SCANNING NEAR-FIELD OPTICAL MICROSCOPY R. Delville June 17, 2005
Imperial College London, Photonics Group Peter T¨ or¨ ok’s research group Supervisor: Dr Edward Grace
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THANKS
Many thanks to Peter T¨or¨ok 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.
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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 piezoelectric transducers that move the optical fiber while simultaneously sampling the detected signal. Key words: acquisition board, DAC, ADC, sampling, buffers, piezoelectric transducers, optical fiber, photoreceptor, interferometer, fringes, interference.
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Contents 1 General overview
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1.1
SNOM . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1.2
Goals of the project . . . . . . . . . . . . . . . . . . . .
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2 Control System 2.1
2.2
Materials
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. . . . . . . . . . . . . . . . . . . . . . . . .
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2.1.1
Output operations . . . . . . . . . . . . . . . .
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2.1.2
Input operations . . . . . . . . . . . . . . . . .
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Programming . . . . . . . . . . . . . . . . . . . . . . .
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2.2.1
Objectives . . . . . . . . . . . . . . . . . . . . .
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2.2.2
Program features . . . . . . . . . . . . . . . . .
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3 Determination of the flexure stage specifications
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3.1
Properties of the flexure stage . . . . . . . . . . . . . .
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3.2
Aims and principles . . . . . . . . . . . . . . . . . . . .
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3.3
Experimental setting . . . . . . . . . . . . . . . . . . .
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3.4
Results and analysis . . . . . . . . . . . . . . . . . . .
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3.4.1
Raw data . . . . . . . . . . . . . . . . . . . . .
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3.4.2
Theory . . . . . . . . . . . . . . . . . . . . . . .
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3.4.3
Displacement response . . . . . . . . . . . . . .
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3.4.4
Distortions
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3.4.5
Phase shift
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Conclusion . . . . . . . . . . . . . . . . . . . . . . . . .
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3.5
4 Simulation experiment
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4.1
General purpose . . . . . . . . . . . . . . . . . . . . . .
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4.2
Principles . . . . . . . . . . . . . . . . . . . . . . . . .
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4.3
Experimental setting . . . . . . . . . . . . . . . . . . .
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4.4
Triggering and acquisition . . . . . . . . . . . . . . . .
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4.5
Program modifications . . . . . . . . . . . . . . . . . .
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Method of analysis . . . . . . . . . . . . . . . . . . . .
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4.7
Results . . . . . . . . . . . . . . . . . . . . . . . . . . .
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4.8
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . .
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5 SNOM
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5.1
Aims and principles . . . . . . . . . . . . . . . . . . . .
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5.2
Experimental setting . . . . . . . . . . . . . . . . . . .
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5.2.1
Dimensioning requirements . . . . . . . . . . . .
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5.2.2
Positioning of the flexure stage . . . . . . . . .
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Results . . . . . . . . . . . . . . . . . . . . . . . . . . .
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5.3
6 Conclusion
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General overview
1.1
SNOM
Scanning near-field optical microscopy opened a new era in optical microscopy, bringing the spatial resolution at the 50-100 nm level using visible or near infrared light. This resolution is well below the diffraction 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 dimensions 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 nm (b) AFM scan of 30 nm gold balls gold balls
Figure 2: AFM techniques can be applied to SNOM imaging
The SNOM has applications in fields such as surface chemistry, biology, 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 control system driving the flexure stage while simultaneously sampling the detected signal. This task is carried out by an acquisition board 1
Pictures from www.nanonics.co.il
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capable of managing simultaneous ADC and DAC operations. Designing the driving program has been the first step towards making the SNOM. The second step is built on the control system to measure the specifications of the flexure stage. It makes use of a Michelson interferometer 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 2.1
Control System 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 example 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 Translation 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.
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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 2.2.1
Programming 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 features. • 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 encoding. 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 accessible 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 desired 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 alternatively 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 internal clock. Internal clock is the best choice for our needs (for input and output). • Triggers: The board supports two triggered scan modes: internally 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 generating 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 multiple 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 overwrites 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 samples (buffer full), the operation stops. The subsystem waits for another trigger to restart the operation. This way, one can control the start of acquisitions (at the falling edge of the triggering signal) and the time length δτ of the acquisition: δτ =
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number of samples sampling f requency
(1)
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 2
Picture from Melles Griot Tutorial ’Fundamentals of Positioning’, www.mellesgriot.com
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Figure 3: Longitudinal flexure movement. The actuator is here a drive knob but might 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 (figure 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. 3
Picture from Melles Griot Tutorial ’Fundamentals of Positioning’, www.mellesgriot.com
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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
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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 3.4.1
Results and analysis 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. Raw data
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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 )
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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 = U12 + U22 + U1 U2 [exp i(k1 .r1 (t)) + exp −i(k1 .r1 (t))]
(7)
I = U12 + U22 + 2 U1 U2 cos(k1 .r1 (t))
(8)
I = a + b cos(φ(t))
(9)
with φ(t) = k1 .r1 (t) = k x(t)
(10) (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 distri16
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 proportional to the displacement x(t) of the flexure system: x(t) =
φ(t) 2π φ(t) = k 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
1 b(t) exp[j φ(t)] (15) 2 √ with j = −1 and * denoting the complex conjugate. Next, Equation c(t) =
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 symmetrically 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 broadened 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
Frequency spectrum
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Figure 7: Phase analysis
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yields nonzero imaginary parts after inverse transformation. By applying 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 response at a fixed voltage, in particular its resonance frequency. Moreover, 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 frequency response 35
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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 experimented (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. Displacement 30Hz 7V
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Figure 10: Displacements at different frequencies and voltages
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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. Raw signal 60Hz
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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 move22
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 effect becomes significant above 100Hz and until 200Hz. It alters the brightness of the fringes but not their width. Raw signal 160Hz
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Figure 12: Offset variation
3.4.5
Phase shift
The last experiment with the Michelson interferometer aims at determining 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 inter23
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 frequency 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)
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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 following part, the control system will be upgrade to a 2D scanning.
4 4.1
Simulation experiment 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
DAC and photodiode output 100Hz
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Figure 13: Phase shift between the driving signal (blue) (replicated to underline the shift) and the flexure stage response (red). The phase shift increases with frequency and undergoes an inversion at the resonance
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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 experiment, 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 generated 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 circuitry (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.
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Figure 16: Control and acquisition system for 2D scanning
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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 allow the user to set up parameters easily through a window interface. Therefore, before each experiment, one can choose the number of desired samples, the sampling frequency of the ADC and DAC, the amplitude 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 transfer. 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 following structure : the data are divided into packets coding for the values acquired between two triggers. Each packets has a header which includes 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 Matlab program 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 optical 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 wavelength 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 (coating 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 mounting 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 dimensioning.
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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: µ
d θ = 2 arctan 2f
¶ (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: ω02
r2 ³
= 1+ 37
π r2 4 λ f
´2
(20)
Figure 23: The focal point where the two Gaussian beams intersect has a finite width 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 corresponding 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 adjustments 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 optimum 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)
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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-topeak 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 y direction (in µm). The spacing between fringes is roughly 2 µm.
6
Conclusion
To conclude, the project has achieved its goals including understanding the principles underlying scanning optical microscopy. At the same time, the successful development of a complex control system has pro42
vided an insight into digital/analogue data processing concepts. The possibilities of the acquisition board have also been successfully exploited to meet the needs of the experiments while important specifications 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 solving, acquisition of concepts and gaining knowledge in experimental know-how.
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References [1] V. Deckert A. Rasmussen. New dimension in nano-imaging: breaking 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 using the fourier-transform method. J. Opt. Soc. Am A, 3(6):847– 855, 1986. [4] Y. Skarlatos C. Karaaliog. Fourier transform method for measurement 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.
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