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Integration of a new position sensor based on four quadrant fiber optic bundle to measure the cantilever deflections in atomic force microscopy head

Younes Boukellal1, a
and Sebastien Ducourtieux1
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use,
distribution, and reproduction in any medium, provided the original work is properly cited.
DOI: 10.1051/
Owned by the authors, published by EDP Sciences, 2015
metrolo /
17 International Congress of Metrology, 1 0 0 (20 5 )
th 1
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Integration of a new position sensor based on four quadrant
fiber optic bundle to measure the cantilever deflections in
atomic force microscopy head
1 French National Metrology Institute / Laboratoire National de Métrologie et d’Essais (LNE)-29 avenue Roger Hennequin Trappes/ France
Résumé. Cet article présente l’implémentation d’une tête pour microscope à Force Atomique intégrant un capteur original en
remplacement à une photodiode quatre quadrants dans la méthode du levier optique. Ce capteur est composé d’un bundle de fibres à quatre
quadrants permettant de mesurer la déflexion du levier tout en s’affranchissant des sources de chaleurs liées à l’électronique de
conditionnement de la méthode de mesure. Le bundle est constitué de 40 000 microfibres avec un arrangement customisé permettant
d’obtenir une surface à quatre quadrants identiques en entrée. Avant le développement du premier prototype, le bundle de fibres a été
modélisé et évalué expérimentalement par comparaison à une photodiode quatre quadrants [1]. A partir des données de modélisation et des
données expérimentales, la réponse des deux capteurs est similaire. Comme le capteur a été développé pour son utilisation en AFM, il a été
intégré dans une tête AFM et a été testé en conditions réelles d’utilisations dans le but de générer les premières images AFM. Des courbes
d’approches en mode tapping et contact ont également été obtenues afin d’évaluer la linéarité et la sensibilité du bundle de fibres aux
déflexions du levier.
Fiber optic, Fiber optic bundle, atomic force microscopy, optical beam deflection method, displacement sensor, tapping mode, contact mode.
Atomic force microscope (AFM) was introduced by
Binnig, Quate, and Gerber as a method for high resolution
topographic imaging of both insulators and conductors. In
AFM, the sample to be imaged is brought close to a
sensing tip attached to a small cantilever. Interaction
forces between sample and tip deflect the cantilever.
Cantilever deflections can be measured using various
techniques: optical beam deflection, interferometry self-
sensing methods. For quantitative imaging, it is necessary
to understand the system used for detection of cantilever
deflection and torsion. In most AFMs the sensing system
for cantilever motion is used as a null detector.
Consequently the quality of the measurement and its
accuracy depends critically on the detection system. The
most widespread method is the optical beam 
       onto
the centre of a quadrant photodiode (QPD). The
operation of such a position sensing detector is quite
simple. A laser beam with Gaussian spot falls on the
centre of the detector. By combining the signal detected
by A, B, C and D quadrants, the displacement of the laser
spot relative to the centre of the quadrant detector can be
approximated by using the following formula :
Also, the related intensity variation is normalized by the
sum intensity of the four quadrants given by A+B+C+D.
to take into account any possible fluctuation of the laser
beam intensity. However for low noise applications, it is
necessary to integrate the photodiode very close from its
conditioning electronic circuit or even directly on the
circuit. This implies several heat sources induced by the
conditioning circuit itself which could disturb the
deflection measurement or even the overall behaviour of
the instrument (thermal dilatation, thermal drift…).This is
specifically the case in the field of dimensional
nanometrology in which instruments are supposed to
work at 20°C and where any heat sources can critically
affect the thermal and dimensional stability of the
instrument by creating local thermal gradient. To counter
this, the QPD and its conditioning electronic circuit
placed inside the instrument has been replaced by a
thermically passive sensor. The aim of our approach was
to externalize the heating system from the instrument
itself by using optical fibers and by mimicking the
functioning principle of the QPD used for position
sensing applications. After several investigations, this led
to the development of a first prototype based on quadrant
structured fiber optic bundle shown on figure 1.
Article available at or
Figure 1. On the left picture, the fiber optic bundle with one
common input structured in four quadrants and four outputs.
The ferrule serves as a holder. On the right picture, the light of
four power LEDs of different colours is injected from the
outputs solely to distinguish the quadrants geometry on the
The optic fiber bundle has an active surface area of 10
mm diameter that comprises 40.000 borosilicate’s fibers
of 50  core diameter spread over the four quadrants.
The gap between quadrants is fixed to 50 μm and is
similar to quad cell photodiode. Deflection and torsion
signals are then processed using a homemade electronic
conditioning circuit. Before the integration of the bundle
on the AFM, it has been modelled and experimentally
evaluated. Results showed that the fiber optic bundle
response is very similar to the one of quad cell
photodiode. This results have been subject to an article
Integration and test of the bundle on an AFM head
In order to test the fiber bundle in real conditions, we
integrated it temporarily in an AFM developed at LNE. It
has a very simple architecture in which it was relatively
easy to replace the four-quadrant photodiode and its
electronic conditioning circuits by the optic fiber bundle
and its conditioning circuit. We also replaced the laser
diode by a fibered superluminescente diode (SLD). In this
way, the main heat sources in the AFM head has been
Figure 4: modified AFM head using optical lever method
(OBD) to detect the deflection of cantilever. The OBD is based
on the use of fiber optic bundle (4) and fibered
superluminescente diode (1). The focused laser spot delivered
by a fibered superluminescente diode is reflected on the
backside of cantilever (5) and the reflected beam is directed
onto the surface of quadrant fiber bundle (4) to sense the power
variation. A piezo actuator (2) is used for cantilever modulation
(tapping mode). Two manual translation stages (3) are used to
set the position of the laser spot on the bundlesurface.
This setup was used to test the ability of the bundle to
correctly detect deflections of the cantilever either in
contact mode or tapping mode. For this test, a tip from
NCHR NanoWorld has been used. The cantilever is
rectangular, measuring 125 micrometers long (lc) and has
a stiffness of 42 N/m. the reflected laser beam length lcp is
80 mm. With these parameters, it is possible to trace back
the movement of the laser spot on the bundle using the
following equation
Equation 2:
a is the laser spot displacement on the bundle surface.
Considering a deflection ȴnj about 50 nm, the laser spot
displacement ȴĂ on the bundle is evaluated to 96 μm. For a
similar displacement, it has been shown in [1] that the bundle
response is linear. The first test was performed in order to
validate the approach curves either in tapping mode or in
contact mode on Silica wafer. This allowed the evaluation of
the sensitivity of the deflection measurement system based on
the whole SLD + tip/cantilever + optic fiber bundle + electronic
conditioning circuit.
Figure 5. Contact mode approach curve. The conversion of the
normalized deflection from the arbitrary unit to nm unit is done
considering the linear slope in the repulsive regime equal to 1
and the substrate hard enough and does notdeform.
By analysing the figure 4, one can see that the
measurement system can detect a small deflection below
1 nm. The noise level of the deflection measurement on
the approach curve before contact (region between -60
and -10 nm) reaches 0.1 nm. From this data and using
Equation 2, the noise level of the laser spot fluctuation on
the surface of the bundle has been estimated to 192 nm.
Using the Hooke’s law (f = kz) and stiffness of the
cantilever k (42 N/m), we reach a noise level for
measuring force f of 4.2 nN. We reproduced this test in
Tapping mode by oscillating the tip at near its resonant
frequency (310 kHz). The tapping curve curve approach
is shown in the following figure.
Web of Conferences
Figure 6. Tapping mode approach curveFor tapping mode, the
oscillation amplitude of the tip has not been fully damped with
the sample surface to avoid damaging it. The system response
has been calibrated in the same way as for the contact mode.
The tip oscillation achieved 21 manometers and the noise level
is less than 0.01 nm, which is ten times less than in contact
mode. This noise reduction results from the use of lock-in
amplifier to demodulate the signal.
Finally, a topography images has been performed on two
different samples and using Tapping mode. This allowed
the validation of the integrated deflection measurement
Figure 7. On the left, a 2.5 μm x 2.5 μm image of 2d calibration
specimen composed of cellulose acetate with periodicity of
2160 lines/mm, 0.463 micrometers pitch and 31 nm of step
height .On the right, topography image of SiO2 nanoparticles
with an average diameter of 50 nm. The images have been
processed using Mountains Map software. These images show
that the deflection measurement system based on the use of fiber
optic bundle instead of four quadrant photodiodes works
perfectly and is capable of delivering a very good qualityimage
[1]Y. Boukellal and S. Ducourtieux H 2015 Meas. Sci. Technol.
26. 1 doi:10.1088/0957-0233/26 /1/015201
17 International Congress of Metrology
... At a minimum separation, the probing ball suddenly jumps to impinge the surface of the RUT. The AC registers a substantial (Boukellal and Sebastien, 2015). The surface forces cause the snapin (Bos, 2008 andPark et al., 2006). ...
... It is not possible to mathematically concatenate the displacement with the extrapolated point of contact because there is a discontinuity (Brach andDunn, 1992 andLi et al., 2016). Researchers extrapolated the deflection data by discounting the discontinuities that have compromised the accuracy (Boukellal and Sebastien, 2015). Figure 5 shows the cross section of the workpiece, along with the PS and carriage. ...
The inaccurate deflection behavior of the probing system degrades the performance of the diameter-measuring machines. In this experiment, the probing is improved, applying an autocollimator and an angular positioning datum. We have devised this datum using a liquid wedge. A ring gauge is chosen as a workpiece to evaluate the deflection behavior of the probing system. The improved uncertainty of the probing is found as low as 40 nm. Subsequently, the inner diameter of the ring gauge is measured on this experimental setup. By employing a simulation, we aligned the workpiece. The deflections of the stylus are optimized to achieve zero deflection error at the zenith points. Consequently, the swing of the probe at the zenith points is combined with the rectilinear displacement of the workpiece to estimate the inner diameter. The uncertainty of the measurement of the ring gauge is improved up to 140 nm.
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