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## Function: GRnormalize()

0 void GRnormalize(float *fri, int frinum, int npoint, float srate,float *response)

This routine generates an array of complex numbers from the swept sine information in a frame, and an overall calibration constant. Multiplying this array of complex numbers by (the FFT of) the raw IFO data yields the (FFT of the) differential displacement of the interferometer arms , in meters: . The units of are meters/ADC-count.

The arguments are:

fri: Input. Pointer to an array containing swept sine data. The format of this data is fri[0]=, fri[1]=, fri[2]=, fri[3]=, fri[4]=, fri[5]=,... and the total length of the array is fri[0..frinum-1].
frinum: Input. The number of entries in the array fri[0..frinum-1]. If this number is not divisible by three, something is wrong!
npoint: Input. The number of points of IFO output which will be used to calculate an FFT for normalization. Must be an integer power of 2.
srate: Input. The sample rate in Hz of the IFO output.
response: Output. Pointer to an array response[0..s] with in which will be returned. By convention, so that response[0]=response[1]=0. Array elements response[] and response[] contain the real and imaginary parts of at frequency . The response at the Nyquist frequency response[N]=0 and response[N+1]=0 by convention.

The absolute normalization of the interferometer can be obtained from the information in the swept sine file, and one other normalization constant which we denote by . It is easy to understand how this works. In the calibration process, one of the interferometer end mirrors of mass is driven by a magnetic coil. The equation of motion of the driven end mass is

 (4.10.22)

where is the driving force and is the differential length of the two interferometer arms, in meters. Since the driving force is proportional to the coil current and thus to the coil voltage, in frequency space this equation becomes
 (4.10.23)

We have substituted in equation () which relates and . The IFO voltage is directly proportional to the quantity recorded in the IFO output channel: , with the constant being the ratio of the analog-to-digital converters input voltage to output count.

Putting together these factors, the properly normalized value of , in meters, may be obtained from the information in the IFO output channel, the swept sine calibration information, and the quantities given in Table  by

 (4.10.24)

where the denotes Fourier transform, and denotes frequency in Hz. (Note that, apart from the complex conjugate on , the conventions used in the Fourier transform drop out of this equation, provided that identical conventions (,) are applied to both and to ).

 Description Name Value Units Gravity-wave signal (IFO output) varies ADC counts AD converter sensitivity ADC 10/2048 Swept sine calibration S(f) from file Calibration constant

The constant quantity indicated in the above equations has been calculated and documented in a series of calibration experiments carried out by Robert Spero. In these calibration experiments, the interferometer's servo was left open-loop, and the end mass was driven at a single frequency, hard enough to move the end mass one-half wavelength and shift the interferences fringes pattern over by one fringe. In this way, the coil voltage required to bring about a given length motion at a particular frequency was established, and from this information, the value of may be inferred. During the November 1994 runs the value of was given by
 (4.10.25)

Author: Bruce Allen, ballen@dirac.phys.uwm.edu