40m QIL Cryo_Lab CTN SUS_Lab TCS_Lab OMC_Lab CRIME_Lab FEA ENG_Labs OptContFac Mariner WBEEShop
 OMC elog, Page 8 of 9 Not logged in
ID Date Author Type Category Subject
198   Sun Jul 6 03:56:40 2014 KojiOpticsCharacterizationHOM measurement with PZT vol swept

Cavity FSR/TMS measurement (2014/7/5) with PZT voltages swept from 0V to 200V (50V step)

Attachment 1: Cav_scan_response_PZT1.pdf
Attachment 2: Cav_scan_response_PZT2.pdf
Attachment 3: OMC_HOM_140705.pdf
199   Sun Jul 6 08:31:14 2014 KojiOpticsCharacterizationHOM measurement with PZT vol swept

3rd OMC, HOM diagram at PZT1=0V and PZT2=50V.

First coincidence with the carrier is the 32nd-order carrier mode. Very good.

Attachment 1: HOM_plot.pdf
202   Tue Jul 8 18:54:54 2014 KojiMechanicsCharacterizationPZT characterization

Each PZT was swept with 0-150V 11Hz triangular wave.
Time series data for 0.2sec was recorded for each PZT.

The swept voltage at the resonances were extracted and the fringe number was counted.
Some hysteresis is seen as usual.

The upward/downward slopes are fitted by a linear line.

The average displacement is 11.3nm/V for PZT1 and 12.7nm/V.

The PZT response was measured with a FFT analyzer. The DC calibration was adjusted by the above numbers.

Attachment 1: PZT_Scan.pdf
Attachment 2: I1OMC_PZT_Response.pdf
205   Thu Jul 10 23:22:28 2014 KojiOpticsCharacterizationI1OMC QPD

QPD#              QPD1       QPD2 Housing#          #006       #007 Diode#            #50        #51 Shim              1.25mm 03  1.25mm 02   (1.25mm = D1201467-10) ------------------------------------- Power Incident    123.1-13.0 uW  124.5-8.0 uW Sum Out            77.0 mV   82.5 mV Vertical Out      -24.0 mV  - 8.8 mV Horizontal Out      4.2 mV    9.0 mV SEG1              -11.6 mV  -16.0 mV SEG2              -12.6 mV  -18.0 mV SEG3              -25.2 mV  -24.4 mV SEG4              -21.4 mV  -21.4 mV ------------------------------------- Spot position X   -21   um  -19   um  (positive = more power on SEG1 and SEG4) Spot position Y   +102  um  +47   um  (positive = more power on SEG3 and SEG4) ------------------------------------- Responsivity[A/W] 0.70      0.71 Q.E.              0.82      0.83 -------------------------------------

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

206   Fri Jul 11 00:06:33 2014 KojiOpticsCharacterizationI1OMC PD

DCPD#             DCPD1      DCPD2 Housing#          #009       #010 Diode#            #07        #10 Shim              1.00mm 01  1.00mm 02   (1.00mm = D1201467-09) ------------------------------------- Power Incident     11.1 mW   10.6 mW Vout                7.65 V    7.33 V Responsivity[A/W]   0.69      0.69 Q.E.                0.80      0.81 ------------------------------------- photo              2nd        1st

PD alignment confirmation

207   Sun Jul 13 17:46:28 2014 KojiOpticsCharacterizationOMC backscatter measurement

Backscattering reflectivity of the 3rdOMC was measured.

Attached: Measurement setup

1) A CVI 45P 50:50 BS was inserted in the input beam path. This BS was tilted from the nominal 45 deg so that the reflection of the input beam is properly dumped.
This yielded the reflectivity of the BS deviated from 45deg. The measured BS reflectivity is 55%+/-1%.

2) The backward propagating beam was reflected by this BS. The reflected beam power was measured with a powermeter.

3) The powermeter was aligned with the beam retroreflected from the REFL PDH and the iris in the input path. The iris was removed during the measurement
as it causes a significant scatter during the measurement.

4) While the cavity was either locked or unlocked, no visible spot was found at the powermeter side.

The input power to the OMC was 14.6mW. The detected power on the powermeter was 66.0+/-0.2nW and 73.4+/-0.3nW with the cavity locked and unlocked, respectively.
This number is obtained after subtraction of the dark offset of 5.4nW.

Considering the reflectivity of the BS (55+/-1%) , the upper limit of the OMC reflectivity (in power) is 8.18+/-0.08ppm and 9.09+/-0.09ppm for the OMC locked and unlocked respectively. Note that this suggests that the REFL path has worse scattering than the OMC cavity but it is not a enough information to separate each contribution to the total amount.

Impact on the OMC transmission RIN in aLIGO:

- The obtained reflectivity (in power) was 8ppm.
- For now, let's suppose all of this detected beam power has the correct mode for the IFO.
- If the isolation of the output faraday as 30dB is considered, R=8e-9 in power reaches the IFO.
- The IFO is rather low loss when it is seen as a high reflector from the AS port.
- Thus this is the amount of the light power which couples to the main carrier beam.

When the phase of the backscattered electric field varies, PM and AM are produced. Here the AM cause
the noise in DC readout. Particularly, this recombination phase is changing more than 2 pi, the fringing
between the main carrier and the backscattered field causes the AM with RIN of 2 Sqrt(R).

Therefore, RIN ~ 2e-4 is expected from the above of backscattering.

Now I'm looking for some measurement to be compared to with this number.

First, I'm looking at the alog by Zach: https://alog.ligo-la.caltech.edu/aLOG/index.php?callRep=8674

I'm not sure how this measurement can be converted into RIN. Well, let's try. Zach told me that the measured value is already normalized to RIN.
He told me that the modulation was applied at around 0.1Hz. The maximum fringe velocity was 150Hz from the plot.
At 100Hz, let's say, the RIN is 2e-6 /rtHz. The fringe speed at 100Hz is ~70Hz/sec. Therefore the measurement stays in the 100Hz freq bin
only for delta_f/70 = 0.375/70 = 5.3e-3 second. This reduces the power in the bin by sqrt(5.3e-3) = 0.073.

2e-6 = 2 sqrt(R) *0.73 ==> R = 2e-10

This number is for the combined reflectivity of the OMC and the OMC path. Assuming 30dB isolation of the output Faraday
and 20% transmission of SRM, the OMC reflectivity was 5e-6. This is in fact similar number to the measured value.

If I look at the OMC design document (T1000276, P.4), it mentions the calculated OMC reflection by Peter and the eLIGO measurement by Valera.
They suggests the power reflectivity of the order of 1e-8 or 1e-7 in the worst case. This should be compared to 8ppm.
So it seems that my measurement is way too high to say anything useful. Or in the worst case it creates a disastrous backscattering noise.

So, how can I make the measurement improved by factor of 100 (in power)

- Confirm if the scattering is coming from the OMC or something else. Place a good beam dump right before the OMC?

- Should I put an aperture right before the power meter to lmit the diffused (ambient) scatter coming into the detector?
For the same purpose, should I cover the input optics with an Al foil?

- Is the powermeter not suitable for this purpose? Should I use a PD and a chopper in front of the OMC?
It is quite tight in terms of the space though.

- Any other possibility?

Attachment 1: OMC_backscatter.pdf
208   Tue Jul 15 03:00:42 2014 KojiOpticsCharacterizationOMC backscatter measurement

Presence of the misaligned SRM (T=20%) was forgotten in the previous entry.
This effectively reduces the OMC reflectivity by factor of 25.

This is now reflected in the original entry. Also the argument about the power spectram density was modified.

 Quote: First, I'm looking at the alog by Zach: https://alog.ligo-la.caltech.edu/aLOG/index.php?callRep=8674 I'm not sure how this measurement can be converted into RIN. Well, let's try. Assuming his measurement is done with the single bounce beam from an ITM, and assuming this plot is already normalized for RIN, we may need to multiply the number on the plot by factor of two or so. Then it's about factor of 5 lower RIN than the expected RIN. And in terms of R, it is 25 times lower.

209   Tue Jul 15 03:34:16 2014 KojiOpticsCharacterizationOMC backscatter measurement

Backscatter measurement ~ 2nd round

Summary

- The backscatter reflectivity of the 3rd OMC is 0.71 ppm

- From the spacial power distribution, it is likely that this is not the upper limit but the actual specular spot from the OMC,
propagating back through the input path.

Improvement

- The power meter was heavily baffled with anodized Al plates and Al foils. This reduced many spourious contributions from the REFL path and the input beam path.
Basically, the power meter should not see any high power path.

- The beam dump for the forward going beam, the beamsplitter, and the mirrors on the periscope were cleaned.

- The power meter is now farther back from the BS to reduce the exposed solid angle to the diffused light

- The REFL path was rebuilt so that the solid angle of the PD was reduced.

Backscattering measurement

- Pin = 12.3 +/- 0.001 [mW]

- RBS = 0.549 +/- 0.005

- Pback = 4.8 +/- 0.05 [nW] (OMC locked)       ==> ROMC(LOCKED) = 0.71 +/- 0.01 [ppm]

- Pback = 3.9 +/- 0.05 [nW] (OMC unlocked)   ==> ROMC(UNLOCKED) = 0.57 +/- 0.01 [ppm]

Note that the aperture size of Iris(B) was ~5.5mm in diameter.

V-dump test

- Additional beam dump (CLASS A) was brought from the 40m. This allowed us to use the beam dump before and after the periscope.

- When the beam dump was placed after the periscope: P = 0.9+/-0.05nW

- When the beam dump was placed before the periscope: P=1.0+/-0.1nW

===> This basically suggests that the periscope mirrors have no contribution to the reflected power.

- When the beam dump was placed in the REFL path: P=2.1+/-0.1nW

Trial to find backward circulating beam at the output coupler

The same amount of backreflection beam can be found not only at the input side of the OMC but also transmission side.
However, this beam is expected to be blocked by the beamsplitter. It was tried to insert a sensor card between the output coupler
and the transmission BS, but nothing was found.

In order to see if the detected power is diffused light or not, the dependence of the detected light power on the aperture size was measured.
Note that the dark offset was nulled during the measurement.

IRIS B aperture   detected diameter   power
[mm]       [nW]  1.0        1.1
 2.5        2.6  4.25       4.0  5.5        4.6  8.0        5.3  9.0        6.1 11.0        6.3 15.0        7.0

We can convert these numbers to calculate the power density in the each ring.
(Differentiate the detected power and aperture area. Calculate the power density in each ring section, and plot them as a function of the aperture radius)

This means that the detected power is concentrated at the central area of the aperture.
(Note that the vertical axis is logarithmic)

If the detected power is coming from a diffused beam, the power density should be uniform.
Therefore this result strongly suggests that the detected power is not a diffused beam but
a reflected beam from the OMC.

According to this result, the aperture size of 2.6mm in raduis (5.5mm in diameter) was determined for the final reflected power measurement.

Attachment 1: OMC_backscatter.pdf
210   Thu Jul 17 02:19:20 2014 KojiMechanicsCharacterizationI1OMC vibration test

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

- 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

211   Sun Jul 20 17:19:50 2014 KojiMechanicsCharacterizationI1OMC vibration test ~ 2nd round

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

- 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.

Attachment 1: I1OMC_vibration_test.pdf
213   Mon Jul 21 01:02:43 2014 KojiMechanicsCharacterizationSome structual mode analysis

Prisms

Fundamental: 12.3kHz Secondary: 16.9kHz

DCPDs

Fundamental: 2.9kHz Secondary: 4.1kHz

QPDs

Fundamental: 5.6kHz Secondary: 8.2kHz

217   Wed Aug 27 23:13:13 2014 KojiOpticsCharacterizationCollection of the power budgetting info

L1 OMC Cavity power budget

H1 OMC Cavity power budget

3IFO OMC Cavity power budget

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.

Attachment 1: PZT_response_FEA.pdf
241   Tue Sep 8 11:18:10 2015 KojiOpticsCharacterizationPBS Transmission measurement

Motivation: Characterize the loss of the Calcite Brewster PBS.

Setup: (Attachment 1)

- The beam polarization is rotated by an HWP
- The first PBS filters out most of the S pol
- The second PBS further filters the S and also confirms how good the polarization is.

- The resulting beam is modulated by a chopper disk. The chopping freq can be 20~1kHz.

- The 50:50 BS splits the P-pol beam into two. One beam goes to the reference PD. The other beam goes to the measurement PD.

- Compare the transfer functions between RefPD and MeasPD at the chopping frequency with and without the DUT inserted to the measurement pass.

- The PBS shift the beam significantly. The beam can't keep the alignment on the Meas PD when the crystal is removed.
Therefore the "On" and "Off" states are swicthed by moving the PBS and the steering mirror at the same time.
The positions and angles of the mounts are defined by the bases on the table. The bases are adjusted to have the same spot position for these states as much as possible.

Device Under Test:

Brewster polarizer https://dcc.ligo.org/LIGO-T1300346

The prisms are aligned as shown in Attachment 2

Between the prisms, a kapton sheet (2MIL thickness) is inserted to keep the thin air gap between them.

Result:

Set1: (~max power without hard saturation)
PD1(REF) 10dB Gain (4.75kV/A) 6.39V
PD2(PBS) 10dB Gain (4.75kV/A) Thru 4.77V, PBS 4.75
Chopping frequency 234Hz, FFT 1.6kHz span AVG 20 (1s*20 = 20s)

Thru 0.748307, PBS 0.745476 => 3783 +/- 5 ppm loss
Thru 0.748227, PBS 0.745552 => 3575 +/- 5 ppm
Thru 0.748461, PBS 0.745557 => 3879 +/- 5 ppm
Thru 0.748401, PBS 0.745552 => 3806 +/- 5 ppm
Thru 0.748671, PBS 0.745557 => 4159 +/- 5 ppm
=> Loss 3841 +/- 2 ppm

Set2: (half power)
PD1(REF) 10dB Gain (4.75kV/A) 3.20V
PD2(PBS) 10dB Gain (4.75kV/A) Thru 2.38V, PBS 2.37
Chopping frequency 234Hz, FFT 1.6kHz span AVG 20 (1s*20 = 20s)

Thru 0.747618, PBS 0.744704 => 3898 +/- 5 ppm loss
Thru 0.747591, PBS 0.744690 => 3880 +/- 5 ppm
Thru 0.747875, PBS 0.744685 => 4265 +/- 5 ppm
Thru 0.747524, PBS 0.744655 => 3838 +/- 5 ppm
Thru 0.747745, PBS 0.744591 => 4218 +/- 5 ppm
=> Loss 4020 +/- 2 ppm

Set3: (1/4 power)
PD1(REF) 10dB Gain (4.75kV/A) 1.34V
PD2(PBS) 10dB Gain (4.75kV/A) Thru 1.00V, PBS 0.999
Chopping frequency 234Hz, FFT 1.6kHz span AVG 20 (1s*20 = 20s)

Thru 0.745140, PBS 0.741949 => 4282 +/- 5ppm loss
Thru 0.745227, PBS 0.741938 => 4413 +/- 5ppm
Thru 0.745584, PBS 0.741983 => 4830 +/- 5ppm
Thru 0.745504, PBS 0.741933 => 4790 +/- 5ppm
Thru 0.745497, PBS 0.741920 => 4798 +/- 5ppm
Thru 0.745405, PBS 0.741895 => 4709 +/- 5ppm
=> Loss 4637 +/- 2ppm

Possible improvement:

- Further smaller power
- Use the smaller gain as much as possible
- Compare the number for the same measurmeent with the gain changed

- Use a ND Filter instead of HWP/PBS power adjustment to reduce incident S pol
- Use a double pass configuration to correct the beam shift by the PBS

To be measured

- Angular dependence
- aLIGO Thin Film Polarizer
- HWP
- Glasgow PBS

Attachment 1: setup.JPG
Attachment 2: CaF2Prism.jpg
Attachment 3: CaF2Prism2.JPG
242   Wed Sep 9 01:58:34 2015 KojiOpticsCharacterizationPBS Transmission measurement

Calcite Brewster PBS Continued

The transmission loss of the Calcite brewster PBS (eLIGO squeezer OFI) was measured with different conditions.
The measured loss was 3600+/-200ppm.
(i.e. 900+/-50 ppm per surface)
The measurement error was limited by the systematic error, probably due to the dependence of the PD response on the spot position.

I wonder if it is better to attenuate the beam by a ND filter instead of HWP+PBS.

o First PBS power adjustment -> full power transmission, OD1.0 ATTN Full Power
PDA20CS Gain 10dB
Thru 0.746711, PBS 0.744155 => Loss L = 3423 +/- 5ppm

o Same as above, PDA20CS Gain 0dB (smaller amplitude = slew rate less effective?)
Thru 0.748721, PBS 0.746220 => L = 3340 +/- 5ppm

o Same as above but OD1.4 ATTN
Thru 0.744853, PBS 0.742111 => L = 3681 +/- 5ppm

o More alignment, more statistics
(PDA20CS 0dB gain =  0.6A/W, 1.51kV/A)
PD(REF, 0dB) 0.426V = 0.47W
PD(MEAS, 0dB) Thru 0.320V, PBS 0.318V = 0.35W, L = 6000+/-3000ppm

Chopping 234Hz, TF 1.6kHz AVG10
Thru 0.745152, PBS 0.742474 => 3594 +/- 5 ppm
Thru 0.745141, PBS 0.742467 => 3589 +/- 5ppm
Thru 0.745150, PBS 0.742459 => 3611 +/- 5ppm
Thru 0.745120, PBS 0.742452 => 3581 +/- 5ppm
Thru 0.745153, PBS 0.742438 => 3644 +/- 5ppm
=> 3604ppm +/-25ppm

o More power

Attenuation OD 1.0
PD(REF, 0dB) 0.875V = 0.97W
PD(MEAS, 0dB) Thru 0.651V, PBS 0.649V = 0.72W, L = 3100+/-1600ppm

Chopping 234Hz, TF 1.6kHz AVG10
Thru 0.746689, PBS 0.743789 => 3884 +/- 5ppm
Thru 0.746660, PBS 0.743724 => 3932 +/- 5ppm
Thru 0.746689, PBS 0.743786 => 3888 +/- 5ppm
Thru 0.746663, PBS 0.743780 => 3861 +/- 5ppm
Thru 0.746684, PBS 0.743783 => 3885 +/- 5ppm
=> 3890ppm +/- 26ppm

o Much less power

Attenuation OD 2.4
PD(REF, 0dB) 67.1mV = 74.0mW
PD(MEAS, 0dB) Thru 53.7V, PBS 53.5V = 59mW, L = 3700+/-1900ppm

Thru 0.745142, PBS 0.742430 => 3640 +/- 5ppm
Thru 0.745011, PBS 0.742557 => 3294 +/- 5ppm
Thru 0.744992, PBS 0.742537 => 3295 +/- 5ppm
Thru 0.745052, PBS 0.742602 => 3288 +/- 5ppm
Thru 0.745089, PBS 0.742602 => 3338 +/- 5ppm
=> 3371ppm +/- 151ppm

o Much less power, but different gain

Attenuation OD 2.4
PD(REF, 20dB) 662mV = 73.1mW
PD(MEAS, 20dB) Thru 501V, PBS 500V = 55.3mW, L = 2000+/-2000ppm

Thru 0.744343, PBS 0.741753 => 3480 +/- 5ppm
Thru 0.744304, PBS 0.741739 => 3446 +/- 5ppm
Thru 0.744358, PBS 0.741713 => 3553 +/- 5ppm
Thru 0.744341, PBS 0.741719 => 3523 +/- 5ppm
Thru 0.744339, PBS 0.741666 => 3591 +/- 5ppm
=> 3519ppm +/- 58ppm

Using the last 4 measurements, mean loss is 3596, and the std is 218. => Loss = 3600+/-200ppm

243   Thu Sep 10 04:03:42 2015 KojiOpticsCharacterizationMore polarizer optics measurement (Summary)

Brewster calcite PBS (eLIGO Squeezer OFI)

Loss L = 3600 +/- 200ppm
Angular dependence: Attachment 1

In the first run, a sudden rise of the loss by 1% was observed for certain angles. This is a repeatable real loss.
Then the spot position was moved for the second run. This rise seemed disappeared. Is there a defect or a stria in the crystal?

Wave plate (eLIGO Squeezer OFI?)

Loss L = 820 +/- 160ppm
Angular dependence: Attachment 2

Initially I had the similar issue to the one for the brewster calcite PBS. At the 0 angle, the loss was higher than the final number
and high asymmetric loss (~2%) was observed in the negative angle side. I checked the wave plate and found there is some stain
on the coating. By shifting the spot, the loss numbers were significantly improved. I did not try cleaning of the optics.

The number is significantly larger than the one described in T1400274 (100ppm).

Thin Film Polarlizer (aLIGO TFP)

Loss L = 3680 +/- 140ppm @59.75 deg
Angular dependence: Attachment 3

0deg was adjusted by looking at the reflection from the TFP. The optics has marking saying the nominal incident angle is 56deg.
The measurement says the best performance is at 59.75deg, but it has similar loss level between 56~61deg.

Glasgow PBS

It is said by Kate that this PBS was sent from Glasgow.

Loss L = 2500 +/- 600ppm
Angular dependence: Attachment 4

Attachment 1: eLIGO_PBS.pdf
Attachment 2: HWP.pdf
Attachment 3: TFP.pdf
Attachment 4: Glasgow_PBS.pdf
244   Wed Sep 23 17:49:50 2015 KojiOpticsCharacterizationMore polarizer optics measurement (Summary)

For the Glasgow PBS, the measurement has been repeated with different size of beams.
In each case, the PBS crystal was located at around the waist of the beam.
Otherwise, the measurement has been done with the same way as the previous entries.

Beam radius [um]  Loss [ppm]
 160              5000 +/-  500  390              2700 +/-  240 1100              5300 +/-  700 1400              2500 +/-  600 (from the previous entry) 2000              4000 +/-  350

Attachment 1: Glasgow_PBS_spotsize.pdf
245   Tue Dec 15 13:38:34 2015 KojiElectronicsCharacterizationEOM Driver linearity check

Linearity of the EOM driver was tested. This test has been done on Nov 10, 2015.

- Attachment 1: Output power vs requested power. The output start to deviate from the request above 22dBm request.

- Attachment 2: Ctrl and Bias voltages vs requested power. This bias was measured with the out-of-loop channel.
The variable attenuator has the voltage range of 0~15V for 50dB~2dB attenuation.

Therefore this means that:

- The power setting gives a voltage logarithmically increased as the requested power increases. And the two power detectors are watching similar voltages.

- And the servo is properly working. The control is with in the range.

- Even when the given RF power is low, the power detectors are reporting high value. Is there any mechanism to realize such a condition???

Attachment 1: Output_linearity.pdf
Attachment 2: Ctrl_Bias.pdf
246   Tue Dec 15 13:39:13 2015 KojiElectronicsCharacterizationPhase noise measurement of aLIGO EOM drivers

This measurement has been done on Dec 1st, 2015.

The phase noise added by the EOM driver was tested.

The test setup is depicted in the attached PDF. The phase of the RF detector was set so that the output is close to zero crossing as much as possible with the precision of 0.5ns using a switchable delay line box. The phase to voltage conversion was checked by changing the delayline by 1ns. This gave me somewhat larger conversion factor compared to the sine wave test using an independent signal generator. This was due to the saturation of the phase detector as the LO and RF both have similar high RF level for the frequency mixer used.

The measurement has done with 1) no EOM driver involved, 2) one EOM driver inserted in the RF path, and 3) EOM drivers inserted in both the LO and RF paths.

I could not understand why the measurement limit is so high. Also the case 2 seems too low comsidering the noise level for 1) and 3).

At least we could see clear increase of the noise between the case 1) and 3). Therefore, we can infer the phase noise added by the EOM driver from the measurements.

Note: The additional phase noise could be associated with the original amplitude noise of the oscillator and the amplitude-to-phase conversion by the variable attenuator. This means that the noise could be corellated between two EOM drivers. The true test could be done using a PLL with a quiet VCO. Unfortuantely I don't have a good oscillator sufficient for this measurement.

Attachment 1: phase_noise.pdf
Attachment 2: phase_noise_9MHz.pdf
247   Tue Dec 15 13:42:37 2015 KojiOpticsCharacterizationDimensions / packaging of HQE PDs

The dimensions of a high QE PDs was measured as well as the ones for C30665. (Attachment 4, Unit in mm)
They seemed to be very much compatible.

The PDs came with the designated case (Attachment 1). The bottom of the case has a spongy (presumably conductive) material.

Diodes have no window. Each came with an adhesive seal on it. (Attachment 2)
There is a marking of a serial at the side.

I opened one (Attachment 3). The sensitive area looks just beautiful. The seal was reapplied to avoid possible contamination.

Attachment 1: PC147842.jpg
Attachment 2: PC147846.jpg
Attachment 3: PC147848.jpg
Attachment 4: HQEPD_dimension.pdf
251   Sat Feb 20 19:11:22 2016 KojiElectronicsCharacterizationDark current measurement of the HQE PD and other PDs

Dark current of the HQE PD and other PDs were measured.

- The HQE PDs were loaded on the new PD transportation cages (Attachment 1)
The PDs are always shorted by a clean PD plugs. The PD element is still capped with Kapton seals.

- The assignment of the container/slot and the PDs are as follows

 Slot \ Container A B C D E 1 A1-23 B1-22 C1-07 C1-11 C1-17 2 A1-25 B1-23 C1-08 C1-12 C1-21 3 B1-01 C1-03 C1-09 C1-14 D1-08 4 B1-16 C1-05 C1-10 C1-15 D1-10

- The measurement has been done with KEITHLEY sourcemeter SMU2450.

- The result is shown in Attachment 2. Most of the PDs show the dark current of ~3nA at 15V bias. C1-05 and C1-07 showed higher dark current at high V region. We should avoid using them for the aLIGO purpose. I hope they are still OK at low bias V if there is no noise issue (TBC). You can not read the PD names on the plot for the nominal ones, but that's OK as they are almost equivalent.

- As a comparison, the dark current of a C30655 (serial #10) was measured. Considering a DC current due to an anbient light (although the PD was covered), the dark current of the HQE PD seems double of C30655.

- Taking an advantage of having the setup, I took the same measurement for the Laser Comp. PDs in ATF. I gave the identification as #1 and #2. #1 has full-length legs while #2 has trancated legs. As Zach reported before, they showed significantly high dark current. (Attachment 3)

Attachment 1: P2197992.jpg
Attachment 2: PD_dark_current.pdf
Attachment 3: PD_dark_current_others.pdf
252   Sun Mar 6 02:13:28 2016 KojiOpticsCharacterizationPD glass reflections

On friday, I removed a glass cover of a G30655 with a PD can cutter.

When a beam shoots a Perkin Elmer/Excelitas PD, we usually observe three reflections.
We always wonder what these are.

When the glass window is illuminated by a beam, I could see two reflections. So they are the front and rear reflection from the glass windows.

Attachment 1: P3048124.JPG
Attachment 2: P3048125.JPG
253   Sun Mar 13 21:22:27 2016 KojiElectronicsCharacterizationDark current measurement of the HQE PD and other PDs

Transfered for RGA scan

B4 (C1-05) -> F1
C1 (C1-07) -> F2

254   Sun Mar 13 22:02:09 2016 KojiOpticsCharacterizationHQEPD QE measurement (direct comaprison)

Direct comparison of the PD responsibities

We can expect 5% increase of the QE with the new PD.

P-pol 10deg incident

Power meter Ophir RM9C (Systematic error +/-5%)
Vbias = 6V

C30665GH (#07)
Incident: 7.12mW
Reflection: 0.413mW (=> R=5.8%)
PD output: 5.690+/-0.006V
=> Responsibity 0.799+/-0.001 A/W
=> QE = 0.931+/-0.001

HQE PD (A1-23)
Incident: 7.15mW
Reflection: 0.020+/-0.1mW (=> R=0.28%)
PD output: 6.017+/-0.007V
=> Responsibity 0.842+/-0.001 A/W
=> QE = 0.981+/-0.001

Note that there is a 5% systematic error with the power meter.

255   Sat Mar 26 01:49:48 2016 KojiOpticsCharacterizationHQEPD QE

Calibration of the transimpedance

Use KEITHLEY 2450 as a calibrated current source. Model 2450 has the current source accuracy of 0.020%+1.5uA at 10mA range. For 6mA current output, the error is 3uA (0.05%).

The output of the current amp at 103 Ohm setting was 6.0023V when -6.000mA current was applied. i.e R_trans = 1000.4 +/- 0.5 Ohm. This is a negligible level.

QE of the diodes (As of 07/30/2016)

Refer E1800372

Attachment 1: QE1.png
Attachment 2: QE2.png
256   Sat Mar 26 17:39:50 2016 KojiElectronicsCharacterizationHQEPD dark noise

Dark noise measurement for 6 HQEPDs and 1 C30665. All of these showed sufficiently low dark current noise levels compared with the noise level of the DCPD preamp. The measurement was limited by the input noise (ADC) noise of the FFT analyzer as the line noises were too big.

The measurement has been done with the transimpedance of 1e7. The bandwidth of the measurement was 50kHz.

Attachment 1: PD_dark_current.pdf
257   Sat Mar 26 18:22:24 2016 KojiElectronicsCharacterizationBaking / Contamination tests of the PDs

For the production of the aLIGO PDs, the following transfer of the PDs were carried out
A1-23 Cage A1 -> G1
A1-25 Cage A2 -> G2

The cage A will be baked at 75degC to see if this improves AMU=64 emission.

At the same time, we will put C1-05 (F1) and C1-07 (F2) into the contamination test cavity.

259   Tue Apr 5 18:22:40 2016 KojiElectronicsCharacterizationBaking / Contamination tests of the PDs

Possible reduction of the QE was observed after air-bake at 75degC.

Yesterday I received Cage G from Bob for intermediate test of the PD performance after air bake but before vacuum bake.
This cage was prepared to be the production pair.

According to the ICS, https://ics-redux.ligo-la.caltech.edu/JIRA/browse/Bake-8047
the PDs were air baked at 75degC for 48 hours.

I took the PDs to my lab to check if there is any issue in terms of the performance.
- Dark current: No change observed
- Dark noise: No noise increase observed
- QE: Probably reduced by ~0.5%.

Here I attached the result of the QE measurement. I have measured the QEs of the baked ones (A1-23 and A1-25) and the reference. Since the reference PD has not been baked, this gives us the measure of the systematic effect. The reference showed the reduction of ~0.1%. Assuming this reduction came from the systematic effect of the measurement system, I observed at least 0.5% QE reduction (A1-23). Note that the previous measurement of 99.8% for A1-25 was too high and dubious. But both A1-23 and A1-25 showed ~0.4% lower QEs.

So I believe the air-baking process reduced the QE.

Another evidence was that now I could clearly see the beam spots on these air-baked-PDs with an IR viewer when the PDs were illuminated with a 1064nm beam. Usually it is difficult to see the spot on the PD. The spot on the reference PD was still dark. So this difference was very obvious. I was afraid that something has been deposited on the surface of the photosensitive element. The surface of the diodes looked still very clean when they were checked with a green LED flash light.

Attachment 1: QE_after_air_bake.pdf
260   Tue Apr 5 21:20:15 2016 KojiElectronicsCharacterizationMore dark noise measurement

All survived PDs have been measured.

Attachment 1: PD_dark_current.pdf
266   Tue Aug 23 23:36:54 2016 KojiOpticsCharacterizationInspection of the damaged CM1 (prev H1OMC)

1. Calum and GariLynn checking the CM1 defect from the front side.
2. Same as above
3. Close up of the defect
4. Using dino-lite microscope to get a close up view of the defect from the front surface.
5. Same as 4
6. Finished for the day and setting up a safefy clamp
7. Finally a tefron cover was attached.

Attachment 1: P8238983.jpg
Attachment 2: P8238986.jpg
Attachment 3: P8238987.jpg
Attachment 4: P8238989.jpg
Attachment 5: P8238990.jpg
Attachment 6: P8238994.jpg
Attachment 7: P8238996.jpg
267   Thu Aug 25 02:17:09 2016 KojiOpticsCharacterizationInspection of the damaged CM1 (prev H1OMC)

Initial inspection results by Calum, et al.
https://dcc.ligo.org/LIGO-E1600268

276   Tue Mar 28 21:04:27 2017 KojiElectronicsCharacterizationPDH amp

Attachment 1: PDH amp RF part (before the preamp was installed)

Attachment 2: RF-AF transmission

Attachment 3: Attachment 3: LO dependence

Attachment 4: RF amp gain (saturation)

Attachment 5: Input/output noise level

Attachment 6: Attachment 6: Preamp/DCPD out buffer AF circuit

Attachment 1: DSC_0269.JPG
Attachment 2: RF_to_AF_conversion.pdf
Attachment 3: LO_dependence.pdf
Attachment 4: RFamp_gain.pdf
Attachment 5: PreampNoise.pdf
Attachment 6: preamp.png
286   Sat Jul 29 18:44:38 2017 ranaElectronicsCharacterizationPDH amp

attachment 6: DCPD preamp looks like the opamp is wired for positive feedback?

287   Sat Jul 29 21:42:51 2017 KojiElectronicsCharacterizationPDH amp

The polarities indicated in the right circuits were opposite, obviously.

291   Thu Feb 22 20:21:02 2018 KojiOpticsCharacterizationaLIGO EOM test

POSTED to 40m ELOG

292   Mon Apr 2 17:27:04 2018 KojiOpticsCharacterizationaLIGO EOM test

2nd optical test http://nodus.ligo.caltech.edu:8080/40m/13725

296   Wed May 30 16:40:38 2018 KojiMechanicsCharacterizationEOM mount stability test

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

297   Wed May 30 17:44:23 2018 KojiOpticsCharacterization3IFO EOM surface check

3IFO EOM dark microscope images courtesy by GariLynn and Rich

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

Attachment 1: IMG_5756.JPG
Attachment 2: IMG_5757.JPG
Attachment 3: IMG_5758.JPG
Attachment 4: IMG_5759.JPG
Attachment 5: Looking_at_Hole2.png
298   Mon Jul 2 11:30:22 2018 KojiElectronicsCharacterization3IFO EOM impedance measurement

[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.

Attachment 1: impedance_eom.pdf
Attachment 2: EOM_Z_DATA.zip
299   Mon Jul 2 12:29:01 2018 KojiElectronicsCharacterizationImpedances of individual components (3IFO EOM)

[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.

Attachment 1: impedance_coils.pdf
Attachment 2: impedance_xtals.pdf
Attachment 3: q_coils.pdf
Attachment 4: component_models.pdf
Attachment 5: liso_models.zip
301   Tue Jul 3 12:07:47 2018 Rich AbbottElectronicsCharacterizationNotes on 3rd IFO EOM

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

Attachment 1: EOM_Analysis2.pdf
302   Wed Jul 4 18:30:51 2018 KojiElectronicsCharacterizationEOM circuit models

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.

Attachment 1: eom_models.pdf
Attachment 2: eom9.pdf
Attachment 3: eom24.pdf
Attachment 4: eom45.pdf
Attachment 5: 180704_3IFO_EOM_model.zip
303   Thu Jul 26 20:57:07 2018 KojiElectronicsCharacterization9MHz port tuned impedance

[Rich Koji]

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

Attachment 1: impedance_eom.pdf
Attachment 2: eom9.pdf
Attachment 3: eom_models_9MHz.pdf
304   Tue Aug 7 15:43:12 2018 KojiElectronicsCharacterizationNew LLO EOM stuffed

[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.

Attachment 1: P_20180806_154457.jpg
Attachment 2: impedance_eom.pdf
Attachment 3: impedance_eom_zoom.pdf
305   Wed Aug 8 17:32:56 2018 Rich AbbottGeneralCharacterizationModulation Index Test Setup at 40m Lab

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

Attachment 1: 40mLabModIndexSetup.pdf
306   Thu Aug 9 11:24:29 2018 KojiGeneralCharacterizationModulation Index Test Setup at 40m Lab

[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.

 Frequency [MHz] Response [rad/V] modulation depth  required (LHO) [rad] Required drive [Vpk] Required drive [dBm] 9.1 0.09 0.22 2.4 17.8 24.1 2.9e-3 0.014 4.8 23.7 45.5 0.053 0.28 5.3 24.5 118.3 0.021 0.010 0.48 3.6

Attachment 1: modulation_depth.pdf
Attachment 2: modulation_depth_zoom.pdf
311   Thu Jan 10 20:42:54 2019 KojiOpticsCharacterizationFSR / HOM Test of OMC SN002

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
312   Thu Jan 10 20:45:00 2019 KojiOpticsCharacterizationPZT test cable

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.

Attachment 1: OMC_PZT_wiring.pdf
313   Sat Jan 12 22:49:11 2019 KojiOpticsCharacterizationPM-SM patch cable mode cleaning effect

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.

\begin{align} P_{\rm omcrefl} & = a P_{\rm nofib} + b P_{\rm fib} \nonumber \\ P_{\rm fibout} & = P_{\rm omcrefl} + (1-b) P_{\rm fib} \nonumber \\ P_{\rm tot} & = P_{\rm nofib} + P_{\rm fib} \nonumber \end{align}

and

\begin{align} P'_{\rm omcrefl} &= a P'_{\rm nofib} + b P'_{\rm fib} \nonumber \\ P'_{\rm fibout} &= P'_{\rm omcrefl} + (1-b) P'_{\rm fib} \nonumber \\ P_{\rm tot} &= P'_{\rm nofib} + P'_{\rm fib} \nonumber \end{align}

With the calibration between the refl PD and the power meter measurement,
\begin{align} P_{\rm tot} &= 52.5 \pm 0.2 {[mW]} \nonumber \\ P_{\rm fibout} &= 35.5 \pm 0.2 {\rm [mW]} \nonumber \end{align}
\begin{align} P_{\rm omcrefl} &= 0.78 \pm 0.01\,\,{\rm [mW]} \nonumber \\ P'_{\rm omcrefl} &= 0.460 \pm 0.006\,\,{\rm [mW]} \nonumber \\ P'_{\rm fibout} &= 20.4 \pm 0.13 \,\,{\rm [mW]} \nonumber \end{align}

The solution of the equations is
\begin{align} a &= (4 \pm 4) \times 10^{-4} \nonumber \\ b &= 0.0219 \pm 0.0005 \nonumber \end{align}

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%.

Attachment 1: fiber_mode_cleaning.pdf
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)
History:
Measurement date 2013/5/31, Installed to L1 2013/6/10~

Attachment 1: OMC_HOM_130531.pdf
Attachment 2: HOM_PZTV.pdf
Attachment 3: HOM_plot_PZT0_0.pdf
Attachment 4: Cav_scan_response_HOM.pdf
ELOG V3.1.3-