IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 52, NO. 6, DECEMBER 2003
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A Displacement-Measuring Instrument
Utilizing Self-Mixing Interferometry
M. Norgia, Member, IEEE, and S. Donati, Fellow, IEEE
Abstract—We develop a self-mixing laser interferometer for the
measurement of displacements on a generic target surface. The
measurement is based on the bright-speckle tracking, a technique
we have recently proposed to solve amplitude fading associated
with the speckle statistics when the displacement to be covered is
well in excess of the speckle longitudinal size. We implement the
dynamical tracking of speckle maxima with piezo actuators and a
phase-sensing loop. Also, we use an automatic gain control, based
on a liquid crystal attenuator, to improve the amplitude statistics.
Details of digital signal acquisition with adaptive signal processing
through a field programmable gate array are discussed.
The resulting instrument offers sub- m resolution in the measurement of displacement up to 500 mm of total shift, has virtually
no need for alignment, and has very relaxed target-surface requisites, yet works with a very simple and inexpensive set-up.
Index Terms—Laser measurements, optical feedback, optical interferometry, rough surfaces, semiconductor lasers, speckle.
I. INTRODUCTION
R
ECENTLY, we have proposed and experimentally
demonstrated [1] a principle to perform an interferometric measurement of displacement on a noncooperative (or
rough) surface.
As it is well known, the optical field returning from a noncooperative target is affected by the speckle-pattern statistics, and,
in particular, we may occasionally find dark speckles, with a
field amplitude much less than the average, for which the useful
interferometric signal becomes so small to generate an error. Indeed, classical displacement interferometers work with a corner
cube as a target, which needs a very careful alignment process
[2]–[4].
Our method consists of dynamically tracking the relative
plane as the target
maximum of the speckle field in the
moves along the -axis. This strongly decreases the probability
of signal fading, and makes the measurement feasible on a
diffusing surface even for large displacements, much larger
than the (average) speckle longitudinal size.
deflection of the laser
To this end, we have used an
beam projected onto the target, with the aid of piezoceramic
actuators moving a small lens collimating the laser output [1].
To obtain the error signals necessary for the maximum-amplitude tracking, we superpose small-amplitude modulations to
Manuscript received February 20, 2002; revised June 30, 2003. This work was
supported in part by the SELMIX Project and in part by the FAR 60% Contract.
M. Norgia is with the Dipartimento di Elettronica, Università di Pavia, Pavia,
Italy, and also with the Istituto Nazionale di Fisica della Materia (INFM), Milano, Italy (e-mail: michele.norgia@unipv.it).
S. Donati is with the Dipartimento di Elettronica, Università di Pavia, Pavia,
Italy.
Digital Object Identifier 10.1109/TIM.2003.820451
Fig. 1. Basic elements of a self-mixing interferometer.
the and drives, then perform a synchronous detection and
low-pass filtering of the result, and lastly feed it back to the
drive.
In the actual tracking of bright speckles, the spot projected
m, typically)—unnoticeon the target moves very little (
able by eye—and the distance error by parallax is negligible.
Nevertheless, the speckle statistics are much improved [1], and
the system jumps from one bright speckle to the next when it
approaches a nearly zero-intensity point, not so uncommon in
a normal speckle field. Also, the error due to speckle jump is
-step measurement.
negligible [1], at least in a
By tracking the amplitude to the speckle maximum, we ensure that the signal is never too weak. To improve the statistics
further, we add an automatic gain control (AGC) made by an
optical attenuator and photodetector feedback loop. With this
expedient, the interferometric signal is also prevented from becoming excessively large.
II. SELF-MIXING INTERFEROMETER
As in [1], we used an injection (or self-mixing) interferometer
to develop the principle of speckle tracking. The self-mixing
configuration (Fig. 1) is particularly attractive from the application point of view because, as well known [5], [6], it is selfaligned, has a minimum part-count, and is immune to stray light
disturbances.
On the other hand, to function properly, we have to care about
the fractional level of field amplitude returning back to the laser
cavity. We shall keep this fraction neither too small (the weakfeedback regime) nor so large (the strongly collapsed-coherence
regime), to stay within the moderate-feedback regime characterized by one switching of the interferometric signal per -pe-displacement), as shown in Fig. 2. This situation is
riod (or
the most desirable from the point of view of easy development of
the instrument, because we shall just look at the interferometric
waveform (Fig. 2, bottom) and count the upward switchings as
and the downward switchings as
increments to get
the measurement of displacement [5], [6].
0018-9456/03$17.00 © 2003 IEEE
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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 52, NO. 6, DECEMBER 2003
Fig. 2. When the diffusing target oscillates of a few micrometer (top trace), the
interferometric self-mixing signal waveform exhibits upward (and downward)
of displacement
switchings at each new positive (and negative) increment
(bottom trace). The switching start appearing in the interferometric waveform
= amplitude increment
at > , and they mark a half-wavelength
up to < : .
C 1
C 46
(1 = 2)
1
In addition, the method could be refined to go well beyond
the half-wavelength of resolution, as discussed in [7], or with
another method in [8].
In terms of the feedback parameter [5], the moderate-feed, a conback regime corresponds to require that
dition that can be satisfied by controlling the power attenuation
of the go-and-return path. Indeed, is given by
(1)
where is the target distance, is the linewidth enhancement
is the
factor, is the mode mismatch coefficient ( 0.5),
is the refractive index, and
is the refleclaser length,
tivity of the laser output facet.
through a liquid crystal (LC)
We implement the control of
optical attenuator, fed by the peak-to-peak signal amplitude detected by the photodiode. The gain control is capable of compressing the signal dynamic range by a factor of 20.
III. WORKING ON A DIFFUSING TARGET
The basic optical setup of the instrument is shown in Fig. 3.
As a photodetector, we use the monitor photodiode mounted in
the laser package behind the laser chip (a distinctive feature of
self-mixing is that the signal is impressed on the optical field
and can be read everywhere on the beam).
A small (5-mm diameter, 4.6-mm focal length) collimating
piezo-actuator stage, at the focal
lens is mounted on an
distance from the laser output facet. By actuating the piezo, the
lens is moved transversally with respect to the beam and the
position of the spot projected on the target is changed. As a
consequence, the random sample of target surface illuminated
by the beam also changes, and the field returned in the laser too.
Fig. 3. Optical setup of the instrument. Light emitted by the laser is collimated
on the target with the aid of a small objective lens. This lens is mounted on X-Y
piezo-drives which move transversally the lens optical-axis and hence the spot
position on the target. The signal detected by a photodiode placed on the rear
facet of the laser is used for a servo loop ending on the X-Y drives and arranged
so as to keep the photocurrent locked to a local maximum, or to track a bright
speckle. Last, a liquid crystal attenuator (made by a LC film and a polarizer) is
the actuator for a control loop looking at signal amplitude and making the AGC
(automatic gain control) function.
This is equivalent to scanning the receiver across the speckle
projected back into the laser by the target. By scanning around
a quiescent point, we can find maxima and minima of speckle
intensity. We can arrange a servo loop to keep the photodetected
signal amplitude at a maximum, and this means that we lock the
optical system to a bright speckle.
Electronically, this optical servo loop is implemented
by adding a low-amplitude sensing-modulation to the
slowly-varying drive signal of the piezo, both on the and
axes, and by detecting whether the modulation carried by the
photodetected signal is in phase (slope up to the maximum)
or in antiphase (slope down to the maximum) with respect to
the piezo drive. Then we make a (positive/negative) correction
to the drive signal of the piezo until the photodetected signal
has only the second harmonic of the sensing-modulation signal
(centering on the maximum).
The photodetected signal is also used to drive the liquid
crystal attenuator (LCA), again resulting in a feedback loop
aimed to keep the amplitude nearly constant (AGC). The
AGC response is made much slower than the bright-speckle
tracking response, to avoid interference between the two loops.
With the LCA, we are able to smooth the variations in signal
amplitude as due to the statistics of the bright speckle, and
regime.
work consistently in the single-switching
The only adjustment required to system operation is a -axis
alignment of the collimated beam on the target.
As an example additional to those already reported in [1], we
show in Fig. 4 a statistical sample representative of the amplitude
distribution obtained from a cooperative target surface, with
and without speckle-tracking system and optical AGC.
The cooperative surface we used is the Scotchlite tape, a superdiffusing surface containing refracting micro-spheres or a
cat’s-eye texture which enhance the diffusivity in the direction
of illumination. The practical gain in reflectivity, with respect to
the ideal diffuser, is 20–50 (20 in our case), a factor very useful
also at largest
to match the attenuation budget and have
NORGIA AND DONATI: DISPLACEMENT-MEASURING INSTRUMENT
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TABLE I
PROBABILITY OF C < 1 (%), FOR SOME TARGET MATERIALS, WITH AND
WITHOUT THE SPECKLE-TRACKING SYSTEM
Fig. 4. Amplitude distributions (or probability density function) of the signal
received from a superdiffusing target (Scotchlite tape) by the self-mixing
interferometer in several control situations, all normalized to an amplitude
A = 1 when C = 1. Line with diamonds: all controls off (normal speckle
statistics, fairly close to Rayleigh distribution, dashed line); dotted line: AGC
off and speckle-tracking on (small values occurrence is strongly decreased).
White bar: AGC on (with AGC servo at A = 2:8) and speckle-tracking off.
Black bar: AGC and speckle tracking on.
distance. The constraint of having a cooperative optical surface may appear objectionable in a measurement instrument,
however the target surface is readily painted with a drop of
varnish and this treatment is surely much less invasive than
that of attaching a corner-cube retroreflector as in conventional
interferometer.
As we can see in Fig. 4, reporting a typical sample of
1000-points measurement of the amplitude statistics, when
all controls are off we start with a broad range of amplitudes
, and
and a not so small percentage of cases with
progressively sharpen the distribution around the selected mean
with the bright-speckle tracking and the AGC,
value
and the
reducing the mean square deviation to
cases to less than 0.15%.
percentage of
cases we would
With respect to the 10% probability of
with an ideal
obtain when using an average amplitude
diffuser, the improvement is quite substantial (this is a typical
value for a paper target [1]). Yet, there may still be rare cases
left, in which the amplitude is too small and the measurement
is invalid (or, it shall be repeated). In the practical operation of
the instrument, however, we got the confidence that the above
value is quite acceptable.
meaOther experimental data on the probability of
sured on several target surfaces, illuminated by the laser at a
50-cm distance, are shown in Table I.
IV. ELECTRONIC PROCESSING
In Fig. 5, we report the basic elements we used in the processing of the signal out of the photodiode. The target displacement is measured by counting the sharp transitions in the signal
waveform (Fig. 2). First, we time-differentiate the signal by an
analog circuit, obtaining positive/negative spikes that will be
increment of distance. Then, we may
counted up/down as a
Fig. 5. Block scheme of the electronic processing (trans-Z corresponds to
transimpedance amplifier).
proceed either with an analog or digital processing of the signal
as detailed below.
For the good working of the AGC and of the speckle tracking
system it is necessary to always have a signal, which measures
the amplitude of the back reflection. To have the self-mixing
interferometric signal available even when the target is at rest,
we superpose a triangular modulation signal on the dc bias
current I of the laser. In this way, because of the dependence
from the drive current, a optical
of wavelength
is developed, z being the target
pathlength signal
, we have to subtract the
distance. But, as it is also
triangular modulation signal [Fig. 6(a)] from the photodiode
signal [Fig. 6(c)], so as to recover the self-mixing signal
[Fig. 6(d)]. The amplitude of this signal is directly used by
the controller for driving the LC attenuators and is the input
of the speckle tracking system [1].
The triangular modulation waveform has a frequency of
20 kHz and is low-pass filtered at 300 kHz [Fig. 6(a)]. This
modulation does not affect the measurement of displacement
(output of the up-down counter), because it is zero mean.
(after the
In Fig. 7, we report a self-mixing signal with
triangular waveform subtraction), the derivative of the original
signal and the derivative of the triangular wave. As it can be
seen, the triangular wave is useful to push up the positive peaks
and pull down the negative ones, improving discrimination
accuracy. The low-pass filter is useful because it cleans the
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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 52, NO. 6, DECEMBER 2003
to 6 cm/s in our prototype). In this way, we ensure that there are
always at least one positive and one negative pulse per period.
This is useful also in the digital signal processing, to develop an
adaptive count-threshold.
V. ANALOG AND DIGITAL SIGNAL PROCESSING
A. Analog
In the analog-processing version of the instrument, the target
displacement meter can be developed as follows [5].
The signal derivative (trace b in Fig. 6) is used as the input of a
pair of comparators, with positive and negative thresholds. The
output pulses are sent to two 4-bit up-down buffer-counters. The
two overflow outputs of the buffers drive a commercial up-down
. In this way, the
counter, with scale factor equal to
instrument display has a nominal resolution of 0.1 mm. The
two up-down buffers are used because of the low speed of the
commercially available, low-cost counters with integral display
and scale factor adjustment.
B. Digital
Fig. 6. Curve a: triangular laser current modulation, low-pass filtered. Curve
b: signal derivative. Curve c: signal at the monitor photodiode. Curve d:
self-mixing signal, difference between curves c and a.
<
Fig. 7. Top trace: self-mixing signal with C
1. Middle trace: derivative of
the signal without subtraction of the triangular wave. Bottom trace: derivative
of the triangular wave.
waveform from spikes and allows to reset the delay between the
laser amplitude and wavelength modulation. The wavelength
modulation, to which a thermal component do contribute, has a
response time of about 1 , whereas the amplitude modulation
has much shorter response time. This means that the pulses
with respect to the square
in Fig. 7 are delayed of about 1
wave (derivative of the triangular). Filtering prevents the pulse
from jumping in the wrong semi-period of the square wave.
Frequency and amplitude of the triangular wave are chosen
so as to match the performance of maximum target speed (set
To fully exploit the circuit speed, we started with a field programmable gate array (FPGA) to pre-process the signal. An
8-bit analog-to-digital converter samples the signal derivative
samples/s and gives the input to the FPGA. The basic alat
gorithm we have implemented consists in counting the positive
and negative pulses for 0.4 ms, then transmitting the difference
to a computer by the serial RS232. The internal up-counter is incremented when the sequence 0-0-1 comes out as a result of the
comparison with the positive threshold. This sequence avoids
multiple counts of a single pulse. Unlike the analog processing,
the threshold is not kept fixed: it is changed every two periods
of the triangular waveform (each 0.1 ms). The new threshold is
set at the 70% of the signal maximum in the previous period. In
this way, we obtain an adaptive threshold dynamically changing
with the actual signal amplitude. The block-scheme of the algorithm is shown in Fig. 8, only for the positive count; for the
negative one the algorithm is the same.
There are additional reasons to prefer an adaptive threshold.
First, the self-mixing signal amplitude depends on the target
distance [5], and thus on the amount of feedback. Working with
a diffusive target and on substantial span of target displacement
(about 1m) we have both causes of amplitude variations.
Moreover, the sharp up/down transitions of the signal exhibit
different amplitudes, depending on the C value [see bottom trace
in Fig. 2, or the peak amplitude in Fig. 6(b)], thus the positive
threshold is normally different from the negative one.
Periodically, the difference between the up and down counts
is stored in 1 byte to be transmitted, and the internal counters
are reset to 0. The byte transmission, by RS232 at 115.2 kb/s,
is made during the signal processing of the next period (1 byte
each 0.4 ms). In this way, the personal computer receives the
displacement data at a low data-rate.
A program of acquisition has been developed with the
software Labview, especially useful for its flexibility. The
processing consists in multiplying data by the scale factor
, then adding to the total displacement. The single byte is
NORGIA AND DONATI: DISPLACEMENT-MEASURING INSTRUMENT
Fig. 8. Block scheme of the signal elaboration in the FPGA: adaptive threshold
and serial transmission.
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Fig. 9. Computer screen, working as a virtual instrument, shows the time
evolution of target speed (top trace) and of total displacement (bottom trace).
also a measurement of the target speed (averaged in the time
between transmissions).
A picture of the computer screen during a measurement is
shown in Fig. 9, displaying target speed and total displacement
as a function of time. The target was moved, by hand, a few
centimeters on a slit.
VI. INSTRUMENT PERFORMANCES
The resolution of the instrument is
(about 400 nm), as
limited by the fringe counting method. With the current modulation, we need to perform a time-average in order to get the
same resolution, which can be simply done by the acquisition
computer.
In our prototype, the maximum speed of the target is 6 cm/s,
limited by the bandwidth of the analog electronics. The frequencies of the triangular wave and of the serial transmission are
chosen according to this limit.
The response time of the adaptive threshold is about two
periods of the triangular wave (100 ), much less than the
response time of the system.
The response speed of the speckle-tracking system is 100 Hz,
enough to compensate for the ambient-related vibration, while
the LC attenuator response has a cutoff at 1 kHz.
An alert-LED is switched on when the amplitude of the selfmixing signal becomes too low. In this case, the measurement
can be wrong and should be repeated.
When we use Scotchlite as a target surface, the probability of
correct operation is very high. Yet the instrument can work also
over other kind of surfaces, exhibiting the performances outlined in Table I. The instrument in this case is especially useful
for vibration measurement, when a single error does not affect
the entire measurement. The limitation in this case is the transmission rate to the computer, and we can measure a maximum
vibration frequency up to about 1 kHz.
In Fig. 10, there is shown a photo of the instrument, made
of two boxes, one containing the power supplies and the electronics, the other with the optical head.
Fig. 10. Instrument photo: (left) the optical head and (right) the box with
power supply and electronics.
VII. CONCLUSION
In this paper, we have presented the development of a self-displacements
mixing interferometer capable of measuring
of a noncooperative target (i.e. without a corner-cube) on a
substantial distance (e.g., 0.5 to 1 meter) without any optical
adjustment but the initial pointing on the target. Several types
of surfaces have been compared quantitatively. We have also
outlined the electronic processing issues, both analog and digital,
and presented some experimental results obtained with our
prototype.
REFERENCES
[1] M. Norgia, S. Donati, and D. D’Alessandro, “Interferometric measurements of displacement on a diffusing target by a speckle tracking
technique,” IEEE J. Quant. Electron., vol. 37, pp. 800–806, June
2001.
[2] M. Francon, Optical Interferometry. New York: Academic, 1966.
[3] S. Donati, Optoelectronic Instrumentation. Upper Saddle River, NJ:
Prentice-Hall, 2003.
[4] T. Bosch and M. Lescure, Eds., “Selected paper on laser distance measurement,” in SPIE Milestone Series, 1995, vol. MS115.
[5] S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometry for measurement of displacements without ambiguity,” IEEE J.
Quantum Electron., vol. 31, pp. 113–119, Jan. 1995.
[6] S. Donati, L. Falzoni, and S. Merlo, “A pc-interfaced, compact laser
diode feedback interferometer for displacement measurements,” IEEE
Trans Instrum. Meas., vol. 45, pp. 942–947, Oct. 1996.
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[7] S. Merlo and S. Donati, “Reconstruction of displacement waveform with
a single-channel laser-diode feedback interferometer,” IEEE J. Quantum
Electron., vol. 33, pp. 527–531, Apr. 1997.
[8] N. Servagent, F. Gouaux, and T. Bosch, “Measurement of displacement
using the self-mixing interference in a laser diode,” J. Opt., vol. 29, pp.
168–173, 1998.
M. Norgia (M’99) was born in Omegna, Italy, in 1972. He received the degree
(with honors) in electronics engineering, with a thesis on noise in optical amplifiers, and the Ph.D. degree in electronics engineering and computer science
from the University of Pavia, Pavia, Italy
He is a Post-Doctorate Researcher at the University of Pavia. In 1997, he spent
five months as Visiting Student at C.S.E.L.T., Torino, Italy, where he worked
on fiber Bragg gratings. His main research interests are noise in optical amplifiers, interferometry, microelectromechanical sensors, and chaos in semiconductor lasers. He is the author of about 20 papers.
S. Donati (M’75–SM’98–F’02) received the degree in physics (with honors)
from the University of Milano, Milano, Italy.
He has been a Full Professor of optoelectronics at the University of Pavia,
Pavia, Italy, since 1980, where he also leads the Optoelectronics Group of 12
people (of which four are staff). He started research at CISE, Milano, on photodetectors and on laser instrumentation. In 1975, he joined the University of
Pavia as a full-time Lecturer, teaching courses in electronics circuits, electronic
materials and technologies, and electrooptic systems. He has conducted research
in electronics (noise in CCD and coupled oscillators), electrooptics (laser interferometry, fiber gyros, and fiberoptics current sensors), and, more recently,
all-fiber components for communications (couplers, isolators, polarization components) and optoelectronic interconnect-ions. He has cooperated in several
R&D programs with national companies active in the areas of communications, instrumentation and avionics. He has authored one book, Photodetectors,
(Englewood Cliffs, NJ: Prentice-Hall, 2000), about 200 papers, and holds 10
patents. From 1986 to 1992, he was the Director of the Italian scientific review in electronics “Alta Frequenza- Rivista di Elettronica” of AEI. He was the
Chairman of the Italian Optoelectronics Society from 1992 to 1996. He started
the Fiber Optics Passive Components (WFOPC) International Conference in
1998, as its Chairman. He chaired the international meeting ODIMAP II in 1999
and ODIMAP III in 2001. He was also the Guest Editor for the Special Issue
on Interferometry of the Journal of Optics (June 1998) and the Special Issue on
Optical Distance Measurements of Optical Engineering (January 2001).
Dr. Donati is a member of AEI, APS, OSA, and IMAPS, and has organized
several national and international meetings and schools. In 1997, he founded
and is presently the Chairman of IEEE-LEOS Italian Chapter. He was also
the Guest Editor of a Special Issue on Fiber Optics Passive Components
(September/October 1999) of the IEEE JOURNAL OF SELECTED TOPICS IN
QUANTUM ELECTRONICS.