Download Super-Resolution Fluorescence Microscopy by Structured Light

DISS. ETH No.
13916
Super-Resolution
Fluorescence
Microscopy by Structured Light
Illumination
Dissertation submitted to the
SWISS FEDERAL INSTITUTE OF TECHNOLOGY
ZURICH
for the
of
degree
Doctor of Technical Sciences
presented by
Jan Tillman Frohn
Dipl. Phys.
born
February 28,
citizen of
accepted
1971
Germany
recommendation of
on
Prof. Dr. A.
Prof. Dr. H. J.
Stemmer,
Tiziani,
Zurich,
2000
examiner
co-examiner
Acknowledgments
The research work
period
presented
from fall 1997 to fall 2000 in the
Institute of Robotics. It
at the
in this thesis has been carried out in the
I wish to thank my advisor Prof.
who introduced
croscopy
Nanotechnology Group
embedded in the
by
me
to the idea of
structured
of his young and
at the
poly project NANO-II
Technische Hochschule Zürich".
"Eidgenössische
Firstly
was
light
dynamic
increasing
illumination.
group
Dr.
Andreas Stemmer
the resolution of
The
mi¬
inspiring atmosphere
essential for the
was
light
success
of my
work.
Furthermore,
taking
I
am
very
grateful
to Prof.
Dr.
the role of co-advisor of my thesis and for
H. J. Tiziani for
enlightening
discus¬
sions.
Special
thanks
are
due to Jakob Zbaeren who showed
thetic aspect of fluorescence
scientific
me
beyond
an
es¬
the pure
one.
I very much
me
microscopy
which goes
appreciate the support of Helmut Knapp who
thousands of useful hints and
Last but not
least,
Nanotechnology Group
I want to thank my likeable
for
gave
tips.
sharing joys
Ill
and
colleagues
struggles
with
me.
in the
IV
Contents
Abstract
IX
Kurzfassung
XI
Definition of terms
1
XIII
Mathematical conventions
XIII
Abbreviations
XVI
Introduction
1.1
Historical outline
1
Resolution enhancement
1.1.1
2
Summary
3
Theory
by
harmonic excitation
of the method
4
7
13
3.1
The
3.2
Fluorescence
3.3
1
microscope
as
linear shift invariant
(LSI) system
13
17
3.2.1
Fluorescence
3.2.2
Dye-saturation
Harmonic excitation
3.3.1
Interference
3.3.2
Image
3.3.3
OTF
polarization
21
23
light microscopy (HELM)
generating apparatus
reconstruction
design
...
24
24
32
36
V
VI
4
5
CONTENTS
The HELM setup
41
4.1
General considerations
41
4.2
The beam
43
splitting
unit
4.2.1
Illumination spot size
45
4.2.2
The
piezo
46
4.2.3
The
coupling
actuator
unit
48
4.3
The overall system
50
4.4
System stability
52
Results
5.1
5.1.1
5.2
55
Achievable resolution
by
HELM
55
Discussion
56
Measuring biological samples
61
5.2.1
Materials and Methods
61
5.2.2
Discussion
62
the OTF
5.3
Measuring
5.4
Determination of
70
geometric parameters of illumination
mesh
5.5
6
72
Influence of defocus
on
HELM
77
Three-dimensional HELM
6.1
The limitation of
6.2
Approaches
79
optical sectioning microscopy
...
enhancement
6.2.1
6.2.2
82
The confocal
Image
Computational
6.2.4
Standing
wave
microscopy
84
84
excitation methods
85
harmonic excitation
85
3D-OTF extension
6.4
A three-dimensional HELM setup
by
(I2M)
methods
6.3
6.5
82
microscope
interference
6.2.3
6.4.1
80
for axial resolution
87
Two-beam interference
88
the incident beam vectors
6.4.2
Choosing
6.4.3
A setup with minimal number of DOF
Simulation results
89
....
90
92
CONTENTS
6.6
7
VII
Conclusion
95
Conclusion
101
APPENDIX
A
Optical trapping
105
in interference fields
105
A.l
Physical background
107
A.2
The setup for
109
A.3
Results
113
References
117
Curriculum Vitae
127
optical trapping
VIII
CONTENTS
Abstract
Optical
many
far-field
microscopes
disciplines
with
sample preparation
of
lying physics
derstood.
image
essential tools for
are
in science and
engineering. They
high imaging speed. Furthermore,
formation in
light microscopes
Therefore, image interpretation
particularly
in
additionally
takes
investigations
is much
scanning probe techniques.
advantage
of very
deeply
are
more
the under¬
applications
Unfortunately,
ited
by
Fluorescence
microscopy
specifically staining
individual
imately
During
distinguished
240
nm
the last
in
case
decade,
hance the resolution of
the confocal
a
optical
far-field instruments is lim¬
criterion. It
of green
light
predicts
that two
points
and oil-immersion
objectives.
various efforts have been undertaken to
optical microscopes.
The most
is the confocal
diffraction limited
microscope
large
if their lateral distance falls below approx¬
light microscopy
vancement in
By scanning
biology
Rayleigh
a
and medicine.
the resolution of
the well known
cannot be
in
un¬
evident than
components of the object. Today, fluorescence microscopy has
number of
in
combine convenient
and,
in
en¬
ad¬
scanning microscope.
light spot through
the
increases the lateral resolution
1.5 under ideal conditions
common
addition, drastically
by
specimen,
a
factor of
enhances the
optical sectioning capability.
In this
copy
thesis,
(HELM)
a
method called harmonic excitation
is described which allows
lateral resolution in fluorescence
one
to
more
light
micros¬
than double the
microscopy by illuminating the
IX
spec-
ABSTRACT
X
imen with
cessing
mesh-like interference pattern and electronic postpro¬
a
of the
images. The employed interference pattern
full field of view and
recorded
are
by
a camera.
images for different positions of the
From these five
images, additional
information not accessible in conventional fluorescence
be extracted
by
A setup
plane
of
alized.
a
an
fore,
a
HELM
factor of
harmonic
of artificial
patterns in the object
as
biological samples
resolution of approx.
optical
than 1.5
excitation
well
as
outperforms
even
more
true
a
can
interference of laser beams has been
microscope by
Images
microscopy
algebraic approach.
producing
HELM achieves
the
covers
be shifted in two dimensions relative to the
actuators. Five
specimen by piezo
pattern
can
the lateral
resolving
and, additionally,
100
re¬
show that
nm.
There¬
power of CFM
avoids
by
disadvantages
of
scanning methods.
A further part of the thesis deals with
tension of HELM.
a
three-dimensional
three-dimensional
ex¬
Basically,
possible by
imaging
stepping the focus through the object and acquiring a stack of twodimensional
tional
as
numeric
achieve
axially.
are
well
as
confocal
simulations,
an
a
the axial
microscopes
resolving
power of
is far below the lateral
conven¬
one.
By
three-dimensional HELM device is shown to
unrivaled resolution of approx. 100
Since the system
nm laterally as well as
requirements for three-dimensional HELM
similar to those of confocal
tems could become
a
However,
images.
is
commercial
point
a
superior
of view.
devices,
it is
expected
that such sys¬
alternative to confocal ones,
even
from
Kurzfassung
sind unerlässliche
Optische Fernfeldmikroskope
in vielen Gebieten
suchungen
von
für Unter¬
Werkzeuge
und Technik.
Forschung
Sie kom¬
Abbildungsgeschwin¬
Probenpräparation
digkeit. Außerdem sind die physikalischen Grundlagen der Bildent¬
binieren einfache
mit hoher
in Fernfeldmikroskopen gut verstanden. Das macht die Bild¬
interpretation wesentlich einfacher als beispielsweise bei Rasterson¬
stehung
denverfahren. Darüberhinaus
einzelne
Komponenten
Auf Grund dieser
trum in
Biologie
Eigenschaft
von
grünem
te nicht unterschieden
kleiner als
sind viele
vermögen
ungefähr
werden
240
von
nm
können,
wird.
unternommen
optischen Mikroskopen
abgerastert wird,
von
maximal
Fernfeldmikro¬
Es
besagt,
zwei Punk¬
ihr seitlicher Abstand
worden,
zu
die Probe mit einem
Mikroskop
optischen
wenn
ist das konfokale
auflösung
Anwendungsspek¬
Während des letzten Jahrzehnts
fokalen
einen Faktor
anzufärben.
Olimmersionsobjektiven
Weiterentwicklung
Lichtfleck
Spezifität
Rayleighkriterium begrenzt.
Licht und
Anstrengungen
von
Fluoreszenzmikroskopie,
besitzt sie ein breites
Auflösungsvermögen
durch das bekannte
daß im Fall
die
und Medizin.
Leider ist das
skopen
ermöglicht
der Probe mit hoher
um
erhöhen.
Mikroskop.
das
Auflösungs¬
Die bekannteste
Indem beim kon¬
beugungsbegrenzt
kann einerseits die seitliche
kleinen
Auflösung
um
1.5 erhöht und andererseits die Tiefen¬
drastisch verbessert werden.
In dieser Arbeit wird eine
Methode, genannt
XI
"harmonie excita-
KURZFASSUNG
XII
light microscopy" (HELM), beschrieben,
tion
seitliche
peln,
Auflösung
indem die Probe mit einem
leuchtet wird und die
Bilder anschließend
Piezostellgliedern
zweidimensional verschoben werden.
mit einem
Fluoreszenzmikroskopie
algebraischen Ansatz
beweisen,
daß HELM eine
erreicht.
von
aufgenom¬
welches
System aufgebaut,
optische Auflösung
immer noch
von
von
um
Laser¬
biologischen
ungefähr
Auflösungs¬
übertrifft HELM das seitliche
Folglich
vermögen des konfokalen Mikroskops
nm
Probe
zugänglich wären,
sowohl künstlichen als auch
von
zur
Objektinformationen,
nicht
mittels Interferenz
Beleuchtungsmuster
strahlen erzeugt. Bilder
100
wei¬
rekonstruiert werden.
Im Rahmen dieser Arbeit wurde ein
Proben
relativ
des Musters werden mit einer CCD-Kamera
ortsharmonische
digital
Fünf Bilder für verschiedene
Aus diesen Bildern können zusätzliche
welche mit normaler
die
zu
Das Interferenzmuster deckt das volle Ge¬
sichtsfeld ab und kann mittels
Stellungen
ermöglicht,
es
mehr als
verdop¬
gitterartigen Interferenzmuster be¬
aufgenommenen
terverarbeitet werden.
men.
die
Fluoreszenzmikroskopen
von
einen Faktor
mehr als 1.5 und vermeidet außerdem die Nachteile
von
rastern-
den Verfahren.
Ein weiterer Teil der Arbeit
sionalen
ale
Erweiterung
Mikroskopie möglich,
sionalen Bildern
indem
aufnimmt,
Probe wandern lässt.
beschäftigt
man
während
Allerdings
einen
man
daß das
Auflösung
anforderungen
skope ähneln,
eine
von
bleibt die axiale
Auflösung
Mikroskops
ungefähr
100
nm
beträgt.
denjenigen
überlegene
zeigen,
zum
konfokalen
Gesichtspunkten.
Da die
System¬
für konfokale Mikro¬
wird erwartet, daß ein dreidimensionales
auch unter kommerziellen
sowohl
deutlich hin¬
eines dreidimensionalen HELM-Aufbaus
für ein solches Gerät
Alternative
zweidimen¬
zurück. Numerische Simulationen
Auflösungsvermögen
sowohl seitlich als auch axial
Stapel
den Fokus axial durch die
des konventionellen als auch des konfokalen
ter der seitlichen
sich mit einer dreidimen¬
HELM. Grundsätzlich ist dreidimension¬
von
HELM-System
Mikroskop
sein
könnte,
Definition of terms
Mathematical conventions
A boldface variable
scalar
product
r
denotes
a
rs
The modulus of
strokes and is
n-dimensional vector
of two vectors is defined
a
=
(!)
y
rt s.
J2r*s*-
(generally complex)
=
vector is denoted
by
vertical
£>,<,
\.=
where the asterix denotes the
the fraktur letter
3(/)(k)=
The inverse transform is
ÎTV)(r)
=
(2)
i
complex conjugate.
The n-dimensional Fourier transform of
by
The
given by
|v|
denoted
(ri,... ,rn).
by
$
a
and is defined
function
/
:
Rn
—>
C is
by
ff(r)e^dr1...drn.
(3)
given by
(2^T / /(k)
XIII
e-rk *i
•
•
•
<**»•
(4)
XIV
DEFINITION OF TERMS
The two- and three-dimensional space is of
particular
context of this work.
The letters x, y
coordinates in two-
three-dimensional real space,
letters
kx,ky
dimensional
or
or
kx,ky,kz
reciprocal
or
x, y,
interest in the
denote the Cartesian
z
respectively.
denote the coordinates in two-
respectively
space,
two- and three-dimensional Fourier
.
transform,
As
a
or
The
three-
notation for the
the tilde
~
is used
as
well:
oo
oo
f f
f(kx,ky):=d(f)(kx,ky)=
The n-dimensional convolution
defined
f(x,y)e«k*x+kyyîdxdy.
(denoted by
the
(5)
symbol <C^)
is
by
<
/,
9 >
(r)
/ /(s) g{r -a)dsx... dsn.
=
The n-dimensional correlation
(denoted by
the
symbol <>)
(6)
is defined
by
<f,g>(r)=
With these
definitions,
ff(a)g*(a-T)dSl...dsn.
the
following
basic Fourier theorems
(7)
are
obtained:
Convolution theorem:
3(«/,
2
»)=£(/)£(</)
(8)
Autocorrelation theorem:
3(//*)=(2^<3(/), 3(/)>-
^
MATHEMATICAL CONVENTIONS
Scaling
For
XV
Theorem:
g(r)
=
/(or)
the
following
$(g)W
=
relation holds:
-$(/)(-)
a
\a
J
(10)
Translation theorem:
For
g(jc)
=
/(r
—
a)
the
following
relation holds:
3(«7)(k)=3(/)(k)e»k
Dirac's delta distribution
(H)
representation:
*(r"z):=(2^/e'k(r"')dfcl"A
(12)
fulfills
/(r)=
[ f(s)S(r-s)dSl...dsn
for any continuous function
/.
(13)
XVI
DEFINITION OF TERMS
Abbreviations
2D
two-dimensional
3D
three-dimensional
AFM
ASWFM
Atomic force
Axial
microscope
standing
wave
fluorescence
CFM
Confocal fluorescence
DNA
Deoxyribonucleic
DOF
Degree
Electron
FM
Fluorescence
HRP
acid
of freedom
EM
HELM
microscope
microscope
microscope
microscopy
Harmonic excitation
Horseradish
light microscopy
peroxidase
I2M
Image
interference
microscopy
I5 M
Image
interference
microscopy with
incoherent interference illumination
LSI
LSWFM
NA
Linear shift invariant
Lateral
standing
wave
fluorescence
OSM
Optical sectioning microscopy
OTF
Optical
PSF
SNOM
SNR
TIR
microscope
Numerical aperture
Point
transfer function
spread
Scanning
function
near-field
Signal-to-noise
optical microscope
ratio
Total internal reflection
Chapter
1
Introduction
1.1
Historical outline
Today's
human
by employing
One
knowledge
in natural sciences could
important class of such
the word
microscope
was
instruments
used for
a
length
scale not
directly
a
ufacturing
microscopes
was
underlying physical principles
understanding
man¬
microscopes
were
Ernst Abbe
were
not
investigated
wave
image formation
development, however, imaging
satisfactorily
out of scope of Gauß's
framework of
of
in op¬
by Carl Friedrich Gauß who
geometric optics. These geometric optics
formed the basis for instrument
effects
and
achieved in 1840
established fundamentals of
erties of
The his¬
close interweavement between
progresses.
A first milestone for the
tical
a
it
variety of physical properties
accessible to the human eye.
tory of microscopy is characterized by
scientific advancements in the
perceptivity.
microscopes. Originally
optical magnifiers but, today,
denotes instruments which visualize
on
are
be achieved
only
technical instruments to extend the human
the
ray-optical
imaging
description
of
light
1
understood
process in
and found
as
treatment.
a
a
prop¬
diffraction
In
microscope
1872,
in the
simple relationship
CHAPTER 1
2
between achievable resolution and
His investigations
whose resolution approximates the limit
employed light
lens
in
the realization of
glass manufacturing permitted
of
of the
wavelength
with advancements
together
INTRODUCTION
grinding
optical
the
imposed by
microscopes
nature
wave
light
In
1924, De Broglie studied the properties of electron beams and
found out that these
(EM)
1986)
1936,
be described
can
Prom that point, the idea of
length
evident
was
and M
F
In
fact, eight
microscopes
with very short
as waves
building
wave¬
electron microscope
an
years later E
Ruska
(Nobel
Price
Knoll realized the first EM using magnetic lenses
Krause could demonstrate
ter than 100
nm
EM with
an
the
and, thus, outperform
Technical advancements
in
power of
resolving
EM
gle deoxyribonucleic
design
made it
optical
possible
(T Komoda, 1966) and to observe
(DNA) molecules (J Dubochet, 1970)
acid
the sixties, the scanning electron microscope became
sible and could extend the
three-dimensional
Optical
applicability
microscopes,
incompatible
ration
is
however,
new
with
living
were
specimens
dehydrated Secondly,
required and, thirdly,
the specimen
technically
sin¬
In
fea¬
of EMs to surface imaging of
objects
still essential due to several
herent drawbacks of electron microscopy
must be
In
resolution of bet¬
a
to achieve atomic resolution
is
and
as
First,
the
object
under observation
relatively complicated sample
a
the radiation dose sometimes
The first restriction,
however,
in¬
the majority of EMs
can
be
prepa¬
destroys
overcome
by
the
environmental scanning electron microscopes at the expense of
a
lower resolution
In the
eighties,
actions between
one
was
neling
[10]
a
a
variety of
scanning
the scanning
tunneling
current between
In the
following
a
In
1984,
and the
The first
sample emerged
microscope which
measures
the tun¬
metallic tip and the surface of the specimen
years,
measured using scanning
microscopes using short range inter¬
probe
the
probe
the scanning near-field
physical properties
microscopes
optical
were
that could be
strongly
microscope
extended
(SNOM)
was
in-
HISTORICAL OUTLINE
1 1
3
vented which enables measurement of
restricted
by
the
force microscope
(AFM)
light [66]
developed
was
without
optical properties
propagation of
wave
which
In
1986,
the force
measures
teraction between tip and
sample [9]
Scanning probe
based
interactions
(e
on
physical
various
[46],
surements
[59])
lateral force measurements
it could be demonstrated that the scanning
in
aqueous environments
However,
probe
scanning
more, the
the local
into
object
as
approach
least,
to
images
influenced
are
the scanning
overcome some
electron microscopy
are
today
applicability
tions of
light
specimens
with
have become
specific
a
probe
microscopes,
Many problems
systems
to image
microscopy
high
1For
an
[60, 75, 13]
overview
was
By
article
were
to further extend the
found
in
for investiga¬
biological
(FM)
is
capable
specimens
as
localizing DNA
living
scanning
[82]
can
techniques1
sequences [25] or
cells
and have
successfully
[16]
optical
the invention of the confocal scanning
see
re¬
of selec¬
dyes
An important improvement concerning the resolution of
croscope
[79]
Advanced fluorescence
standard tool for
far-field microscopes
A
resolution with sufficient
components of the
molecules
capability
are
microscopy
particularly
perform immunological investigations [58, 72]
proven their
microscopes cannot
light
attempts
Fluorescence microscopy
imaging individual
be bound to
variety of phys¬
[80]
of far-field
chemical contrast
a
Further¬
complicated
restricted to surfaces
is
probe techniques
incitements for several
biological
often
by
disad¬
comparison to
of these limitations
search require microscopes that combine
tively
common
in
is
probe
The drawbacks of electron and scanning
and
some
very slow
are
its imaging process
which combine scanning
or
[76]
interactions
Last but not
an
promising
tip-sample
and
function
probe techniques
microscopes share
interpretation of scanning probe
ical effects
mea¬
developed
were
in¬
microscopes
potential
far-field microscopes due to the mechanical scanning
optical
see
well
One is, that these methods
vantages
as
as
surface
g
being
the atomic
a
focused laser beam
through
mi¬
the
CHAPTER 1.
4
overcame
Abbe's century old
significantly
increase the three-
specimen, these types of microscopes
limit
by
factor of 1.5 and could
a
dimensional
become
an
The
imaging capabilities. Today
essential tool for
high
INTRODUCTION
the confocal
in cell
investigations
microscope has
biology.
intensities of the focused laser beam in the confocal
microscope enabled the development of methods for resolution
hancement based
[22, 41]
or
on
non-linear effects such
stimulated-emission
number of suitable
as
two-photon absorption
depletion [50].
dyes, however,
en¬
Due to the restricted
non-linear methods
are
not
yet
rou¬
tinely employed.
Another approach to increase the resolution does not affect the
image formation but the image interpretation. By electronic post¬
processing of images produced by conventional
a
croscopes,
knowledge
prion
methods
a
significantly
are
problem
about the
sensitive
sample
mi¬
a
these
images, specifically posing
microscopy.
Resolution enhancement
1.1.1
light
be achieved if
can
[19, 21]. However,
present
noise in the
against
in fluorescence
is
confocal
or
enhanced resolution
by
harmonic exci¬
tation
Since Ernst Abbe's
works,
produce Airy patterns
common
as
points
what
made.
the
amounts to
A
frequency
sively
more
as
27%.
The
the contrast
dip
is the well known
This radius is de¬
for two
universal definition for resolution
spectral
just resolved
Rayleigh criterion, however,
assumptions about the observable
domain. From the
transfers
The most
two self-luminous
ring of the Airy pattern.
Rayleigh distance;
arbitrary
light microscopes
known to
are
(see Fig. 1.1).
to
radius of the first dark
as
light microscopes
sources
According
Rayleigh,
points
just resolved if their lateral separation equals the
criterion.
considered
noted
point
definition for resolution of
Rayleigh
are
far-field
from
object spectrum,
components within
a
can
the
is
contrast
some¬
dip
are
be obtained in
microscope exclu¬
bounded
region, called
HISTORICAL OUTLINE
1 1
Figure
Image produced by
1 1
the
separated by
the
passband
reasonable
a
Rayleigh
the extent of the
HELM
is
(l
fact that
The
disciplines
heterodyne
conversion
signals
can
are
is more
In
(HELM),
brought
described
in
this
by employing
The
patterns
is
2
key
idea of
communications engineering and
principle
in
passband
microscopes
than doubled
excitation
in
light
is
known
Basically, frequency
be shifted
with harmonic functions
object spectrum
the extent of the
microscopy
widespread practice
a
many other
or
light
passband
sinusoidal)
e
Thus,
for the resolution of
measure
sources
(incoherent imaging)
of the microscope
space harmonic
microscope for two point
light
a
distance
In harmonic excitation
thesis,
5
domain
frequency
mixing
by
modulation
additional components of the
HELM,
into the
frequency
as
mixing describes the
passband
of the microscope
by
this shift
The idea of
croscopy
described
copy
nized
2
as
it
more
required
one in
From the
a
the image
scaling
was
not
by
in
the
for
optical
mi¬
The method
resolution
object plane
theorem for Fourier transforms
to
high
to
and
a
micros¬
synchro¬
plane
frequency representation
corresponds
applied
[57, 56]
Lukosz
practical
moving mask
spatial representation
microscope
mixing has first been
than 30 years ago
then, however,
width of the
the
frequency
of
a
For this reason,
a
function
an
narrowing of the
(Eq 10)
is
it follows that the
reciprocal
extension of the
point
response
to the width of
passband
of the
CHAPTER 1
6
In relation to Lukosz's
[30, 31]
realized
a
laser
shows two
by illuminating
Secondly,
by
This
source
structures
ted
key
in
the
the
is
the method
microscopes
can
a
of
mask
way to
even
in
described
an
this thesis
produce
high
fine illumination
resolution microscopes
postprocessing of the
on
is
interference pattern of
the image
easily implemented
in
the harmonic excitation
First,
practical
object plane
be
one
the specimen with
synchronized
using electronic
the
method,
differences
INTRODUCTION
plane
has been omit¬
images
As
a
result,
conventional fluorescence
Chapter
2
Summary of
The
objective
thod without
sential for
chapters
of this
chapter
the method
briefly
is to
it with details.
overloading
the HELM
understanding
summarize the HELM
Aspects
principle
are
In the two-dimensional HELM setup four laser
plane
as
croscope under
a
waves, interfere in the
be written
can
I(x, y)
u
=
angle
common
Neglecting scaling factors,
where
the
me¬
not
es¬
discussed later in
to the
optical
47msin(a)/A
is the
+
Ax)
+
cos(uy
wavelength
of excitation and
sample
a
the fluorescence
density
of
in
x-
</>
which
can
of
mi¬
a
(see Fig. 2.1).
I of the elec¬
glass,
(2.1)
Ay),
of the harmonic
A is the
vacuum
Ax, Ay describe the shift of the pattern
and y-direction, respectively (see subsec¬
derivation of
is
+
spatial frequency
n=1.52 is the refractive index of
tion 3.3.1 for
axis
resulting intensity pattern
cos(wx
relative to the
beams,
object plane
as
2 +
=
a
excitation,
the
are
3 and 4.
be considered
tric field
which
Eq. 2.1).
proportional
dye-molecules tp,
For the illuminated
to the excitation
the latter called
7
sample,
intensity I times
original image
in the
CHAPTER 2
Figure
Optical
2 1
train for
SUMMARY OF THE METHOD
generation of
two-dimensional interference
a
(a)
pattern in the object plane of the microscope
laser beam is
sity
that
cross
polarization
and not
are
split by
at
E is
the
orthogonally
(only
2
shown)
phase
and
the
image plane,
to
slip
and
inten¬
only antiparallel
beams
Piezo-actuated mirrors P
axis
object by
angle
to 70°
equal
The electrical
y-interference patterns
optical
The beam's
glass block, corresponding
cover
x-
the
the
microscope
so
interfere
ones
of the
through
coupled
oil-immersed to the slide
in the
to
A collimated
top view
BS into four beams of
axis OA of the
oriented
cut view
are
splitters
optical
parallel
used to vary the
pendently (b)
beam
a
to
glass
the
inde¬
The four laser beams
block GB which is
optical
in the water
layer
axis is a=55°
between slide
9
following
(see
text
section
3.2):
4>(x, y)
~
With
denoting
ip{x, y)I(x, y)
=
(2.2)
the two-dimensional Fourier transform of
obtains for the spectrum of the illuminated
Eq.
2.1 into
2.2 and
Eq.
A
=
4>(K, ky)
4
=
=
4>{kx, ky) +elAx i}(kx
The spectrum
<f>
is
+ u,
ky) +e~lAx i}(kx
positive and negative reciprocal
frequency domain,
described in two
with
an
tion
(OTF,
the
nents of the
dimensions,
section
sample,
3.1).
a
in
as
In
passband
cut-off radius
(about
emission
kc
=
540
is
a
of the
this
are
well
occurrence
spatially
shift,
the
can
three, by
in
called the
frequency
reconstructed,
irrecoverably
compo¬
while outside
lost. For fluorescence mi¬
region centered
where A is the
at the
origin with
vacuum-wavelength
for the fiuorescein-like
dyes)
of
and NA is the
objective.
high frequency regions
passband
of the
Eq.
of the
2.3
as
to extract the individual
high
by
a
Through
2.2 shows the
the current setup.
must be
postprocessed
components A..E and
resolution
image.
result
optical spectrum
microscope. Fig.
images acquired for HELM, however,
arrange these to the final
In
be
transfer func¬
optical
the
passband,
be
can
multiplication
a
harmonic excitation is the basis of HELM.
into the
electronically
kx- and fc^-axis
where the OTF is non-zero,
enhanced support of the OTF that is achieved
The
the
along
direction, respectively.
of the shifted spectra B..E in
additional
brought
is
as
regions
circular
47rNA/A,
nm
numerical aperture of the
The
or
principle,
region the information
croscopy, the
+
(2.3)
u)
-
imaging property of the microscope
called the support of the OTF
this
space
instrument-specific function,
see
ky)
u,
superposition of the original spectrum A plus
four spectra B..E that have been shifted
in
-
E
u) +e-lAy 4>(kx, ky
+
C
=
=
$(kx, ky
a
B
D
=
elAy
variable,
a
sample (by inserting
using the convolution theorem Eq. 8):
one
This is
to
re¬
possible by
CHAPTER 2
10
Figure
The enhancement of the support of the OTF
2 2
standing
copies
nents
to
the
of the circular
The four circular
spatial frequency
five
from
passband
B,C,D,E from Eq
citation
shows the circular
passband
(b)
microscopy with cut-off frequency kc
OTF of HELM
recording
(a)
excitation
wave
fluorescence
shaped
SUMMARY OF THE METHOD
2 3,
(a)
correspond
The
respectively
relocated
are
to the compo¬
displacement
u
is
equal
images for which the nodes and antinodes of the
pattern
are
of
of the harmonic excitation
at different
In the setup, the
positions.
(Ax, Ay) are sequentially adjusted to
(tt/2,0), (tt,0), (0, 7t/2), (0, 7t) by piezo actuators.
y-phase
means
for standard
is the cloverleaf-
regions 1,2,3,4
and
by
offsets
x-
the values
ex¬
and
(0,0),
For the Fourier transforms of the five
holds with the
5
x
five
is
5 set of linear
spectral
performed
obtained
of the
on
the measured
Numerically,
images and the
pixel. By doing
which, additionally,
so, the
a
can
be solved for the
fast Fourier transform
set of linear
equations
is
spectral components A...
E
have been attenuated
microscope. The remaining computational task
components back
them
is obtained which
equations
components A..E.
solved for every
are
acquired images, Eq. 2.3
appropriate coefficients e±îAx and e±îA». Thus, a
taking
to their
personal computer
together require only
for
a
the OTF
is to shift the
original position and, finally, superimpose
into account the attenuation
All calculation steps
by
512
x
512
image.
by
a
the
microscope's
few seconds
on a
OTF.
standard
11
Fluorescent beads with
Figure
2 3
HELM
(left)
The
1 pm
a
diameter of 200
and standard fluorescence
wavelength
microscopy (right)
of emission is 540
nm
of the
objective
beads
approximates the Rayleigh limit which
tions
The almost invisible contrast
the
is 1 4
right image
is
a
one
nm
tightly packed
for these condi¬
between the individual beads in
are
not
point
has to take into account that, for water im¬
mersed beads, the effective NA of the
smaller
is 240
consequence of the fact that the beads
Furthermore,
sources
with
Scale bar is
and the numerical aperture
The center-to-center distance of the
dip
imaged
nm
objective (nominal
4)
becomes
which
approxi¬
1
[44]
Fig.
2.3 shows beads with
mately equals
the
The HELM
Rayleigh
a
diameter of 200
nm
limit for standard fluorescence
microscopy.
image (left) demonstrates that such beads
clearly distinguished,
dard fluorescence
even
when
they
are
closely packed.
microscopy image (right),
in
can
be
In the stan¬
contrast, the individual
beads remain blurred. In relation to the confocal fluorescence micro¬
scope, there
•
are
several
advantages
of HELM:
The resolution enhancement relativ to conventional FM amounts
to
more
confocal
than
a
factor of 2
scanning
compared
to 1.5 which is achieved
under ideal conditions
[78].
by
CHAPTER 2
12
•
In
all
HELM,
photons entering
image formation
path
In
CFM,
HELM
is
mental
reasons
well
as
based
on
confocal
contrast,
can
devices,
As
a
exploited
in
vs
for
the imaging
the fraction of
the
signal-
CFM,
funda¬
result,
deteriorated
high speed
imaging
imposed by
In
subsection 5
11)
mechanical scanning limit
speed
and
principle
tive to confocal
ones
be
pinhole
a
imposed by dye-saturation (see
practical
reasons
the
is
well suited for
the imaging
For these
the lenses
which contribute to the image
to-noise level of CFM
as
in
makes it necessary to trade off resolution
photons
•
SUMMARY OF THE METHOD
as
the system requirements for microscopes
of harmonic excitation
HELM systems could become
ones
are
a
similar to those of
commercial alterna¬
Chapter
3
Theory
The
3.1
a
general perspective,
very
waves
within
gether
with the
ent
media,
time
a
e.g.
microscope
boundary
the
by
the
propriate
directly
by
to write the
the Maxwell
or
equations
[45].
interfaces at the lens surfaces
disturbance at any
be described
by
point
to¬
it is
equations using the electric field
as
as
The
in three-
E(r, t)
the electric field
important optical effects such
well
as
more
this
ap¬
one
is
photon absorption
molecules.
The considerations
nochromatic)
are
restricted to the
excitation. As
a
and, therefore,
can
case
of time harmonic
consequence of the harmonic
the electric field vector E at any
harmonic
by
magnetic induction B(r, t). For this thesis,
related to
atoms
propagation of electromagnetic
conditions for the transitions between differ¬
air-glass
can
the
is described
dependent electromagnetic
dimensional space
as
linear shift invari¬
as
(LSI) system
ant
From
microscope
point
r
be written
13
e
I3
(mo¬
excitation,
in space is also time
by using
the
complex
time-
CHAPTER 3
14
microscope
k
,-'
\/
object plane
Figure
independent
The
3 1
G
R3 and E(r)
In the context of this
notation
E(r)
notation,
to
C3.
the
complex time-independent
implicit
dependence
time
3.1.
can
describe linear
a
microscope according
imaging
to
Fig.
between
imaging property of the microscope
work of linear system
plane
(3.1)
as
well
elliptical
as
po¬
light.
Now,
is denoted
mapping
6.
by
theory.
3.1 is considered which per¬
object plane
can
and
image plane.
be described in the frame¬
The electrical disturbance in the
the Greek letter
<f>
and that
one
object
in the
image
notation, the microscope's imaging process is
mapping of functions <f> : R2 —> C3 to functions 8 : R2 —> C3. This
plane by
a
G
work,
Eq.
one
forms two-dimensional
The
Re(E(r)erat),
=
is used with the
given according
larized
image plane
notation:
E(r,t)
With this
axis
optical
;
microscope system studied
E(r,t)
where
THEORY
Using
this
is characterized
Linearity
by
the
The response of the
turbances in the
following
two basic
microscope
object plane
to
is the
a
properties:
superposition of dis¬
superposition of the
re¬
sponses to the individual disturbances:
0{\4>1
+
ii4>2)
=
\0{4>1)
+
ii0{4>2).
(3.2)
3 1
THE MICROSCOPE AS LSI SYSTEM
This property
is
consequence of the
a
15
of the Maxwell
linearity
equations
Shift invariance The response to
a
shifted disturbance
is
the shifted
response to the unshifted disturbance
0(#u
with u, v,
G
a
microscope
optical
approximation
completely
disturbance,
0(#u))(v
+
The shift
a),
axis
invariance is
aberrations
increase
Nevertheless,
the shift
as
(3 3)
mirroring of the
not
strictly
good
invariance is a
described
(LSI) systems,
by
the imaging property
the response of the system to
the so-called point
spread
function
(PSF)
a
point
(3 4)
where ö denotes the two-dimensional Dirac's delta-distribution
a
LSI system to
arbitrary
an
can
1
9(6(u))= PSF(u),
response of
true
for points far away
to the real situation
For linear shift invariant
be
=
M2 and where magnification and
neglected
is
for real microscopes
from the
a))(v)
+
disturbance
can
be
The
seen
to
be the convolution of the disturbance with the PSF of the system
0(</>(u))
E=13
0
Linearity
1
/ 4>{w)5{vL-w)dvldv2
9
Linearity
((j>(v)S(u
4>{v)6 (ö(u
—
—
v)) dv\dv2
v)) dv\dv2
(3 5)
1Henceforth, only
problems,
scalar fields
the PSF-formahsm
can
are
be
considered for
easily
simplicity
For non-scalar
extended to vector fields
as
well
CHAPTER 3.
16
Shift
/
invariance
THEORY
4>(v)PSF(u-v)dv1dv2
R2
Eq_6
For
optical systems,
is called the
of the
one
6
According
generally,
scribed
to
the Fourier transform of the
(OTF).
obtains
the convolution theorem
Eq. 3.7,
the
a
=
4>
PSF
x
4>x
=
imaging property of
a
a
microscope
microscope
a
theory [33, 12].
Except
for
(3.7)
microscope (or,
system)
LSI
can
pupil
scalar
by
the coherent
scaling factors,
turns out to be the
more
be de¬
in Fourier space.
be calculated
can
(Eq. 8):
OTF
simple multiplicative filtering operation
The coherent OTF of
diffraction
a
>
For the Fourier transform
the transmission characteristic of
by
OTF of
by using
</vPSF
<
=
point spread function
transfer function
optical
image 9
(3.6)
<</>,PSF>
function of the
objec¬
tive.
In
case
of incoherent illumination
not be described
is
a
fixed
no
adequately by
emission
incoherent emitters
coherent OTF is
object
is the
a
are
linear in
the
object
amplitude
object points.
as
can¬
there
Instead,
intensity. The derivation of the
straightforward:
squared amplitude
scalar system with circular
For
high NA objectives,
Calculations
taking
and include the
theory
is
complex
field
intensity is appropriate since systems of
The
intensity
response to
(autocorrelation theorem, Eq. 9).
[77]
fluorescence,
a
response to
point object.
a
There¬
is used for
employed by
OTF
covers
components.
are
shown in
theory
high NA optics.
qualitative descriptions
the
high
pupil
the scalar
of
image
reconstruction
NA effects
as
one
The coherent and incoherent OTF
is not
Fig.
well
as
3.2.
strictly applicable.
into account the vector nature of
case
in¬
point
the incoherent OTF is the autocorrelation of the coherent
fore,
for
or
relation between different
phase
description by
a
In this
light
thesis,
also exist
the scalar
while the measured OTF
algorithm.
imperfections
The measured
in the
optical
FLUORESCENCE
3 2
17
1
08
06
04
02
0
-4-2024
spatial frequency [1/|am]
Figure
540
(dashed line)
Coherent
3 2
transfer functions for
an
objective
The rotational
and incoherent
with
(solid line) optical
NA of 1 4 and
wavelength
of
two-dimensional OTF is obtained
by
a
a
symmetric
rotating the graphs around the ordinate
nm
3.2
In this
Fluorescence
section, the basic properties of fluorescence and
fluorescence
microscopy
will be discussed.
fied energy level scheme for
excited states is
orders of
electromagnetic
This is
coherently.
as
by
it allows
the
one
theory
excitation
then the
a
and emit —to
very
important
to describe the
of incoherent
a
impact for
and, hence, about six
exciting oscillation. As
ns
of
the coherence of the
very
simpli¬
a
The lifetime of the
exciting
good approximation—
in¬
property of fluorescence emission
image formation of the microscope
imaging regardless of the coherence of
light.
Because the transition from
an
period
fluorophores destroy
wave
Fig.
typical fluorophore.
in the order of 1
typically
magnitude larger
consequence, the
a
a
its
3.3 shows
electrical
dipole transition,
ground
level so to the exited state si is
the fluorescence
absorption
rate
(FAR)
CHAPTER 3
18
Figure
3 3
Simplified representation
phore
Higher
vibrational sublevels
the
absorption,
excited state si from which it
possible by
fluorescence
are
quickly
shown)
or
energetic
indicated
is excited into
fluorophore
brational relaxation, not
of the
a
is
proportional
to the
parallel
absorption dipole
depending
an
on
cence
absorption
modulus of the
state.
for
photon
energy
fluorophores
fluorophore
strength
oriented
moment:
c|Endm|2,
absorption dipole
one
isotropically
would
(3.8)
moment
electric field
polarized light,
arbitrary polarization states,
distributed
probably expect
rate of the ensemble is
complex
For linear
=
is
by
and
c
is
a
particular fluorophore [71, chapter 2].
ensemble of N
considered. In this case,
(vi¬
state so
The energy
of the
efficiency
to the square of the electrical field
where ridm is the normalized
Now
(not shown)
The fraction of the exited
FAR
constant
By photon
ground
energy and emission
is called the quantum
the
fluoro-
relaxes to the lowest sublevel
Relaxation to the
absorption photon
radiatively
thin lines
a
non-radiative conversion both followed
by
is the well known Stokes shift
that relax
of
states
vibrational sublevel of the
vibrational relaxation to the lowest sublevel of so
difference between
by
THEORY
proportional
independent
this is in fact
fluorophores
is
that the fluores¬
to the
of the
squared
polarization
quite obvious, but,
it is not evident. As the interference
3.2.
FLUORESCENCE
19
generating apparatus of the setup produces
complicated polarization
lations
are
required
(see
states
to validate the
excitation
patterns with
3.3.1),
further calcu¬
subsection
expectation for such polarization
states.
For isotropically distributed fiuorophores,
phores dN oriented per solid angle dil is
dN
the number of fiuoro-
N
(3.9)
_
~dQ
The normalized
of
fiuorophores
polar angles Ç
~
4tt'
absorption dipole
oriented in
and rj,
a
moment ridm
direction
respectively,
/
ridm
absorption
fiuorophores.
affecting
Thus,
ellipsis
the
number
exciting
the electrical field vector
(3.10)
.
rate of the
To
general applicability,
of the
a
cos(C) cos(ry) \
=1 sin(C) cos(ry)
V
sin(?7)
/
To obtain the fluorescence
larization
to
the azimuthal and
is
has to be summed up for all
without
belonging
specified by
ensemble, Eq.
simplify
it is assumed that the po¬
electric field is within the
can
3.8
the calculations
be written
x-y-plane.
as
ExelP*
E=
where the real field
account for
an
I
Eye*Pv
amplitudes Ex, Ey
arbitrary amplitude
the fluorescence
absorption
rate
I
and the
and
FARj-
(3.11)
,
eVx,
ev»
polarization.
For
phase
ellipticity
of
factors
of the ensemble
one
obtains
CHAPTER 3.
20
FARE
\Vndm\zdN
c
=
THEORY
all
fluorophores
cN
|Endmrdfi
A-k
all orientations
2tt
it/2
ExelPœ \
cN
I
cos(C) cos(ry)
sin(C) cos(ry)
sin(ry)
\
EyetPy
A-k
0
0
-tt/2
/
tt/2
cos(ry) cfoy d£
2tt
cN
(77) dr]
cos
A-k
^cos^(C)
x
-tt/2
£2
cos2(^
-
px) sin2(C)
+
El sin2(py
2tt
cN A
4^"
E2X
3
-
px) sin2(C) d(
2tt
cos2 (C)dC
+
sin2(Ç)dÇ
E2y
f(E2x+E2y)^f\n2.
For
spatially
N within
a
distributed
fluorophores,
tp
denoting
the number of
fluorophores
volume element dV is
N
where
(3.12)
is the
density
the quantum
the fluorescence
</>
,M
of
=
fluorophores
efficiency
(3.13)
dVip,
of the
in the
specimen.
ffuorophore,
one
With
QE
obtains for
emitted per volume
=
QE^>=^,WIEWr<.
(3.14)
FLUORESCENCE
3.2.
Eq.
of
21
3.14 is the basic relation
distributed
isotropically
the exciting
what
In the
light.
form
simpler
describing
the fluorescence emission rate
fiuorophores
literature, Eq.
for any
3.14
polarization
state
be found in
a some¬
can
of
using the intensity instead of the electric field and
omitting scaling factors:
</>(r)
Eq.
3.15 is
specialization
is
setting
it
proportional
(i.e. J(r)
excitation
Eq.
oc
of
Eq.
If the
to the
V>(r)i"(r).
(3.15)
3.14 for excitation with
to the energy flux
proportional
[26, chapter 20].
wave
field
a
|E|2
for which
oc
generalized intensity
squared
|E(r)|2), Eq.
or
modulus of the
plane waves
intensity of the
I is defined
complex
3.15 is also valid for the
by
electric
complicated
patterns used in HELM.
3.15 is very fundamental for HELM. It states that the
of dyes in the specimen tp is modulated by the exci¬
intensity I before being imaged by the microscope.
density
tation
Fluorescence
3.2.1
In this
light
The
subsection,
will be
briefly
degree
of
polarization
the effect of
discussed.
polarization
polarization
Fig.
of emitted fluorescence
3.4 shows the
p is defined
<p\\ +
geometry considered.
by
<p±
where
and
<f>\\ and </>j_ is the fluorescence emission polarized along the yx-axis, respectively. In general, the degree of polarization is de¬
pendent
sion
the
on
dipole
rotational
angle
between
moment, the
mobility.
fiuorophores
are
absorption dipole
angular
For many
isotropically
distribution of
situations,
it
can
moment and emis¬
fiuorophores
and its
be assumed that the
distributed and that their orientations
CHAPTER 3
22
THEORY
iy
J!
Figure
Geometry
3 4
electrical
observed
(</>_!_)
of excitation is
polarization
circle represents the
the first
for observation of the
along
one
parallel
to
labeling
are
fixed.
y-axis
[7].
ß
is the
of
polarization
and the second
one
is reduced
are
3cos2(/3)
cos2(/3)
-
occurs
by
important for dye molecules
fluorophores
dyes
bound to
specific
are
</>
is
discriminated,
one
perpendicular
used later to describe
(3.17)
'
and emission
for coincident
ones
(/?
=
free to rotate, the
lifetime of the excited state
embedded in
Fluorescence
1
+ 3
absorption
the orientation of the
as
The grey
y-axis
po becomes
perpendicular
fluorophores
The
polarization
=
between
the maximum
the minimum for
If the
is
the
to
The minimum and maximum value for po
respectively,
0),
angle
(</>||)
polarization
Po
where
degrees
is consistent to the
microscope geometry
the
Two
the
the
Then,
parallel
region containing fluorophores
the z-axis
The axis
of
degree
are
dipole
+1/2
dipole
moment
and
—1/3,
(/?
moments
=
90°).
degree
of
polarization
fluorophores changes during
thermal motion
[73, 71].
the
This effect
in aqueous environment but not for
solids,
e.g. fluorescent
molecules in
polymer
biological specimens,
beads. For
the situation
FLUORESCENCE
3 2
be
can
more
vanishing
complicated
number of
As mentioned before
rophores
have
a
restricted but not
dye
lifetime of about 1
effect which
[70]
saturation"
fiuorophores
the imaging
the
in
rate cannot exceed
on
fraction of the
non-negligible
an
As
a
speed
a
fiuorophores
"ground
consequence of the
the fluores¬
ground state,
This imposes
a
of fluorescence microscopy,
steady
state
conditions,
the fluorescence
rate FER
emission
becomes
FER=^—,
(3 18)
Q.Tp + 1
where Tp
is
the lifetime of the excited state and
is
the excitation intensity,
is
the absorbed
emission
rate
photon
not
is
hmC(_>00(FER)
=
—
a
the
is
[70]
energy
linear
even
in
absorption
One
half of its upper limit
For
one
h
isat
i^-
=
with I
section and hv
that the fluorescence
it
as
for infinite excitation intensity
Jsat,
equals
sees
a
cross
excitation power
For the so-called saturating intensity
rate
fiuo-
sufficient
named
is
upper limit
an
typical
For
ns
for confocal scanning
particularly
Under
a
"dye
or
number of
emission
fundamental limit
of
a
this section, the excited states of
in
the excited state,
in
decreasing
cence
have
of rotational freedom
relatively long
a
depletion" [7]
state
dyes potentially
degrees
excitation power,
reside
can
as
Dye-saturation
3.2.2
high
23
limited
is
(see Fig
the fluorescence
Jsat this leads
by
5)
3
emission
to
1/
(3 19)
=
(TTp
typical fiuorophore (Rhodamm B, absorption
For
a
1
10~20
x
m2,
Tp
=
cross
section
Ins, [70]), the saturating intensity Jsat
is
a
=
approx
10iow
It should be
sity of
dyes
at
a
noted,
that
dye
saturation
certain location
is
independent
Consequently, dye
of the den¬
saturation does
CHAPTER 3
24
1
<u
,
r
-*-1
,L
ro
2!
<u
£
o
c
=!
o
M-
(0
05
ro
-
<u
E
i-
ü
c
o
<u
c
o
0 *
excitation
Figure
Dependence
3 5
THEORY
intensity
of fluorescence emission rate
on
excitation in¬
The fluorescence emission rate is normalized to its maximum
tensity
value
not decrease the contrast of
duces the number of
results in
a
fluorescence
a
photons
darker and noisier
emitted
the
re¬
specimen and, thus,
image.
Harmonic excitation
3.3
microscope image but
by
light microscopy
(HELM)
Interference
3.3.1
In this
subsection,
which is
2.1)
an
generating apparatus
expression for the electrical field distribution
the interference
produced by
will be derived.
Fig.
generating apparatus (see Fig.
3.6 shows the
geometry for
one
pair of
(oriented in the x-z-plane and referred to herein
pair (not shown, oriented in the y-z-plane and
as y-pair) is polarized perpendicular to the ones
incident laser beams
as
x-pair).
The other
referred to herein
shown and
can
Due to the
partial
glass boundary,
of four
plane
be considered
independently
the electric field is
waves
later.
reflection of the two incident beams at the water-
with
wave
effectively generated by interference
vectors
ku, ^in kir, &2r-
3.3. HELM
Figure
3 6
tern at
the
and
k2i)
25
Plane
electromagnetic
water-glass boundary
are
waves
For
producing
the interference pat¬
the two incident beams
clarity,
It turns out, that the reflected beams lead to
z-dependence
excitation
the electrical field
E\, E2
of the
intensity
Because all beams
where
are
strength
=
ElT
=
E2l
=
E2r
=
the field
2The negative signs
an
the
y-axis,
a
scalar notation for
is used:
E1e-t(-k*x+k*z\
(3.20)
-E1Re-<k'x-k-z\
E2etAe-<-k*x+k*z^
(3.21)
(3.22)
and
-E2elARe-l<--k*x-k*z\
amplitudes
sin(«j
sin(«j
of the incident
—
+
denser medium.
(3.23)
beams,2
at)
where
(3.24)
at)
of E\T and E21 describe the 180°
optically
unwanted
plane.
polarized along
Eu
are
intensity
an
distribution which reduces the
in the focal
R
reflection at
(ki!
horizontally displaced
phase
shift induced
by
CHAPTER 3
26
is the coefficient of reflection
with aj the incident beam's
3.6)
according
angle
to the Fresnel
THEORY
formulae [12]
(Fig.
to the interface normal vector
and with
at
=
(
arcsin
wa
\
the transmitted beam's
er
to the
angle
sin(at)
«glass
(3.25)
I
/
interface normal vector
«water and ngiass the refractive indices of water and
(with
glass, respectively)
and where
are
kx
=
27rnwater sin(aJ/A
kz
=
27rnwater
cos(«j)/A
the x-and z-component of the
beam
(with
and where
incident
A the
e*A
waves.
accounts for
The
resulting
vector of the
left incident
plane wave)
arbitrary phase
an
By using Eq.
calculations,
Eres
one
=
£ii
=
2E\e%
(E2
For the
+
-
3.23 and
Eq.
Eles
is the
sum
plus
the two reflected
performing
tedious but basic
obtains
Elr
2
3.20 to
shift between the two
electric interference field
of the two incident electric field distributions
ones.
(3.27)
of the incident
wave
wavelength
vacuum
(3.26)
and
+
cos
E2l
(
+
kxx
E2t
f(l
,
Exy^ék*x (1
-
-
R)e-lk*z -R2ism{kzz)
R)e-tk'z -R2isin(kzz)
.
(3.28)
intensity distribution / (more strictly the squared modulus of
the electrical
field,
intensity definition)
see
section 3.2 for motivation of this
one
obtains
generalized
3.3. HELM
27
=
*i
*?F
I
F
{El+Ei)[l+ E2' *2coS(2kxx + A]
\Eies\
—
M„
(1
2R
^)1
+
l + R2
As
can
be
from
seen
the
Eq. 3.29,
and
F\\
(3.29)
Mi
=
consists of two factors
cos(2A;z,^
of the
spatial dependence
which
F±
depend only
on
intensity
the
and
x-
z-coordinate, respectively.
F\\ provides
cosinusoidal x-modulation of the
which is the basis of the HELM method.
the ratio of the field
M|| depends
on
beams.
equivalent
1),
a
For
pure
obtained.
M||
standing
plus
a
propagating
of the
F± leads
to
an
glass boundary.
at the interface
(z
unity
increasing
=
0)
is enhanced
cover
slip,
first to
by
1 +
object
specimen
results in
cover
as
a
=
an
a
depth
standing
additional
node at the water-
by
a
factor of 1
R,
—
the
intensity
M± while the
M± for the antinodal planes
at
z
=
Table 3.1 shows the relative attenuation
different incident beam's
angles
has to be located in direct
ensure
objectives and, secondly,
onto the
the modulation
coefficient of reflection
is reduced
—
In most cases, the
the
one
M\\
to
electrical field is
the field consists of
as
The latter
one.
E2 leading
vanishing
depth
of the incident
intensity distribution.
(n/kz)(l+l/2) with / G N+.
(1
Mj_)/(1 + M±) for
ratio
=
unwanted z-modulation with
For
intensity
amplitudes (E\
amplitudes E\ ^ E2,
For different
DC-component
amplitudes E\, Ei
with nodes of
becomes smaller than
wave
—
field
wave
intensity distribution
The x-modulation
best
imaging fidelity
standard
slip. Then,
a,.
proximity
to
of oil-immersion
sample preparations deposit
the first antinodal
plane
the
of the
CHAPTER 3
28
Table 3 1
M_i
(1-Mj_)/(1
0 14
0 27
0 57
0 20
0 38
0 45
55 3°
0 31
0 57
0 28
80°
59 5°
0 54
0 84
0 08
85°
60 7°
0 73
0 95
0 02
at
at
R
50°
42 1°
60°
49 3°
70°
and 1 52 for
3 24 and
glass
antmodal
by
are
based
on
calculated
is
at
M_l equals
the factor
jr^r
by Eq
according
which the intensity
is
Eq
to
calculated
is
by Eq
The last column shows
decreased for nodal
planes
relative to
ones
plane
of the microscope
enhanced relative to the m-focus components
is
strongly
for incident beam's
increases
it has to be taken into account
subsection 3 3 3
The
and,
as
paragraphs,
electrical field
in
the
pair of incident beams
6)
is
3One possibility
90°)
in
is
at
approximating 90°,
discussing
the
optimal
expression
in
at
was
derived for the
y-polanzed
interference of the x-pair of incident laser
x-z-plane
(oriented
Now,
in
the
the situation when the y-
y-z-plane,
The
not shown
on
the
cover
advantageous
For
an
Fig
of
a
dielectric
slip
of mesh-like interference patterns for
appendix A
in
resulting polarization
to reduce the unwanted ^-modulation would be
coating
4The application
discussed
fa
an
also present will be considered
anti reflection
angles
of the interference field
produced by
beams oriented
when
As this effect
3 4
polarization
In the last
«j
3 25, R
3 29
consequence, the out-of-focus blur for images of three-dimensional
objects
3
refractive index of 1 33 for water
a
z-modulation coincides with the focal
a
Mj_)
Calculated values for the intensity attenuation rate of the nodal
The calculations
planes
+
THEORY
optical trap, working
optical trapping
near
flat incidence
are
(1
e
3.3. HELM
29
the electrical field distribution will be discussed and its
fluorescence will be studied.
following
impact
on
made under the
are
two constraints:
1.
equal amplitudes
2.
points
Then, Eq.
(i.e.
z
=
0)
3.28 becomes
The electric field
beams is
of all four incident beams
at the interface
Eles
For the
The considerations
=
2(1-
R)Eie1^
and
y-polarized
(kxx+
—
interference of the
produced by
with
completely analogous
x-
cos
exchanged
electric field
j
(3.30)
.
y-pair of incident
and
x-
y-coordinates.
Ex and Ey, respectively,
one
obtains
where
Ax
—
scaling
Ay
and
factors
polarization
the
on
electrical field
can
states
Assuming
Ey
=
Ex
=
are
=
see
section
=
shown
(3.31)
(kyy
(3.32)
+
^Y
or
on
the
phase
elliptically polarized.
schematically
angle
to the
in
Fig.
optical
of incident beams and
oc
|E|2 (which
3.2)
2 +
one
difference
cos(wx
+
=
fluorophores,
Two
possible
3.7.
axis at
using
the
are
equi¬
generalized
is consistent with fluorescence
obtains
sin(aj)/A and
identity cos2 (a)
distributed
(kxx + ^ J
neglected. Depending
47T «.glass
and where the
cally
cos
that the beam's
I(y)
u
e^
linearly
are
pairs
intensity definition I
with
cos
position within the interference pattern, the total
be
valent for both
absorption,
e1^
Ax)
+
where
cos(uy
scaling
^(1 +cos(2a))
+
(3.33)
Ay),
factors
are
neglected
is used. For
the fluorescence is
isotropi-
proportional
to the
CHAPTER 3.
30
THEORY
A»
t
S
4X4*
X
•-
4X4*
X
QtQt0
4X4*
X
4
Î -At
Figure
Two
3.7:
possible polarization
x-
and
y-direction, respectively,
maximum
crosses
intensity. The
polarization
panel
at every
illustrates the
in the
position
circular
to
let the
of the interference field.
vanishing
polarization
point
is pure linear
polarization
object plane,
(indicated by circles)
for
the
or
Ax
bright
zones,
electrical field.
for
vectors
(—Ay/2ky)
and
origin coincide with
grey bars illustrate the
indicate the nodes with
shows the electrical
states
displaced by (— Ax/2kx)
The coordinate system is
phase
point of
the
diagonal
The left
offsets
Ax
in
a
=
panel
Ay.
The
(indicated by arrows). The right
Ay + n. Depending on the
=
polarization
can
elliptical (between
be pure linear,
pure
the two extremes, not
shown).
generalized intensity
Eq.
3.33
gives
the interference
distributed
not
as
A second
the situation is different and
describe the fluorescence modulation
point worth mentioning
ization of the fluorescence
if
Thus,
for this case,
modulation of fluorescence introduced
spatial
by
generating apparatus. However, for non-isotropically
fluorophores,
necessarily
defined in section 3.2.
the
light.
is the
This
Eq.
resulting degree
polarization
3.33 does
adequately.
can
be
of
polar¬
neglected
3.3. HELM
•
the
31
ffuorophores destroy
3.2.1)
section
•
the
the
polarization by
(see
thermal motion
or
imaging properties of the microscope
are
not affected
by
the
polarization.
Both conditions may not be true
and,
in those cases, the effective mod¬
ulation function may be different from
distributed
Eq.
3.33
even
for
isotropically
ffuorophores.
Generalization for non-ideal interference geometry
Now,
the
3.33)
will be
of
description
intensity distribution
generalized
in the
to account for non-ideal
object plane (Eq.
condi¬
experimental
tions.
The
equations describing the
3.32 and
Eq. 3.31, respectively)
x-
and
are
y-polarized
based
on
the
electric field
(Eq.
idealiza¬
following
tions:
1.
The
and
x-
y-pair of incident beams
x-z-plane
Minor
out-off-plane components of the
tors lead to
and
are
in the
slight
a
assumed to be oriented
y-z-plane, respectively.
rotation
of
the
incident beam's
x-
and
wave vec¬
electric
y-polarized
field distribution.5
2.
The beam's
angles
at to the
optical
axis
are
equivalent
for all
incident beams.
Different angles of
tial
frequency of
electnc
BBy
and
this
field
the
the incident beams lead to
dommantly
x-
and
a
different
spa¬
dommantly y-polarized
distribution.
rotation, the polarizations
«-axis, respectively.
dommantly «-polarized
are
To indicate this
not
fact,
longer exactly parallel
the
to the
naming dommantly
electric field distribution is used.
x-
x-
and
CHAPTER 3
32
The field
3
Differences
the
in
the electric
of
of all four incident beams
amplitudes
(Eq
field
3 32 and
Eq
intensity distribution
sulting
be modified
I{y)
in
=
the
2 +
a
equivalent
reduced modulation
depth
distribution
the above described
Considering
distributions
lead to
amplitudes
are
THEORY
following
Mx cos(Ua;r
generalizations
for the electric field
3 31 under ideal
conditions), the re¬
conditions) has to
(Eq
3 33 under ideal
form
+
Ax)
My cos(u„r
+
+
(3 34)
A„),
where
fcos(jx)\
_
(3 35)
Vsin(7x)/
u
with ux, 7X and
the
the
Mx, My
ux, uy, 7-r, 7y,
sity distribution
Eq
is a
very
3 34 with the
an¬
generated by
and with uy, ^y and
values for the y-pair
6
the
in
Image
3.3.2
(3 36)
J
beams, respectively,
corresponding
graphical illustration)
a
V œshy)
of the intensity distribution
depth
pair of incident
x-
denoting
(-smbvA
V
Mx denoting the spatial frequency rotational
and modulation
gle
=u
V
(see Fig
3 8
My
for
appropriate values for
good approximation
to the real inten¬
experimental setup
reconstruction
In this subsection the influence of the non-uniform excitation pattern
the image
on
6In Eq
of the
field
34,
it
was
implicitly
moduli of the
distributions,
holds for
a
3
squared
the microscope will be studied and
produced by
le
it
was
assumed that the total intensity
dominantly
assumed
\EX
+
Ey\2
equals
dominantly y-polarized
by
minor
imperfections
in
the
only,
l e
=
\EX\2
for jx
+
\Ey\2
the
sum
electric
This relation
jy It remains, however,
good approximation for the small rotational angles jy < 1° and jy < 1° caused
orthogonally polarized
fields
ic-and
an
experimental setup
=
3 3
HELM
Figure
33
Schematic
3 8
produced by
algebraic approach
an
extended
With
~
representation of the non-ideal intensity pattern
the interference
for reconstruction of the
passband
denoting
J(k)
=
Eq.
specimen spectrum within
will be derived.
the Fourier transform of
the spectrum I of the
transform of
generating apparatus
a variable, one obtains
intensity pattern by calculating the Fourier
3.34:
87r2(5(k)+27r2Ma;
,iAa
(5(k
+ ux
e-*A*<5(k-<
2tt2M„
„«A,
(5(k
+ uy
e-lAyö(k-Uy)
(3.37)
where ö is Dirac's delta function
cos(a)
To
are
=
7}(ela
+
simplify
introduced:
e~*a)
further
(Eq. 12)
and where the
identity
is used.
calculations,
the
following
scale-shift operators
CHAPTER 3.
34
si(F(v
=
-F(v)
is the identical
s2(F(v
=
MxF(v
+
s3(F(v
=
MxF(v
s4(F(v
=
MyF(v
ss(F(v
=
MyF(v-uy).
-
+
The inverse scale-shift operators
«i
l
=
THEORY
(3.38)
mapping,
(3.39)
ux),
(3.40)
ux),
Uy),
are
(3.41)
and
(3.42)
given by
(3.43)
«l,
^1(f(v)):=Ü4F(v"Ul)
(3.44)
S3"1(f(v)):=if(v
(3.45)
Ul)
+
*yj>
M„
(3.46)
and
^(f(v)):=77nv + U:
(3.47)
M„
In
optical
Thus,
the
frequency domain,
described
as a
multiplication
transfer function
one
imaging property of the microscope
of the fluorescence spectrum
(OTF)
T of the
microscope (see
obtains for the spectrum 6 of the
<f>
is
with the
section
3.1).
image produced by the
microscope
e
=
3q=
15
E^8
=
(3.48)
T4>
T
T{$I)
(3.49)
T«V>,/»
4si(^)
+
eîA-S2(V>)
+
e-îA*s30/0
eîA» sS)
+
e"*A" ss(^)
+
?
(3.50)
HELM
3 3
35
where <C^ denotes the convolution
tors
are
neglected.
five
Experimentally,
y-phase
operation and where scaling fac¬
offsets
images d3
are
recorded for which the
set to different values
are
(Ax, Ay)
(0, tt). Eq.
by piezo-actuators.
is
(0, 7t/2)
3.48 holds for each of the
with the
5
x
and
set to
appropriate coefficients e±îAx and
5 set of linear
and
In the
(0,0), (tt/2,0), (tt,0),
setup, the pair
sequentially
x-
e±îA»,
acquired images
thus
resulting
in
a
equations:
M
s
(h\
/4
1
1
1
1\
4
1
—1
1
1
4
-1
-1
1
1
4
1
1
1
—1
\4
1
1
-1
02
03
=
T
04
W
The components
Sj(V0
can
-V
be calculated
(*S)\
«2(V')
S3(i>)
s4(V>)
(3.51)
\S5$)J
by
inversion of matrix
M:
/0~i\
/si(V>)\
«2(^)
S3(V0
s4(V>)
02
1
=
^M"1
W^V
03
04
w
/
0
0
1
4
-1-H
1
4
l—1
2
1
4
-1-î
=
T
4
2
4
±±i
0
0
0
0
w
In each
row
of
from components
Eq. 3.52,
the
0
1 \ (h\
0
0
02
0
0
03
—*
-i+»
2
4
_1"V
2
4
/
original spectrum tp
Sj(tp) by shifting
it in the
(3.52)
04
\hj
can
opposite
be calculated
direction
(i.e.
CHAPTER 3
36
with the
multiplication
with the
shift operator
inverse
)
s
and
THEORY
by rescalmg
OTF
inverse
M-le
^
where 6
is
=
CM
\
3
|
3
m
y
notation for the vector
a
and where the
subscript
j
of
These five equations for indices j
reconstruct the
For
points
original spectrum
certain index j,
a
of definition of
main
Eq
1
=
5
3 53
the basic relations to
are
be evaluated
can
For
an
for those
only
(T(kx, ky)) ^ 0,
3 53 for index j
Eq
6$
j-th component
from the measured images
domain where s~
frequency
in
consisting of components d\
vector denotes its
a
(3 53)
1<J<5,
called the do¬
ideal fluorescence
microscope, the
radius
support of the OTF, T, is a circular region with a
kc where kc
47rNA/A, NA is the numerical aperture of the
=
emission wavelength (see section 3 1)
Recalling
47, the domains of definition for the particular in¬
microscope and A the
Eq
Eq
3 43 to
dices j
1
=
5
of definition
microscopy
trast, for j
the
is
can
be determined
equals
as
in
the circular
For instance, for j
passband
the shift operator
2
=
kx-8xis
3
s^1
is
a
The
obtained
is
as s^
resulting passband
the total of the domains of definition for the indices j
resulting
clover leaf
3.3.3
OTF
In the
trum
overlap
can
3 53 for
shaped passband
is
shown
regions of the circles 1
than
one
index j
for different indices should be
level
As
con¬
along
for HELM
The
9, the original
spec¬
=
1
3 9
design
5
m
Fig
To achieve
ratio of the final image, the results obtained
noise
In
shifts
5
Fig
in
3
be calculated from the measured images
more
1 the domain
the identical mapping
different circular region
positive direction
=
of conventional fluorescence
noise
is
a
high signal-to-noise
by evaluating Eq
weighted according
amplified by
the
by evaluating Eq
inverse
to their
3 53
respective
of the denominator
HELM
3 3
Figure
37
The
3 9
the circular
(b)
frequency kc
information
are
pattern
(see Fig
equal
Eq. 3.53,
i.e.
Wj
=
s~
to
3
the
the
index j
of HELM
The
The
object
1...5
by
displacements
ux
regions
of the harmonic excitation
spatial frequencies
weights w3
are
set to the value of the
to estimate of the
53 w3s3
-l
=
shows
8)
these
original
weights w0,
denominator,
the
following
spectrum within the clover
for HELM is obtained:
shaped passband
V'est
(a)
HELM
by
microscopy with cut-off
passband
corresponding
(T(kx,ky)). By using
expression -i/>est
leaf
shows the extended
3 53 with the
and Uj,
enhancement achieved
for standard fluorescence
be reconstructed within the five circular
can
applying Eq
in
passband
passband
I
v
M-le\
h
3=1
V
(3.54)
T
j=i
To calculate the spectrum of the final
tional modifications to
noise
amplification
Eq.
3.54
are
image
introduced.
when the denominator
in
HELM,
First,
5^,=i s71(r^)
two addi¬
the maximum
tends to
zero
CHAPTER 3
38
(1
at the
e
Secondly,
are
boundary
of the
to reduce the
apodized by
of the spectrum
ripple
modifications,
?/>h of the HELM
image
*y)
chosen
is
is
current noise,
noise
of the
the
The influence of the
spread
of the
passband
=
noticeable
rections
It
20
is
studied
is
Th
As
is
on
10)
for setting
acquired
dark
dependent
and frame
analog-to-digital
quantization)
function
grabber
For
converter
values between
samples Except
7-limitation
Th
numerically
simple
can
case
be reduced
of
a
for the
Tr
sets in,
on
the
Fig
resulting point
3 10a and
constant OTF
in
the
Fig
Th
lobes,
=
1
most
diagonal
di¬
originating
constructively,
this level
by smoothly reducing
frequency Fig
used for the HELM images
page
55
well known from basic Fourier transform
towards the cut-off
7The equation
2 2
in camera
could interfere
sources
properties, the side lobes
finally
level of the
into account the fact that such overshoots
hardly acceptable
value of
(3
be seen, that the PSF has strong side
from different point
is
noise
the negative overshoot of about 26%
Taking
)
M"**
where the
apodisation
(PSF)
can
ac¬
transfer function for HELM
3 10b show the situation for the
and 7
circuits
camera, 8-bit
resulting optical
function
into
1
results for the measured
outermost region of the
equals
=
shot noise, temperature
noise
(uncooled
yield good
by
analog
and, finally, quantization
20 and 50
Taking
obtained
to the total
according
influenced
the system used
is
E-71
7
0
images which
Tn(kx,ky)
5
Ta(kx,k.
The limiter 7
has to be limited
\
mm
=
HELM)
the final equation for reconstruction
/
-i/>H
for
the final image, the Fourier spectra
in
appropriate function
an
count the above
passband
THEORY
7
With
the
3 10c shows the OTF
Th chosen that
way, the
Th within the clover leaf shaped passband (see Fig
is
,.
T^kx'ky)
T
.
,
=
,
(M
l-\K-
Jk|2
+
|kp\2
^-bK-)
'
(356)
HELM
3 3
39
negative overshoot
PSF
As
can
be
a
non
could
Fig
3
largely
be avoided
of 60°
is
not
isotropic
trum
is
sample
approach
experimental
could
amsotropy without
some
missing
into account
computational
within the missing regions
main
to reduce the
a
application
[2, 19]
in
parts of the object
priori
knowledge
potentially yield
reconstruction of the
the
object
directions
diagonal
an more
of band
With such al¬
in
spec¬
about the
Applied
non-negativity of the intensity distribution
as
the
laser beams oriented
to the HELM images
possible by taking
such
eight
six or
add-ons would be the
the reconstruction of
HELM,
leading
this amsotropy
Experimentally
by employing
extrapolation algorithms
gorithms,
OTF
This
45°, respectively
or
Another interesting
the need for
to
9, the PSF for HELM
circularly-symmetric
multiples
in
seen in
consequence of the amsotropy of the interference pattern
is a
to
reduced to about 13% while the width of the
is
largely preserved
is
information
frequency
isotropic point spread
do¬
function
where
km
is
the
maximum
cut-off
frequency
=
u
(3 57)
+ kc
and where
fc2+«2_2„ I 1
\l
-
—
-q
I
(3 58)
with
2u(ky/kX)2
i +
(3 59)
and with
(ky/kxy
«<%fcl)2fcc2
is
the cut-off
frequency
quadrant only,
do not fulfill this
and at the
kx
«
—
for
l e
«
direction of k
>
condition,
diagonal
kx, ky
in
ky
—
axes
ky
0 and
the
mirror
must be
and
kx
«
kx
>
3 59 and 3 60
Eq
ky
For
reciprocal
symmetry of Th
employed,
ky
(360)
must be
l e
apply
space
at the
to
one
half
points which
kx- and fcy-axis
the appropriate transformations
performed
befor
applying Eq
3 56
CHAPTER 3
40
Figure
Optical
3 10
transfer functions for HELM
point spread functions (right) for
(a)
and
and 7
=
(b)
show the situation for
20,
and also 7
=
(c)
20
and
(d)
for
a
two
a
different
and
corresponding
functions Th
1
apodisation Tn(kx, ky)
function
3
apodisation
(Eq
56)
constant
smoother
(left)
apodisation
THEORY
=
Chapter
4
The HELM setup
In this
chapter,
the setup which is used to achieve resolution enhance¬
ment in HELM is described.
The basic
goal
of the setup is the
generation of
mesh-like interference pattern in the
As has
already
been mentioned
result of interference of four
cross
in the
object plane
object plane
(see chapter 2),
mutually
of the
coherent laser beams which
requirement for the HELM setup
preparations
should be usable. Standard
slip
slide
(size typically
which form the
exist to
1.
microscope.
this pattern is the
microscope.
One essential
a
two-dimensional
General considerations
4.1
of
a
of the
couple
same
x
mm
specimen
25
are
optics
sample preparations
consist
mm
x
imaging
1
mm)
and
thin
cover
elegant
two
the
as
it
objective (see Fig.
partly employs
and for illumination. No
41
a
Basically,
possibilities
specimen chamber:
coupled through
This arrangement is rather
for
sample
chamber.
the laser beams to the
The laser beams
4.1).
75
is that standard
problems
the
arise
CHAPTER 4
42
Figure
fluorescence
plane
filter
Simplified optical
4 1
shown
spot
in
objective
The collimated beams
the back focal
plane
coupling
interference pat¬
an
simplicity only
focused
by
a
or
unit would be
microscope
as
optical parameters
as
objective (infinity
two
lens to form
beams
a
focal
with the condenser used for trans¬
A drawback of this arrangement
illumination
type of
are
For
of the microscope
with the translation stage
the
for generation of
tram
the
by illuminating through
tern
are
back focal
THE HELM SETUP
strongly
the unit's
connected to
design
or
the fact that
one
particular
would be influenced
focal distance of the
corrected
is
not) and,
by
objective, type
last but not
least,
of
the
available ports of the microscope
2
The laser beams
backside
an
the
through
arrangement
same
are
coupled
the slide
is
direction
the fact that the direct laser
as
the fluorescence
to record the interference
filter from the imaging
vantageous
ily
as
to the specimen chamber from the
One fundamental difference of such
pattern by
path
light
light
This allows
obtained from these non-fluorescence images
hand,
could
potentially
light
in
one
removing the fluorescence
of the microscope
This
geometric parameters of the pattern
the residual laser
travels
can
is
be
ad¬
eas¬
On the other
which passes the fluorescence filter
deteriorate the fluorescence image
This draw-
THE BEAM SPLITTING UNIT
4 2
turned out to be
back, however,
monochromatic laser
reason
for that
splitting
unit
that
is
Last but not
light
backside-arrangement
be realized
can
a
to
one
Advantageous
particular
microscope
(the
and
equal
unit
in
light
A rotatable
ratio of 1 1
mutually
exceeds
a
Three
produce
path lengths
the
with
can
with
an
upright
4 2
few millimeters
is
resolution achievable with
long
one
tied
inverted
(with
an
of the microscope
and
as
to the beam
a
polarizer
are
splitting
beam
serve
orientation
with
equal intensity
length
an
a
split¬
Because
least to
a
few
the crossing beams
length
of the laser
of the used ylr-ion
only and, hence,
distance condensers poses
by
couplers
for setting the
splitters
the coherence
(Om-
serves as
unit
fiber
equivalent (at
The coherence
rough
mW)
488 nm, power 120
non-polanzmg
used for
closely
an
An ylr-ion laser
integrated pigtail-style
long
on
con¬
unit
four laser beams of
as
distance
not
be used
by production imperfections),
coherent
still usable and
is
is
a
de¬
elegant
an
long
a
object plane
Fig
in
of the four beams
1Trans-illumination
By
generate four coherent laser beams
coupled
A/2-wave-plate
millimeters caused
are
is
fiber with
incident laser power
the
shown
is
It
source
It
even
543-AP-A01, wavelength
coherent
made
that the setup
splitting
to
optical single-mode
was
possible
fact,
serves
mchrome
ting
the
intensity that interfere
The arrangement used
a
still
case) and
stage)
normal
splitting
for the beam
of the two arrangements,
cons
type of microscope
The beam
The beam
of
are
is
appropriate translation
4.2
One
remarkably simpler
stage with little modifications
trans-illummation images
1
strictly
using the
setup
a
plane parallel arrangement
into account the pros
sign, the translation
least,
be used
can
decision for the backside arrangement
denser
due to the
negligible, probably
attenuation ratio of the fluorescence filter for the
high
Taking
43
no
problem
the lower
CHAPTER 4
44
OT
®
fiber
-
1
polarization
maintaining
single mode
fiber
fiber
coupler
X/2
THE HELM SETUP
coupler
waveplate
<8>
polarizing
Ar-laser
beam
splitter
lens
4J
beam
4fc
splitter
beam
shutter
A
splitter
ÎJ»
I
1
piezo
shutter
£""
*<F-#-^-#-Jft
I
shutter
I
coupling
^j
unit
(f M shutter
beam
1
Figure
4 2
to
X
Optical
and ® denote
the paper
splitter
piezo:o\ •#
train of the beam
translatory degrees
plane, respectively
rotational
degrees
the paper
plane, respectively
splitting
The
unit
symbols
of freedom within and
The
of freedom around
symbols
axes
T
parallel
and
and
-.—».
perpendicular
c=> denote
perpendicular
to
4 2
THE BEAM SPLITTING UNIT
laser
is
to be
specified
acceptable
The
for two beams
to
mirrors
move
Four shutters
imen
These shutters
optical
axis in
During
are
the
for
one
or
piezo-
laser beams
more
the four beams to
aligning
cross
at the
an
optical
interference trap
are
appendix A
in
spot size
(focal length /
weak lens
a
of sub-micrometer sized
optical trapping
First results of such
The beam diameter at the output of the
1 5 mm,
by
object plane
Illumination
4.2.1
varied
the work with the HELM setup, the idea of using the mesh-
arose
presented
slightly
to block
provided
are
helpful
be
can
the excitation pattern relative to the spec¬
like interference pattern for
particles
well within the
and, consequently,
mm
range
path length
actuated
300
45
focus the laser beam
=
fiber
colhmatmg
300
Gaussian beam optics
mm)
[68] predict
is
coupler
used to
a
is
slightly
beam waist
diameter wj of
wf
where A
the
is
wavelength
2
of the incident beam
Fig
4
3)
is
uniform
extent of the field of
image
x
2Eq
is
a
4 1
The
(4 1)
125/xm,
light
and wq
experimental
sample
view
is
the beam waist diameter
value
x
512
strictly
holds
good approximation
plane
pixels
only
However,
employed
on
63
x
CCD-chip
NA 1 4
140 /xm,
of 2 5
25/xm
x
or
1
see
large spot
view
The
objective,
and for the
amounts to 25 /xm
magnification
for
processed
or
40 /xm
6, respectively
if the primary beam waist coincides with the focal
for the
as
(roughly
This rather
illumination within the field of
for the
intermediate
an
of the lens
and focal
of
distance of 8 3 /xm
of 512
40 /xm for
plane
it
pixel
size
=
TIWq
close to the theoretical expectation
size ensures
the given
=A^—
long
does not exceed
a
large
as
primary beam waist diameter
(15 mm)
the distance between primary beam waist
few meters
CHAPTER 4
46
Figure
4 3
Image
beams
are
of the illumination
by shutters)
polystyrene beads with
tributed
blocked
lOx NA 0 2
It
can
a
be shown
negligible
a
that,
beam
one
(three
scattering sample of statistically dis¬
diameter of 200
2)
4
nm
is
is set to
a
imaged
with
an
position where
Scale bar is 100 pm
for this geometry, the curvature of the
in the field of view
few centimeters between the
waist.
ellipsis produced by
(see Fig
The lens
objective
the spot diameter is minimal
fronts is
A
THE HELM SETUP
even
when there is
object plane
Therefore, displacements
of the lens
and the
can
wave-
distance of
a
secondary
beam
be used to extend the
spot size.
4.2.2
In
set
The
HELM,
to five
the
piezo
phase
offset of the interference pattern is
different values.
crucial that the
known
actuator
During acquisition
offset is constant.
phase
creeping of common piezoelectric
of
one
sequentially
image
it is
For this reason, the wellactuators
causes
problems.
THE BEAM SPLITTING UNIT
4 2
An alternative to
physical
piezoelectric
47
actuators
difference between the two
is
electrostrictive
are
that
piezoelectric
remanently polarized during manufacturing (and, consequently,
be
operated
below the Curie temperature to maintain
while electrostrictive
ated
slightly
view, there
remanently polarized
not
ones are
above the Curie temperature
four
are
linear for
actuation
are
relation to
in
strongly
is a
is
approximately
quadratic
applied voltage
an
is
factor between five and ten
a
This
potentially
amplifiers,
as
function
these
are
in
relation to
problem
a
poses
with
designed
not
more
tem¬
actuators
The electrical capacity of electrostrictive actuators
by
of
one
perature dependent for electrostrictive
4
oper¬
reduced for electrostrictive
piezoelectric
The mechanical extension for
3
are
ones
and creep
Hysteresis
polarization)
and
practical point
a
applied voltage
an
actuators while it
piezoelectric
for electrostrictive
2
are
must
differences
key
The mechanical response to
1
From
The
ones
actuators
is
increased
piezoelectric
common
ones
high voltage
for such strong capacitive
loads
As the
dence
are
is
linearity
of
minor
of the actuator
impact for
(XIRE 0710L,
They
are
for the
(Fig
The
4
operated
high capacitive
4)
a
,
self-made
load
(approx
as
the temperature
indepen¬
electrostrictive piezo actuators
Finally,
XINETICS Inc
with
well
HELM,
well suited for the demands
tors
as
electrostrictive stack actua¬
Devens
MA, USA)
were
chosen
high voltage amplifier designed
9,2 /xF)
The measured
curve
confirms the expectation about the actuator characteristic
hysteresis
piezoelectric
is
1% which
actuators
is
about
one
tenth of
a
typical
value for
CHAPTER 4
48
Ë
350
|
300
THE HELM SETUP
TO
g
250
£Z
|
200
150
-
£
ioo
50
«
>
0
2*0
5
10
15
piezo
Figure
4 4
25
plotted against
shown is the response to
The
a
triangular
coupling
30
voltage [V]
The measured actuator characteristic
interference pattern is
4.2.3
20
the
The
applied voltage
control
position of the
The
trajectory
voltage
unit
As has been mentioned in the
beams
are
the slide.
coupled
to the
To achieve
duced
by
the beam
(TIR)
at the
beginning of this chapter, the laser
specimen chamber from the backside through
this,
hypotenuses
oil-immersed to the slide
termines the beam's
nodal
the four
splitting
unit
plane parallel
undergo
of four custom-made
( Fig. 4.5).
angle
a
to the
The
spacing of the interference pattern,
setup allowing
one
NA oil-immersion
choice).
to
directly
a
glass prisms
design
optical
axis
of these
and,
as
a
which
are
prisms de¬
result,
the
is set to 55° in the current
observe of the laser
objective (see
laser beams pro¬
total internal reflection
section 5.1.1 for
light through
a
a
high
discussion of this
4.2.
THE BEAM SPLITTING UNIT
49
TIR
\
/
TIR
TIR
/
i
TIR
epoxy
resin
i i
aluminum frame
optical
axis
a"
objective
Figure
4.5:
prisms
are
TIR at the
The
hypotenuses
plane parallel
(approx. 0.2°,
caused
coupling
glued together
to
the
shown
unit,
to
(a)
couple
of the
by laser light which
(b)
for
cut view.
the laser beams to the
prisms, the beams
object plane.
exagerated
top view,
The
prism
clarity)
to
are
block is
Four
glass
sample. By
"bent" out of
slightly
a
rotated
avoid power fluctuations
is back-reflected into the laser
cavity.
CHAPTER 4.
50
Figure
4.6:
Cut view
is moved between the
the
along
optical
THE HELM SETUP
showing
axis
how the
sample
microscope desk and the interference generating
apparatus.
The
assembly
of the four
coupling unit) together
ence
splitting
verted
to fit
unit
microscopes)
on
as
or
shown in
it
can
x-y-translation stage
can
Fig.
be
replaced. Fig.
edge
of the interference
by
can
Fig.
an
the
to herein
as
unit form the interfer¬
be attached to the
4.6
(for
180° around
using
used; only
inverted
clamp
use
with in¬
lateral axis
a
microscope,
mechanism for
4.6 illustrates how the slide is moved
in the air gap between the upper
lower
unit
4.5 and
When
(referred
4.5
splitting
be rotated
upright microscopes.
the slide must be
4
Fig.
in
generating apparatus. The coupling
beam
the
prisms
with the beam
of the
edge
specimen stage and the
generating apparatus (the
gap is approx.
mm).
4.3
The overall
The interference
croscope
(Zeiss
system
generating apparatus
Axiovert
100,
see
is mounted
Fig. 4.7).
on an
inverted mi¬
The used
camera
is
THE OVERALL SYSTEM
4 3
Figure
an
on
an
uncooled industrial
the microscope to
acquisition
with
with
a
required
(Pic-Port,
one
apparatus
(LV-8500,
Leutron
Vision,
connected to the bottom port of
image
deterioration caused
paths
data,
by
imper¬
A standard
control the
image calculations
mea¬
The computer
grabber allowing pixel-synchronous
Leutron
image
Vision, Glattbrugg, Switzerland)
card
(ADIODA-12,
MESSCOMP
the computer
runs
and
GmbH,
A dedicated real-time operating system
for measurement control
DOWS NT 4 0
generating
the standard folded
perform
frame
analog input-output
an
that
in
is
used to read out image
is
Wasserburg, Germany)
as
which
minimize
surement sequence and
equipped
interference
CCD-camera
grade
optical components
personal computer
is
the
inverted Zeiss Axiovert 100 microscope
Glattbrugg, Switzerland)
fect
of
Photography
4 7
mounted
51
is
not
under MS WIN¬
(the one for measurement control as well
reconstruction) is programmed in C++ using the
The software
for image
BORLAND C++-Builder 4 0
The choice of C++
as
programming
CHAPTER 4
52
THE HELM SETUP
PC
(WINDOWS NT)
acquisition
control and
postprocessing
software
interference
generating
apparatus
laser
high-voltage amplifier
Figure
language
4 8
Schematic of the HELM system
and the realization of the
command line program
ensure
image
easy
An overview of the system is shown in
Fig.
to different
4.8.
The measured interference pattern is shown in
practical
avoid
interest is the
stability
Fig.
4.9.
One
point
of the interference pattern.
To
expensive materials like INVAR, the interference generating
paratus mainly consists of aluminum parts which have
thermal coefficient of extension.
into
as
platforms.
System stability
4.4
of
algorithm
reconstruction
portability
an
acceptable
interference
range,
a
very
To nevertheless
compact design
bring
was
rather
ap¬
large
thermal drift
chosen for the
generating apparatus. Experimentally, the thermal drift
of the pattern has been determined to be
system
a
in thermal
equilibrium
typically
20
nm/min
with the environment. As
phase
for
a
offset
4 4
SYSTEM STABILITY
errors
of
one
53
tenth of the nodal
tolerable, thermal
spacing (20 nm) turned
drift limits the
onds. For the uncooled
acquisition
CCD-camera,
this
since the dark current does not allow
ever, for cooled
cameras
the limitation could be
set
during
INVAR.
a
long
overcome
term measurement
or
imposes
longer
it could become
easily
time to
a
a
no
out to be
just
few tens of
sec¬
additional limit
exposure times.
restriction.
by recalibrating
In this
the
How¬
case
phase
off¬
using advanced materials like
54
CHAPTER 4
THE HELM SETUP
Chapter
5
Results
Achievable resolution
5.1
As test
100
nm
available fluorescent
were
distance
is
used
below that
For
far below the
(240
croscopy
nm
one
for
a
closely packed beads,
Rayleigh
NA=1 4
with
slip
com¬
diameter of
the center-to-center
and green
objective
Inc
device,
a
limit for standard fluorescence
,
light)
mi¬
and also
To stabilize the structures, the
surface of the beads
microspheres, Polysciences
cover
beads with
polystyrene
of confocal devices
carboxylate-modified
late
HELM
for the achieved resolution of the HELM
objects
mercially
by
(Fluoresbnte
Warrington PA)
YG
polylysme (poly-L-lysme hydrobromide,
carboxy-
linked to the
was
MW 36
kDa,
Sigma, Buchs, Switzerland)
To compare the
region of
H2O
resolving
standard illumination
1A
short
images
comply
in
power of different
immersed beads
note to
this thesis
(Fig
pixelation
The
pixel
5
band-limited
imaged
using HELM
and confocal scanning
and printing resolution of all
distance of the
with the Shannon criterion
generated by
was
lb),
acquired
(Fig
(Fig
light
images
to
55
one
same
5
5
la),
1
lc)
microscopic
was
The quasi-continuous images
interpolation
the
techniques,
chosen to
printed
quarter of the original pixel
were
size
CHAPTER 5
56
As
reference for the actual locations of the individual
a
atomic force microscope image
acquired
(Fig
also given
is
Id)
5
The resolution of the HELM image
individual beads
is
HELM, although
limit
not
possible
for HELM
the latter
in
the
even
when
In the standard fluorescence microscopy image
remain
Choosing
the
(see
blurred
axis
(Fig
4
5)
3 9
on
page
in
HELM
is
also
2 3
3 1
on
195
nm)
37)
vs
trading
of
28)
page
is a
contrast,
page
11)
amsotropy and
most noticeable
The
are
an
in
subsequent
bicubic
interpolation procedure
for the
granular
opti¬
to
interpolation
smoothes the
structure of
e
is
to the
pixel
g
near
the
in
observation
mesh spacing of
allows
the
one
to
directly
objectives
edges
diagonal
in
good
5 lc
of the
of the
directions
beads,
in
Fig
agreement with the
required printing
noise
Fig
a
vs
Tab
the images of the beads show
passband,
zones
plane (see
the focal
(55° leading
overshooting
the dark
experimental
at to the
frequency (see
cut-off
maximum
and, additionally,
compromise
Due to the non-isotropic
reason
in
amsotropy of the resulting passband and
The chosen value
good
angle
observe the interference pattern with oil-immersion
with
on
spatial frequency of excitation
unwanted decrease of excitation intensity
5 la
3b,
5
can
closely packed
are
Fig
Fig
the beam's
which determines the
The choice of at requires
some
micros¬
of excitation
spatial frequency
One important parameter
Fig
which approx¬
Discussion
5.1.1
cal
Fourier space
in
nm
they
in
close to the
5 3a demonstrates that such beads
Fig
clearly distinguished by HELM,
the individual beads
possible
is
is
limit for standard fluorescence
Rayleigh
The HELM image
diameter of 200
a
Distinguishing
but
ones
100-nm beads
resolving
5 3 shows beads with
imately equals
copy
an
was
superior to that of
clearly
is
5 2 illustrates the achieved resolution gam
Fig
Fig
beads,
which
in air
the standard and also to that of the confocal image
be
RESULTS
original
resolution
images and
This
is
the
5 1
ACHIEVABLE RESOLUTION BY HELM
Figure
Identical
5 1
polystyrene
1 /xm
Plan
(a)
Apo
beads
was
of
area
imaged
imaged using
63x NAl 4
diameter
using
was
a
set to
an
on a
(b)
Apo
nm
diameter fluorescent
techniques
Zeiss Axiovert
was
Scale-bar
image (c)
lOOx NAl 4
length
microscope
imaged through
The confocal
Leica Plan
was
with
is
a
identical lenses
recorded
objective
The
on
a
pinhole
67% of the inner Airy-disk diameter, the resolution
deterioration due to this finite
recorded with
of 100
sample
HELM
objective
using standard illumination
Leica NTSP
a
with different
57
atomic force
pinhole
size is about 15%
microscope (Topometrix
[69]
(d) was
MS)
Accurex II
CHAPTER 5
58
Figure
The Fourier transforms of the HELM
5 2
of the standard
image Fig
Fourier transform in
5 lb
logarithmic
a
RESULTS
5 la and
image Fig
Shown is the modulus of the
complex
scale
function
theoretically predicted point spread
given
in
Fig.
3.10d
on
page 40.
A
more
isotropic resolution together with
is achievable
by employing
This has been shown
various orientations.
recent work
citation
a
for
patterns
rotatable
almost
[35]
at
more
a
isotropic
a
0°,
120° and 240°
are
at the expense of
higher acquisition
one
men
leading
chamber
approach
to TIR at the
[20]. However,
to thin
cut-off
frequency
experimentally
Here,
in
along
a
very
harmonic
ex¬
produced sequentially by
the
point spread function
additional mechanical
is
degree
time.
A further resolution enhancement is
values
high
somewhat different setup.
phase grating. As expected,
of freedom and
a
than four laser beams oriented
possible by increasing
glass-water boundary
around the
at to
speci¬
the evanescent illumination restricts the
specimens and does
not allow
one
three-dimensional
ACHIEVABLE RESOLUTION BY HELM
5.1.
Figure
5.3:
Fluorescent beads with
HELM
(a)
and standard fluorescence
2 /xm.
The
microscope system
identical to the
ones
imaging which
is
HELM devices
expected
In
5.1a and
to be
as
with
the
specimen preparation
is
are
area
of
application
for future
ratio and
imaging speed
in relation to confo-
microscopy
scanning confocal fluorescence microscopy (CFM),
ited
light spot
light
emitted
By
imaged
5.1b, respectively.
crucial
a
nm
microscopy (b). Scale-bar length
(see chapter 6).
Signal-to-noise
cal
Fig.
in
diameter of 200
a
well
as
59
means
of
a
is scanned
by
the
of CFM is increased
hole
across
specimen
pinhole
in
by
a
a
vs.
the lenses
can
Regarding
be collected
this
Conversely,
by
the
a
using the
an
diffraction lim¬
and the fluorescence
secondary image plane,
factor of 1.5 for
resolution.
the
specimen
is collected
[69, 85, 78]. Unfortunately,
noise level
the
the
objective.
same
resolving
infinitesimally
pinhole
necessitates
in HELM all
power
small
pin¬
trading
off
photons entering
camera.
experimental data,
it is
striking
that the
signal-to-
CHAPTER 5
60
(SNR)
ratio
noise
of the HELM image
of the confocal image
laser power
Fig
5 lc
5 la
for the reduced SNR of the confocal image
photon-blockmg pinhole
the
and
noise
(see
the
2)
roughly
pattern
at
applies
half of the
rate of the
only
to
million for
a
in
orders of
for the
magnitude
parallel
to
one
one
of HELM
A
in
spot
Jspot
2
is
Fig
to
or
tt
Fig
in
speed
Fig
lOOnm
5 1
HELM,
CFM this
one
per
is
several
are
of CFM than
to the
proportional
a
higher photon
acquisition
up image
dye
polarizing
field of
view
beam
size
0 12 mWs
measurement
actually
saturation
The intensity
flux
(or
a
lOOnm
x
(see
5 lc
size
in
for the
though
X
splitter, acquisition
140 (im
X
140 /im
X
Assuming 25% security
0 16 mWs
5 1
above the saturating
2) Therefore, dye
striking
SNR difference
the saturating intensity
5 mW
25 (im
W
nr
subsection 3 2
object plane
25 /im
occurs
the focal
16xlOn^r
magnitude
even
in
roughly
is
,,
one reason
Laser power
time 6 5 s,
geometric spot
size
by
sequential operation
two orders of
5 la and
25 /im,
spot
In
the interference
limited to values that
=
assumed to be
Confocal image
4 mW out of
limited
5mW
area
one
tion), acquisition
saturation
consequence, the total
a
acquired photons,
or
intensity of typical fiuorophores
between
As
=
spot
saturation
dye
single-point
Since the SNR
laser power
=
is
reason
both)
of the CFM used
This value
is
fiuorophores (approx
for moderate laser powers
even
/Spot
is
is
illuminated
common
estimation illustrates that
rough
CFM
SNR
increase
combination of
the
smaller for the
square root of the number of
allows
are
pixel image)
flux from the specimen
photon
integrated
One
the above described
CFM
in
fiuorophores
tiny fraction of the
1024x1024
a
speed
fiuorophores
time, whereas
one
is
one
Due to the finite lifetime of the excited state,
maximum emission
one
superior to that
Another very fundamental effect increasing
the imaging
limiting
subsection 3 2
is
the total time
mWs, respectively2
0 16 mWs and 32
was
Fig
though
even
RESULTS
(manufacturer specifica¬
HELM image
time 16 s, image
l/cos(55°)
Laser power
size
25 /im
=> Laser energy
factor to account for
errors
X
in
in
MEASURING BIOLOGICAL SAMPLES
5 2
of the
particular fiuorophore
embedded
the beads
in
Concerning high speed
are
performed
contrast to
in
dye
culties of
CFM, however,
the
advantages
experimental
required
required
is
the
by
multi-point
newer
Fig
in
Fig
grade
speed
can
also be
seen
in
5 la
16s
was
Taking
5 lc
compared
into account the
CCD camera, this
is a
is
to 6 5
s
for the
higher signal-to-
achieved with
uncooled
an
clear difference
Measuring biological samples
5.2
HELM
was
used with
5 7 show different
various
polymer
preparation methods
tubulin filaments
portant role
in
5 8 and
Fig
propriate stammg
are
for
employed routinely
are
3
biological samples
embedded rat tissues
presence and localization of
cells
per image
The total acquisition time for the five images
ratio of the HELM image which
industrial
as
the field of imaging
in
data
for HELM
confocal image
noise
per line
one scan
problems
scans
and the mechanical scanning diffi¬
be reduced
can
five
only
as
[47, 86]
scanners
The
where
CFM,
problem
saturation
not known
is
imaging, HELM also reduces the
linked to mechanical scanning mechanisms
Both the
61
e
hormones
g
5 4 to
Fig
diagnostic
can
purposes
be studied
by
ap¬
5 9 show cell cultures where the
Fig
immunostained
spatial organization
Fig
Similar specimen
Tubulin filaments
play
an
im¬
and transport mechanisms within
[3, chapter 16]
5.2.1
Materials and Methods
The tissue
Histological samples
(2-hydroxyethyl methacrylate)
3I gratefully
samples (Fig
thank Jakob
5 4 to
Fig
5
sample (Fig
5
9)
resin
and,
using
and
a
microtubule
Ueh
in
GMA
microtome,
semi-
embedded
were
Zbaren, Inselspital, Bern,
7)
thank Rosemarie Sutterhn and Prof
microtubule
samples
a
for
supplying histological
sample (Fig
5
8)
Aebi, Biozentrum, Basel,
Likewise,
I
for the other
CHAPTER 5
62
(approx
thm sections
from the
750
of different
use
the four tissue sections
nm)
were
Fig
5 4 to
Due to the very weak penetration of the
7)
5
was
section surface
attached to
oxidase
a
In the next step, suitable
dextran
(HRP)
chain with
polymer
(EnVision,
sites
Dako
bound onto the primary antibodies
HRP-antibodies
were
available,
sites
thus
antibodies
horseradish per¬
fluorochrome
used to visualize the reaction sites
providing
added
were
secondary
Diagnostics, Zug, Switzerland)
Finally,
eral hundred fluorochrome conjugates
for
same
restricted to the
is
numerous
the
molecules into
primary antibodies
Firstly, appropriate
to the tissue section
procedure
basically
large antibody
the GMA resin, the immunohistochemical reaction
Apart
knives
glass
the lmmunostammg
antibodies,
(Fig
cut with
RESULTS
can
bind to the
conjugated
whereby
sev¬
HRP
numerous
strong fluorescence signal despite the
a
limited antigen epitopes present
in
the surface
of the
layer
resin
sec¬
tions
Tubulin filaments
(Fig. 5.8)
cells
After fixation
by
suitable
a
was
a
Human endothelial cells
primary
conjugated
Tubulin
sample
Human fibroblasts
mary
mouse
binding
numerous
seven
cultured
Finally
(a
few
slides
on
followed
applied
was
visualization
hundred)
fluo¬
anti-biotm antibodies to the reaction sites
of human
were
grown
anti-mouse
ftuorophore-to-protem
therefore,
of
on
gingiva
a
cover
anti-/3-tubulm antibody
rophore conjugated
The
were
anti-/3-tubulm antibody
secondary biotmylated antibody
achieved with the
rochrome
immunostained in human endothelial
ratio
fluorophores
was
antibody
was
per
7 0
fibroblasts
applied
was
(Fig. 5.9)
After fixation
slip
Finally
a
a
pri¬
fluo-
used for visualization
(manufacturer specification),
antigen epitope
is
the
maximum
achievable
5.2.2
Discussion
Concerning
the
histological samples Fig
that the HELM images show
a
granularity
5 4 to
Fig
5
7,
it
is
of the fluorescence
striking
emission
MEASURING BIOLOGICAL SAMPLES
5 2
which
visible
hardly
is
probably
does not
the standard FM images
in
is
cannot
to be
expected
to real
correspond
of the vesicles amounts to
and, hence,
partially
the observation
a
result of the
stammg procedure employed binds
is
required
biological
This
a
that,
the
as
multiplication
size
[3, chapter 13]
The
granularity
The
fluorophores
of fluorescence
to
one
emission
compensate for the relatively low number of antigens
to
as a
granularity
sample preparation
few hundred
available for immunochemical reactions
is
This
structures
few hundred nanometers
a
fully explain
specific antigen epitope
63
result of the
beled antigen epitopes
high
(with
a
The presumption
polymer
in
resolution of
few hundred
the individual la¬
HELM,
fluorophores attached)
resolved and lead to the
granular
power of HELM shows
stammg artifacts which
the
Hence,
structure
are
are
high resolving
hardly
visible
in
the standard FM images
For cell culture
procedures
of
were
samples
sample (Fig
lium cell
sample (Fig
lium cell
sample
to the fibroblast
expected
in
5 8 and
Fig
subsection 5 2
Fig
1)
5
As
a
9, different stammg
was
5
5
is a
brightness
factor of approx
a
Since this
for the
seven
few hundred for the endothe¬
The observed
higher by
sample
as a
9)
8)
while it
the number
result,
per labeled antigen epitope amounts to
fluorophores
fibroblast
than
(see
used
brightness
of the endothe¬
four
difference
result of the different stammg
in
is
relation
much less
procedures,
it
is as¬
sumed that the number of antigen epitopes available for stammg
higher
in
the fibroblast
image
along
Fig
the filaments
5 8c
fluorescence
sample
is
confirmed
observation that the fluorescence distribution
experimental
uniform
This assumption
even
emission is
of available antigens,
in
Fig
5 9 than
shows little gaps
observed
however,
is
The
along
reason
not clear
in
Fig
5 8
was
by
is
the
more
The HELM
the filaments where
no
for the different number
CHAPTER 5.
64
Figure
5.4:
secreted
by
Rat pancreas semi-thin
the
/3-cells
plastic
of the islets of
section.
RESULTS
The hormone insulin
Langerhans
is immunostained.
Prior to release from the cells, insulin is contained in secretory vesicles
granules
by
cytoplasma. (a)
FM, respectively. Scale
within the
standard
small detail of
(a)
and
and
(b)
are
imaged by
bar is 10 pm.
(b), respectively.
(c)
and
Scale bar is 1 pm.
or
HELM and
(d)
show
a
5.2.
MEASURING BIOLOGICAL SAMPLES
Figure
5.5:
glucagon
Rat
secreted
pancreas
by
semi-thin
or
HELM and
(d)
show
a
granules
by
section.
the a-cells of the islets of
tained. Prior to release from the cells,
vesicles
plastic
within the
standard FM,
small detail of
(a)
glucagon
cytoplasma.
respectively.
and
65
(a)
The
Langerhans
hormone
is immunos-
is contained in secretory
and
(b)
are
imaged by
Scale bar is 10 pm.
(b), respectively.
(c)
and
Scale bar is 1 pm.
CHAPTER 5
66
Figure
5 6
matotropin
Rat
hypophysis (pituitary gland)
is immunostained
hormone, sematotropin, which
ules within the
imaged by
(c)
and
1 pm
(d)
The
show
a
by
sematotroph
plastic
section
cells secret the
is contained in secretory vesicles
cytoplasma prior
HELM and
semi-thin
RESULTS
to
release from the cells
standard FM,
small detail of
(a)
respectively
and
(a)
growth
or
and
Se-
gran¬
(b)
are
Scale bar is 10 pm
(b), respectively
Scale bar is
5.2.
MEASURING BIOLOGICAL SAMPLES
Figure
5.7:
tained.
Rat
kidney
Laminin and
semi-thin
collagen
basement membranes which
(b)
are
imaged by
bar is 10 pm.
(c)
and
Scale bar is 1 pm.
show
Laminin is immunos-
structural support for
epithelial
HELM and
(d)
section.
fibrils compose the basal lamina
provide
build selective barriers between
and
plastic
67
a
by
layer
of
epithelia
and
cells and connective tissue,
(a)
standard FM,
small detail of
(a)
respectively.
and
Scale
(b), respectively.
CHAPTER 5
68
Figure
5 8
Microtubules in human endothelial cells
of the tubulin filaments is about 25
imaged by
(c)
and
1 pm
(d)
HELM and
show
a
by
nm
standard FM,
small detail of
(a)
The actual diameter
[3, chapter 16] (a)
respectively
and
RESULTS
and
(b)
are
Scale bar is 10 pm
(b), respectively
Scale bar is
5.2.
MEASURING BIOLOGICAL SAMPLES
Figure
5.9:
Microtubules in
a
69
cell culture of human
gingiva fibroblasts.
nm.
[3, chapter
16]. (a) and (b) are imaged by HELM and by standard FM, respectively,
(c) and (d) show a small detail of (a) and (b), respectively. Scale bar
The actual diameter of the tubulin filaments is about 25
is 1 pm.
contrast
low
The structured
of the
luminosity
relation to the
camera
of the
images
background
had to be set to
sample.
in
Fig.
is
a
a
result of the fact that the
very
high
value for the relative
Therefore, the noise level is increased in
5.4 to
Fig.
5.8.
CHAPTER 5.
70
the OTF
Measuring
5.3
RESULTS
reconstruction in HELM by applying Eq. 3.55 requires at least
approximate knowledge of the optical transfer function of the mi¬
Image
an
The OTF
croscope.
predicted
cut-off
the measured
To
and
were
modeled
were
the
the calculations.
was
on
a
point
Secondly,
light
over an area
acts
as
which
effective
on a cover
Additionally
(Zeiss
wavelength
x
the
[55].
filter
ideal
which
is
computed
was
an
of 540
nm.
assumed to be free from
First,
by
easily
53
pixel
in the
finite
pixel
a
Fig.
or
the
,
this,
in
conjunction
termines the
of the
of
shape
bandwidth,
the
with the
passband
DIC)
itself is not
were
ad¬
thickness of 170±5 /jm.
a
calculated
curve
communication Dr.
The manufacturer's
of the
objective
and the tube lens for
both components
material
a
were
imperfections.
spatial frequency
for HELM. As
spatial frequency
incoming
the beads
Most crucial for HELM is the usable bandwidth of the
since
x
size and finite bead
frequency
5.10.
calculations,
geometric
/jm
object plane)
the CCD-camera
optical system consisting
In the
con¬
The attenuation at the theo¬
selected for
1.4 Oil
to the
be introduced into
size
Göttingen (personal
63x
the beads
CCD-pixels (8.3
nm
The cut-off
in
nm
Two
sources.
opposed
optical conditions,
presented
for
Apochromat
Plan
as
to the measured and scalar curves,
Faulstich, 1999)
was
the
as
diameter of 100
point
CCD-pixels integrate
introduced
assure
slip
[33],
can
nm
approximates
low-pass
obtained from Carl Zeiss in
A.
to 53
28%, respectively.
affected at all. To
curve
well
different from
In this case, the spec¬
the finite size of the
As the
frequency
size is 10% and
sorbed
source, and
chip corresponding
retical cut-off
a
as
circles.
besmc-function
taken into account.
an
served
nm
uniformly emitting
spectrum of
8.3 /jm
of 540
introduced in the OTF calculations:
as
trum is the well-known
stant
as
noticeably
beads with
OTF, polystyrene
wavelength
emission
corrections
theory [33]
from scalar
turned out to be
ones.
measure
an
expected
frequency
a
of
microscope
excitation, de¬
practical
measure
for which the value of the OTF
MEASURING THE OTF
5 3
71
measured
scalar
08
-
06
-
04
-
02
-
theory
computation
manufacturer's
j_
0
12
3
4
5
[1/u.m]
Figure
5 10
Measured and calculated
spatial frequency
factor of 2n from the
theory
is
a
is
4.9//xm
imposes
an
transfer function
The
per pm which is different
by
a
used elsewhere in the text
The 1%-bandwidth
whereas the measured
difference of 20%.
tween and
optical
pairs
angular frequency
below 1% is used.
drops
in line
specified
is
one
expected
The manufacturer's value
upper limit for what
from scalar
3.95//xm
(4.45//xm) is
is about
can
which
in be¬
be achieved with the
microscope.
Various
possible
reasons
manufacturer's cut-off
tolerances of the
objective
ditional components
filter)
exist for the 10% difference between the
frequency
and the measured
and tube lens
as
well
(OPTOVAR magnification
will deteriorate the
one.
as
For
example,
imperfect
image. Furthermore, the fluorescence
sion of the beads is not monochromatic
as
ad¬
system, fluorescence
emis¬
assumed in the calculations.
CHAPTER 5
RESULTS
characteristic of
fluorophores
72
Last but not
at the
least,
glass-water
the
embedded
rophores
Measurements
Eclipse
E800 with
Again,
the
angular
interface
in
complicated
also
performed
for
than that
a
cut-off
frequency
(NIKON
objective)
NIKON system
NIKON Plan Fluor 100x 13 Oil DIC
experimental
of fluo¬
one
[5]
media
homogeneous
were
a
emission
is more
was
about 25% less than
expected
Measurements
performed by
other groups also report noticeable
differences between measured and
25%
approx
ditions,
fer
by
were
the OTF
performed
was
theory
conditions
instead of
edge-object
under
were
are
Cut-off
reported
quite different
broadened
reported
are
frequencies
by
The
con¬
which dif¬
[74] and [83] but the
(non-fluorescence mode,
in
point-object)
For the image reconstruction
OTF of the microscope
is
HELM,
the measured
geometric
parame¬
algorithm
of
used
Determination of
5.4
properties of the
are
comparable experimental
not considered
about 50% from
experimental
imaging
functions which
relation to theoretical expectation
in
measurements
predicted
[51], point spread
In
microscope
ters of illumination mesh
To determine the orientation and
pattern,
one
bright-field
from the imaging
orescence
filter,
light
is
alternatively,
of
light
of the interference
is
acquired
4
from the laser beams
several orders of
magnitude
Without the flu¬
is
dominant
weaker
the correlation between the measured image and
term for the interference
cence
image
of the microscope
the direct
the fluorescence
ically,
path
spatial frequency
I\> with the fluorescence filter removed
images
[35]
pattern with
the mesh parameters
Using bright
working independently
can
an
since
Numer¬
analytical
varying orientation and
spatial
also be determined from the fluores¬
field images for that purpose has the
of the SNR of the fluorescence images
advantage
DETERMINATION OF MESH PARAMETERS
5 4
frequency
maximized
is
to the
according
following
73
expression
max
cos
where / and
is
the
pixel
m
(
m
dux
the
are
Ax
Ay
and
)
mj
distances
x-
and
the
in
(
)
^y)
tional
due to
filter
fore,
there
or
in
not
a
the image,
Fortunately,
for all images
easily
Assuming
be
Ax,Ay
(ex + TT, ey), (ex,
acquired
ey +
that, by applying Eq
the
the absolute
is
reconstructed
1, el£x, e~l£x,
ely
vr/2)
images become
and
(ex,
ey +
and mechanical
offset ex and ey
There¬
bright-field
phase
n)
offset
and
common
offset pairs
phase
(ex,ey), (ex
It
be
can
additional
=
e~*e», respectively
adjustment
can
5
+
n/2,ey),
easily
3 53 with the given coefficients of matrix
For the indices j
and
to addi¬
slightly wedge-
optical path
the
phase offsets,
original spectrum tp multiplied by
tors
a
rise
determined from the fluorescence images
additional constant
for the five
corrected
gives
coincidence between
spatial
fluorescence image
can
probably
ideally infinity
absolute
is no
and d
the removal
Unfortunately,
path
displacements
(5 2)
,
2, the phase off¬
expression 5
in
of the fluorescence filter from the imaging
shaped
)
Ay
y-pixel coordinates, respectively,
also determined
are
(
object plane
the maximization
By performing
sets
)
(
+
l
dwy
Uy
+cos
U-œ
+Ax
^y
+AX+cosdUy+
^cc
M_1,
complex phase
5 these
1
shown
phase
Depending
on
factors
fac¬
are
temperature
of the HELM setup, the constant
phase
have any value between 0 and 2n
To determine ex and ey from the measured fluorescence images,
the reconstructed spectra for different indices j
5)
1
5
to
a
are
compared
in
the appropriate
Since the fluorescence filter
lateral
displacement
is
affect the lateral image position
systems
However
wavelength
the
if the system
parallel
tilted
of the beams
beam
in
is
by 45°
(denoted
overlap
relative to the
This lateral beam
case
not
of
parallel
displacement
leads to
a
optical
V'j=fcj
in
k
=
More foraxis
infinity
corrected for
it leads
does not
displacement
beams
ideally infinity
as
regions
corrected
a
lateral image shift
certain
CHAPTER 5.
74
mally
ex and
calculated
are
ey
RESULTS
by
u-xe
ex
=
arg -f—
^=1
arg
=
(5.3)
and
—
M-le
M-le
arg -^—
=
=
(5.4)
arg
M-le
%=i
where
Eq.
3.53 is inserted and where the fact that the OTF T is
real number is used.
are
averaged
for
a
few
account for the real
tp:J=k,k
=
1...5
1, e~lx, elx,
an
points
phase
are
precise results, Eq.
in the
5.3 and
a
Eq.
5.4
appropriate overlap region.
To
offsets ex and ey, the reconstructed spectra
with the inverse phase factors (i.e.
e*e», respectively) before Eq. 3.55 is employed
multiplied
e~*e» and
to calculate the
influence of
To achieve
spectrum of the final image. Fig. 5.11 illustrates the
intentionally
introduced
phase
offset
error
of
n
on
the
resulting images.
Fig.
5.12 shows the
resulting images
introduced mesh parameter
errors.
with various
intentionally
The conclusion is that
errors
of
0.1% and 0.25° in spatial frequency and orientation angle, respectively,
do not
significantly
surpassed by
deteriorate the
the correlation
images.
procedure.
This accuracy is
easily
DETERMINATION OF MESH PARAMETERS
5 4
Figure
in
5 11
HELM
The influence of absolute
Scale bar 1 pm
(a)
shows
modulus of the Fourier transform of
phase
by
n
offset ex determined
This
looks like
an
in
the
overlap
echo image
region
Fig
For images
by applying Eq
for image reconstruction
errors on
detail of
a
(a)
shifted components of the spectrum
the cancellation
phase
5 3
was
effectively
As
a
In
75
image formation
5 4a
(b)
(c)
and
shows the
(d)
the
x-
intentionally changed
the
inverts
horizontally
(d) clearly
(b) the
result
image
spatial
domain
shows
image
CHAPTER 5.
76
Figure
5.12: The influence of mesh parameter
in HELM. Scale bar 1 pm.
A detail of
with standard fluorescence
microscopy, (b)
image.
was
In
(d)
the
x-angle
intentionally changed by
struction.
ux
(c)
and
was
In
(e)
and
(f),
changed by 0.1%
Fig.
0.25° and 1°,
image formation
5.4 is shown,
is the
jx determined
(a)
is
corresponding
imaged
HELM
by applying Eq.
for
5.2
respectively,
image recon¬
spatial frequency of excitation
0.5%, respectively.
the determined
and
errors on
RESULTS
INFLUENCE OF DEFOCUS ON HELM
5 5
Influence of defocus
5.5
For defocused
rithm
OTF
in
is
also altered
increasing
one
[33, 12, 24]
HELM
used
by
As
consequence, the effective HELM-
a
the image reconstruction
Because the width of the OTF
the HELM-OTF
defocus,
HELM
on
the effective OTF of the microscope lenses be¬
objects,
different from the
comes
77
frequencies Experimentally,
shows
basically
reduced for
gap at medium
a
the influence of defocus
is
algo¬
shown
is
Fig
in
5 13
For increasing
noticeable
is
scaling procedure
most
nm
îmmersion
for
various
a
objectives [44]
defocus
z
z
In
to
nm
depth
to scalar
most
result of the
a
defocus of about
high NA
is
oil-
calculated
The calculations
theory
the value of the OTF at half the cut¬
are
in
6
Therefore,
good agreement
the
with
predictions
6The parameter
numerical aperture
nm
a
the OTF
55% of the m-focus value
results about focus sensitivity of HELM
240
side-lobes,
is
of focus of
[12, chapter 9],
according
240
=
frequency drops
theoretical
This
of visible image deterioration for
result of the very low
show that for
off
level
which sets the most negative value to black and the
occurrence
is
background
to white
positive
The
200
the images show stronger
defocus,
the increased
for NA=1
m
used
as m
=
4, A=540
in
the calculations
^r—z
nm
Therefore,
and ra=l 52
in
m
[12]
=
1
can
be rewritten using the
corresponds
to
a
defocus of
CHAPTER 5.
78
Figure
5.13:
Influence of
fluorescent beads of the
with HELM
(bottom)
The
are
slip
In
images
which
(d)
a
same
obtained
cover
to
show four different 100
by
an
a
slip
imaged
grey-scale
range.
and 200 nm,
of 0.6° relative to the
same
(top)
of all
plane
left at the
images
are
and
on a
cover
object plane.
size located approx.
with the focal
brightness
diameter
respectively.
preparation of beads dried
angle
embedded bead of the
is
nm
in HELM.
nm
with standard FM
sample imaged
by using
interface. Contrast and
the full
(c)
image formation
errors on
for defocus of 0, 105
inclinated
gelatine
behind the
water
was
focusing
Images (a)
Scale bar 1 pm.
RESULTS
1-2 pm
cover
slip-
scaled to span
Chapter
6
Three-dimensional
HELM
In the previous
the HELM method
chapters,
framework of two-dimensional imaging
For
tions, investigating the three-dimensional
is
of major interest
ping the
focus
the specimen
index
of
this requires
vestigations
in
structural
Unfortunately,
show
1In
200
potential
OSM has become
is
artifacts
has been
interference
reported
in
the
applica¬
possible by step¬
acquiring
a
stack
an
with low refractive
belong
to this class
important tool for
in¬
biology
strongly
(see
contrast to fluorescence
nm
specimens
the axial resolution achievable
standard microscopes
is
and, thus,
weakly absorbing objects
heterogeneity Typical biological
objects and, therefore,
of
("optical sectioning microscopy", OSM)
of two-dimensional images
Evidently,
large
area
structure of the specimen
Three-dimensional imaging
through
discussed
was
a
for
limited
section 6
imaging,
phase
a
1)
79
1
very
sensitive
contrast) [43]
and,
in
even
fluorescence with
worse, the images
Several attempts have been
high
axial resolution of approx
imaging
modes
(e
g
differential
CHAPTER 6
80
THREE-DIMENSIONAL HELM
made to enhance the axial resolution
common
being
ferent known methods for
HELM,
high
referred to herein
In this
dif¬
chapter,
micros¬
the three-dimensional extension
3D-HELM,
as
The limitation of
6.1
microscopy, the most
resolution three-dimensional
Afterwards,
copy will be discussed
of
optical
in
the confocal scanning microscope
will be studied
mi¬
optical sectioning
croscopy
In the
following,
the considerations will be restricted to the
fluorescence microscopy,
l e
incoherent imaging
two-dimensional case, the microscope
can
be
described
completely
by
their
(denoted
three-dimensional OTF
which
can
be calculated
(shown schematically
by
degrees
6
1)
is
a
of
can
linear
torus-like
The
be derived
defocus2 [29, 24]
theory [33]
scalar diffraction
Fig
in
various
a
1, LSI systems
3
3D-OTF)
as
as
of
to the
transfer function
optical
herein
from the two-dimensional OTF for
section
in
case
analogy
be described
can
As mentioned
shift invariant system
In
The 3D-OTF
object
with two
key
properties
1
The support of the OTF
cone-shaped
(generally
very low
known
as
frequency
parallel
"missing cone")
The spectrum of
to the
x-y-plane,
are
hardly
resolved
2With OTFZ0(kx,ky) denoting
OTF(fcj;, ky,kz) can be easily shown
with respect to the zo-coordinate
by
averaging the values
along
As
the
[54]
the
a
at
consequence,
region
not
ori¬
consists of
Consequently,
such
The fact that the resolution for
2D-OTF
for
defocus
z0,
to be the Fourier transform of
The 2D-OTF
fcz-axis
even
are
slice-shaped objects
mainly
a
the origin
object spectrum
for instance,
components within the cone-shaped
objects
does not include
A;z-axis centered
components of the
transferred at all
ented
(the passband)
region around the
can
the
3D-OTF
OTFZ0(fcj;, ky)
be obtained from the 3D-OTF
THE LIMITATION OF OSM
6 1
Figure
The support of the three-dimensional OTF of
6 1
Shown
microscope
The OTF
tion
is
is a
kx-kz
exactly
particular objects
to
as
cut-view
within
can
break down
conical region around the A;z-axis
completely
often referred
is
image
corresponds
is
singular
at the origin
independent
highly-resolved
This property of
to the fact that the average
of the defocus of the
consequence, the contrast of thick
the
fluorescence
artifactual imaging
the OTF
an
a
a
of the rotational symmetric func¬
zero
The 3D-OTF becomes
2
81
objects
m-focus information
is
is
intensity of
3
object
strongly
overlaid
As
reduced
by
a
a
as
strong
out-off-focus blur
Due to these unfavorable properties of
orescence
high
ied
microscopes,
resolution
in
in
in
with standard flu¬
three-dimensional space have been
the last three decades
discussed
3D-imagmg
alternative methods to achieve
The most relevant
ones
an
uniformly
intensely
will be
stud¬
shortly
the next section
Conservation of average intensity is a consequence of the fact that all photons
entering the lenses contribute to the image produced by the microscope
CHAPTER 6
82
for axial resolution
Approaches
6.2
THREE-DIMENSIONAL HELM
enhancement
The confocal
6.2.1
microscope
In confocal fluorescence microscopy
out-off-focus planes
a
secondary
microscope
image
can
are
partially
(CFM), photons originating
blocked
by
of the microscope
plane
a
small
6
2a)
be shown to be the autocorrelation of the standard
The extent of the
doubled
passband
direction
is
However,
the achievable resolution gam
in
of the OTF towards
is
lateral
nm
pinhole, consequently
1
are
as
well
less due to the
[14] and, thus,
photon efficiency
The
a
high peak
result,
by
the
newer
an
is
minimum
noise
less
4For
speed
These
photon
illuminating
number of
pinhole,
practical
rea¬
difficulties, however,
[47, 86]
CFM
in
2)
subsection 3 2
As
flux emitted from the specimen
magnitude
the whole specimen
photons
is
required
the fundamental imaging
wavelength
the
scanners
fluorophores (see
fluorescence microscopy, this relation
account the
small
[49, 23, 85, 78]
by
intensities of the focused laser beam
saturate the
the total
level,
objectives
mfimtesimally
caused
multi-point
limited to values several orders of
methods
decline
rapid
drawbacks
be reduced
potentially
axial
in
still inferior to the
The scanning data acquisition limits—at least for
can
(see
cones
as
The lateral resolution
achieved for
sons—the achievable imaging
2
is
the real resolution gam
In addition to the limited
mam
missing
at best for NA 1 4 oil-immersion
about 0 8 /xm
one is
CFM has two
nor
lateral
relation to standard fluorescence microscopy
These ideal values
one
in
high spatial frequencies
of the order of 150
and the axial
in
The OTF of the confocal
OTF4 [75, 54] and has neither singularities
Fig
from
located
pinhole
is an
in
for
speed
a
parallel
Since
certain
signal-to-
limitation
approximation
difference between excitation and
is
lower than for
not
emission
is
much
taking
light
a
into
AXIAL RESOLUTION ENHANCEMENT
Figure
83
Qualitative illustration of passband enhancements achieved
6 2
(a)
different
approaches
by
confocal
microscopy, l2M, l5M, ASWFM and LSWFM, respectively
(f)
is the
Panels
(e)
by
resulting passband
to
show the
passbands
obtained in 3D-HELM for
one
combination of excitation patterns with various orientations
cal
was
particular
Only
confo¬
and 3D-HELM allow simultaneous enhancement of lateral
microscopy
well
as
achieved
axial resolution
lower for CFM than for
parallel
methods
(see
also subsection
5.1.1).
A derivative of the CFM is the so-called
a
second
objective
such
By using
about 120
pared
nm
an
is used for
one
and for
imaging
purposes.
arrangement, the axial resolution is improved
while the lateral resolution remains
to the CFM. The
ments of
4n-microscope [39, 40]. Here,
illuminating
objective
4n-arrangement
unchanged
is very sensitive to
relative to the other and it
to
com¬
displace¬
requires digital
CHAPTER 6
84
image processing to
remove
THREE-DIMENSIONAL HELM
artifacts originating from the
extremely
non-uniform OTF
As the
47T-microscope does,
employs
second
a
method
image interference microscopy
objective
The images
superimposed
on
a
But,
in an
increased axial resolution
A further
making
of the
development
As
a
the
is
focal
plane
is
inating from
device
is
selectively
an
incoherent
120
nm
Just
as
approx
(see Fig
2c)
6
to relative
illuminated
displacements
processing of the images
and
I5 M
light
still
a
high
resulting
missing
(see Fig
cone
6
2b)
interference with
"image
(I5M) [38] Here,
in¬
the
interference of two beams orig¬
The axial resolution of this
source
outperforms the lateral one
4n-microscopy, I2M and I5M are sensitive
and, thus,
of the
even
objectives
Furthermore,
not increased at all
is
by
is
also
coherently
additional
transferred
are
coherent interference illumination" microscopy
(I2M)
non-scanning
are
artifactual
potentially
I2 M
a
result,
there
However,
is
objectives
of the specimen
the images
it
contrast,
the two
CCD-chip [36, 37]
frequency components
the OTF
in
produced by
axial
in
microscopy (I2M)
interference
Image
6.2.2
in
and require
digital post¬
the lateral resolution of
I2M
relation to standard fluorescence
microscopy
Computational
6.2.3
Another
approach
for lateral
itself but
one)
employs digital
such
struction of
OTF
to
is
noise
for increased axial resolution
microscopy
image processing
sometimes also
in
algorithms
[8, 2, 1, 42, 53, 18, 19] Taking
as
some
possible
in
(and
does not address the image formation
tional information
knowledge
methods
the microscope
to extract addi¬
into account
non-negativity of the intensity distribution,
a
priori
recon¬
parts of the spectrum outside the support of the
In practice,
the images,
however,
particularly
such methods
posing
a
problem
are
in
susceptible
fluorescence
3D-0TF EXTENSION BY HARMONIC EXCITATION
6 3
excitation methods
6.2.4
Standing
Different
approaches addressing
nodal and antmodal
ployed
selectively
to
standing
thm
are
wave
excitation have been
wave
ing
wave
For
Another
wave
400
ASWFM)
tenth of the
cone in
based
in
For
which
objects
an
axial
wavelength
emission
the imaging
the OTF
em¬
(axial
[52]
was
is
still
remains
(see
interference fields with their nodal
on
to the
parallel
optical
LSWFM)
demonstrated [64, 65],
has been
be
3)
is
planes
missing
axis
(lateral standing
An axial resolution of about
fluorescence microscope,
nm
can
of the excitation pattern,
period
one
as a
approach
and antmodal
object plane
arbitrary objects, however,
artifactual
6 2d and section 6
Fig
Interference fields with their
to the
fluorescence microscope,
[6, 28, 54]
potentially
proposed
stand¬
by
excite individual sections of the specimen
resolution of the order of
found
axial resolution enhancement
planes parallel
relation to the
in
85
which
is
an
improvement
to standard fluorescence microscopy but still inferior to the lateral
resolution
wave
(see Fig
patterns
on
Another related
Here,
a
topographic
jection of
the
depth
tern
a
2e)
The effect of
technique
fringe pattern
Digital
arbitrarily
is
is
onto the
encoded
image processing
is
oriented
formally
standing
section 6 3
in
topometry by fringe projection
map of the specimen
information
information
6.3
6
the 3D-OTF will be studied
object
in
the
is
obtained
surface
phase
By
by oblique
[88]
pro¬
this projection,
shift of the
used to reconstruct the
fringe pat¬
topographic
[87]
3D-OTF extension
harmonic exci¬
by
tation
The effect of excitation with
on
the 3D-OTF
dimensional
can
case
a
three-dimensional interference pattern
be described
(see
in
far-reaching analogy
section 3 3 1 and 3 3
2)
to the two-
An excitation pattern
CHAPTER 6.
86
generated by
interference of two laser
J(r) according
distribution
intensity
J(r)
1 + M
=
where M is the modulation
tion, A
are
accounts for
=
an
depth,
beams5
cos(ur
u
87r3(5(k)
+
+
is the
arbitrary phase
4tt3M
can
be described
by
an
to
A)),
(6.1)
spatial frequency
of excita¬
offset and where
The Fourier transform I of the
neglected.
J(k)
THREE-DIMENSIONAL HELM
[elAö(k + u)
+
where ö denotes Dirac's delta function.
scaling factors
intensity distribution is
e~îAc5(k
-
Introducing
u)]
(6.2)
,
the
following
scale-shift operators
one
si(F(v))
=
F(v),
s2(F(v))
=
MF(v
S3(F(V))
=
MF{w
(6.3)
+
-
u)
(6.4)
and
u)
(6.5)
obtains for the spectrum 6 of the three-dimensional
duced
by
the
T
=
where
tp
scaling
#i,#2
2si(V>)
is the fluorescence
factors
an(i
following
3
^3
x
image
pro¬
microscope:
are
f°r
„«A
,-»A
S2W
S3W
spectrum and T is the 3D-OTF and where
neglected. By sequential acquisition
phase
(6.6)
offsets of
3 set of linear
Ai,A2
equations
and
of three
images
A3, respectively,
the
is obtained:
(6.7)
5
Section 6.4
explains why
ference for 3D-HELM.
the considerations
are
restricted to two beam inter¬
A THREE-DIMENSIONAL HELM SETUP
6.4.
The
object spectrum
can
be reconstructed
((M-^e)
V>
in
S2
and S3 shift
\
1 < j <
T
^
0 for at least
the vector ±u in
becomes the total of the
plus
j
<
two shifted
copies.
in desired di¬
reciprocal
be obtained
by employing
space
can
reciprocal
to
patterns with appropriate orientations.
lateral
Thus,
space.
as
a
well
passband regions
cut-off
high
section,
analyzed.
possible
ployed.
a
be
su¬
axial resolution enhancement
as
time in 3D-HELM.
one
practical
In section
can
frequency throughout
A three-dimensional HELM
In this
three
with
passband
a
be achieved at
6.4
As
3.
the effective
copies of the 3D-passband shifted
perimposed
1.
one
space,
Additional
6.2f illustrates how such additional
Fig.
index 1 <
one
reciprocal
original
(6.8)
3,
rections in
excitation
can
s;1
by
by
/J
s^1^)
regions where
passband
is
=
87
6.3,
realization of
a
setup
3D-HELM device will be
it is shown that extension of the
3D-passband
if interference patterns with various orientations
In relation to the
2D-setup
described in
are
em¬
there
chapter 4,
are
major differences:
In
2D-HELM,
two
overlaid in the
patterns with orthogonal orientation
object
space at
one
Urne.
This enables
were
one
to
enhance the resolution in two dimensions without the need for
deflection units.
cal
as
one
In
3D-HELM,
would have to
various orientations.
patterns oriented
Therefore,
along
propriate deflection
this method becomes
overlay
more
a
practical setup
selected orientations
units.
unpracti¬
than two patterns with
will
produce
sequentially by
ap¬
CHAPTER 6
88
Figure
Superposition
6 3
vectors pi
and p2
For
of two
THREE-DIMENSIONAL HELM
mutually
coherent beams with
pi is assumed to be
simplicity,
parallel
wave
the
to
x-axis
2.
In
the
2D-HELM,
propagation
vectors of the incident
reside within the lower half space
the
from the backside
specimen
the
3D-HELM,
as
the beams
the slide
through
vectors of the two
propagation
(see
reside in the lower and upper half space
This
3.
In
requires
a
2D-HELM,
parallel
second
the
objective
mechanical
plates.
coupled
(Fig. 4.5).
degrees
in
a
beams
subsection
6.4.1).
linearly polarized
are
would
3D-setup
of freedom
(DOF)
depth (see
with
Ensur¬
depth.
require additional
for rotatable half-wave
Using circularly polarized light
duced modulation
to
In
interfering
orientation for maximum modulation
ing parallel polarization
beams
for illumination.
beams
interfering
are
subsection
instead leads to
6.4.1)
a
re¬
but makes the
setup remarkably simpler.
The
following
HELM setup in
6.4.1
subsections will discuss the realization of
more
with
3D-
Two-beam interference
We consider the interference of two coherent
Fig.
a
detail.
6.3. The two
opposite
plane
sense
waves are
of rotation.
plane
assumed to be
The
complex
waves
according
to
circularly polarized
electric fields of these
64
A THREE-DIMENSIONAL HELM SETUP
be described
waves can
89
by
(6 9)
(6 10)
where
|pi|
|pi|
=
K with K
=
of excitation and
J(r)
intensity distribution
7(r)
Except
to
Eq
the
|Ei
=
for
E2|2
+
=
one
(l
4
1
C0°S(a)
~
+
6 1 with the modulation
a
is
(pi
—
cos([Pl
-
phase offset, Eq
depth
of excitation
spatial frequency
the difference vector
where A
the
wavelength
For the
obtains
factors and
scaling
^p
=
the refractive index of the medium
is
n
u
p2) only,
a
M
pi
=
(1
=
—
—
p2]r))
6 11
corresponds
cos(a))/2
As
p2
(6 11)
u
and with
depends
on
rotation of both incident beam
vectors around the dashed horizontal line
m
Fig
6 3 leaves the
pattern
unaffected
|pi
identity cos(2a)
By
using
rewritten
p2|
—
=
2
According
Eq
to
the shift vector
As shown
2K
sm(a/2)
—
1,
and
by
using the
the modulation
trigonometric
M
depth
can
be
as
M
6.4.2
=
cos2 (a)
u
6
^f^=(M)2
12, M
a
proportional
desired
zero
for
u
to the
=
(612)
modulus of
squared
0
the incident beam vectors
subsection 6 4
Pi and p2 for
is
and becomes
Choosing
m
=
1, the choice of the incident beam
spatial frequency
of excitation
u is
vectors
ambiguous
CHAPTER 6
90
In this
subsection,
P2 reside
in
Given
a
particular
choice will be derived for which pi and
the lower and upper half space,
desired
0,6
and uz >
a
THREE-DIMENSIONAL HELM
the incident beam vectors
Pl2
respectively
of excitation
spatial frequency
are
<
'IK
set to
(6 13)
(6 14)
2
K2
P2a
|u|
"
uy\
2
with
2
P22
Pia
u
1
VLt
(6 15)
4'
Uf,
(6 16)
Pia
if2
P2y
This choice fulfills
u
=
pi
—
-
p2
(6 18)
Plj
,
|pi|
=
|p»21
makes the z-components of pi and P2 the
A
6.4.3
A
possible
6uz
not
> 0
change
=
K
inverse
and, additionally,
of each other
setup with minimal number of DOF
realization for
setup makes
(6 17)
and
lœ-\
Pli
use
implies
a
3D-HELM setup
of the fact
no
the pattern
that,
for the
essential restriction
(Eq
6
1)
as
is
shown
particular
in
Fig
6 4
The
choice of incident
the transformation
u
-u
does
A THREE-DIMENSIONAL HELM SETUP
64
91
laser
[circularly
polarized)
^
CCD
M1V
Figure
Proposed setup
6 4
for 3D-HELM
minimum number of DOF
beam into two beams of
through
two
objectives
A beam
This arrangement
splitter
equal intensity
01 and 02
mirror M3 located in the focal
serves
for
plane
setting
the
A dichromatic mirror Ml allows
with
a
optical
on
specimen
[63]
A
focal
common
Abbe-Konig prisms
axis
a
An actuated
respectively
off-
Rl and
piezo actuated
phase
offset of the interference pattern
acquisition of the fluorescence image
CCD-camera
beam vectors described in subsection
P2
collimated laser
of LI and L2 sets the
Rotatable
one
a
Two lenses LI and L2 form
R2 rotate the focal spots around the
mirror M2
splits
which illuminate the
spot in the back aperture of 01 and 02,
axis distance of the focal spots
BS
requires the
the
object plane
have
6.4.2, the projections of
equivalent length.
This
pi and
corresponds
to
the fact that the off-axis distances of the focal spots formed in the
back apertures of the two
If the DOFs for CFM
3D-HELM,
objectives
required
are
in
equivalent.
practice
it turns out that 3D-HELM
are
requires
related to those of
one
additional DOF:
CHAPTER 6
92
THREE-DIMENSIONAL HELM
3D-HELM
CFM
Pattern orientation
2
Lateral scanning
2
Pattern spacing
1
Pinhole radius
1
z-Translation stage
1
z-Translation stage
1
Phase offset
1
E
5
E
4
The drawback of the additional DOF
pensated by
In
CFM,
the lower
the fastest DOF requires
piezo actuated
stage
per
require
mirror
one scan
3D-image only,
lower
it
is
should not cost
one scan m
than
that
a
per line
The other DOFs require
drastically simplify
practical
simulations
540
are
excitation
nm
m
based
on a
wavelength
realization of 3D-HELM
m
nm
and
an
is
calculations,
3D-HELM,
be
employed
particular
an
approximation
simulations,
is
object
this approx¬
For the 3D-HELM
computationally apodized
withm
cosine-bell
a
variety of possible combinations of shift directions
for
passband
extension
The simulations
combinations of shift vectors given
sulting passband
4,
of
15 /jm
object spectrum
a
of 1
wavelength
objective
valid if the thickness of the
used without any modifications
the
passband by
In
can
is
is
The
presented
emission
the calculations
This approximation
For the standard fluorescence microscope
imative OTF
are
numerical aperture of the
of 488
The 3D-OTF used
[24]
does not exceed approx
the
the actu¬
for CFM
one
In this section, simulation results for 3D-HELM
given
one scan
Since these
Simulation results
6.5
an
In 3D-HELM the
offset and the z-translation
several tens of seconds
for 3D-HELM
expected
more
phase
2D-image
per
is com¬
for the 3D-HELM actuators
one scan
for setting the
speed requirements
design,
ator
l e
3D-HELM, however,
m
speed requirements
is
shown
schematically
m
m
Fig
Tab
6 5
cover
three
6 1
The
Case
(b)
re¬
is
a
SIMULATION RESULTS
6 5
case
normalized
number of
minimal
shift vectors
required
modulation
[kx, ky, kz)
images
depth
a
(0 5,0,0)
(0,0,0 65)
(0 5,0,0 325)
(0,-0 5,0 325)
(-0 5,0,0 325)
(0,0 5,0 325)
(0,0,0 65)
(0 5,0,0 325)
(0,-0 5,0 325)
(-0 5,0,0 325)
(0,0 5,0 325)
(0 5,0,0 975)
(0,-0 5,0 975)
(-0 5,0,0 975)
(0,0 5,0 975)
c
d
are
The
performed
particular
for
images
very
is
simple
used
7The
the
The
minimum
one
since
Therefore,
first
employed
object spectrum
regions
known
3
0 23
11
0 31
19
0 31
combinations of shift vectors the simulations
is
modulation
only
one
the OTF
are
normalized with respect to
471"^A
depth
The number of
is
calculated
shift direction
(as
well
shift vector requires
For each additional
is
2N + 1 with N the number of
within the
Therefore, only
which
frequency
(per 2D-section)
7
—
The shift vectors given
the incoherent cut-off
vectors
1
—
b
Table 6 1
93
a
as
the
PSF)
to the
not
shift
6 12
A^-axis
symmetric
total of three images to reconstruct
original passband plus
shift vector,
is
employed
by Eq
parallel
required
the
the two shifted
unshifted
component
two additional images per further shift vector
passband
is
are
already
required
CHAPTER 6
94
Figure
Schematic
6 5
by using
THREE-DIMENSIONAL HELM
representation of the passband regions obtained
the combinations of shift vectors
given
in Tab
6 1
The
panels
(a)
(e) correspond to the cases (a) to (e) from Tab 6 1 Shown is a
projection on the kx-kz-p\ar\e (top row) and on the kx-ky-p\ar\e (bottom
to
row)
with respect to the
kx- and A^-coordinate. Case (c) employs
five shift directions. The OTF
respect
to the
well
by using
metry corresponds
diagonal
to that
one
of
direction in the
fluorescence
microscopy (case (a)).
each
For each of these cases, the
is calculated.
First,
the 3D-PSF of 3D-HELM.
a
objects clearly
figure
are
microscope's
parallel
case
are
a
total of
symmetric with
increases the
(c)
also
and
The sym¬
(d),
data
in
Fig.
given
shows calculations for standard
response to two different
point-like object
Secondly,
diameter of 2 /im oriented
Such slice
(c).
kx-ky-plajie
For
case
Additionally,
a
the PSF
four additional shift directions.
6.8 and 6.9.
objects
as
kx- and fey-coordinate. Case (d) further
axial resolution
for the
as
a
infinitesimally
to the
illustrate the
is simulated to obtain
x-y-plane
imaging
thin slice with
is considered.
artifacts present in
CONCLUSION
6 6
case
Table 6 2
to
point
in
Fig
95
FWHM
FWHM
FWHM
lateral
axial
axial
point
point
a
200
nm
480
nm
2270
125
nm
470
nm
410
nm
c
125
nm
180
nm
220
nm
d
125
nm
115
nm
120
nm
objects
Fig
are
of the responses
extracted from the
are
graphs
shown
6 9
optical sectioning microscopy (see Fig. 6.7a).
the simulations
The results of
summarized in Tab. 6.2.
Conclusion
6.6
The simulation results
in the 100
excitation
well
as
demands
nm
range
by choosing
size which is
an
especially
practical
can
useful
be
the lateral
feature,
adjusted
for 3D-HELM
to the
given
frequency
the
spécifie
vectors.
in Tab. 6.1
eight
is
images
same
higher
times
in 3D-HELM
number of
realization of
as
well
in CFM is twice that
microscopy. Therefore, the
original images
times faster to obtain the
a
isotropic resolution
it must be related to the maximum voxel
the cut-off
Consequently,
almost
the Shannon criterion. In lateral
imposed by
volume of the
For
an
required images
of standard fluorescence
an
appropriate combination of shift
high. However,
direction,
in CFM.
show that
be achieved in three-dimensional harmonic
axial resolution in 3D-HELM
rather
in axial
clearly
can
light microscopy. As
The number of
seems
The data
nm
(FWHM)
The full widths at half maximum
6 8 and
2 /xm0
b
and slice
standard
as
slice,
can
some
maximum voxel
in 3D-HELM than
photons
3D-HELM,
as
one
be
acquired eight
per voxel.
aspects have
to be
CHAPTER 6.
96
Figure
6.6:
Calculated
THREE-DIMENSIONAL HELM
point spread functions for for 3D-HELM. Panels
(a) to (d) correspond to to the respective cases in Tab. 6.1. Shown is a
kx-kz-sect\or\ of the three-dimensional PSF. To enhance the visibility of
the side lobes,
a
non-linear grey scale with 7
1.2
=
was
used.
Scale bar
is 1 pm.
considered
come a
time. It is
an
more
serious
carefully
problem
than in 2D-HELM. Thermal drift could be¬
due to the
expected, however,
strongly
that drift
problems
optimized design and/or computational
image
reconstruction
algorithm.
regions
but not
of the different
least,
the
as
well
as
required.
in three
passband copies
efficiency
drift
Furthermore,
for pattern parameter estimation is
sible in two dimensions
extended data
of the
a
different
Basically,
by analyzing
in 3D-HELM
algorithm
acquisition
be handled
by
compensation by the
can
is of
approach
this is pos¬
the
overlap
[35]. And,
major
concern
last
due
6 6
CONCLUSION
Figure
HELM
Calculated responses to
6 7
Panels
Shown is
visibility
a
(a)
to
(d) correspond
a
slice
to to
object (diameter
the
respective
kx-kz-sect\or\ of the three-dimensional image
of the side lobes,
a
2
cases
non-linear grey scale with 7
pm)
in 3D-
in Tab 6 1
To enhance the
=
used
1.2
was
an
unrivaled
Scale bar is 1 /jm
to the
To
high
volume of data.
conclude,
3D-HELM has the
potential
resolution in three dimensional space.
inherent
advantages compared
ing pinhole
relevant.
one
is
required
The cost of the
of CFM.
case
a
imposed by dye
experimental setup
are
HELM has
to CFM since neither
limitations
The additional
the two-dimensional
solvable.
nor
to achieve
Furthermore,
problems
technical
is
photon
some
block¬
saturation
comparable
are
to that
of 3D-HELM in relation to
ones
and
are
expected
to be
CHAPTER 6
98
THREE-DIMENSIONAL HELM
lateral PSF
lateral PSF
lateral PSF
axial PSF
-0 5
0
axial PSF
05
-08-06-04-02
[um]
0
lateral PSF
(diagonal)
lateral PSF (x)
axial PSF
0
02
04
Figure
(d)
6 8
06
-04-03-02-01
the different
case
0
01020304
[um]
Calculated point
refer to
(diagonal)
lateral PSF (x)
axial PSF
[um]
to
02040608
[um]
lateral PSF
16-04-02
(x)
(y)
(a)
scalmgs
on
to
spread
(d)
functions
of Tab
the abscissae
6 1
m
3D-HELM
Graphs (a)
paid to
Attention should be
6 6
CONCLUSION
99
1
p^^^
^
y
08
1
06
S
04
-
02
U
0
-2-15-1-050051
152
I
I
[|xm]
x
I
-2-15-1-050
L
05
1
15
2
[um]
diagonal
diagonal
x
~
-2-15-1-050051
152
"«'
I
Figure
6 9
to
(d)
of Tab
'W
~
152
[|xm]
Calculated lateral responses to
parallel
I
-2-15-1-050051
[um]
oriented
I
to
6 1
the
a
thin slice of 2 pm diameter
fe^-A^-plane Graphs (a)
to
(d)
refer to
cases
(a)
CHAPTER 6
100
THREE-DIMENSIONAL HELM
1
-
08
>.
-
<7>
-
06
-
04
"s.
-
02
-
-"l
3
I
-2
-1
I
I
0
1
i^->
2
I
I
0
3
I
-1
-0 5
z[|xm]
I
0
05
1
z[|xm]
1
08
ë
h
06h
04
02
0
-06-04-02
0
02
04
06
-04-03-02-01
z[|xm]
Figure
to
(d)
parallel
of Tab
the abscissae
to
6 1
01020304
z[|xm]
Calculated axial responses to
6 10
oriented
0
the
a
thin slice of 2 pm diameter
fe^-A^-plane Graphs (a)
Attention should be
paid
to
to
(d)
refer to
the different
cases
scalings
(a)
on
Chapter
7
Conclusion
This thesis concentrates
cence
A
on
resolution enhancement in far-field fluores¬
microscopy by illuminating the specimen with structured light.
method,
called "harmonic excitation
been introduced and realized which
light microscopy" (HELM),
has
employs space-harmonic intensity
patterns generated by interference of laser beams
to
than double
more
the resolution.
The first part of the thesis is
field distribution in the
pattern
on
the
a
theoretical
object plane
image formation.
study
of the electrical
and of the influence of the
Frequency
domain
analysis
that additional information not accessible in conventional
can
be extracted.
For that purpose,
shifts of the pattern must be
images
acquired
and
for different
light
shows
microscopy
translatory
postprocessed
electroni¬
cally.
In
a
next
step,
a
was planed and realized. The main compo¬
generating apparatus which produces a two-
setup
nent is the interference
dimensional mesh-like interference pattern in the
a
mesh-like pattern allows
one
sions without mechanical actuators to rotate the
design
issue
was
the
stability
object plane. Using
to enhance the resolution in two dimen¬
pattern.
of the pattern for the
101
A critical
relatively long
CHAPTER 7
102
Sufficient
time
acquisition
design reducing
could be achieved
stability
thermal drift and
CONCLUSION
by
by
compact
a
using electrostrictive actuators
Since the interference generating apparatus illuminates the specimen
from the backside
path
were
The
no
modifications
is
in
of
difficulties
The
paraxial theory
not restricted to any
optical
transfer function calculated
transfer function under
of
samples
a
sample
verify
an
was
can
Compared
speed
was
well
as
the
enhancement,
imaged
acquir¬
histological samples
was
limitations
widely
achieved
same
is
not
of
HELM has
subject
of
res¬
practical
an even
no
photon
to fundamental imag¬
the small illumination spot
imposed by
ad¬
Images
showed that the
objects
area
and,
used confocal microscope,
Furthermore,
and
biolog¬
as
with HELM
also be achieved with
to the
efficiency reducing pinhole
ing
tested with artificial
the resolution
various
olution enhancement
better resolution
by
atomic force microscope for reference
microtubules and of
interest
conditions and
images with the fluorescence filter removed
of fluorescent beads
with
ditionally,
pre¬
path
The HELM-method
To
sub-pixel
measuring the
by carefully
comparable optical
brightfield
from the imaging
ical
by
turned out to be too inaccurate and the orientation
These hurdles could be mastered
ing additional
showed
algorithm
image reconstruction
an
of the interference pattern had to be determined with
cision
the imaging
of microscope
implementation
mam
slide,
For this reason, the setup
required
particular type
two
the
through
size
in
confocal microscopy
A further topic of the thesis
dimensional imaging
to
generate
entation
setup
is
in
the extension of the method to three-
A modified setup
space harmonic interference
three-dimensional space
comparable
with that
resolution gam of this device
provides
is
an
the need for
one
was
The
proposed
which allows
complexity
any desired
of the
of confocal devices
analyzed by
almost isotropic resolution
a
is
patterns with
in
lateral scanning mechanism
numeric
the 100
nm
one
ori¬
proposed
The achievable
simulations
It
range without
These properties
are
not
103
achieved
by
any other method.
The next step would be the realization of
HELM setup and the
algorithm.
construction
HELM
are an
It is
employing
complications
efficiency
provide
and
long image acqui¬
by
that these issues
the
can
high
by
add-ons to
three-dimensional
unrivaled resolution combined with
high speed imaging capability.
volume
be solved
algorithms and, probably, experimental
an
re¬
in three-dimensional
limitations caused
expected, however,
three-dimensional
appropriate image
object and/or pattern position. Then,
HELM would
ton
computational
smart
calibrate the
Possible
a
increased mechanical drift due to the
sition time and
of data.
implementation
of the
high pho¬
104
CHAPTER 7
CONCLUSION
A
Appendix
in
Optical trapping
interference fields
This thesis is part of the NANO-II
project
at
the
"Eidgenössische
Technische Hochschule Zürich" where NANO stands for "Non-contact
Assembly
jects".
and
of
and Non-contact
Nano-Objects
The
goal
of the
project
manipulating objects
is to
study
Analysis
of Nano-Ob-
methods for
in the sub-micrometer range.
visualizing
The HELM
setup described in this thesis produces interference patterns which
expected
to be
applicable
to
optical trapping
obvious to also consider the
first results for
are
well.
as
manipulation aspect.
optical trapping
Therefore,
In this
it
are
was
appendix,
with HELM-like interference patterns
presented.
Generally,
vorable since
nipulating
methods
light
are
used for
non-contact methods for
problems
tool
are
are
avoided. One
optical traps. Here,
employed
particle handling
with adhesive forces between
important class of such
forces exerted
to control their motion.
optical trapping
works with
105
on
and
ma¬
non-contact
particles by
The most
strongly
very fa¬
are
object
intense
common
setup
focused laser beams.
APPENDIX A
106
Under suitable
the laser focus forms
conditions,
[4, 11, 34]
dielectric
well
as
erate laser powers
metallic
as
of
Manipulation
[61]
illumination
time-multiplexed
OPTICAL TRAPPING
a
[81] particles
even
few
is
by
or
particles
for mod¬
possible by
methods
holographic
using
well for
potential
a
[67]
In practice,
ten essential
which make
ped
parallel handling
Parallel
bright
force
which
denoted
Till
as
less than
one
particle
in
crystals,
non-contact
are
trap¬
result of the dominant
form
a
regular
array
matter
To meet the requirements
must be reduced to notice¬
sizes
Potential
micrometer
traps he
of¬
is
interference traps have been realized for rela¬
micrometer) objects only
few
of the NANO-II project, the
ably
as a
optical
or
objects
by optical traps
Basically, particles
Suspended particles
optical crystal
today, however,
tively large (a
be achieved
of such patterns
[15, 84, 17]
gradient
is
zones
number of
large
a
can
of interference patterns
use
within the
of
manipulation
applications
particle transport
and
of such
[27]
the field of writing diffractive structures
controlling
or
optical
photonic
the
crystal¬
by
electron
lization of macromolecules for structural investigations
microscopy
The connection to HELM lies
patterns used for harmonic
trapping
very small
particles
the interference field
in
the
as
setup
wells
zones
are
However,
an
this observation gives
1A transport
demonstrated
by
by
Therefore,
[32, 62]
Using
extent
probability
and, together
rise
to the
using
a
of
slightly larger
D
Hafliger
in
a
beads
(200
nm
a
source
one
in
potential
the
bright
predictions,
complete trapping
1
diameter)
beam TIR setup
similar
100 mW ylr-ion
with theoretical
assumption that
a
which allows
of presence
stronger laser
a one
of
HELM system turned out to be
trapping forces
greater
increased
could be observed
could be achieved
a
capable
the intensity of
beads could still escape from the
polystyrene
100-nm
to be
expected
Unfortunately,
built within two semester theses
to focus the laser beams to
laser,
well
presented
too small to achieve sufficient
was
the fact that the interference
in
excitation
could
be
recently
A 1
PHYSICAL BACKGROUND
A.l
107
Physical background
In this section, the basic forces exerted
fields will be discussed
to be consistent with
To
on
particles
in
electromagnetic
the mathematical
simplify
the Gaussian system of units
literature,
and
description
used
is
[45, appendix]
The
of
size
wavelength
act
a
Rayleigh
as
Rayleigh
known
employed light
dipole
As
scatterers
scatterer
is
a
polarized
[45]
characteristic
time harmonic
( 100
of interest
particles
of the
electromagnetic
is
given
128
the
Therefore,
result of
A
Rayleigh
is
scatterer
For
ir5nm f m?
the refractive index of the
R
energy flux
[84]
is
-
gradient
pwhere E
is
the
=
complex
t
sphere
force
is
lx
Rb S,
2There
A
and S
is
is,
however,
for the
a
more
is
m
the
the time
one
is
the
vacuum
averaged
by
l^rijRS V(|E|2)'
electric field
to be the dominant
zero
a
(A 1)
(A2)
strength [84]
since
studied,
the
gradient
force
is
the lateral energy flux of the
field distribution vanishes due to the lateral symmetry
almost
to
the scat¬
spherical particles,
medium,
given
For the two-beam interference setup
expected
exposed
forces,
embedding medium,
and
particle
the radius of the
The
field,
to the well
by
ratio of refractive indices of
wavelength,
particles basically
field experiences two
fgrad
well below the
according
3cA4
where nm
is
external electric
an
and radiates
tering force Fscat and the gradient force
the scattering force
less)
nm or
small axial force component
relevant setup described
in
2
This axial force becomes
section A 2
APPENDIX A
108
Since the
defined
force
gradient
For
one,3
conservative
is a
this
spherical particle,
a
OPTICAL TRAPPING
potential
can
be
be calculated
by
potential
a
can
integrating Eq A 2
r
W(r)
J -Fgrad(r)
=
dr
-cm
=
R3
|E(r)|2,
(A 3)
oo
where the
potential
Eq A
duced
this
3 allows
to calculate the
one
the electric field
end,
pattern has
flux S of
a
strength
|S|
where
c
medium
is
(1
the
velocity
of
light
(see Fig
{E\ and E<i
140 /jm
calculated
by
using
£i
Eq A
=
3)
4
in
4
=
the two
3The
curl of the
the definition of
a
gradient
potential
=
in¬
To
of the illumi¬
by
is
(A4)
the refractive index of the
a
the
In
HELM,
beam diameter of
amplitudes
22, respectively)
/ERG
101
=
is
\
used
of the
can
be
/a
n
2Ei
beams
cos
is
is
(1
ERG
according
( kxx +
zero
(A 5)
—r,
10~7 J) [45,
=
of the interference pattern
amplitude Eles
force field
is
given
3 20 and 3
Eq
y-polanzed
Eres
zones
0)
as
i—
The electric field
generated by
bright
Therefore,
where the Gaussian energy unit ERG
appendix]
spherical particles
focused to
/87r|S|
£2
well
potential
particles) [45, chapter 7]
are
=
The modulus of the energy
wave is
and nm
33 for water immersed
incident beams
the
W(oo)
e
^|E|2,
=
four laser beams of 25 mW each
approx
small
to be calculated first
plane electromagnetic
of the
depth
on
m
infinity (l
at
zero
the HELM interference field
by
nation
set to
is
energy
—
J
for
Eq
3 28
(A 6)
,
due to V
unambiguous except
to
X
an
(VF)
=
0
Therefore,
additive constant
A.2.
THE SETUP FOR OPTICAL TRAPPING
where the
reflection at the
partial
In the antinodal zones,
the
slip
cover
neglected (i.e.
Since the
Eles equals 2E\.
the maximum field
x-polarized field,
is
109
amplitude Emax
R
=
0).
is true for
same
of the two-
dimensional pattern becomes
Emax
a/2
where the factor
mersed
=
1.59
the
J
2.86
results from the
orthogonality
beads
cm is 0.147.
potential
a
W0
well
=
is obtained for 100
=
depth
1.5
nm
1.33, refractive
(nm
Inserting Eq. A.7 and
two to three orders of
x
10-16ERG
=
1.5
calculations,
prediction
strongly
The
the HELM setup is not
is in
complete agreement
increased
A.2
The
was
a
few
ence, the
In the
key
(A.8)
4
x
temperature, the
10~21 J and, hence,
Wq (k
Kelvin).
expected
to
is the Boltzmann
According
to these
trap particles. This
with the observations.
one
For this
to achieve
a
intensity.
setup for optical trapping
significant
is similar to the HELM
differences exist.
trapping setup provides only
interference pattern to reduce
A
polystyrene
the value of cm into
built which enables
optical trap setup (Fig. A.l)
ever,
and y-
room
=
than
magnitude larger
different setup
index of
10~23J
x
At
diameter beads.
and T is the temperature in
a
x-
of
average kinetic energy is of the order of kT
reason,
of the
well depth Wq can be calculated by applying
appropriate material constant cm. For water im¬
polystyrene
[48]),
constant
(A.7)
cmJr,
V
potential
with the
Eq. A.3
=
field components.
polarized
Now,
Eq. A.3
V2x2E1
=
a
one-dimensional
complexity
a
focal
(fringe-like)
and costs.
difference is the reduced diameter of the
trapping setup, lenses with
setup. How¬
As the most obvious differ¬
length
illuminating spot.
of 18.4
mm are
placed
APPENDIX A
110
L1
Figure
A 1
used for
Setup
laser beam is
P1
split by
beam
Two lenses LI and L2
PI and P2 form
slip
A collimated
BS into two beams of
equal intensity
18 4
mm
A vertical translation of the beams
the
position
of the focal spot
angle
L2
optical trapping experiments
splitters
(focal length
changes
for
P2
focal spot in the water
a
OPTICAL TRAPPING
of incidence
by
air)
in
and two
(illustrated by
cover
the dashed
maximum ±2.5° without
An inverted
glass prisms
between slide and
layer
line)
affecting
microscope (not shown)
the
serves
observing
in direct
proximity of the prisms resulting
diameter of 7.6 /jm for the used laser
waist diameter wq
=
1.5
HELM,
of 200.
a
theoretical beam waist
(Eq. 4.1, primary
beam
mm).
The measured value is
plained by
in
source
aberrations and
roughly
by
10 /xm; the difference
measurement
the reduced spot size leads to
an
errors
intensity
[62].
can
be
ex¬
In relation to
increase
by
a
factor
A 2
THE SETUP FOR OPTICAL TRAPPING
2
111
-
£15o
a=
3
"q.
05
ra
-
0
-
0
10
20
30
40
incident
Figure
A 2
Amplitude
one
layer
60
70
80
in direct
90
coefficient of the transmitted beam for
Shown is the ratio of the electric field
water transition
water
50
angle [degree]
proximity
to
a
glass-
amplitude
in the
the interface relative to the incident
The dashed line indicates the critical
angle
(61°)
for TIR
the criterions for choosing the angle of incidence a.%
quite different for optical trapping than for HELM. The reasons
Furthermore,
are
for
choosing
5.1.1)
do not
propagating
at smaller than the critical
apply
waves
to
amplitude
for TIR
trapping experiments. Trapping
[15]
well
as
the achievable electrical field
one
angle
as
with evanescent
strength
is of
(see
is
subsection
possible
ones
[48].
with
Since
major importance, the
coefficient of the transmitted beam relative to the incident
(Fresnel formulae, [12])
illustrates that
working
enhances the electric field
four times increased
should be taken into account.
near
strength by
intensity.
incidence is approx. 184
the critical
The
a
angle
Fig. A.2
is favorable
factor of two
fringe spacing
as
resulting
for these
this
in
angles
a
of
nm.
As in the HELM setup,
a
piezo
actuator is
provided
to shift the
APPENDIX A
112
Figure
A 3
ZEISS
microscope
of the
Photography
OPTICAL TRAPPING
trapping setup mounted
The two visible
adjustment
knobs
on
serve
an
inverted
for
aligning
the illumination spots relative to each other
interference
a
sawtooth
perpendicular
and
relative to the immersion medium.
fringes
voltage
Fig. A.4
to the
to the
show
actuator,
fringes
an
expected
is
photographs
of the
glass-water interface,
intensity
800 in relation to the HELM
tions
leading
of 1.2
(4
x
x
to
Eq. A.3,
10~20 J which
one
is
obtains
slightly
Fig. A.3
to be achievable.
amplitude amplification
is enhanced
setup.
By applying
particle transport
trapping setup.
Due to the reduced spot size and the
the
effective
by
a
By re-performing
an
the calcula¬
expected potential
well
the setup described makes
probability
of presence for
observable. Such
an
a
sense
depth
above the average kinetic energy
10~21 J). Though the estimated potential well depth of
?>kT may not be sufficient for
at the
factor of approx.
approx.
complete (i.e. long term) trapping,
for two
particles
reasons:
within the
an
increased
zones
should be
First,
bright
observation would validate the theoretical calcu-
A 3
RESULTS
Figure
A 4
Visible
are
Bottom view of the
lations.
the
Secondly,
by employing
A.3
power
is
expected
the beam
splitter)
to be achievable
and/or increasing
the
viscosity
medium to reduce thermal motion.
Results
To test the
beads with
As
complete trapping
a
stronger laser
a
embedding
optical
trapping setup with removed base plate
optical components (prisms, mirrors and
flexible joints for aligning the optical paths
and two
of the
113
trapping behavior of the setup fluorescent polystyrene
a
diameter of 100
axis at
expected,
escape from
was
the beads
one
fringe
statistical method
presence
was
set to
was
nm were
slightly
were
and
not
cross
used. The beam's
below the critical
completely trapped,
over
to another
i.e.
one.
needed to find out whether the
nonuniform.
angle
angle
to the
for TIR.
they
could
Therefore,
a
probability
of
APPENDIX A
114
slip
cover
A 5
Figure
of the interference
Geometry
OPTICAL TRAPPING
zone
In contrast to the HELM setup, the interference
in the
optical trap setup
zone
is at the slide-water
interface
Due to the small spot size and the flat
the water
layer,
ones even
for
a
angle
of the beams in
the reflected beams do not interfere with the incident
very thin water
A statistical
with
analysis
is
of
layer
few micrometer
a
possible by measuring
CCD-camera and
the scattered
light
it to the scattered
a
relating
intensity
intensity
without interference.4 For this analysis, the total light intensity on the
CCD-chip
for
an
ensemble of scatterers is assumed to be the
the intensities of the individual
wave
of
one
individual
ones.
The
Rayleigh particle
is
proportional
particle position [45, chapter 25]. Therefore,
on
the
CCD-chip
It
can
be calculated
J
Ij=C
field of
where p is the
C is
a
constant.
(Eq. 3.28)
Now,
the incident beam
£„»
4The
=
light
to
|E|2
at the
light intensity
p(r)|E(r)|2,
(A.9)
dr
object plane
and where
the field distribution of the interference field
a
glass-water
R
=
0,
see
2Eie-tk'z cos(kxx)
fluorescence
due to the
(i.e.
the total
view
has to be rewritten in
beam reflected at the
of
by
of the scatterers in the
density
sum
intensity of the scattered
+
somewhat different form. Since the
transition does not interfere with
Fig. A.5), Eq.
(E2
-
3.28 becomes
Ex)etk'xe-tk'z,
(A.10)
turned out to be useless for quantitative measurements
rapid photo-bleaching
A.3.
RESULTS
where the
115
shift A is set to
phase
applicability. Taking
\Eres\A
cos(2x))
view,
are
one
E(
=
Ei
+
sin2(x)
where the identities
used.
zero
the modulus of
+
^-(1
=
without
Eq.
—
{El
cos(2x))
+
interference pattern.
For the first
second
El)
+
2E1E2
image
For the
acquired
cos2(x)
^(1
=
+
\
J ^ caa(2kxx)
the first beam
was
(A.12)
dv
view
sample
with total intensities
was
blocked
both beams could interfere.
intensities
particle
distribution and
of immersed
and
11^2
blocked
(i.e. E\
According
beads,
three
It, respectively.
(i.e. E2 =0), for the
0) and for the last
=
to
Eq. A.12,
the total
are
For the ratio
h
=
CNEf,
h
=
CNEl
Il
=
CN{E\+El)
It/(Ii +12)
i,
_
h +h
intensity
ratio
one
(A.14)
and
+
=
l +
(A.16)
K,
E\ approximately equals E2. By evaluating
Eq. A.16,
For 100
(A.15)
2CE1E2K.
obtains
the correlation K between
bution and interference pattern
total intensities.
(A.13)
E21+El+2E1E2K
E\+ El
where it is assumed that
the
same
image the second beam
image
and
Eq. A.9
into
where K describes the correlation between
were
general
(A.ll)
=K
field of
images
the
obtains
With N the number of scatter ers in the field of
(
IJ=CN
affecting
one
2E1E2 œs(2kxx),
by inserting Eq. A.ll
obtains
A.10
nm
can
particle
distri¬
be calculated from the measured
diameter beads immersed in
a
mixture
APPENDIX A
116
of 50%
glycerin
To validate the
prepared,
an
method,
here the
zero
of approx
to
nm
the setup
is
well
depth
to be sufficient for
by
J
increased
was
of the
was near
particles,
of presence
probability
constructed to function with the
is
a
in
the
as
well
laboratory,
factor of ln5nw
100
^
mw
2
By
the
=
using
a
in
the
6
25
common
5 W laser of
well
potential
depth
Therefore,
'
would be of the order of 80 kT which
is
the
expected
complete trapping
estimation of 3fcT
optical paths
correlation of 0 15 for mobile
found
slip
certainly independent
is
the measured value for K
of Nd-YAQ lasers
available
would be increased
potential
slightly
a
was
cover
agreement with the estimated potential well depth
wavelength
this type which
BThe
expected,
0 15
=
5
?>kT
Fortunately,
1064
a
is in
zones,
correlation K
of beads fixed to the
distribution
(0 02) Furthermore,
corresponding
bright
As
a
sample
a
particle
interference pattern
to
50% water,
OPTICAL TRAPPING
Therefore,
is
based
on
infinitesimal small
the value should be
particles
interpreted carefully
and lossless
as
"of the
order of kT"
6The
are
factor
=
isa
result of the fact that the
inversely proportional
to the
wavelength
gradients
of the
in
an
interference field
employed light
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Curriculum Vitae
Personal data:
Name:
Jan Tillman Prolin
Date ol birth:
28nd ol
Place ol
Bonn, Germany
origin:
Nationality:
February,
1971
German
Education:
1977-1981
Primary school, Bonn, Germany
1981-1990
Secondary
(Gymnasium), Bonn, Germany
school
Degree: Abitur
1990-1992
University
Degree:
1992-1996
University
Diploma
1997-2000
ol
Bonn, Germany
Intermediate
ol
diploma
in
physics
Freiburg, Germany
thesis
on
selective emitters lor
thermophotovoltaic
energy conversion
Degree: Diploma
physics
in
Nanotechnology Group,
Institute ol
Swiss Federal Institute ol
Robotics,
Technology (ETH)
Ph.D. research and
supervision ol student projects
in the field ol
science
nano
(ETH Zurich)
Stuttgart)
Thesis advisors: Prol. A. Stemmer
Prol. H. J. Tiziani
(University
ol
and
Collateral engagement:
1989-1992
Development
telescopic
1992-1997
ol power and
analog
electronics for
camera cranes
Development
ol electronics and software for second
generation telescopic
camera cranes
127