design and characterization of integrated optical devices ... · of diabetic and anaemic patients,...
TRANSCRIPT
UNIVERSITA’ DEGLI STUDI DI PAVIA FACOLTA’ DI INGEGNERIA
Dottorato di Ricerca in Ingegneria Elettronica,
Informatica ed Elettrica
XXIII Ciclo
Design and Characterization of Integrated Optical Devices
for Biophotonics
Tesi di Dottorato di Lorenzo Ferrara
Anno 2010
Contents
INTRODUCTION ................................................................................................................................................. 4
CHAPTER 1 – INTRODUCTION ON SINGLE CELL MANIPULATION THROUGH OPTICAL FORCES ........................ 6
1.1 ORIGIN OF OPTICAL FORCES .................................................................................................................... 6
1.1.1 RAYLEIGH REGIME (a << λ/20) .......................................................................................................... 7
1.1.2 LARGE PARTICLES REGIME (a >> λ) ................................................................................................... 8
1.2 OPTICAL TRAP ........................................................................................................................................ 11
1.2.1 SINGLE-BEAM OPTICAL TRAP ......................................................................................................... 12
1.2.2 DUAL-BEAM OPTICAL TRAP ............................................................................................................ 14
CHAPTER 2 – OPTICAL TWEEZERS ................................................................................................................... 17
2.1 OPTICAL TWEEZERS IN LITERATURE ...................................................................................................... 17
2.1.1 STANDARD OPTICAL TWEEZERS ..................................................................................................... 17
2.1.2 FIBER OPTIC TWEEZERS .................................................................................................................. 20
2.2 TOTAL INTERNAL REFLECTION FIBER OPTICAL TWEEZERS .................................................................... 22
2.2.1 WORKING PRINCIPLE ...................................................................................................................... 22
2.2.2 NUMERICAL ANALYSIS .................................................................................................................... 25
2.2.3 NUMERICAL RESULTS: TRAPPING FORCES ..................................................................................... 27
2.2.4 NUMERICAL RESULTS: ESCAPE ENERGY ......................................................................................... 29
2.3 FABRICATION OF A TOTAL INTERNAL REFLECTION OPTICAL FIBER TWEEZERS .................................... 33
2.3.1 FABRICATION OF THE FOUR-FIBER BUNDLE ................................................................................... 33
2.3.2 FABRICATION BY FOCUSED ION BEAM ........................................................................................... 34
2.3.3 FABRICATION BY TWO PHOTON LITOGRAPHY ............................................................................... 39
2.4 EXPERIMENTAL RESULTS ....................................................................................................................... 41
2.4.1 FIB-FABRICATED TOFT: EXPERIMENTAL RESULTS........................................................................... 41
2.4.2 TWO-PHOTON LITHOGRAPHY FABRICATED TOFT: EXPERIMENTAL RESULTS ................................ 44
CHAPTER 3 –DISCRETE ELEMENTS OPTICAL STRETCHER ................................................................................ 50
3.1 INTRODUCTION ..................................................................................................................................... 50
3.1.1 CELL MECHANICAL PROPERTIES ..................................................................................................... 50
3.1.2 EXPERIMENTAL TECHNIQUES FOR PROBING CELL MECHANICAL PROPERTIES .............................. 53
3.2 EXPERIMENTAL SETUP ........................................................................................................................... 59
3.2.1 OPTICAL PART ................................................................................................................................. 59
3.2.2 FLUIDIC PART .................................................................................................................................. 61
3.3. EXPERIMENTAL RESULTS ...................................................................................................................... 66
3.3.1 RESULTS ANALYSIS .......................................................................................................................... 66
3.3.2 EXPERIMENTAL RESULTS ON RED BLOOD CELLS ............................................................................ 71
3.3.3 EXPERIMENTAL RESULTS ON CANCER CELLS .................................................................................. 75
CHAPTER 4 – INTEGRATED OPTICAL STRETCHER ............................................................................................ 79
4.1 STRUCTURE OF AN INTEGRATED OPTICAL STRETCHER ......................................................................... 79
4.1.1 DESIGN ............................................................................................................................................ 79
4.1.2 SIMULATIONS ................................................................................................................................. 81
4.1.3 FABRICATION .................................................................................................................................. 84
4.2 EXPERIMENTS ........................................................................................................................................ 90
4.2.1 EXPERIMENTAL RESULTS WITH A ROUND-SECTION MICROCHANNEL ........................................... 92
4.2.1 FABRICATION OF A SQUARE-SECTION MICROCHANNEL AND EXPERIMENTAL RESULTS ............... 94
CONCLUSIONS ................................................................................................................................................. 99
APPENDIX A – MATLAB PROGRAMS .............................................................................................................. 101
BIBLIOGRAPHY ............................................................................................................................................... 107
INTRODUCTION
In molecular and cellular biology an impelling demand has arisen for the development of tools
able to select, isolate and monitor single cells or cell clusters. Experiments on single cells have the
potential to uncover information that would not be possible to obtain with traditional biological
techniques, which only reflect the average behavior of a population of cells. In the averaging
process, information regarding heterogeneity and cellular dynamics, that may give rise to a
nondeterministic behavior at the population level, is lost. Obvious reasons for the existence of this
heterogeneity are different genotypes and variations due to the cell cycle stage or age; even in a
monoclonal population, with the same history and in the same environment, different phenotypes
can exist due to the Stochastic nature of gene expression. Thus it is necessary to perform
experiments on a single cell level, in order to determine how the cells really react and thus get a
complete picture of how cells function.
The exploitation of optical forces represents an accurate, non-invasive and gentle manipulation
technique for individual cell studies. Nowadays there are two biophotonic tools that can provide
complementary information on cell properties: the optical tweezers (OT) and the optical stretcher
(OS). OT allow easy trapping and manipulation of individual cells using a laser beam heavily
focused and, combined with fluorescence analysis, represents a flexible tool for cell monitoring
and sorting. OS relies on a double-beam trap obtained through two counterpropagating fiber
beams. The radiation pressure exerted by the two beams is perfectly counterbalanced so that the
total force acting on the centre of mass of a trapped cell is zero. However the stress distributed
over the cell surface can cause deformation on the cell. By increasing the laser power, the cell
elongation along the beam axis becomes measurable. It is a powerful device for the investigation
of cell mechanical properties that can open new scenarios for the comprehension of the basic
biological mechanisms and for the early detection of several diseases.
The goal of my thesis work is the fabrication and improvement of such novel devices, supported by
a dedicated numerical model, based on a ray-optics approach, able to provide an accurate
description of the optical forces and to identify the optimal fabrication parameters. The
exploitation of optical tweezers in all-fiber technology for trapping and manipulation of biological
specimens would represent a real break-through in many applications, overcoming most of the
problems related to the bulky structure of standard-tweezers based on an optical microscope; the
development of a fully integrated optical stretcher (FIOS), which is the integration on the same
chip of both microfluidic and optical functions for optical stretching could lead to a simple and
miniaturized optical device suitable for real medical analysis.
My thesis is structured as follows. In Chapter 1 I explain the origin of optical forces and their
interaction with a spherical object in Rayleigh and Large Particle regime. Then I show how to
obtain an optical trap, with a single focused beam or with two counterpropagating beams.
In Chapter 2 the standard optical tweezers and the first developments of fiber optical tweezers are
introduced, describing their structures, advantages and limitations. Then I show the working
principle of the fiber tweezers proposed in our laboratory: the TOFT device (Total internal
reflection optical fiber tweezers). It is the first single-fiber tweezers able to guarantee 3D trapping
with a long working distance based on a new approach that combines two concepts: i) exploitation
of fiber bundles, ii) achievement of tight focusing by total-internal-reflection at the
microstructured fiber end-faces. Two strategies for the end-fiber microstructuration are
investigated: micromachining through focused ion beam and two photon polymerization
lithography. For each fabrication I will report the experiments and results achieved.
Chapter 3 describes the importance of cell mechanical properties in the biological field and the
methods to measure them. I introduce the theory of the optical stretcher and its implementation
with discrete elements. This device has been used in the frame of different collaborations with
biologists and medics; I’ll describe either the results obtained with the analysis of red blood cells
of diabetic and anaemic patients, or the experiments performed on metastatic lymphocytes and
fibroblasts.
Finally, Chapter 4 describes the design and fabrication of the fully integrated optical stretcher,
accomplished by fabricating waveguides and microfluidic channels on the same substrate of fused
silica through a recently developed technique based on femtosecond laser writing. This FLICE
(Femtosecond Laser Irradiation followed by Chemical Etching) technique is very simple and
practical and, combined with chemical etching, guarantees extreme flexibility and 3D capabilities.
A first implementation of FIOS with a round section of the microchannel is tested probing the
viscoelastic properties of red blood cells. A second implementation of FIOS, with a square section
microchannel, is also described, as well as the characterization of the trapping force and the
results in red blood cells stretching.
CHAPTER 1 – INTRODUCTION ON SINGLE CELL MANIPULATION THROUGH OPTICAL
FORCES
This chapter briefly reviews the physical principles at the basis of the mechanism for single cell
manipulation without physical contact. The origin of optical forces will be first described and
secondly different configuration of optical traps exploiting optical forces will be analyzed.
1.1 ORIGIN OF OPTICAL FORCES
Since the beginning of the seventeenth century, the German astronomer Johannes Kepler
proposed that the reason why comet tails point away from the sun is because they are pushed in
that direction by the sun’s radiation. In 1873, James Clerk Maxwell predicted in his theory of
electromagnetism that light itself can exert an optical force, or radiation pressure, when hitting an
object. Anyway this effect was not demonstrated experimentally until the turn of the century since
radiation pressure is extraordinarily feeble; indeed milliwatts of power impinging on an object
produce forces that are only in the order of piconewtons. The advent of lasers in the 1960s finally
enabled researchers to study radiation pressure through the use of intense, collimated sources of
light. The pioneer of such studies was Arthur Ashkin who, with his coworkers, demonstrated that,
by focusing laser light down into narrow beams, small particles, such as few micron-diameter
polystyrene spheres, could be trapped, displaced and even levitated against gravity using the force
of radiation pressure [1]1.
The effect of optical forces on macroscopic objects can be disregarded, since their weight is much
higher than the intensity of optical forces. Anyway these forces become significant on the scale of
macromolecules, organelles, and even whole cells, whose mass is in the order of 10 -12 kg. A force
of ten piconewtons can indeed tow a bacterium through water faster than it can swim, halt a
swimming sperm cell in its track, or arrest the transport of an intracellular vesicle. A force of this
magnitude can also stretch, bend, or otherwise distort single macromolecules, such as DNA and
RNA, or macromolecular assemblies, including cytoskeletal components such as microtubules and
actin filaments.
1 A. Ashkin, “Acceleration and trapping of particles by radiation pressure”, Physical Review Letters, Vol. 24, No. 4, 1970
The origin of the optical forces exerted on a dielectric particle can be ascribed to the momentum
transfer resulting from the refraction and reflection of the incident photons. The interaction
between the electromagnetic radiation and a particle it is based on the radiation scattered by the
particle itself. To better describe this interaction, it’s worth to consider two different scattering
regimes on the basis of the ratio between the particle dimension and the radiation wavelength.
1.1.1 RAYLEIGH REGIME (a << λ/20)
When the particle dimension is smaller than the wavelength, the optical forces can be calculated
following the Rayleigh approximation. Under this condition the particle is treated as an induced
small dipole immersed in an optical field oscillating at frequency ν. The forces acting on this dipole
are of two species: (i) the scattering (or radiative) force originated by momentum changes of the
light caused by scattering, and (ii) the gradient (or dipole) force due to the Lorentz force acting on
the induced dipole. The scattering force is proportional to the laser intensity and its effect is to
push the particle along the laser beam propagation (z-axis in our consideration) while the gradient
force moves the particle toward the gradient of the optical intensity.
Figure 1.1: Sketch of a particle in the Rayleigh regime
Since a dipole has a proper resonance frequency ν0 the induced dipole is attracted toward the
region of maximum intensity or it is repelled from it according to the forcing optical field, in
particular if it is red-detuned (ν < ν0) or blue-detuned (ν > ν0). Within the zeroth-order
approximation in a paraxial Gaussian beam description (λ << ω0) the scattering and gradient force
produced by a laser beam are given by Florin et al. [2]2
rIm
ma
c
nzrFscatt
2
2
2
4
652
2
1
3
128ˆ
(1)
2 E.L. Florin, A. Pralle, E.H.K. Stelzer, J.K.H. Horber, Appl. Phys. A 66 (1998) S75.
rEm
manrFgrad
2
2
23
0
2
22
12
(2)
where the position vector r is referred to the beam center at the minimum waist, ž is the unit
vector along the z-axis, ε0 the dielectric constant in the vacuum, c is the speed of light, and m is
the ratio between the refractive index of the particle n2, and that of the surrounding medium n1
(m = n2/n1). The intensity I(r) is defined as a time-average of the Poynting vector S(r, t) which is
related to the electric and magnetic field components by
zrEcn
rHrEtrSzrIT
ˆ2
Re2
1,ˆ
202* (3)
In presence of strongly focused laser beams, higher-order contributions are required for
describing the transverse and longitudinal components of the electric and magnetic fields.
1.1.2 LARGE PARTICLES REGIME (a >> λ)
In the large particles regime, commonly referred to as Mie regime, the particle size is much larger
than the radiation wavelength (a >> ).
In this case, since the particle is not affected by temporal variations of the electric field, we can
describe the interaction between radiation and particle through a ray optics approach. The
electromagnetic beam is then decomposed in a set of rays, each one carrying a fraction of the
total power of the optical beam. The behavior of optical rays, when crossing the interface
between two media having different refractive index (n1 and n2), can be evaluated by Snell's law
to calculate the propagation direction
2211 sinsin nn (4)
and by Fresnel relations to calculate, depending on the polarization of the radiation, the amount
of power that is reflected from the surface.
1221
1221
coscos
coscos
nn
nnr
(5)
2211
2211
coscos
coscos
nn
nnr
(6)
In this way the beam can be described by geometrical considerations on the direction of the rays.
Figure 1.2: Sketch of a particle immersed in an electric field in the case of large particle regime.
In order to describe the effect of radiation pressure, we consider a spherical particle with
refractive index n2 immersed in a homogeneous medium of index n1, and we analyze only the
effect of a single ray composing the Gaussian beam. We also suppose that the radiation
wavelength is such that the optical absorption of the particle is negligible. When a ray hits the
interface between two different media it gives rise to two components, one reflected and one
transmitted, each one carrying a small portion dW of the total power of the beam, as shown in
Figure 3. Indicating with the angle between the ray incident on the particle and the normal to
the surface, and with n the refractive index of the particle normalized to the external medium n =
n2/n1, the angle of refraction is given by Snell's law:
n
sinsin (7)
To evaluate the power associated to the transmitted and the reflected rays is necessary to use the
Fresnel coefficients (Eq. 1.2 and 1.3). We will indicate with R and T respectively the reflection and
the transmission coefficients of the beam power, which are related to the Fresnel coefficients by
the relations R = |ρς, π|2 e T = 1-R.
Figure 1.3: Ray optics description of the behaviour of an optical ray hitting a spherical particle.
The light beam transmitted into the first interface hits the inner surface of the sphere and divides
into two components, one reflected back into the particle and one transmitted outside. This
process creates an infinite number of rays gradually decreasing in optical power that emerges
from the sphere at different points and with different propagation directions. In particular, being
dW the power of the incident ray, it follows that the first reflected ray will have a power of RdW,
while the rays transmitted after passing through the particle will have a gradually decreasing
power of T2dW, RT2dW, R2T2dW, etc. It is possible to describe the forces that are exerted at each
point of refraction, and decompose them into the components along z and y axis. It should be
noted that the first beam is reflected at an angle equal to π+2θ with the z axis, while the
successive rays transmitted form an angle respectively equal to α, α+β. Α+2β, .... with the direction
of incidence, where the values of and are retrievable through purely geometrical
considerations:
2 (8)
2 (9)
Adding the terms of the force along z and y axis produced by the individual rays we obtain:
...2coscoscos2cos 22111 RRTc
dWnR
c
dWn
c
dWnFz (10)
...2sinsinsin2sin 2211 RRTc
dWnR
c
dWnFy (11)
Using a complex notation FTOT = Fz + iFy and an exponential notation we obtain:
0
21 2sin2cos1j
jij
TOT eRTiRc
dWnF (12)
This series highlights that the contribution of force related to the transmitted beam decreases as a
geometric series, hence we can obtain the following expression:
221
11 T
Re
eRe
c
dWnF
i
ii
TOT
(13)
Inserting the values of and described above and dividing the force in real and imaginary
components (respectively along z and y directions), it is possible to retrieve the final formula of
the force produced by a beam having optical power dW
2cos21
2cos22cos2cos1
2
21
RR
RTR
c
dWnFS (14)
2cos21
2sin22cossin2sin
2
21
RR
RTR
c
dWnFG (15)
These equations give a quantitative estimate of the forces, and highlight the generation by a light
beam of two distinct components of the forces, one parallel and the other perpendicular to the
beam direction, which, by following the description given for the Rayleigh regime, can be
respectively called "scattering force" and "gradient force”. The effect of the first component is to
push the particle along the beam direction, while the second tends to pull the particle towards the
center of the beam, where the intensity is higher.
1.2 OPTICAL TRAP
An optical trap is a stable equilibrium point in space of the optical forces acting on a particle. If we
consider a dielectric particle near the axis of a laser beam, it will experience a force because of the
transfer of momentum from the scattering of photons incident on the particle to the particle itself.
The resulting optical force, as described above, can be decomposed into two components: a
scattering force, parallel to the light propagation, and a gradient force, in the direction of the
spatial light gradient, i.e. perpendicular to the propagation direction.
1.2.1 SINGLE-BEAM OPTICAL TRAP
For most conventional situations, the scattering force dominates. However, if there is a steep
intensity gradient, as it happens near the focus of a tightly focused laser beam, the second
component of the optical force, the gradient force, is no more negligible and must be taken into
account. When the axial gradient component of the force, which pulls the particle towards the
focal region, is equal to the scattering component of the force, which pushes it away, a stable
trapping in all three dimensions is achieved. In order to fulfill this condition a very steep gradient
in the light intensity is needed and it might be produced by sharply focusing the trapping laser
beam to a diffraction-limited spot by means of a high NA objective. As a result of this balance
between the gradient and the scattering force, the axial equilibrium position of a trapped particle
is located slightly beyond the focal point. For small displacements from the equilibrium position,
the gradient restoring force is simply proportional to the offset from the equilibrium position, i.e.,
the optical trap acts as Hookean spring whose characteristic stiffness is proportional to the light
intensity.
Figure 1.4: Schematic of a single-beam laser trap. The variation of photons’ momentum originates a force on the particle that pulls it towards the focus of the beam.
Refraction of the incident light by the sphere corresponds to a change in the momentum carried
by the light, hence to a force F = dP / dt. By Newton’s third law, an equal and opposite force
proportional to the light intensity is imparted to the sphere. When the particle’s refractive index is
greater than that of the surrounding medium, the optical force arising from refraction is directed
as the intensity gradient. Conversely, for an index lower than that of the medium, the force is in
the opposite direction with respect to the intensity gradient. In the case of a uniform sphere in
large particle regime, optical forces can be directly calculated in the ray-optics regime by
decomposing the laser beams into optical rays. As shown in Figure 1.4, the rays that hit the
particle change their propagation direction because of refraction at the interfaces. The external
rays contribute to the axial gradient force, whereas the central rays are primarily responsible for
the scattering force. Thanks to the strong focusing of high NA objectives the gradient force can be
sufficiently strong to counterbalance the scattering force, anyway an expansion of the Gaussian
laser beam, to slightly overfill the objective entrance pupil, can increase the ratio of gradient to
scattering force, resulting in improved trapping efficiency.
Depending on the position of the particle center O respect to the beam focus, the resulting
trapping force will pull the particle in different directions so as to move the particle towards the
equilibrium position, as schematically shown in Figure 1.5.
Figure 1.5: Schematic of the optical trapping force direction acting when the particle is displaced from the equilibrium trap position [3]3
1.2.2 DUAL-BEAM OPTICAL TRAP
As proposed by A. Ashkin [1], a stable optical trap can also be achieved by exploiting two equal
counterpropagating Gaussian beams, see Figure 1.6.
Figure 1.6: Schematic of a dual-beam laser trap, as proposed by A. Ashkin [1].
In this case the gradient forces pull the particle towards the axis of the beams while the scattering
forces push the particle in the middle of the two beams where they’re balanced. In this condition,
the trapping setup is similar to a spring system. In fact we can assume the case in which the
particle is translated in the z direction, along the beam axis. if P is the power transmitted by the
fibers, and the light from the fibers can be represented by a Gaussian beam with waist w0 at the
fibers face, then the intensity at the fiber faces is given by l0 = 2P/(πw02). For a plane wave with
intensity I, the scattering force on a sphere of radius R is given by (rπ2)IQpr/c. Let z = 0 at the center
point between the fibers. Using an approximation in which the intensity and the phase of the
trapping beams are constant over the area of a sphere with radius R, we can express the total
scattering force as
3 A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime”, Biophysical
Journal, Vol. 61, 1992
22
2
0,
22
2
0,
2121 zSd
wQaP
zSd
wQaPF
g
ggprg
r
rrprr
s
(16)
where a = 2R2/c, d-1 = λ/(πwo2), S is the separation between the two fiber faces, and A and Q are
the wavelength and radiation pressure coefficient, respectively, for the designated color. Let zeq be
the value of z for which the force given in the above equation is zero. When a particle is displaced
from Zeq, a restoring force results from the increase in intensity with decreasing distance from the
fiber face. This restoring force is simply a manifestation of the scattering force and can be
expanded to first order in ε = z - zeq, resulting an equation of the form F = -ke, where k is given by
2222
2
0,
2222
2
0,2
4416
rr
rrprr
gg
ggprg
dS
wQP
dS
wQPaSk
(17)
k as a function of S is a maximum when S is approximately twice the Rayleigh range.
The above discussion assumes that the two trapping beams are exactly counter-propagating, i.e.
that the two optical fibers are perfectly aligned. However, as shown in Figure 1.7, there are two
possible types of fiber misalignment: a positional misalignment, in which the beams are
propagating in the ±z direction but the two fibers are translationally displaced, and a rotational
misalignment, where both fiber faces still have their centers on the z axis but are at skewed angles
to each others' faces and therefore the two light beams are not counter-propagating. Both types
of misalignment may occur at the same time.
Figure 1.7: (a) Schematic of the forces for each of the two fibers that compose the trap. (b)÷(d) Directions of the total forces
when the fibers are (b) perfectly aligned, (c) translationally misaligned, and (d) rotationally misaligned [4]4.
The alignment of the two counter-propagating beams to within a fraction of the beam waist is the
critical point for good trapping operation. For example, if the fibers are translationally misaligned,
then the particle can oscillate back and forth between the two fiber faces instead of finding a
stable trap position. It is worth to note that even a misalignment translation of 2 m between the
two fibers causes a significant decrease in the trapping efficiency.
4 A. Constable et al., “Demonstration of a fiber-optical light-force trap”, Optics Letters, Vol. 18, No. 21, 1993
CHAPTER 2 – OPTICAL TWEEZERS
This chapter reviews some of the different configurations of the single-beam optical tweezers.
After a brief introduction on the tweezers presented in literature, our proposal to realize a fiber
optic tweezers is introduced. Working principle, fabrication techniques and experimental test are
presented.
2.1 OPTICAL TWEEZERS IN LITERATURE
Optical tweezers allows trapping and manipulating singe cells without physical contact. Because of
this peculiar feature they are widely used for many different applications, above all in the
biological field. For this reason it is interesting to review some implementations of optical tweezer
starting from the first proposal.
2.1.1 STANDARD OPTICAL TWEEZERS
Nowadays many implementations of an optical tweezers are available and there is still a great
effort in researching new improved solutions. The simplest configuration uses a Gaussian laser
beam, expanded by a system of thin lenses. The beam is then reflected by a mirror and focused on
the sample by a microscope objective [Fig. 2.1].
Fig. 2.1: Basic principle of single-beam optical tweezers
The first working optical trapping scheme, proposed in 1978 and demonstrated in 1986 by A.
Ashkin [55, 66], simply consisted in bringing a laser beam to a diffraction-limited focus using a good
lens, such as a microscope objective. Figure 2.2 shows the schematic of this optical tweezers.
Fig. 2.2: Schematics of a standard Optical Tweezers
The alignement of the beam with the objective might be critical, hence the beam exiting the laser
usually requires to be expanded in order to overfill the back aperture of the objective; for a
Gaussian beam, the beam waist is chosen to roughly match the objective back aperture. A simple
Keplerian telescope is sufficient to expand the beam, then a second telescope, typically in a 1:1
configuration, is used for manually steering the position of the optical trap in the specimen plane.
If the telescope is built such that the second lens, L4 in Figure 2.1, images the first lens, L3, onto
the back aperture of the objective, then a movement of L3 lens corresponds to a movement of the
5 Ashkin A. 1978. Trapping of atoms by resonance radiation pressure. Phys.Rev. Lett. 40:729-32
6 Ashkin A, Dziedzic JM, Bjorkholm JE, Chu S. 1986. Observation of a singlebeam gradient force optical trap for dielectric particles. Opt. Lett.
11:288-90
optical trap in the specimen plane with minimal perturbation of the beam. Because lens L3 is
optically conjugate to the back aperture of the objective, motion of L3 rotates the beam at the
aperture, which results in translation in the specimen plane with minimal beam clipping. If lens L3
is not conjugate to the back aperture, then translating it leads to a combination of rotation and
translation at the aperture, thereby clipping the beam. Additionally, changing the spacing between
L3 and L4 changes the divergence of the light that enters the objective, and the axial location of
the laser focus. Thus, L3 provides manual three-dimensional control over the trap position. The
laser light is coupled into the objective by means of a dichroic mirror (DM1), which reflects the
laser wavelength, while transmitting the illumination wavelength. The laser beam is brought to a
focus by the objective, forming the optical trap. For back focal plane position detection, the
position detector is placed in a conjugate plane of the condenser back aperture (condenser iris
plane). Forward scattered light is collected by the condenser and coupled onto the position
detector by a second dichroic mirror (DM2). Trapped objects are imaged with the objective onto a
camera. Dynamic control over the trap position is achieved by placing beam-steering optics in a
conjugate plane to the objective back aperture, analogous to the placement of the trap steering
lens. For the case of beam-steering optics, the point about which the beam is rotated should be
imaged onto the back aperture of the objective.
This is the basic setup for an optical tweezers; nowadays it is implemented with additional optics
like an acousto-optic deflector that provides time-sharing multi-trap, or a liquid crystals space light
modulator (SLM) that allows holographic multitraps in the same time, or with an axicon that
transform the Gaussian beam into a Bessel beam, useful to have many trapping point along the
beam axis. The particle tracking can be well analyzed by a four-quadrant photodiode instead of a
CCD: this technique improve the measurement precision and velocity.
Despite optical tweezers have been successfully used in many applications, the bulky structure of
standard optical tweezers, as well as the expensive setup, limit their diffusion among biological
labs. In addition, the use of standard optical tweezers in turbid media or in thick samples presents
significant challenges, being difficult to achieve the tight focusing necessary for optical trapping.
The realization of an optical tweezers based on a single optical fiber would turn this device into a
miniaturized and handy diagnostic tool, suitable for many relevant applications, like in vivo
biological operations, where standard tweezers cannot be successfully exploited.
2.1.2 FIBER OPTIC TWEEZERS
The realization of optical tweezers based on optical fibers would allow a miniaturized, versatile
and handy tool to be obtained, suitable for many applications relevant to biology and fundamental
physics, such as in vivo biological manipulation or in-vacuum single-particle X-ray spectroscopy.
The typical approach for the development of fiber-optical tweezers makes use of two fibers, as
discussed in Chapter 1, aligned so that the laser beams exiting from the fibers are counter-
propagating along a common optical axis. In this case, the axial scattering forces are
counterbalanced, so that is quite easy to obtain a stable optical trap, but the set-up requires a
critical alignment between the two fibers and manipulation in three dimensions is quite limited.
A single-fiber approach would solve these problems, but as in the standard optical tweezers
configuration, a strong focusing of the laser beam is needed to realize the optical trap. The
simplest idea is that of building a lens on top of the fiber. Conventional silica fiber tips can be
shaped into tapered lenses, but their performance when immersed in a medium such as water
depends critically on the radius of curvature of the fiber tip. Since many important systems are
dispersed in water, it would be desirable to have fiber tweezers that could work robustly in such a
liquid. Since the refractive index of water nw =1.33 is close to that of silica ns =1.45 the focusing of
light is not effective, typically resulting in large spot sizes and small working focal lengths. This
renders the optical trap ineffective in applications that require trapping of micron-scale particles.
Decreasing the radius of curvature of the fiber tip enhances the focusing of light, but also causes
light leakage through the fiber cladding, resulting in a decrease in efficiency of the optical trap.
In his paper, Taguchi7 proposed a fiber tweezers based on a single microlensed optical fiber.
Microsphere could be manipulated to the forward and backward, or right and left directions
synchronized to the optical fiber. Anyway, being the numerical aperture achieved with this lens
insufficient to obtain a real three dimensional trapping, such a solution allowed only two
dimensional trapping, being the trapping in the third dimension given by electrostatic phenomena.
7 Taguchi “Single laser beam optical trap”
Fig. 2.3: Side view image of the typical relation between the laser beam axis and optically trapped sphere in the solution proposed by Taguchi [7]
On the other hand, Liu8 obtained a purely optical 3D trapping by means of single fiber through
highly tapered fibers. The probe was made from a single mode optical fiber with a core diameter
of 9 μm, which was tapered by heating and drawing technology, heating the waist zone of the
tapered fiber and drawing at high speed of 1.6 mm/s until the fiber break at the waist point. The
parabola-like profile fiber tip was obtained from the surface tension of the fused quartz material.
In this case the trapping point gets very close to the fiber tip, making it difficult to trap a particle of
large size without physical contact.
8 Liu “Tapered fiber optical tweezers for microscopic particle trapping”
Fig. 2.4: (a) The intensity of the optical field emerging from the fiber probe; (b)Yeast cell trapped by a single tapered fiber optical tweezers [8].
2.2 TOTAL INTERNAL REFLECTION FIBER OPTICAL TWEEZERS
In order to obtain an efficient fiber optical tweezers, we proposed a different approach that
exploits the total internal reflection phenomenon to achieve the high NA necessary to obtain the
optical trap.
2.2.1 WORKING PRINCIPLE
As discussed in chapter 1, to increase the gradient force component, a Gaussian beam must be
focused on the particle by a high NA objective so as to counterbalance the scattering force that
pushes the particle away. Moreover, considering a strongly focused Gaussian beam in an optical
ray regime, the central on-axis rays contribute mainly to the scattering force, yielding a negligible
contribution to the axial gradient force.
As to suppress the on-axis scattering force, we decided to use a bundle of optical fibers that
behaves approximately as a fiber with annular core and we cut the cores of the fibers at an angle θ
so that the propagating light experiences total internal reflection (TIR) at the interface with the
surrounding medium, as shown in Figure 2.5. Hence optical beams are first deflected into the
cladding and then transmitted out of the fibers converging all in the same point, at a large angle
with respect to the fiber axis. The resulting structure provides, for optical trapping purposes, the
equivalent effect of a focused beam, with the advantage that the scattering force in the axial
direction is highly suppressed. We indicate such a tweezer as TIR-based optical fiber tweezer
(TOFT).
Fig. 2.5: Scheme of the total internal reflection optical fiber tweezers. (a) Cross section of the annular core fiber: the optical beam experiences reflection in correspondence of the fiber cut and refraction at the fiber–medium interface. The φ angle
determines the equivalent NA of the fiber probe. (b) Annular core fiber: the core is represented with the dark gray area. (c) Optical fiber bundle: the tweezers working principle can also be applied to a fiber bundle provided that the fiber cores (dark gray
circles) are symmetrically positioned around the bundle axis.
By simple trigonometric considerations, and by using Snell law, it is possible to express the angle
of convergence φ through the following relation (nF and nM being the refractive indexes of the
fiber and the surrounding medium, respectively):
(18)
As a consequence, the structure provides a focusing effect corresponding to that obtained using
an objective with an equivalent NA given by NAeq = nM sin(Φ). The NAeq can be more conveniently
expressed as a function of the fiber parameters:
(19)
Taking nF = 1.45 and considering nM = 1.33 as the refractive index of the surrounding medium
(water), by cutting the fiber surfaces at an angle θ slightly beyond the critical angle for TIR (θc =
66.5°), the structure behaves like an optical system with NAeq = 1.06, a value very close to that of
the typical objectives used in bulk optical trapping arrangements. The position of the trapping
point can also be easily evaluated through ray optics considerations. If the diameter of the core
annulus is, as an example, D = 110 μm, the trapping position is about 40 μm away from the point
of TIR, thus allowing a high degree of freedom in sample manipulation.
It is possible to fabricate TOFT with bigger bundles; the adding of more fibers increases the final
dimension of the probe, but it can exploit additional features. In Fig. 2.6 we show some example
of the possible functions that could be realized using the proposed structure. In a) the possibility
to realize multiple traps along the probe axis, just by using a different cutting angle θ on three of
the fibers, is shown. A possible steering of the fiber beams necessary to realize multiple traps at
the same distance from the probe end is shown in b). As depicted in c), it is also interesting to
notice that the radiation pressure that can be exerted, on a trapped particle, by using the light
output from the central fiber can be used to slightly modify the trapping position, thus allowing to
realize a particle translation or oscillation. Finally in d) a schematic representation of an optical-
analysis configuration is used. Some fibers (e.g. those with pink cores in the figure) can be used to
trap the particle, while other fibers (blue cores in the example) can optically excite the sample,
and the central fiber can be used for the collection of the emitted signal. It is also interesting to
notice that different fibers can be used for the different tasks (e.g. a large-mode-area fiber can be
used to increase signal collection)
Fig. 2.6: Schematic representation of different functionalities that could be obtained using the fiber-bundle TOFT. a) multiple traps realized along the probe axis by using a different cutting angle θ on three of the fibers, (b) steering of the fiber beams
necessary to realize multiple traps at the same distance from the probe end c) oscillation of the trapped particle by using the light output from the central, d) optical-analysis configuration, e.g. pink core fibers can be used to trap, while blue-core ones can
optically excite the sample; the central fiber can be used for the collection of the emitted signal.
2.2.2 NUMERICAL ANALYSIS
The starting point of the calculation is the evaluation of the spatial distribution of the amplitude
and phase of the optical field in the far field through a bidimensional Fourier transform. The
limitation due to the classical paraxial approximation, which cannot be applied to strongly focused
or tilted beams, has been overcame by using the angular spectrum decomposition representation
[9]9. Once the radial intensity distribution in the far field is known, the angular distribution of the
rays is derived from the gradient of the optical phase, whereas the power carried by each ray is
determined through the corresponding field amplitude in the far field. The frame of reference
used in the calculations is shown in Figure 2.7. The axis of rotational symmetry for all the
considered beams is the z-axis. Each ray is identified by three parameters: the angle φ formed
9 L. Novotny, B. Hecht, Principles of Nano-Optics, Cambridge University Press, New York, USA, 2006
between the ray direction and the z-axis, the azimuthal angle β, and the carried optical power. The
simulations regarding a standard microscope-based OT have been performed considering a
Gaussian beam characterized by a filling factor equal to 1 impinging on a high-NA objective, where
the filling factor is defined as the ratio between the beam waist and the objective radius [3]. The
quantity NA, thus, represents, for the Gaussian beam, the value of the maximum angle between
the rays and the z-axis, φmax. It is worth noticing that, by using such a large filling factor, a
significant fraction of the optical power, carried by the tails of the Gaussian beam, is not collected
by the objective and is consequently lost. The results presented in the following do not take into
account this effect, because all the analyzed parameters are normalized with respect to the optical
power that is focused on the particle, and not to the optical power input to the structure.
Conversely, in the case of the TOFT, no significant power loss is present, and we calculate the
quantity NAeq using the definition given in the previous section. The numerical calculation of the
optical forces is performed by following the approach proposed in [3] and considering the trap
geometry reported in Figure 2.7.
Figure 2.7: a) Ray decomposition of the optical beam: the generic ray is determined through the angles and . In the Gaussian case the angle max determines the beam NA. b) Generic ray incident on the spherical particle.
For sake of simplicity in Figure 2.7 we show the case in which the center of the particle lies on the
beam axis z, whereas in the following we will consider any displacement in the xyz frame of
reference. The trapping beams are described through a distribution of optical rays, each of them
forming an angle with respect to the beam axis. For a given , the ray is incident on the sphere
forming an angle with the direction perpendicular to the surface. The total force (FT) exerted by
each ray on the particle can be obtained as the vectorial sum of the scattering and gradient
component as discussed in Chapter 1.
z
y
max
a)
z
y
o
Optical ray
b)
2.2.3 NUMERICAL RESULTS: TRAPPING FORCES
In the previous chapter we defined the optical force arising from the radiation pressure of rays
composing a Gaussian beam incident on a dielectric particle in the geometric optical regime.
Starting from the equations describing the behavior of the gradient and scattering force we can
define the efficiency of the optical trap in the case of TOFT configuration.
We start by considering a Gaussian beam tightly focused with a maximum converging angle φmax =
70°, corresponding to a NA ≈ 1.25 that represents a typical situation in standard OTs, assuming
water as the surrounding medium (nM = 1.33). For all the calculations reported hereafter, we will
consider a wavelength λ = 1070 nm and a spherical particle with radius r = 5 μm and refractive
index 1.59. It is convenient to express the forces through the dimensionless Q-factor defined as
Pn
cFQ
M
T
(20)
FT is the total force exerted on the sphere and is obtained by integrating the contributions
generated by all the rays composing the beam and intercepting the sphere surface. The value of Q
is, thus, independent of the optical power, and it represents a figure of merit of the trapping
efficacy. The behavior of Q in the yz-plane for the Gaussian beam is reported in Fig. 2.8.
Figure 2.8: Q-factor for a Gaussian beam in standard optical tweezers. The inset shows the optical field distribution.
As expected, the optical forces in the case of the Gaussian beam lead to a trapping position just
beyond the beam focus, and the maximum Q-value is about 0.35. Let us now consider the Q-factor
of an optical trap obtained by an annular core fiber through the TOFT working principle depicted
in the previous section. The optical field is calculated considering that the total power is carried by
the rays emitted by an annulus of diameter D = 110 μm with a beam width equal to 6 μm. Through
the angular spectrum decomposition technique, it is also possible to take into account the
diffraction experienced by the beam in yz-plane. The cutting angle is θ = 70° leading to a NAeq ≈
0.93. It is important to notice that such a NAeq corresponds to a converging angle φ = 45° much
lower than that of the previous case. Nevertheless, as shown in Figure 2.9, a stable equilibrium of
the forces is found, even if smaller Q-values (maximum Q = 0.2) are produced.
Fig. 2.9: Q-factor for annular core fiber TOFT. The inset shows the optical field distribution.
Considering that the structure has a cylindrical symmetry, any displacement of the sphere from
the trapping point can be described using only the z-coordinate and the distance from the z-axis.
As a consequence, the Q diagrams of Figures 2.8 and 2.9 can be applied to any displacement
direction in the xy-plane. At last, we simulated the case of the four-fiber bundle. The optical field
distribution is obtained considering that the total power carried by the annular core is now
distributed over four Gaussian sources (each with mode field diameter equal to 6 μm)
symmetrically disposed along the annulus, as shown in Figure 2.5(c). We consider two out of the
four fibers having the axis lying in the xz-plane and the other two fibers with the axis in the yz-
plane. It is important to highlight that, in the bundle case, the cylindrical symmetry is broken and,
differently from the previous situations, the forces depend on the displacement direction in the
xy-plane. The most critical trapping positions, however, are found to be in the xz- and yz-planes,
where the contribution of the scattering force is most relevant. Congruently with the previous
graphs, we show also in this case the Q-values in the yz-plane [Figure 2.10]; for symmetry reasons,
the force distribution in the xz-plane is identical.
Figure 2.10: Q-factor for a four-fiber bundle TOFT. The inset shows the optical field distribution.
Also in this situation, a stable trap is formed in the beam convergence region, with values of the Q-
factor similar to those of the annular case. As the total power is concentrated in the four beams, a
strong gradient force is present along their propagation path, pushing the particle toward the
center of each optical beam and somehow distorting the force distribution in the trapping region.
A better performance could be obtained by using fibers with a larger mode size and by increasing
the number of fibers included in the bundle. The obtained results confirm that, as far as the TOFT
operation in the Mie regime is concerned, the fiber bundle and the annular core fiber are
equivalent structures leading to similar optical force distributions.
2.2.4 NUMERICAL RESULTS: ESCAPE ENERGY
In order to evaluate the trapping strength of the proposed TOFT and to compare its performances
with those of the standard OT exploiting a Gaussian beam, we calculated the minimum energy, per
unit power of the optical beam, necessary for a particle to escape the trap. We call this quantity
εesc. As is well known, the potential energy cannot be defined for the total optical force, as the
scattering component is not conservative. Hence, to find εesc, we start considering the work per
unit power (ε) that has to be done against the optical forces to move a particle from the center of
the trap toward a target point (TP). The work is obtained by integrating the total force FT exerted
on the sphere along linear trajectories connecting the center of the trap to TP:
(21)
The obtained values, in the three cases of Gaussian beam, annular cora fiber TOFT and fou-fiber
bundle TOFT, are shown in Figures 2.10, 2.11 and 2.12, as a function of the TP position. Lower
energy regions are indicated with a darker color. The value of εesc, which gives a straightforward
indication of the trapping strength and of the most probable escape path for the trapped particle,
can be recovered by such diagrams. The meaning of εesc can be easily understood by considering
the analogous case of a potential well induced by conservative forces. A particle in a stable
equilibrium point lies at the bottom of a potential well, and it can escape only if its energy is higher
than the minimum energy barrier. For any possible linear escape trajectory, we evaluate the
maximum value of ε: in such a way, we find a quantity εMAX analogous to the energy barrier
associated to each linear trajectory. The minimum among the calculated values of εMAX is then
simply defined as εesc, and the corresponding trajectory is the most energetically favored escape
path. As expected, for the Gaussian beam [Figure 2.11], εesc is found considering a particle
movement along the z-axis. A particle lying in the center of the trap (y = 0, z = 0) needs about 2.15
fJ/W to leave the trap following the z-axis.
Fig. 2.11: Work per unit power ε for bulk OT using a strongly focused Gaussian beam.
On the contrary, for TOFT with the annular core fiber [Fig. 2.12] we find εesc considering as escape
path the directions of propagation of the slanted rays coming from the annulus. The result is quite
intuitive as, due the TOFT geometry, the scattering force is strongly suppressed along the z-axis,
whereas it has a maximum along the beam propagation direction. In this case, εesc is about 1,75
fJ/W, which is slightly lower than the previously obtained value.
Fig. 2.12: Work per unit power ε for annular core TOFT.
Finally, we also consider the TOFT based on the fiber bundle shown in Fig. 2.13.We still find that
the most favored escape paths are along the propagation directions of the beams emitted by the
fibers, with an εesc value similar to that found for the annular core case.
Fig. 2.13: Work per unit power ε for four-fiber bundle TOFT.
To understand the origin of this difference in the εesc values, Figure 2.14 compares the results
obtained, for the Gaussian beam and for the annular-core-based TOFT, as a function of the NA.
The values of the TOFT εesc show a linear increase as a function of NAeq and higher values with
respect to the Gaussian case. Conversely, εesc of the Gaussian beam has a nonlinear growth
characterized by an increase in the curve slope for NA > 1. This different behavior can be explained
recalling that in both cases, εesc is found along the directions where the scattering force has the
maximum impact. The scattering force in the Gaussian case is essentially due to the rays on axis
that carry a considerable power especially at low NA and give a negligible contribution to the
gradient restoring force. On the contrary, in the TOFT annular case, the maximum scattering
contribution is given by the rays coming from the annulus and strongly slanted with respect to the
z-axis. As a first consequence, in the annular core case the total scattering force is not
concentrated in the same z-direction, but it is distributed along the whole cone of rays. Second,
the crossing-beam geometry lowers the contribution of the scattering component. It is worth
noticing that Figure 2.14 highlights that the TOFT efficiency can be highly improved by increasing
the device NAeq. Such a result can be easily obtained by decreasing the cutting angle θ shown in
Figure 2.4(a). The TIR can still be guaranteed even for θ < θc by properly coating the fiber surface
with metal. Finally, it is very interesting to analyze εesc as a function of the trapped particle radius.
Fig. 2.14: εesc calculated as a function of the NA for the focused Gaussian beam and of the NAeq for the annular core fiber TOFT.
2.3 FABRICATION OF A TOTAL INTERNAL REFLECTION OPTICAL FIBER
TWEEZERS
The TOFT fabrication process has been made in collaboration with the BIONEM laboratory of the
University of Magna Graecia in Catanzaro and the Italian Institute of Technology, IIT, in Genova. It
is divided in two separate steps: the first one concern the assembly of the bundle and the second
regards the realization of the angled surface necessary to obtain total internal reflection.
2.3.1 FABRICATION OF THE FOUR-FIBER BUNDLE
The first step of the fabrication is made in the Quantum Electronics Laboratory in Pavia. We take a
bundle of four optical fibers 2 meters long with reduced cladding of 80 μm; the fibers are single
mode at 1070 nm, exhibiting a mode field diameter of about 6.1 μm. First we stripe the fibers end
in order to reduce their dimension, then we insert the four tips in a capillary with an internal
diameter of 200 μm. We glue the fibers in position and we insert another bigger capillary with an
internal diameter of 650 μm to reduce the fragility of the bundle, as schematically shown in Figure
2.15.
Fig. 2.15: First steps for the fabrication of a TOFT
We then fill the gaps between the fibers with an epoxy resin, Epo-Tek 301-2 FL, which, once solid,
will held the fibers in position. In order to achieve a better penetration of the resin inside the
capillary, we put the probes in a vacuum chamber for 15 minutes, and then we let the air in: the
air pressure will push the resin deeper inside the capillary. After three days the resin becomes
solid and we can proceed with a polishing machine that will reduce the roughness of the fibers
surface under 1 m, so as to obtain a good optical quality of the fiber surface. The probes are then
sent to the BIONEM Laboratory in Catanzaro for the second step of the fabrication process. At the
moment two different techniques have been exploited to fabricate the TOFT: in one case the cores
of the fibers are cut at the desired angle to achieve total reflective by digging holes in them
through a focused ion beam, in the other case prisms, having the correct angle for beam
reflection, are fabricated on the surface of the fibers for the same purpose.
2.3.2 FABRICATION BY FOCUSED ION BEAM
After the polishing, the probe is put in a sputtering system to deposit a thin film of gold onto the
fibers surfaces. By first creating gaseous plasma and then accelerating the ions from this plasma
into a gold target, the material is eroded by the hitting ions via energy transfer and is ejected in
the form of neutral particles - either individual atoms, clusters of atoms or molecules. As these
neutral particles are ejected, they will travel in a straight line unless they come into contact with
the TOFT, coating it with a tin film of about 40 μm. A schematic representation of the sputtering
technique described above is shown in Figure 2.16.
Fig. 2.16: Principle of the sputtering technique
Once covered by a metal layer, the probe is inserted in a scanning electron microscope (SEM) with
a focused ion beam (FIB) tower. While the SEM uses a focused beam of electrons to image the
sample in the chamber, a FIB setup instead uses a focused beam of ions to drill holes onto the
sample. The FIB uses Liquid-metal ion sources (LMIS), in particular gallium ion sources. Gallium
metal is placed in contact with a tungsten needle and heated. Gallium wets the tungsten and an
electric field, greater than 108 volts per centimeter, causes ionization and field emission of the
gallium atoms. Source ions are then accelerated to an energy of 5-50 keV and focused onto the
sample by electrostatic lenses. LMIS produce high current density ion beams with very small
energy spread. A modern FIB can deliver tens of nA of current to a sample, or can image the
sample with a spot size on the order of a few nanometers.
Fig. 2.17: Scheme of FIB imaging
As shown in Figure 2.17, the gallium (Ga+) primary ion beam hits the sample surface and sputters
a small amount of material, which leaves the surface as either secondary ions or neutral atoms.
The primary beam also produces secondary electrons. As the primary beam rasters on the sample
surface, the signal from the sputtered ions or secondary electrons is collected to form an image. At
low primary beam currents, very little material is sputtered and the FIB systems can easily achieve
5 nm imaging resolution. At higher primary beam currents, a great deal of material can be
removed by sputtering, allowing precision milling of the specimen down to a sub micrometer
scale. The fiber-end faces of the TOFT are then microstructured through FIB milling; the core
regions at the fiber surfaces are properly shaped in such a way as to obtain TIR at the fiber
core/water interface. The image [Figure 2.18] of the micromachined probe, taken at the scanning
electron microscope, shows the milling of the four-fiber bundle with a trapezoidal shape,
preferred to a rectangular one to minimize the damage to the sample.
Fig. 2.18: FIB milling steps implemented to fabricate a four-fiber bundle TOFT
The overall structure presents a very good symmetry and the surfaces are of excellent quality,
anyway there are some limitations. First of all there are strict conditions on the cutting angle θL,
which cannot be under 66,5° in order to have total reflection at the glass-water interface, and over
74° to obtain a gradient force high enough to trap the particle. Another problem is that the cut
angle θL cannot be perfectly achieved in the FIB process. Indeed, while the ions dig the core of the
fiber at the designed angle, some of the extruded material re-deposes on the hole, thus creating
heavy roughness on the core interface. Moreover the ion beam diverges as long as it goes deeper
in the fiber, thus varying the cutting angle of the nucleus. Hence, the divergence of the beam and
the re-deposition of the extruded material vary the angle θL by ± 1%. The depth of the hole is also
crucial, in fact we cannot verify, with the SEM vision, if the cut parameter set in the configuration
exactly matches the final cut. The dig duration is quite long, it takes about half an hour for each
fiber core; it is possible to reduce the time amount adding a gas etching to the ion beam, but the
result is often destructive for the probe surface.
A big effort has been spent in increasing the performance of the optical tweezers fabrication
process, in order to achieve better cuts in less time. The first implementation was the change of
the dig geometry. First we define two trapezia, the smaller one superimposed to the bigger one. In
this way the FIB first excavated the fiber core, obtaining the desired angle and shape, then, with
the second trapezium, the dirt deposed on the cut was removed. We also switched to a bigger
hole, so that the alignment between the hole and the core was less strict [Fig. 2.19].
(a) (b)
Figure 2.19: Double-trapezoidal shape of the beam cut. We moved from a) 10x20x10 μm to b) 10x20x15 μm
We also changed the sputtering parameters, adding a second layer of Nickel with a thickness of 80
μm on the gold one. In this way the fiber surface became more resistant to the gas etching,
allowing the use of XeF2, and reducing the drilling time without compromising the integrity of the
tweezers. The different results obtained in the holes fabricated with and without the Nickel layer
are shown in Figure 2.20.
Fig. 2.20: FIB milling with XeF2 etching a) with Au layer and b) with Ni and Au layer
Finally, we set a higher beam current, which improved the fabrication time. This way we increased
the number of ions hitting the probe, excavating the core more efficiently as shown in Figure 2.21.
Fig. 2.21: FIB milling with beam current of a) 7nA and b) 20 nA
After all these modification of the fabrication process, we verified the realized cutting angle and
the depth of the hole. Since it has not been possible to perform this test directly on a TOFT
sample, we glued two microscope slides together with a UV resin and we proceeded with the ion
milling on the glass-resin-glass interfaces [Figure 2.22].
Fig. 2.22: Scheme of the process used to verify the cutting angle
Then we put the glasses in a solution with acetone to remove the UV resin and we inserted one of
the glasses in the SEM chamber to observe the side view of the obtained cutting angle, like that
shown in Figure 2.23.
Fig 2.23: side-view of the FIB milling
From this verification we calculated an error of ±1° on the angle, due to the material re-deposed
and to the divergence of the beam. The cuts were also deeper respect to the set parameters of
about 15%. Thanks to these results, we then readjusted the parameters reducing the milling time.
As final result, we reduced the milling time from 26 to 14 minutes/fiber.
We tried also to reduce the limitations on the cutting angle θL, by sputtering a layer of 40 μm of Au
and Ni on the fibers core of the micro-machined probe, so as to obtain total internal reflection
even at lower cut angle. Anyway this coating didn’t solve the problem since it was quickly burned
by the radiation exiting from the cores under test.
2.3.3 FABRICATION BY TWO PHOTON LITOGRAPHY
The main limitations of the FIB approach come from the fact that is very difficult, if not impossible,
to obtain more complicated geometries, and from the high cost of running the FIB equipment.
Two-photons lithography recently showed its ability to create microoptics of arbitrary shape on
the end-face of an optical fiber.
The micro-prisms fabrication on each of the four fiber cores is performed by using a two-photon
lithography setup where a 100-fs pulsewidth, 80-MHz Ti:sapphire laser oscillator is used as the
excitation source, and a dry semi-apochromatic microscope objective, NA = 0.70, is used for beam
focusing. A specific fiber holder is mounted on a xyz piezo-stage with an 80 m travel range on all
axes, for positioning in horizontal and vertical directions. The fiber holder is designed in such a way
to let the laser beam, coming from the microscope objective, to pass through a glass coverslip and
then focalize in a photopolymerizable material droplet where the fiber bundle is immersed. A
precision linear translator controls the fiber-coverslip distance. A commercial UV curing adhesive
(NOA 63, Norland) is used as a photopolymer for fabrication due to its good adhesion to glass,
easy processing, suitable refractive index (1.56 for the polymerized resin), and very low cost. The
laser wavelength is tuned to around 720 nm and a variable attenuator, made by a half-waveplate
and a polarizer, is used to decrease the laser power at the sample plane to 4 mW. The beam is
expanded by a telescope, to obtain overfilling of the focusing microscope objective, and is then
reflected by a 45° short-pass dichroic mirror which transmits in the visible part of the spectrum for
imaging purposes. A lens images the sample, illuminated by using a light-emitting diode (LED) light
source, onto a CCD camera for fiber alignment, focusing and real-time monitoring of the
polymerization process. A computer-driven mechanical shutter is used to control the exposure
time for each pixel. A dedicated LabVIEW-based software was written to convert the point-by-
point defined structures into piezo stage positions and to control the synchronization of the
movements with the mechanical shutter.
The time needed to expose a single microprism is typically around 10 min. After the completion of
exposure for all of the four microprisms, the fiber bundle is retracted from the droplet and the
photopolymerizable material that did not cross-link is removed by washing for a few seconds with
acetone and methanol, leaving the 3-D structure attached to the fiber top. The fabricated solid 3-D
microstructures are then observed by using a scanning electron microscope (SEM). In Figure 2.24
are shown the results of this technique.
(a) (b)
Fig. 2.24: SEM images of a) the microstructured TOFT fabricated with the two-photon lithography and b) profile of the prism.
2.4 EXPERIMENTAL RESULTS
This section reviews the results obtained in testing the TOFT fabricated with both the described
technologies. Experiments concerning trapping and manipulation of either dielectric or biological
samples are shown.
2.4.1 FIB-FABRICATED TOFT: EXPERIMENTAL RESULTS
The probes have been first tested by coupling an Yb-doped fiber laser emitting at 1070 nm into the
four fibers composing the bundle. The probe fibers are connected to the laser through a 1×4 fiber-
optic coupler, and the optical power carried by each fiber is controlled by fiber variable optical
attenuators in each path, yielding an extremely compact and stable setup, as schematically shown
in Figure 2.25.
Fig. 2.25: Experimental setup used to test the four-fiber bundle TOFT
At first we controlled that each beam focuses in the same point, thus providing the focusing effect
necessary to trap particles. This experiment has been done by observing the beams with a
microscope objective with high NA; the focal plane was set so as to see the fiber surfaces at first,
then we observed the light distribution on focal planes with a growing distance from the fiber, the
images taken during this characterization are shown in Figure 2.26.
Fig. 2.26: Sequence of images showing the beam focusing of the four-fibers bundle TOFT
TOFT effectiveness has been successfully demonstrated by trapping water suspended polystyrene
spheres (of refractive index nP = 1.59) having a diameter of 10 μm. In Figure2.27 we report a
sequence of twelve images (obtained using a 10× objective) showing the TOFT and a particle that
is first trapped, and then, moved under the microscope objective without escaping from the
trapping position. In order to guarantee that the trapping effect was purely optical, we kept the
probe at a distance of few millimeters from the cover slip, and we verified that the trapping effect
vanished when the light beam was turned off.
Fig.2.27. Sequence of images showing the movement of a trapped polystyrene bead.
The experimental setup used for the trapping experiment was essentially the same used for tha
beam characterization with the only exception that the TOFT was mounted on a 3-axis
micromanipulator in order to move the trapped particle in a controlled manner.
A final experiment has been performed to demonstrate simultaneous particle trapping and optical
analysis. The probe end was immersed in a water suspension of 10 m-diameter fluorescent
beads. The experimental set-up is shown in the inset of Figure 2.28. By using two dichroic mirrors,
either trapping or fluorescence excitation radiations (λ = 1070 nm and λ = 408 nm, respectively)
were coupled into the fiber probe. The fluorescence signal emitted by the trapped bead was
collected by the probe itself, transmitted by the dichroic mirrors, and then detected through a
spectrometer with 10-nm spectral resolution. The optical spectra measured with and without a
fluorescent bead trapped by the fiber tweezers are reported in Figure 2.28. The optical analysis
function is very effective thanks to the short distance between the bead and the probe end,
probe-end, which acts both as excitation source and signal collector.
Fig. 2.28: Fluorescence experiment
2.4.2 TWO-PHOTON LITHOGRAPHY FABRICATED TOFT: EXPERIMENTAL
RESULTS
By using the same experimental setup exploited for the characterization of the FIB fabricated
TOFT, we evaluated the efficiency of the two-photon lithography fabricated TOFT, by trapping red
blood cells and polystyrene beads.
Again, we started verifying the good focusing of the four fibers, as shown in Fig. 2.29.
Fig. 2.29: Sequence of images showing the beam focusing of the four-fibers bundle TOFT
Then we moved to the trapping of 10 μm polystyrene beads. To do so, we put the bundle end face
parallel to the microscope slide and we pushed it inside a drop of solution with dielectric particles.
After turning the laser on, we were able to trap a particle of polystyrene with all the four beams,
and, as we can see in Fig. 2.30, we were able to translate the TOFT without losing the trap.
(a) (b)
(c) (d)
(e) (f)
Fig. 2.230: Sequence of images showing a 10 μm polystyrene beads trapped by the TOFT. In a) the scattering of the trapped particle is visible. In b)-c) we apply an IR filter to the microscope and we translate the tweezers to the risght. In d)-e)-f) we
translate the tweezers in the focus plane.
Then we tested thid device with a solution of red blood cells. An example of trapping is shown in
Fig. 2.31: the cell is captured only by a couple of fiber, after that we switch to a four-fiber trap, and
finally we continue the trapping with the second couple.
(a) (b)
(c) (d)
(e) (f)
(g) (h)
(i)
Fig. 2.31: Sequence of trapping and translation of a red blood cell. The trap is performed first by the internal prisms [a-d], then by all the four fibers [], last by the external prisms [e-f]. In i) we lost the red blood cell escape the trap.
We also managed to fabricate a dual trap TOFT, cutting two couple of prisms at different angles.
With this technique we put the base for multi-trap reliable fiber optical tweezers. We tested a
device with the two focusing points distant 10 μm from each other in a 10 μm polystyrene beads
solution. In Figure 2.32 we can see the effective trapping of two beads, while in Figure 2.33 we
show a sequence of images where the polystyrene bead moves from the nearest trap to the
external trap when we switch the power of the fibers.
Fig. 2.32: Double-trap of polystyrene beads
(a) (b)
Fig. 2.33: Sequence of trapping of polystyrene bead. We start by trapping the bead with the external beams (a), that create the nearest trapping point. Then (b) we switch to the second couple and the bead change position.
As we demonstrated, this technique is very reliable. Respect to the other implementation, this one
is cheaper and the fabrication process is faster. Moreover, thanks to the external realization of the
prisms, the validation of the refraction angle is far easier and the good adhesion of the UV resin
makes this technique very stable.
CHAPTER 3 –DISCRETE ELEMENTS OPTICAL STRETCHER
This chapter is composed by two main sections; one introduces the importance of cell
mechanical properties in the biological field and the methods to measure them, the second one is
devoted to the description of the optical stretcher which has been implemented and used to
measure the elasticity of many samples.
3.1 INTRODUCTION
3.1.1 CELL MECHANICAL PROPERTIES
Cell mechanical properties are largely determined by the cytoskeleton, a polymeric network of
various filaments, which plays an important role in many cellular processes. There are three
different types of filaments that, together with their accessory proteins, collectively form the
cytoskeleton. Actin, a semi-flexible polymer that is 7-9 nm in diameter, is made of actin protein
monomers arranged in a paired helix of two protofilaments. Short actin filaments are arranged as
a three-dimensional meshwork underlying the cell membrane. In addition to networks, actin can
also form bundles such as stress fibers that are present between cell-substrate attachments.
Microtubules are rod-like polymers of ~25 nm in diameter, and are composed of 13 protofilaments
each, a linear polymer of tubulin protein subunits. They extend outward, like spokes, from the
centrosome or microtubule organizing center to the actin cortex at the cell periphery. The flexible
intermediate filaments are made of subunits of keratin, vimentin, desmin or neurofilament
protein. They have a diameter of 8 to 12 nm, which is intermediate between that of microtubules
and actin, and perform multiple roles. In one instance, they form a fibrous network that spans the
cell interior and connects the nucleus to the cell membrane.
Figure 3.1: Cartoon of filaments composing the cytoskeleton
These cytoskeletal polymer assemblies interact with themselves and with one another with the aid
of several proteins such as crosslinking-, bundling- and motor-proteins. This results in a composite
polymeric material that is the basic framework for various cellular activities. While cells also
contain nuclei and other organelles and are surrounded by the cell membrane, these structures do
not seem to contribute as much to a cell’s resistance to external forces. The cytoskeleton is not
only the main determinant of cell mechanics; it is also involved in many vital cellular processes.
Cells expend energy to regulate their biochemical environment and actively control the conditions
that lead to filament polymerization, severing, bundling, cross-linking, and sliding. In this way, the
cytoskeleton is always changing and adapting to its environment. The dynamic nature of this
system is critical for processes such as differentiation, mitosis, motility, intracellular transport,
phagocytosis, and mechanotransduction. This link between the processes mediated by a well-
regulated cytoskeleton and cellular mechanical properties can be exploited to study these
processes. Whenever a cell alters its cytoskeleton, its mechanical properties change, and this can
be monitored by appropriate techniques. Changes can be brought about by physiological
processes, by pathological perturbations, or in response to manipulations of a researcher. While
any cellular process that involves the cytoskeleton can be the target of such a study, there are
some examples that seem most promising. Among physiological processes involving the
cytoskeleton, the effects of mitosis on cell mechanics can be used to discriminate proliferating
cells from postmitotic cells. Differentiated cells will also likely have a distinct cytoskeleton from
progenitor cells, which may be identified in a heterogeneous population. Likewise, motile cells
such as activated macrophages can be discriminated from stationary or non activated cells. The
cytoskeleton can also be modified by the addition of certain drugs and chemicals or by specific
genetic modifications. Toxins such as cytochalasins, latrunculins, phalloidin, nocodazole, taxol, or
bradykinin, which disrupt or stabilize specific targets in the cytoskeleton, lead to measurable
changes in the physical properties of cells. Similarly, the influence of unknown chemicals, drugs, or
molecules and the effect of overexpression or knockout of certain genes on the cytoskeleton can
be tested by monitoring the mechanical resistance of cells. Viability tests also fall into this
category, as dead cells certainly will exhibit different mechanical properties from live cells. This
could be useful for drug-screening applications or for assessing transfection efficiencies.
There are also many well-known examples of pathological changes that affect the mechanical
properties of cells. These include cytoskeletal alterations of blood cells that cause capillary
obstructions and circulatory problems; genetic disorders of intermediate filaments that lead to
problems with skin, hair, liver, colon, and motor neuron diseases such as amyotrophic lateral
sclerosis, and various blood diseases including malaria, sickle-cell anemia, hereditary
spherocytosis, or immune hemolytic anemia. Especially well investigated is the progression of
cancer where the changes include a reduction in the amounts of constituent polymers and
accessory proteins, and restructuring of the cytoskeletal network, with a corresponding change in
cellular mechanical properties. All of these examples suggest that mechanical properties can serve
as a cell marker to investigate cellular processes, to characterize cells, and to diagnose diseases.
From polymer physics we know that the mechanical strength of a network of filaments does not
depend linearly on the constituent proteins. Indeed even small changes in molecular composition
of the cytoskeleton and its accessory proteins are dramatically amplified in cell mechanical
properties. Thus, unlike many other techniques such as Western blots, gel electrophoresis,
microarrays, or FACS analysis, the measured parameter contains a built-in amplification
mechanism. This benefit is accompanied by the ability to determine this parameter for single cells,
not on cell populations. A few altered cells can be identified in principle against the background of
many unaltered cells, leading to an excellent signal-to-noise ratio. This is especially important
when only few cells are available in the first place. In addition, the intrinsic nature of the
mechanical properties renders any sort of tagging preparation (radioactive or fluorescent labeling,
and so on) unnecessary, saving time and cost, while leaving the cells alive, intact, and ready for
further analysis or use.
3.1.2 EXPERIMENTAL TECHNIQUES FOR PROBING CELL MECHANICAL PROPERTIES
A wide variety of experimental biophysical probes have been used to extract the mechanical
properties of cells [10]10. Figures 3.2, 3.3 and 3.4 schematically show different experimental
methods used for biomechanical and biophysical probes of living cells. In particular Figure 3.2
shows: (a) atomic force microscopy (AFM), (b) magnetic twisting cytometry (MTC) and (c)
instrumented depth-sensing indentation method. In these three techniques, a portion of the cell
surface could be mechanically probed at forces on the order of 10-12÷10-6 N and displacements
smaller than 1 nm. In AFM, local deformation is induced on a cell surface through physical contact
with the sharp tip at the free end of a cantilever. The applied force is then estimated by calibrating
the deflection of the cantilever tip, which is detected by a photodiode.
MTC entails the attachment of magnetic beads to functionalized surfaces. A segment of the cell
surface is deformed by the twisting moment arising from the application of a magnetic field.
Elastic and viscoelastic properties of the cell membrane or sub-cellular components are then
extracted from the results through appropriate analysis of deformation.
Finally in the indentation test, the applied load and the depth of penetration of an indenter into
the specimen are recorded and used to determine the area of contact and hence the hardness of
the cell. The contact equation allows obtaining the determination of the elastic modulus of the
specimen.
Figure 3.2: Schematics of experimental methods used for biomechanical and biophysical probes of living cells. (a) atomic force microscopy (AFM), (b) magnetic twisting cytometry (MTC), (c) instrumented depth-sensing indentation.
Figure 3.3 shows: (d) laser/optical tweezers (OT), (e) mechanical microplate stretcher (MS), (f)
micro-postarray deformation (mPAD) with patterned microarrays that serve as cell substrates. In
10
Biomechanics and biophysics of cancer cells, Suresh
these cases, forces over the range of 10-12÷ 10-7 N can be induced on the whole cell while
submicrometer displacements are optically monitored. With OT, a laser beam is aimed at a high
refractive index dielectric bead attached to the cell. The resulting attractive force between the
bead and the laser beam pulls the bead towards the focal point of the laser trap. Two beads
specifically attached to diametrically opposite ends of a cell could be trapped by two laser beams,
thereby inducing relative displacements between them, and hence uniaxially stretching the cell to
forces of up to several hundred piconewtons. Another variation of this method involves a single
trap, with the diametrically opposite end of the cell specifically attached to a glass plate which is
displaced relative to the trapped bead.
In the microplate stretcher, displacement-controlled extensional or shear deformation is induced
between two functionalized glass plates to the surfaces of which a cell is specifically attached.
In mPAD, a patterned substrate of microfabricated, flexible cantilevers is created and a cell is
specifically tethered to the surfaces of these micro-posts. Deflection of these tiny cantilevers due
to focal adhesions can then be used to calibrate the force of adhesion. Other patterns, such as
discs and spherical islands, can also be created using micro and nano-fabrication techniques to
design different substrate geometries.
Figure 3.3: Schematics of experimental methods used for biomechanical and biophysical probes of living cells. (d) laser/optical tweezers (OT), (e) mechanical microplate stretcher (MS), (f) micro-postarray deformation (mPAD).
Finally Figure3.4 shows three others techniques: (g) micropipette aspiration (MA), (h) shear flow
technique and (i) substrate stretcher. In MA, a portion of a cell or the whole cell is aspirated
through a micropipette by applying suction. Observations of geometry changes along with
appropriate analysis then provide the elastic and viscoelastic responses of the cell, usually by
neglecting friction between the cell surface and the inside walls of the micropipette.
Figure 3.4(h) instead shows a method where the biomechanical response of populations of cells
could be extracted by monitoring the shear resistance of cells to fluid flow. Shear flow
experiments involving laminar or turbulent flows are also commonly performed using a cone-and-
plate viscometer consisting of a stationary flat plate and a rotating inverted cone. Alternatively,
cells could be subjected to forces from laminar flow in a parallel plate flow chamber.
The mechanics of cell spreading, deformation and migration in response to imposed deformation
on compliant polymeric substrates to which the cells are attached through focal adhesion
complexes is illustrated schematically in Figure 3.4(i). With this technique a cell injury controller
exerts a rapid positive pressure of known amplitude and duration on the substrate. The
deformation of the silastic membrane, and thus the stretch of the cells growing on the membrane,
is proportional to the amplitude and duration of the air pressure pulse.
Figure 3.4: Schematics of experimental methods used for biomechanical and biophysical probes of living cells. (g) micropipette aspiration (MA), (h) shear flow technique and (i) substrate stretcher technique.
3.1.3 OPTICAL STRETCHER WORKING PRINCIPLE
The configuration of dual-beam optical trap described in Chapter 1 is particularly interesting in the
biological field because it allows either trapping in a stable and simple way any micro-particles
under test, or measuring cells mechanical properties with high precision, thanks to the possibility
of applying high forces in a controlled manner. To understand the origin of the forces that deform
the trapped cells we can rely on the dual beam theory already discussed in Chapter 1. To simplify
the trapping theory in the ray optics approach (2πr/λ<<1) we suppose that each portion of the
particle surface appears as flat to the incident beams, so that we can approximate the cell with a
square box with a refractive index n2 higher than that of the surrounding medium n1. If we
consider a single Gaussian beam incident on the surface, it will carry a momentum p = n1 E/c,
where E is the energy of the beam (Minkowski form).The beam momentum is proportional to the
refractive index, so it will increase while entering in the cell. We have to consider that some light is
always reflected at the interface, so we have
(22)
where R is the reflection coefficient at normal incidence. Anyway since cells are almost
transparent, the reflection is almost negligible. The momentum variation gives rise to a force that
tends to accelerate photons and, for Newton third law, this force is balanced by a mechanical
force acting on the surface of the cell in the opposite direction, and proportional to Δp:
(23)
Figure 3.5: Schematics of the forces exerted by a single beam on the surface of a particle.
At the second interface, as sketched in Figure 3.5, the photon exiting the particle will experience a
decrease in the momentum hence the force arising on the surface cell will be directed along the
propagation direction of the beam. In conclusion, when the beam passes through the particle
surfaces, it stems two forces acting on those interfaces in the direction opposite to the
momentum increment, thus pulling the two surfaces outwards.
The second beam, entering the particle from the right as in Figure 3.6, will generate the same
force contributes on the surfaces. So, by increasing power, the particle stretches.
Figure 3.6: Schematics of the forces in an optical stretcher.
Whereas we consider spherical particles instead of cube, we obtain a stress profile like that shown in Figure 3.7.
Figure 3.7: Stress profile of a spherical particle trapped in a dual beam laser
The stress profile shown in Figure 3.7 is anyway an approximated result, given by the analytic
function in the form: () = 0 cos2(), which has been used by Guck et al. in [11]11. In this
approximation multiple reflections inside the particle have been disregarded. In literature there
are more accurate approaches that define the stress profile.
In his paper Chiu [12]12 used a Ray optics (RO) approach to calculate the deforming stress acting
on the surface of a cell trapped by an optical stretcher. The cells studied can be well approximated
by non absorbing spheres with an isotropic index of refraction. Cells are almost transparent in the
near infrared, so absorption can be neglected. The focusing power of the spherical cell
concentrates the refracted rays to a smaller area on the second interface, resulting in peaks on the
stress distribution around certain angular positions, as shown in Figure 3.8.
Figure 3.8: Stress profile σ in Chiou approach at different distances D between the laser source and the particle [12].
11
Stretching biological cells with light, Guck 2002
12 Local stress distribution on the surface of a spherical cell in an optical stretcher, Chiou 2006
A different approach has been proposed by Boyde et al. [13]13. They determine the
electromagnetic fields for the incidence of a monochromatic laser beam on a near-spherical
dielectric particle with a complex refractive index. The perturbation approach to solve Maxwell’s
equations in spherical coordinates employs two alternative techniques to match the boundary
conditions: an analytic approach for small particles with low eccentricity and an adapted point-
matching method for larger spheroids with higher aspect ratios. The results obtained through
these calculations are shown in Figure 3.9.
Figure 3.9: Time-averaged radial stresses for a spheroid in aqueous solution trapped in a double-beam laser. The laser cell distances are z0=±60 μm (left), z0= ±120 μm (middle), and z0 = ±200 μm (right).
A further approach has been proposed by Nichols, [14]14. It extends the ray-optics model by
considering the focusing by the spherical interface and the effects of multiple internal reflections.
Simulation results for red-blood cells (RBCs) show that internal reflections can lead to significant
perturbation of the deformation, leading to a systematic error in the determination of cellular
elasticity
13 Interaction of Gaussian beam with near-spherical particle: an analytic-numerical approach for assessing scattering
and stresses, Boyde 2009
14 Determination of cell elasticity through hybrid ray optics and continuum mechanics modeling of cell deformation in
the optical stretcher, Nichols 2009
Figure 3.9: Calculated stress distributions on a 10 μm diameter sphere trapped in an optical stretcher with a fiber separation of
200 μm. The cosine-squared approximation (dotted line) is compared to the RO model (solid line) (a) ignoring or (b) allowing for multiple internal reflections.
In his paper Nichols concludes that the cosine squared angular dependence of the optical stress
acting on the surface of a spherical cell can be a valid approximation to the RO stress distribution if
the fiber separation is carefully chosen according to the cell radius. But this approximation also
does not account for beam focusing and internal reflections that will occur within the cell that lead
to regions of high optical. The inclusion of internal reflections significantly alters and reduces the
range of fiber separations that would need to be selected, giving an important indication for the
realization of the experiments.
3.2 EXPERIMENTAL SETUP
This section is devoted to the description of the optical stretcher apparatus developed during the
research activity and results obtained in the characterization of the cell elasticity.
3.2.1 OPTICAL PART
The setup used to trap and stretch the cells in the dual-beam configuration in schematically shown
in Figure 3.10, particularly for what concern the optical part of the apparatus.
Figure 3.10: Scheme of the experimental apparatus of the implemented optical stretcher.
An Ytterbium–doped fiber laser at a wavelength λ=1070 nm is used as source. This choice is due to
the absorption spectrum of biological sample. As we can see in Figure 3.11, the window between
700 and 1100 nm presents low absorption coefficient. For higher wavelength there is a higher
absorption of water, while for lower wavelength we have high absorption of melanin and
hemoglobin.
Fig. 3.11:Absorption spectra of cells main components
The use of a near infrared laser beam helps in avoiding the heating of the trapped cell, thus
lowering the death probability.
The beam from the laser propagates through an optical insulator, which has been introduce to
block the back reflections, and is then split into two paths by an optical coupler 50%/50%. It must
be noticed that the power isn’t divided exactly in two, so we provided each path with a variable
optical attenuator. In this way we can introduce bending power losses in order to have the same
final power at the fibers tips. After the VOAs we put a couple of couplers 99%/1%; the 1% port of
the first one provides a monitor that gives information about the optical power travelling in that
branch, while the 1% port of the second monitor serves to check for the coupling between the two
fibers, providing information about their alignment. Finally, the tips of the fibers are put on two
sleighs and translated with a couple of 3-axys micromanipulators.
3.2.2 FLUIDIC PART
The second part of the setup is the fluidic part that is used to deliver the cell suspension in the
region where the two fibers are facing.
The microfuidic system is observed with an inverted phase contrast microscope, which is very
useful in biological applications because it enhances the small difference between the refractive
index of water and cells; indeed with a bright field microscope it’s not possible to see the cells. The
images are captured by mean of a CCD camera Stingray for b/w pictures or Nikon for RBG images.
DROP CONFIGURATION
The first implementation of the fluidic part of the optical stretcher was very simple. It consisted in
two counter propagating optical fibers having the tip inserted in a drop of solution containing the
particles we wanted to analyze. Each fiber was stably put in a V-groove on an aluminum sleigh
translated by a 3-axis micromanipulator.
Figure 3.12: Sketch of the drop configuration fluidic apparatus
With this setup we have been able to trap many kinds of microparticles, either biological (stem
cells, red blood cells, yeast) or non-biological (polystyrene beads, liquid crystals), as shown in
Figure 3.13.
(a) (b)
(c) (d)
Figure 3.12: Examples of trapped samples. a) Polystyrene beads, b) liquid crystal cell, c) red blood cell, d) yeast organisms.
Anyway it has not been possible to obtain a fine stretching. The reasons are many. First there’s the
very interaction between fibers and the solution. A lot of particles tend to attach to the tip of the
fibers, with a consequent loss of power. Moreover the translation of a fiber stems pressure forces
that move the liquid, making it very challenging to trap a particle. The 3-axys micromanipulator
offers 3 controlled way of freedom, but nothing can be done with rotations and we lacked a
guiding structure in order to solve rotation misalignment of the fibers. Water turbulence also
makes the system unstable, creating small oscillations of the fibers tip and making difficult to
follow the particles. Finally the flow cannot be controlled, so it happens that more than one
particle get trapped between the two fibers, preventing us from having stretching. This setup was
nevertheless very useful in force measurement, as described in Appendix C.
CAPILLARY-AIDED CONFIGURATION
In order to get rid of some of the problems showed by the first configuration, we realized a second
implementation, following the idea of optical tweezers suggested by Constable [15]15. Our goal
was to provide a guiding capillary for the optical fibers, to make an automatic alignment. The
scheme is showed in Figure 3.14. On a microscope slide we glued a big glass capillary, forming a
smooth water-tight seal. Then we pushed two pieces of smaller capillaries along the previous one,
providing a little gap for the solution drop. Finally we aligned the fibers pressing them against the
couple of smaller capillaries, which formed a backstop for the fibers and provided a V groove in
which they sat. This way we achieved a good alignment and we reduced the water motility thanks
to the barrage of the capillary.
Figure 3.14: Sketch of the capillary-aided configuration fluidic apparatus.
15
Demonstration of a fiber-optical light-force trap-Constable(1993)
Unfortunately also this configuration showed some problems. First of all, the capillaries weren’t
always well aligned and, because of the bending of the fibers, we couldn’t modify the alignment
with micromanipulators. We lacked the translations of the fibers, so we couldn’t follow the
particles, we could only wait for the particles to approach the trapping area and try to remove
other approaching particles. Like the previous setup we had problems with the dirt attached to the
fiber-ends, which was now enhanced by the contact between fibers and microscope slide. In fact
the particles suspended in the solution gradually settled on the glass, creating a layer of dirt that
prevented from having a good trapping and a clear imaging (Fig. [3.15]).
Fig. 3.15: Trapped polystyrene beads in capillary-aided configuration. The dirt prevents from good imaging and trapping
MICROFLUIDIC CHANNEL CONFIGURATION
The last implementation got rid of all the problems of the setups described. In order to obtain a
microfluidic circuit to deliver the cells between the two fibers, but without inserting the fibers in
the solution we followed the scheme suggested in [16]16. We took a glass square capillary with an
16
The Optical Stretcher-A Novel Laser Tool to Micromanipulate Cells-Guck(2001)
internal and external dimension of 80 m and 160 m respectively and we glued it inside a couple
of round capillary with internal and external diameters of 200 and 350 m respectively. Each
capillary is inserted and glued in two butterfly needles, which are in turn glued to a couple of
microscope slides. The two slides are connected with a couple of smaller glass rectangular
capillaries, in order to have the square one suspended. A scheme and a picture of the final
microfluidic circuit is shown in Figure 3.16.
(a) (b)
Figure 3.16: (a) Scheme and (b) picture of the microfluidic circuit configuration.
The solution is then inserted in a butterfly needle with a syringe and it is pushed along the
microfluidic system until it reaches the other end. There are many advantages respect to the
previous implementation.
Figure 3.17: Schemeof the flow control
The optical and fluidic parts are separated, thus preventing the problem of dirt deposition
on the fiber tip
The flow is totally controllable, as sketched in Figure 3.17, so that we can get rid of inertial
motion and we can achieve only one trapping at a time
The inside of the microchannel can be cleaned, thus it is reusable
The fibers facing the square capillary are aligned with a couple of 3-axys micromanipulators
and the rotational misalignment can be corrected pushing the fibers until the tip touches
the capillary surface.
The flat interfaces between fibers, air, glass and water reduce power losses and beam
deflections. Thanks to the flow control we can trap, stretch and release one cell at a time
3.3. EXPERIMENTAL RESULTS
In this chapter the experimental results obtained through the microfluidic channel configuration of
the optical stretcher are reported so as the automatic method used to analyze them.
3.3.1 RESULTS ANALYSIS
In order to get information about the elongation of the cells we need a software able to analyze
the pictures taken with the CCD [Fig. 3.18] and describe the edges of the trapped particles. For this
purpose we wrote some Matlab programs, each one with a specific task.
Fig. 3.18: Image of a trapped red blood cell acquired with a CCD camera
a) Croppa_figure.m
This program loads the CCD images and asks the user to define a cropping area, in order to
shrink the size of the picture [Fig. 3.19]. This helps the following analysis, reducing the
elaboration time and deleting external elements that interfere with the elasticity
measurement.
Fig. 3.19: cropped image of a swollen red blood cell
b) Analisi_multipla.m
Once the images are cropped around the cell, this program convert them into grayscale and
exalt the contrast. Then it asks the user to point at the center of the cell and it convert the
image in polar coordinates. At this point the image looks as in Fig 3.20
Fig. 3.20: Image of a red blood cell in polar coordinates
Now the white annulus representing the border of the cell is stretched along the x axis. The
program then asks the operator to define the area in which the border is, so the user indicates a
point over the white layer and a point below it. The image is then filtered with a threshold and
“derivate” in order to enhance the intensity gaps. Then the program finds the middle point in the
white string for each column of the figure and defines a rough profile; applying an inverse Fourier
transform to this line we are able to extract the dominant frequencies of the original data [Fig.
3.21a] , thus obtaining a smooth profile [Fig. 3.21b].
(a) (b)
Fig. 3.21: a) dominant frequencies and b) profile of the trapped cell
The information about the x and y dimension of each cell are saved in a txt file
c) Risultati_totali.m
The last program loads each files txt and put all the information in an excel file. This way we
get a sheet for the x and y dimension and for the ratio between the two dimensions of each
cell for increasing power. Scheming the ratio x/y related to the increasing power P give the
information of the cell stretching.
In order to evaluate the mechanical response of the cytoskeleton, we use two different
approaches.
a) Step
With a LabView program we set a laser power sufficient to trap the sample under test.
Then we abruptly switch the laser power to a power high enough to deform the cell and
with the same program we drive the CCD camera to acquire images of the trapped cells
every 500 μs. We expect a deformation profile as schemed in Fig. 3.22: a high slope for few
seconds after the power change, then a slow excursion till the higher deformation. This
technique is useful to measure the response time of the cell to the stress.
Fig. 3.22: example of a deformation profile for a step-stretching
b) Ramp
With another LabView program we set the initial laser power at a level sufficient for
trapping. Then we slowly increase the power at regular step, taking a snapshot of the cell
at every step until we reach a defined maximum value, high enough to have a sensible
deformation without damaging the cell. Then we decrease the power level in the same
manner. We expect a behavior like that schemed in Fig. 3.23. This measure is useful to
measure the elasticity of the cell and to verify the viscoelastic behaviour of the
deformation.
(a) (b)
Fig 3.23: example of a) x-elongation and b) x/y ratio of a cell under ramp-stretching
Not all the measurements are good for the elasticity measurement, so we have to get rid of the
cells with an unexpected behavior. In fact some cells rotate when the stress is applied, or they
6,5
7
7,5
8
10 100 190 280 370 280 190 100 10
RB
C X
dim
en
sio
n [
μm
]
Optical power at fiber end [mW]
X elongation
0,951
1,051,1
1,151,2
1,25
10 100 190 280 370 280 190 100 10
x/y
rati
o
Optical power at fiber end [mW]
x/y ratio
move vertically and change their focal plane as they become stretched. This slight change of focus
can cause an apparent shift in the measured axial length and is often avoidable by increasing the
trap power slightly. While rotations can usually be eliminated by good flow control, their effect on
the strain curves is indistinguishable from an active behavior of the cells. Data can be improved
further by removing cells whose response does not conform to a true passive viscoelastic
deformation. First we can remove cells that don’t respond to the applied stress. Further selectivity
can be achieved by removing cells where the rate of deformation becomes negative while the
stress is still being applied, and where the cell does not relax back after the stress has been
reduced. These abnormal responses are likely caused by reorientation of the cell relative to the
trap in addition to the deformation itself. Removing these cells from the analysis lead to a reduced
ensemble of viscoelastically deforming cells. These cells are the ideal candidates to be individually
fit in order to obtain physical values useful to describe their mechanical properties.
Fig. 3.23: ideal and unexpected behaviour of cells to applied stress
We applied the stretching technique to different cells; in this work we show the results of the
analysis of red blood cells and tumor cells.
3.3.2 EXPERIMENTAL RESULTS ON RED BLOOD CELLS
9,50E-01
9,70E-01
9,90E-01
1,01E+00
1,03E+00
1,05E+00
1,07E+00
1,09E+00
1,11E+00
1,13E+00
1,15E+00
10 55 100 145 190 235 280 325 370 325 280 235 190 145 100 55 10
x/y
rati
o
Optical Power at fiber end [mW]
Cells responses
Ideal curve
movement
no stretch
anelastic
Red blood cells are the simplest cells to analyze, thanks to their lack of organelles and internal
nuclei. Red blood cells appear in the resting state with a biconcave shape; this is the minimum
energy state. But the RBCs constantly change their shapes as they’re subjected to a range of fluid
forces in the circulation, as in the capillaries, where they fold along a longitudinal axis assuming an
asymmetrical shape. This asymmetrical shape is maintained thanks to continuous movement of
the membrane around the cytoplasm. Thus the RBC spends little of its time in discoid shape in the
microcirculation. In addition, a wide variety of chemical perturbations induce shape changes, as
the low concentration of fatty acids, modest changes of pH, decrement in ATP and more. In
particular we’ve analyzed the cytoskeleton change in red blood cells affected by three kind of
diseases, in order to exploit the differences between healthy and diseased cells and create the
basis for early diagnostic tests.
DIABETES MELLITUS
We tested the potential of the stretching technique in biological field collaborating first with the
Dipartimento di Medicina interna, Istituto di cura Santa Margherita in Pavia, in order to analyze
the red blood cells of geriatric patient affected by diabetes mellitus type 2; this is a metabolic
disorder that is characterized by high blood glucose in the context of insulin resistance and relative
insulin deficiency. Among the hemorheologic changes in the blood samples, there is an increment
of the aggregation and viscosity, probably due to a decrement in the membrane elasticity. These
conditions prevent the erythrocytes from adapt its shape in order to reach the smaller capillaries,
thus determining the occurrence of complications. The goal of this collaboration was verifying the
relation between the elasticity of the red blood cells and the status of diabetes, applying the
stretching technique to healthy and diabetic patients.
The RBCs were diluted in a hypotonic solution in order to swollen their shapes to simplify the
elasticity analysis. Each blood sample was composed of 10 μl of blood, 4 ml of distilled water, 4 ml
of physiological solution, then we added calcium albumin and glucose to provide nourish to the
cells and heparin to prevent the cells from attaching to the capillaries walls. The final
concentration was 50000 cells in a ml solution. Adding distilled water brings to a swollen cell, but
this stress can break the RBC membrane, so that part of the Hb exits from the cell. This cause a
change in the RBC refraction index, and the cell appears black with a phase contrast microscope
[Fig. 3.24 c]. In our measurement we analyze only the healthy ones.
(a) (b) (c)
Fig. 3.24:a) Biconcave red blood cell in isotonic solution. b)Swollen RBC in hypotonic solution. c) Ghost RBC
We analyzed the blood samples of 10 diabetic geriatric patients and 10 healthy geriatric patients.
For each one we trapped and stretched 50 red blood cells, in order to get a good statistic of
elongation. Each cell was stressed with a ramp approach with an optical power at fiber ends
increasing from 10 to 370 mW, then decreasing back to 10 mW . The pictures were analyzed with
a MatLab software in order to get information about the x and y dimensions and their ratio. These
results were averaged over all the red blood cells measured for each patient.
Then we averaged the results over all the patients in the same group and we compared the two
groups. As shown in Fig. 3.25 it is clear that healthy RBCs are more elastic than diabetic ones, thus
contributing to the circulation complications.
1,00
1,05
1,10
1,15
1,20
1,25
1,30
1,35
x/y
ra
tio
Optical power at fiber end [mW]
diabetic
healthy
Fig. 3.25: comparison in the deformation of healthy (white lines) and diabetic (blue lines) red blood cells
HHT E SDS
We collaborated with the Dipartimento di Patologie Umane Ereditarie in Pavia to analyze the
behaviour of red blood cells affected by two kind of ereditary diseases that can bring the patient
to develop anemia. These pathologies are the Hereditary Hemorrhagic Telangiectasia (HHT) and
the Shwachman-Diamond Syndrome (SDS). HHT is a genetic disorder that leads to abnormal blood
vessel formation in the skin, mucous membranes, and often in organs such as the lungs, liver and
brain. It may lead to nosebleeds, acute and chronic digestive tract bleeding, and various problems
due to the involvement of other organs. These lesions may bleed intermittently, which is rarely
significant enough to be noticed but eventually leads to depletion of iron in the body, resulting in
iron-deficiency anemia. SDS is a rare congenital disorder characterized by exocrine pancreatic
insufficiency, bone marrow dysfunction, skeletal abnormalities, and short stature. The most
common haematological finding, neutropenia, may be intermittent or persistent and the low
neutrophil counts leave patients at risk of developing severe recurrent infections that may be life-
threatening. Anemia and thrombocytopenia may also occur. Bone marrow is typically hypocellular,
with maturation arrest in the myeloid lineages that give rise to neutrophils, macrophages,
platelets and red blood cells. Patients may also develop progressive marrow failure or transform
to acute myelogenous leukemia.
Basically, both diseases can develop anemia, but for different processes. HHT causes a continuous
production of red blood cells in response to the frequent bleeding, so we assume that they’re
“younger” than the cells of a healthy patient. SDS lowers the generation of red blood cells, thus
they will be “older” than those of a healthy patient. We verified this supposition comparing the
elasticity of healthy and diseased red blood cells.
We prepared the same solution indicated in the diabetes experiment and we used the ramp
technique to evaluate the deformation and the viscoelasticity of the samples. This work is
currently under progress, but the earlier results are reassuring: as we can see in FIg. 3.25, the
deformation curve of HHT patients is higher than the SDS, indicating that older cells are stiffer and
demonstrating that we can distinguish the cells from each group.
Fig. 3.25 HHT and SDS Deformation
3.3.3 EXPERIMENTAL RESULTS ON CANCER CELLS
The effectiveness of the optical stretcher as a marker for biological investigation and disease
diagnosis has been demonstrated by Guck and Kas in their study of tumoral cells17 [17]. During the
cell’s progression from a fully mature, postmitotic state to a replicating, motile, and immortal
cancerous cell, the cytoskeleton devolves from a rather ordered and rigid structure to a more
irregular and compliant state. The changes include a reduction in the amount of constituent
polymers and accessory proteins and a restructuring of the available network. These cytoskeletal
alterations are evident because malignant cells are marked by replication and motility, both of
which are inconsistent with a rigid cytoskeleton. Taken together, these changes in cytoskeletal
content and structure are reflected in the overall mechanical properties of the cell as well. Thus,
measuring a cell’s rigidity provides information about its state and may be viewed as a new
biological marker. We are collaborating with two medical groups for the analysis of tumoral cells:
the CNR of Pavia for the study of fibroblasts and the IIT of Genova for the analysis of lymphocytes.
LYMPHOCYTES
We’ve conduct experiments on three mutations of lymphocytes, analyzing their deformation
under a step-stretching. The cells lines were IM9, K562 and JURKAT.
IM9 [Fig. 3.26] is a lymphocytes mutation caused by multiple myeloma, a cancer of plasma cells.
They cause bone lesions and they interfere with the production of normal blood cells in the bone
marrow . Most cases of myeloma also feature the production of a paraprotein, an abnormal
antibody that can cause kidney problems and interferes with the production of normal antibodies
leading to immunodeficiency.
17
Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence-
Guck(2005)
Fig. 3.26: IM9 cell
K-562 [Fig. 3.27] is an erythroleukemia cell line derived from a chronic myeloid leukemia patient in
blast crisis. Recent studies have shown the K562 blasts are multipotential, hematopoietic malignant
cells that spontaneously differentiate into recognisable progenitors of the erythrocyte, granulocyte
and monocytic series. K562 cells were the first human immortalised myelogenous leukaemia line to
be established. The cells are non-adherent and rounded, are positive for the bcr:abl fusion gene and
bear some proteomic resemblance to both undifferentiated granulocytes and erythrocytes.
Fig. 3.27: K562 cell
Jurkat cells [Fig. 3.28] are an immortalized line of T lymphocyte cells that are used to study acute
T cell leukemia, T cell signaling, and the expression of various chemokine receptors susceptible to
viral entry, particularly HIV. Their primary use is to determine the mechanism of differential
susceptibility of cancers to drugs and radiation.
Fig. 3.28: Jurjat cell
We’ve performed a step-stretching of the three kind of cell starting from an initial fiber power of
35 mW and switching to 405 mW. The results are shown in the following figures.
Fig. 3.29: Elongation along the x-axis of IM9 cells in a step-stretching
We can see that the curve arrives at a regime value after 3 seconds. From the analysis we verified
the fragility of these cells, in fact many cells break the membrane during the stretching process.
Their dimensions are also very variable, they can measure from 9 to 20 μm in diameter.
Fig. 3.30: Elongation along the x-axis of K562 cells in a step-stretching
k562 cells are more stable and resistant to stretching and thir dimension is more omogeneous,
going from 13 to 18 μm. They also take 3 seconds to reach full elongation.
Jurkat cells are the most resistant and the ones with a more homogenous shape. They reach the
full elongation in 3 seconds and they vary from 10 to 15 μm.
CHAPTER 4 – INTEGRATED OPTICAL STRETCHER
4.1 STRUCTURE OF AN INTEGRATED OPTICAL STRETCHER
4.1.1 DESIGN
Although the effectiveness of the OS has been widely demonstrated, the typical set-up, based on
assembling optical fibers with glass capillaries or PDMS microchannels, presents some criticality
mainly due to the fine and stable alignment required between discrete optical and microfluidic
components. Thus the idea of developing an optical stretcher integrated on a chip made of fused
silica. The lab-on-chip approach offers many advantages; it provides devices with very small
dimensions, low cost and high reproducibility and it integrates microfluidic and optical functions
onto a single chip.
A previous work [18]18 reported on the realization of a GaAs/AlGaAs chip for the fabrication of
integrated traps exploiting a dual beam scheme. The chip, including both laser sources and
microfluidic channel, has a quite complex fabrication procedure. Although efficient trapping was
obtained, it should be noted that the use of semiconductor integrated lasers could reduce the chip
flexibility due to the limited power available, the poor spatial quality of the optical beams and the
insurgence of heating effects. In addition, the chip substrate is not transparent to visible light, thus
preventing straightforward imaging of trapped cells obtainable through an optical transmission
microscope.
Fig. 4.1: Concept diagram showing basic implementation of Dholakia’s integrated optical stretcher
Recently, femtosecond lasers have been demonstrated to be valuable tools for micromachining of
transparent materials; differently from standard fabrication technologies this innovative
18 S. Cran-McGreehin, T. F. Krauss, and K. Dholakia, “Integrated monolithic optical manipulation,” Lab Chip 6(9), 1122–1124 (2006).
technique, if combined with chemical etching, is able to provide direct writing of both optical
waveguides and microfluidic channels, ensuring extreme flexibility and accuracy, together with
intrinsic three-dimensional capabilities. The use of femtosecond lasers for micromachining of
optofluidic devices has already proved to be successful in several bio-photonic applications.
Fig. 4.2: scheme of an integrated optical stretcher on a fused silica chip
The integrated chip is based on a fused silica glass substrate, thus providing high transparency for
cell imaging, and represents a significant improvement in terms of stability, robustness and optical
damage threshold over existing optical cell stretchers. Optical trapping and manipulation of red
blood cells (RBCs) in the optofluidic chip are obtained by means of two counter-propagating
beams coming from two integrated optical waveguides orthogonal to the microfluidic channel.
The delivery of the cell suspension to the trapping region is accomplished by an easy connection of
the microchannel to an external fluidic circuit, which guarantees a controlled flow and a high-
throughput analysis. A fiber laser source is butt coupled to the waveguides in the chip, delivering
the light required for the trapping and stretching of cells. Since glass absorption in the wavelength
range adopted in the experiments (near infrared) is very low, the high powers needed for optical
stretching can be easily coupled without heating appreciably the chip. Moreover, the high spatial
quality of the trapping beams is guaranteed by the waveguide spatial mode distribution.
The device we propose is user-friendly and reliable as it doesn’t require any critical alignment
between discrete optical and fluidic elements. In addition, it allows very stable and reproducible
operation, which is a very important asset when quantitative analysis of the cell deformability is
required.
4.1.2 SIMULATIONS
In order to optimize the performance of the IOS we first perform a careful design through
numerical simulations. The design variables are the distance between the waveguide end-faces
and the waveguide mode size, which are in principle dependent on the size of the cells under test.
In our monolithic approach such parameters are fixed once the chip is fabricated, and they must
be defined in advance taking into account the target application of the device. The numerical
analysis of trapping efficiency is based on the beam decomposition approach. The spatial
distribution of the optical field is obtained by assuming that each waveguide emits a Gaussian
beam that propagates according to paraxial approximation. Afterwards, the beams are
decomposed into a set of optical rays that are defined at each propagation step along the beam
propagation axis. The amplitude and the wave-front curvature of the Gaussian beams are used to
assess the optical power associated to each ray and their propagation direction. Once the optical
field at each position is known, the optical force exerted on a particle is calculated as the sum of
the scattering and the gradient components of each ray. The total optical force distribution is then
computed by summing all the contributions due to the two beams. As already introduced in
Chapter 2, the effectiveness of an optical trap is evaluated through the escape energy εesc, defined
as the minimum energy needed by a particle to escape the trap, starting from its center. In order
to find the value of εesc for a specific trap, we first calculate the work (εTP, work per power unit)
that has to be done against the optical forces to move a particle along a straight line connecting
the centre of the trap to any possible target point in the surrounding space. Once the εTP
distribution is known, one can determine the path energetically most favorable. The energy
needed to escape the trap following such a path corresponds to εesc. Such a parameter can be
adopted as a straightforward figure of merit to compare the effectiveness of a specific trap
configuration. The most stable configuration will exhibit the maximum value of εesc.
We numerically optimize the device parameters by considering the trapping of spherical particles
with a radius Rp = 3.5 mm and refractive index nP = 1.38, surrounded by a medium with refractive
index nM = 1.33. We will consider red blood cells (RBCs) in hypotonic solution as experimental
target samples. Indeed in such a situation the cells tend to swell, loosing their typical disk-like
shape and becoming more similar to a sphere. The beam waist at the working wavelength of 1070
nm is initially set at w = 4 mm that is a value easily attainable through the fs-laser writing
technology. Figure 4.3 reports the distribution of εTP of a specific dual beam optical trap obtained
considering a distance L between the waveguide end-faces equal to 150 mm.
Fig. 4.3: a) Basic scheme of the optofluidic chip: the two waveguides emit counter-propagating Gaussian beams. The sample under test flows into the microchannel. L is the distance between the two waveguide end-faces; Δy indicates possible
misalignment between the waveguide axes. b) Plot of the work per power unit εTP produced by the dual beam trap. The beams
(w = 4 mm) are emitted by two waveguides characterized by L = 150 mm; εTP is expressed in fJ/W.
We note that a deviation of RBC shape from a sphere-like particle could lead to a slightly reduced
value of the trapping stiffness. The two beams propagate along the z-axis and a perfect alignment
of the two beams in the transversal direction is considered, i.e. the axes of both beams are at y =
0. As expected, εTP behaves like a smooth potential well where the stable trapping position lies in
the midpoint (z = 0) along the beam axis. Figure 4.4 reports the value of the escape energy εesc
calculated for each trapping configuration obtained by changing the distance L and the transversal
waveguide misalignment Δy.
Figure 4.4: Contour plot of the escape energy εesc expressed in fJ/W as a function of the transversal misalignment Δy and the
distance L between the waveguide end-faces.
It can be easily observed that the most stable trap, corresponding to the maximum εesc, is
obtained for L = 148 mm and Δy = 0. It is worth noting that for L < 100 mm and L > 250 mm the
value of εesc becomes considerably lower and the trap cannot be considered as stable. The wide
range of stable trapping is consistent with the fact that the optical beams are not focused and the
trapping condition is obtained through the counterbalancing of the beams scattering components.
On the other hand Figure 4.4 underlines that a transversal misalignment of Δy ≈ 1 mm already
leads to a sensible variation of the trapping stiffness. The fs-laser writing fabrication procedure
guarantees accuracy in the waveguides transversal position of the order of 100 nm thus
preventing any criticality due to such misalignment. From the results shown in Figure 4.4 it is clear
that the use of an integrated chip, where L is fixed and Δy is negligible, allows improving the
reliability and the efficiency of the device.
It is important to point out that the trap characteristics are dependent also on the mode size w.
Anyway we found that variations of the beam waist by an amount δw = ±1 mm do not affect
significantly the trapping stiffness. On the contrary, the trapping efficiency is strongly dependent
on the size of the particle under test. Figure 4.5 shows εesc for several values of Rp, while keeping w
= 4 mm. It is interesting to notice that εesc presents a marked peak in correspondence of a precise
value of the distance L. This behavior can be explained considering that the force applied by a
Gaussian beam along the propagation axis is not a monotonic function of the distance from the
waist, but it has a maximum value at a position depending on the beam waist and on the particle
size. From Figure 4.5 it is quite clear that once all the IOS parameters are fixed, a variation of the
particle size can lead to a significant variation of the trapping conditions. For this reason different
parameters should be chosen according to the size of the particles that have to be trapped in each
specific application. The IOS approach is however particularly versatile; in fact, different optical
traps can be monolithically fabricated across the same microchannel with different L values and
this increases the range of particles that can be efficiently trapped in the same device.
Fig. 4.5: εesc as a function of the distance L between the waveguide end-faces for three different values of the radius of the
particle under test.
Nevertheless, considering a single waveguides pair, the analysis reported in Figure 4.5 allows
choosing the set-up configuration that minimizes the effects of polydispersity that is very common
in biological samples. In the case of RBCs the radius typically varies from 3 mm to 4 mm;
consequently, the optimum distance between the waveguides should vary between 120 mm and
180 mm. The configuration with L = 149 mm, that is the optimum for particle with Rp = 3.5 mm,
guarantees the most efficient and uniform trap performance for all the RBCs under test.
4.1.3 FABRICATION
The critical parameters in the fabrication of the device are the microchannel diameter, the
waveguide mode size and the optical distance between the waveguide end-faces. For the
microchannel diameter a value of about 100 μm is chosen, since the capillaries used in the fiber-
based OS have an internal dimension of the same order; the distance between the waveguide end-
faces should range between 200 μm and 400 μm; the target mode size for the waveguides is set to
3.5 μm radius in order to match the fiber single mode at 1.07 μm wavelength. Indeed, in the
trapping and stretching experiments a laser wavelength of λ ≈1 μm is chosen due to the following
reasons: i) availability of compact fiber lasers with average power sufficient to achieve trapping
and stretching of cells; ii) very low absorption of glass and cells; iii) possibility to filter out the laser
light used for trapping, keeping the full spectrum of visible light for the cell imaging.
For the fabrication of the integrated optical stretcher we used a FLICE technique, that is
Femtosecond laser irradiation followed by chemical etching; it is a powerful technique able to
directly fabricate buried microchannels and waveguides and to create large access holes on the
side facets of the chip in order to achieve easy connection with external capillary tubes. The
schematic of the set-up used for femtosecond irradiation of the sample is reported in Fig. 4.6.
Fig. 4.6: Scheme of the experimental set-up for laser micromachining. The femtosecond laser power is controlled by a halfwave plate (λ/2 WP) and a Glan Thomson polarizer (GT POL). Second harmonic generation (SHG) is performed and the laser beam is
steered by mirrors (M) to a microscope objective (OB) that focuses the fs-pulses inside the glass substrate, mounted on a computer-controlled 3D motion stage.
We use the second harmonic (515 nm) of a cavity-dumped Yb:KYW oscillator providing 350-fs laser
pulses at repetition rates up to 1 MHz. The laser beam is focused by a microscope objective inside
the sample; the latter is translated by a computer-controlled motion stage. The glass is
transparent for the used wavelength; however the high peak intensity achieved by focusing the
femtosecond laser pulses induces a nonlinear absorption mechanism consisting of a combination
of multiphoton absorption and avalanche ionization. The occurrence of this phenomenon is
experimentally indicated by the emission of white light from the electron plasma generated at the
laser focus. A first consequence of the irradiation of the nanostructured glass is a slight darkening
of the glass color in the modified region. This is consistent with a red shift of the absorption
spectra of the glass, corresponding to a refractive index variation through a Kramers-Kronig
mechanism. Moreover we have an increase in HF etching rate of fused silica, correlated to the
decrease of the Si-O-Si bond angle induced by the hydrostatic pressure or compressive stress
created in the irradiated region. When fused silica is irradiated, the modifications induced by the
femtosecond laser pulses can be classified into three categories depending on the laser processing
conditions: a) for a low fluence, a smooth modification is achieved, resulting mainly in a positive
refractive index change with a very weak selectivity in etching; b) for a moderate fluence, sub-
wavelength nanocracks are produced, yielding a high etching selectivity of the irradiated volume
with respect to the pristine one (up to two orders of magnitude); c) for high fluence, a disruptive
modification is obtained with the creation of voids and microexplosions. In particular, regime a) is
typically suited for waveguide fabrication, while regime b) is the one employed in the first step of
the FLICE technique for microchannel production. Regime c) can be used for direct laser ablation.
This technique is exploited in this work to create large access holes on the side facets of the chip in
order to achieve easy connection with external capillary tubes. The access-hole diameter of 350 is
designed to exactly match the outer diameter of the capillary tubes; this tailoring is achieved by
irradiating multiple coaxial helixes with different radii and with a pitch of 2 μm [Fig. 4.7]. The
number of coaxial helixes depends on the desired size of the access hole; for a 350 μm diameter, 3
helixes are written with diameters of 80 μm, 160 μm, and 240 μm, respectively. The two access
holes are connected by a straight line that, once etched, will provide a slowly tapered
microchannel with a uniform central portion of 80 μm diameter where the optical trapping is
achieved. The channel walls have a minimum radius of curvature of 40 μm and show the typical
surface pattern obtained with this technology providing an estimated roughness in the 300-500
nm range.
Fig. 4.7 Irradiation of access holes and round-section microchannel
Irradiation is performed at 600 kHz repetition rate with a pulse energy of 290 nJ at the second
harmonic wavelength of 515 nm. The laser polarization is set perpendicular to the microchannel
axis, which is placed at a depth of 400 μm with respect to the top surface. With the high-
repetition-rate laser an irradiation speed of 1 mm/s is feasible; therefore, although complex
structures are irradiated, the processing of the full chip. The chip is then immersed in an ultrasonic
bath with 20% of hydrofluoric acid (HF) in water for 4.5 hours to obtain the 3-mmlong buried
microchannel [Fig. 4.8].
Fig 4.8: a) access holes and microchannel structures after irradiation and b) after final etching
Waveguide writing in the fused silica sample is performed in the same conditions used for the
irradiation step in the microchannel fabrication, i.e. focusing through a 50 × objective the
frequency-doubled cavity-dumped Yb:KYW laser; however, this time the laser is operated at a
repetition rate of 1 MHz since in this regime the fabricated waveguides exhibit lower propagation
losses [Fig. 4.9].
Fig. 4.9: waveguides irradiation
Waveguide writing parameters are optimized in order to have the best guiding properties at the
operating wavelength of 1 μm. A pulse energy of 100 nJ and a translation speed of 0.5 mm/s
allows obtaining single mode waveguides at the operating wavelength with a mode intensity
radius at 1/e2 equal to ~4 μm and an ellipticity factor of 1.1. Measured propagation losses at the
operating wavelength are equal to 0.9 dB/cm.
Multiple sets of waveguides can be fabricated on the two sides of the microchannel, with a
separation between the waveguide end-faces of 100, 130, 180 and 300 μm. Each set is composed
of 3 waveguides, laterally spaced by 80 μm, that are fabricated at various depths with respect to
the axis of the microchannel, i.e. + 5, 0 and −5 μm. In this way different depth positions of the trap
are experimentally tested. Moreover, this approach could be exploited to fabricate several parallel
traps able to intercept cells flowing at different heights, thus improving the measurement
throughput.
So, the overall fabrication process can thus be summarized in the following steps: i) the
femtosecond laser is set to a repetition rate of 600 kHz and the structures for the microchannels
are irradiated (typically several structures are fabricated on the same glass substrate); ii) The laser
repetition rate is switched to 1 MHz without losing the alignment and the sets of waveguides are
written in each device; iii) the substrate is cut and different chips with 3 mm × 8 mm size are
obtained; iv) etching of the microchannels is performed by immersion in the HF solution. Since the
irradiation of both microchannels and waveguides is performed before chemical etching, the
writing of the waveguides is interrupted 500 μm before the edge of the chip, in order to avoid any
etching of the regions corresponding to the waveguides. After the etching the two end-faces are
polished in order to expose the waveguide input ends and perform efficient fiber coupling [Fig.
4.10].
Fig. 4.10: Microscope image of the integrated optical stretcher
Once a chip is fabricated, it is connected to external fluidic and optical circuits. Using a set-up
composed by an optical microscope and accurate translation stages, external capillaries are
inserted in the access holes. Once the capillary is firmly inserted it is glued by a drop of UV-curable
resin. The external circuit is essentially made of two butterfly needles glued to the capillaries; the
tubes at the other hand of the butterfly needles act as reservoirs. Cell suspension is transported
through the trapping region by a controlled microfluidic flow; this is obtained by varying the
relative heights of the two reservoirs and can be finely adjusted with a micromanipulator.
Fig. 4.11: Connections of the integrated optical stretcher
Optical fibers are aligned to the waveguides input-facets by means of two translation stages. Butt-
coupling is presently used in order to have a flexible set-up, able to test all the waveguides in the
chip; however, in a final device the fiber will be permanently pigtailed to the waveguide following
the standard procedure developed for photonic devices in telecommunications (typical additional
losses ~0.5 dB).. The chip connected to the capillaries and the fibers is also glued by UV-curable
resin on a thin glass slide to increase robustness of the connections but still allowing imaging of
the channel content with a high magnification objective.
4.2 EXPERIMENTS
The schematic diagram of the experimental set-up used to demonstrate the effectiveness of the
integrated optical stretcher is shown in Fig. 4.12. A CW ytterbium fiber laser with an emitting
power up to 5W at 1070 nm, is used as light source. The beam coming from the laser is split in two
branches by means of a 50%-50% fiber coupler (FC1). The optical power in each arm is then
controlled by variable optical attenuators (VOAs) and monitored using the 1% port of a 99%-1%
fiber coupler (FC2a); this enables to finely balance the optical power at the output of the two
fibers. In order to optimize the light coupling into the chip-integrated optical waveguides, a second
99%-1% fiber coupler (FC2b) is added in the fiber line: the power coupled into one waveguide,
transmitted through the microchannel and collected by the second waveguide, is thus monitored
in the opposite branch. All the fiber components are single mode at the working wavelength as
well as the spliced bare end-fibers. The VOAs are specified for operation up to 2 W of optical
power, while we verified the FCs up to 4 W. Given the high optical threshold of the fused silica
chip, the current set-up can also be used to stretch cells other than RBCs, where higher power may
be needed.
Fig. 4.12: experimental setup
The chip is mounted on an inverted microscope equipped for phase contrast microscopy
(TE2000U, Nikon). Phase contrast images of optical trapping and stretching are acquired by a CCD
camera (DS-Fi1, Nikon). The pixel size for all the employed magnifications was calibrated with a
grating; this allows for absolute distance measurements with a resolution of 0.055 μm/pixel in the
case of a 40 × objective.
The trapping and stretching capabilities of the chip have been tested on RBCs. The cell suspension
is prepared by diluting 10 μL of blood in 8 ml of hypotonic solution in which the RBCs acquire a
quasi-spherical shape with a radius of ~4 μm; the cell suspension is inserted in the microfluidic
circuit with a syringe. For an easy imaging of the flowing cells, the typical value of the cell speed is
set in the 10-50 μm/s range.
4.2.1 EXPERIMENTAL RESULTS WITH A ROUND-SECTION MICROCHANNEL
First experiments are performed on the circular cross-section microchannel chip. RBCs optical
trapping is achieved with an estimated optical power at each waveguide output of about 20 mW.
Figure 4.13 shows a sequence of a few frames demonstrating how the trapped RBC is stable in its
position even if a background flow is present (flowing cells are out of focus since they are
travelling at different heights in the microchannel).
Fig. 4.13: CCD sequence of frames demonstrating the optical trapping of a single RBC; solid arrow indicates the trapped cell, while dashed arrow points to an out-of-focus cell flowing below the trap.
Moreover, we observe a controlled movement of the trapped RBC along the beam axis obtained
by unbalancing the optical forces applied on the two sides of the dual beam trap. The force
unbalance is easily achieved by varying the output power of one of the two waveguides, which can
be finely tuned by adjusting the corresponding VOA [Fig. 4.14].
Fig. 4.14: CCD sequence of frames showing the motion of two trapped RBCs along the trap axis obtained by varying the output power of the bottom waveguide
When a single cell is stably trapped in the microchannel it can be stretched along the trap axis by
simultaneously increasing the optical forces applied to the cell by the two counterpropagating
beams. Experimentally this is achieved by raising the emitted power from the laser source.
Therefore, the trap is still stable and a progressive stretching of RBC is observed. Figure 4.15 shows
a sequence of frames demonstrating the optical stretching of a single RBC. The cell can be
elongated up to 25% of its initial size when increasing the waveguide output power to 300 mW.
Fig. 4.15: CCD sequence of frames showing the optical stretching of a RBC from its initial shape to 25% elongation along the beam axis.
However, in order to achieve such a clearly visible elongation the cell is stretched into its plastic
deformation regime. By stretching the cell with lower optical power smaller deformations are
observed in the elastic regime, but the lens effect induced by the curvature of the microchannel
prevents from a reliable retrieval of the cell contour.
4.2.1 FABRICATION OF A SQUARE-SECTION MICROCHANNEL AND
EXPERIMENTAL RESULTS
To solve this lens-effect problem, the square cross-section microchannel chip is used.
We designed and implemented an irradiation path to obtain a square cross-section channel (SC),
as shown in Figure 4.16.
Fig. 4.16: Sketch of the femtosecond laser beam irradiated path representing the structure that will create the microchannel with square cross-section.
This is obtained by irradiating two coaxial helixes, with a pitch of 2 mm, with rectangular cross-
section one inside the other. The irradiated helixes have a cross-section height and width of 45
mm and 30 mm, respectively, for the inner one and 70 mm and 60 mm, respectively, for the
external one. The microchannel is then terminated by two access holes with circular cross-section
that are obtained by irradiating three coaxial helixes with diameters of 60 mm, 130 mm and 200
mm, respectively, a pitch of 2 mm and a length of 800 mm per side. While in the portions of the
microchannel closer to the access holes the etching smoothes out the corners of the rectangular
cross-section, in the central portion of the channel, where the HF solution arrives later and acts for
a shorter time, the channel closely follows the irradiation path with a sharp rectangular shape
(Figure 4.17).
Fig. 4.17: Comparison between the fabricated microchannels with round (RC) and square (SC) cross-sections. Different sections of the channels are also shown: at the access hole entrance (SEC.AA), at the interface between access hole and the microchannel
(SEC.BB), and in the center of the microchannel (SEC.CC).
Irradiation is performed with a pulse energy of 300 nJ and a translation speed of 1 mm/s, leading
to an overall irradiation time of about 60 minutes for the complete structure. The chemical etching
is executed immersing the chip in an ultrasonic bath with 20% of HF in water. A 4.5 hours etching
produces the microchannel, which is 400-mm buried under the top surface, has a 2-mm length, a
central rectangular cross-section of 85x75 μm, and two 800-μm-long access holes.
To test this new device we first characterized the coupling losses and the trap quality of the
waveguides. We evaluated the coupling losses facing couple the light in each couple of
waveguides, in order to evaluate the coupling losses inside the chip when the microchannel is
empty, then we do the same measurements filling the channel with the RBC suspension. The
estimate losses from the left fiber to the trapped cell are in the order of 5 dB in every waveguide.
The trapping quality of each set of waveguides has been characterized trapping particles flowing at
different velocities, then lowering the optical power of the waveguides until the particle escaped
from the trap. From the distance covered in a specific amount of time we measured the escape
velocity of the cell at different trapping power for each set of waveguide [Fig. 4.18]
Fig. 4.18: Escape velocity of a red blood cell at different trapping power in the microchannel. The dots represent the experimental measurement, the lines come from simulations.
The experimental results are in good matching with the simulations. In the same way we can
measure the axial forces exerted on the trapped particle by the optical forces:
rvF 6
Where η is the viscosity of water, which is approximately 10 -3 N s/m2, r is the radius of the
sphere, and v is the velocity. The Fig. 4.19 shows the relation between axial force of the trap and
the power between the waveguides at different distances.
Fig. 4.19: Axial force exerted on a trapped particle for different power and distance of the waveguides.
After the characterization we tested the stretching of red blood cells. First we trapped a red blood
cell at a power of 35 mW inside the microchannel [Fig. 4.20]
(a) (b)
Fig. 4.20: a) trapped red blood cell and b) edge contour exploited by Matlab.
Then we increased the optical power to 300 mW and, as shown in Figure 4.21, the particle
stretched.
(a) (b)
Fig. 4.21: a) stretched red blood cell and b) edge calculated with Matlab
Although efficient, the square-channel microchannel brings a big problem, that is the roughness of
its wall due to the etching process. This roughness can prevent from acquiring a good imaging of
the sample, thus making the exploitation of the contour of the cell more difficult. Currently we’re
investigating possible solution, from the different concentration of hydrofluoric acid in the etching
solution to the choice of another substrate or the use of laser ablation for the microchannel
fabrication.
CONCLUSIONS
In this thesis work it has been tackled the realization of biophotonics tools based on the
exploitation of optical forces. Two different devices have been studied that can be used either to
trap or to stretch micro-particle prevalently for biological applications: a fiber optic tweezers,
whose working principle is based on total internal reflection (TOFT) and an optical stretcher
implemented with fiber optics or in a fully integrated chip version (FIOS).
For what concern the first device, we have fabricate, through focused ion beam milling, a first
implementation of TOFT achieving good results in the trapping of polystyrene beads. The work of
improvement of this technique has made then more efficient, but the internal microstructures of
the TOFT limits the angle control, thus preventing from a perfect focusing symmetry of the four
fibers. The second implementation, based on two-photon polimerization lithography, has been
successfully tested both with polystyrene beads and with red blood cells, providing stable traps
and the possibility to achieve multiple traps at the same time. This handy tool will be suitable for
many applications relevant to biology and fundamental physics, such as in vivo biological
manipulation or in-vacuum single-particle X-ray spectroscopy.
The second device has been implemented first in a discrete elements configuration, following the
description found in literature. The optical stretcher has proven to be very useful in the
investigation of viscoelastic properties of different biological samples. Thanks to many
collaborations with biomedical research groups, experiments on different kind of cells and
diseases have been performed. In particular the studies on diabetic red blood cells and the
resulting discrepancy between the elasticity of healthy and diseased cells gave us the possibility to
better understand the uprising of microcircularity problems. We’ve also analyzed red blood cells of
patients affected by genetic diseases, characterized by genetic mutations that affect the
membrane proteins. Due to the rarity of these diseases, the analysis aren’t yet concluded, we
haven’t still analyzed enough patients to have a good statistic, but the earlier results are very
reassuring and we plan to integrate this analysis with Raman spectroscopy to achieve better
results. For what concern the work on tumoral cells, we are evaluating the possibility to
distinguish the evolution of the disease by analyzing the mechanical properties of healthy tumoral
and metastatic cells. It is known indeed that cancer cell posses a reduced cytoskeleton, thus they
are softer. The opportunity to exploit these measurements to distinguish between healthy and
cancer cells would be of great help in putting the base for the realization of early diagnosis
devices.
The optical stretcher has been also fabricated in its integrated version, i.e. by fabricating both the
microchanell and the two facing waveguides on a chip. The integration of an optical stretcher has
proven the effectiveness of the FLICE technique, a fabrication process very simple and performing,
as well as the advantages of the fused silica as a chip substrate, thanks to its transparency and the
low IR absorption. We’ve considered two microchannel fabrication processes, one with a round
section and one with a square section; for both approaches we’ve characterized the trapping
forces, and we have been successful in the trapping and stretching of red blood cells. This system
is reliable, and can be further improved adding a fiber pigtail to solve the power loss at fiber-
waveguide interface and adding a sorting system. The integrated optical stretcher with a square-
section microchannel avoids the aberration of the lens effect, but much work must be done in
order to get rid of the roughness of the walls, that sometimes prevent from a good profile
acquisition; many different solutions are currently under evaluation.
APPENDIX A – MATLAB PROGRAMS
Programma “croppa_centro.m”
clear all
close all
misure=[1:1:17]
%misure=1
bau = [1:1:50]
for j = 1:length(bau)
a= num2str(j);
b = ['seq',a];
cd ('..')
cd (b);
for i=1:length(misure)
close all
corrente=misure(i);
Immagine = imread([num2str(corrente),'.bmp']);
figure,imshow(Immagine);
I=Immagine;
set(gcf,'renderer','zbuffer')
title(['DOPPIO CLIC AL CENTRO'])
[x,y]=getpts(gcf);
y_centro=round(y);
x_centro=round(x);
if i==1
title(['DOPPIO CLIC BORDO DI RITAGLIO'])
[x,y]=getpts(gcf);
y_ritaglio=round(y);
x_ritaglio=round(x);
distanza=max(abs(x_ritaglio-x_centro),abs(y_ritaglio-y_centro));
end
a=x_centro-distanza;
b=y_centro-distanza;
Icrop = imcrop(I,[a b 2*distanza 2*distanza]);
figure,imshow(Icrop);
set(gcf,'InvertHardcopy','off')
set(gcf,'PaperPositionMode','auto')
set(0,'DefaultFigurePaperPositionMode','auto')
nomf=[num2str(corrente) '_crop.bmp'];
imwrite(Icrop,nomf,'bmp')
end
end
Programma “analisi_immagine.m”
clear all
close all
bau = [1:1:50]
Immagine=imread('9_crop.bmp');
Igr=Immagine;
figure, image(Igr), colormap(gray(256)), axis equal
misure=[1:1:17];
Igrigio = histeq(Igr);
figure, imshow(Igrigio), colormap(gray(256)), axis equal
I2 = Igr;
I_doub_originale = double(I2);
I_doub = max(max(I_doub_originale))-I_doub_originale;
figure, surf(I_doub),shading interp, view(2), colormap gray, axis equal
set(gcf,'renderer','zbuffer')
title(['DOPPIO CLIC AL CENTRO'])
[y,x]=getpts(gcf);
y_centro=round(y);
x_centro=round(x);
corrente=misure(1);
Immagine = imread([num2str(corrente),'_crop.bmp']);
Igr=Immagine;
Igrigio = histeq(Igr);
I2 = Igrigio;
I_doub_originale = double(I2);
I_doub_figura = double(Igr);
I_doub = max(max(I_doub_originale))-I_doub_originale;
dim_im=size(I_doub);
estremo=min([x_centro, y_centro, dim_im(2)-x_centro, dim_im(1)-y_centro]);
Npa=200;
Nps=250;
vett_rad=linspace(0,2*pi,Npa);
vett_mod=linspace(0,estremo,Nps);
[THETA, RHO] = meshgrid(vett_rad, vett_mod);
UNI = ones(length(vett_mod), length(vett_rad));
XC = x_centro.*UNI;
YC = y_centro.*UNI;
XI = XC + RHO.* cos(THETA);
YI = YC + RHO.* sin(THETA);
M_POLAR=interp2(I_doub,YI,XI);
figure
surf(M_POLAR), view(2), shading interp, colormap(gray(256));
set(gcf,'renderer','zbuffer')
dim= size(M_POLAR);
a=dim(1)
b=dim(2)
title(['DOPPIO CLIC LIMITE SUPERIORE'])
[x,y]=getpts(gcf);
y_superiore=round(y);
x_superiore=round(x);
title(['DOPPIO CLIC LIMITE INFERIORE'])
[x,y]=getpts(gcf);
y_inferiore=round(y);
x_inferiore=round(x);
Fascia_taglio=abs(y_superiore-y_inferiore)
M_POLAR1=M_POLAR([y_inferiore:y_superiore],:);
figure,surf(M_POLAR1), view(2), shading interp, colormap(gray(256));
set(gcf,'renderer','zbuffer')
for j = bau(1):length(bau)
a= num2str(j);
b = ['seq',a];
cd ('..')
cd (b);
for i=1:length(misure)
corrente=misure(i);
Immagine = imread([num2str(corrente),'_crop.bmp']);
Igr=Immagine;
Igrigio = histeq(Igr);
I2 = Igrigio;
I_doub_originale = double(I2);
I_doub_figura = double(Igr);
I_doub = max(max(I_doub_originale))-I_doub_originale;
dim_im=size(I_doub);
estremo=min([x_centro, y_centro, dim_im(2)-x_centro, dim_im(1)-y_centro]);
Npa=200;
Nps=250;
vett_rad=linspace(0,2*pi,Npa);
vett_mod=linspace(0,estremo,Nps);
[THETA, RHO] = meshgrid(vett_rad, vett_mod);
UNI = ones(length(vett_mod), length(vett_rad));
XC = x_centro.*UNI;
YC = y_centro.*UNI;
XI = XC + RHO.* cos(THETA);
YI = YC + RHO.* sin(THETA);
M_POLAR=interp2(I_doub,YI,XI);
M_POLAR1=M_POLAR([y_inferiore:y_superiore],:);
M=M_POLAR1.^2;
SOGLIA=0.15.*max(max(M));
[CONFR] = find( M < SOGLIA);
MZ=M;
MZ([CONFR])=0;
[MASSIMI,POS_MASSIMI]=max(MZ,[],1);
RAGGI=RHO([POS_MASSIMI+y_inferiore]);
spettro=fftshift(fft(RAGGI));
fattN=max(spettro(:));
spettro=spettro./fattN;
spettroF=spettro;
[FILTRO_F] = find( abs(spettroF) < 0.01);
spettroF([FILTRO_F])=0;
raggiofiltrato=ifft(ifftshift(spettroF.*fattN));
BORDOX = x_centro + raggiofiltrato.* cos(vett_rad);
BORDOY = y_centro + raggiofiltrato.* sin(vett_rad);
x_fin = max(BORDOX) - min(BORDOX)
y_fin = max(BORDOY) - min(BORDOY)
rapporto = x_fin / y_fin
dimen=size(I_doub_originale);
calib=0.074;
ax=linspace(0,(dimen(2))*calib,dimen(2));
ay=linspace(0,(dimen(1))*calib,dimen(1));
assex=ax-y_centro*calib;
assey=ay-x_centro*calib;
bordo_Y=BORDOY*calib-y_centro*calib;
bordo_X=BORDOX*calib-x_centro*calib;
figure(100), clf
set(gcf,'position',[10,200,1000,500])
subplot(1,2,1)
plot(THETA(1,:),RAGGI), view(2), shading interp, colormap(gray(256));
set(gcf,'renderer','zbuffer')
hold on
plot(THETA(1,:),raggiofiltrato,'r')
subplot(1,2,2)
surf(assex,assey,I_doub_figura), view(0,-90), shading interp, colormap(gray(256));
xlabel('x [\mum]','Fontsize',14)
ylabel('y [\mum]','Fontsize',14)
axis equal
hold on
plot(bordo_Y,bordo_X,'r','LineWidth',2)
set(gca,'FontSize',14,'Fontangle','italic')
set(gcf,'renderer','zbuffer')
nomf=['bordo_' num2str(corrente) '.jpg'];
eval(char(cellstr(['print -djpeg ' nomf])));
x_fin_micron = max(bordo_X)-min(bordo_X)
y_fin_micron = max(bordo_Y)-min(bordo_Y)
rapporto_micron=y_fin_micron/x_fin_micron
ax=y_fin_micron;
ay=x_fin_micron;
STRETCHING(1,i) = corrente;
STRETCHING(2,i) = x_fin_micron;
STRETCHING(3,i) = y_fin_micron;
STRETCHING(4,i) = rapporto_micron;
nome_file_risultati = char(['risultati_',num2str(corrente),'.mat']);
variabili_da_salvare = char([' corrente ax ay rapporto_micron ']);
comando_salvataggio = char(['save ',nome_file_risultati,variabili_da_salvare]);
eval(comando_salvataggio)
end
save (['risultati','.txt'], 'STRETCHING','-ascii','-double','-tabs')
end
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