templates to be designed (how to handle it?)
  • Things to be tested:
    • R&T of each mirror
    • Cavity ref/trans/finesse
    • PD QE / incident angle
  • What PD do we use?
  • CCD beam analyzer (Zach: It is fixed.)
  • PD angle measurement
  • Obtain EG&G 3mm PDs


  • Electronics / CDS electronics / software
  • Things to be tested
    • QPD/PD pre-selections (QE/noise)
    • Functionality test of QPD/PD/PZT

Shipping, storage etc

    - Lab renovtion
    - Mechanics design
    - Glue training
    - Mirror delivery
    - Basic optics test
    - Cavity test
    - Suspending test
    - Shipping to LLO

Open questions
    Two optical designs
    Clamp design / stencil design
    gluing-installation procedure

  448   Fri Aug 26 22:29:02 2022 KojiGeneralGeneralTool Shipping Prep

Shipping preparation for the LLO trip

Started July 15, 2022 and finished Aug 30. So it took ~1.5 months (with a couple weeks of break)

Class B special tools

  • Screw Drivers 1
    • https://www.steritool.com/
    • https://www.steritool.com/precision-screwdrivers-mini.aspx
  • Screw Drivers 2
    • What I have seems S555Z-7
    • https://www.starrett.com/
    • https://www.starrett.com/dms/flipbooks/Cat-33/index.html?page=354
  • Allen Wrenches
    • Bondhus: These are not made of SS, but of so called protanium steel. I have a chrome finish one (BriteGuard) and K14 gold finish one (goldguard).
    • https://intl.bondhus.com/pages/goldguard-ball-end
    • https://intl.bondhus.com/pages/briteguard-ball-end
  • Scissors
    • VWR - Stainless Steel
    • Unknown PN /  probably this?
    • https://us.vwr.com/store/product/4527635/vwr-dissecting-scissors-sharp-blunt-tip
  • Forceps
    • VWR - Stainless Steel
    • https://us.vwr.com/store/product/4531765/vwr-hemostatic-forceps
  • Wire cutters
    • Looks like they are orthodontic wire cutters. One has the marking "Orthomechanic Stainless Steel" but the company does not sell cutters anymore. The other has a marking "333" but the company is unknown. Similar products can be found on Amazon
  • Long nose pliers - straight stainless steel
    • https://www.aventools.com/
    • https://www.aventools.com/long-nose-pliers-stainless-steel-6-2
  • Bent nose pliers - stainless steel
    • unknown 
  • Tweezers
    • Excelta 
    • The short one is 20A-S-SE. The longer one is 24-SA-PI, maybe?
    • https://www.excelta.com/
    • https://www.excelta.com/straight-laboratory-instruments-forceps
    • https://www.excelta.com/style-24-24-6-sa
  • Mighty-Mouse spanner
  • 2x driver bits for the digital torque wrench

First Contact Kit

  • FC bottole / PEEK mesh

Bonding kit (excl EP30-2 bond)

  • reinforcement bars (4 types)
  • bonding liner powder
  • tools: spatula / bond applying rod

Power meters (excl Power meter controller)

  • Thorlabs Thermal
  • Thorlabs Photodiode
  • Thorlabs Integrating Sphere


  • preamp + power cable
  • PD testing kit (PD connector / DB9 break out / grabber-BNC)
  • Nitrile gloves

Cable bracket replacement kit

  • PEEK cable bracket (Helicoiled)
  • Cable pegs (x4 salvaged / spare)
  • fastners
  • kapton sheet
  • cable ties

Optics / Optomechanics

  • Optical fiber / spare fiber
  • OMC transport feet
  • OMC backscatter inspection prisms

Misc tools

  • digital torque wrench

=== Action done on Aug 30 ===

Fiber MM setup / Fiber coupler mount
Glass Beamdumps (for optical testing)
Flipper mirror
Thorlabs fiber coupler tool
General bent nose plier for fiber
Thorlabs collimator tiny allen
Spare High QE PDs

Spare OMC bags / Zip bags

Balance Mass 10g Qty 8 (Different Type D11*** 1.25" dia), 20g Qty 10 / Mass damper D1700301 -04 / Mass damper screws SHCS 1/4-20 x 1.25 Qty 25 / 1" screws and 1 1/8" screws

Shipping request: https://services1.ligo-la.caltech.edu/FRS/show_bug.cgi?id=25002

=== Low supply! ===

  • Masks
  • 7.0 gloves supply low
  • 7.5 glove completely gone
  • Wet vectra cloth
  • Dry vectra cloth
  4   Wed Jun 20 20:37:45 2012 ZachOpticsConfigurationTopology / parameter selection

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.


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, nmax, and then use this extra information to better select the length.


  • 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 nmax 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.


For the bowtie, the nmax = 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 nmax = 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



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 (nmax = 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 (nmax = 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.



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: LRT = 1.150 m
  • Non-bowtie: LRT = 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.

  278   Fri May 26 21:53:20 2017 KojiGeneralConfigurationTrans RF PD setup

Recent work

- DC output of the trans RF PD was connected to the BNC patch panel. => Now CH4 of the scope is monitoring this signal

- The RF sweep signal from the network analyzer is connected to the power combiner for the EOM drive via the SMA patch panel.

- The trans RF PD was aligned first to the leakage beam. It turned out that this signal is too weak. Then the PD was aligned to one of the main OMC transmission. For this purpose, the OMC DCPD (T) was removed from the OMC breadboard.

- It seems that there is a significant amount of RF AM from the EOM. I suspect it is associated with the residual S-pol and birefringence of the steering mirrors (45deg HR). But the HWP at the output of the Faraday is fixed on the Faraday body with a screw and cumbersome for fine adjustment. A PBS and an HWP are added right before the EOM. This made the fiber coupler slightly misaligned. I suppose this new setup still has S&P on the fiber too. Thus, readjustment of the fiber rotations at the input is necessary.

Next step

- Input power to the fiber should be determined before the EOM. Otherwise, touching the HWP before the EOM causes too much power change at the optics of the OMC side.

- Precise adjustment of the RFAM is still necessary.

- The OMC curved mirror should be held by the new fixture.

- Check the beam spots

- Measure cavity parameters. (transmission/FSR/HOM/etc)

==> Then the curved mirror and the PZT will be glued on the prism

  279   Tue Jun 6 00:49:48 2017 KojiGeneralConfigurationTrans RF PD setup

Last week, I further worked on the RF system to install 20dB coupler on the agilent unit and setup the R channel. This allowed me to make the FSR/TMS measurement of the OMC.

And today several optical improvement has been done.

- The input/output fiber couplers were adjusted to have the maximum transmission through the PBS right before the OMC.
- The HWP on the output side of the faraday was adjusted to have ~40mW input to the OMC.

Then, the OMC curved mirror is now held by the new in-situ gluing fixture instead of the conventional fixture attached upside down.
The OMC was ocked again and the input alignment was adjutsed. The fixture is blocking the QPD path, so it's not possible to confirm the proper alignment of the cavity (w.r.t. the QPD paths).

The precise positions of the spots could not be confirmed as the battery of the IR viewer was empty. Quick check of the spots by the card tells that the spot on the CM2 (PD side) is slightly too close to FM2 (output coupler). I wonder if this could be solved by rotating the curved mirror.

Otherwise everything look good. Let's try to glue the curved mirror tomorrow.

Note: Spot on CM2 is too close to the edge of the hole on the mounting prism. The meausrementof CM1 is telling that the curverture center is located 2.7mm upper side of the center of the mirror if the HR side arrow is up (and it is the case). If we move the arrow to the QPD path side (90deg CW viewed from the face side), this corresponds to ~1.1mrad CCW tilt in Yaw (viewed from the top of the prism). According to the matrix calculation (T1500060) this will induce ~1.5mm shift of the beam. This should be tried before gluing.

  280   Tue Jun 6 22:00:36 2017 KojiGeneralConfigurationTrans RF PD setup

- Replaced the PZT with the one used from the beginning. This must be PZT #21. After the replacement, the spot positions look very good. I even went up. So I decided this is the configuration to proceed to the gluing. The CM1 mirror has the HR arrow at the top.

- The input beam was realigned w.r.t. the OMC.

- Tried to use the IR viewer with the new rechargable battery brought from the 40m. But the view still didn't work. The possibility is a) the viewer is broken b) the battery is empty.

- Tried to use the stainless clean regulartor for the UHP N2. The outlet has a short tube with a different diameter. The O.D. of the old tube is 6.3mm, while the new one is 9.5mm. If I insert the thinner tube in the new tube, it approximately fits. But I don't believe this is the way...

  462   Mon Nov 21 19:13:35 2022 KojiGeneralGeneralTransmission measurement (2nd deep cleaning of OMC #1)

OMC Transmission measurement after the 2nd deep cleaning

The 2nd deep cleaning didn't improve the transmission. (See Attachment 2)
The measured loss was 0.044+/-0.002


  134   Fri May 31 14:07:54 2013 KojiOpticsCharacterizationTransverse Mode Spacing measurement afte the baking

Measurement for pitch

Free Spectral Range (FSR): 264.9703 +/− 0.0007 MHz
Cavity roundtrip length: 1.131419 +/− 0.000003 m
Transverse mode spacing (TMS): 57.9396 +/− 0.0002 MHz
TMS/FSR: 0.218664 +/− 0.000001
Assuming the line width of the cavity 1/400 of the FSR...
- the 9th modes of the carrier is 12.8 line width (LW) away from the carrier resonance
- the 13th modes of the lower f2 sideband are 5.7 LW away
- the 19th modes of the upper f2 sideband are -6.8 LW away

Measurement for yaw

Free Spectral Range (FSR): 264.9696 +/− 0.0004 MHz
Cavity roundtrip length: 1.131422 +/− 0.000002 m
Transverse mode spacing (TMS): 58.0479 +/− 0.0002 MHz
TMS/FSR: 0.219074 +/− 0.000001
- the 9th modes of the carrier is 11.3 line width (LW) away from the carrier resonance
- the 13th modes of the lower f2 sideband are 7.8 LW away
- the 19th modes of the upper f2 sideband are -3.7 LW away

The followings are the previous values before the bake
[from this entry]

- After everything was finished, more detailed measurement has been done.

- FSR&TMS (final)
FSR: 264.963MHz => 1.13145m
  TMS(V): 58.0177MHz => gamma_V = 0.218966
  TMS(H): 58.0857MHz => gamma_H = 0.219221
  the 9th modes of the carrier is 10.8~11.7 LW away
  the 13th modes of the lower f2 sideband are 7.3~8.6 LW away
  the 19th modes of the upper f2 sideband are 2.6~4.5 LW away

  265   Mon Aug 22 12:58:16 2016 KojiGeneralGeneralUV bond samples -> Garilynn

- FS base + Mounting Prism

- FS or SF2 1/2" piece + FS or SF2 1/2" piece

- FS? plate + FS or SF2 1/2" piece + FS or SF2 1/2" piece + FS? plate

  62   Thu Feb 7 23:01:45 2013 KojiOpticsCharacterizationUV epoxy gluing test

 [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.

  89   Mon Apr 1 03:23:48 2013 KojiOpticsGeneralUV power calibration

[Koji Lisa Jeff Zach]

Eric G bought a UV power meter from American Ultraviolet.

Our UV illuminator was calibrated by this power meter.

The first blast (i.e. cold start): 3.9W/cm^2

After many blasting: 8.3W/cm^2

The spec is 20W/cm^2

  239   Sun Sep 6 16:50:51 2015 KojiElectronicsGeneralUnit test of the EOM/AOM Driver S1500118

TEST Result: S1500118

Additional notes

- Checked the power supply. All voltages look quiet and stationary.

- Checked the internal RF cables too see if there is any missing shield soldering => Looked fine

- Noticed that the RFAM detector board has +/-21V for the +/-24V lines => It seems that this is nominal according to the schematic

- Noticed that the RFAM detector sensitivity were doubled fomr the other unit.
  => This is reated to the modification (E1500353) of  "Controller Board D0900761-B Change 1" (doubling the monitor output gain)

- Noticed that the transfer function of the CTRL signal on the BNC and the DAQ output.
  => This is reated to the modification (E1500353) of  "Servo Board D0900847-B Change 1"  (servo transfer function chage)
  => The measured transfer function did not agree with the prediction from the circuit constants in this document
  => From the observation of the servo board it was found that R69 was not 200Ohm but 66.5 Ohm (See attachment 1).
       This explained the measured transfer function. The actuator TF has: P 2.36, Z 120., K -1@DC (0.020@HF)

- Similarly, the TF between the CTRL port on the unit and the CTRL port on the test rig was also modified.

Noise level

Attachment 2

- The amplitude noise in dBc (SSB) was measured at the output of 27dBm. From the test sheet, the noise level with 13dBm output was also referred. From the coherence of the MON1 and MON2, the noise level was inferred. It suggests that the floor level is better than 180dBc/Hz. However, there is a 1/f like noise below 1k and is dominating the actual noise level of the RF output. Daniel suggested that we should check nonlinear downconversion from the high frequency noise due to the noise attenuator. This will be check with the coming units.

  11   Tue Jul 24 11:41:29 2012 KojiGeneralGeneralUseful references

Nicolas Smith,
LIGO Document T0900383-v1
3mm Photodiode Characterization for Enhanced LIGO

Tobin Fricke,
LIGO Document P1000010-v1
Homodyne detection for laser-interferometric gravitational wave detectors

Nicolas Smith,
LIGO Document P1200052-v1
Techniques for Improving the Readout Sensitivity of Gravitational Wave Antennae

  32   Wed Nov 7 01:28:20 2012 KojiOpticsCharacterizationWedge angle test (A1)

Wedge angle test

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



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.



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


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


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

wedge_measurement.png[Click for a sharper image]

  56   Sat Jan 19 20:47:41 2013 KojiOpticsCharacterizationWedge measurement with the autocollimator

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.

  59   Mon Feb 4 00:39:08 2013 KojiOpticsCharacterizationWedge measurement with the autocollimator and the rotation stage


  • 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.


  • 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)


  • \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


  60   Wed Feb 6 02:34:10 2013 KojiOpticsCharacterizationWedge measurement with the autocollimator and the rotation stage


  • 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)


  • \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



  • 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)


  • \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


  66   Fri Mar 1 23:52:18 2013 KojiOpticsCharacterizationWedge measurement with the autocollimator and the rotation stage


  • E1:   α = 0.672 deg, β = +0.0 arcmin (0 div up)
  • E2:   α = 0.631 deg, β = - 0.3 arcmin (-0.15 div down)
  • E3:   α = 0.642 deg, β = +0.0 arcmin (0 div up)
  • E4:   α = 0.659 deg, β = +1.4 arcmin (0.7 div up)
  • E5:   α = 0.695 deg, β = +0.5 arcmin (0.5 div up)
  • E6:   α = 0.665 deg, β = - 0.4 arcmin (-0.2 div down)
  • E7:   α = 0.652 deg, β = +1.0 arcmin (0.5 div up)
  • E8:   α = 0.675 deg, β = +2.0 arcmin (1.0 div up)
  • E9:   α = 0.645 deg, β = - 2.4 arcmin (-1.2 div down)
  • E10: α = 0.640 deg, β = +2.2 arcmin (1.1 div up)
  • E11: α = 0.638 deg, β = +1.6 arcmin (0.8 div up)
  • E12: α = 0.660 deg, β = +1.6 arcmin (0.8 div up)
  • E13: α = 0.638 deg, β = +0.8 arcmin (0.4 div up)
  • E14: α = 0.655 deg, β = +0.4 arcmin (0.2 div up)
  • E15: α = 0.640 deg, β = +1.4 arcmin (0.7 div up)
  • E16: α = 0.655 deg, β = +0.6 arcmin (0.3 div up)
  • E17: α = 0.650 deg, β = +0.8 arcmin (0.4 div up)
  • E18: α = 0.640 deg, β = +2.4 arcmin (1.2 div up)


  • \theta_H = ArcSin[Sin(α) / n]
  • \theta_V = ArcSin[Sin(β) / n]/2
  • E1:   \theta_H = 0.460 deg, \theta_V =   0.000 deg
  • E2:   \theta_H = 0.432 deg, \theta_V =  -0.0034 deg
  • E3:   \theta_H = 0.439 deg, \theta_V =   0.000 deg
  • E4:   \theta_H = 0.451 deg, \theta_V =  0.016 deg
  • E5:   \theta_H = 0.475 deg, \theta_V =  0.011 deg
  • E6:   \theta_H = 0.455 deg, \theta_V =  -0.0046 deg
  • E7:   \theta_H = 0.446 deg, \theta_V =  0.011 deg
  • E8:   \theta_H = 0.462 deg, \theta_V =  0.023 deg
  • E9:   \theta_H = 0.441 deg, \theta_V =  -0.027 deg
  • E10:   \theta_H = 0.438 deg, \theta_V = 0.025 deg
  • E11:   \theta_H = 0.436 deg, \theta_V = 0.018 deg
  • E12:   \theta_H = 0.451 deg, \theta_V = 0.018 deg
  • E13:   \theta_H = 0.436 deg, \theta_V = 0.0091 deg
  • E14:   \theta_H = 0.448 deg, \theta_V = 0.0046 deg
  • E15:   \theta_H = 0.438 deg, \theta_V = 0.016 deg
  • E16:   \theta_H = 0.448 deg, \theta_V = 0.0068 deg
  • E17:   \theta_H = 0.444 deg, \theta_V = 0.0091 deg
  • E18:   \theta_H = 0.438 deg, \theta_V = 0.027 deg
  53   Thu Jan 10 18:37:50 2013 KojiOpticsCharacterizationWedging of the PZTs

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?

ELOG V3.1.3-