Enhancing the molecular sensitivity using compressed...
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Nearfield IR Spectroscopy:
Enhancing the molecular sensitivity using compressed sensing and other techniques
B. Kästner, P. Hermann, A. Hornemann, G. Ulrich, A. Hoehl,
C. Elster, G. Wübbeler, F. Schmähling
Funded by
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PTB:
• National Metrology Institute (NMI)
• Federal Ministry of Economics and Technology (BMWi)
• 170 Mio. € budget, plus external funding
• Approx. 1300 permanent staff and 550 non-permanent staff including 110 PhD students
• 600 scientific papers per year
Metrology:
• Science and application of correct
measurement
• Traceability of results to the SI through
national standards
• Determination of results with verification of uncertainty
Hermann von Helmholtz
Physikalisch-Technische Bundesanstalt
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Berlin-Adlershof
Adlershofer PTB Labs
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L. Novotny, S. J. Stranick; Annu. Rev. Phys. Chem. 2006
PTB laboratory at BESSY II
Metrology Light Source (MLS)
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IR Spectrometry Group - Activities
Understand interactions of drug with cell membrane
Where? Nanometer scale resolution - nearfield !
→Metrology: quantify/localize drugs in membranes & bacterial cells
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IR Spectrometry Group - Activities
Measurement requirements, example:
Antibiotic: Triclosan Escherichia coli
Required sensitivity: 20 molecules in 50 nm voxel
State of the art : Dj = 0.25° , tint 500 s (see below, NeaSNOM 2018)
→ 500 molecules (derived from PTB measurements on triclosan)
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Enhancing the sensitivity
o Nearfield IR Spectroscopy using s-SNOM
o Compressed Sensing
o Radiation Sources and Detection
o Tailored AFM Probes
o Conclusion
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Nearfield IR Spectroscopy: s-SNOM
Combination of
IR Spectroscopy and Atomic Force Microscopy
B. Kästner et al. ACS Omega 2018
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s-SNOM Principle
IR Radiation incidenton metal cone (antenna)
Focus << l
A. Huber et al. Nano Lett. 2008
Detection of radiation scatteredfrom antenna as dressed dipole
→ scattering-type SNOM
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Background suppression
o Strong field between tip and
substrate (of high refractive index)
o Field enhancement depending exponentially on the distance
o In tapping mode: periodic emission with higher harmonics
o Background suppression: higher harmonic demodulation
Detection voltage signal nU
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Nearfield Spectroscopy
FTn nU U=
nU
P. Hermann et al., Optics Express 2014
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Scattered Signal: Interpretation
→Absorption in grazing incidence, see Mastel et al. Appl. Phys. Lett. 2015
Wavenumber
Abs nU
Arg nU
Arg nU
Interpretation:
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Reflectivity R forweak oscillator (organics):
For strong oscillator (e.g. SiC):
Scattered Signal: Interpretation
Abs nU Interpretation:
R
Abs nU
R
Abs nU
Measuring Absorption and Reflectivity in one measurement
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Enhancing the sensitivity
o Nearfield IR Spectroscopy using s-SNOM
o Compressed sensing
o Radiation sources and detection
o Tailored tips
o Conclusion In collaboration withM. Raschke
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What is Compressed Sensing
Without Compressed Sensing -> compresses only the data
y Compression Storage/Transmission
Decompression y
Measurement
Example: digital imaging / JPEG
• DCT of Image y
• Only largest k components are stored
• Decompression before viewing
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m Measurements and matrix A (m x n, n>>m)
What is Compressed Sensing
Requirement for Reconstruction:
y must be sparse in a suitable basis, i.e.:
𝑦 𝑡1 ,… , 𝑦(𝑡𝑚)
𝜙1 𝑡 ,𝜙2 𝑡 ,…
𝑦 𝑡 =
𝑖=1
𝐾
൯𝑧𝑖 𝜙𝜋 𝑖 (𝑡
Compressed Sensing -> Measurement itself is compressed
y Compressed Measurement Storage/Transmission
Reconstruction y
min𝑧
||z||0 𝑦 = 𝐴𝑧under
with 𝐴𝑖𝑗=𝜙𝜋𝑗𝑡𝑖 , 𝑖 = 1,… ,𝑚 , 𝑗 = 1,… , 𝑛
Principle:
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Compressed Sensing -Example
Application to a 2D map of SNOM spectra:
44 x 41 = 1804 spectra
How many interferometer samples:
Spectral range
Resolution
→ Sweep interferogram over
x = 1600 mm at 1024 samples
Datapoints: 1804 x 1024 1.8 x 106
with typical integration time of 10 ms→more than 5 hours
16 cm −D =
13200 cm −
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Compressed Sensing - Example
Sample:
6H-SiC with Graphene
Indent to generate
2D strain:
Strain induced
spectral shift
B. Kaestner, F. Schmähling, A. Hornemann, G. Ulrich, A. Hoehl, M. Kruskopf, K. Pierz, M. B. Raschke, G. Wübbeler, C. Elster, Optics Express 2018
1 in cm −
3Abs U
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Compressed Sensing - Example
Complete sampling ofn = 1024 points
Simulate a compressed measurement:
2U
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Compressed Sensing - Example
Random sub-sampling ofm = 114 points at xi
n = 1024
→ Only use 1/9th of measurement samples
2U
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Compressed Sensing - Example
Reconstruction of
complete interferogram:
( )2 1 2( ),..., ( )T
my U x U x=
A
- the vector of weightsz
( )ij j iA x=- matrix Solve optimization problem:
0min z z
y Az=subject toFourier basis function(in this case)
0z number of nonzero elements of z
2U
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Result of reconstruction
Compressed Sensing - Example
Measured
Sub-sampled
Reconstructed
Fourier Transform
2U
2Abs U 2Arg U
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➢Out of 1024 basis functions choose the 50 most frequent ones
➢ Fix this sub-set of 50 functions for the whole 2D map
Compressed Sensing - ExampleIncorporation of further prior knowledge:
1. Similar spectral components across 2D map (1804 pixel)
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➢The determination of the z-coefficients by fitting to
fixed basis set, i.e. solve
➢Augment by regularization functional which favours
similar values for 8 neighboring pixels
➢Regularization parameter determined by L-curve
principle
Compressed Sensing - ExampleIncorporation of further prior knowledge:
2. Coefficients of basis functions vary smoothly
y Az=
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Compressed Sensing - Example
Hypothesis: sensitivity enhancement by measuring 1/9th
samples at 9 fold increased integration time
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Enhancing the sensitivity
o Nearfield IR Spectroscopy using s-SNOM
o Compressed sensing
o Radiation sources and detection
o Tailored tips
o Conclusion
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Synchrotron radiationAdvantage of synchrotron radiation: ultra-broadband spectrum
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Metrology Light Source, Berlin-Adlershof
For comparison: Bechtel et al, PNAS 2014
Synchrotron radiation
Pulsed at 500 MHz, 30 ps
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Detection
Requirements: scattered nearfield from tip VERY WEAK!
Judge by NEP:
Signal power for SNR = 1 for ½ sec integration time
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Detection
Ultimate limit: shot noise of optical radiation t
2
2p c
h Pf l
D=
D
For monochromnatic light of l = 10 mmAverage power P = 200 mW x ¼ (due to beamsplitter)
1210 W / Hz−
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Best experience with
Mercury Cadmium Telluride photoconductive detectors
Manufacturer specifies 12NEP =10 W/ Hz−
Detection
☺
But
Typicalmeasurement range
Novel detector conceptor
Increase signalscattered from tip
~ radiation intensity
in VnU m
P. Hermann et al.Optics Express 2017
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Enhancing the sensitivity
o Nearfield IR Spectroscopy using s-SNOM
o Compressed sensing
o Radiation sources and detection
o Tailored tips
o Conclusion
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Tailored TipsAntenna model: see Mastel et al. Nano Lett. 2017:
Choose: 4 mm long tip forresonance around l = 10 mm
A A AZ R iX= +
gap AX X− =
Resonance for:
gap gap gap 2
ihZ R iX
D= + = −
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Tailored Tips
600 800 1000 1200 1400 1600 1800 2000 2200
0.1
1
10
100 NanoAndMore
Neaspec
FIB
S
4 /
mV
Frequency / cm-1
Result: Measured spectrum on Au surface
But:alignment ciritical; need robust determination of field enhancement
Tailored tip
Gain: almost x 10
Luca Boarino, Giulia April
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Field enhancement - determination
E. Pfitzner, X. Hu, H. W. Schumacher, A. Hoehl, D. Venkateshvaran, M. Cubukcu, J.-W. Liao, S. Auffret, J. Heberle, J. Wunderlich, and B. KästnerarXiv1808.10767, 2018.
In collaboration with:
J. Wunderlich, Hitachi Cambridge LaboratoryE. Pfitzner, J. Heberle-group, FU Berlin
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Field enhancement - determination
By scanning a magnetic
nanowire:
E. Pfitzner et al., arXiv1808.10767, 2018.
Anomalous Nernst Effect
leads to generation of VT
How to acess field enhancement:
• Tip heats chip surface at its position (x0,y0), map VT(x0,y0)
• Relate VT(x0,y0) – map to temperature profile T(x,y) by comparing
to on-chip heaters and sensors
• Obtain power dissipation underneath tip, and corresponding field
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Field enhancement - determination
VT
M
( ) ( )0 0 0 0, , , ,TV x y T x y x y→
How to obtain:
E. Pfitzner et al., arXiv1808.10767, 2018.
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Field enhancement - determination
Comsol simulations by Xiukun Xu, PTB
Obtain using external heaters:
Heaters andT-sensors
Magnetic wire
( ) ( )0 0 0 0, , , ,TV x y T x y x y→
ANE ANE 0
ANE 0.054 V/KT
S
TV N M l
y
N
m
m
=
=
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Field enhancement - determination
Comsol simulationsby Xiukun Xu, PTB
300 K
325 K
-0.5 0 0.5Tip position y
0 (µm)
Simulation
-0.5 0 0.5Tip position y
0 (µm)
-0.8
-0.4
0
0.4
VT (
µV
)
Power loss at tip apexPloss = ?
Power loss at tip apexPloss = 4 GW/m2
-0.6
0
0.6
VT (
µV
)
Pin = 0.01 GW/m2
Field enhancement: 25
E. Pfitzner et al., arXiv1808.10767, 2018.
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ConclusionsStandard s-SNOM ignores any prior knowledge.
Compressed sensing: exploit prior knowledge at measurement stage
• Spectral sparsity
• Spatial smoothness
• Future: Spectra of individual components
→Rapid hyperspectral imaging or sensitivity enhancement
Further strategies for enhancing molecular sensitivity:
• Novel detector concepts
• Tailored Nearfield-AFM tips
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Peter Hermann, Arne HoehlAndrea Hornemann
Georg Ulrich, Gerhard UlmClemens Elster, Gerd Wübbeler
Marko SchmählingXiukun Xu, Hans SchumacherKlaus Pierz, Mattias Kruskopf
Emanuel PfitznerPiotr PatokaEckart Rühl
Jörg FeikesMarkus Ries
Tobias GoetschGodehard Wüstefeld
Acknowledgements
Jörg WunderlichMurat Cubukcu
Luca Boarino, Giulia April
Funded by