Summary of LIGO interferometer calibration and the production of
interferometer noise spectra
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Interferometer calibration typically refers to the determination of the ratio
between the signal recorded at the antisymmetric port, and an independent
physical measurement of the differential motion of test masses. The primary
reference for calibrating interferometer readout is the 1.06 micron wavelength
of the Nd:YAG laser.

Control signal calibrations are obtained from measurements of simple
interferometric subsystems such as a locked Michelson. Calibrations
are transferred to end test mass control signals by locking a single
interferometer arm and modulating the length of the cavity.

The frequency response of the instrument over the detection bandwidth
(40 Hz-7 kHz) is obtained by injecting sinusoidal length excitations into the
control signals of test masses, and recording the response at the
antisymmetric port photodiode. This transfer function will be employed to
produce displacement equivalent noise.

A noise spectrum in the form of an amplitude spectral density of the q-phase
demodulated anti-symmetric port photodiode (AS_Q) is obtained. The
displacement-equivalent noise spectrum is produced by dividing this AS_Q
spectrum by the measured transfer function, and scaling the result by the
appropriate control signal calibration.

The displacement spectral density (m/sqrt(Hz)) calibration data is converted
into an equivalent strain spectral density (h(f) strain/sqrt(hz)) by dividing
by the interferometer arm length. Finally, the spectrum is plotted log amplitude
vs log frequency with a frequency resolution per point of 0.125 Hz or 0.002*f
depending on which is larger. Narrow spectral lines in the original data, such as
the line and its harmonics, if they exceed twice the average value in the frequency
resolution element, are plotted at the original amplitude. The rms value of a line
remains the plotted amplitude * sqrt(initial bandwidth).

Rana Adhikari, Michael Landry, Rainer Weiss