Japanese Journal of Applied Physics
Vol. 45, No. 3B, 2006, pp. 1904–1908#2006 The Japan Society of Applied Physics

Feed-Forward Compensation for High-Speed Atomic Force Microscopy
Imaging of Biomolecules
Takayuki U CHIHASHI1;2 , Noriyuki K ODERA1 , Hisanori I TOH1 , Hayato Y AMASHITA1 and Toshio A NDO1;2;3
1

Graduate School of Natural Science and Technology, Kanazawa University, Kakuma-machi, Kanazawa 920-1192, Japan
CREST, Japan Science and Technology Agency (JST), 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan
3
Frontier Science Research Organization, Kanazawa University, Kakuma-machi, Kanazawa 920-1192, Japan
2(Received July 3, 2005; accepted November 28, 2005; published online March 27, 2006)

High-speed imaging by atomic force microscopy (AFM) requires the implementation of a fast control of tip–surface distanceto maintain a constant interaction force. In particular, a well-controlled low load force is essential for observing soft biologicalmolecules without causing damage to the sample. The accurate control of tip–surface distance where only feedback control isused is intrinsically diﬃcult particularly for fast scanning. Here, we demonstrate that the combination of feedback and feedforward control is useful for a more accurate distance control. We evaluate the bandwidth performance of the closed loop withand without feed-forward compensation using a model AFM system.We show that the combination of feedback and feedforward control yields a greater than two fold improvement in bandwidth. We have applied this technique to the observationof myosin V and actin ﬁlaments at a high scanning rate. [DOI: 10.1143/JJAP.45.1904]
KEYWORDS: atomic force microscope, high-speed imaging, protein, feed-forward compensation

1.

Introduction

Biomolecules such as protein and nucleic acid function
via intermolecular interaction and structural changes. Therefore, to elucidate the molecular function and expression
mechanisms, it is highly desirable to observe the dynamic
processes of individual molecules. To date, there has been
no measurement technique with both suﬃcient spatial andtemporal resolutions.
Atomic force microscopy (AFM) is well known as a
powerful tool for observing individual molecular structureswith a high resolution in an aqueous solution.1) However,conventional AFM does not have a suﬃcient time resolution.
Typically a few minutes are required to take one image. This
slow scan speed is ineﬀective for samples that move quickly
and undergo rapid structural changes. Although several
attempts to improve the scan performance of AFM havebeen carried out to date, the image capture rate has remained
at several frames per second or less.2–5) Recently, Humphriset al. achieved an imaging rate of less than 20 ms/frame
using a microresonator as a sample stage.6) However, as thistechnique is based on the contact mode without feedback
control, it can be used only for samples that are hard, robust
and tightly ﬁxed onto a substrate. In 2001, we developed ahigh-speed AFM that can image soft biomolecules at 80 ms/
frame in the tapping mode.7,8)
In order to achieve high-speed AFM imaging, all thedevices that compose the AFM system must exhibit a fast
response. The development of various devices, such as smallcantilevers,9) and high-speed deﬂection sensors, and techniques, such as amplitude detection,8) active damping of thescanner10) and dynamic proportional, integral and derivative(PID) feedback control,11) have made high-speed measurement feasible. However, to carry out measurements on soft
biological samples, it is necessary to decrease loading force
from the tip. In tapping-mode AFM, the averaged loading
force Fa at a cantilever resonant frequency is given by:
Fa ¼ k  ðA0  As Þ=Q;E-mail address: tuchi@kenroku.kanazawa-u.ac.jp

ð1Þ

where k is the spring constant of the cantilever, A0 is the freeoscillation amplitude of the tip, As is the set-point amplitude
for the feedback control and Q is the quality factor of thecantilever. In order to reduce loading force, it is necessary tobring set-point amplitude close to free oscillation amplitude.
However, feedback bandwidth decreases as set-point amplitude approaches free amplitude.
Now, suppose the cantilever is scanning over the steepest
down hill of a sample having a sinusoidal wave shape with aheight of h and a periodicity of , and the sample stage is
moved horizontally at a velocity of Vs . The spatial frequencyof 1= is converted to a temporal frequency of f  Vs =,which corresponds to the required feedback bandwidth.
After one cycle of the cantilever’s oscillation at a frequencyof fc , sample height is lowered by h sinð=2Þ, where ¼ ð f = fc Þ  2. If, however, the sample surface is notpresent, the cantilever’s tip end would go by A0  As at thedownswing. The oscillation tip should touch the sample
surface at the bottom of every swing. Hence, the following
relationship should hold.

fc 1 A0  As
f < sinð2ÞhFrom this relationship, in order to increase feedback
bandwidth, A0  As should be increased. Thus, the two
aspects of soft tapping and fast imaging are in conﬂict.
In this study, we employed feed-forward compensation in
conjunction with feedback control to satisfy these two
conﬂicting requirements. This technique was already implemented in contact-mode AFM by Schitter et al.12) However,the quantitative evaluation of its performance and the highspeed AFM imaging of soft biomolecules have not yet been
carried out. An evaluation of bandwidth with and without
feed-forward compensation shows that we can eﬀectively
increase feedback bandwidth. Furthermore, we have applied
this technique to the fast imaging of soft biomolecules.
2.

Experimental

We used a laboratory-built high-speed AFM, the details of
which are described in previous papers.7,8) AFM images
were acquired in the tapping mode. The cantilever we used

1904

Jpn. J. Appl. Phys., Vol. 45, No. 3B (2006)

T. UCHIHASHI et al.

RMS-DC

cantileveramplitude

set pointsample stage&
scannererror signal
Z

X Y

PID

PC
image

start trigger and clock signal
synchronized with X scanning pixel

memory 1AD
DA
memory 2
feed-forward controller

Fig. 1. Block diagram of combination control of feedback and feed-forward.

was a specially designed one provided by Olympus; its
resonant frequency was about 800 kHz in water and thespring constant was about 100 pN/nm. The carbon tip wasgrown on the cantilever by electron beam deposition.
Figure 1 shows a block diagram of the combination of the
feedback and feed-forward control. The feed-forward controller consists of 12 bit D/A, A/D converters, twomemories and two high-speed analogue switches. The
feed-forward controller starts to record the input signal tomemory 1 triggered by the start signal from the scan
controller. The input signal is recorded into memory 1
synchronized with the clock signal of scanning pixel. Afterthe clock number reaches the predetermined number, whichis the same as the pixel number of the X scanning line, therecorded signal is output from memory 1 synchronized withthe clock, and simultaneously the input signal is recorded inmemory 2. These processes are repeated until one frame iscompleted. The addition signal of the PID feedback anderror signals are used as the input signal for the ﬁrst X
scanning line. After the second X line, the addition signal of
the PID, error and also feed-forward signals are recorded. It
should be noted that the error signal is also used as the feedforward signal. In an aqueous environment, the Q value ofthe cantilever is not so large, typically less than 5. Therefore,
the error signal reﬂects the deviation of the tip trajectoryfrom the actual geometry, which is essential for compensating the feedback delay. The input gain of the feed-forward

signal for the PID output is set at lower than 1, typically 0.5,
because, when the surface geometry would rapidly change ineach line, a large feed-forward gain increases the inaccuracyof the topographic measurement on the contrary. On theother hand, the gain of the error signal is set at about 0.1,
which is basically decided by the ratio of the inversed opticallever sensitivity of the deﬂection sensor and the piezoelectric
constant. In our case, they are about 15 and 90 nm/V,
respectively. Therefore, the gain of the error signal should beless than 0.17.
To facilitate the quantitative performance evaluation of
feed-forward compensation, we used a mock AFM circuit
consisting of a second-order low-pass ﬁlter with the same
resonance properties of the Z-scanner, and a threshold circuitthat can simulate a decrease in the cantilever’s oscillation
caused by the tip–sample contact. A mock sample topography was produced by a function generator. The detailsof this circuit will be given in a separate paper. For theevaluation using the mock AFM circuit, the oscillation
frequency and amplitude of the mock cantilever were set at
800 kHz and 0.1 V, respectively. A sinusoidal wave with afrequency of 7.3 kHz and an amplitude of 0.1 V was used as
the mock sample topography.
3.

Results and Discussion

Figure 2 shows a comparison of pseudo-AFM images
produced by the mock AFM circuit without and with feed-

1905

Jpn. J. Appl. Phys., Vol. 45, No. 3B (2006)

T. UCHIHASHI et al.

(a)Voltage [V]

0.4

(b)

0.04

(c)

-0.4

-0.04

(f)

(e)

Voltage [V]

0.4

(d)

0.04

(g)

-0.4

(h)

-0.04

Fig. 2. Pseudo-AFM images produced by mock AFM under only feedback [(a)–(d)] and combination control [(e)–(h)]. Topography[(a) and (e)], topographic cross-sectional proﬁles [(c) and (g)], error images [(b) and (f)] and error cross-sectional proﬁles [(d) and(h)]. The feed-forward gain and error gain are 0.5 and 0.1, respectively.

0phase delay [degrees]

forward compensation. Here, the set-point amplitude for
feedback control was set at 98% of the cantilever’s freeamplitude. The scan direction was from left to right. As
shown in Figs. 2(a) and 2(c), the topography in the case ofwithout feed-forward compensation exhibits a distorted
sinusoidal shape because the tip cannot touch the surface,as the surface topography has lowered due to the large setpoint amplitude. On the other hand, as shown in Figs. 2(e)and 2(g), using feed-forward compensation the topographyshows a sinusoidal shape. The height diﬀerence in the caseof with the feed-forward compensation increases about
180% compared with that without feed-forward compensation. Also, the error signal in the case of with feed-forward
compensation decreases to about 85% of that without feedforward compensation as shown in Figs. 2(d) and 2(f).
To quantitatively evaluate the bandwidth in the case of the
combination of feedback and feed-forward controls, wemeasured the phase diﬀerence between the sinusoidal waveof the mock sample topography and the signal applied to themock Z-scanner. Figure 3 shows the phase delay in the caseof the combination controller with respect to the mocksample topography as a function of the frequency of themock sample topography for diﬀerent set-point values. The
closed circles and triangles correspond to phase delay
measured with only the feedback control at the set-point
amplitudes of 98 and 80%, respectively. The open circles
and triangles correspond to the phase delay under the
combination control with feed-forward compensation at the
set-point amplitudes of 98 and 80%, respectively. In the caseof 98% set-point amplitude, the phase delay in the case ofwithout feed-forward compensation is signiﬁcant and the
bandwidth, which is deﬁned as the frequency at which thephase of 45 deg is delayed, is about 9 kHz. However, withthe addition of feed-forward compensation, the bandwidth isimproved to 51 kHz. In the case of 80% set-point amplitude,
the bandwidths for without and with feed-forward compensations are about 31 and 70 kHz, respectively. Thus,
bandwidth is signiﬁcantly improved by the combination of
the feedback and feed-forward controls. This evaluation was
carried out under the ideal condition that the topography did
not change each X scanning line. However, as long as the

-50

-100

-150
100

101

102

frequency [kHz]Fig. 3. Phase delay in the case of feedback and combination control withrecpect to the mock sample topography as function of frequency of mocksample topography. The closed circles and triangles correspond to phasedelay measured with only the feedback control at the set-point amplitudesof 98 and 80%, respectively. The open circles and triangles correspond tophase delay under the combination control at the set-point amplitudes of
98 and 80%, respectively.

topographies of individual X lines are not markedly diﬀerent, feed-forward compensation works even though theextension of bandwidth is suppressed.
To conﬁrm the validity of this technique, we measured
soft biomolecules at a high speed. Figures 4(a) and 4(b)show high-speed AFM images of myosin V taken at 60 ms/
frame without and with feed-forward compensation, respectively. The scan size was 150  150 nm2 . The scan direction
was from right to left on the images. In comparison with the
topographic images, we can note that the contour of the
myosin molecule where the feed-forward compensation is
employed becomes clearer than that taken with only the
feedback control. Figures 4(c) and 4(d) show the crosssections of topographic and error images at the line indicatedby white broken lines in Figs. 4(a) and 4(b), where this partof the molecule does not move very much in each frame.
The solid and dotted lines correspond to the cross sections of
the images with and without feed-forward compensation,
respectively. We can observe that the height diﬀerence isslightly increased by using feed-forward compensation.
Also, in the feed-forward controlled system, it can be noted

1906

Jpn. J. Appl. Phys., Vol. 45, No. 3B (2006)

T. UCHIHASHI et al.

(a)height [nm](a)Error [nm]

(b)

5 (c)
4
3
2
1
0

1.5

(d)

1.0
0.5
0

0

distance [nm]150

Fig. 4. High-speed AFM images of myosin V taken at 60 ms/frame with(a) feedback and (b) combination control, respectively. The scan size was
150  150 nm2 with 200  200 pixels. The cross-sectional proﬁles for the(c) topographic and (d) error images measured with feedback (solid lines)
and combination control (broken lines) are compared. The crosssectioned part of the image is indicated by white broken lines on theimages. The images were scanned from right to left scan.

that the rising edge of the topography becomes steep, whichmeans that the phase delay is compensated. On the other
hand, the error signal decreases to 60% with the addition of
feed-forward compensation.
Figure 5 shows successive images of myosin V captured
at 37 ms/frame with a scan size of 100  100 nm2 . These
images were taken under a combination of feedback andfeed-forward control. Although it is diﬃcult to observe fromthese six images, some parts of the molecule, particularly
those surrounded by a white broken circle, are moving inevery frame probably due to Brownian motion. Thus, thecombination of feedback and feed-forward control works
even for moving samples.
Actin is a more fragile protein than myosin V. Therefore
it is more diﬃcult to clearly observe it at high speeds
without damaging the sample. Figures 6(a) and 6(b) shows
topographic images taken with and without feed-forward
compensation, respectively. These images were acquired at
60 ms/frame. The set-point amplitude for feedback control
was 90% of the free amplitude of 2.5 nm. In Fig. 6(a), we
can observe the half pitches of the double-helix turn of aﬁlament. After feed-forward compensation is cut, the rightside of the ﬁlament trails and the image quality deteriorates
markedly. In order to improve image quality, the set-point
amplitude should be decreased to about 80% of the free

0 ms

(b)

37 ms

74 ms

Fig. 6. AFM images of actin ﬁlament measured under (a) feedback and(b) combination control. These images were acquired at 60 ms/frame.
The set-point amplitude for feedback control was 90% of the freeamplitude of 2.5 nm. The scan size was 200  200 nm2 with 100  100
pixels.

amplitude. In that case, however, the actin ﬁlament is easily
swept out by the AFM tip. Since the quality factor and thespring contant of the cantilever used here were about 3 and100 pN/nm, respectively, the loading forces with andwithout feed-forward compensation were about 8 and 17
pN, respectively. Therefore, in this case, the loading force
could be reduced to about one-half by feed-forward
compensation.
Figure 7 shows successive images of an actin ﬁlamenttaken at 60 ms/frame. The set-point amplitude was 91% of
the free oscillation amplitude of 18 nm, which is a relatively
large amplitude. The image shown in Fig. 7(a) was taken
under the combination control. Although this image wascaptured after 59 frames from the ﬁrst scan, the actin
ﬁlament suﬀered only minor damage. Figures 7(b)–7(f)show the images taken with only feedback control imediately after the image shown in Fig. 7(a) was captured. They
are displayed every eight frames. In the case of feedback
control alone, not only does the image quality deteriorate,
the actin ﬁlament is also easily destroyed. From theseresults, we can note that feed-forward compensation isuseful for the clear imaging of fragile molecules at a small
loading force.
4.

Conclusions

In summary, we have applied feed-forward compensation
to high-speed AFM for observing biological molecules. By
feed-forward compensation in conjunction with feedback
control, the tip can trace a surface more accurately, which
increases measured height and decreases error signal.
Bandwidth evaluation using the mock AFM circuit showedthat the bandwidth in the case of combination control ismore than twice that with only feedback control. Whenapplied to the fast imaging of myosin V and actin ﬁlaments,
this new technique improves image quality and decreases

111 ms

148 ms

185 msFig. 5. Successive AFM images of myosin V captured at 37 ms/frame under combination control. The scan size is 100  100 nm2 with100  100 pixels.

1907

Jpn. J. Appl. Phys., Vol. 45, No. 3B (2006)(a)T. UCHIHASHI et al.

(b)

(c)

0 ms

480 ms

(d)

(e)

(f)

960 ms1440 ms

1920 ms

Fig. 7. Successive images of actin ﬁlament taken at 60 ms/frame under (a) the combination and (b)–(f) the feedback control. The setpoint amplitude was 91% of the free oscillation amplitude of 18 nm. For (b)–(f), images are displayed every eight frames. The scansize was 200  200 nm2 with 100  100 pixels.

phase delay even at a scanning rate of 60 ms/frame. Also thedestruction of fragile actin ﬁlaments is minimized. Thus, thistechnique can compensate the insuﬃcient bandwith of
feedback control and oﬀers a signiﬁcant improvement forthe soft imaging of fragile biomolecules with fast scanning.

3)
4)
5)

Acknowledgements
This research was supported by Core Research for
Evolutional Science and Technology (CREST) of the Japan
Science and Technology Agency (JST) and Industrial
Technology Research Grant Program in ’04 from New
Energy and Industrial Technology Development Organization (NEDO).

6)
7)
8)
9)
10)

1) H. G. Hansma, J. Vesenka, C. Siegerist, G. Kelderman, H. Morrett,R. L. Sinsheimer, V. Elings, C. Bustamante and P. K. Hansma:
Science 256 (1992) 1180.
2) M. B. Viani, T. E. Schæﬀer, G. T. Paloczi, L. I. Pietrasanta, B. L.
Smith, J. B. Thompson, M. Richter, M. Rief, H. E. Gaub, K. W.

11)
12)

1908

Plaxco, A. N. Cleland, H. G. Hansma and P. K. Hansma: Rev. Sci.
Instrum. 70 (1999) 4300.
T. Sulchek, R. Hsieh, J. D. Adams, S. C. Minne, C. F. Quate andD. M. Adderton: Rev. Sci. Instrum. 71 (2000) 2097.
T. Sulchek, G. G. Yaralioglu, C. F. Quate and S. C. Minne: Rev. Sci.
Instrum. 73 (2002) 2928.
B. Rogers, T. Sulchek, K. Murray, D. York, M. Jones, L. Manning,
S. Malekos, B. Beneschott, J. D. Adams, H. Cavazos and S. C. Minne:
Rev. Sci. Instrum. 74 (2003) 4683.
A. D. L. Humphris, M. J. Miles and J. K. Hobbs: Appl. Phys. Lett. 86(2005) 034106.
T. Ando, N. Kodera, D. Maruyama, E. Takai, K. Saito and A. Toda:
Proc. Natl. Acad. Sci. U.S.A. 98 (2001) 12468.
T. Ando, N. Kodera, D. Maruyama, E. Takai, K. Saito and A. Toda:
Jpn. J. Appl. Phys. 41 (2002) 4851.
M. Kitazawa, K. Shiotani and A. Toda: Jpn. J. Appl. Phys. 42 (2003)
4844.
N. Kodera, H. Yamashita and T. Ando: Rev. Sci. Instrum. 76 (2005)
053708.
T. Ando, T. Uchihashi, N. Kodera, A. Miyagi, R. Nakakita andH. Yamashita: to be submitted to the STM05 conference paper.
G. Schitter, F. Allgœwer and A. Stemmer: Nanotechnology 15 (2004)
108.