[Joe, Koji, Liyuan, Philip, Stephen]
Work done on 16.04.2019

Finishing assembly of transport box
Assembly worked fine except for the clamping structure to clamp the lid of the transport box to the bottom part.
It seemed that some of the plastic of these clamps became brittle during the baking. The plastic was removed and the
clamps where wiped clean. It appears that the clamps can't be locked as they should. Still the transport box should be fine
as the long screws will mainly clamp the two parts together.

Preparing the transport box to mount the breadboard
The lid of the the transport box was placed upside down and clamped to the table. All peak clamping structures where pulled back as far as possible.

Preparation and cleaning of the breadboard
We unpacked the breadboard and found lots of dust particles on it (most likely from the soft paper cover which was used). We used the ionized nitrogen gun
at 25 psi to get rid of the majority of particles and cross-checked with a bright green flash light before and after blowing. The second stage of cleaning was done
below the clean room tent and included the wiping of all surfaces. The breadboard was then placed into the prepared lid of the transport box and clamped with peak
screws.

Unpacking of the template
The previously cleaned template was unpacked while the last layer of coverage was removed below the cleanroom tent.

Template adjustment on the breadboard
All peak screws of the clamping structure of the template where removed. The template was placed onto the breadboard only seperated by peak spacers.
All peak screws have been inserted for horizontal clapming. A calipper was used to measure the distance of each edge of the template to the edge of the
breadboard. For documentation the labeled side of the bradboard (facing away from the persons on the pictures) of the upside down breadboard is defined to 
be the south side, continuing clockwise with west, north and east. First rough alignment was done by shifting the template on the breadboard and then the 
peak screws where used for fine tuning. The caliper values measured where:
North   C 8.32mm     E 8.52 mm     W 8.41 mm
East     C 8.08 mm
South   C 8.32 mm
West    C 8.02 mm
(E indicating east side position, W indicating west side position and C indicating center position)

[Stephen, Philip, Koji, Joe]

Breadboard D1200105 SN06 was selected as described in eLOG 338. This log describes unwrapping and preparation of the breadboard.

Relevant procedure section: E1300201 section 6.1.5

Breadboard was unwrapped. No issues observed during unwrapping.

• Attachment 1: packaging of SN06.

Visual inspection showed no issues observed in breadboard - no large scratches, no cracks, no chipping, polished area (1 cm margin) looks good.

• Attachment 2: engraving of SN06.

Initially the breadboard has a large amount of dust and fiber from the paper wrapping. Images were gathered using a green flashlight at grazing incidence (technique typical of optic inspection).

PROCEDURE IMPROVEMENT: Flashlight inspection and Top Gun use should be described (materials, steps) in E1300201.

• Attachment 3: particulate before Top Gun, large face.
• Attachment 4: particulate before Top Gun, small face.

Top gun was used (with medium flow rate) to remove large particulate. Breadboard was placed on Ameristat sheet during this operation.

• Attachment 5: particulate after Top Gun

Next, a clean surface within the cleanroom was protected with Vectra Alpha 10 wipes. The breadboard, with reduced particulate after Top Gun, was then placed inside the cleanroom on top of these wipes. Wiping with IPA Pre-wetted Vectra Alpha 10 wipes proceeded until the particulate levels were acceptable.

Joe and Koji then proceeded with placing the breadboard into the transport fixture.

Apr 16, 2019
Borrowed two laser goggles from the 40m. (Returned Apr 29, 2019)
Borrowed small isopropanol glass bottole from CTN.

Apr 19, 2019
Borrowed from the 40m:
- Universal camera mount
- 50mm CCD lens
- zoom CCD lens (Returned Apr 29, 2019)
- Olympus SP-570UZ (Returned Apr 29, 2019)
- Special Olympus USB Cable (Returned Apr 29, 2019)

After having dug into the past email, it turned out that these wires were the ones already replaced from the original teflonwires. The length of them were confirmed to be ~19" (480mm). 

We are going to use E6, E9, E11, and E14 for BS1, SM1, SM2, and SM3. They (and E18) are all very similar.

The attachment is the excerpt from T1500060 with some highlighting

We are going to use B6 for the DCPD BS (BS2), and B1 for the QPD BS (BS3). Their role can not be swapped.

B6 has the best loss among the available ones, while the perpendicularity is not so critical due to the short arm.

B1 has the OK perpendicularity, while the loss is also moderately good.

The attachment is the excerpt from T1500060 with some highlighting.

We are going to use A5 and A14 for FM1 and FM2. (The role of these two can be swapped)

The reason for the selection is the better perpendicularity among the available prisms.

A11 has the best perpendicularity among them. However, the T didn't match with the others. The pair of A5 and A14 has a good matching with small compromise of the perpend.

The attachment is the excerpt from T1500060.

D1200105 SN006 was selected as the breadboard for OMC(004).
The reason is the best parallelism among the unused ones.

The attached is the excerpt from T1500060 with the #006 highlighted.

Attachment 1: Shadow sensor setup for the PZT displacement test

Attachment 2: PZT endurance test. 4 PZTs were shaken at once.

Attachment 3~5: Function generator setup 100Hz, 3.5Vpp 1.75Voffset (meant be displayed for 50Ohm load)

Attachment 6: The above setting yields 7Vpp unipolar signal @Hi-Z load

Attachment 7: The output was monitored with a 1/10 probe with the PZTs connected. This shows 10Vmax 0Vin -> Good. This photo was taken at 17:35.

Attachment 8: The test is going well @9:15 next day. (t=15.7hours = 5.6Mcycles)

Attachment 9: The test went well. The modulation was stopped @15:35. (t=21hours = 7.6Mcycles)

[Koji, Philip]

Today we tested the functionality of the four remaining PZTs (11,12,13 and 22) .  Each PZT was placed within a collimated 500um beam.
Roughly half of the beam was blocked by the PZT. The PZT and a PD then acted as shadow sensor. Each PZT was tested with 0 and
150 V. The resulting power change then could be converted into a displacement of the PZT using the beam diameter.

The open light value for each of these tests was 3.25 V.

PZT 11:
0 V supply voltage     --> 1.717 V on PD
150 V supply voltage --> 1.709 V on PD
delta = 0.008 V

PZT 12:
0 V supply voltage     --> 1.716 V on PD
150 V supply voltage --> 1.709 V on PD
delta = 0.007 V

PZT 13:
0 V supply voltage     --> 1.702 V on PD
150 V supply voltage --> 1.694 V on PD
delta = 0.008 V

PZT 22:
0 V supply voltage     --> 1.770 V on PD
150 V supply voltage --> 1.762 V on PD
delta = 0.008 V

0.008 V --> 0.24% change in power on PD --> about  3.8 um displacement assuming no light which is blocked
by the PZT is hitting the PD.

We further started to drive all four PZTs over night with 100 V (half of their range) at 100 Hz.
We additionally display the impedance to ensure none of them degrades.

All four PZTs seem to be connected to Teflon coated wires. It needs to be checked if these
fulfill the vacuum compatibility requirements.

Sub-ASSY #10

Attachment #1: Mounting Block SN021

Attachment #2: PZT-Mounting Block bonding looks just excellent.

Attachment #3: The other side of the PZT-Mounting Block bonding is also excellent.

Attachment #4: The mirror-PZT bonding also look excellent. Some barrel fracture is visible at the lower left of the mirror.

Sub-ASSY #9

The most fractured unit among four.

Attachment #1: Mounting Block SN017

Attachment #2: Two large removals well visbile. The bottom right corener was chipped.

Attachment #3: Another view of the chipping.

Attachment #4: PZT-mounting block bonding look very good.

Attachment #5: Another view of the PZT-mounting block bonding. Looks very good too.

Attachment #6: Fractures bonded on the fixture.

Attachment #7: Front view. The mirror-PZT bonding look just fine.

Sub-ASSY #8

Probably the best glued unit among the four.

Attachment #1: Mounting Block SN007

Attachment #2: Overall look.

Attachment #3: Some fracture on the barrel visible.

Attachment #4: It is visible that a part of the PZT removed. Otherwise, PZT-Mounting Block bonding looks pretty good.

Attachment #5: The other side of the PZT bonding. Looks fine.

Attachment #6: Fractured PZT visible on the fixture parts.

Attachment #7: Fractured glass parts also visible on the fixture parts.

Attachment #8: MIrror bonding looks fine except for the glass chip.

Sub-ASSY #7

Probably the best glued unit among the four.

Attachment #1: Mounting Block SN001

Attachment #2: PZT-Mounting Block bonding looks completely wet. Excellent.

Attachment #3: The other side of the PZT-Mounting Block bonding. Also looks excellent.

Attachment #4: Overall look.

Attachment #5: The mirror-PZT bonding also look excellent. The mounting block surface has many EP30-2 residue. But they were shaved off later. The center area of the aperture is clear.

Attachment #6: A small fracture of the mirror barrel is visible (at 7 o'clock).

[Koji Stephen]

(Friday afternoon) We retrieved the PZT sub-assemblies to the clean room.

We started removing the ASSYs from the fixtures. We noticed that some part of the glass and PZT are ripped off from the ASSY and stuck with the fixture. For three ASSYs (except for #9), the effect is minimal. However, ASSY #9 has two large removals on the front surface, and one of the bottom corners got chipped. This #9 is still usable, I believe, but let's avoid to use this unit for the OMC. Individual inspection of the ASSYs is posted in the following entries.

This kind of fracture events was not visible for the past 6 PZT sub-ASSYs. This may indicate a few possibilities:
- More rigorous quality control of EP30-2 was carried out for the PZT ASSY bonding. (The procedure was defined after the past OMC production.) The procedure leads to the strength of the epoxy enhanced.
- During the strong and fast thermal cycling, the glass was exposed to stress, and this might make the glass more prone to fracture.

For the production of the A+ units, we think we can avoid the issues by modifying the fixtures. Also, reliable temperature control/monitor technology should be employed. These improvements should be confirmed with the bonding of spare PZTs and blank 1/2" mirrors before gluing any precious components.

[Stephen Koji]

The baking of the PZT subassemblies was more complicated than we initially thought.

The four PZT subassemblies were placed in the air bake oven A. We meant to bake the assemblies with the ramp time of 2.5h, a plateau of 2h at 94degC, and slow ramp down.

The oven controller was started and the temperature has been monitored. The ramping up was ~20% faster than expected (0.57degC/min instead of 0.47degC/min), but at least it was linear and steady.

Once the temperature reached the set temperature (around t=120min), the temperature started oscillating between 74 and 94degC. Stephen's interpretation was that the PID loop of the controller was not on and the controller falled into the dead-bang mode (=sort of bang-bang control).

As the assembly was already exposed to T>70F for more than 2.5hours, it was expected the epoxy cure was done. Our concern was mainly the fast temperature change and associated stress due to thermal expansion, which may cause delamination of the joint. To increase the heat capacity of the load, we decided to introduce more components (suspension balance weights). We also decided to cover the oven with an insulator so that the conductive heat loss was reduced.

However, the controller thought it was already the end of the baking process and turned to stand-by mode (i.e. turned off everything). This started to cause rapid temp drop. So I (Koji) decided to give a manual heat control for mind cooling. When the controller is turned off and on, it gives some heat for ramping up. So the number of heat pulses and the intervals were manually controlled to give the temp drop of ~0.5degC/min. Around t=325, the temperature decay was already slower than 0.5degC/min without heat pulse, so I decided to leave the lab.

We will check the condition of the sub-assemblies tomorrow (Fri) afternoon.

[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).

Also brought to the 40m on 10 April, in preparation for PZT subassembly bonding:

- new EP30-2 epoxy (purchased Jan 2019, expiring Jul 2019 - as documented on documents attached to glue, also documented at C1900052.

- EP30-2 tool kit (maintained by Calum, consisting of mixing nozzles, various spatulas, etc)

Already at the 40m for use within PZT subassembly bonding:

- "dirty" ABO A with temperature controller (for controlled ramping of curing bake)

- clean work areas on laminar flow benches

- Class B tools, packaging supplies, IPA "red wipes", etc.

Upon reviewing EP30-2 procedure T1300322 (current revision v6) and OMC assembly procedure E1300201 (current revision v1) it appears that we have gathered everything required.

Preparation for the PZT subassembly bonding (Section 6.2 and 7.3 of T1500060 (aLIGO OMC optical testing procedure)
- Gluing fixture (Qty 4)
- Silica sphere powder
- Electric scale
- Toaster oven for epoxy mixture qualification

- M prisms
- C prisms
- Noliac PZTs

- Cleaning tools (forceps, tweezers)
- Bonding kits (copper wires, steering sticks)
- Thorlabs BA-2 bases Qty2
- Razor blades

OMC(002) repair completed

When the cable harness of OMC(004) is going to be assembled, the cable harness of OMC(002) will be replaced with the PEEK one. Otherwise, the work has been done.

Note that there are no DCPDs installed to the unit. (Each site has two in the OMC and two more as the spares)

More photos: https://photos.app.goo.gl/XdU1NPcmaXhATMXw6

QPD#              QPD1       QPD2
Housing#          #004       #008
Diode#            #44        #46
Shim              (see OMC ELOG 323)
-------------------------------------
Power Incident    252.3 uW  266.0 uW
Sum Out           174.2 mV  176.0 mV   +0.3
Vertical Out      + 4.7 mV  +19.0 mV   +0.2
Horizontal Out    -16.1 mV  - 8.0 mV   +0.0
SEG1              -52.4 mV  -53.  mV   -0.1
SEG2              -37.6 mV  -47.  mV   -0.1
SEG3              -41.8 mV  -34.  mV   -0.1
SEG4              -43.7 mV  -36.  mV   -0.1
-------------------------------------
Spot position X   +39   um  +15. um  (positive = more power on SEG1 and SEG4)
Spot position Y   - 8.1 um  -56. um  (positive = more power on SEG3 and SEG4)
-------------------------------------
Responsivity[A/W] 0.69      0.66
Q.E.              0.80      0.77
-------------------------------------

Arrangement of the segments
View from the beam
/ 2 | 1 X
|---+---|
\ 3 | 4 /

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

I(w,x,y) = Exp[-2 (x^2 + y^2)/w^2]/(Pi w^2/2)

(SEG_A+SEG_B-SEG_C-SEG_D)/(SEG_A+SEG_B+SEG_C+SEG_D) = Erf[sqrt(2) d/w]

d: distance of the spot from the center
w: beam width

The beam height in the cavity became totally different from the previous one and the shims needed to be much thicker than before. This is probably because of the alignment of the newly-glue curved mirror.

As the beam height is 2~2.5mm higher, two shims need to be stacked. The preliminary check of the heights using the alignment disks (dummy PDs) suggested the following combinations.

QPD1(SHORT)  D1201467-03 (SN 007) + D1201467-03 (SN 008) (2.0 mm + 2.0 mm = 4 mm)
QPD2(LONG)   D1201467-01 (SN 001) + D1201467-01 (SN 002) (1.5 mm + 1.5 mm = 3 mm)
DCPD1(TRANS) D1201467-02 (SN 006) + D1201467-03 (SN 005) (1.75mm + 2.0 mm = 3.75 mm)
DCPD2(REFL)  D1201467-02 (SN 002) + D1201467-03 (SN 006) (1.75mm + 2.0 mm = 3.75 mm)

This resulted that the fixing button head socket screws for the PD housings to be replaced from 5/16" to 7/16". Stephen kept CLASS A spare screws from Jeff's time.

For the DCPD alignment, a cap-removed Excelitas 3mm InGaAs PD is used. -> This needs to be returned to the PD stock next time.

- DCPD1 was aligned using the zoomed CCD image (Attachment 1). Once the beam is aligned, the angle was tweaked to have the reflection nicely dumped by the glass beam dump (Attachment 2).

- DCPD2 was aligned too. (Attachment 2/3)

- The two housings were fastened by a torque wrench at 2 inch lb.

Next step:

Continue with the QPDs. The QPD amp was already set.

Notes:
The cable of the CCD monitor has a problem -> need to check what's wrong
The servo box probably have large offset at the output stage or somewhere (but not input stages).

There was a concern that the transmission from CM1 has additional fringes. The shape of the transmitted beams from CM1, CM2, and FM2 (main) werecaptured with WinCamD.
Indeed CM1 and CM2 have the fringes, but it does not exist in the main transmission. So it seems that the fringes are associated with the curved mirrors. But how???

== Office Depot ==
Really Useful Box 9L x 6 (delivered)
Really Useful Box 17L x 5 (ordered 4/4)
P-TOUCH tape (6mm, 9mm, 12mmx2, 18mm) (ordered 4/4)

== Digikey ==
9V AC Adapter (- inside, 1.3A) for P-TOUCH (ordered 4/4)
12V AC Adapter (+ inside, 1A) for Cameras (ordered 4/4)

== VWR ==
Mask KIMBERLY CLARK "KIMTECH Pure M3" ISO CLASS 3 (ordered 4/4)

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.

OMC #002 Optical tests

• FSR measurement (done, 2019/1/8-9, 2019/4/1)
• TMS measurement (done, 2019/1/9)
• TMS measurement (with DC voltage on PZTs) (done, 2019/1/10)
• Cleaning (done, 2019/3/19)
• Power Budget (done, 2019/3/19, 2019/4/1)
• PZT DC response (done, 2019/3/27)
• PZT AC response (done, 2019/3/27)
• QPD alignment (done, 2019/4/5)
• DCPD alignment (done, 2019/4/4)
• Beam quality check (done, 2019/4/4)

(Backscattering test)

(Cabling / Wiring)

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

(Baking)
(First Contact)
(Packing / Shipping)

OMC (002) after repair
History:Mirror replacement after the damage at H1. Measurement date 2019/1/10

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

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

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

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

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.

Mode cleaning capability of an optical fiber was measured. The conclusion is that the leakage of the non-fiber mode to the fiber output is insignificant and also practically negligible.

The tested fiber was Thorlabs 5-m Polarization Maintaining Single-Mode fiber (P3-1064PM-FC-5, PM Patch Cable, PANDA, 1064 nm, FC/APC, 5m).

The output mode cleaner was used as a mode analyzer. The fiber input was aligned and the misaligned so that the amount of higher order mode for the fiber is changed. The fiber output has been mode matched to an output mode cleaner. Therefore excess mode mismatch when the fiber input was misaligned, was accounted as the leakage higher order mode.

For each alignment state, the OMC transmission (in V), the OMC reflection (in V), and the OMC reflection with the OMC unlocked were measured. The voltages were measured with a digital multimeter (non-portable unit). With the fiber input beam aligned to the fiber, the fiber input and output powers were measured with a power meter.

With the input beam aligned
- Fiber input: 52.5 +/- 0.2 [mW]
- Fiber output: 35.5 +/- 0.2 [mW] (~68% coupling)
- Reflection PD offset: -0.00677 +/- 0.00001 [V]

- Refl PD reading with the OMC unlocked: 6.32 +/- 0.01 [V]
- Refl PD reading with the OMC locked: 0.133 +/- 0.002 [V]
- OMC Trans PD with the OMC locked: -1.72 +/- 0.01 [V] 

With the input beam misaligned
- Refl PD reading with the OMC unlocked: 3.63 +/- 0.01 [V]
- Refl PD reading with the OMC locked: 0.0752 +/- 0.001 [V]
- OMC Trans PD with the OMC locked: -1.00 +/- 0.01 [V] 

The naive mode matching was 0.9779 +/- 0.0003 and 0.9775 +/- 0.0003 without and with misalignment. We initially had roughly 17mW of non-fiber mode incident. And it was increased by roughly 15mW. For the misaligned case, the amount of the OMC-matched carrier was also reduced due to the misalignment. So the actual fiber mode cleaning effect needs more careful quantitative analysis.

The power budget at each part of the setup was modeled as shown in Attachment 1. The blue numbers are the measured values.
The factor a is the ratio of the leakage non-fiber mode into the fiber transmission.
The factor (1-b) is the mode matching of the fiber mode into the OMC mode.

and

With the calibration between the refl PD and the power meter measurement,
 

The solution of the equations is

So, the leakage of the non-fiber mode to the fiber output is insignificant. Moreover, the number is practically negligible because the mismatching between the fiber and OMC modes is of the order of percent and dominated by the aberration of the collimator (i.e. the OMC reflection looks like concentric higher-order LG modes) with the order of 1~2%.
 

As OMC SN002 already has the PZTs connected to the Mighty-Mouse connector, a test cable with a female mighty-mouse connector was made.

A small imperfection: When the cable was inserted to the connector shell, I forgot to mirror the pin out. Therefore the color and pin number do not match.

OMC SN002 = Former LHO OMC which CM1 was destroyed by the lock loss pulse in 2016. This OMC needs to be optically tested before storage.

The test items:

• [done] FSR measurement with offset PDH locking (FM->AM conversion)
• [done] FSR/finesse measurement with the EOM RFAM injection
• [done] TMS measurement with input miaslignment and the trans RFPD misalignment: with no PZT offset
• [done] TMS measurement with input miaslignment and the trans RFPD misalignment: with PZT offsets
   
• PZT response
• Mirror cleaning
• Power budget
• Diode alignment: shim height
• PD/QPD alignment

I'm still not satisfied/done with the solution to this, but this has gone too long without an update and anyway probably someone else will have a direction to take it that prevents me spinning my wheels on solved or basic questions.

The story will have to wait to be on the elog, but I've put it in the jupyter notebook. Basically:

• I considered the polarization-separated OMC in several configurations. I have plots of DARM referred noise (measured free-running and controlled noise for the current OMC, thermal theoretical noise curve, scattered light) for the case of such an OMC with one lambda/2 waveplate oriented at 45 degrees. This is the base case.
• I also considered such an OMC with a lambda/2 both before and after the OMC, where their respective polarization axes can be arbitrary (I look at parameter space near the previous case's values).
  • I optimize the BHD angle to balance the homodyne (minimize the E_LO^2 term in the homodyne readout).
  • I then optimize the rotations of the lambda/2 polarization axes to minimize the noise
  • For the optimum that is closest to the base case, I also plotted DARM referred length noise.

It's clear to me that there is a way to optimize the OMC, but the normalization of my DARM referred noise is clearly wrong, because I'm finding that the input-referred noise is at least 4e-11 m/rt(Hz). This seems too large to believe. 

Indeed, I was finding the noise in the wrong way, in a pretty basic mistake. I’m glad I found it I guess. I’ll post some plots and update the git tomorrow. 

I started some analytic calculations of how OMC mirror motion would add to the noise in the BHD. I want to make some prettier plots, and am adding the interferometer so I can also compute the noise due to backscatter into the IFO. However, since I've pushed the notebook I wanted to post an update. Here's the location in the repo.

I used Koji's soft limit of 0.02 degrees additional phase accumulation per reflection for p polarization.

[Koji Gautam]


With Gautam's help, I ran a coating design code for an HR mirror with the standard quarter-wave design. The design used here has 17 pairs of lambda/4 layers of SiO₂ and Ta₂O₅ (=34 layers) with the fused silica as the substrate to realize the transmission of tens of ppm. At the AOI (angle of incidence) of 4 deg (=nominal angle for the aLIGO OMC), there is no significant change in the reflectivity (transmissivity). With 95% of the case, the phase difference at the AOI of 4 deg is smaller than 0.02 deg for given 1% fluctuation (normal distribution) of the layer design and the refractive indeces of the materials. Considering the number of the OMC mirrors (i.e. 4), the total phase shift between P and S pols is less than 0.08 deg. This makes P and S resonances matched well within 1/10 of the cavity resonant width (360/F=0.9deg, F: Finesse=400).

Of course, we don't know how much layer-thickness fluctuation we actually have. Therefore, we should check the actual cavity resonance center of the OMC cavity for the polarizations.

Attachment 1 shows the complex reflectivity of the mirror for P and S pols between AOIs of 0 deg and 45 deg. Below 30 deg there is no significant difference. (We need to look at the transmission and the phase difference)

Attachment 2 shows the power transmissivity of the mirror for P and S pols between AOIs of 0 deg and 45 deg. For the purpose to check the robustness of the reflectivity, random fluctuations (normal distribution, sigma = 1%) were applied to the thicknesses of each layer, and the refractive indices of Silica and Tantala. The blue and red bands show the regions that the 90% of the samples fell in for P and S pols, respectively. There are median curves on the plot, but they are not well visible as they match with the ideal case. This figure indicates that the model coating well represents the mirror with the transmissivity better than 70ppm.

Attachment 3 shows the phase difference of the mirror complex reflectivity for P and S pols between AOIs of 0deg and 45deg. In the ideal case, the phase difference at the AOI of 4deg is 1x10^-5 deg. The Monte-Carlo test shows that the range of the phase for 90% of the case fell into the range between 5x10^-4 deg and 0.02 deg. The median was turned to be 5x10^-3 deg.

Attachment 4 shows the histogram of the phase difference at the AOI of 4deg. The phase difference tends to concentrate at the side of the smaller angle.

0. If you have an RF signal whose waveform is , the amplitude is constant and 1.

1. If the waveform , the amplitude has the DC value of 1 and AM with the amplitude of 0.1 (i.e. swing is from 0.9 to 1.1). Therefore the RMS RIN of this signal is 0.1/1/Sqrt(2).

2. The above waveform can be expanded by the exponentials.

Therefore the sideband carrier ratio R is 0.025/0.5 = 0.05. This corresponds to 20 log10(0.05) = -26dBc

In total, we get the relationship of dBc and RIN as , or R = RIN/sqrt(2)

[Rich Koji]

The impedances of the new LLO EOM were measured with the beat note setup at the 40m PSL (as described in the previous ELOG entry.

At the target frequencies (9.1MHz, 24.1MHz, 45.5MHz, 118.3MHz), the modulation responses were (0.09, 2.9e-3, 0.053, 0.021) rad/V.

This corresponds to the requirement for the driving power as follows.

Attached is a block diagram of the test setup used in the 40m lab to measure the modulation index of the IO modulator

[Rich, Dean, Koji]

Stuffed all inductors for the new LLO EOM. As the impedances were sensitive to the positions of the inductors in the housing, they were glued with a glue gun.
Also the lid of the housing significantly change the stray capacitance and lowers the resonant frequency (meaning lowers the Q too), we decided to tune the matching circuit without the lid.

The attached plots show the measured impedances. They all look well tuned and matched. We will prepare and perform the optical measurement at the 40m.

[Rich Koji]

The 9MHz port was tuned and the impedance was measured.

The circuit models for the 3IFO EOM (before mods) were made using LISO.
Then the modification plan was made to make it a new LLO EOM.

Impedance data, LISO model, Mathematica files are zipped and attached at the end.

Attached please see my notes summarizing the models for the electrodes and inductors within the 3rd IFO EOM

Koji, Rich

We took apart the unit removed from the 3rd IFO (Unit serial number aLIGO #3, XTAL 10252004) to see what makes it tick.  Koji has done a fine job of adding the plots of the impedance data to this log book.  Attached are some details of the physical construction showing the capacitor values used in shunt before the coils.

[Rich Koji]

The impedances of the individual components from the 3IFO EOM (before modification) were tested.
Each component was modeled by LISO. The LISO model (in PDF and txt) are attached at the end of the entry.

Coils
There are three inductors taken from the EOM unit. They showed the Q ranging from 150~300.
Their impedances are compared with the coil taken from the 9MHz port of the spare EOM (=current LHO EOM).
The inductance of the 8.7MHz inductor indicated higher L but still higher Q.

Todd made a replica of the 45.3MHz coil. He used a silver plated wire and it actually showed highest Q of ~400.

Crystal capacitance
The crystal capacitances were measured by attaching a test rig on the DB15 connector of the crystal housing. The rig was calibrated such that the impedances of the attched components on the rig were measured. They showed somewhat similar feature with parasitic resonances at ~50MHz. Above this frequnecy the capacitance went down (i.e. Abs(Z) went up). This indicates there are stray series LCR in pararrel to the crystal. Not sure what is the cause of this.

The central (24.1MHz) port showed smaller capacitance. This probably means the plates for the central port is smaller. Not sure the actual dimensions of the plates for this unit.
 

[Rich Koji]

3IFO EOM (before any modification) was tested to measure the impedance of each port.

The impedance plot and the impedance data (triplets of freq, reZ, imZ) were attached to this entry.

3IFO EOM dark microscope images courtesy by GariLynn and Rich

Attachment1/2: Hole #1
Attachment3/4: Hole #2
Attachment5: Hole #2

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