8/18/06Gxxxxxx Introduction to Calibration Brian O’Reilly SciMon Camp 2006 Brian O’Reilly SciMon Camp 2006

8/18/06Gxxxxxx Frequency 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 t 0 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 t 0 to other times.

8/18/06Gxxxxxx A(f) D D (f)  (t)C D0 (f) DARM_ERR  + s=h(t)+n(t) DARM_CTRL s res =(L x -L y )/L  + DARM_CTRL_EXC

8/18/06Gxxxxxx ActuationActuation A x (f) A y (f) EXC x (t) kyky kxkx  DARM feeds back to the ETMs. Measuring the actuation has typically been the least accurate and most angst-ridden part of the calibration.

8/18/06Gxxxxxx Actuation Function  Calibrate 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

8/18/06Gxxxxxx Actuation 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

8/18/06Gxxxxxx Actuation Function ?

8/18/06Gxxxxxx Compensate the Electronics

8/18/06Gxxxxxx The Payoff… Small Errors

8/18/06Gxxxxxx Digital Filters Know them perfectly?

8/18/06Gxxxxxx The Input Matrix

8/18/06Gxxxxxx Sensing 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.

8/18/06Gxxxxxx Open Loop Gain Discrepancy L1 H1 5-10% error on response at 2 kHz

8/18/06Gxxxxxx Model Inputs

8/18/06Gxxxxxx Frequency Domain Calibration  Measure Open-Loop Gain at a reference time t 0  G 0 (f) = A(f)C D0 (f)D D (f)  h(f,t) = R DERR (f,t)DERR(f,t)  Similar equations for AS_Q  Measure Open-Loop Gain at a reference time t 0  G 0 (f) = A(f)C D0 (f)D D (f)  h(f,t) = R DERR (f,t)DERR(f,t)  Similar equations for AS_Q

8/18/06Gxxxxxx Propagate  This value stays within ~5% of unity, barring any problems with the code.

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8/18/06Gxxxxxx Errors on the Response  By breaking the error down into these components we identify problem areas.

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8/18/06Gxxxxxx Finally  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.