1. LIGO-G040541-00-D LIGO calibration during the S3 science run Michael Landry LIGO Hanford Observatory Justin Garofoli, Luca Matone, Hugh Radkins (LHO), Rana Adhikari, Peter Fritschel (MIT), Patrick Sutton (Caltech), Brian O’Reilly (LLO), Xavier Siemens (UWM), Gabriela González, Andres Rodriguez (LSU), Martin Hewitson (GEO) GWDAW9 December 19, 2004 Annecy, France

2. LIGO-G040541-00-D GWDAW9, 19 Dec 2004 2 Overview 1.Calibration basics 2.Calibration improvements for S3 1.Line strengths in all IFOs 2.Accurate DC calibrations 3.Checks on systematics 3.S4 photon calibrator

3. LIGO-G040541-00-D GWDAW9, 19 Dec 2004 3 IFO review

4. LIGO-G040541-00-D GWDAW9, 19 Dec 2004 4 Calibration method Measure open loop gain G, input unity gain to model Extract sensing function C=G/AD from the model Produce response function at time of the calibration, R=(1+G)/C Now, to extrapolate for future times, monitor single calibration line in AS_Q error signal, plus any changes in gain beta, and form alphas Can then produce R at any later time t, given alpha and beta at t Independent time-domain method (spearheaded by Xavier Siemens with input from Martin Hewitson) uses frequency domain filters as input. Calibrated frames available for use by analysis groups Xavi also demodulates lines, which allows for a nice check on alphas and betas (frequency domain method assumes alpha and beta real, whereas demodulated lines are complex)

5. LIGO-G040541-00-D GWDAW9, 19 Dec 2004 5 Sample error budget: S2 H1

6. LIGO-G040541-00-D GWDAW9, 19 Dec 2004 6 Calibration improvements I Effect of line amplitude on error in product of alpha and beta

7. LIGO-G040541-00-D GWDAW9, 19 Dec 2004 7 S3 V3 ,  coefficients: L1 Error: 0.5% Over all of S3:  variation: 15%  variation: 4%

8. LIGO-G040541-00-D GWDAW9, 19 Dec 2004 8 S3 Calibration errors Errors from reference models in S3 ~ errors in S2 (5-10%) Random variations, errors in alpha, beta (60 sec integration time):  error  S3 variation  S3 variation L10.5%15%4% H10.3%4%1% H20.7%6%2% In S2: 0.7% (L1), ~3% (H1, H2).

9. LIGO-G040541-00-D GWDAW9, 19 Dec 2004 9 Calibration improvements II DC calibration

10. LIGO-G040541-00-D GWDAW9, 19 Dec 2004 10 Calibration improvements II ETMx Asymmetric Michelson Lock configuration by feeding Back to ETM Instead of ~6% error on the ETM calibration, ~2% Lots of checks on actuation strength calibration: toggling, Michelson swinging, free swinging AS_Q, tidal actuators Important for hardware injections

11. LIGO-G040541-00-D GWDAW9, 19 Dec 2004 11 Calibration improvements III understanding systematics Use of true dc calibration requires good understanding of systematics Assess systematic error in digital filter compensation, e.g. dewhitening filters Digital Control signal Digital Anti-dewhitening filter DAC Analog dewhitening filter

12. LIGO-G040541-00-D GWDAW9, 19 Dec 2004 12 S3 response function R comparison V2: assumes digital compensation is perfect V3: uses hardware measurement

13. LIGO-G040541-00-D GWDAW9, 19 Dec 2004 13 S4: Photon calibrator previously installed and tested – laser troubles with rotating polarization recently reinstalled, awaiting laser safety approval expect limited test for S4: independent check on magnitude of calibration (and timing, too) Oddvar Spjeld, LLO

14. LIGO-G040541-00-D GWDAW9, 19 Dec 2004 14 Conclusions LIGO frequency domain calibration improving in accuracy with each science run S3 calibration makes use of several new measurements Anticipate independent check with photon calibrator for S4

15. LIGO-G040541-00-D GWDAW9, 19 Dec 2004 15 Contributions to the Error Magnitude: Phase: R(f i,t) = 1 +  (t)  (t) G(f i )  (t) C(f i )

16. LIGO-G040541-00-D GWDAW9, 19 Dec 2004 16 News on calibration since Aug LSC meeting Not enough!… Coefficients: validation studies of “new” method (using demodulated line) Models: »Codes were succesfully reviewed (P. Fritschel), no errors found. –V2 model version reviewed; V3 mods will need to be assessed »Work in progress on LHO models (to incorporate hardware/digital filters) »Work in progress: systematic model/measurement comparison for different calibration runs in L1. Validation (use of!) X. Siemen’s h(t) frames has started…

17. LIGO-G040541-00-D GWDAW9, 19 Dec 2004 17 Hardware measurements

18. LIGO-G040541-00-D GWDAW9, 19 Dec 2004 18 S3 V3 ,  coefficients V2 (from P. Sutton’s SenseMon) »  from SenseMon averaging input matrix »  from SenseMon’s line amp, , and G 0 (f 0 ) V3: use Xavier Siemens’s code to generate demodulated lines in ASQ, DARM, EXC »Complex  = ( 1/D 0 )*(DARM-EXC)/ASQ »Complex  = -(D 0 /G 0 )*ASQ/DARM »Complex  = -(1/G 0 )*(DARM-EXC)/DARM »Non-zero mean of imaginary part indicates errors in reference functions D 0,G 0 (at cal freq). »Standard deviations of imaginary parts are error estimates in real part (and depend on sampling frequency). Compare consistency of Xavi’s output and existing model

19. LIGO-G040541-00-D GWDAW9, 19 Dec 2004 19 “New” method: validation steps 1.Calculate coefficients at the reference time »Q: Is <Im(  =0? (There’s not a fix if it isn’t!) ANS: YES »Q: Is <Re(  equal to one?  If not, check consistency with input matrix coefficients used for D 0 A: Differences from unity are consistent with precision used in input matrix coefficient (!). »Q: Is <Im(  =0, and <Re(  =1 ? If not, check whether error in G 0 mag and phase are consistent with previous estimates A: G 0 “Errors” found are ~2 deg, 2%, consistent with error estimates for model parameters and comparison with measurements.

20. LIGO-G040541-00-D GWDAW9, 19 Dec 2004 20 “New” method: validation steps H1, reference time G 0 phase “error”: 1.5 deg

21. LIGO-G040541-00-D GWDAW9, 19 Dec 2004 21 “New” method: validation steps 2.With “fixed” D 0, G 0, calculate coefficients at some selected long science segments. Q: Are =0? Are consistent with V2? ANS: yes. 3.Calculate coefficients ,  at reference time and selected segments, with same method, but using the calibration line at 150 Hz. Q: Are =0? (If not, are errors in D 0, G 0 reasonable?) A: yes (H1, H2), maybe (L1) Q: Are same as from 900 Hz line? A: yes (within larger errors, due to smaller SNR).

22. LIGO-G040541-00-D GWDAW9, 19 Dec 2004 22 H1 reference time, From 151.3 Hz line

23. LIGO-G040541-00-D GWDAW9, 19 Dec 2004 23 Calculate coefficients for all of S3. Q: Is =0? Is the distribution of Gaussian? Is time series of stationary? A: yes (H1, H2), no (L1). Observed drift in L1 is ~ +/- 1 deg: not explained (yet), but is within error in phase for G 0 (927.7 Hz). “New” method: validation steps

24. LIGO-G040541-00-D GWDAW9, 19 Dec 2004 24 S3 V3  coefficient: H1

25. LIGO-G040541-00-D GWDAW9, 19 Dec 2004 25 S3 V3  coefficient: L1

26. LIGO-G040541-00-D GWDAW9, 19 Dec 2004 26 S3 V3 ,  coefficients: H1 Error: 0.3% Over all of S3:  variation: 4%  variation: 1%

27. LIGO-G040541-00-D GWDAW9, 19 Dec 2004 27 H1