Atomic Force MicroscopyHigh-Performance Demodulation and Model-Based Nanomechani-cal Identification

Michael R. P. Ragazzon

Department of Engineering Cybernetics,Norwegian University of Science and Technology (NTNU)

November 18, 2019,KTH Royal Institute of Technology, Stockholm

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Outline

Introduction

High-performance DemodulationProblem FormulationLyapunov DemodulatorComparison of Demodulation TechniquesGeneralized Lyapunov demodulator

Model-based Nanomechanical IdentificationIntroductionSystem modelingParameter identificationOperation ModesExperimentsConclusion

Research Directions

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 1

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Outline

Introduction

High-performance DemodulationProblem FormulationLyapunov DemodulatorComparison of Demodulation TechniquesGeneralized Lyapunov demodulator

Model-based Nanomechanical IdentificationIntroductionSystem modelingParameter identificationOperation ModesExperimentsConclusion

Research Directions

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 2

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

About me

About me

— From Oslo, Norway.

— Graduated with Master’s (2013) and PhD (2018) at NTNU in Trondheim.

— Currently Postdoc. at NTNU.

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 3

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Introduction

Atomic force microscopy (AFM)

Mirror

Functiongenerator

Demodulator

ControllerUz

A

xyz Piezoactuator

Aref

Piezo modulator

DetectorLaser

Sample

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 4

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Outline

Introduction

High-performance DemodulationProblem FormulationLyapunov DemodulatorComparison of Demodulation TechniquesGeneralized Lyapunov demodulator

Model-based Nanomechanical IdentificationIntroductionSystem modelingParameter identificationOperation ModesExperimentsConclusion

Research Directions

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 5

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Problem Formulation

Problem Formulation

Estimate amplitude a(t) and phase ϕ(t) in

z(t) = a(t) sin(ω0t + ϕ(t)). (1)

Evaluate in terms of the following metrics:

— Tracking bandwidth

— Noise evaluation (total integrated noise, TIN)

— Rejection of frequency components away from ω0 (off-mode rejection)

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 6

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Problem Formulation

Problem Formulation

Estimate amplitude a(t) and phase ϕ(t) in

z(t) = a(t) sin(ω0t + ϕ(t)). (1)

Evaluate in terms of the following metrics:

— Tracking bandwidth

— Noise evaluation (total integrated noise, TIN)

— Rejection of frequency components away from ω0 (off-mode rejection)

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 6

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Problem Formulation

AFM Demodulation Techniques

Demodulators

Rectification(non-synchronous)

Mixing(synchronous)

Open loop Closed loop

- Mean abs. deviation- Peak detection- RMS-to-DC- Peak hold

- Lock-in amplifier- HB lock-in amplifier- Coherent

- Kalman filter- Lyapunov demodulator

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 7

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Problem Formulation

AFM Demodulation Techniques

Demodulators

Rectification(non-synchronous)

Mixing(synchronous)

Open loop Closed loop

- Mean abs. deviation- Peak detection- RMS-to-DC- Peak hold

- Lock-in amplifier- HB lock-in amplifier- Coherent

- Kalman filter- Lyapunov demodulator

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 7

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Lyapunov Demodulator

Lyapunov DemodulatorUpdate law given by1

˙x = γc(z − z

), (2)

z = cT x (3)

where γ determines the estimation bandwidth.

[sin(ω0t)cos(ω0t)

]

z a‖·‖2

eγ 1

s−x

c

φatan2(·)

1Michael R P Ragazzon, Michael G Ruppert, David M Harcombe, Andrew J Fleming, andJan Tommy Gravdahl (2018). “Lyapunov Estimator for High-Speed Demodulation in Dynamic Mode AtomicForce Microscopy”. IEEE Transactions on Control Systems Technology 26.2, pp. 765–772.

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 8

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Lyapunov Demodulator

Experimental Results

−80

−60

−40

−20

0

Magnitude(dB)

LIA slow

LIA fast

Lyapunov slow

Lyapunov fast

0.1 1 10 100−360

−270

−180

−90

0

Frequency (kHz)

Phase

[deg]

Frequency response

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 9

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Lyapunov Demodulator

Experimental Results

0 0.1 0.2 0.3 0.40

0.5

1

1.5

2

Time (ms)

Amplitude(V

) Input

LIA fast

Lyapunov fast

Time domain

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 9

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Lyapunov Demodulator

Lock-in amplifier vs Lyapunov

0.5 1 10 50

1

10

100

Bandwidth (kHz)

TIN

(mV)

LIA

Lyapunov

Total integrated noise (TIN) vs bandwidth

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 10

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Comparison of Demodulation Techniques

Sensitivity to other frequency components

Off-mode rejection2

2Michael G Ruppert, David M Harcombe, Michael R P Ragazzon, S O Reza Moheimani, andAndrew J Fleming (2017). “A Review of Demodulation Techniques for Amplitude-Modulation Atomic ForceMicroscopy”. Beilstein Journal of Nanotechnology 8.1, pp. 1407–1426.

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 11

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Comparison of Demodulation Techniques

High-speed AFM Experiments

High-speed AFM experiment, 31 lines per second (∼8 s per image).Top: LIA at low bandwidth. Bottom: Lyapunov at high bandwidth.

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 12

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Comparison of Demodulation Techniques

Multifrequency Lyapunov AFM Experiment

Phase demodulation at the first five harmonics of the cantilever.3

3David M Harcombe, Michael G Ruppert, Michael R P Ragazzon, and Andrew J Fleming (2018).“Lyapunov Estimation for High-Speed Demodulation in Multifrequency Atomic Force Microscopy”. BeilsteinJournal of Nanotechnology 9.1, pp. 490–498.

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 13

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Generalized Lyapunov demodulator

Generalized Lyapunov demodulator4

— Lyapunov demodulator achieves high demodulation bandwidth.

— However, only first-order filtering.• Can we increase the filter order?

4Michael R P Ragazzon, Saverio Messineo, Jan Tommy Gravdahl, David M Harcombe, andMichael G Ruppert (2019). “Generalized Lyapunov Demodulator for Amplitude and Phase Estimation by theInternal Model Principle”. In Proc. IFAC Mechatronics. Vienna, Austria, p. 6.

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 14

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Generalized Lyapunov demodulator

Indirect filter design

K Gu

y

v2

Amplitude andphase retrieval

a

ωc

r

Modulated signal(measurement)

Internal model of sinusoidInternal filter

Demodulator loop, T Composer

ϕ

a

ϕε

v1

— Design K (s) such that the demodulator loop T (s) becomes a desiredbandpass shape.

— Perfect tracking is guaranteed for any stable K (s).

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 15

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Generalized Lyapunov demodulator

Direct filter design

−ωc

s

Tr

v2

Amplitude andphase retrieval

a

Demodulator filterComposer ϕ

v1

— Design T (s) directly as a bandpass filter.

— Perfect tracking is guaranteed by the condition T (jωc) = 1.

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 16

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Generalized Lyapunov demodulator

Direct filter design

−ωc

s

Tr

v2

Amplitude andphase retrieval

a

Demodulator filterComposer ϕ

v1

— Design T (s) directly as a bandpass filter.

— Perfect tracking is guaranteed by the condition T (jωc) = 1.

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 16

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Generalized Lyapunov demodulator

Bode plot T (s)

30 35 40 45 50 55 60 65 70 75 80−40

−20

0

Magnitude(d

B)

30 35 40 45 50 55 60 65 70 75 80

−200

0

200

Frequency (kHz)

Phase

(deg

)

3 kHz bandwidth

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 17

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Generalized Lyapunov demodulator

Tracking frequency response

0.1 1 10 100

−40

−20

0

Frequency (kHz)

Magnitude(d

B)

1 10 100 1000

Frequency (kHz)

3 kHz bandwidth 30 kHz bandwidth

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 18

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Outline

Introduction

High-performance DemodulationProblem FormulationLyapunov DemodulatorComparison of Demodulation TechniquesGeneralized Lyapunov demodulator

Model-based Nanomechanical IdentificationIntroductionSystem modelingParameter identificationOperation ModesExperimentsConclusion

Research Directions

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 19

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Introduction

Introduction

— Single- and multifrequency AFM allow mechanical properties to be gathered.

— However, interaction forces are inherently nonlinear and often requires:• linearization• multifrequency demodulation• consideration of harmonics

to relate the observables to mechanical properties.

— Here, we relate the sample properties directly from the observables usingtime-domain dynamic models.

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 20

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Introduction

Introduction

— Single- and multifrequency AFM allow mechanical properties to be gathered.

— However, interaction forces are inherently nonlinear and often requires:• linearization• multifrequency demodulation• consideration of harmonics

to relate the observables to mechanical properties.

— Here, we relate the sample properties directly from the observables usingtime-domain dynamic models.

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 20

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Introduction

Introduction

— Single- and multifrequency AFM allow mechanical properties to be gathered.

— However, interaction forces are inherently nonlinear and often requires:• linearization• multifrequency demodulation• consideration of harmonics

to relate the observables to mechanical properties.

— Here, we relate the sample properties directly from the observables usingtime-domain dynamic models.

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 20

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

System modeling

Cantilever dynamics

Approximation by first resonance mode.

MD + KD + CD = Fmod + Fts. (4)

x

z

Z

Z0

D

R

Rest position

Tip

Sample

Cantileverdeflection

X

h

δ

K,C

k, c

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 21

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

System modeling

Contact model

Modified Hertz contact model.

Fts = E ′δ32 + cδ (5)

E = 34 R−

12 (1− ν2)E ′ (6)

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 22

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Parameter identification

Parametric model

Combining the previous cantilever and sample models gives the system

Ms2D + CsD + KD − Fmod = csδ + E ′δ1.5. (7)

Rewrite (7) as

w ′ =[

cE ′

]T [ sδδ1.5

](8)

= θTφ′ (9)

Persistently exciting φ→ exponential convergence of parameters.

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 23

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Parameter identification

Parametric model

Combining the previous cantilever and sample models gives the system

Ms2D + CsD + KD − Fmod = csδ + E ′δ1.5. (7)

Rewrite (7) as

w ′ =[

cE ′

]T [ sδδ1.5

](8)

= θTφ′ (9)

Persistently exciting φ→ exponential convergence of parameters.

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 23

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Parameter identification

Parametric model

Combining the previous cantilever and sample models gives the system

Ms2D + CsD + KD − Fmod = csδ + E ′δ1.5. (7)

Rewrite (7) as

w ′ =[

cE ′

]T [ sδδ1.5

](8)

= θTφ′ (9)

Persistently exciting φ→ exponential convergence of parameters.

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 23

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Parameter identification

Parameter estimator

Least squares method with forgetting factor.5

w = θTφ (10)

ε = (w − w)/m2 (11)

m2 = 1 + αφTφ (12)˙θ = Pεφ (13)

P = βP− PφφT

m2P (14)

P(0) = P0 (15)

5P A Ioannou and J Sun (1996). “Robust Adaptive Control”. Upper Saddle River, NJ: Prentice Hall.

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 24

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Operation Modes

Procedure

x

y

Cantilever tip

t

Z0

Fmod

X

DSample

Intermittent contact

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 25

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Operation Modes

Procedure

x

y

Cantilever tip

t

Z0

Fmod

X

DSample

In-contact dynamic mode.

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 26

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Experiments

Experimental setup

Park Systems XE-70 AFM and setup.

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 27

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Experiments

Experiment: Two-component Polymer Sample

0 0.5 1 1.50

0.5

1

1.5

X (µm)

Y(µm

)

0

20

40

60

nm

(a) Topography

0 0.5 1 1.50

0.5

1

1.5

X (µm)

Y(µm

)

1.2

1.4

1.6

1.8

nm

(b) Amplitude

0 0.5 1 1.50

0.5

1

1.5

X (µm)

Y(µm

)

107

108

109

Pa

(c) Elastic modulus

0 0.5 1 1.50

0.5

1

1.5

X (µm)

Y(µm

)

0

50

100

µNs/m

(d) Damping coefficient

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 28

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Experiments

Experiment: Two-component Polymer Sample

0 1 2 3 4 5 60

100

200

Time (s)

Z(nm)

Z mean

Z envelope

(a) Vertical tip position

0 1 2 3 4 5 60

2

4

6

8·10−5

Time (s)

c(N

s/m)

0

5

10

15

20

25

k(N

/m)

(b) Parameter estimates

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 29

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Conclusion

Advantages

— Handles nonlinear force interactions naturally.

— Time-domain approach, circumvents the need• for linearization,• to consider harmonics,• demodulation, either single- or multifrequency.

— Can modify the cantilever and sample dynamics separately.

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 30

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Conclusion

Challenges

— Signal-to-noise ratio of the cantilever is frequency dependent.

— Some nonlinear parametric models are challenging.• Eg. adhesion and plasticity.

— Can we trust the deflection signal under in-contact dynamic mode?

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 31

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Outline

Introduction

High-performance DemodulationProblem FormulationLyapunov DemodulatorComparison of Demodulation TechniquesGeneralized Lyapunov demodulator

Model-based Nanomechanical IdentificationIntroductionSystem modelingParameter identificationOperation ModesExperimentsConclusion

Research Directions

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 32

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Research Directions

Issues with in-contact dynamic mode

Laser

Sample

xy Piezoactuator

Shaker

z Piezo

Z

Photodetector

In-contact dynamic mode

Can the deflection measurement be trusted?

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 33

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Research Directions

Tip-actuated cantilever

Sample

xy Piezoactuator

Shaker

z Piezo

Z

Magneticfield

Magneticparticle

Fm

Tip-actuated cantilever

Can the deflection measurement be trusted?

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 34

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Research Directions

Model improvements

k0

k1 k2

d1 d2 dj

kj

Generalized Maxwell model

— Extension to more general, frequency dependent viscoelastic models.

— Deeper insight into the forces involved.

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 35

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Research Directions

Model improvements

Sample

xy Piezoactuator

Shaker

z PiezoZ0

D

Fd (D)

Fk (D)Fts(δ; S)

External and internal cantilever forces

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 36

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Thank You

Thank you for your attention!

Questions?

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 37

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Bonus slides

Noise vs Bandwidth

Total integrated noise

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 38

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Bonus slides

Experimental setup

Ux, Uy , Uz

State machine(control logic)

D

D,Fmod

DA

DDemodulator

XYZControllerdX, dY, dZ

X, Y

Z δ

h

Parameter estimator

Leastsquares

estimator

k, cw

φSignal

filtering

Z0

A′ sin(ω0t)FmodEnable estimator

Block diagram of the control logic and parameter estimator.

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 39

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Bonus slides

Experimental setup

— Implemented on a commercial AFM, Park Systems XE-70.

— All aspects controlled by our own algorithms.

— Real-time implementation at 200 kHz on a dSpace computer.

— Spherical carbon tip cantilever, radius 40 nm (B40_CONTR).

— Cantiler parameters M,K ,C determined a priori.

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 40

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Bonus slides

Plant dynamics

Cantileverdynamics

XYActuator

hFts

Fmod

Uz

Ux, Uy X,Y X, Y

D

D

Z0Z0 Z δ Sample

k, cZ

Actuator

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 41

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Bonus slides

Experimental results: Time-varying parameters

0 50 100−2

−1

0

1

2·10−5

Time (s)

c(N

s/m

)

−0.5

0

0.5

k(N

/m)

Time-varying sample parameter estimates during indentation.

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 42

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Bibliography

Bibliography I

Harcombe, David M, Michael G Ruppert, Michael R P Ragazzon, and Andrew J Fleming(2018). “Lyapunov Estimation for High-Speed Demodulation in Multifrequency AtomicForce Microscopy”. Beilstein Journal of Nanotechnology 9.1, pp. 490–498.

Ioannou, P A and J Sun (1996). “Robust Adaptive Control”. Upper Saddle River, NJ: PrenticeHall.

Ragazzon, Michael R. P. (2018). “Parameter Estimation in Atomic Force Microscopy:Nanomechanical Properties and High-Speed Demodulation”. PhD Thesis. Trondheim,Norway: NTNU, Norwegian University of Science and Technology.

Ragazzon, Michael R P, Saverio Messineo, Jan Tommy Gravdahl, David M Harcombe, andMichael G Ruppert (2019). “Generalized Lyapunov Demodulator for Amplitude and PhaseEstimation by the Internal Model Principle”. In Proc. IFAC Mechatronics. Vienna, Austria.

Ragazzon, Michael R P, Michael G Ruppert, David M Harcombe, Andrew J Fleming, andJan Tommy Gravdahl (2018). “Lyapunov Estimator for High-Speed Demodulation inDynamic Mode Atomic Force Microscopy”. IEEE Transactions on Control SystemsTechnology 26.2, pp. 765–772.

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 43

Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions

Bibliography

Bibliography II

Ragazzon, M.R.P., J.T. Gravdahl, and K.Y. Pettersen (2018). “Model-Based Identification ofNanomechanical Properties in Atomic Force Microscopy: Theory and Experiments”. IEEETransactions on Control Systems Technology.

Ruppert, Michael G, David M Harcombe, Michael R P Ragazzon, S O Reza Moheimani, andAndrew J Fleming (2017). “A Review of Demodulation Techniques forAmplitude-Modulation Atomic Force Microscopy”. Beilstein Journal of Nanotechnology 8.1,pp. 1407–1426.

Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 44