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Introduction to CalibrationIntroduction to CalibrationIntroduction to CalibrationIntroduction to Calibration

Brian O’Reilly

SciMon Camp 2006

Brian O’Reilly

SciMon Camp 2006

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Frequency Domain CalibrationFrequency Domain Calibration

We model the DARM loop in MATLAB Compare this model to measurements of the open-

loop gain, electronics in the Actuation and Sensing chains and DC value of the Actuation.

Optical and loop gain are tracked by time-dependent coefficients which are generated on minute or second time scales.

These coefficients are used to propagate measurements at t0 to other times.

We model the DARM loop in MATLAB Compare this model to measurements of the open-

loop gain, electronics in the Actuation and Sensing chains and DC value of the Actuation.

Optical and loop gain are tracked by time-dependent coefficients which are generated on minute or second time scales.

These coefficients are used to propagate measurements at t0 to other times.

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A(f)

DD(f)

(t)C D0(f)

DARM_ERR

+

s=h(t)+n(t)

DARM_CTRL

sres=(Lx-Ly)/L

+

DARM_CTRL_EXC

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ActuationActuationActuationActuation

Ax(f) Ay(f)

+

++

EXCx(t)

kykx

• DARM feeds back to the ETMs.• Measuring the actuation has typically been the least accurate and most angst-ridden part of the calibration.

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Actuation FunctionActuation FunctionCalibrate the ASQ signal for a simple Michelson This establishes the length scale in AS_Q counts.

Use it to calibrate ITMs:

Use single arms to calibrate ETMs with ITMs

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Actuation FunctionActuation Function

Treat mass as a simple pendulum.

Knowing the DC value we can set the scale for the transfer function.

Methods for measuring DC value explicitly have also been tried: sneaky poles

Treat mass as a simple pendulum.

Knowing the DC value we can set the scale for the transfer function.

Methods for measuring DC value explicitly have also been tried: sneaky poles

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Actuation FunctionActuation Function

?

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Compensate the ElectronicsCompensate the Electronics

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The Payoff… Small ErrorsThe Payoff… Small Errors

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Digital FiltersDigital Filters

Know them perfectly?

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The Input MatrixThe Input Matrix

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Sensing FunctionSensing Function

Model as a cavity pole Have to understand the

sensing electronics chain Photodiode, Whitening,

Demodulation, Anti-Aliasing etc.

How well do we know the cavity pole?

How well do we know C(f)? Not directly measured.

Model as a cavity pole Have to understand the

sensing electronics chain Photodiode, Whitening,

Demodulation, Anti-Aliasing etc.

How well do we know the cavity pole?

How well do we know C(f)? Not directly measured.

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Open Loop Gain DiscrepancyOpen Loop Gain DiscrepancyL1 H1

5-10% error on response at 2 kHz

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Model InputsModel Inputs

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Frequency Domain CalibrationFrequency Domain Calibration

Measure Open-Loop Gain at a reference time t0

G0(f) = A(f)CD0(f)DD(f)

h(f,t) = RDERR(f,t)DERR(f,t)

Similar equations for AS_Q

Measure Open-Loop Gain at a reference time t0

G0(f) = A(f)CD0(f)DD(f)

h(f,t) = RDERR(f,t)DERR(f,t)

Similar equations for AS_Q€

DERRR ( f , t) =1+ G( f , t)

DC ( f , t)=

1+ γ (t)0G ( f )

D0γ(t)C ( f )

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PropagatePropagate

This value stays within ~5% of unity, barring any problems with the code.

This value stays within ~5% of unity, barring any problems with the code.

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Errors on the ResponseErrors on the Response

By breaking the error down into these components we identify problem areas.

By breaking the error down into these components we identify problem areas.

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FinallyFinally

After diligent work we feel we can control calibration errors to the level of 5-10%.

Doing better than this is hard, but: 15Mpc/10 = 1.5Mpc = range of L1 during S2!!

Other ways to calibrate: HEPI or Tidal Actuators VCO Photon Calibrator time-domain h(t)

Calibrating eLIGO or advLIGO will present a new set of challenges.

After diligent work we feel we can control calibration errors to the level of 5-10%.

Doing better than this is hard, but: 15Mpc/10 = 1.5Mpc = range of L1 during S2!!

Other ways to calibrate: HEPI or Tidal Actuators VCO Photon Calibrator time-domain h(t)

Calibrating eLIGO or advLIGO will present a new set of challenges.