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

EDIT (ZK): Added input q parameters for OMMT 

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

Bowtie

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

Here is an illustration of the geometry:

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

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

Non-bowtie

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

Geometry:

q parameters, defined as above:

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

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

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

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

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

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

Parts list:

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

EDIT (ZK): Koji points out that (1 - Ti) should really be the non-resonant reflectivity of the aligned cavity, which is much closer to 1. However, it should *actually* be the non-resonant reflectivity of the entire OMC assembly, including the steering mirror (see bottom of post). The steering mirror has T ~ 0.3%, so the true results are somewhere between my numbers and those with (1 - Ti) -> 1. In practice, though, these effects are swamped by the other errors.

More information about the power-dependent visibility measurement:

As a blanket statement, this measurement was done by exact analogy to those made by Sam and Sheon during S6 (c.f. LHO iLog 11/7/2011 and technical note T1100562), since it was supposed to be a verification that this effect still remains. There are absolutely better ways to do (i.e., ways that should give lower measurement error), and these should be investigated for our characterization. Obviously, I volunteer.

All measurements were made by reading the output voltages produced by photodetectors at the REFL and TRANS ports. The REFL PD is a BBPD (DC output), and the TRANS is a PDA255. Both these PDs were calibrated using a Thorlabs power meter (Controller: PM100D; Head: S12XC series photodiode-based---not sure if X = 0,2... Si or Ge) at the lowest and highest power settings, and these results agreed to the few-percent level. This can be a major source of error.

The power was adjusted using the HWP/PBS combination towards the beginning of the experiment. For reference, an early layout of the test setup can be seen in LLO:5978 (though, as mentioned above, the REFL and TRANS PDs have been replaced since then---see LLO:5994). This may or may not be a "clean" way to change the power, but the analysis should take the effect of junk light into account.

Below is an explanation of the three traces in the plot. First:

• TRANS: TRANS signal calibrated to W
• REFL_UL: REFL signal while cavity is unlocked, calibrated to W
• REFL_L: REFL signal while cavity is locked, calibrated to W
• Psb: Sideband power (relative to carrier)
• Ti: Input mirror transmission (in power)

Now, the traces

1. Raw transmission: This measurement is simple. It is just the raw throughput of the cavity, corrected for the power in the sidebands which should not get through. I had the "AM_REF" PD, which could serve as an input power monitor, but I thought it was better to just use REFL_UL as the input power monitor and not introduce the error of another PD. This means I must also correct for the reduction in the apparent input power as measured at the REFL PD due to the finite transmission of the input coupler. This was not reported by Sam and Sheon, but can be directly inferred from their data.
   • trans_raw = TRANS ./ ( REFL_UL * (1 - Psb) * (1 - Ti) )
   • Equivalently, trans_raw = (transmitted power) ./ (input power in carrier mode)
2. Coupling: This is how much of the power incident on the cavity gets coupled into the cavity (whether it ends up in transmission or at a loss port). Sheon plots something like (1 - coupling) in his reply to the above-linked iLog post on 11/8/2011.
   • coupling = ( REFL_UL * (1 - Ti) - REFL_L ) ./ ( REFL_UL * (1 - Psb) * (1 - Ti) )
   • Equivalently, coupling = [ (total input power) - (total reflected power on resonance) ] ./ (input power in carrier mode)
3. Visibility: How much of the light that is coupled into the cavity is emerging from the transmitted port? This is what Sam and Sheon call "throughput" or "transmission" and is what is reported in the majority of their plots.
   • visibility = TRANS ./ ( REFL_UL * (1 - Ti) - REFL_L )
   • Equivalently, visibility = (transmitted power) ./ [ (total input power) - (total reflected power on resonance) ]
   • Also equivalently, visibility = trans_raw ./ coupling

The error bars in the measurement were dominated, roughly equally, by 1) systematic error from calibration of the PDs with the power meter, and 2) error from noise in the REFL_L measurement (since the absolute AC noise level in TRANS and REFL_L is the same, and TRANS >> REFL_L, the SNR of the latter is worse).

(1) can be helped by making ALL measurements with a single device. I recommend using something precise and portable like the power meter to make measurements at all the necessary ports. For REFL_L/UL, we can place a beam splitter before the REFL PD, and---after calibrating for the T of this splitter very well using the same power meter---both states can be measured at this port.

(2) can probably be helped by taking longer averaging, though at some point we run into the stability of the power setting itself. Something like 30-60s should be enough to remove the effects of the REFL_L noise, which is concentrated in the few-Hz region in the LLO setup.

One more thing I forgot was the finite transmission of the steering mirror at the OMC input (the transmission of this mirror goes to the QPDs). This will add a fixed error of 0.3%, and I will take it into account in the future.

I found that, in fact, I had lowered the modulation depth since when I measured it to be 0.45 rads --> Psb = 0.1.

Here is the sweep measurement:

This is Psb = 0.06 --> gamma = 0.35 rads.

This changes the "raw transmission" and "coupling", but not the inferred visibility:

I also measured the cavity AMTF at three powers today: 0.5 mW, 10 mW, and 45 mW input.

They look about the same. If anything, the cavity pole seems slightly lower with the higher power, which is counterintuitive. The expected shift is very small (~10%), since the decay rate is still totally dominated by the mirror transmissions even for the supposed high-loss state (Sam and Sheon estimated the roundtrip loss at high power to be ~1400 ppm, while the combined coupling mirrors' T is 1.6%). I have not been able to fit the cavity poles consistently to within this kind of error.

 For various reasons, I had to switch NPROs (from the LightWave 126 to the Innolight Prometheus).

I installed the laser, realigned the polarization and modulation optics, and then began launching the beam into the fiber, though I have not coupled any light yet.

A diagram is below. Since I do not yet have the AOM, I have shown that future path with a dotted line. Since we will not need to make AMTFs and have a subcarrier at the same time, I have chosen to overload the function of the PBS using the HWP after the AEOM. We will operate in one of two modes:

1. AMTF mode: The AOM path is used as a beam dump for the amplitude modulation setup. A razor dump should physically be placed somewhere in the AOM path.
2. Subcarrier mode: The AEOM is turned off and the HWP after it is used to adjust the carrier/subcarrier power ratio. I chose a 70T / 30R beamsplitter for the recombining, since we want to be able to provide ~100 mW with the carrier for transmission testing, and we don't need a particularly strong subcarrier beam for probing.

One thing that concerns me slightly: the Prometheus is a dual-output (1064nm/532nm) laser, with separate ports for each. I have blocked and locked out the green path physically, but there is some residual green light visible in the IR output. Since we are planning to do the OMC transmission testing with a Si-based Thorlabs power meter---which is more sensitive to green than IR---I am somewhat worried about the ensuing systematics. I *think* we can minimize the effect by detuning the doubling crystal temperature, but this remains to be verified.

 EDIT (ZK): Valera says there should be a dichroic beam splitter in the lab that I can borrow. This should be enough to selectively suppress the green.

[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)

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.

My hypothesis about the input-side collimator turned out to be correct.

I removed the fiber from the collimator and mount at the input side, and then injected the illuminator beam from this side. Since we already saw a nice (but dim) IR beam emerging from the output side the other night, it followed that that collimator was correctly attached. With the illuminator injected from the input side, I also saw a nice, collimated red beam emerging from the output. So, the input collimator was not properly attached during our previous attempts, leading to the abysmal coupling.

The problem is that the mount does not allow you to remove and reattach the fiber while the collimator is already attached, and the dimensions make it hard to fit your fingers in to tighten the fiber to the collimator once the collimator is in the mount. I disassembled the mount and found a way to attach/reattach the fiber that preserves the tight collimator contact. I will upload a how-to shortly.

With this fix, I was able to align the input beam and get decent coupling:

EOM path: ~70%

AOM path: ~50%

[Koji, Zach]

We installed the MMT that matches the fiber output to the OMC on a 6"x12" breadboard. We did this so that we can switch from the "fauxMC" (OMC mirrors arranged with standard mounts for practice locking) to the real OMC without having to rebuild the MMT.

The solution that Koji found was:

z = 0: front face of the fiber output coupler mount

z = 4.8 cm: f = 35mm lens

z = 21.6 cm: f = 125mm lens

This should place the waist at z ~ 0.8 m. Koji has the exact solution, so I will let him post that.

The lenses are on ±0.5" single-axis OptoSigma stages borrowed from the TCS lab. Unfortunately, the spacing between the two lenses is very close to a half-integer number of inches, so I had to fix one of them using dog clamps instead of the screw holes to preserve the full range.

Koji also built the periscope (which raises the beam height by +1.5") using a vertical breadboard and some secret Japanese mounts. Part of it can be seen in the upper left corner of the photo below---sorry for not getting a shot of it by itself.

As Koji noticed that the AOM efficiency was very low, I figured I would try looking at it with a fresh set of eyes. The end result is that I have to agree that the AOM appears to be broken.

First, I measured the input impedance of the AOM using the AG4395A with the impedance test kit (after calibrating). The plot is below. The spec sheet says the center frequency is 200 MHz, at which Z_in should be ~50 ohms. It crosses 50 ohms somewhere near 235 MHz, which may be reasonable given that the LC circuit can be tuned by hand. However, it does surprise me that the impedance varies so much over the specified RF range of ±50 MHz. Maybe this is an indication that something is bad.

I removed the cover of the modulator (which I think Koji did, as well) and all the connections looked as I imagine they should---i.e., there was nothing obviously broken, physically.

I then tried my hand at realigning the AOM from scratch by removing and replacing it. I was not able to get better than 0.15%, which is roughly what Koji got.

So, perhaps our best course of action is to decide what we expect the Z_in spectrum to look like, and whether that agrees with the above measurement.

[Koji, Zach]

Tonight, we locked the "fauxMC". We obtained a visibility of >99%.

Koji had aligned it roughly last night, but we wanted to have a couple steering mirrors in the path for this practice cavity (the periscope mirrors will serve this function in the real setup), so we marked the alignment with irises and installed two extra mirrors.

After obtaining flashes with the WinCam placed at the output coupler, we removed the WinCam and put a CCD camera at one of the curved mirror transmissions and used this to get a strong TEM₀₀ flash. Then, we installed the REFL PD/CCD, swept the laser PZT and optimized the alignment by minimizing the REFL dips. Finally, we connected the RF electronics and locked the cavity with the LB box. We used whatever cables we had around to trim the RF phase, and then Koji made some nice SMA cables at the 40m.

One thing we noticed was that we don't have enough actuation range to keep the cavity locked for very long---even with the HV amp (100V). We are going to offload to the NPRO temperature using an SR560 or pomona box circuit. We may also make an enclosure for the cavity to protect it from the HEPA blasting.

Tomorrow, after we do the above things, we will practice measuring the transmission, length (FSR) and mode spectrum of the cavity before moving on to the real McCoy.

 D1300507

https://alog.ligo-la.caltech.edu/aLOG/index.php?callRep=7395

I’ve borrowed the black and decker toaster oven to dry some sonicated parts. It is temporarly located in the QIL lab. 

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.

We have measured the dimensions and mass of the OMC glass plates/breadboards:

• ^* orientation is relative to "front" face, i.e. long-short face with S/N on it, with S/N upright.
• Height measurements were made twice, once at each end.
• TMeasurements of 03, 05, 02, and 06 were done in the open in the OMC lab.  This was not thought to be too much of an issue since the plates
  are already covered with particulate matter from the tissue paper that they were wrapped in. 
  Measurements of 04 and 01 were done on the optics table, under the clean room enclosure.

Note by Koji:

• The scale of the bake lab was used. (Max 60kg, Min resolution of 1g)
• The dimensions were measured by a huge caliper which Jeff brought from Downs.
• S/N 01, 03, 04 look pretty similar. They should be the primary candidates.

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

are there any measurements of the BRDF of these things? I'm curious how much light is backscattered into the incoming beam and how much goes out into the world.

Maybe we can take some camera images of the cleaned ones or send 1-2 samples to Josh. No urgency, just curiosity.

I saw that ANU and also some labs in India use this kind of blue/green glass for beam dumps. I don't know much about it, but I am curious about its micro-roughness and how it compares to our usual black glass. For the BRDF, I think the roughnesss matters more for the blackness than the absorption.

I attempted to fit the data taken by Koji of the beam spot precession at the CCD in order to find the location of the curvature bottom in terms of its distance (d) and angle () from the centre of the mirror. This was done using the method described in a previous similar measurement  and Section 2.1.3 of T1500060.

Initially, I attempted doing a circle_fit on python as seen in Attachment 1, and even though more points seem to coincide with the circle, Koji pointed out that the more appropriate way of doing it would be to fit the following function:

since that would allow us to measure the angle more accurately; is the anti-clockwise measured angle that the curvature bottom makes with the positive x direction.

As seen on the face of the CCD, x is positive up and y is positive right, thus, plotting it as the reflection (ref. Attachment 2) would make sure that  is measured anti-clockwise from the positive x direction.

The distance from the curvature bottom is calculated as 

r: radius of precession on CCD screen (value obtained from fit parameters, uncertainty in this taken from the std dev provided by fit function)

R: radius of curvature of the mirror 

L: Distance between mirror and CCD

R = 2.575  0.005 m (taken from testing procedure doc referenced earlier) and L = 0.644  0.005 m (value taken from testing doc, uncertainty from Koji)

	d (mm)	(deg)
C7	0.554  0.004	-80.028  0.005
C10	0.257  0.002	-135.55  0.02
C13	0.161  0.001	-79.31  0.06

Using the measurements of PZTs 12,13 taken by Stephen, I estimated the wedging angle and orientation following Section 2.3.1 of T1500060. The results can be found in Attachment1 and is summarised as follows.

For PZT 12, PZT 13 respectively:

Avg. height = 2.0063 mm, 2.0035 mm

Wedge direction (from the same direction as in the doc: positive right) = 120 deg, 120 deg

Wedge angles = 45.8 arcsec, 30.6 arcsec

This was done assuming that the measurements were taken uniformly at intervals of 60deg along the inner rim of the PZT. The diameter (2r) of the inner rim, according to T1500060, is 9mm. The measured heights were fitted with the function

as depicted in Attachment2 to find wedging angle and orientation .

Aim: To find the combinations of mounting prism+PZT+curved mirror to build two PZT sub-assemblies that best minimises the total vertical beam deviation.

(In short, attachment 1 shows the two chosen sets of components and the configuration according which they must be bonded to minimize the total vertical angular deviation.)

The specfic components and configuration were chosen as follows, closely following Section 2.3.3 of T1500060:

Available components:

Mounting prisms: 1,2,12,14,15 (Even though there is mention of M17 in the attachments, it can not be used because it was chipped earlier.)

PZTs: 12,13

Curved mirrors: 10,13

Method:

For a given choice of prism, PZT and mirror, the PZT can be placed either at 0deg or 180deg, and the mirror can rotated. This allows us to choose an optimal mirror rotation and PZT orientation which minimises the vertical deviation.

Total vertical angle 

 was measured by Koji as described in elog 369.

,              are the wedge angle and orientation respectively and were measured earlier and shown in elog 373 . 

,               The measurement of the location of the curvature bottom (d, ) of the mirrors is shown in elog 372 . The optimal  is to be found.

These steps were followed:

1. For every combination of prism, PZT, and mirror, the total vertical deviation was minimized with respect to the angle of rotation of the curved mirror computationally (SciPy.optimize.minimize). The results of this computation can be found in Attachment 2: where Tables 1.1 and 2.1 show the minimum achievable deviations for mirrors C10 and C13 respectively, and Tables 1.2 and 2.2 show the corresponding angle of rotation of the mirrors  .
2. From the combinations that show low total deviations (highlighted in red in Attachment 2), the tolerances for 5 arcsec and 10 arcsec deviations with mirror rotation were calculated, and is shown in Tables 1.3, 1.4, 2.3, 2.4 of Attachment 2.
3. While calculating the tolerances, the dependence of the vertical deviations with rotation were also plotted (refer Attachment 3).
4. Two sets from available components with low total deviation and high tolerance were chosen. 

Result:

These are the ones that were chosen:

1. M14 + PZT13 at 0deg + C13 rotated by 169deg anticlockwise (tot vertical dev ~ -3 arcsec)
2. M12 + PZT12 at 0deg + C10 rotated by 88deg clockwise (tot vertical dev ~0 arcsec)

The method of attaching them is depicted in Attachment 1.