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Multiplexed demodulation of quasi-static
measurands without a receiving
C. M c G a r r i t y and D.A. Jackson
Indexing ternis: Optical scnsocr, Fibre optic sensors
The classical technique of dual wavelength interferometry is used
to detennine the absolute OPD of very short cavities using a
paramel ric plot of the relative interferometric intensifies. A
network of eight :jensors is demonstrated with phase resolution of
1Smratl corresponding to 0.2nm with an unambiguous range of
Measuring the absolute optical path difference (OPD) of an interferometric sensor is a key goal of optical fibre sensing. Early work
used dual-wavelength interferometry with pseudo-heterodyne
processing for passive sensors. This requires the sensor to have a
path imbalance of -1 cm [I]. Problems were experienced with laser
amplitude modulation and high tcmpcrature cross-sensitivity
caused by the path imbalance. White light interferometry (WLI)
has received attention as it overcomes this difficulty and produces
subnanometre resolution [2]. WLI reduces wavelength stability
requirements but does require a stable receiving interferometer or
a stable reference cavity. We present an application of the classical
technique of dual-wavelength interferometry for measuring very
short cavities. \Ne demonstrate that one representation of the data
allows demodulation of quasi-static measurands from zero OPD
to the effective wavelength using the relative intensity of the two
interferograms. The short cavity length reduces temperature sensitivity. This technique does not require a receiving interferometer,
but does require the sensor to be perturbed, and it provides comparable resolution and range to conventional dual-wavelength
0 . 2 0 . L 0.6 0.8
intensity of second interferograrn,a.u
points are points of ambiguity. An extension of this concept to
three dimensions can eliminate these crossing points. Using a third
wavelength to produce a 3-D LF, crossing points need not occur
as the 2-D data occupies a volume of space. The third wavelength
only provides this third degree of freedom.
The concept was experimentally verified using a Mach-Zehnder
(MZ) combined with simple electronics to distinguish the interferograms. A computer sampled the resulty. To distinguish the
interferograms the lasers were amplitude modulated at 5 and
7kHz. The output was mixed with these frequencies and lowpass
filtered to produce the interferograms. The resoltuioii of the A/D
is 12bits. The least significant bit (LSB) accuracy is 1 part in 4096.
Samples therefore have a resolution of 0.2nm or 1.5mrad at 827
nin. Sufficient optical power and careful electronic design ensure
the noise is <0.5 LSB.
Fig. 2 Network multiplexing eight interjhrometer sensors
7 c x 5:opped:
7367 Acquisitions
Fig. 1 Lissujous representing intcrfefcronwter OPD using two wavelengths
Two laser sources with specific wavelength differences illuminate the sensor. The separate interferograms can be combined in a
parametric plot to generate a Lissajous figure (LF) as shown in
Fig. 1. The X axis is the intensity of the smaller wavelength and
the Y axis is the intensity of the larger wavelength. Displaying the
interferograms as a LF represents their relative phase in two
dimensions. The trace represents the OPD from zero to the effective wavelength. Zero OPD occurs at the top right hand corner.
The solid tract: begins there and extends to half of the effective
wavelength. The dotted trace represents the OPD from this point
to the full effective wavelength. Although not every point in this
figure is unique, any finite length of the trace is unique. Performance is optiinised by making a careful choice of wavelengths. Fig.
1 was produced for demonstration using wavelengths of 800 and
Clearly any finite part of the trace is unique rather than any
individual point, so the technique requires the phase to be subject
to constant ch,ange. Most single measurements of the intensities
provide the relative phase and the absolute OPD, but the crossing
20th June 1996
Vol. 32
No. 13
Multiplexing using this technique is straight forward. The network illustrated in Fig. 2 uses a combination of frequency and
time division multiplexing successfully demonstrated with interferometric sensors 131. Acousto-optic modulators are used as both
switches and isolators. Simultaneous pulses of light from each pair
of lasers are launched into the network. The 50m length of fibre
delays the signal from the second sensor of each pair by 0 . 5 p .
The detector receives signals from two pairs separated in the frequency domain. Fig. 3a shows a sample of the signal. The ‘dead
space’ in the timing is deliberate as the AOM is on at this time.
The AOM is off when pulses are returning. Fig. 3b indicates the
time demultiplexing of one pulse. This pulse contains frequency
multiplexed signals from two sensors. The sampling frequency is
filtered out and the signal is processed using the scheme described
above. Modulation frequencies of 3 , 5 , 7 and 9kHz were applied
to the four lasers. The wavelengths of the laser pairs were 827nm.
833nm (effective wavelength 1 1 4 . 8 ~ and
) 823nm, 8301x11 (effective wavelength 97.58pi).Eight low finesse Fabry-Perot sensors
were fully demodulated for quasi-static signals up to -100Hz.
Seven of these sensors consisted of a cleaved fibre end and a mirror. One sensor (No.5) consisted of a GRIN lens partially coated
with aluminium and a mirror.
lised. A reference sensor would provide a fixed point on the LF
against which to check wavelength calibration.
In conclusion we have reported the use of a novel representation of the classical dual-wavelength technique which allows the
unambiguous demodulation of quasi-static measurands for very
short cavities with comparable resolution to WLI, but without the
requirement of a stabilised receiving interferometer.
0 IEE 1996
I M a y I996
Electroiiics Lerrers Online No: I9960771
C. McGarrity and D.A. Jackson (Applied Optics Gvoup, Physics
Luhorcilorj., Ciiiwrsilj of Kent, Cunterbury, Kent CT2 7 N R , United
and JONES, J.D.c.:
’Pseudoheterodyne detection scheme for optical interferometers’,
Elerrion. Lerr., 1982. 18, (25), pp. 1081-1083
2 PATTEN. R A : ’Michelson interferometer as a remote gauge’, Appl.
Opr., 1971. 10. (12), pp. 2717-2721
3 McGARRITY. C., CHL. B.C.B., and JACKSON, D.A.: ‘Multiplexing Of
Michclson intcrfcromctcr scnsors in a matrix array topology’, Appl.
Opt., 1995. 34. (7); pp. 1262-1268
4 DAUDRIDGE. . A . TVETEN. A.B , and GIALLORENZI, T : ‘Homodyne
demodulation scheme for fiber optic sensors using phase generated
carrier‘. IEEE Trciris. Microii,. Theory Tech., 1982, MTT-30, (IO),
pp. 1635-1641
Simple technique for apodising chirped and
unchirped fibre Bragg gratings
R. Kashyap, A. Swanton and D.J. Armes
Fig. 4 Results j i k m sensor No.5 ond sensor No.1
No.5. b No.]
Electronic noise from the time demultiplexing contributes to the
total noise. The noise level approaches 0.5 LSB. Fig. 4 shows two
partial LFs of the experimental results from sensor No.5 (left hand
side) and sensor No.1. Three samples are displayed. The small
traces in each plot are two separate samples of a signal of
IOOmrad at IOOHz applied to the mirror. The long traces are samples of several minutes of natural drift. The traces represent drifts
of 915.6nin (No.5) and 909.2nm (No.1). The software controlling
data acquisition easily determines the size of periodic signals and
their mean OPD, or the absolute OPD of single samples.
The visibility of sensor No.5 is constant over the full range. The
resolution of this sensor is constant and is the same as the MZ
(0.2nm). Divergence from the bare fibre means the visibility is
maximised about the central third of the range. About this OPD
the conversion resolution is < 0.5 LSB. The drop in visibility near
zero OPD and near 1 0 0 p causes the noise to increase to 0.68
LSB, which halves the resolution.
The simple scheme used to separate the interferograms is limited
to short cavities to ensure no phase modulation occurs. The mixing and filtering process produces the same output as the phase
generated carrier technique [4] for larger OPDs. This problem can
be minimised by ensuring the modulation is minimal and optimising the mixing electronics. Alternatively it can be eliminated using
a diffraction grating to separate the interferograms.
The technique requires wavelength stability and amplitude stability. Small changes can be compensated in the processing if
detected. An adjustment is required if the power of one laser
changes. The LF then has a different aspect ratio. The spacing
between traces is also scaled so the relative phase is still unambiguous. The range is maintained but the resolution is compromised.
Wavelength drift of either laser changes the position of the trace.
This effects the range but not the resolution. The first half of the
LF is always unique. Careful choice of the wavelengths ensures a
large ‘window’ to maintain the uniqueness of the second half. At
least one of the lasers of each pair should be temperature stabi-
For the first time, a simple technique is reported for apodising
chirped or unchirped gratings of arbitrary length. Also reported
for the first time is the fabrication and measurement of
unapodised and apodised l O O m m long, step-chirped fibre gratings
with a dispersion parameter of -1.6ns-n1n-’ and a bandwidth of
up to 0.75nm. It is shown that long chirped gratings may be
fabricated at predetermined wavelengths in standard
telecommunications fibre for dispersion compensation.
Introduction: The step chirped grating (SCG) has been demonstrated to be highly effective for producing fibre Brdgg gratings of
arbitrary dispersion and reflection profile [I]. In particular, the
Bragg wavelength and chirp can be pre-programmed into the
phase mask for easy replication into a fibre by either scanning [l,
21. or by the use of an interferometer. Apodisation, i.e. the gradual
change in the refractive index modulation, of chirped fibre gratings is necessary when the coherence length of a signal determined
by the bandwidth of the chirp is a few per-cent of the length of the
chirped gating. Thus, apodisdtion has been implemented by several workers [3, 41, but these methods use either active variable
control during the writing of the grating [4], or some post-processing to tailor the amplitude of the refractive index profile of the
grating along its length. These methods, while producing good
results, need careful calibration of the response of the fibre [3], or
active control of the amount of dither applied to the fibre as a
function of scan-position [4]. This Letter demonstrates an
extremely simple method of apodisation of fibre gratings of arbitrary chirp and profile, usable for all types of gratings, and it is
shown that step-chirped phase masks of l00mm length with
0.75nm bandwidth may be written with a constant dispersion
Phase inaslcs: Previously, the only report of the SCG has been for
low dispersion over a broad bandwidth 151. These gratings have
been shown to completely compensate for dispersion of ultra-high
bit-rate transmission (100Gbit/s) over -4km 161. However, narrow
band, highly dispersive SCGs have not so far been reported. In the
20th June 1996
Vol. 32
No. 13
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