Signal digitalizing by undersampling, an approach for the
data acquisition of the interferometer to be used aboard the
LISA satellite
Wei Zhou, Claus Braxmaier
Hochschule f
¨
ur Technik, Wirtschaft & Gestaltung,
Brauneggerstr. 55, 78462 Konstanz, Germany
Abstract:
We present a method for digitalizing narrowband signal by undersampling to
reduce the hardware for the data acquisition and processing of an interferometer.
Keywords: Data acquisition, undersampling, interferometer
1. Introduction
A compact laser interferometer for translation and tilt metrology has been presented in [1]. It
is going to serve as a demonstrator for an optical readout of the free-floating proof mass position
and tilt aboard the LISA (Laser Interferometer Space Antenna, a ESA/NASA collaborative space
mission) satellites.
The measurement signal i
m
and the reference signal i
r
are proportional to cos(∆ωt − φ(t)) and
cos(∆ωt) respectively. ∆f =
∆ω
2π
is the heterodyne frequency of the interferometer. φ(t) is given
by φ(t) =
4π
λ
∆l(t). In order to obtain the phase of the measurement signal φ(t), in-quadrature
measurement has been used to get the two signals S
1
=
1
2
AB ·cos(φ(t)) and S
2
=
1
2
AB ·sin(φ(t)) at
first. Then φ(t) can be calculated by φ(t) = tan
−1
(
S
2
S
1
). Fig. 1 shows the schematic of this technique.
Here, the measurement has bee n carried out by hardware. The computer merely computes the value
of tan
−1
(
S
1
S
2
). Of course the digitalizing of both signals i
m
and i
r
can be done directly at the output
of the interferometer, i.g. directly behind the diodes, so that the in-quadrature measurement can
be carried out by software on the computer. Even though quicker data acquisition units can be
used, the speed of computer gives the limit of real-time processing, because the quicker the data
acquisition is, the more data have to be processed in computer. Usually it is desirable to have a
higher heterodyne frequency to minimize the influence of noise. Consequently, a very hight speed
of the com puter would be necessary.
In this paper, data acquisition by deliberate undersampling is discussed. For phase signal φ(t),
which doesn’t change very fast, i.g. it has only a very narrow bandwidth, we will see that a high
sampling rate is not necessary, especially for static measurement, where φ(t) is a constant. In that
1
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