Embed Size (px)
Citation preview
SCANNING NEAR-FIELD
OPTICAL MICROSCOPY
R. Delville
June 17, 2005
Imperial College London, Photonics Group
Peter Torok’s research group
Supervisor: Dr Edward Grace
1
THANKS
Many thanks to Peter Torok and his friendly team for accepting
me to do my final year project. Special thanks to Edward Grace, my
supervisor, who helped me throughout the year to carry through this
project. I would like to underline the quality of his supervising and
his teaching, as well as the patience he showed whenever I needed his
help.
2
Abstract
This project aims to develop and understand a simple scanning near-field
optical microscope (SNOM). This is applied to know small-scale phenomena
such as two beam interference and the field in the focal region of lenses. A key
part of this project has been to develop the control system to drive the piezo-
electric transducers that move the optical fiber while simultaneously sampling
the detected signal.
Key words: acquisition board, DAC, ADC, sampling, buffers, piezoelec-
tric transducers, optical fiber, photoreceptor, interferometer, fringes, interfer-
ence.
3
Contents
1 General overview 5
1.1 SNOM . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Goals of the project . . . . . . . . . . . . . . . . . . . . 6
2 Control System 7
2.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.1 Output operations . . . . . . . . . . . . . . . . 7
2.1.2 Input operations . . . . . . . . . . . . . . . . . 7
2.2 Programming . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.1 Objectives . . . . . . . . . . . . . . . . . . . . . 8
2.2.2 Program features . . . . . . . . . . . . . . . . . 8
3 Determination of the flexure stage specifications 10
3.1 Properties of the flexure stage . . . . . . . . . . . . . . 10
3.2 Aims and principles . . . . . . . . . . . . . . . . . . . . 11
3.3 Experimental setting . . . . . . . . . . . . . . . . . . . 11
3.4 Results and analysis . . . . . . . . . . . . . . . . . . . 11
3.4.1 Raw data . . . . . . . . . . . . . . . . . . . . . 11
3.4.2 Theory . . . . . . . . . . . . . . . . . . . . . . . 13
3.4.3 Displacement response . . . . . . . . . . . . . . 16
3.4.4 Distortions . . . . . . . . . . . . . . . . . . . . 17
3.4.5 Phase shift . . . . . . . . . . . . . . . . . . . . 20
3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . 20
4 Simulation experiment 22
4.1 General purpose . . . . . . . . . . . . . . . . . . . . . . 22
4.2 Principles . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.3 Experimental setting . . . . . . . . . . . . . . . . . . . 23
4.4 Triggering and acquisition . . . . . . . . . . . . . . . . 23
4.5 Program modifications . . . . . . . . . . . . . . . . . . 25
4
4.6 Method of analysis . . . . . . . . . . . . . . . . . . . . 26
4.7 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . 27
5 SNOM 28
5.1 Aims and principles . . . . . . . . . . . . . . . . . . . . 28
5.2 Experimental setting . . . . . . . . . . . . . . . . . . . 28
5.2.1 Dimensioning requirements . . . . . . . . . . . . 30
5.2.2 Positioning of the flexure stage . . . . . . . . . 32
5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
6 Conclusion 35
5
1 General overview
1.1 SNOM
Scanning near-field optical microscopy opened a new era in optical mi-
croscopy, bringing the spatial resolution at the 50-100 nm level using
visible or near infrared light. This resolution is well below the diffrac-
tion limit of light and allows to overcome the restrictions of classical
(far-field) optical techniques [1]. This is made achievable by the use
of small tapered probe with sub-wavelength aperture. An image is
formed through scanning the probe in the near-field of the sample
surface. The probe is either a source or a detector of radiation. There
are four possible modes of operation with SNOM (figure 1) depending
on how the light is emitted and collected. There are different technical
Figure 1: Modes of operation with SNOM
possibilities for the probe [1]:
• Tapered optical fibers with metal-coating, leaving at the end a
sub-wavelength aperture(50 nm or larger).
• A standard AFM cantilever with a hole of sub-wavelength dimen-
sions in the center of the pyramidal tip.
• The tip of a tapered pipette.
The resolution of an SNOM measurement is defined by the size of
the aperture (typically 50-100 nm). The distance between the probe’s
6
tip and the sample surface is usually controlled through a feedback
mechanism that is unrelated to the SNOM signal. A topographic
imaging is possible by coupling the SNOM with a shear force feedback.
Therefore optical images can be directly correlated with conventional
AFM measurements (see figure 2(a) and 2(b)1).
(a) SNOM scan of 30 nmgold balls
(b) AFM scan of 30 nmgold balls
Figure 2: AFM techniques can be applied to SNOM imaging
The SNOM has applications in fields such as surface chemistry, biol-
ogy, material science, microelectronics. This is a promising technology
with many new potential applications.
1.2 Goals of the project
The goal of this project is eventually to build a simple SNOM capable
of imaging small-scale phenomena such as two beam interference. As
described in section 5.2, the intended device will use a fiber as a probe,
a flexure stage to position the fiber tip and a photodiode to measure
the light collected by the fiber. The probe, working in collection mode,
will be able to scan over an interference area produced by two laser
beams. An image of the fringe pattern is to be made.
The first part of the project focuses on the development of the con-
trol system driving the flexure stage while simultaneously sampling
the detected signal. This task is carried out by an acquisition board1Pictures from www.nanonics.co.il
7
capable of managing simultaneous ADC and DAC operations. Design-
ing the driving program has been the first step towards making the
SNOM.
The second step is built on the control system to measure the spec-
ifications of the flexure stage. It makes use of a Michelson interferom-
eter to determine the way the stage responds to an applied signal.
At this stage, the driving system has been developed for 1-dimensional
application. The next part tackles a 2-dimensional scanning. Software
development is followed by an experiment aimed at testing the system
in a real situation. In addition, tools which analyze the data acquired
by the board have been developed and tested at the same time.
Eventually, a SNOM capable of imaging a fringe pattern is to be
designed and built. The correct functioning of the device relies on all
the previous developments.
2 Control System
2.1 Materials
The control system is build on the acquisition board DT3004 from
Data Translation. The board performs ADC and DAC operations. It
comes with software to develop customized applications. A few exam-
ple programs, carrying out the basic operations, are also provided by
the manufacturer. The programming environment is Microsoft Visual
C++. To interact with the board through the software, Data Trans-
lation provides a set of functions compatible with its product range.
The input and output of the board are accessible from a screw panel
wired to the acquisition board. To generate and acquire signals, the
two subsystems (DAC and ADC) are used simultaneously.
8
2.1.1 Output operations
The board features a fixed analog output resolution of 12 bits (4096
levels). It supports two analog output channels (DAC0 and DAC1).
It can output bipolar analog output signals in the range of 10 V.
The board provides an internal D/A output clock for pacing analog
output operations. The maximum frequency supported is 200 kHz
(200 kSamples/s). The frequency is set up by the user in the software.
The board provides also different ways to start the acquisition (trigger
sources): Software trigger - The operations start when the software is
run. External digital (TTL) trigger - the operations start with a rising
or falling edge of an external TTL source connected to the board (via
the screw panel).
2.1.2 Input operations
The sampling and digitization of the acquired signal are also done
by the acquisition board. The ADC features a fixed analog input
resolution of 16 bits(65536 levels); The board supports 8 differential
analog input channels, i.e. 8 different signals can be acquired at the
same time. The DT3004 board provides gains of 1, 2, 4, and 8. It
can measure bipolar analog input signals between -10 V to +10 V
and provides an internal A/D sample clock for pacing analog input
operations in continuous mode. The maximum frequency supported
for a single channel is 100 kHz. Conversions start on the falling edge
of the counter output.
2.2 Programming
2.2.1 Objectives
The program to be developed must have the following features:
• Must run simultaneously the DAC and the ADC subsystems, in
9
order to generate one or two output signals and acquire an input
signals.
• Must allow the user to easily select the output/input signals fea-
tures.
• Must control when the data outputs and inputs occur to meet
experimental demands.
2.2.2 Program features
The program driving the board has been written in C++ language.
A set of predefined functions, provided by DT Translation, is used to
set and run the board. It makes use of a console window to interact
with the user. The programming flowcharts for continuous ADC or
DAC operations are similar. The way to proceed is described in the
DT3000 Series User’s Manual. Amongst the numerous setting for the
ADC or DAC subsystems, it is worth to underline the followings:
• Encoding : Binary data encoding or twos complement data en-
coding. The DT3004, makes use of the latter one.
• Channels: Input and output data go through a channel while
being processed in the board. These channels are directly acces-
sible for wiring on the board’s screw panel. The board supports
8 differential analogue input channels and 2 differential analogue
output channels (DAC0 and DAC1). The number of channels de-
sired is set in the program. We used 1 input channel for the data
stream coming from the photodiode, and 1(2) output channels
for 1(2) dimension scanning.
• Channel List Size and Channel List Entry: The flexible
DT3004’s environment allows the user to define the order and
the number of times he wants to process the different channels.
10
For example, to output two signals, the software processes alter-
natively the two output channels DAC0 and DAC1. The channel
list size is then 2 and the channel list entry is DAC0 first and
DAC1 second.
• Channel gain: For A/D operations, the board supports gains
of 1, 2, 4 and 8. The gain has been set to 1 for all experiments.
For D/A operations, only a gain of 1 is available.
• Clocks: The DT3000 Series boards provide two clock sources for
pacing analogue input operations in continuous mode: internal
and external. Output operations can only be done with an in-
ternal clock. Internal clock is the best choice for our needs (for
input and output).
• Triggers: The board supports two triggered scan modes: in-
ternally retriggered and externally retriggered. When the board
detects an trigger signal, the board scans the channel list once,
then waits for another internal retrigger signal.
• Buffering: Particular attention has to be paid for buffering as
it is an essential part for successful operations. First of all, the
wrapping mode has to be specified in the software. A single wrap
mode is used for the DAC. In this mode data is processed from
a single buffer continuously. This is particularly useful for gener-
ating repetitive analog output data. For the ADC, two wrapping
modes have been used. In the case when the ADC subsystem is
started by the software and acquires data continuously, the mul-
tiple wrapping mode is the most adapted. The data is written to
the allocated buffers continuously(the user can choose the number
of buffers allocated); when the buffers are filled, the board over-
writes the data starting at the beginning of the first buffer. This
mode offers a large amount of buffering. The situation is different
11
when we wish to control precisely the buffering as required in the
two last experiments. Here the size of the buffer is set by the
number of samples we wish to acquire between each triggering.
The software specifies the wrapping mode as disabled, so each
time the ADC has finished acquiring the desired number of sam-
ples (buffer full), the operation stops. The subsystem waits for
another trigger to restart the operation. This way, one can con-
trol the start of acquisitions (at the falling edge of the triggering
signal) and the time length δτ of the acquisition:
δτ =number of samples
sampling frequency(1)
3 Determination of the flexure stage specifications
3.1 Properties of the flexure stage
To move an optical fiber over a few microns precisely, the best solution
is to use a flexure stage driven by piezoelectric actuators. This is the
most accurate technology for nanopositioning. A flexure stage relies
on the elastic deformation of a solid material, so there is no friction
or stiction as in bearing design [2]. Actuators are the devices that
physically apply the force on the elastic material. The deformation of
this material then causes the movement of the stage. (see figure 32 for
illustration). In absence of friction, stiction and travel imperfections,
the actuator defines the resolution and repeatability of the device.
Piezoelectric actuators provide the highest resolution motion. They
expand and contract when a voltage is applied, hence applying a force
on the elastic material.
The MDT631 flexure stage from THORLABS has been used for all
the experiments. The stage itself is a small metal cube with a flat
2Picture from Melles Griot Tutorial ’Fundamentals of Positioning’, www.mellesgriot.com
12
Figure 3: Longitudinal flexure movement. The actuator is here a drive knob butmight be replaced by a piezoelectric actuator. A small arcuate movement adds to
the translation.
surface for mounting the optical part that needs to be moved. The
drives used in the MDT631 and most of the flexure stage are based on
PZT ceramics and offer nanometer resolution but only offer a 10-100
µm range. A single stage can also provide multiple axes of motion if
it is equipped with more than one flexure. Our device provides 3 axes
of motion.
Apart from their low distance of travel, another drawback of this
system is that the piezoelectric actuator exhibits some hysteresis (fig-
ure 43) and other non-linearities. In addition, the whole stage has a
non linear frequency response due to resonances arising in the elastic
materials and piezoelectric actuators.
3.2 Aims and principles
Due to the non linear effect described in the previous section, the
stage will not respond with a perfect sinusoidal movement if driven by
a sinusoidal signal. The aim of the first experiment is to determine the
displacement response of the flexure stage. This is done at different
frequencies in order to select the most adapted response that will be
used in the SNOM experiment.
3Picture from Melles Griot Tutorial ’Fundamentals of Positioning’, www.mellesgriot.com
13
Figure 4: Hysteresis effect on piezoelectric actuators.
3.3 Experimental setting
The experiment makes use of a Michelson interferometer to produce
a fringe pattern. The experimental setting is schematized figure 5.
One of the mirrors is mounted on the flexure stage and is moved
back and forth along the x axis. The other mirror is slightly tilted to
produced the fringe pattern. The beam, coming from a Helium-Neon
laser, is first divided by a splitter cube and travels along two different
paths before interfering in the observation area. A photodiode collects
the light in the interference area. The flexure stage is driven by the
Figure 5: Michelson interferometer with a mirror mounted on the flexure stage
14
control system developed earlier on. The DAC has been programmed
to output a sine signal driving the flexure stage back and forth along
a chosen direction. Meanwhile, the ADC acquires data coming from
the photodiode.
3.4 Results and analysis
3.4.1 Raw data
The light intensity distribution obtained for an acquisition with a
driving sinusoidal signal of 50Hz is plotted figure 6. It shows the
fringe pattern modulated by the flexure stage motion. The velocity of
the flexure stage is faster in the middle of its back and forth motion
(higher signal frequency) than in the edges. One can easily locate
the turning point where the motion’s direction is inverted. To know
quantitatively the actual displacement of the flexure stage, a deeper
analysis of the data is necessary.
0 2 4 6 8 10 12 14 16 18 207.5
8
8.5
9
9.5
10Raw data 50Hz 2V amplitude
time (ms)
sig
nal
am
plit
ud
e
Figure 6: Output from the photodetector
15
3.4.2 Theory
What sees the photodiode can be described with the electromagnetic
theory of light. The field at the detector is composed of the light
coming from the two beams. The length r1(t) of the path 1 is varying
in time since the mirror is moving.
E1 = U1 exp i(k1.r1(t)− ω t + φ1) (2)
E2 = U2 exp i(k2.r2 − ω t + φ2) (3)
The total field at the detector is:
Etot = E1 + E2 (4)
When looking at the intensity of the signal I, one can eliminate the
term −ω t as it cancels out. Furthermore, we can choose φ1 = 0 and
k2.r2 + φ2 = 0 since these terms are not time dependent.
I = Etot E∗tot (5)
I = [U1 exp i(k1.r1(t)) + U2] [U1 exp−i(k1.r1(t)) + U2] (6)
I = U21 + U2
2 + U1 U2 [exp i(k1.r1(t)) + exp−i(k1.r1(t))] (7)
I = U21 + U2
2 + 2 U1 U2 cos(k1.r1(t)) (8)
I = a + b cos(φ(t)) (9)
with
φ(t) = k1.r1(t) (10)
= k x(t) (11)
where x(t) is the displacement of the flexure stage along the x-direction.
A method used in holographic interferometry, the interference phase
measurement using the Fourier transform method, can be applied to
unravel the entangled signals [3, 4, 5]. The measured intensity distri-
16
bution i(t) may be written in the form:
i(t) = a(t) + b(t) cos[φ(t)] (12)
where a(t) describes the offset signal and b(t) the amplitude of the
signal (the time dependency for a and b comes from noise variations).
φ(t) is the interference phase to be determined from i(t). It is propor-
tional to the displacement x(t) of the flexure system:
x(t) =φ(t)
k=
2π φ(t)
λ(13)
where λ = 633 nm is the wavelength of the laser.
Equation 12, can be rewritten as:
i(t) = a(t) + c(t) + c∗(t) (14)
where
c(t) =1
2b(t) exp[j φ(t)] (15)
with j =√−1 and * denoting the complex conjugate. Next, Equation
14 is Fourier transformed, giving:
I(ν) = A(ν) + C(ν) + C∗(ν) (16)
Assuming that the background intensity is slowly varying compared
with the fringe spacing, the amplitude spectrum will be a trimodal
function with A broadening the zero peak and C and C* placed sym-
metrically to the origin. This is effectively the spectrum obtained after
having applied a FFT in Matlab to the acquired data (figure 7(b)).
Next, one of the two symmetrical parts, say C*, as well as the broad-
ened zero peak is filtered out. Figure 7(c) shows the filtered version
of the spectrum. This remaining spectrum is no longer symmetrical;
thus it does not belong to a real function in the spatial domain but
17
0 2 4 6 8 10 12 14 16 18 207.5
8
8.5
9
9.5
10Raw data
time (ms)
sig
nal
am
plit
ud
e
(a) Signal from the photodiode
−4 −3 −2 −1 0 1 2 3 4
x 104
0
1
2
3
4
5
6
7
8
9
10
x 105
frequency Hz
amp
litu
de
Frequency spectrum
(b) Fourier-transformed signal
−2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5
x 104
0
1
2
3
4
5
6x 10
5
frequency Hz
amp
litu
de
Filtered frequency spectrum
(c) Signal after filtering
0 2 4 6 8 10 12 14 16 18 20 −4
−3
−2
−1
0
1
2
3
4
time (ms)
ph
ase
(deg
rees
)Wrapped phase
(d) Wrapped phase
0 2 4 6 8 10 12 1.4 16 18 20−20
0
20
40
60
80
100
120
140
time (ms)
ph
ase
(deg
rees
)
Unwrapped phase without sign inversion
(e) Unwrapped phase without sign inversion
0 2 4 6 8 10 12 14 16 18 20−25
−20
−15
−10
−5
0
5
10
15
time (ms)
ph
ase
(deg
rees
)
Unwrapped phase after sign inversion
(f) Unwrapped phase after inversion
Figure 7: Phase analysis
18
yields nonzero imaginary parts after inverse transformation. By ap-
plying the inverse Fourier transform, c(t) is obtained. From c(t) the
interference phase is calculated point-wise by:
φ(t) = Im(log(c(t)) (17)
where Im denotes the imaginary part. At this stage the phase is still
wrapped and varies between -π and π (figure 7(d)).
The unwrapping of the phase (done by the Matlab function unwrap)
and the correction of the phase sign (which changes at every direction
turning point of the stage translation) lead to the final picture of the
interference phase (figure 7(f)).
Finally, equation 13 states that the phase is proportional to the
displacement of the flexure stage (see figure 8).
Figure 8: Displacement of the flexure stage
3.4.3 Displacement response
The phase analysis can be repeated at different frequencies and driving
voltages for the flexure stage. This allows to work out its frequency re-
sponse at a fixed voltage, in particular its resonance frequency. More-
over, by looking at the curves obtained, one can select a frequency
where the nonlinearity of the stage is minimal. This frequency will
19
then be use to drive the stage in the SNOM setting.
A set of measures have been carried between 30 and 250 Hz with
1V amplitude. For each frequency the maximum displacement have
been measured and the result is plotted figure 9. It shows a sharp
resonant peak just before 180 Hz, a slow increase from 30 to 100Hz
and a steep decline after the resonance. These values correspond to the
50 100 150 200 2500
5
10
15
20
25
30
35frequency response
frequency Hz
dis
pla
cem
ent
mm
Figure 9: Frequency response curve of the flexure stage
amplitude of the displacement curve obtained after a phase analysis.
Around the resonance peak (180Hz) it becomes difficult to use the
phase analysis method to determine a displacement as the signal is
highly distorted and oscillates too rapidly for the sampling rate to
keep up (the oscillations can be seen but the resolution is poor). An
evaluation of the displacement can be made by counting the number
of fringes that the fiber sees on its travel.
A wide range of range of frequencies and voltages have been experi-
mented (figure 10) in order to work out the best setting for the SNOM
experiment. For reasons explained in section 4.4, we wish a response
signal exhibiting the most linear rising slope possible. It turned out
that higher frequencies exhibits a straighter slope. Nevertheless it is
20
better to stay away from the resonance frequency as severe distortions
impair the quality of the response. 100Hz/5V is a satisfying setting.
0 50 100 150−4
−2
0
2
4
6
8
10
12
14x 10
−6 Displacement 30Hz 7V
time (ms)
dis
pla
cem
ent
(m)
time (ms)d
isp
lace
men
t (m
)
Displacement 60Hz 4V
0 10 20 30 40 50 60−2
0
2
4
6
8
10x 10
−6
0 05 10 15 20 25 30 35 40 45 50 −2
0
2
4
6
8
10
12x 10
−6
time (ms)
dis
pla
cem
ent
(m)
Displacement 80Hz 4V
0 5 10 15 20 25 30 −3
−2
−1
0
1
2
3
4x 10
−6
time
dis
pla
cem
ent
(m)
Displacement 140Hz 1V
0 5 10 15 20 25 30 35−2
−1
0
1
2
3
4
5
6x 10
−6 Displacement 120Hz 1V
time (ms)
dis
pla
cem
ent
(m)
Figure 10: Displacements at different frequencies and voltages
21
3.4.4 Distortions
Setting into motion
Distortion of the signal, due to the setting into motion of the flexure
stage, have been observed at the beginning of some acquisitions. At
the very beginning the signal is heavily distorted and meaningless
(see figure 11(a)). A bit further, a meaningful signal emerges but it is
not totally repeatable between periods (e.g. the turning points occur
at different amplitude values) (see figure 11(b)). This situation only
occurs when the ADC is set to start at the same time as the DAC
(both triggered by software). Because this distortion disappears after
a short while as the signal stabilizes, this effect is not observed if the
stage is driven by a function generator started before the acquisition
or if the ADC is triggered externally after the DAC. In both situations,
the stage has already been set into motion when the acquisition starts,
hence the flexure stage response has had the time to stabilize.
800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800
7.5
8
8.5
9
9.5
Raw signal 120Hz
time
sig
nal
am
plit
ud
e
(a) Signal right after the start of the DAC
1100 1102 1104 1106 1108 1110 1112 1114 1116 1118 1120
7.5
8
8.5
9
9.5
10
Raw signal 60Hz
time (ms)
sig
nal
am
plit
ud
e
(b) Signal almost stabilized
Figure 11: Distortion of the signal as the flexure stage is set into motion
Offset variation
As we get closer to the resonance frequency, the offset of the signal is
increasingly modulated by the deformation of the flexure stage. Close
to the resonance, non-linear displacements such as the arcuate move-
22
ment (figure 4) are exacerbated. As a consequence, the beam reflected
from the moving mirror is slightly deviated, shifting the position of
the fringe area. This leads to a variation of the signal offset. This
is illustrated figure 3.4.4. This variation reaches its maximum at the
resonant frequency (it is even saturating the photodiode). This ef-
fect becomes significant above 100Hz and until 200Hz. It alters the
brightness of the fringes but not their width.
0 200 400 600 800 1000 12007
7.5
8
8.5
9
9.5
10
Raw signal 160Hz
time
sig
nal
am
plit
ud
e
0 100 200 300 400 500 600 700 800 900 10006
6.5
7
7.5
8
8.5
9
9.5
10Raw signal 180Hz
time
sig
nal
am
plit
ud
e
Figure 12: Offset variation
3.4.5 Phase shift
The last experiment with the Michelson interferometer aims at de-
termining the phase shift between the driving signal and the flexure
stage. One can expect a time delay between the driving signal and the
stage response. The experiment looks at the frequency dependence of
this phase shift.
To compare the two signals, the output of the DAC is sent into a
second ADC channel. Through the software the board can be set to
acquire alternatively two ADC channels. On the screw panel, one is
wired to the photodiode output as previously and the other directly
to the DAC output (also accessible from the screw panel). The inter-
23
leaved signals are then disentangled with a Matlab program and plot
and the same figure for a phase shift analysis. The results for different
frequencies and voltages are plotted figure 13.
The phase shift increases with frequency until the resonance fre-
quency where it undergoes an inversion. We can derive for each phase
shift, a time shift between the driving signal and the flexure stage
response (which might be useful for triggering considerations).
The time shifts are the following:
Frequency(Hz) Time delay(ms)
30 0.10
50 0.13
100 0.20
130 0.21
160 0.24
170 0.28
180 -0.07
3.5 Conclusion
The Michelson experiment allowed us to determine some important
specifications of the flexure stage and a range of frequencies suitable
for the SNOM’s experiment. Furthermore the control system has been
proven successful to drive and monitor the experiment. In the follow-
ing part, the control system will be upgrade to a 2D scanning.
4 Simulation experiment
4.1 General purpose
The last preliminary step before mounting the SNOM is to develop
and test the control system as it will be used with the SNOM. The
24
200 400 600 800 1000 1200 1400 1600
−1
−0.5
0
0.5
1
DAC and photodiode output 50Hz
time
sig
nal
am
plit
ud
e
500 600 700 800 900 1000
−1
−0.5
0
0.5
1
DAC and photodiode output 100Hz
time
sig
nal
am
plit
ud
e
1200 1300 1400 1500 1600 1700 1800 1900
−1
−0.5
0
0.5
1
1.5DAC and photodiode output 130 Hz
time
sig
nal
am
plit
ud
e
100 200 300 400 500 600
−1
−0.5
0
0.5
1
DAC and photodiode output 160Hz
time
sig
nal
am
plit
ud
e
700 750 800 850 900 950 1000
−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
DAC and photodiode output 170Hz
time
sig
nal
am
plit
ud
e
600 650 700 750 800 850
−1.5
−1
−0.5
0
0.5
1
1.5
DAC and photodiode output 180Hz
time
sig
nal
am
plit
ud
e
Figure 13: Phase shift between the driving signal (blue) (replicated to underlinethe shift) and the flexure stage response (red). The phase shift increases with
frequency and undergoes an inversion at the resonance
25
goal is to achieve a 2 dimensional scanning, while doing an appropriate
acquisition. The experimental setting emulates the conditions for the
control system has it will be in the last experiment.
4.2 Principles
The flexure stage provides 3 axes of motion. The first experiment was
designed to move the stage along one axis. In order to be able to scan
over a 2 dimensional area, the second experiment adds the vertical
dimension (z-axis) to the movement.
To replicate the conditions that will be used for the SNOM experi-
ment, one have to look at how we intend to move the fiber in the fringes
area. The fiber will scan back an forth at a rapid pace along the y
direction while moving slowly up and down along the z-direction. The
resulting scanning (illustrated figure 16) covers the area of interest.
To implement such a control system, two signals have to be gener-
ated from the board and sent to the driver of the flexure stage. The
signal for the y-axis drive is a sinusoidal wave as the one used in the
first experiment. For the z-axis, a slow frequency triangle signal is
generated.
One can wonder why the same type of signal is not used for both
directions and why the high frequency movement along y is not driven
by a triangle wave. Ideally, a triangle wave would generate a linear
displacement of the flexure stage, making life easier to analyse the
fringe pattern. The situation is actually inverted. The frequency
spectrum of a triangular wave is composed of several frequency peaks
which might correspond to the different resonance frequencies of the
flexure stage (there is a certain number of resonance beyond the first at
180Hz). The resulting displacement would suffer more non-linearities
than if the stage was driven by a sinusoidal wave, which has only one
Fourier frequency. Thus, a sinusoidal wave avoids to have complicated
26
cross-interactions between the driving signal and the stage response.
Instead of moving a photoreceptor over a surface to collect light, the
experiment was set up so that the light source follows the same path as
the photoreceptor would have done. By relativity of the movements,
both situations are equivalent. The moving light source is generated
by an oscilloscope set in mode XY which input are the two signals
from the DAC. Whereas for the SNOM device the two signal would
position the flexure stage in space, in this experiment they position
the spot of light on the oscilloscope’s screen.
4.3 Experimental setting
Figure 14: Experimental setting
A photoreceptor is placed in front of the oscilloscope screen. An
opaque mask with a cut-out is placed between them. As the light
spot is moving over the screen and comes across the cut-out slit, the
photodiode detects the light passing through the hole. The purpose
of the hole is to create a recognisable pattern of light. Eventually,
27
we want to reconstruct an image of the screen showing the pattern
of light. This image would match with what a moving photoreceptor
would see when scanning over such a pattern of light.
4.4 Triggering and acquisition
To reconstruct the image, we need to know where the spot of light is
when the data are acquired. This requires a synchronization of the
acquisition with the position of the spot. In other words, ADC and
DAC must be synchronized.
One possible solution consists in starting the two subsystems (DAC
and ADC) simultaneously (by the software or an external signal) and
carry out the acquisition at exactly the same rate for both of them
(fDAC = fADC). This required to be sure that the subsystems start at
exactly the same time and run with equal frequency without a drift.
These conditions remain uncertain.
A better solution consists in using repetitive trigger signals to start
acquisition in the ADC. The idea is to trigger the ADC acquisition
at the start of the sine rising slope of sinusoidal driving signal (i.e.
at the beginning of the line) and end it before the sine peak (i.e.
before the end of the line) (illustrated on figure 16). By this way the
ADC acquisition is coupled to one of the DAC output and it becomes
possible to fully controlled the synchronisation between output and
input.
The TTL-like trigger signal is generated with a comparator cir-
cuitry (see figure 15). The amplitude of the sine signal is compared to
a voltage set by a potentiometer. Whenever this voltage amplitude is
above the sine amplitude, the output signal is set to +15V, otherwise
it falls to -15V. As a consequence, the TTL-like signal has the same
frequency as the sine wave and the falling edge occurs when the sine
amplitude exceeds the threshold value. In the software, the ADC is
28
set to start with an external trigger on the falling edge.
Figure 15: Triggering system
Acquiring data only during the rising slope implies that only one
horizontal line over two is actually sampled and always in the same
direction. However, considering the high frequency of the sine wave
relatively to the vertical movement, it give a satisfying resolution for
the picture. In addition, when the vertical scanning occurs in the
other direction, the other set of lines is sampled. By interleaving the
two acquisition on the final picture, one can increase the resolution by
a factor 2.
Figure 16 described how the scanning and acquisition are done. The
scanning path is the result of the simultaneous driving by a triangle
wave in the Z direction and a sine wave in the Y direction. The
sampling is illustrated by the red dots. Ideally the acquisition time
slot must fit in the linear part of the slope to avoid a distorted image.
In the figure 16 the buffer length is 6 for the sake of the argument.
In the actual experiment it would be a few hundreds (up to 512).
The number of lines and columns would be a few hundreds as well
(typically 500x500). The z-scale is overstretched for the clarity.
29
Figure 16: Control and acquisition system for 2D scanning
30
4.5 Program modifications
A series of modifications has been added to the program running the
board to meet the demands of the experiment. It includes:
• Two channels have been set on the DAC. One channel (DAC0)
outputs the triangle wave, and the other (DAC1) outputs the sine
wave. The frequency of each channel is half the frequency of the
DAC clock.
• A specific buffering has been set for the ADC. As said before,
between each triggering signal, we wish to fill up one buffer which
size fits in the rising slope of the sinusoidal signal. In order to
do so, the first approach has been to set up the board without a
wrapping mode and let the user define the length of the buffer. It
turned out that, set in this mode the board cannot be retriggered
repeatedly. Data is written to the allocated buffer until no more
space is available. At this point the operation and the subsystem
stop. Once the subsystem have been stopped, no more operations
are possible. Hence, the repetitive triggering signal has no effect
on the subsystem. Any wrapping mode (single or multiple) is also
unsuitable because data are written continuously. The subsystem
starts on the first triggering signal and then ignores the followings.
The only solution is to set up a channel list operating on one
channel. The DT3004 allows to define a channel list size up to
512 entries. The number of entries corresponds to the number of
samples we want to acquire between two triggers. All the entries
are then set to be processed in the same channel. The wrapping
mode is disabled and a series of buffers are set up to provide
enough space to store the input data. When the subsystem is
started it scan over the entry list sending the data through the
same channel. When it come to the end of the entry list, the
31
acquisition is stopped. Nevertheless, the subsystem stays ready
to resume acquisition on the next falling edge.
Besides, the program has been added additional features to al-
low the user to set up parameters easily through a window interface.
Therefore, before each experiment, one can choose the number of de-
sired samples, the sampling frequency of the ADC and DAC, the am-
plitude and frequency of the DAC’s output signals.
4.6 Method of analysis
The data obtained from the experiment are stored in a computer
file. This raw data need to be processed in order to reconstruct a
2-dimensional image. This is done by a Matlab program. The data
are sent from the board in binary format since it allows a faster trans-
fer. In addition to the data from the ADC, the board’s software is
designed to send additional information, such as the number of lines
in an image frame, the number of samples for each acquisition and the
corresponding number of line and frame in the scanning.
Figure 17 describes how the Matlab program handles the data to
build an image. The stream of data sent by the board has the follow-
ing structure : the data are divided into packets coding for the values
acquired between two triggers. Each packets has a header which in-
cludes the number of samples in a packet, its frame number and its
line number. These bits of information are generated in the board’s
software during the acquisition.
4.7 Results
Using the procedure described above, the program organizes the data
to form the image. The reconstructed picture is shown figure 18.
It shows a well-reconstructed bright slit matching the cut-out in the
32
Figure 17: The sampled data are stored as a stream of binary bits. The Matlabprogram identifies the packets corresponding to the lines and reconstructs the
frame
mask.
Figure 18: Image obtained from the simulation
By changing the trigger level, the bright slit is shifted right or left.
Besides, different parameters set in the board, such the number of lines
and samples, the ADC and DAC sampling rate, have an influence on
the image displayed. Different set of parameters have been tried to
ensure the relevance and the reliability of the data processing.
33
4.8 Conclusion
The control system is now completed. The driving system was proved
successful to handle a 2-dimensional scanning, while the acquisition
system has the features required for a fully controlled sampling. The
tools are ready to move on the last experiment, the SNOM itself.
5 SNOM
5.1 Aims and principles
The last part deals with the building of a scanning near-field opti-
cal microscope. So far the tools to drive the system and to analyse
the data have been developed. Now we face the following technical
challenges:
• create an interference area for the fiber to scan
• mount a fiber on the flexure stage to look at the interference area
• collect the light at the other end of the fiber
Since the observation scale of the SNOM ranges over only a few
micrometers, dimensioning, positioning and adjusting of the system
become critical. The final goal is to get images of a fringe pattern.
Knowing the specifications of the flexure stage displacement, one can
then work out the distance between fringes.
5.2 Experimental setting
The experimental setting is described figure 19.
The light source is a laser Helium-Neon emitting at 633 nm (red)
with 4 mW output. The laser beam is divided through a splitter cube
(25 mm x 25 mm) (figure 20). If the splitter is correctly positioned,
34
Figure 19: SNOM setting
two parallel beams come out. A lens will then focus the two beams
at the focal point. The interference area occurs where the two beams
overlap, roughly at the focal length from the lens.
Figure 20: Division of the beam in the splitter cube
The fiber has been purchased from Fibercore. The design wave-
length ranges from 633 nm to 688 nm. The attenuation is 11dB/km.
The numerical aperture (N.A.) is 0.16. The fiber end is stripped (coat-
ing removed) and cleaved (the end face tip is cut by a specific cleaver)
before being loaded into a fiber chuck. The fiber chuck secures the
fiber in place with a spring clip. The fiber is side-loaded into the
chuck preventing the end face of the fiber from being damaged. Once
loaded with the fiber, the fiber chuck is inserted into a mounting block
which can be bolted down on the top of the flexure stage. The mount-
ing block is equipped with a chuck rotator designed to hold and rotate
35
a fiber chuck through 360 degrees. The figure 21 depicts the final stage
device.
Figure 21: The fiber mounted on the flexure stage follows the motion
5.2.1 Dimensioning requirements
In order to be able to see fringes and get the most out of the light
signal, a list of dimensioning considerations have to be considered. It
includes:
1. There must be enough fringes over the scanning range of the fiber
tip (the more the better).
2. The interference area must be larger than the scanning span,
while staying relatively small to concentrate energy on few fringes
(to maximize the contrast).
3. The angle at which the two beam interfere must roughly fit into
the acceptance cone of the optical fiber (specified by the numerical
aperture) to optimize the coupling of the light into the fiber.
The following considerations give indications for relevant dimen-
sioning.
36
1. At 100Hz/8V the fiber would cover a distance of 15 µm. The
fringes’ width δ (see figure 22) is roughly given by:
δ ≈ λ
sin(θ)(18)
where λ is fixed by the laser wavelength λ = 633 nm; θ is the
angle between the two focused beams (figure 22). θ depends on
the distance d between the two parallel beams after the splitter
and the focal length f of the lens:
θ = 2 arctan
(d
2 f
)(19)
Figure 22: The two beams interfere to produce fringes
2. Laser beam can be described as Gaussian beam. This involved
that the two beams have a finite width in the focal region of the
lens where they interfere (figure 23).
A collimated gaussian beam of radius r, traversing a lens of focal
f, will be focused at a distance f, where the size of the minimum
beam waist ω0, is given by:
ω20 =
r2
1 +(
π r2
4 λ f
)2 (20)
37
Figure 23: The focal point where the two Gaussian beams intersect has a finitewidth ω0
It is sensible to assume that the interference area will be roughly
the size of ω0.
3. The fiber has a numerical aperture of 0.16 = sin(θc). The corre-
sponding critical angle is θc = 0.16 rad = 9.2 degrees. If θ > θc
the coupling efficiency of the light into the fiber will be reduced.
f and d are the two parameters easily adjustable on the experimental
setting. The best compromise between the dimensioning requirements
leads to d = 1.4 cm and f = 3 cm. For these parameters we get:
• δ ≈ 1.5 µm. It allows to have roughly 10 fringes in the scanning
range.
• ω0 ≈ 80 µm. This is large enough to encompass the scanning
range while not being overstretched.
• θ ≈ 0.45 rad ≈ 26 degrees.
It would be better to have tighter fringes, but this comes at the cost
of a larger angle θ which is already beyond θc. A significant fraction
of the power is lost because we exceed the critical angle. Nevertheless
38
the SNR (Signal To Noise Ratio) remains satisfactory justifying the
tradeoff with the number of fringes.
5.2.2 Positioning of the flexure stage
Coupling efficiently the laser beam into the optical single mode fiber
is crucial to obtain a good SNR at the photodiode. It requires an
optimal position and angle for the incoming beam. To launch the
light successfully into the fiber, the stage must be accurately aligned
to the incoming, collimated laser beam. Any angular errors severely
reduce the maximum coupling efficiency that can be obtained.
To achieve the best SNR at the photodiode, the following adjust-
ments have been made:
• Adjust the Z-planarity and centering of the laser beam once it is
mounted on the fixed platform.
• Adjust the Z-planarity and centering of the beam after it has
gone through the cube splitter.
• Adjust the Z-planarity and centering of the beam after it has
gone through the lens.
• Align the flexure stage to the optical axis of the lens where the
two beam cross each other.
• Tweak the stage with the help of the oscilloscope to get an opti-
mum signal. Try to get an evenly distributed signal between the
two beams. When correctly placed, bolt down the stage.
• Drive the flexure stage and check if fringes with a good SNR
appear. Tweak the stage with the thumbscrews if necessary. (The
stage provides 3mm of fine manual displacement along the three
axes).
39
5.3 Results
The first set of images shows a clear fringe pattern (figure 24 and 25
) with a satisfying contrast. Nevertheless the fringes width are not
even because we are sampling the signal during a change of direction
when the stage moves slower. Bearing in mind that we want to start
the acquisition at the beginning of the linear part of the rising slope,
the trigger level needs to be adjust to do so. At a fixed driving
Figure 24: Image of the interference area acquired at 100Hz/8V
frequency, the velocity of the flexure stage is set by the applied voltage.
The scanning is faster on figure 24 (100Hz/8V) than on figure 25
(100Hz/4V), so more fringes can be seen. Moving the trigger level
will shift the start of the acquisition relatively to the flexure stage’s
position. Figure 26 illustrates this shift and also shows the edges of
the interference area as the fringe contrast gets weaker on the top of
the image.
In section 3.4.4, a phase shift between the signal and the actual
motion has been observed and quantified. This shift has to be taken
into account when adjusting the triggering level. To monitor when the
trigger level occurs in relation to the stage motion, the TTL signal can
40
Figure 25: Image of the interference area acquired at 100Hz/5V
Figure 26: Shift of the acquisition by changing the trigger level (100Hz/5V)
41
be recorded on a supplementary ADC channel. The number of samples
then determines the length of the sampling and can be adjusted to get
a symmetric acquisition.
The pictures have been acquired with at 100Hz with 8V peak-to-
peak voltage. During the acquisition slot (fitting in the linear part
of the sinusoidal driving signal) the stage has a constant velocity of
13 mm.s−1. Since the time scale on the sampled image is known,
one has just to multiply the time by the velocity to get the actual
distance between fringes. An acquisition done in the right time slot
and displaying a distance scale is depicted figure 27. The distance
between fringes (δ ∼ 2 µm) is coherent with the rough calculation
done in section 5.2.1 (δ ∼ 1.5 µm).
Figure 27: The x-axis shows the distance travelled by the flexure stage along the ydirection (in µm). The spacing between fringes is roughly 2 µm.
6 Conclusion
To conclude, the project has achieved its goals including understand-
ing the principles underlying scanning optical microscopy. At the same
time, the successful development of a complex control system has pro-
42
vided an insight into digital/analogue data processing concepts. The
possibilities of the acquisition board have also been successfully ex-
ploited to meet the needs of the experiments while important spec-
ifications of the flexure stage had been determined. Finally, in the
final experiment, all the previous developments have been combined
together to build a simple and working SNOM which gives images
of an interference area showing a set of fringes. Overall, the project
has been purposeful in helping people develop skills in problem solv-
ing, acquisition of concepts and gaining knowledge in experimental
know-how.
43
References
[1] V. Deckert A. Rasmussen. New dimension in nano-imaging: break-
ing through the diffraction limit with scanning near-field optical
microscopy. Anal Bioanal Chem, pages 165–172, 2005.
[2] S. Rick. Getting in position. SPIE’s oemagazine, 2004.
[3] T. Kreis. Digital holographic interference-phase measurement us-
ing the fourier-transform method. J. Opt. Soc. Am A, 3(6):847–
855, 1986.
[4] Y. Skarlatos C. Karaaliog. Fourier transform method for measure-
ment of thin film thickness by speckle interferometry. Opt. Eng.,
42(6):16941698, 2003.
[5] C Gorecki. Interferogram analysis using a fourier transform method
for automatic 3d surface measurement. Pure Appl. Opt., 1:103–110,
1992.
44
