As mentioned earlier it is very important that the system used
for sensing the optical fringe movement on the output of the
interferometer can resolve strains in space of
or lower, or differences in the lengths of the two arms of less
than
, a minute displacement compared to the wavelength of light
m. A limitation to the sensitivity of the optical readout
scheme is set by shot noise in the detected photocurrent. From
consideration of the number of photoelectrons (assumed to obey
Poisson statistics) measured in a time
it can be shown [49] that the detectable strain sensitivity depends on the level of
laser power
P
of wavelength
used to illuminate the interferometer of arm length
L, and on the time
, such that:
or
where
c
is the velocity of light and
h
is Planck's constant and we assume that the photodetectors have
a quantum efficiency
1. Thus achievement of the required strain sensitivity level
requires a laser, operating at a wavelength of
m, to provide
W power at the input to a simple Michelson interferometer.
This is a formidable requirement; however there are a number of
techniques which allow a large reduction in this power
requirement and these will be discussed in the next section.
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Gravitational Wave Detection by Interferometry (Ground
and Space)
Sheila Rowan and Jim Hough http://www.livingreviews.org/lrr-2000-3 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |