IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 44, NO. 11, NOVEMBER 2008
1089
Secure Chaotic Transmission on a
Free-Space Optics Data Link
Valerio Annovazzi-Lodi, Senior Member, IEEE, Giuseppe Aromataris, Mauro Benedetti, Member, IEEE, and
Sabina Merlo, Senior Member, IEEE
Abstract—In this paper, we numerically demonstrate secure
data transmission, using synchronized “twin” semiconductor
lasers working in the chaotic regime, which represent the transmitter and receiver of a cryptographic scheme, compatible with
free-space optics technology for line-of-sight communication links.
Chaotic dynamics and synchronization are obtained by current
injection into the laser pair of a common, chaotic driving-signal.
Results of simulations are reported for the configuration in which
the chaotic driving-current is obtained by photodetection of the
emission of a third laser (driver), chaotic by delayed optical feedback in a short cavity scheme, selected with different parameters
with respect to the laser pair. The emissions of the synchronized,
matched lasers are highly correlated, whereas their correlation
with the driver is low. The digital message modulates the pumping
current of the transmitter. Message recovery is performed by
subtracting the chaos, locally generated by the synchronized
receiver laser, from the signal obtained by photodetection (at the
receiver side) of the chaos-masked message transmitted in free
space. Simulations have been performed with the Lang-Kobayashi
model, keeping into account both attenuation of the optical signal
in a line-of-sight configuration, and noise. Security has been
investigated and demonstrated by considering the effect, on synchronization and message recovery, of the parameter mismatch
between transmitter and receiver.
Index Terms—Chaos, cryptography, communication systems.
I. INTRODUCTION
PTICAL chaotic cryptography [1], [2] is a hardware technique for secure transmission, which makes use of a pair
of lasers routed to chaos. A standard DFB telecommunication
laser operating in a chaotic regime, for example by back-reflection from a remote mirror, exhibits a widened spectrum, typically in the order of 10–100 GHz; its emission in the time domain is amplitude modulated, showing a non periodic and very
complex, apparently random, behavior, which, however, can be
described on the basis of a deterministic model.
In the cryptographic schemes, one of the sources is used
for the transmission, i.e., to codify the message with chaos;
O
Manuscript received November 12, 2007; revised April 04, 2008. This work
was supported in part by the Italian Ministry of University and Research (MUR),
under a PRIN-COFIN 2005 contract, and in part by EU Project PICASSO IST2005-34551.
V. Annovazzi-Lodi and G. Aromataris are with the Dipartimento di Elettronica, Università degli Studi di Pavia, 27100 Pavia, Italy (e-mail: valerio.
[email protected]; [email protected]).
M. Benedetti and S. Merlo are with the Dipartimento di Elettronica, Università degli Studi di Pavia, 27100 Pavia, Italy (e-mail: [email protected];
[email protected]).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/JQE.2008.2001929
the other one is used at the receiver for message extraction.
In the basic scheme, chaos is simply superposed over the
message to strongly reduce its signal-to-noise (S/N) ratio, thus
implementing the so-called chaos masking [3]. Extraction of
the hidden message from chaos is based on the synchronization
of transmitter and receiver, i.e., on the generation of the same
chaotic waveform at both ends of the channel. Synchronization
can be obtained by optical injection of a fraction of the transmitter laser output into the receiver laser, which, under suitable
conditions, replicates the chaotic regime of the transmitter but
does not replicate the message. Message extraction is simply
performed by making the difference between the signal coming
, and the chaotic signal
from the transmitter
replicated at the receiver. However, it is very difficult, for an
eavesdropper, to extract the message, because effective synchronization relies on the use of ‘twin’ lasers, i.e., two lasers
with very similar parameters (typically, the two devices must be
not only of the same model, but also selected in close proximity
from the same wafer).
After initial investigations on basic principles, more recently
work has been focused towards the application of all-optical
chaotic cryptography to real networks. Digital transmission on
a metropolitan network [4] has been performed. Analog transmission of radio and video signals [5], [6] on optical fibers has
been also reported. Several basic functional blocks have been
already studied and experimentally demonstrated, such as the
chaotic signal repeater [7], modules for point—multipoint connections [8], for two channel transmission [9], for wavelength
multiplexing [10] and for wavelength conversion [11].
In addition to fiberoptic networks, transmission links based
on free-space optics (FSO) technology, that exploit a modulated laser beam traveling in open space through the atmosphere,
have been envisaged and designed. Point-to-point connections,
between two locations on the line-of-sight, are commercially
available [12]. Free-space optics links (FSOL) represent an interesting alternative to fiber optics links for small/medium private networks because their installation and maintenance is less
expensive and because they are license free. Point-to-point optical interconnections may also work by diffuse radiation, exploiting reflection and diffusion of the walls and the ceiling of
a room [13]. Another important application of free-space optics technology is represented by optical transmission links between satellites. Information security remains, however, a major
issue in free-space optical networks. The absence of protected
propagation increases the risk of eavesdropping and makes this
kind of systems intrinsically non-secure. The schemes of optical chaotic cryptography already studied for fiber transmission
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IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 44, NO. 11, NOVEMBER 2008
Fig. 1. Optical configuration for secure data transmission with semiconductor lasers as Tx and Rx, which are routed into the chaotic regime and synchronized by
means of current injection of a common, chaotic driving-signal.
can be proposed, in principle, also for this application. However, the different characteristics of the transmitted signal suggest to consider dedicated schemes. More specifically, a major
improvement, in terms of cost and practical feasibility, would be
offered by schemes allowing electrical, instead of optical, signal
amplification.
A possible solution is proposed and analyzed in this paper. In
the scheme illustrated in detail in Section II, optical injection is
replaced by current injection. Two semiconductor lasers (transmitter and receiver) are routed into a synchronized chaotic
regime by means of injection into the pump of a common,
chaotic driving-signal. The reduced bandwidth requirements,
with respect to fiber transmission, make this approach attractive, since low-cost Monolithic Microwave Integrated Circuits
(MMIC) can be used for signal amplification. In Section II,
we also briefly compare our system with other optoelectronic
schemes already present in the literature.
In Section III, we report the equations which describe the
operation of the selected scheme, based on the Lang-Kobayashi
model. Langevin and photodetection noise terms as well as
transmission losses are considered. Results of the numerical
simulations for a baseband digital transmission at 1 Gb/s are reported in Section IV, whereas the results relative to a 100 Mb/s
signal transmitted on a 4.65 GHz carrier are illustrated in
Section V.
II. FREE-SPACE OPTICS CONFIGURATION
The selected configuration for secure chaotic transmission on
a free-space optics data link is illustrated in Fig. 1. As in previously investigated schemes for optical chaos cryptography, we
assume to use a pair of “twin” semiconductor lasers, which are
subject to optical feedback from external reflectors. These lasers
represent the transmitter (Tx) and receiver (Rx) of the communication link.
As shown in Fig. 1, a common, chaotic driving-signal is
superposed to the pumping currents of the laser pair. We
performed numerical simulations for the case in which this
common, chaotic driving-current is obtained by photodetecting
the intensity emission of a third laser (driver, Drv in Fig. 1),
chaotic by delayed optical feedback, selected with different parameters with respect to the matched laser pair. Under suitable
conditions, this common chaotic input forces the Tx and Rx
lasers to generate highly correlated chaotic waveforms (i.e., to
synchronize to each other); their output waveforms are however
different from that generated by the Drv.
The message to be transmitted modulates the pumping
current of the transmitter as in standard Chaos Shift Keying
(CSK) [1]–[3] for secure data transmission. Message recovery
can be attained by subtracting the chaos locally generated
by the synchronized receiver, detected by photodiode PD4,
from the chaos-masked message (message + masking chaos
from the Tx) detected by photodiode PD3 after propagation
in free space. Two more photodiodes, PD1 and PD2 are used
for current conversion of the optical chaotic signal, generated
by the driver laser. In principle, they would not be required if
the common chaotic driving were electrically generated and
distributed by a RF link. Security of this cryptographic configuration is supported by specific requirements on Rx/Tx matching
for ensuring good synchronization, as it will be shown in the
following.
Synchronization of semiconductor lasers induced by means
of a common chaotic signal was recently demonstrated numerically and experimentally in [14], for the distribution of secret
communication keys: in this set-up, optical injection from the
chaotic driver laser, into the two response lasers, was required
for inducing the chaotic regime in these (otherwise unperturbed)
lasers and for pursuing synchronization.
Electro-optical injection in chaos cryptography was proposed
by other authors for data transmission along a fiberoptic link. In
[15], Larger et al. generated chaos by exploiting the nonlinearity
of a Mach-Zehnder device in an optoelectronic feedback loop.
Chaotic communications using semiconductor lasers with op-
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ANNOVAZZI-LODI et al.: SECURE CHAOTIC TRANSMISSION ON A FREE-SPACE OPTICS DATA LINK
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TABLE I
PARAMETERS
toelectronic delayed feedback and optoelectronic injection between transmitter and receiver were reported in [16]–[18]. The
chaotic carrier was generated by a semiconductor laser with optoelectronic feedback, and chaotic communication was realized
by synchronizing the receiver laser with the transmitter laser by
means of electrical injection between these two lasers. In these
schemes, feedback/coupling delay times and strengths were required to be carefully adjusted and controlled.
On the other hand, the transmission scheme that we present
in this paper is a modification of the standard all-optical scheme
[1]–[3]. This variant is intended for free space links, where, due
to reduced bandwidth requirements, propagation losses can be
conveniently compensated for by using low-cost electrical RF
amplifiers. Differently from [15]–[18], optoelectronic feedback
is not used in the transmitter or in the receiver. In our architecture, a third laser is required for common chaotic driving, but
no optoelectronic feedback loop needs to be adjusted. Optoelectronic coupling exists between driver and transmitter, and between driver and receiver: in principle, this solution would also
allow for secure multi-point transmission using a single driver.
(3)
(4)
In these equations,
is the slowly varying, complex electric field (normalized, in [m
]) of the driver laser,
is the
the carrier density,
the constant
feedback parameter,
pumping current, the electron charge, the Planck’s constant,
the vacuum impedance with vacuum permittivity and speed of light in vacuum. Definitions and values of
the other parameters are reported in Table I. Equation (4) indi(in [V/m])
cates how to obtain the true electric field
, for future comparisons with
from the normalized field
experimental data.
is the spontaneous emission term,
and
are the Langevin noise terms [20], given by
III. NUMERICAL MODELING
The well known Lang-Kobayashi model [19] for a singlemode semiconductor laser subject to delayed optical feedback
can be easily modified to describe the configuration of Fig. 1.
First of all, we can write the following set of equations for the
driver laser
where
are zero-mean, unit-variance Gaussian distributions and
is the time resolution in the modeling of white
noise.
A set of equations can be written for the transmitter laser
(1)
(2)
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(5)
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IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 44, NO. 11, NOVEMBER 2008
(6)
(7)
(8)
and another set for the receiver laser
(9)
Fig. 2. Numerical RF chaotic power spectra (2.5 MHz resolution bandwidth) of
the driver laser, of the transmitter laser (red trace online) and of the receiver laser
dB)
(blue trace online). For better visualization, we have shifted upwards (
the traces relative to driver and receiver. The difference signal (green trace online) is also reported.
+20
(10)
(11)
(12)
and
are the slowly varying,
In these equations,
]) of transcomplex electric fields (normalized, in [m
is the feedback
mitter and receiver lasers, respectively,
parameter,
and
are the carrier densities,
and
the spontaneous emission terms and
the Langevin noise terms,
having the same form as for the Driver. The other parameters
are specified in Table I.
Whereas the pumping current for the driver laser is constant,
and
the pumping currents of transmitter and receiver,
in (8) and (12), contain also time-varying terms. In
particular, they include the terms
and
which are, respectively, the signals obtained after amplification and filtering
and
from photodiodes
of the output currents
PD1 and PD2 (see Fig. 1), given by
(13)
(14)
These terms contain the common, chaotic driving-signal,
. The dc component of the photodetected currents has
been subtracted, since we assume that the dc working condition
of Tx e Rx lasers is set by their dc pumping currents ( and
). In (13) and (14), and take account of the propagation
losses between driver and transmitter/receiver,
indicates
indicates
the time of flight between driver and transmitter,
the time of flight between driver and receiver. For simplicity,
. The symbol means absolute
we have taken
value, or module of the complex field, and
means the time
and
keep into account the Johnson
average.
noise current of the 50 termination resistance and the shot
noise current due to direct detection. The transmitter current,
due to the
given by (8), contains also the component
message. In the next Section, we report the numerical results
obtained with this model for an example of baseband digital
transmission.
IV. BASEBAND TRANSMISSION
A. Synchronization
The parameters of the laser and of the external cavities were
initially taken identical for both Tx and Rx, whereas some parameters were different for the driver, as reported in Table I. First
of all, we tested the synchronization of transmitter and receiver,
without message transmission. We assumed
mA,
mA. At this current, the
driver laser is chaotic by optical feedback. Fig. 2 illustrates the
RF chaotic power spectrum obtained by photodetection, ampliGHz for all detected
fication, and low-pass filtering (
currents) of the driver laser output at the Tx site after propagation. A similar spectrum would be obtained from PD2 at the Rx
site. We considered attenuation due to free-space transmission
: since losses
for the chaotic driving by taking
were compensated by electrical amplification, the only effect of
attenuation is a reduction of the S/N ratio. Fig. 2 contains also
the RF chaotic power spectra obtained, by photodetecting, respectively, the transmitter laser output after propagation and the
receiver output, both at the Rx site. These lasers are routed into
the chaotic regime and synchronized by current injection of the
common chaotic signal. In this graph, for a better visualization,
the traces relative to the receiver and to the driver were shifted
upwards by 20 dB: transmitter and receiver spectra would be
otherwise superposed, since Tx and Rx were synchronized by
current injection. A factor 10 attenuation suffered in transmission between Tx and Rx was completely compensated for by
amplification. On the other hand, no losses were considered at
the Rx site for the receiver output detected by PD4. The trace
relative to the difference signal between the transmitter and the
receiver is also reported showing a chaos cancellation of approximately 15 dB on the bandwidth of interest. As already specified
for photodiodes PD1 and PD2, in the calculations we took into
account the Johnson noise of the 50- termination resistance
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ANNOVAZZI-LODI et al.: SECURE CHAOTIC TRANSMISSION ON A FREE-SPACE OPTICS DATA LINK
Fig. 3. Simulations of chaotic waveforms I (t); I (t); I (t) (see also Fig. 1)
as a function of time.
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Fig. 5. Simulated current waveforms for a baseband link: (a) original message
I (t); (b) system output with Drv OFF; (c) attenuated, photodetected and amplified transmitter output I (t) with the message masked by chaos (red online);
(d) extracted message I (t) after subtraction at the receiver side in the case of
perfect Tx/Rx matching (green online); (e) unsuccessful message extraction in
case of photon lifetime mismatch 1 = 5% (blue online); (f) unsuccessful
message extraction in case of feedback parameter mismatch 1K = 4% (magenta online).
verified that it is impossible for the eavesdropper to extract the
message by subtracting the Drv output from the Tx output. The
since we neglected any time delay.
maxima occur at
B. Message Recovery
Fig. 4. Cross-correlation as a function of time delay. (a) Tx and Rx. (b) Driver
and Tx. Same results as in (b) are obtained for driver and Rx. Insets: crosscorrelation plots.
To investigate the possibility of using this configuration for
secure data transmission, we numerically studied message recovery at the system output. A pseudo-random NRZ digital mes, with a
sage at 1 Gb/s was used as modulating current
peak-to-peak value of 30 A.
In Fig. 5, we present numerical results relative to temporal
waveforms for comparison among different signals. Trace a
with the original message,
is the modulating current
whereas trace b is the system output without chaotic encryption
(Drv OFF), which describes the channel with all the noise
when the messources. Trace c is the current output
sage is completely hidden by chaos: this would be the signal
tapped by the eavesdropper. Trace d is the extracted message
after subtraction at the receiver, in the case of optimized
synchronization between Tx and Rx (with perfectly matched
parameters, and equal cavity lengths).
C. Effect of the Laser Parameters
and the shot noise for both photodiodes PD3 and PD4. In Fig. 3,
we show typical chaotic waveforms as functions of time of the
relative to Drv,
relative to Tx,
photodetected currents
relative to Rx, in the same conditions as specified for
and
Fig. 2.
In Fig. 4, we show the plot of the cross-correlation function
between the various detected outputs: a peak higher than 98%
is obtained between transmitter and receiver, in agreement with
the results shown in [14], whereas lower correlation is observed
between driver and transmitter or between driver and receiver.
Cross-correlation plots are also reported in the insets, which
clearly show that Tx and Rx were successfully synchronized,
but they were not synchronized to the driver laser, which supports the security of this scheme. Indeed, it has been numerically
The quality of the extracted message, even in presence of attenuations and photodetection noise, is quite good in matched
conditions. However, it is important to investigate the effect on
message extraction of parameter mismatch between Tx and Rx.
We found that the scheme is sensitive to mismatch of most internal and external parameters, as well as to the external cavity
length difference. Typically, a parameter difference of a few percent between transmitter and receiver prevents the message from
being extracted with an acceptable S/N ratio. For example, the
% (trace e)
effects of a mismatch of photon lifetime
and of the feedback parameter
% (trace f) are shown in
Fig. 5. For both cases of parameter mismatch, the original message cannot be recognized in the extracted signal. The security
of the proposed scheme is thus comparable to that of standard
chaotic cryptosystems for fiber transmission.
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Fig. 6. Numerical RF spectra (1.5 MHz resolution bandwidth) for AM transmission of a message at 100 Mb/s on a 4.65 GHz carrier: (a) original message;
(b) transmitted signal, in which the message is hidden by chaos (red online);
(c) recovered message in the case of perfect parameter matching (green online).
Traces a and b were moved upwards by 20 and 60 dB, respectively, for better
readability.
Fig. 7. Simulation in the time domain of AM transmission of a 100 Mb/s message on a 4.65 GHz carrier: (a) original modulating message; (b) demodulated
message without chaos (Drv OFF); (c) demodulated output with message hidden
by chaos (red online); (d) recovered demodulated message in the case of perfect
matching (green online).
around a carrier can be also proposed for a free-space optics
link, which significantly widens the applicability range of our
cryptographic scheme.
V. CARRIER TRANSMISSION
In addition to base-band transmission, the use of a RF carrier
modulated by the message can be considered. Besides allowing
the use of different channels over the same optical wavelength,
this approach provides a method to optimize performances by
positioning the message at the frequency where chaos is larger,
or where synchronization is better. In fact, the use of a carrier
or Manchester coding has been already proposed [21], [22] for
optical chaotic transmission in fiber.
Carrier transmission has been studied numerically by assuming the same parameter set as in Section IV, except for
mA and
. The carrier amplitude,
superimposed to the pump current, was 50 A, and its frequency
was 4.65 GHz. The message was a pseudo-random NRZ digital
signal at 100 Mb/s modulating the carrier in amplitude (AM)
with 100% modulation depth. We tested the system for different
channel attenuations, finding an acceptable S/N ratio of the
recovered message down to
. In Figs. 6 and 7,
typical system performances are shown for
and for attenuation between Tx and Rx of a factor 50. In the simulations, all photodiodes were followed by a band-pass filtering
stage with a 400 MHz bandwidth around the carrier frequency.
In Fig. 6 the RF spectrum of the original message (trace a)
is compared to the spectrum of the extracted message (trace c)
showing only a low distortion of the modulation side-bands. Instead, in the transmitted message (trace b) only the carrier is partially visible, while the side-bands, containing the information,
are hidden by chaos to the eavesdropper. For better readability,
traces a and b in Fig. 6 were shifted upwards by 20 and 60 dB,
respectively.
In Fig. 7, signals are shown in the time domain: trace a is the
original message; trace b is the demodulated message without
chaotic encryption (Drv OFF). Trace c is the demodulated
output when the message is hidden by chaos (eavesdropper
site). Trace d is the extracted message demodulated after subtraction at the receiver, in the case of optimized synchronization.
From these simulations, we can conclude that transmission
VI. CONCLUSION
In this paper, we have analyzed a new scheme for chaotic
cryptography of an optical signal transmitted in a free-space optics link. We have numerically demonstrated both effective message masking and message recovery in a point-to-point connection on the line-of-sight, both in baseband and with a carrier.
The effect of parameter mismatch has been also considered, for
security evaluation.
Further work is required to extend our scheme to operation in
the diffused regime, where the effects of attenuation and dispersion represent a strong limitation [13] even with standard links.
For what concerns attenuation, this is expected to be 1–2 orders
of magnitudes higher than operating with a collimated beam. To
compensate such losses, a strong electrical amplification is required, and the resulting degradation of S/N ratio must be taken
into account. However, the major limitation would probably
come from dispersion due to the presence of multiple paths, with
a corresponding distribution of flight time, resulting in a distortion of the step response and a reduction of the bandwidth. In
the case of chaotic cryptography, these limitations may worsen
the quality of synchronization between transmitter and receiver,
because they modify the injection process on which this synchronization is based.
Future activity will include the evaluation of the impact of
such phenomena on the performances of a diffused transmission
link.
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Valerio Annovazzi-Lodi (M’89–SM’99) was born
in Novara, Italy, on November 7, 1955. He received
the degree in electronic engineering from the University of Pavia, Pavia, Italy, in 1979.
Since then he has been working at the Department
of Electronics of the University of Pavia in the fields
of electronics and electro-optics. His main research
interests include injection phenomena and chaos in
oscillators and lasers, cryptography, optical sensors,
passive fiber components for telecommunications
and sensing, optical amplifiers, transmission via
diffused infrared radiation, micromechanical systems. In 1983, he became a
Staff Researcher of the Department of Electronics of the University of Pavia,
in 1992 an Associate Professor and in 2001 a Full Professor of the same
institution. He is the author of more than 100 papers and holds four patents.
Dr. Annovazzi-Lodi is a member of AEIT and a Senior Member of IEEELEOS.
Giuseppe Aromataris was born in Siderno, Italy,
in 1976. He received the degree in physics in 2006
from the University of Milan, Italy, with a thesis
on covariant quantum measurement of phase on coherent and squeezed states. He is currently working
toward the Ph.D. degree in electronics engineering
with the Optoelectronics Group of the University of
Pavia, Italy.
His research interests include non-linear dynamics
on optically injected semiconductor lasers, with
regard in particular to numerical analysis on optical
chaos synchronization and cryptographic communications systems.
Mauro Benedetti (M’05) was born in Pontevico,
Italy, in 1975. He received the degree in micro-electronics engineering in 2002 and the Ph.D. degree in
electronics engineering in 2006 from the University
of Pavia, Pavia, Italy.
He is currently working as a post-doctoral researcher with the Optoelectronics Group of the
University of Pavia. His main research interests
include nonlinear dynamics in optically injected
semiconductor lasers, with regard in particular to
optical chaos synchronization and cryptography in
fiber-optic communications, characterization of MEMS/MOEMS devices and
Photonic Crystals.
Dr. Benedetti is a member of the IEEE-LEOS and of the SICC (Italian Society
for Chaos and Complexity).
Sabina Merlo (M’2001–SM’2005) was born in
Pavia, Italy, in 1962. She received the degree in
electronic engineering from the University of Pavia,
Pavia, Italy, in 1987, the M.S.E. degree in bioengineering from the University of Washington, Seattle,
and the Ph.D. degree in electronic engineering from
the University of Pavia, Pavia, Italy, in 1991.
In 1993 she became Assistant Professor and
in 2001 she became Associate Professor with the
Department of Electronics of the University of
Pavia. Her main research interests include MEMS,
MOEMS, chaos in lasers, laser interferometry, fiber-optic passive components
and sensors. She holds three patents and is the author of more then 60 papers.
Dr. Merlo She was the recipient of a Rotary Foundation Graduate Scholarship
for studying at the University of Washington, Seattle. he is an Associate Editor of
the IEEE/ASME Journal of Microelectromechanical Systems. She is a member
of AEIT, and Senior Member of IEEE-LEOS.
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