REVIEW OF SCIENTIFIC INSTRUMENTS 76, 053708 共2005兲

Active damping of the scanner for high-speed atomic force microscopy
Noriyuki Kodera, Hayato Yamashita, and Toshio Andoa兲
Department of Physics, Kanazawa University, Kakuma-machi, Kanazawa, 920-1192 Japan

共Received 30 October 2004; accepted 13 March 2005; published online 26 April 2005兲
The scanner that moves the sample stage in three dimensions is a crucial device that limits theimaging rate of atomic force microscopy. This limitation derives mainly from the resonant
vibrations of the scanner in the z direction 共the most frequent scanning direction兲. Resonanceoriginates in the scanner’s mechanical structure as well as in the z piezoactuator itself. We
previously demonstrated that the resonance originating in the structure can be minimized by acounterbalancing method. Here we report that the latter resonance from the actuator can beeliminated by an active damping method, with the result the bandwidth of the z scanner nearlyreaches the first resonant frequency 共150 kHz兲 of the z piezoactuator. © 2005 American Institute ofPhysics. 关DOI: 10.1063/1.1903123兴

I. INTRODUCTION

The atomic force microscope 共AFM兲 is a powerful toolfor high-resolution imaging of biological samples on a substrate in aqueous solution. However, the scan speed of the
AFMs currently available is too slow to capture the dynamic
processes of biological macromolecules in real time. The
scan speed is determined by the bandwidth of feedback operator that keeps the tip-sample interaction force constant bymoving the sample stage up and down depending on thesample height. Since biological samples are soft and fragile,
this feedback operation is indispensable for minimizing theinteraction force. In this feedback operation, various devices
are involved such as cantilevers, a detector for sensing cantilever deflection, a feedback circuit, a z scanner that moves
the sample stage in the z direction, and so on. The various
efforts made to date have been for the purpose of enhancing
feedback speed. Viani et al. used small cantilevers with resonant frequencies of 150 kHz to image DNA and
GroEL-GroES complexes on mica, in liquid.1,2 Yet, theirframe rate was less than 1 / s, because the conventional piezotube scanner they used had a low-resonant frequency inthe z direction. To overcome the low-resonant frequency of
conventional sample-stage scanners, Sulcheck et al.3,5 andRogers et al.4 used a cantilever with an integrated zinc oxide
piezoactuator capable of deflecting itself to keep the tipsample interaction force constant. They achieved a feedback
bandwidth 共i.e., imaging bandwidth兲 of 38 kHz and a frame
rate of ⬃4 / s.3 However, the self-actuating cantilever inevitably becomes very stiff, and hence is inappropriate for theimaging of soft samples. Although it was performed not with
AFM but rather with near-field scanning optical microscopy,
Humphris et al. achieved an imaging rate⬎ 100 frames/ s,
using a scan system that employs the mechanical resonanceof an optical fiber probe to address the sample.6 However,this high-speed is achieved without any feedback operation
to keep the probe-sample distance constant. Therefore, thisa兲Electronic address: tando@kenroku.kanazawa-u.ac.jp0034-6748/2005/76共5兲/053708/5/$22.50

technique is applicable only to the AFM imaging of hardsamples. We optimized all the devices involved in the feedback loop, and were able to produce a high-speed AFM thatmade it possible in the tapping mode of operation to capture
a 100⫻ 100 pixel image within 80 ms.7–9
In enhancing further the imaging rate of our high-speed
AFM, the z scanner is an obvious target for improvement,
because it is the slowest device among those contained in the
feedback loop. The resonant vibrations of the z scanner are
the cause for the slowing of feedback. Resonance due to thescanner’s overall structure usually occurs at a frequency
lower than the resonant frequency of the z piezoactuator itself. This structural resonance can be minimized by suppressing the impulsive forces produced when the z actuator
displaces very quickly. As demonstrated previously, this suppression can be made using two z piezoactuators placed in
the opposite direction to one another. The impulsive forces
produced by one z actuator are countered by the simultaneous displacement of the other z actuator of the samelength, in the counter direction.7 The challenge is to damp
completely the resonant vibrations of the z piezoactuatorsthemselves. A conventional method uses a notch filter to remove a frequency band around the resonant frequency. A
weak point of this method is the slow transient response of
the notch filter. In this article, we show that excellent damping can be accomplished by a method of active vibration
control of the z actuators. Because the quality factor 共Q兲 ofthe z actuators’ resonance is markedly reduced by thismethod, the response speed is greatly enhanced. Although
the phase delay is pronounced with this active damping, it
can be compensated by means of an inverse transform function method. Together with this compensation, the z scanner
can operate from dc up to a high frequency that exceeds its
first resonance frequency, without considerable phase delay.
II. EXPERIMENTS
A. Apparatus

The home-made high-speed AFM apparatus used here isbasically the same as reported previously.7 The z scanner has
76, 053708-1© 2005 American Institute of Physics

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Kodera, Yamashita, and Ando

two piezoactuators placed in the opposite direction to one
another. The z piezoactuators are replaced with customized
stack piezoactuators 共3 ⫻ 3 ⫻ 3 mm3, NEC-Tokin, Tokyo兲
with the self-resonance frequency of 420 kHz and a maximum displacement of 900 nm 共at 100 V兲. A sample stage,
which is a glass of a circular-trapezoid shape with a small
top surface of 1 mm diameter, is attached onto the top of oneof the z actuators via a thin layer of vacuum grease. To
maintain balance, a dummy stage that has the same mass as
the sample stage is attached to the other z piezoactuator. The
amplifier 共M-2331, Mess-Tek. Corp., Saitama, Japan兲 candrive the z piezoactuator 共22 nF兲 at up to 1 MHz. A cantilever tip is in contact with the sample stage surface in order tomonitor displacement of the z actuator. The cantilever is immersed in water, to overcome the problem of the slow response in air due to the high Q value 共⬃200兲. The cantileverdeflection is detected with an optical system whose design
was reported previously.7 These cantilevers are recently developed ones from Olympus; the resonant frequency is⬃800 kHz in water, and the spring constant is⬃100 pN/ nm.10 The cantilever tip is further extended byelectron beam deposition. The open-loop transfer functionsof the z scanner and the entire closed loop transfer functions
are measured with a frequency analyzer 共FRA-5096, NF
Corp., Yokohama兲. Since the resonance frequency of the cantilever is approximately 800 kHz in water, reliable measurements of displacement of the z scanner are limited to frequencies less than ⬃500 kHz.
B. Active damping of z piezovibrations

The open-loop transfer function of the z scanner is represented by curves 共a兲 in Fig. 1. A resonant peak appears
around 150 kHz, with Q = 18. A tiny bump in the gain whichappears around 50 kHz is due to structural resonance of the z
scanner. Without counter-balancing 关curves 共b兲兴, it appears
with a much larger amplitude. Active Q control of cantilevervibration has recently been used for various purposes, suchas sensitizing the tip-sample interaction by increasing Q,11,12
or enhancing the cantilever’s response speed by decreasing
Q.13,14 This technique can be applied to any resonant system.
The output signal from the resonant system to be controlled
is phase shifted by ±90°, and its gain-controlled signal isadded to the signal that drives the system. This addition results in a change in the apparent viscous drag force, andhence enhances or reduces the system’s Q. When this technique is applied to the z actuators, it is necessary to detect thedisplacement of the z actuators, which is not easy to do.
The mechanical response of the z actuators is well approximated by a second-order transfer function
Gpiezo共s兲 =K␻2p
s2 + 共␻ p/Q p兲s + ␻2p,

共1兲

where ␻ p = 2␲ f p, f p is the resonance frequency of the z piezo,
Q p is the quality factor of the z piezo’s resonant vibration,
and K is the ratio of the static displacement to the voltage
applied to the piezo. The input–output relationship is determined only by the transfer function, and is independent of
the other physical properties. Therefore, instead of monitor-

FIG. 1. Open loop transfer functions of the z scanner. 共a兲 Without active
damping and with counter balancing, 共b兲 without active damping andcounter balancing, and 共c兲 with active damping and counter balancing.

ing displacements of the each z piezoactuator, it is possible
to monitor output signals from a resonant system 共“mock” zactuator兲 which is characterized with the same transfer function as that of the z piezo-actuator. We constructed the mockactuator from a LCR circuit that was tuned to have 1 / 冑LC= ␻ p and 冑L / R2C = Q p. The resonance frequency and Q were
adjusted with a variable capacitor and a variable resistor,
respectively. Figure 2 is the block diagram that was used in
the active damping control design. The driving signal
关proportional-integral-differential 共PID兲 output when operated with a feedback loop兴 was branched into two signals tocontrol separately the z piezo for the sample stage displacement and the z⬘ piezo for the counterbalancing. The output
signals from the mock z and z⬘ actuators were phase shiftedby −90° to reduce their Q values, which eventually reduced
the natural Q values 共=18兲 of the real z and z⬘ piezoactuators down to 1 / 2. As shown in Fig. 1 关curve 共c兲 in theupper panel兴, the resonance completely disappeared as a result of this active damping. In addition, the transient response speed of the z scanner was markedly increased, as
shown in Fig. 3. In this measurement, the z scanner wasstarted at t = 150 ␮s, driven by sinusoidal ac signals with afrequency of 150 kHz. Without active damping 关Fig. 3共a兲兴,the z scanner responded slowly with a settling time of about
38 ␮s, while with active damping 关Fig. 3共b兲兴 it responded
very quickly with a settling time of about 1.1 ␮s. These settling times 共␶兲 coincided with the expectation derived fromthe relationship of ␶ = Q / ␲ f p.
C. Inverse transfer function compensation

However, a drawback is that the phase delay became
pronounced as shown in Fig. 1 共lower panel兲; the frequency

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Rev. Sci. Instrum. 76, 053708 共2005兲

Actively damped AFM scanner

FIG. 2. Schematic diagram for the active damping control. The input signal
is the output from the PID controller,
when the feedback operation is made.
The z and z⬘ piezoactuators are separately controlled. When the phasecompensation is made, the circuits ofone PD or two PDs in series with
notch filters in series 共for removing
noise with frequencies higher than
1 MHz兲 are placed just after the input
signal.

that gives a 45° phase delay was lowered from
132 to 51 kHz. At Q = 1 / 2, the transfer function 关Eq. 共1兲兴
becomesGpiezo共s兲 =K.
共1 + s/␻ p兲2

共2兲

Therefore, the phase delay can be compensated with an inverse transfer function, i.e.,
G共s兲 = K⬘共1 + s/␻ p兲2 .

共3兲This inverse transfer function can be constructed by two PD
controllers in series, one of which can be left to the original
PID controller when operated in the closed feedback loop.

FIG. 3. Effect of active damping on the transient response of the z scanner.
In 共a兲, the z scanner has its natural Q共=18兲, while in 共b兲 the z scanner isactively damped so that its Q is reduced to 0.5. The z scanner began to be
oscillated at t = 150 ␮s by ac signals 共lines “1”兲 of 150 kHz. The amplitudeof the ac input signals was attenuated when operated without active damping. The enveloping curves 共gray lines兲 of the z scanner’s displacements
共lines “2”兲 indicate the transient changes in the amplitude of the z-scanner’s
oscillation.

Figure 4 shows the compensation effect of the two PD controllers in series. As a result of the compensation the frequency at the 45° phase delay is extended from51 to 131 kHz, and the gain became nearly even at up to
180 kHz. However, because the phase compensation increases the gain in proportion to the frequency, higher-orderresonant vibrations were increased. We solved this problem
using additional active damping controllers with mock actuators having small Q’s to suppress vibrations at the higher
frequencies 共⬍1 MHz兲. The remaining high-frequency noise
共⬎1 MHz兲 that enters the piezodrive amplifier was removed
by notch filters in series. Because the frequency band eliminated by the notch filters is far from the first resonant frequency of the real piezoactuators, the phase delay around thefirst resonant frequency was not significantly promoted by
the filters. Figure 5 compares the whole closed-loop transfer
functions of the z scanner with and without the active damping. In this measurement the set-point voltage of the PID
circuit was varied by means of sinusoidal signals, and the

FIG. 4. Open-loop transfer functions of the actively damped z scanner obtained without phase compensation 共a兲 and with phase compensation 共b兲.

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Kodera, Yamashita, and AndoRev. Sci. Instrum. 76, 053708 共2005兲

FIG. 5. Closed-loop transfer functions. While the set point of the PID controller is being perturbed, the cantilever deflection is monitored. The transfer
functions are obtained with active damping and phase compensation 共a兲,with active damping without phase compensation 共b兲, and without active
damping 共c兲.

resulting cantilever deflection signals were monitored. In
each measurement of the transfer function, the parameters of
the PID controller were adjusted to achieve the best feedback
condition. The feedback bandwidth 共defined as the frequency
at the 45° phase delay兲 was 7 kHz without the active damping. With active damping, the bandwidth was increased to
29 kHz, and increased further to 50 kHz with the additional
effect of the phase compensation with one PD controller.
Figure 6 depicts the difference in the feedback bandwidths.
The pseudo-AFM images 关Figs. 6共a兲 and 6共c兲兴 were constructed from the cantilever’s deflection signals that responded to the rectangular variations of the set-point level
共corresponding to a 50 nm height change兲. Figures 6共b兲 and6共d兲 show the image profiles along the time axis, together
with the input rectangular signals. Without active damping
the response was very slow, so that the rectangular shape waslargely distorted. With active damping and phase compensation, the input rectangular signals were well restored in the
cantilever’s deflection signals.

FIG. 6. Response of cantilever deflection signal to rectangular variations of
the set point of the PID controller. The upper panels 共a兲, 共b兲 are obtained
without active damping of the z-scanner vibrations, while the lower panels
共c兲, 共d兲 are obtained with active damping. In 共a兲 and 共c兲, pseudo-AFM images constructed from the cantilever deflection signals are shown. In 共b兲 and共d兲, cantilever deflection signals 共lines “1”兲 are shown, together with therectangular perturbation signals 共lines “2”兲.

D. Imaging of myosin V in solution

The better performance of the actively damped z scanner
was further demonstrated by images of a real soft sample
共myosin V molecules兲 being captured. The sample was prepared in the same way as described before.7 Figure 7 shows
images captured successively at 21 frames/ s, with the scansize of 240 nm.17 Although it is hard to see from the six
successive still images of Fig. 7, rapid Brownian movementof the coiled-coil tail region and the tail end was clearly seen

FIG. 7. Successive images of myosin V on mica in buffer solution. The
same area of 240⫻ 240 nm2 was imaged 300 times with 100⫻ 100 pixels.
Only six successive images are shown. The tip speed is 1 mm/ s, and theframe rate is 21/ s. A typical “Y shaped” myosin V molecule is circled in thefirst image.

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053708-5

Rev. Sci. Instrum. 76, 053708 共2005兲

Actively damped AFM scannerwith noises less than those appeared in the images taken
before 共see Fig. 5 in Ref. 7兲. Compared with the extensive
improvement of the z scanner, the imaging rate could not beenhanced greatly 共only about 1.7 times兲. A higher imaging
rate resulted in the appearance of large periodic noises due tothe mechanical vibrations of the sample stage, and in occasional detachment of the cantilever tip from the sample surface. This is because the other elements such as the x scanner, cantilevers, and electric devices are not improved yet.
III. DISCUSSION

High-speed AFM imaging has been long sought, especially in the biological sciences, to allow study of the dynamic behavior of biological macromolecules at work. The
most problematical device in the quest for fast imaging has
proven to be the z scanner. The resonant vibrations in the z
direction that derive from the scanner’s overall structure canbe erased by the counterbalancing method.7 Therefore, an
improvement that remains to be made is to increase the resonant frequency of the z piezoactuator itself. However, thecurrently available piezoactuators are quite limited. To overcome this obstacle, an active damping system with mockactuators was developed. This is quite a simple system compared to the systems in which displacements of the realpiezo-actuators are directly monitored by methods such as
capacitance detection or optical detection. Electric charges
supplied to the piezo-actuator as well as electric charges induced on the piezoend surfaces are supposed to be proportional to the piezo displacement.15,16 These charges can bemeasured by a charge amplifier. Similar to the method wedeveloped here, this method has the advantage that the mechanical design of the scanner does not need to be changed.
However, the piezo-actuator as a capacitor couples electrically with the inductor and resistor elements of the actuator,
and they form an electrically resonant system. This resonant
frequency is usually higher than the mechanical resonant frequency. However, when these frequencies are not markedly
different, the charge measurement 共as an index of the piezodisplacement兲 is disturbed by the electrical resonance.
The z scanner has generally been recognized as the slowest device among those involved in the feedback loop in thetapping mode of the AFM operation. Here, we have found a
way to successfully overcome this issue. The bandwidth of
the z scanner now reaches 131 kHz. When a cantilever tip is
scanning in the x direction over a sample with a periodicityof ␭ at a speed of Vs, the cantilever oscillation amplitude ismodulated at a frequency of f m共=Vs / ␭兲. Therefore, the z
scanner has to move at f m. From this relationship, the wide
bandwidth 共131 kHz兲 achieves scan speeds of up to
1.3 mm/ s for samples with an apparent feature of 10 nm.
The z scanner is not the slowest device any longer. Whichdevice is now the slowest one? We think that it is the cantilevers. In the tapping mode AFM, the bandwidth of thewhole feedback loop cannot exceed one eighth of the cantilever resonant frequency 共f c兲 in water. Even when the cantilever oscillation amplitude is read at the fastest speed 共as wehave done in practice兲, i.e., at every period of the oscillation,
this reading results in a phase delay of 360° ⫻ f m / f c, over theamplitude modulation. This phase delay should not exceed
45°, and hence f m cannot exceed f c / 8. This means that the
feedback bandwidth will never be able to exceed f c / 8. The
resonant frequency of our tiny cantilevers is about 800 kHz
in water, and hence the whole feedback bandwidth cannot
exceed 100 kHz, which is narrower than that of the z scanner.
ACKNOWLEDGMENTS

This work was supported by CREST/JST, Special Coordination Funds for Promoting Science and Technology 共Effective Promotion of Joint Research with Industry, Academia
and Government兲 from JST, and Grant-in-Aid for Basic Research 共S兲 from the Ministry of Education, Sports, Scienceand Technology of Japan.
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See movies placed at the website of www.s.kanazawa-u.ac.jp/phys/biophys/rsi.htm

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