Optical interferometric signal generator based on electrical phase-locked
loop technique
Lih-Wuu Chang and Ching-Ting Lee
a)
Institute of Optical Sciences, National Central University, Chung-Li, Taiwan, Republic of China
Pie-Yau Chien
Material Research Center, Chung-Shan Institute of Science and Technology, Lung-Tan, Tao-Yuan, Taiwan,
Republic of China
͑Received 10 April 1997; accepted for publication 25 November 1997͒
To simulate a phase-modulated interferometer, a novel electrical signal generator has been
demonstrated. There are two phase-locked loop ͑PLL͒ circuits used in our system to process the
phase signal. The first PLL is adopted as a voltage-controlled phase shifter, and the second PLL is
used to amplify the phase signal to get a phase shift with a dynamic range over Ϯ16
rad. This
system can be further modulated with sinusoidal, sawtooth, and triangular wave forms for
interferometric signal detection. © 1998 American Institute of Physics. ͓S0034-6748͑98͒01903-0͔
I. INTRODUCTION
Many interferometer systems have been demonstrated
successfully. In these systems, the phase-modulated interfer-
ometer is the most popular system that can be employed in
various fields for sensing physical parameters. The informa-
tion that we would like to detect exists within the change of
optical phase delay.
1–6
It is well known that the fiber-optic
gyroscope ͑FOG͒ and the Michelson interferometer can be
employed to measure the rotation signal of an object
3–5
and
the signals of distance and velocity,
7–10
respectively. Fur-
thermore, the all-fiber Mach–Zehnder interferometer and
Fabry–Perot interferometer are usually employed as the sen-
sors of temperature, strain, and pressure.
11–13
In order to ob-
tain an output signal with high sensitivity and a good linear
scale factor, the optical phase delay of an interferometer has
to be dynamically biased by an external modulation signal,
and then followed by a suitable electrical demodulation.
1–3
When the optical phase delay is modulated by a periodic
signal, several high-order harmonic components are gener-
ated due to the nonlinear transfer curve of the interferometric
signal. In general, the fundamental component of the output
signal can be obtained using an electric lock-in technique.
1
Furthermore, the harmonic components at fundamental and
second-order terms can be adopted to implement a so-called
pseudoheterodyne
2,5
detection using a quadrature summation
technique. Meanwhile, the components at second- and
fourth-order terms can be used to stabilize the modulation
index of a phase-modulated interferometer,
6
especially in the
FOG, which requires a high stability on the modulation in-
dex. For a triangular phase-modulation wave form used in
the interferometer,
2,3
a synchronized gating followed by the
phase-locked tracking filter technique has been developed to
measure the rotation rate on an open-loop FOG with a wide
dynamic range.
3
There are many standard engineering softwares ͑
SPICE
,
MATHEMATICA
, etc.͒ that can be used to analyze the ideal
case of the optical interferometric system output and obtain a
good simulation result in the computer. However, it cannot
offer a real-time electric simulation output for electronic de-
modulation design. In this article, we will demonstrate an
electrical interferometric simulation system to generate the
same output signal as that of the optical interferometric sys-
tem, and it also supplies electric designers an on-line simu-
lation signal-for-signal demodulation. Figures 1͑a͒ and 1͑b͒
show the constructions of an optical interferometric system
and an electrical interferometric simulation system, respec-
tively. For optical interferometers, the output signal of the
systems will be disturbed due to the optical path difference
varying and polarization changing, and it needs an electrical
feedback servo to avoid signal fading. We successfully use
low-cost and low-noise electronic circuits together with a
phase-modulation facility to generate the same output signal
as that of optical interferometry, and its noise can be mini-
mized simultaneously. By just applying a dc bias voltage
mixed with an external modulation signal to the electrical
interferometric simulation system, the simulated interfero-
metric signal can be obtained easily. The phase shift of the
output signal of the electrical interferometer is modulated
and amplified by using the phase-locked loop ͑PLL͒ tech-
nique.
II. THEORETICAL ANALYSIS
Figure 2 shows the block diagram of our electrical inter-
ferometric simulation system. A signal S
r
(t) with angular
frequency
r
and reference
r
is adopted as a reference sig-
nal. The frequency of signal S
r
is reduced to
r
/N through a
frequency divider and it is denoted as S
N
(t). The signal
S
N
(t) is then sent into phase-locked loop 1 ͑PLL1͒, which
acts as a voltage-controlled phase shifter ͑VCP͒. The total
phase-modulation signal
tot
consists of an external phase-
modulation signal
e
, time-varying voltage
n
,andadc
phase bias
dc
, and that is combined with the phase-detector
output
e1
of PLL1. The loop filter is used to null out the
a͒
Author to whom correspondence should be addressed.
REVIEW OF SCIENTIFIC INSTRUMENTS VOLUME 69, NUMBER 3 MARCH 1998
12460034-6748/98/69(3)/1246/7/$15.00 © 1998 American Institute of Physics