1

Index Introduction ................................................................................................................ 3

Chapter 1 .................................................................................................................... 4

Fluorescence Correlation Spectroscopy (FCS) .......................................................... 4

1.1 History ................................................................................................................. 4

1.2 Conceptual basis and theoretical background ...................................................... 6

1.2.1 “Burst” trace ..................................................................................................... 6

1.2.2 Point Spread Function ....................................................................................... 8

1.3 Fluorescence Correlation Spectroscopy............................................................. 10

1.3.1 Theory ............................................................................................................. 10

1.3.2 Processes which can be monitored by FCS .................................................... 16

1.3.3 Physical models for the autocorrelation function ........................................... 19

1.3.4 Statistical accuracy in FCS ............................................................................. 20

Chapter 2 .................................................................................................................. 23

Single-molecule fluorescence instrumentation ........................................................ 23

2.1 Introduction ........................................................................................................ 23

2.1.2 Optical arrangement for single-molecule detection ........................................ 26

2.1.3 Epi-fluorescence far-field microscopy............................................................ 26

2.1.4 The PSF in single-photon confocal epi-fluorescence illumination systems ... 30

2.1.5 Spectral discrimination ................................................................................... 32

2.1.6 Excitations sources ......................................................................................... 34

2.1.7 Microscope objective for single-molecule fluorescence detection ................. 36

2.2 Detectors for single-molecule fluorescence experiments .................................. 39

2.2.1 Point detectors ................................................................................................ 40

2.2.2 Imaging detectors ............................................................................................ 43

Chapter 3 .................................................................................................................. 46

Practical Training ..................................................................................................... 46

3.1 Introduction ........................................................................................................ 46

3.2 Lab overview ..................................................................................................... 46

2

3.3 Biological probes ........................................................................................... 47

3.4 Conformational dynamics of biopolymer ...................................................... 48

3.5 A quantum dots application: .......................................................................... 49

Immuno-Cytochemistry and Fluorescence in situ ............................................... 49

Hybridization ....................................................................................................... 49

Chapter 4 .................................................................................................................. 52

Experimental apparatus ....................................................................................... 52

4.1 Objective of the experiment ........................................................................... 52

4.2 Experimental setup ........................................................................................ 53

4.2.1 Liquid Cristal on Silicon (LCOS) spatial light modulator ...................... 54

4.2.2 The 32x32 SPAD Array .......................................................................... 56

4.2.3 Sample & Filters ..................................................................................... 59

Chapter 5 .................................................................................................................. 61

Experimental procedure and data analysis .......................................................... 61

5.1 Introduction .................................................................................................... 61

5.2 Alignment of the SPAD array ........................................................................ 63

5.3 Experimental measurement ........................................................................... 66

5.3.1 August experiments ................................................................................ 66

5.3.2 Data analysis ........................................................................................... 68

5.3.3 Point-Spread-Function (PSF) analysis .................................................... 76

5.3.4 November experiments ........................................................................... 78

Chapter 6 .................................................................................................................. 80

Conclusions and future prospective ..................................................................... 80

Bibliography ............................................................................................................ 82

3

Introduction

In order to complete the master in “ Nuclear and ionizing radiation technologies” I

spent the six months of the course’s practical part in the Laboratory of Prof. Shimon

Weiss at the University of California Los Angeles (UCLA). During my training period I

worked under the supervision of Dr. Xavier Michalet, on FCS (Fluorescence

Correlation Spectroscopy) measurement with two different kinds of SPAD arrays, a 8x1

and a 32x32 SPAD array both of them developed by the group of Prof. Sergio Cova at

the Politecnico di Milano. In particular I focused my efforts on the experiments with the

32x32 array, including experimental setup optimization, sample preparation and data

analysis.

The thesis is organized in the following way:

• In the Chapter 1 there is an introduction of FCS, history, conceptual basis

and physical model.

• In the Chapter 2 there is an overview in the instrumentation needed for FCS.

• In the Chapter 3 there is a presentation of the lab in which I spent my practical

training period.

• In the Chapter 4 there is the description of the experimental apparatus used

for the measures

• In the Chapter 5 there is the data analysis and the comments on the

experimental results.

• In the Chapter 6 there are the conclusion and the possible future prospective.

4

Chapter 1

Fluorescence Correlation Spectroscopy (FCS)

1.1 History

The understanding of the fluctuation-dissipation relationship in thermodynamics

has been a great achievement of statistical physics.

The theory of Brownian movement, presented by Einstein in one of his famous

1905 papers[1], not only established a macroscopic understanding of the consequence

of the existence of the atom, but also opened up a whole new area of research related to

the study of systems near equilibrium. The experimental support for this atomistic

theory came with Perrin’s observation of Brownian particles of mastic under a

microscope [2]. Macroscopic dynamical properties (the viscosity of the fluid) were

derived from microscopic fluctuations (the diffusion of the probe).

It is humbling to point out that, right at the beginning of the 20th century,

experimentalists had already figured out the importance of reducing the sample size and

using high-power microscopy to unravel atomic wonders.

The explicit formulation of the fluctuation-dissipation theorem states that the

dynamics governing the relaxation of a system out of equilibrium are embedded in the

equilibrium statistics.

In the spirit of this theory, Eigen and followers developed the temperature-jump

technique, where the relaxation of a system after thermal perturbation gives insight into

the thermodynamic equilibrium. Classically, the temperature jump is generated by

capacitance discharge of laser-pulse absorption, and the relaxation toward the

equilibrium is monitored by spectroscopy (e.g. UV absorption or circular dichroism).

Another perturbative technique has been introduced to measure the diffusion of

biomolecules.

5

Fluorescence recovery after photobleaching (FRAP), as its name implies, consist in

monitoring the dynamics of fluorescence restoration in a region after photolysis of the

dyes in this region, due to the diffusion of fluorescent molecules from neighboring

areas. This photodestructive method has been very successful in application to living

cells, specifically to analyze the dynamics of membrane trafficking.

A widely used method to study changes on a molecular scale (10-100 Angstrom) is

based on fluorescence resonance energy transfer (FRET): a transfer of the excitation

between two different fluorophores (donor and acceptor), whose corresponding

emission (donor) and absorption (acceptor) spectra overlap. The efficiency of energy

transfer depends strongly on the distance between the donor and the acceptor: hence one

can take advantage of FRET to follow the association of interacting molecules or to

monitor the distance between two sites within a macromolecule when labeled with two

appropriate dyes.

Fluorescence correlation spectroscopy (FCS) is an experimental technique

developed to study kinetic processes through the statistical analysis of equilibrium

fluctuations. A fluorescence signal is coupled to the different states of the system of

interest, so that spontaneous fluctuations in the system’s state generate variations in

fluorescence. The study of the autocorrelation function of fluctuations in fluorescence

emission gives information on the characteristic time scales and the relative weights of

different transitions in the system. Thus, with the appropriate model of the system

dynamics, different characteristic kinetic rates can be measured (for example

fluctuations in the number of fluorescent particles unravel the diffusion dynamics in the

sampling volume) [3].

Since its invention in 1972 by Madge et al [4], FCS has been used for various

applications, such as measuring: chemical rates of binding-unbinding reactions or

coefficient of translational and rotational diffusion. However, although the principal

ideas behind FCS as well as its main applications were already established at that stage,

the technique was initially poorly sensitive, requiring high concentrations of fluorescent

molecules. Its renaissance came in 1993 with the introduction of the confocal

illumination scheme in FCS by Rigler et al [5].

6

This work generated a lot of technical improvements, pushed the sensitivity of the

technique to the single-molecule level and led to a renewed interest in FCS. The

efficient detection of emitted photons extended the range of applications and allowed

one to probe the conformational fluctuations of biomolecules and the photodynamical

properties of fluorescent dyes.

FCS is a technique which relies on the fact that thermal noise, usually a source of

annoyance in an experimental measurement, can be used to obtain some information on

the system under study.

FCS corrects the shortcomings of its precursors, as it monitors the relaxation of

fluctuations around the equilibrium state in a non–invasive fashion. It relies on the

robust and specific signal provided by fluorescent particles to analyze their motions and

interactions. In combination with FRET, FCS further allows to probe the dynamics of

intra-molecular motion.

1.2 Conceptual basis and theoretical background

1.2.1 “Burst” trace

If the fluorescent analyte is allowed to flow or diffuse in and out of a small

excitation/collection volume defined by a focused laser beam, this gives rise to a

stochastic series of short-lived fluorescence bursts detected above the background noise

level (Figure 1.1). This type of experiment was one of the first used to demonstrate the

feasibility of fluorescence detection of single molecules in solution at room

temperature. However, despite the simplicity of the approach, the stochastic nature of

the data requires sophisticated analysis. Burst often consists of < 100 photons and the

data are therefore dominated by shot noise, in addition each molecule is able to take any

path through the excitation/collection volume which has a spatially dependent excitation

intensity and collection efficiency (also called instrument spread function, see

paragraph 2.1.4) , resulting in a range of burst widths and intensities [6].

7

Figure 1.1 This is the time trace for 10 seconds of beads measurement taken reading one of the 1024 pixel of the 32x32 SPAD array detector. “Bursts” corresponding to the bead diffusing through the focal volume are clearly visible. The burst duration is on the order of 10 ms.

The simplest approach to analyze such transient signal is often called burst analysis.

Burst analysis involves the straightforward counting of bursts, the quantification of the

number of photons in a burst, the length of the burst or the time between bursts

(recurrence time). It has been used quite widely, for example in high-throughput

screening and medical diagnostic applications.

The reliability of screening or identification assays using simple forms of burst

analysis has been improved by developing methods for the coincident detection of two

dye labels attached to a target molecule. In this way the properties of the particular

fluorescence bursts are of somewhat less concern as coincident bursts can be detected

with significantly more confidence, facilitating the discrimination of signals from

uncorrelated background events.

0200400600800

1000120014001600

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

coun

ts

time (ms)

Time trace pixel 24_16 beads

Time trace

8

1.2.2 Point Spread Function

The point spread function (PSF) is defined as the image of an infinitely small point

source of light originating in the specimen (object) space. Because the microscope

imaging system collects only a fraction of the light emitted by this point, it cannot focus

the light into a perfect point. Instead, the point appears widened and spread into a three-

dimensional diffraction pattern.

Depending upon the imaging mode being utilized (widefield, confocal, transmitted

light), the point-spread-function has a different and unique shape and contour. In a

confocal microscope, the shape of the point spread function resembles that of an oblong

ellipsoid of light surrounded by a flare of widening rings.

To describe the PSF in three dimensions, it is common to use a coordinate system

of three axes (x, y, and z) where x and y are parallel to the focal plane of the specimen

and z is parallel to the optical axis of the microscope. In this case, the PSF appears as a

set of concentric rings in the x-y plane (the so-called Airy disk which is commonly

referenced in texts on classical optical microscopy), and resembles an hourglass in the

x-z and y-z planes (Figure 1.2)

Figure 1.2 Surface plot of intensity in an Airy disk at the focal plane.

9

Figure 1.3. PSF mesured using a large area, single-pixel HPD, by recording the fluorescence emitted by a sub-

diffraction size bead scanned through the LCOS-generated spot. The 3 projections XY, XZ, YZ give an idea of the size and shape of the excitation spot. Since FCS measurements depend on excitation and emission PSFs, these measurements allow us to analyze the effect of the SPAD size on these measurements.

The PSF can be defined either theoretically by utilizing a mathematical model of

diffraction, or empirically by acquiring a three-dimensional image of a small fluorescent

bead (see Figure 1.3).

A theoretical PSF generally has axial and radial symmetry. In effect, the point

spread function is symmetric above and below the x-y plane (axial symmetry) and

rotationally about the z-axis (radial symmetry). An empirical point spread function can

deviate significantly from perfect symmetry (as in Figure 1.3). This deviation, more

commonly referred to as aberration, is produced by irregularities or misalignments in

any component of the imaging system optical train, especially the objective, but can

also occur with other components such as mirrors, beamsplitters, tube lenses, filters,

diaphragms, and apertures. The better the microscope alignment, the closer the

empirical PSF comes to its ideal symmetrical shape (there is also an effect due to laser

source, chromatic aberration, etc.).

The performance of both confocal and deconvolution microscopies depend on the PSF

being as close to the ideal case as possible.

10

1.3 Fluorescence Correlation Spectroscopy

1.3.1 Theory

The conceptual basis of FCS is illustrated in Figure 1.4 [7]. At equilibrium,

fluorescent molecules move through a small open region and/or undergo transitions

between different states with different fluorescent yields, resulting in temporal

fluctuations in the fluorescence measured from the region. The temporal autocorrelation

of the fluorescence fluctuations, which measures the average duration of a fluorescence

fluctuation, decays with time. The rate and shape of the decay of the autocorrelation

function provide information about the mechanisms and rates of the processes that

generate the fluorescence fluctuations. The amplitude of the autocorrelation function

provides information about the density (number) of fluorescent species in the sample

region.

Figure 1.4. Conceptual basis of FCS. At equilibrium, fluorescent molecules are transported by diffusion or

flow through an open region or undergo transitions between states of different fluorescent yields, giving rise to fluctuations in the measured fluorescence. The fluctuations δF(t) in the measured fluorescence F(t) from the average fluorescence ‹F› are autocorrelated as G(τ) (the normalized autocorrelation function of the intensity fluctuations). The autocorrelation function, which measures the average duration of a fluorescence fluctuation, decays with time τ: the rate and shape of decay are related to the mechanisms and rates of the processes that give rise to the fluorescence fluctuations. The magnitude of G(τ) is related to the number densities and relative fluorescence yield of different chemical species in the sample region.

Figure 1.6 Schematic representation of the principle of an autocorrelation calculation on a single molecule data set (top). A fluorescence burst (F(t)) is shifted by the integration time (lag time) then multiplied together, F(t)*F(t+lag time τ. The value of the autocorrelation function (G(The points shown are the actual overlap overlap integral is large whereas at longer lag times the overlap integral diminishes to zero. In this way the autocorrelation function contains information on the width on the featur

Autocorrelation curves are generally presented on semi

range of delay times is likely to span many order

autocorrelation function is approximately exponential in many cases and it

read off the approximate lifetime of the decay to get an indication of the timescale of

the measured fluctuations

The autocorrelation function

data shown in figure 1.5

fluctuation events, in this case the width

diffusion in and out of the volume.

Schematic representation of the principle of an autocorrelation calculation on a single molecule data set (top). A fluorescence burst (F(t)) is shifted by the integration time (lag time) τ. The original and shifted traces are

*F(t+τ), and the integrated area is stored as the value of the autocorrelation function at The value of the autocorrelation function (G(τ)) are then plotted on a logarithmic lag timescale (bottom).

The points shown are the actual overlap integrals (normalized) from the data shown (top). At short lag times the overlap integral is large whereas at longer lag times the overlap integral diminishes to zero. In this way the autocorrelation function contains information on the width on the feature in the data set.

Autocorrelation curves are generally presented on semi-logarithmic plots as the

range of delay times is likely to span many orders of magnitude: the shape

autocorrelation function is approximately exponential in many cases and it

read off the approximate lifetime of the decay to get an indication of the timescale of

measured fluctuations.

he autocorrelation function (ACF) for the type of raw single-

data shown in figure 1.5 can be used to obtain information about the timescale of the

events, in this case the width of the fluctuation (bursts) produced by

diffusion in and out of the volume.

12

Schematic representation of the principle of an autocorrelation calculation on a single molecule data

. The original and shifted traces are ), and the integrated area is stored as the value of the autocorrelation function at

)) are then plotted on a logarithmic lag timescale (bottom). integrals (normalized) from the data shown (top). At short lag times the

overlap integral is large whereas at longer lag times the overlap integral diminishes to zero. In this way the

logarithmic plots as the

of magnitude: the shape of the

autocorrelation function is approximately exponential in many cases and it is possible to

read off the approximate lifetime of the decay to get an indication of the timescale of

-molecule diffusion

information about the timescale of the

of the fluctuation (bursts) produced by

13

Note that the ACF is therefore built up from temporally similar signals of many

single-molecules.

Furthermore, the ACF may contain additional information on any other processes which

cause fluctuations on a time scale faster than the occupation times of molecules in the

volume.

Figure 1.7 Autocorrelation function for a 100 nm beads sample (aqueous solution), obtained using one of the

1024 pixel of the 32x32 SPAD Array of Politecnico di Milano.

Figure 1.7 shows the autocorrelation function calculated for a bead sample,

recorded using one channel of the 32x32 SPAD array used in our experiments . As

indicated in figure 1.6, a number of parameters can be extracted from the

autocorrelation function regardless of the mechanism of the fluctuations. The

amplitudes of the decay components give information about the relative strength of the

fluctuations; in the case shown in figure 1.7 we have only one diffusion component and

its amplitude provides a measure of the average number of molecules in the small

excitation/collection volume (proportional to the concentration). Additionally, the decay

rate of the processes gives an indication of the timescale of the processes that cause the

fluctuation.

In FCS of freely diffusing particles the primary fluctuations are due to the presence

or absence of a fluctuating species within the excitation/collection volume. However, in

typical FCS instrumentation a spatial inhomogeneity also exists in the

14

excitation/collection volume that leads to fluctuations without concentration changes.

Thus the amplitude of a given fluctuation is modulated by its position in the volume.

Fluctuations are therefore expressed as spatially weighted concentration changes

according to [6],

�����, �� ���������, �� �1.2�

where �����, �� is the concentration fluctuation and ���� is the excitation PSF convolved with the detection PSF.

Integration over the entire sample volume gives the total fluorescence signal

fluctuation and, assuming the existence of a single fluorescent species, the amplitude of

the fluorescence fluctuations is given by:

����� � ���������, �� ���. �1.3�

The total fluorescence signal is given by,

���� � ��������, �� ��� �1.4�

and the average fluorescence signal is thus:

������ ������ � ���� ���. �1.5�

Combining equations (1.1), (1.3) and (1.5) yields the fluorescence fluctuation

autocorrelation function ,

���� � ������������������, �����������, � � ���������� ������ ! ���� ���"# , �1.6�

15

where ������, �����������, � � ��� is referred to as the correlation function of a concentration fluctuation at some point �� at time t with the concentration fluctuation at a point ������ at some later time t + τ.

Equation (1.6) can be extended to a solution containing several different chemical

species by representing the fluorescence signal as the sum of different signals.

The particular case of G(0) represents the correlation of a molecule at ������ with a molecule at �� at the same instant. In a sample in which there are no long-range interactions, there is no spatial correlation and therefore fluctuations are only correlated

at the same instant at the same position (and all positions are equivalent). In this limit it

can be shown that equation (1.6) reduces to,

��0� & ������#�������# , �1.7�

where γ is a constant depending on the excitation and detection PSF (called emission

PSF) shape . Equation (1.7) then, is the relative mean square amplitude of fluctuations,

which for independent random molecular processes can be shown to be inversely

proportional to the average number of processes (). Thus,

��0� & 1() . �1.8�

a typical value of γ for common experimental geometries is ≈ 0.5 and depends on

���� and on the detection efficiency profile (emission PSF) with a weak dependence on sample volume shape.

Thus G(0) depends strongly on the number of fluorescent molecules in the sample

volume, and so FCS can probe sample concentration directly. This has been exploited in

a number of studies.

An interesting result of fluctuation analysis of this type is that it is not necessary to

have only single-molecule within the excitation PSF. In fact if, on average, a small

numbers of molecules are present in the PSF then temporal fluctuations in the

fluorescence signal will still be detected when one molecule enters or leaves the

volume; the fluctuations caused by a sing

Single-molecule sensitivity is only entirely lost if, when one molecule leaves the

volume (by diffusion or chemical reaction) it is immediately replaced by another, in

which case the fluctuations tend to zero. FCS is

single-molecule fluctuations over quite a broad range of concentration.

Experiments are, however, best performed in conditions where fluctuations are

maximized, that is, at or near

1.3.2 Processes which can be monitored by FCS

A number of common physical phenomena can affect and influence the

autocorrelation function of a diffusion single

1.1). They are summariz

Figure 1.8 Schematic of some of the processes diffusion experiment. White circle represent active fluorescent molecules (a) diffusion of a single labeled molecule in the inhomogeneous excitation volume, (b) triplet crossing causing intermittent fluorescence , (c) reversible binding with a second molecule that iconformational changes that induce changes in the amount of emitted fluorescence, and (e) photobleaching.

will still be detected when one molecule enters or leaves the

volume; the fluctuations caused by a single molecule are still being probed.

molecule sensitivity is only entirely lost if, when one molecule leaves the

volume (by diffusion or chemical reaction) it is immediately replaced by another, in

which case the fluctuations tend to zero. FCS is therefore, in principle, sensitive to

molecule fluctuations over quite a broad range of concentration.

Experiments are, however, best performed in conditions where fluctuations are

maximized, that is, at or near single-molecule concentrations (typically < 1 nM)

Processes which can be monitored by FCS

A number of common physical phenomena can affect and influence the

on of a diffusion single-molecule fluorescence experiment (figure

hey are summarized in figure 1.8 [6].

Schematic of some of the processes leading to fluctuations in a singleexperiment. White circle represent active fluorescent molecules (a) diffusion of a single labeled molecule in

the inhomogeneous excitation volume, (b) triplet crossing causing intermittent fluorescence , (c) reversible binding with a second molecule that is not fluorescent but quenches the fluorescence of the labeled molecule, (d) conformational changes that induce changes in the amount of emitted fluorescence, and (e) photobleaching.

16

will still be detected when one molecule enters or leaves the

le molecule are still being probed.

molecule sensitivity is only entirely lost if, when one molecule leaves the

volume (by diffusion or chemical reaction) it is immediately replaced by another, in

principle, sensitive to

molecule fluctuations over quite a broad range of concentration.

Experiments are, however, best performed in conditions where fluctuations are

cally < 1 nM).

Processes which can be monitored by FCS

A number of common physical phenomena can affect and influence the

ce experiment (figure

ctuations in a single-molecule fluorescence

experiment. White circle represent active fluorescent molecules (a) diffusion of a single labeled molecule in the inhomogeneous excitation volume, (b) triplet crossing causing intermittent fluorescence , (c) reversible binding

s not fluorescent but quenches the fluorescence of the labeled molecule, (d) conformational changes that induce changes in the amount of emitted fluorescence, and (e) photobleaching.

17

The main component which generally dominates the autocorrelation function is

diffusion (figure 1.8(a)). The Stokes-Einstein relation gives the translational diffusion

coefficient D of a particle in a viscous medium,

+ ,-. �1.9�

where k is the Boltzmann constant, T is the temperature in degrees K and f is the

friction coefficient for the particle in the fluid.

In the simple case of a spherical particles f is given by[6],

. 601� �1.10�

where 1 is the viscosity of the solvent and r the hydrodynamic radius (sometimes called the Stokes radius) of the sphere.

A typical diffusion time (the time taken to go across the PSF) for a small molecule

at room temperature in water is thus of the order 75µs (given a PSF radius of ≈ 250nm,

a solution viscosity of 1.04*10-3Nsm-2 at 293K and a molecular hydrodynamic radius of

10Å). Although this only represents the time taken to go across the PSF along the

shortest path it nevertheless gives an idea of the approximate timescale on which

diffusion processes will be observed in the autocorrelation function. Diffusion is rarely

the only source of fluctuation in FCS experiments. Triplet state blinking (figure 1.8(b))

modulates the fluorescence output of the molecule causing “blinking” on a

characteristic timescale of a few µs and therefore generates fluctuations that can be

observed in the autocorrelation function. In addition, the environment of the dye

molecule has been shown to greatly influence the photophysics and hence the measured

parameters as does excitation power.

The timescale of additional photo-induced transient states associated with inter-

molecular processes such as charge transfer reactions upon the binding of a dye to

another molecule have been shown to occur in the 10-100ns time regime (for example

R6G-DNA binding). Other molecular interactions (e.g. binding of a receptor-ligand

complex, figure 1.8(c) may result in slower fluctuations that can occur anywhere in the

autocorrelation function if the bind

fluorescence signal.

Many other mechanisms can influence FCS measurements and are difficult to

assign to a particular timescale. Photo

significant problem when working

Dynamic photobleaching of molecules to a permanent dark state is another and

problematic, especially at large excitation power

Consideration must also be

these photo-induced effects may occur as a function of the path they take through the

excitation volume, introducing another convoluted fluctuation.

Figure 1.9 [6] summarized the contributions of these common processes to the

autocorrelation function in an FCS experiment.

Figure 1.9 Diagram showing the temporal ranges of the processes that affect the autocorrelation of single molecule fluorescence data.

autocorrelation function if the binding event is reversible and modulates the

other mechanisms can influence FCS measurements and are difficult to

o a particular timescale. Photo-induced isomerization has been shown to be a

significant problem when working with particular dyes, for example Cy5.

Dynamic photobleaching of molecules to a permanent dark state is another and

problematic, especially at large excitation power (figure 1.8(e)).

Consideration must also be given to the inhomogeneous excitation

induced effects may occur as a function of the path they take through the

excitation volume, introducing another convoluted fluctuation.

summarized the contributions of these common processes to the

ion function in an FCS experiment.

Diagram showing the temporal ranges of the processes that affect the autocorrelation of single

18

ing event is reversible and modulates the

other mechanisms can influence FCS measurements and are difficult to

induced isomerization has been shown to be a

cular dyes, for example Cy5.

Dynamic photobleaching of molecules to a permanent dark state is another and can be

given to the inhomogeneous excitation profile – all of

induced effects may occur as a function of the path they take through the

summarized the contributions of these common processes to the

Diagram showing the temporal ranges of the processes that affect the autocorrelation of single

19

1.3.3 Physical models for the autocorrelation funct ion

There are a number of models that have been developed for FCS. Generally, in FCS

experiments the data are first processed to yield the autocorrelation function as

described earlier according to equation (1.1). Then a physical model which incorporates

descriptions of the sources of fluctuation is used to fit this function allowing the

physical parameters of interest to be determined. The simplest case is that of diffusional

motion of a fluorescent particle in and out of the PSF.

An analytical expression for the form of the autocorrelation function in the case of a

three-dimensional Gaussian PSF was developed by Aragon and Pecora[8].

���� 1() 21 ��

�3456 21 � ���34

56 #7 � +�

1() 21 ��

�3456 21 � �8#34

56 #7 � +� �1.11�

where () is the average number of fluorescent molecules within the PSF at any instant, and �3 9:;# 4+⁄ and �3� 9=# 4+⁄ are, respectively, the characteristic times of diffusion across and along the illuminated region. K=ωz/ωxy where ωz and ωxy are the

sizes of the beam waist in the direction of the propagation of light and in the

perpendicular direction, respectively (usually ωz > ωxy), assuming a Gaussian

illumination profile. DC is the value of the autocorrelation as τ→∞ (usually DC=1). τD

is called the molecular diffusion time (or correlation time) and is given for one-photon

excitation by,

�3 9>#

4+ �1.12�

where D is the translational diffusion coefficient. In particular, equation 1.12 refers

to the one-photon excitation case only. For a two excitation configuration the

denominator in equation (1.12) must be doubled.

20

As we could expect, the amplitude of the autocorrelation function is inversely

proportional to the average number of molecules in the sampling volume, since the

fluctuations �( ()⁄ in the number of molecules in the sampling volume are inversely proportional to ?() and since G(τ) is second order in the intensity of fluorescence.

Notice that in equation (1.11) each of the directions of translational motion brings

in a term (1 + t / τ)-1/2, so that for a two-dimensional diffusion in the xy plane we have,

���� 1()1

1 � � �3⁄ . �1.13�

In practice, equation (1.13) is also a good approximation to a 3D system with the

illumination conditions such that K2 >> 1 ( τD

21

There are two main sources for the fluctuations δn(t) in the number of detected

photons per sampling time. The first is the statistical nature of the system itself, i.e.

fluctuations in the number N of fluorescent molecules in the sampling volume due to

diffusion or chemical reactions. The relative fluctuations in photon counts due to this

source is related to the fluctuations in N: √AB� �( () ⁄ 1 ?()⁄ . These fluctuations contribute both to the signal G(τ) (as discussed above) and to the noise ?AB�������.

The second source of fluctuations δn(t) is the statistical nature of the photon

emission and detection processes, i.e. the fluctuations in the number of detected photons

per fluorescent molecule (shot noise). These fluctuations contribute to the noise only,

since the fluctuations at different time intervals are not correlated.

Shot noise depends on the total number of detected photons and its relative value is

?AB� �E��� EF⁄ 1 √EF⁄ 1 ?G()⁄ , where υ is an average number of detected photons per molecule per sampling interval.

In most experimental situations and definitely in most of the situations where the

FCS statistics is of concern, υ is small. For example, the typical diffusion time for a

simple dye molecule (e.g. Rhodamine 6G) in the FCS experiments is ≈ 100µs. Then

choosing a sampling time ≈ 1µs and taking the typical count rate of 30000 photons per

second per fluorescent molecule, we get υ ≈ 0.03.

For small values of υ and large (), the shot noise dominates the noise of the correlation function ?AB�������. Taking into account the fact that the shot noise is uncorrelated, the signal-to-noise ratio for the FCS measurement is,

@ (7 ����?AB� ������ H ����I()√- J I√- �1.14�

where T is the total number of accumulated sampling intervals ∆t ( T∆t is the total

duration of the experiment), and we made use of ���� J 1 ()⁄ . Is important to point the two main consequences of equation (1.14). First, as

previously mentioned, for () >> 1 the statistics of FCS is independent of the number of molecules per sampling volume and depends only on the photon count rate per molecule

and the total acquisition time.

22

Second, the S/N dependence on υ is stronger than the dependence on T, which means

for instance that is extremely important to optimize photon detection in the experiment

[1]. Finally, this expression also tells us that arbitrary S/N can be obtained by increasing

the measurement time. This is a crucial point in the context of this work, as this can

equivalently be obtained by accumulating the signal from multiple spots in parallel, thus

reducing the overall experiment duration.

23

Chapter 2

Single-molecule fluorescence instrumentation

2.1 Introduction

The instrumentation necessary to achieve single-molecule fluorescence detection is

relatively straightforward[6]. The main requirements are high optical efficiency

collection and a good signal-to-noise ratio. These are usually achieved by using high

numerical aperture microscope objectives and sensitive detectors such as SPAD (silicon

photon avalanche detector) or CCD (charge-coupled devices).

Optical detection of a single-molecule requires that its optical signal (usually

fluorescence) can be distinguished from the background light arising from other

molecules within the detection volume. This therefore implies that the optical system

must have a high throughput and detection efficiency and that background noise is

efficiently rejected. Generally, the detection of a single molecule is achieved either by

using very low sample concentrations or by immobilizing single-molecules on a surface

with a sparse density and combining either of these approaches with a very small

observation volume (< 0.1 fl). Even when such a small observation volume is used, one

generally still faces the problem of a relatively large background signal from many

solvent molecules, in comparison with the few fluorescence photons from the single

fluorescent molecule of interest. For example, in 0.1 fl water there are ≈ 109 water

molecules. If even a small amount of unwanted signal is emitted from these water

molecules and it overlaps the spectral region of the fluorescence of the single molecule

of interest, the signal-to-background ratio will make measurement impossible.

24

There are three primary sources of background noise:

1. Rayleigh scattering by the solvent molecules. This process result in a background

signal at the excitation wavelength that may leak through the optical detection

filters, which cannot provide 100% efficient rejection.

2. Raman scattering by the solvent molecules. This process result in a photon at both

higher and lower energy compared to the excitation light. However, since

fluorescence of the single molecule of interest will be at longer wavelengths than the

excitation, it is the Raman scattered light at lower energy (Stokes radiation) that is a

concern. Some of these Stokes scattered photons may overlap the detection filter

pass band and therefore contribute to the background signal.

3. Finally, a combination of fluorescence, Rayleigh and Raman scattering from

impurities in the solvent introduced by impurities in the buffer components or by

careless sample preparation.

In addition, the signal-to-noise ratio may also be affected by problems with the

instrumentation such as the stability of the light source, mechanical drift, detectors

noise, and non-linearity.

For a typical fluorescent dye molecule with a quantum yield of 0.8, we might

expect of the order 105-106 fluorescence photons per second to be detected if an

excitation flux of ≈ 100 kWcm-2 is used (i.e. 100 µW excitation power into an

observation volume of 250 nm diameter, an overall detection efficiency of 1%, visible

excitation and a fluorescence cross section of 4x10-16 cm2 for Rhodamine 6G). Even

without any impurities present, the background signal due to Raman and Rayleigh

scattering from the large number of solvent (water) molecules present would be many

orders of magnitude larger. Efficient methods for rejecting this background signal and

for detection of the few fluorescence photons are clearly essential [6].

The most trivial method is by reducing the size of the detection volume. This way,

we minimize the numbers of solvent molecules and therefore minimize the scattered

light.

25

Rayleigh scattered light removal is relatively easy as it is generally spectrally

distinct from the fluorescence emission. Similarly, a good laser excitation/dye emission

choice will allow the fluorescence signal from the molecule of interest to be separated

from Raman scattered light and the fluorescence from impurities by a suitable band-

pass filter (a filter with allows only certain wavelengths of light to be transmitted with

efficiency).

While the intensity of the Raman scattered light is low the large number of solvent

molecule in the volume makes this effect significant. For water (typically the highest

concentration solvent component) the inelastic Raman scattering causes a shift in the

scattered light that leads to a number of bands (due to, for example, the vibration along

O-H or H-O-H). The bands due to Raman scattering are typically expressed as the shift

in wavenumbers (cm-1) of scattering light with respect to the excitation light.

The relationship between wavenumber and wavelength is given by,

KBALEMNOL� PN56" 10QKBALRLES�T EN" �2.1�

For example, for the 532nm (laser used in our experiments) the wavenumber is

18797 cm-1. For water, 8 distinct Raman bands may be observed, the shift of the most

intense band is ≈ 3439 cm-1 and is relatively broad (a half width of around 400 cm-1),

the other bands are generally too weak to be observed. Thus for 532 nm excitation the

scattered light due to Raman shift will occur, principally, at 22236cm-1 (18797 - 3439)

or at a wavelength of ≈ 650 nm.

Since fluorescent dyes usually have quite broad emission spectra, narrow band pass

filters that reject the majority of the unwanted background signals can also reduce the

number of fluorescence photons reaching the detector. Minimizing the sample volume

and the use of appropriate filters are the two most important approaches to improving

the signal-to-noise ratio in single molecule fluorescence experiments.

26

2.1.2 Optical arrangement for single-molecule detec tion

A variety of optical arrangements have been chosen for single-molecule

fluorescence experiments. However, by far the most common approaches are the

confocal epifluorescence, multi-photon epifluorescence, and total internal reflection

geometries. The optical arrangement is mainly determined by the experimental design,

that is whether the molecules of interest are freely diffusing or are fixed in space. In

diffusion experiments, which have the benefit of being relatively simple to set up,

confocal or two-photon illumination is typically used.

2.1.3 Epi-fluorescence far-field microscopy

The epi-fluorescence (episcopic fluorescence) configuration (figure 2.1)[6] is

commonly encountered in microscopy. A single optical element is used to deliver the

excitation light to the sample and to collect the fluorescence emission. In general high

numerical aperture microscope objective is used. ‘One-photon’ excitation (i.e. the use of

excitation photons with energy matching the absorption transition in the fluorescent

molecule of interest) is the most commonly encountered excitation protocol. A

collimated laser beam is reflected off a dichroic mirror into the back-aperture of the

microscope objective. The light is focused to a diffraction-limited spot at the focal

plane, which is placed at the region of interest in the transparent sample (figure 2.2)[6].

The radius of the focused spot perpendicular to the direction of propagation can be

approximated by the half width at half maximum of the Airy disk intensity profile:

K~ 0.51V(W �2.2�

where λ is the wavelength of light used, and NA is the numerical aperture of the

objective lens. Using NA = 1.2 and λ =532nm gives an approximate focal spot diameter

of ≈ 450 nm.

27

Figure 2.1 Illustration of the inverted epi-fluorescence configuration. The excitation beam (grey, collimated or

parallel rays) is reflected towards the sample by a dichroic mirror (essentially a semi-transparent mirror) and focused at a point within the sample at the front focal plane of a microscope objective. In this example the same is represented as a fluid sitting on a thin glass coverslip, as is typical in these inverted configurations. A portion of fluorescence (and scattered excitation light) is collected by the same microscope objective (black rays). The fluorescence is transmitted through the dichroic mirror towards the detector while scattered excitation light is not transmitted but reflected (not shown) back toward the light source.

Figure 2.2 Close up of the excitation volume (not to scale) created by the epi-fluorescence configuration. A

collimated laser beam of width D is focused through a glass coverslip by a microscope objective and brought to a focus some distance above the glass/water interface. The depth of focus Z inside the sample is shown (defined, in this case, as twice the distance from the focal plane to the point at which the intensity has dropped by 1/e). The configuration results in spatial restriction of the beam diameter 2w in the direction perpendicular to the direction of propagation but does not restrict the beam in the direction of propagation.

It should be noted that this figure relates to a theoretical minimum (the diffraction

limit) and that rarely will this level of performance be reached due to a variety of optical

imperfections present in the optical system. Focal spot diameter of around 500nm -1µm

are more typical.

28

This focusing limits the extent of the region in the sample that is excited and

therefore limits the region in which fluorescence or scattering is generated. Some of the

fluorescence photons emitted by molecules in the excitation volume are collected by the

microscope objective and directed by the dichroic mirror to the detection arrangement.

Clearly, single-photon far-field excitation in this manner provides no spatial

reduction of the excitation/collection volume in the direction of propagation of the light

and so additional optics is required in the detection path to minimize this volume.

To achieve this, confocal detection is often employed (figure 2.3)[6].

Figure 2.3 Illustration of the principle of confocal detection to limit the collection volume in the direction of

the propagation of the excitation beam. Light emerging from near the focal plane (black spot) is collected and collimated by the microscope objective and then focused by a second lens to pass through an aperture and onto the detector. Light that originates from in front or behind the focal plane (grey spot) is out of focus at the aperture and only a small portion continues to the detector. The aperture is said to be confocal with the objective. (Optics delivering the excitation light have been omitted for clarity)

Confocal detection uses a small aperture (typically 25-50 µm in diameter ≈

M*Airy diameter, where M is the objective magnification) in the optical detection path.

The light collected by the microscope objective is focused onto this pinhole such that

only light collected from very close to the focal plane ( ≈ 0.5µm ) of the objective will

be transmitted through the pinhole.

29

Light originating from regions away from the focal plane of the objective will be

out of focus at the pinhole and will be rejected to a large extent and will not reach the

detector. The use of this confocal arrangement therefore does not restrict the volume of

excitation but does efficiently reduce the collection volume. The extent to which the

confocal approach is effective is a function of the pinhole size, microscope objective,

and the lens that is used to focus the light onto the pinhole. A common modification to

this principle is to use the point-like nature of some detectors to provide confocality

rather than adding a pinhole in the detection path. For example, the active area of a

single SPAD (silicon photon avalanche detector) that composes the 32x32 matrix of

SPAD used in our set-up, is circular and ≈ 20µm in diameter, which provides inherent

confocality when used with suitable focusing optics. The transmission efficiency of

modern microscope objective at visible wavelength is high, approaching 90%, but the

overall detection efficiency of the objective is a more complex issue.

The fluorescence from a single molecule is emitted in all directions. However the

microscope objective only collects the fluorescence from a solid angle defined by the

numerical aperture (NA = n*sin θ, where θ is the half angle of aperture and n is the

index of refraction of the sample medium).

Furthermore, when the dependence of the collection efficiency on the position of

the molecule within the focal volume is taken into account, the overall objective

detection efficiency at visible wavelength can be as low as 20%.

Although this may seem very low, this represents a practical limitation of using a

single microscope objective and this limitation exists for all forms of microscopy. It is

thus essential to optimize the efficiency of all other elements in the instrument.

Single-photon excitation in an epi-fluorescence configuration combined with

confocal detection provides the necessary spatial reduction of the collection volume that

is required to minimize the background noise, and has the added benefit of simplicity.

However, this approach has two distinct disadvantages. First, the excitation light is only

spatially restricted in one direction (perpendicular to the light path) and although

fluorescence from far outside the focal plane is rejected by the confocal detection

scheme, molecules in the larger excitation volume are continuously irradiated by this

simple arrangement. This causes unnecessary photobleaching of molecules that can

reduce the useful lifetime of the sample, particularly in solid samples.

30

Second the introduction of a pinhole (and associated optics, focusing lens) in the

detection path reduces the overall amount of fluorescence from the single molecule of

interest reaching the detector (in our case this is overcome using a detector with small

active area as discussed earlier).

In one-photon excitation a particular excitation wavelength is required for efficient

fluorescence emission, and generally the difference between this wavelength and the

peak emission wavelength shift (the Stokes shift) is small. Thus all dyes efficiently

excited at the same range of wavelength tend to have spectrally similar emission

wavelengths.

The PSF (more precisely, the convolution of the excitation and collection volumes)

for either one-photon (confocal) or two-photon geometries defines a volume in solution

that is approximately cylindrical, around 500 nm in diameter and 1 µm long (so a

volume of ≈ 0.2 fl) through which the molecules diffuse and are excited.

The configuration can also be used to take images of a surface if the detection volume is

placed at the coverslip/water interface (see figure 2.1 and 2.2) and scanned over the

sample surface.

2.1.4 The PSF in single-photon confocal epi-fluores cence

illumination systems

The instrument PSF is the mathematical function that describes the way in which

light is transformed as it passes through an optical system. In an imaging system the

image recorded by the detector is convoluted with the illumination, transmission and

detection properties of the particular instrument used. In a confocal system one might

first consider the shape of the volume created in solution from the laser beam focused

by the microscope objective, and determine the PSF that describes this volume. The

volume from which light is detected however is further restricted by the confocal

pinhole defining an emission PSF.

The convolution of both PSFs result is a combined pinhole-objective system PSF.

Furthermore, any lens, filter or detector may alter the apparent volume from which light

is detected. The convolution of all of these gives us the instrument PSF and so a

description of the excitation/detection volume through which molecules may pass.

31

The form of the PSF volume defined by a confocal geometry is therefore of crucial

importance for a range of fluctuation spectroscopy methods, in particular fluorescence

correlation spectroscopy (FCS). Fluctuation techniques generally rely on measuring the

photon count distribution for a signal detected from a single diffusing dye molecule.

This data is then largely stochastic, different signals being caused by diffusion

along random paths through the volume. Thus to enable a prediction of the resulting

data (for example, to calculate the expected photon count distribution or to determine a

diffusion rate) the sample volume must be well defined.

Despite this apparent complexity, it is perhaps surprising that a simple description

of the PSF for these microscopes has been widely applied in which the sample volume

is described by a three-dimensional Gaussian with a 1/e2 beam waist diameter 2ω0 and a

length 2z0 along the optical axis given by [6]:

X@�FFFFF���� X@�FFFFF�Y, Z, [� LY\ ]^ 2�Y# � Z#9># ^2[#[># _. �2.3�

This simple model has however some weaknesses; in particular, in many cases it

apparently does not describe the shape of volume accurately and can introduce artifacts

into FCS measurements that manifest as, for example, apparent additional species in the

solution. For confocal FCS the discussion of this issue has centered more around the

optimization of experimental conditions to achieve as near a three-dimensional

Gaussian PSF (as defined by equation 2.3) as possible. A detailed study by Hess and co-

workers[10] suggests that the near three-dimensional Gaussian PSF can be obtained by

careful illumination of the sample with a Gaussian laser beam underfilling (i.e. smaller

than the back aperture) of the microscope objective and by using a small confocal

aperture (in our case a point like nature of the SPAD detectors).

32

2.1.5 Spectral discrimination

Background signal rejection is critical for successful implementation of single-

molecule detection. We have discussed the origins of the background signal: Rayleigh

and Raman scattered light (from the sample, solvent and impurities) and extraneous

fluorescence (from impurities). We have already discussed the requirement to minimize

the excitation/collection volume to reduce these background signals. We will now

consider methods to “condition” the detected signal to remove background noise by

using spectral discrimination.

Spectral discrimination is the selection of certain wavelength (or energy) photons

using thin-film dielectric, glass or notch filters or diffraction gratings.

Glass color filters (or absorption filters – material showing differential wavelength

dependent absorption of light) are relatively inexpensive, easily cleaned, and have

optical properties that are stable over long periods of time. Their principal disadvantage

is to rely exclusively on absorption to reduce background signal. The amount of

background noise rejection therefore depends on the thickness of the filter, which in

turn affect the transmission of the fluorescence signal.

Furthermore, the glasses used for these filters can themselves be fluorescent which, in

the worst case, could generate a signal overlapping in wavelength with the desired

fluorescence signal, effectively reducing the overall signal-to-noise ratio. In general,

glass color filters are therefore not preferred for single-molecule fluorescence

experiments.

Thin-film interference filters are composed of thin films of dielectric material, each

approximately the thickness of the wavelength of light, layered in stack. The reflections

from the interfaces between the layers interfere constructively or destructively

depending on the wavelength of the light, the thickness of the layers, and the refractive

index of the layer material. Filters consisting of many stacked layers can be designed to

pass narrow wavelength bands (from a few nanometers wide band pass to tens of

nanometers wide) with transmission efficiencies of 80-95% at visible wavelengths.

Auto-fluorescence of these filters is low and the blocking of wavelength outside the

pass band can be very high (several order of magnitude lower transmission than in the

band pass).

33

However, like glass color filter, interference filter also suffer from a number of

disadvantages. The dielectric material forming the thin films tends to be quite soft,

which means that the filters are easily damaged and can degrade.

Single-molecule detection experiments usually incorporate three main type of thin-

film interference filters, often called excitation, dichroic, and emission filters (figure

2.4)[6]. Excitation filters may be required when broad emission wavelength lamps are

used, or even when laser sources are used to reject the unwanted luminescence or other

laser emission lines that might overlap with the detection wavelength range of the

experiment.

Figure 2.4 Illustration of the three filter types used in single molecule fluorescence experiments. a) The excitation filter selects the correct excitation wavelength from a multiple wavelength light source. b) The dichroic filter, through which the excitation light passes, reflects the returning emitted fluorescence from the sample separating it from most of the scattered excitation light which is re-transmitted. c) The emission filter removes much of the remaining scattered light and any unwanted fluorescence. The right-hand panels illustrate the transmission characteristic of typical examples of each filter.

34

Dichroic filters (or dichroic mirror) are generally used at angle of incidence of 45°

and are used to separate light into two (or more) color ranges. In single-molecule

instrumentation, these filters enable the use of the epifluorescence configuration

discussed previously.

Generally the excitation light is reflected by the dichroic and the back propagating

fluorescence from the sample is transmitted through the dichroic into the detection

pathway (or vice versa depending on whether the dichroic is long- or short- pass) while

the reflected or backscattered excitation light is transmitted through the filter back

towards the source and away from the detection path.

Since any filter is non-ideal it will transmit/reflect a portion of the unwanted

wavelength and so in single-molecule detection it is a matter of placing different types

of filters in series until sufficient blocking is achieved and the signal-to-noise ratio is

acceptable (acknowledging some loss of the desired signal with each filter addition).

The dichroic filter alone is rarely sufficient to provide the required spectral

discrimination and therefore emission filters are placed in front of the detector(s) to

reject light outside a desired band pass (or above or below a particular wavelength).

2.1.6 Excitations sources

The excitation source for single-molecule studies is chosen on the basis of the

excitation wavelength that is required, which in turns depends on the fluorophore to be

used. Since single-molecule detection requires a fluorophore with a high quantum yield,

by far the most commonly used are specifically designed fluorescent dyes. Although a

very broad range of these dyes is available, in general, the one chosen for single-

molecule fluorescence experiments have absorption bands in the blue-green region of

the spectrum because of the availability of laser excitation source in that region.

Laser with gain media such as argon ion (488 or 514nm) and Nd:YAG (532nm)

provide a stable and controllable source, are typically already polarized and have

collimated beams and Gaussian intensity profiles perpendicular to the direction of

propagation. Regardless of the excitation type or wavelength, the stability of the light

source is critical.

35

Any fluctuations in the fluorescence intensity from an analyte caused by

fluctuations in the output of the light source (or poor pointing stability of the beam) can

severely affect the results of experiments that rely on photon counting statistics such as

FCS, PCH and FRET.

Poor pointing stability (i.e. variation in the direction of laser beam) can also cause

changes in the excitation volume in confocal arrangements. Even if a perfect light

source, free from all intensity fluctuations, is incident on a detector then the output of

the detector (photon counts per given time interval) is not steady but exhibits

fluctuations within a Poisson distribution.

This is because the quantum mechanical nature of the interaction of a photon with a

detector leads to there being a statistical probability that the arrival of the photon results

in an output signal. Since single-molecule fluorescence detection involves the counting

of small numbers (< 200) of photons in short time interval (< ms), such inherent

fluctuations caused by the detection process can be the dominant source of noise in the

experiment. However, this phenomenon can also be used as a convenient test of the

stability of the instrumentation. If the scattered light or fluorescence from a

concentrated sample that does not induce variation in intensity is measured, then the

output of the detector should follow a Poisson distribution in counts per unit time

interval (figure 2.5)[6]. Any deviation from this (i.e. broader distribution ) indicates that

fluctuations are occurring over and above those induced by the stochastic nature of

photon detection and is indicative either of laser intensity fluctuation or shortcomings of

the instrumentation in term of mechanical stability.

36

Figure 2.5 Photon count histogram of an ideal scatteres placed at the laser focus. The collected photon count

distribution (circle normalized) is fitted exactly by a Poissonian function (line) indicating that there are no fluctuations in the detected signal arising from instability of the light source or other instrumentation.

2.1.7 Microscope objective for single-molecule fluo rescence

detection

The choice of the microscope objective is one of the most important issue in the

single-molecule detection system. In many experiments it is critical for the generation

of a small excitation volume. In epifluorescence geometries it also collects the

fluorescence from the sample. Microscope objective are compound lenses, consisting of

many individual elements. In general the design is intended to provide the required

magnification, a small focal spot, and, as far as possible, an aberration-free image with

high collection efficiency. As far as single-molecule fluorescence experiments are

concerned, the suitability of a microscope objective can be assessed by considering the

numerical aperture, the magnification, whether the objective is oil immersion or

designed to operate in air, and the degree of aberration correction.

37

The numerical aperture (NA) of an objective describes the solid angle over which

light is collected by the lens.

The NA is defined by[6],

(W E sin�c� �2.4�

where n is the refractive index of the imaging medium and µ is the half angle of the

solid cone defined by the collected light (figure 2.6)[6]. In microscopy, NA is important

because it indicates the resolving power of a lens. The size of the finest detail that can

be resolved is proportional to λ/NA, where λ is the wavelength of the light. A lens with

larger NA will be able to visualize finer detail than a lens with a smaller numerical

aperture, and also collect more light and will generally provide a brighter image.

Figure 2.6 (a) The numerical aperture of an objective is defined in terms of the half angle of the cone of rays

(µ). The effect of using an immersion oil is shown in (b) and (c) – peripheral rays which are refracted out of the cone defined by the numerical aperture when the space between the coverglass and objective is filled with air, propagate into the front lens of the objective when refraction is eliminated by filling the space with index matching oil.

38

In microscopes with an inverted design (the objective pointing upwards as in our

experiment) it is necessary to image through a thin coverglass. In this case when the

medium between the objective and coverslip is air (Figure 2.6 (b))[6], the numerical

aperture is limited to a value of ≈ 1 due to refraction at the coverslip – air interface. To

achieve a higher NA, an immersion objective is required. An oil immersion objective

has a high refractive index oil layer between the frontmost objective lens and the

coverglass (Figure 2.6(c)) where the oil and the coverglass are generally chosen to

match closely the refractive index of the objective. There are objectives with different

immersion fluids, but most commonly with water or oil, which have refractive index of

approximately 1.33 and 1.51, respectively. Water immersion objective are designed

(corrected)to image on aqueous sample through a number 1.5 coverslip (thickness ≈

170µm). They are preferable to oil immersion objective when imaging deep (≈ 10 µm)

in the sample, because of reduced aberration. Typically, in practice, water immersion

objective provide numerical apertures of up to 1.2 and oil objectives of up to 1.45. It

should be remembered that whatever the NA of the objective, the NA of the system is

(to an approximation) limited by the lowest refractive index substance between the

objective and sample. Thus a 1.45 NA objective, even when used with the correct

coverslip and immersion oil, would still have a reduced NA if the light as being focused

(or collected) through an aqueous solution, in other words if the specimen is not in

contact with the coverslip. For work in aqueous conditions where the sample is not in

contact with the coverslip (in diffusion experiments it is desirable to place the detection

volume several µm into the solution, to prevent artifact from molecules attached to the

nearby surface), the NA is effectively limited to a value close to the refractive index of

the solvent used (≈ 1.33 for water).

The NA can have a large effect on the collection efficiency of the objective. For

example, NAs of 1.45, 1.3, and 0.95 correspond to 40%, 26% and 10% of the total

possible sphere of collection around an objective. Thus small improvements in NA can

result in significantly more photons at the detector.

Optical aberrations can degrade the quality of images, change the light distribution

at the focus, reduce the resolving power, and increase the focal spot size (therefore

increasing the sample volume) of an objective.

39

The primary aberrations commonly experienced in microscopy are spherical, coma,

lateral and longitudinal chromatic, curvature of field, and astigmatism. Fortunately, high

NA objectives are often corrected for these aberrations to a great extent and they are

therefore not usually an issue from the point of view of single-molecule fluorescence

measurements.

2.2 Detectors for single-molecule fluorescence

experiments

The choice of detector is a critical stage in the development of a single-molecule

fluorescence experiment. In general the detector should fulfill the following requests:

1. high quantum efficiency (QE) over the spectral range of interest,

2. good linearity of quantum efficiency over the spectral range of interest,

3. sufficiently fast time response for the application,

4. low noise (i.e. low average dark count), permitting single-molecule

detection.

We will focus our discussion to detectors suitable for work in the visible and near-

infrared part of the optical spectrum: photomultiplier tubes (PMTs), avalanche

photodiodes (APDs), in particular single-photon avalanche diodes (SPADs) and

electron multiplying charge-coupled devices (EMCCDs).

These detectors may be divided in two categories. PMTs and SPADs (as well

APDs) are single point detectors, the single output of which is proportional (not for

SPADs and not PMTs used on single- photon counting mode) to the integrated light

intensity impinging on the detector area.

Such detectors can be used for fluctuation spectroscopy using light collected from a

point within the sample or the sample could be raster scanned to record and image.

CCDs are imaging detectors that contain an array of detector elements and the object

plane of the sample can be imaged directly onto the detector surface. The suitability of

each of these type of devices for a given single molecule spectroscopy application

depends on the way the devices work.

40

2.2.1 Point detectors

Point detectors are detectors which do not provide position information, but are not

necessarily of small dimension. For instance, most single-photon avalanche photodiodes

used in SMS have a sensitive area with a diameter of a few dozen to a couple hundred

micrometers, whereas photomultipliers have typically diameters of several millimeters.

This has some practical consequences for collection efficiency and design of the

detection path. As discussed before, point detectors are mostly used in a confocal setup

to detect photons emitted from a small volume excited in the sample. The smaller the

sensitive area, the lower the magnification of the collection optics needed to focus the

collected light onto this sensitive area, and the more difficult the alignment of the

detector for maximum detection efficiency[11].

As was just mentioned, there are two general types of point-detectors used for

single-molecule applications: photomultiplier tubes (PMT) and single-photon avalanche

photodiodes (SPAD). In both kinds of devices, each detected photon is first converted

into a charge carrier/s (photo-electron or electron-hole pair), which is/are then amplified

by several order of magnitude in a rapid avalanche process. The basic layout of a typical

PMT is illustrated in figure 2.7.

Figure 2.7 Illustration of the basic principle of operation of a PMT.

The photon strikes the photocathode, is absorbed and generates a photoelectron

with a certain quantum efficiency determined by the photocathode material. When a

photoelectron is produced it is accelerated towards the first dynode by the electric field

created by focusing electrode. The photoelectron strikes the first dynode and result in

the generation of secondary electrons (again with a certain efficiency), each of which is

41

accelerated in an electric field and strikes a subsequent dynode, generating further

secondary electrons. The process of amplification continues down the dynode chain

until the anode collects the electron emitted by the final dynode and an external circuit

detects this current. PMT’s often suffer from poor linearity in output current over a

large range of intensities, often have low quantum efficiency (typically < 25%) and also

a narrow spectral response. Dark current, generated when no light is falling on the

photocathode, due to thermionic emission of electron, is a source of noise in PMTs that

can be reduced by cooling. Multiplication noise (i.e. the variation in output signal for

any given single photon impinging on the photocathode due to the chain of probabilities

involved in the amplification process) is also an issue with PMTs at very low light level.

The single-photon avalanche diodes (SPADs) are semiconductor devices based on a

p-n junction reversed biased at a voltage (Va) higher than the breakdown voltage (Vb)

(figure 2.8). At this bias, the electric field is so high (higher than 3×105 V/cm) that a

single charge carrier injected in the depletion layer can trigger a self-sustaining

avalanche. The current rises swiftly (sub nanosecond rise-time) to a macroscopic steady

level, in the milliampere range. If the primary carrier is photo-generated, the leading

edge of the avalanche pulse marks (with picosecond time jitter) the arrival time of the

detected photon.

The current continues until the avalanche is quenched by lowering the bias voltage

Vd down to or below Vb : the lower electric field is not able any more to accelerate the

carriers to impact-ionize with lattice atoms, therefore current ceases. In order to be able

to detect another photon, the bias voltage must be raised again above breakdown[12].

Figure 2.8 Thin SPAD cross section

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These operations require a suitable circuit, which has to:

1. sense the leading edge of the avalanche current;

2. generate a standard output pulse synchronous with the avalanche build-up;

3. quench the avalanche by lowering the bias down to the breakdown voltage;

4. restore the photodiode to the operative level. This circuit is usually referred to as

a quenching circuit.

The simplest quenching circuit is commonly called Passive Quenching Circuit and

composed of a single resistor in series to the SPAD. This experimental setup has been

employed since the early studies on the avalanche breakdown in junctions. The

avalanche current self-quenches simply because it develops a voltage drop across a

high-value ballast load (about 100 kΩ or more). After the quenching of the avalanche

current, the SPAD bias Vd slowly recovers to Va, and therefore the detector is ready to

be used again. A more advanced quenching scheme is called active quenching. In this

case a fast discriminator senses the steep onset of the avalanche current across a 50 Ω

resistor and provides a digital (CMOS, TTL, ECL, NIM) output pulse, synchronous

with the photon arrival time.

Besides photon-generated carriers, also thermally-generated carriers (through

generation-recombination processes within the semiconductor) can fire an avalanche

process. Therefore, it is possible to observe output pulses also when the SPAD is kept in

dark: the resulting average number of counts per second is called dark count rate and is

the key parameter in defining the detector noise.

It is worth noting that the reciprocal of the dark count rate defines the mean time

that the SPAD remains biased above breakdown before being triggered by an undesired

thermal generation. Therefore, in order to work as a single-photon detector, the SPAD

must be able to remain biased above breakdown for a sufficiently long time (e.g., longer

than few milliseconds, corresponding to a count rate of few kilo counts per second,

kcps).

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Both APDs and SPADS are reverse biased semiconductor p-n junctions. However,

APDs are biased close to, but below the breakdown voltage of the semiconductor. This

high electric field provides an internal multiplication gain only on the order of few

hundreds, since the avalanche process is not diverging as in SPADs. The resulting

avalanche current intensity is linearly related to the optical signal intensity.

As mentioned in the previous paragraphs, the possibility to obtain for these

detector a very small size of their sensitive area (from ≈ 20 to ≈ 100 µm), offer the

advantage that they can also function as the confocal “aperture” in epifluorescence

microscope, removing the need for a pinhole and hence increasing the overall

detection efficiency. In addition, as will be discussed in the next chapter, the

possibility to build this devices in mono-dimensional or bi-dimensional array,

combined to the use of micro-lens array or spatial light modulator that generate an

array of excitation spot matching the SPAD array, make it possible to parallelize the

acquisition of the data in FCS measurement, resulting in a faster data acquisition

process.

2.2.2 Imaging detectors

Imaging detectors comprise a two dimensional array of typically micron scale

detector elements that can each be addressed by readout circuitry so that an image of the

sample can be acquired. A suitable optical arrangement must be used to image the

object onto the plane of the detector array. CCDs are by far the most common imaging

arrays; in these each detector element is formed from a charge storage device. Incident

photons generate charge carriers in each element which are accelerated and are stored

using an applied potential. The amount of charge stored in these “well” will thus be

proportional to the integrated light intensity that has fallen on that elements of the array.

Readout of the array is achieved by movement of the charge from each element of the

array to the next, either on an individual basis or line by line, as illustrated in figure 2.9.

The readout process is a limiting factor on the frame rate of CCD cameras.

This is determined by the speed of the electronics that move the charge, the time

required to clear out residual charge between exposures, and the speed of reading the

signal from the output register.

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Figure 2.9 Schematic representation of the structure of a typical CCD. Elements are read out sequentially by

first moving charge downwards line by into an output register using a series of electrodes. This register is then read out one element at time and the signals amplified by an external electronic current amplifier. In the EMCCD system on-chip gain is provided before external amplification to lift even very low signals well above the read out noise floor.

To be suitable for single molecule detection a CCD should fulfill a number of

requirements: its spatial and temporal resolution should be appropriate to the

application, the quantum efficiency (QE) of converting photons arriving at the CCD

surface to charge generation is high, and the dynamic range (i.e. the range of input

intensities that can be accommodated) should be large. CCD quantum efficiency is

defined by the physical structure of the pixel elements and the electrodes as well as the

semiconductor material used. The QE also tend to be a strong function of temperature

and so all high-sensitivity CCD cameras are equipped with cooling as optimal operation

temperatures can be as low as -90°C.

The basic CCD detector is not suitable for fast frame rate, low light level

applications because of the frequency dependent read out noise (from electronic circuit

amplification) and gain must be introduced in order to render these devices capable of

single molecule detection. Intensified CCDs (ICCD) and electron multiplying CCDs

(EMCCD) are the two most common system that are used. ICCD were the first

development of CCDs intended to extend the detection sensitivity to near single

incident photon level.

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They generally combine a micro channel plate (MCP, essentially an array of small

PMTs ) onto the front of the CCD array. These devices are however complex,

expensive, affected from noise dues, especially, from cross talk between MCP elements

on adjacent pixels and with finite lifetime. An alternative configuration is used in

EMCCD technology. The EMCCD uses an additional register between the output

register and the output amplifier, called the gain register (Figure 2.9). High potentials

applied to the