1. Calibration Accuracy of LIGO Interferometers Brian O’Reilly LIGO Livingston Observatory Rana Adikhari (MIT), Peter Fritschel (MIT), Gabriela Gonzalez(LSU), Michael Landry(LHO), Luca Mattone(LHO), Hugh Radkins(LHO), Akiteru Takamori (LHO), Patrick Sutton (PSU) 5 th Edoardo Amaldi Conference on Gravitational Waves July 6-11, 2003 - Tirrenia - Italy

2. Calibration Basics interferometer digital filters pendulum R: Response Function  Calibration Line Amplitude G: Open Loop Gain = C.A.D Brian O'Reilly: New notation for the loop means the figure needs to be updated. Brian O'Reilly: New notation for the loop means the figure needs to be updated.

3. Calibration Basics We choose a time t 0 and measure  0,G 0 and R 0. This allows us to extrapolate to any time t using the amplitude of the calibration line (or lines). The amplitude  (t) is a function of the alignment dependent on the carrier power in the arms and the sideband power in the recycling cavity.  (t) is tracked throughout the science segments. Preliminary extrapolations between times where we made measurements show promise.

4. Three measures of optical gain L1 H1

5. Contributions to the Error Magnitude: Phase: Where the W x and w x are weight functions which depend on the phases and magnitudes of the parameters. Note that errors in the actuation function and the digital filters contribute unweighted to the error on the phase or magnitude of the response function. The accuracy of the determination of these quantities will govern the overall accuracy of the calibration.

6. Plots of Weights Brian O'Reilly: Add plots of the weights that go with the errors on the previous page. Brian O'Reilly: Add plots of the weights that go with the errors on the previous page.

7. Consequences for Searches Errors on amplitude and phase enter the S/N ratio at second order. However, in the event of a detection amplitude errors will linearly affect determination of the distance to the source. (LIGO-T960189-00-E, B. Allen) Binary Inspirals: Bursts: Calibration information used for evaluating efficiency for burst waveforms as a function of their amplitude. In requiring consistency of waveforms between two detectors. Calibration uncertainties feed directly (via efficiency) into final event rate limit.

8. S/N

9. Effect on Burst Analysis

10. Consequences for Searches Stochastic: Uncertainties in amplitude and phase affect cross-correlation statistic linearly. With time-varying noise, segments are combined with a weight whose error depends linearly on amplitude errors of the calibration but is insensitive to phase errors. Periodic: Dependence is quadratic on calibration errors and thus insensitive to first order.

11. Measurements of the Actuation During the first science run we measured A to an accuracy of approximately 10%. Brian O'Reilly: Discuss methods and accuracies of the various actuation measurement methods. Brian O'Reilly: Discuss methods and accuracies of the various actuation measurement methods.

12. Measurements of the Filters Brian O'Reilly: Show some slides on the measurements of the filters. Brian O'Reilly: Show some slides on the measurements of the filters.

13. Conclusions