Interferometer Characterization at the 40m prototype

Goals

To help the DRMI commissioning that will be performed at the sites.

Motivations

In the aLIGO schedule the DRMI test will start around of May 2012 at LLO.

The purpose of the 40m DRMI work is to produce a handbook of DRMI characterization which can be handed to the LLO people. This handbook will include the why, the howto, and the results for all of the DRMI characterization done here. In addition, we will deliver all of the scripts, screens, codes, etc. which are used to do these tests. The intention is to make the whole DRMI process, plug and play. The commissioning tests that will be performed at LLO should be tested at the 40m so that the people at the sites can easily do all the commissioning tests and spend their time on the difficult problems.

Contents

Interferometer Characterization at the 40m prototype
1. Goals
2. Motivations
Plan for DRMI Characterization at the 40m
References

Plan for DRMI Characterization at the 40m

Noise Budget

Requirements

Shot Noise
Dark (RFPD) Noise
ADC Noise
Laser Amplitude noise
Laser Frequency Noise
Oscillator Noises
DAC Noise
Coil Driver Noise
Seismic Noise
Loop cross-coupling (PRC -> MICH, PRC -> SRC, etc.)
Coupling from Angular motions (e.g., oplevs, osems)

How To

pyNDS for data getting
Python based NB code (copy of matlab based eLIGO code)
CDS Oscillator/Lockin used for noise coupling measurements
CDS NoisePowerChop part for incoherent noise couplings

Results

Schnupp asymmetry measurement and its adjustment

Requirement

 Schnupp asymmetry = 3.42 [cm] +/- 0.3 [cm]

The Schnupp asymmetry determines the reflectivity r and transmissivity t of the Michelson for the f1 and f2 sidebands when the carrier is kept in the dark condition. In the design the f2 sideband should be critical coupling in the dual recycling cavity [1] [2]. To achieve the critical coupling we should adjust r and t properly by tuning the asymmetry.
According to a simulation the asymmetry should be within the precision of XXX mm to achieve more than 95 % of the maximum power build up.

How to measure

Here two example methods are introduced:
- (1) based on a measurement of the MICH transmissivity at frequency of AM sidebands [3]
- (2) based on a measurement of the difference in the optical phase of each arm at frequency of PM sidebands (needs each FP cavity locked) [4]
Since we've already been able to lock both FP arms the second method was performed to measure the asymmetry at the 40m.

Results

Here is the result from the first measurement [4]
- ```
Lsa = 3.64 [cm] ± 0.32 [cm]  
```

PRC length measurement and its adjustment

Requirements

$/!\$ The required precision should be reviewed also from point of view of the sensing matrix
```
lprc = 6.7538 [m] +/- 3 [mm]  
```
In order to successfully lock a power recycled interferometer with Fabry-Perot arms a technique broadly used is to choose the PRC length such that the sidebands resonate in PRC. In our design the PRC length has been chosen to let both f1 and f2 sidebands resonate in PRC [1] [2]. The precision required to get those sidebands resonate is simply depending on the linewidth of PRC for both sidebands.
As shown in the plot below the length must be adjusted within 3 mm precision to get more than 90 % of max build up for both sidebands.
- Fig.1 An example plot of macroscopic PRC length scan and the intracavity power.

How to measure

There are two major methods to measure the PRC length:
- (1) A technique uses another auxiliary laser to scan the frequency.
- (2) To sweep the sidebands' frequency.
There are several techniques to measure the absolute length of a cavity. Here are the references [2] [5 ] [6][7]

Results

SRC length measurement and its adjustment

Requirements

$/!\$ The required precision should be reviewed also from the point of view of the sensing matrix
```
lsrc = 5.39915 [m] +/- 1.5 cm  
```
Similar to the PRC length, the f2 sidebands should resonate in SRC to get cleaner signal [1]. According to the linewidth of SRC for the f2 sidebands the tolerance of the length can be determined.
As shown in the plot below the length must be adjusted within 1.5 cm precision to get more than 90 % of max build up for the f2 sideband.
- Fig.2 An example plot of macroscopic SRC length scan and the intracavity power.

How to measure

Essentially the same as the PRC length measurement

Results

Recycling gain measurements

Design

 Carrirer    = XX  f1 sideband = YY  f2 sideband = ZZ

Since the recycling gain is related to loss in the recycling cavity, measuring the recycling gain tells us the amount of loss in the recycling cavity. The usual amount of loss is expected to be XX ppm per round trip. If we find unacceptably big loss, it might be due to a clipping or some obvious loss.
In addition to the gain of the carrier light, the recycling gain of f1 and f2 tells us the reflectivity of the Michelson which is determined by the Schnupp asymmetry.

How to

Carrier recycling gain measurement with POP (POX/POY)
- lock MICH and measure the amount of beam at POP
- lock Power-Recycled Michelson and align the cavity
- measure POP again and the ratio between that with and without PRCL gives you the recycling gain
Sidebands recycling gain measurement
- do the same things and measure the gain at each frequency using Optical Spectrum Analyzer (OSA)

Results

 Carrirer    = XX  f1 sideband = YY  f2 sideband = ZZ

Tuning of Locking protocol

Requirements

The lock of DRMI has to be robust and repeatable. Some threshold values and initial gains should be tuned to routinely acquire the lock.
In addition to those, the boost filters should be triggered at appropriate timing and by appropriate thresholds.

How to

Locking of MICH will be triggered if the ASDC signal goes to MMM% of the max power.
Locking of PRC will be triggered when 2 x f1 signal goes above XXX in AAA port.
Locking of SRC will be triggered when 2 x f2 signal goes above MMM in AAA port.
Boost filters will be on if YYY signals goes above MMM

Notes

MICH is controlled such that the amount of carrier going to AS becomes zero. So the MICH control should be triggered when ASDC goes below a certain value.
If PRC is locked the AM sideband at 2 x f1 and 2 x f2 will resonate.
If SRC is locked the AM sideband at 2 x f2 will resonate.

Sensing Matrix Verification

Expected matrix from Optickle

How to

At first the ITMs must be balanced at a particular frequency so that one can excite purely the MICH DOF.
Measure the TF matrix between all mirrors LSC_EXC and the RFPD I&Q signals.
Compare with Optickle-based matrix.
Use matrix residuals as another handle on optical plant imperfections.

Results

Measurement of Spot Positions in DRMI

Requirements

```
off-centering on each optic < 2 mm  
```

How to

Use the standard A2L technique after coils are balanced.

results

```
YAW = XXX mm   PIT = XXX mm 
```

Reflectivity check

Expected values

 REFL = XXX (when PRMI, carrier locked)   REFL = XXX (when PRMI, sidebands locked)  REFL = XXX (when DRMI)

This test is useful for finding a mismatch in the mode matchings

How to

Measure the light power coming into a PD at the REFL port.

Results

 REFL = XXX (when PRMI, carrier locked)   REFL = XXX (when PRMI, sidebands locked)  REFL = XXX (when DRMI)

Calibration of Actuator responses

In the process of the noise budgeting one has to measure the MIMO closed-loop transfer functions. For this purpose, the calibration of actuators on BS, ITMs, PRM and SRM are necessary. Unlike the optical gains, the actuator responses shouldn't vary, therefore the use of the actuator responses as references in estimation of the noise budget is fairly reliable.

How to

Free-Swinging Michelson Bootstrap. Once the estimation of the optical gain is done, the BS and ITMs can be calibrated. [8] [9].

After the calibration of the BS and ITMs, the PRM and SRM can be calibrated by referencing them to the ITMs in the DRMI configuration.

In summary here is the steps to calibrate the responses

  1. Calibration of the Michelson sensor
  2. Calibration of the BS and ITMs actuators
  3. Calibration of the PRC sensor and the PRM actuator response
  4. Calibration of the SRC sensor and the SRM actuator response

Comparison of measured actuation coefficients with analytic estimates.

Results

See [9] for the details

     BS = 2.190e-08 / f^2     [m/counts]
     ITMX  = 4.913e-09 / f^2   [m/counts]
     ITMY  = 4.832e-09 / f^2   [m/counts]
     PRM   = 2.022e-08 / f^2  [m/counts]
     SRM   = 2.477e-08 / f^2  [m/counts]

Our DAC have +/-5V single ended outputs with 16 bit resolution. Therefore the DACs conversion factor is 10V/2^16 counts = 0.000152587890625 [V/counts]. With this DAC factor, we obtain the following actuator responses.
- ```
     BS   =  138.21 / f^2 [um/V]
     ITMX =  32.20 / f^2 [um/V]
     ITMY =  31.67 / f^2 [um/V]
     PRM  =  162.33 / f^2 [um/V]
```

Diagonalization of LSC Output Matrix into the Canonical DOF basis

Requirements

```
Precision  < 5%  
```
We want the LSC system to be diagonal to minimize weird loop effects around the UGF.

How to

Measure sensing matrix.
Invert.

F2A filter adjustment

Requirement

```
 Precision < 0.25 % 
```
Pushing a suspension longitudinally cause a misalignment because of the inherent force to torque coupling in a suspended mirror [10] and also because of the imperfections in the suspensions construction and actuation coefficients.

How to

We will use a version of the eLIGO F2A scripts that utilizes the LOCKIN modules inside of the suspension screens (no AWG or ezlockin/TDS issues).
An instructions

Results

High frequency coil balancing successful. Estimated balancing accuracy is NN%
Low frequency suspension balancing successful. Estimated balancing accuracy is NN%

3f locking test

Requirements

Since 3f locking doesn't use the carrier light the signal level is generally small. Therefore one has to make sure the SNR are big enough to robustly keep DRMI on resonance.

How to

Noise budgeting
Sensing matrix

Optickle simulations

Results

Modulation Depth Measurements

How to

Set up some OSAs

Results

An OSA was installed on the REFL path. The measurement has been done when all the mirrors except PRM were intentionally misaligned. In this condition the direct reflection from PRM goes to the OSA without having any interferences.
- ```
  LO frequency = 11065910 Hz
  Gamma@11MHz = 0.136 [rad]
  Gamma@55MHz = 0.1572 [rad]
```
-55 MHz

-11 MHz

Carrier

+11 MHz

+55 MHz

Peak height [V]

1.2838

0.961753

203.7

0.955951

1.283775

To estimate the modulation depth, the following equation was used :

     Gamma = sqrt( 4R / (1+2R) ),
     where R=[peak height of a SB] / [carrier's peak height]

IFO modeling

How to

Any kinds of measurements listed here must be verified by a simulation.
There are several tools that can model and simulate interferometers in numerical ways. For example: finesse [11 ], Optickle , Looptickle and Lentickle .
See this page for details

Regular EVO meeting

Meeting summary page

References

[1] R.Abbott et al, " Advanced LIGO Length Sensing and Control Final Design "LIGO-T1000298-v2 (2010)

[2] A.Stochino, " Design and Characterization of Optical Cavities and Length Sensing and Control System of an Advanced Gravitational Wave Interferometer " 40m svn (2010)

[3] O.Miyakawa, " Michelson asymmetry length " old 40m Elog (2004)

[4] J.Rollins, " Schnupp asymmetry measurement " 40m elog #4821 (2011)

[5] M.Rakhmanov et al, " Characterization of the LIGO 4km Fabry-Perot cavities via their high-frequency dynamic response to length and frequency variations " CQG (2004)

[6] A.Araya et al, " Absolute-length determination of a long-baseline Fabry-Perot cavity by means of resonating modulation sidebands " Applied optics (1999)

[7] M.Rakhmanov et al, " An optical vernier technique for in situ measurement of the length of long Fabry-Perot cavities " Meas.Sci.Technol (1999)

[8] R.ward, " Length Sensing and Control of an Advanced Prototype Interferometric Gravitational Wave Detector "PhD Thesis LIGO-P1000018-v1 (2010)

[9] K.Izumi, " Calibration of actuators : BS, ITMX and ITMY " 40m elog #4721

[10] P.Fritschel, " Digital Suspension Filter Design "LIGO-T010140-01(2001)

[11] V.Mandik, old elog entry (2004)

[12] A.Freise and K.Strain, " Interferometer Techniques for Gravitational-Wave Detection "Living Review (2010)

	-55 MHz	-11 MHz	Carrier	+11 MHz	+55 MHz
Peak height [V]	1.2838	0.961753	203.7	0.955951	1.283775