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Function: normalize_gw()
0
void normalize_gw(FILE *fpss,int npoint,float srate,float *response)
This routine generates an array of complex numbers from the
information in the swept sine file and an overall calibration
constant. Multiplying this array of complex numbers by (the FFT of)
channel.0 yields the (FFT of the) differential displacement of
the interferometer arms , in meters:
. The units of are meters/ADCcount.
The arguments are:
 fpss: Input. Pointer to the file in which the swept sine normalization
data can be found.
 npoint: Input. The number of points of channel.0 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 channel.0.
 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

(3.12.9) 
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

(3.12.10) 
We have substituted in equation () which relates
and
.
The IFO voltage is directly proportional to the quantity recorded in
channel.0:
, with the constant
being the ratio of the analogtodigital converter's input voltage to
output count.
Putting together these factors, the
properly normalized value of , in meters, may be obtained
from the information in channel.0, the swept sine file, and the
quantities given in Table by

(3.12.11) 
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
).
Table:
Quantities entering into normalization of the IFO output.
Description 
Name 
Value 
Units 
Gravitywave signal (channel.0) 

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 openloop, and the end mass was driven at
a single frequency, hard enough to move the end mass onehalf wavelength
and shift the interference fringe's 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

(3.12.12) 
 Author: Bruce Allen, ballen@dirac.phys.uwm.edu
 Comments: See comment for calibrate().
Next: Example: power_spectrum program
Up: GRASP Routines: Reading/using Caltech
Previous: Example: print_ss program
Contents
Bruce Allen
20001119