# Calibration Basics Calibration Basics Calibration Accuracy of LIGO Interferometers

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## Calibration Basics Calibration Basics Calibration Accuracy of LIGO Interferometers

Barat College, US has reference to this Academic Journal, 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) 5th Edoardo Amaldi Conference on Gravitational Waves July 6-11, 2003 – Tirrenia – Italy Calibration Basics R: Response Function a: Calibration Line Amplitude G: Open Loop Gain = C.A.D Brian O’Reilly: New notation in consideration of the loop means the figure needs so that be updated. Calibration Basics We choose a time t0 in addition to measure a0 ,G0 in addition to R0 . This allows us so that extrapolate so that any time t using the amplitude of the calibration line (or lines). The amplitude a(t) is a function of the alignment dependent on the carrier power in the arms in addition to the sideband power in the recycling cavity. a(t) is tracked throughout the science segments. Preliminary extrapolations between times where we made measurements show promise.

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Three measures of optical gain Contributions so that the Error Magnitude: Phase: Where the Wx in addition to wx are weight functions which depend on the phases in addition to magnitudes of the parameters. Note that errors in the actuation function in addition to the digital filters contribute unweighted so that 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. Plots of Weights Brian O’Reilly: Add plots of the weights that go alongside the errors on the previous page.

Consequences in consideration of Searches Errors on amplitude in addition to 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 so that the source. (LIGO-T960189-00-E, B. Allen) Binary Inspirals: Bursts: Calibration information used in consideration of evaluating efficiency in consideration of 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. S/N Effect on Burst Analysis

Balance Sheet in addition to Financial Disclosures Objectives of the Chapter Objectives of the Chapter (contd.) Balance Sheet Statement Illustration 5-16 (Contd.) Illustration 5-16 (contd.) Illustration 5-16 (contd.) Definition of Elements of a Balance Sheet: (SFAC No. 6) Assets Assets (contd.) Assets (contd.) Assets (contd.) Assets (contd.) Assets (contd.) Liabilities A. Current Liabilities Contingencies Contingent Liabilities Contingent Losses Contingent Gains Accounting Treatments of Contingencies Accounting Treatments of Contingencies (contd.) Accounting Treatments of Contingent Liabilities & Losses Examples Accounting Treatments of Contingent Liabilities & Losses (contd.) Accounting Treatments of Contingent Gains B. Long-Term Liabilities C. Other Liabilities Stockholders? Equity a. Contributed Capital b. Accumulated Other Comprehensive Income c. Retained Earnings Other Disclosure Issues Other Disclosure Issues Subsequent Event Subsequent Event – Introduction Subsequent Event – Overview Events Require Adjustment of B/S Events Do Not Require Adjustment of B/S but Require Disclosure SEC Regulations Example A Example B (MD&A) MD&A: Critical Accounting Estimates Example C Other Footnote Disclosures Other Footnote Disclosures (contd.) Other Footnote Disclosures (contd.) Fair Value Hierarchy (SFAS 157) Fair Value Measurements Disclosure : Footnote 28 of GE 2008 Annual Report Limitations of the Balance Sheet Ratio Analysis Exhibit 5-3 Exhibit 5-4 Exhibit 5-4 (contd.) Exhibit 5-4 (contd.) Exhibit 5-4 (contd.) Exhibit 5-4 (contd.)

Consequences in consideration of Searches Stochastic: Uncertainties in amplitude in addition to phase affect cross-correlation statistic linearly. With time-varying noise, segments are combined alongside a weight whose error depends linearly on amplitude errors of the calibration but is insensitive so that phase errors. Periodic: Dependence is quadratic on calibration errors in addition to thus insensitive so that first order. Measurements of the Actuation During the first science run we measured A so that an accuracy of approximately 10%. Brian O’Reilly: Discuss methods in addition to accuracies of the various actuation measurement methods. Measurements of the Filters Brian O’Reilly: Show some slides on the measurements of the filters.

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## Savage, J. General Manager

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