REVIEW OF SCIENTIFIC INSTRUMENTS 78, 083702 共2007兲

Tip-sample distance control using photothermal actuation of a smallcantilever for high-speed atomic force microscopy
Hayato Yamashita,a兲 Noriyuki Kodera, and Atsushi Miyagi
Department of Physics, Kanazawa University, Kakuma-machi, Kanazawa 920-1192, Japan

Takayuki Uchihashi, Daisuke Yamamoto, and Toshio Ando
Department of Physics, Kanazawa University, Kakuma-machi, Kanazawa 920-1192, Japan and CREST, JST,
4-1-8 Honcho Kawaguchi, Saitama 332-0012, Japan

共Received 12 April 2007; accepted 2 July 2007; published online 10 August 2007兲
We have applied photothermal bending of a cantilever induced by an intensity-modulated infraredlaser to control the tip-surface distance in atomic force microscopy. The slow response of thephotothermal expansion effect is eliminated by inverse transfer function compensation. By
regulating the laser power and regulating the cantilever deflection, the tip-sample distance iscontrolled; this enables much faster imaging than that in the conventional piezoactuator-based z
scanners because of the considerably higher resonant frequency of small cantilevers. Using thiscontrol together with other devices optimized for high-speed scanning, video-rate imaging of protein
molecules in liquids is achieved. © 2007 American Institute of Physics. 关DOI: 10.1063/1.2766825兴

I. INTRODUCTION

Atomic force microscopy 共AFM兲 has the unique capability to image biomolecules under physiological conditions at
a high spatial resolution.1,2 If the imaging rate of the AFM isenhanced significantly, this unique capability will become
more useful in biological sciences because it enables us topractically observe the dynamic behavior of biological macromolecules. Therefore, various efforts have been made toincrease the scan speed.3–11 In addition, some efforts havebeen made to reduce the tip-sample interaction force without
reducing the scan speed in the tapping mode.10 Owing tothese efforts, the feedback bandwidth has increased to approximately 70 kHz, thereby enabling the capture of moving
protein molecules on video at ⬃48 ms/frame for a scan
range of ⬃240 nm without damaging them.8,10
To widen the scope of biological systems whose dynamic behaviors can be studied by high-speed AFM, efforts
toward further enhancement of the imaging rate are required.
Among the various modes, tapping mode operates most gently on biological samples. This is because, in this mode, theoscillating tip exerts very small lateral forces onto the sample
as long as the feedback bandwidth is sufficiently high tofacilitate the tip to accurately trace the sample topography.12
However, the feedback bandwidth is limited by various factors. The slowest device in the feedback loop is the z scanner
because the capacity of the available piezoactuators is limited. The response speed of the z scanner is approximately
expressed by ␲ f s / Qs, where Qs and f s are the quality factor
and resonant frequency of the z scanner, respectively. Although Qs can be reduced to 0.5 by an active damping
technique,8 f s is almost determined by the required maximum displacement and hardly exceeds ⬃200 kHz in practice.
a兲Electronic mail: yhayato@stu.kanazawa-u.ac.jp0034-6748/2007/78共8兲/083702/5/$23.00

In order to overcome this problem, instead of a conventional piezoactuator-based z scanner, a cantilever deflection
can be used to control the tip-sample distance because it iseasier to increase the resonant frequency of the cantileverthan that of the piezoelectric actuator. One possible technique is the magnetic actuation of a cantilever.13 However,when the cantilever is coated with a magnetic material, its
resonant frequency reduces and it also becomes stiff, whichis inappropriate for high-speed imaging on biologicalsamples. Another possible technique is to actuate the cantilever by laser illumination onto the cantilever. There are several reports in which an intensity-modulated laser beam isirradiated onto a cantilever for actuation.14–17 This actuation
is based either on the irradiation pressure or on the photothermal expansion with gold-coated cantilevers.15 In liquids,
the latter effect is dominant because of the low quality factor
of cantilevers. Although some studies have employed thephotothermal effect for exciting resonant vibrations in cantilevers, this effect has never been used in controlling the tipsample distance. This is because of the slow response of thephotothermal bending of cantilevers due to the slow heattransmission.16 In this study, we have solved this problem byusing an inverse transfer function compensation.
II. EXPERIMENTS
A. Apparatus

The in-house developed high-speed AFM apparatus usedin this study is basically the same as that reported
previously.4 The optical beam deflection method optimized
for small cantilevers was used. In order to detect the cantilever deflection and drive the cantilever simultaneously, we
implemented a 980 nm IR laser as well as a 675 nm redlaser, as shown in Fig. 1. Beams from the red and IR lasers
were introduced into a ⫻20 objective lens and focused ontoa small cantilever with a length of 6 – 7 ␮m, width of 2 ␮m,

78, 083702-1© 2007 American Institute of Physics

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Yamashita et al.

FIG. 1. 共Color online兲 AFM with two laser beams of different wavelengths.
Schematic diagram for the optical system of the AFM. The linearly polarized beams from a red laser diode 共675 nm兲 or an IR laser diode 共980 nm兲
are collimated by the respective collimation lenses 共i-1, i-2兲, passed throughthe respective polarization splitters 共ii-1, ii-2兲, and circularly polarized by
the respective ␭ / 4 wave plates 共iii-1, iii-2兲; then, they enter an objective lens
共v兲 after being reflected by or transmitted through a dichroic mirror 共iv-1,
iv-2兲. The beams reflected back by a small cantilever are separated by thesame dichroic mirror 共iv-1兲. The reflected red laser beam is guided into a
split photodiode through the polarization splitter 共ii-1兲, a band-pass filter
共vi兲, and a spherical planoconvex lens 共vii兲.

and thickness of 90 nm 共resonant frequency: ⬃1.2 MHz inwater; spring constant: ⬃0.2 N / m兲. The backside of the cantilever is coated with gold of thickness less than 20 nm. The
irradiation position of the IR laser onto the cantilever was
adjusted so that maximum cantilever deflection was attained.
An optical band-pass filter with 97% transmission at 675 nm
and 3 ⫻ 10−4% transmission at 980 nm was positioned in
front of the deflection sensor to prevent the interference of
the IR laser with the deflection sensing of the red laser. The
power of the IR laser was modulated using a laser driver
共ALP-6133LA, Asahi data systems, Kanagawa, Japan兲 that is
capable of modulating the laser power up to 200 mW with afrequency in the range of 0 – 10 MHz. However, the maximum laser power illuminated was reduced down to approximately 100 mW after the IR laser beam passed through theobjective lens because the IR laser beam was partly eclipsed
at the objective lens inlet. When the gold-coated surface ofthe cantilever is illuminated, the light absorption induces abimetal action due to heating; this in turn causes the cantilever to bend away from the light source because gold has agreater heat-expansion coefficient than silicon nitride. Figure
2 shows the cantilever displacement as a function of the laser
power. The cantilever bends in proportion to the dc powerchange to approximately 60 nm. The laser power indicated inFig. 2 is not the one actually absorbed by the cantilever butthat measured at the exit of the objective lens. The lightabsorption by gold at 980 nm is very small and the spot sizeof the IR laser focused onto the cantilever is about two times
greater than the cantilever width. Therefore, the absorbed
power should be much smaller than that indicated in Fig. 2.
The effective displacement efficiency was 1.1 nm/ mW.

FIG. 2. DC displacement of the cantilever as a function of the IR laser
power.

and phase responses 共solid lines兲 is already significant
around 10 kHz, which is not consistent with the theoreticalcurves 共dotted lines兲 for the harmonic oscillator. This is because the temperature variation at the illuminated position
and the thermal diffusion length decrease as the modulation
frequency increases.16 In order to utilize the optically driven
bending of the cantilever for a faster control of the tipsample distance, it is essential to eliminate the response delay in the photothermal effect. This can be accomplished byinverse transfer function compensation.18 The time-domain
response of the cantilever to the laser power modulation witha rectangular wave is shown in Fig. 3共b兲. The cantilever response can be well fitted by a double-exponential function
using time constants of 8.4 and 123 ␮s as drawn by a solidline in Fig. 3共b兲. Therefore, the transfer function G共s兲 of thephotothermal response of the cantilever is approximately expressed as G共s兲 = A / 共1 + s / ␻1兲 + B / 共1 + s / ␻2兲 共A + B = 1兲. The
equivalent circuit with the transfer function G共s兲 is the parallel connection of two low-pass filters with time constantsof 1 / ␻1 and 1 / ␻2. We created the inverse transfer function
1 / G共s兲 by using the circuit shown in Fig. 4.18 In Fig. 4共a兲,
G共s兲 represents the equivalent circuit for the photothermal
response of the cantilever. The transfer function M共s兲 of thiscircuit is expressed by M共s兲 = 1 / 关1 + g共G共s兲 − 1兲兴. In the caseof g = 1, a complete inverse transfer function 关i.e., M共s兲
= 1 / G共s兲兴 can be realized. However, in practice there aresome delays in the electronic components such as operational amplifiers. Therefore, the gain factor g should be lessthan 1, and as a result, the complete inverse transfer function
cannot be realized. In order to improve the incomplete inverse transfer function, we used a double loop circuit, asshown in Fig. 4共b兲. Figure 5 shows the frequency spectra of
the cantilever optically actuated under the inverse transfer
function compensation. The gain response is consistent withthe theoretical curve even at the resonant frequency. The
phase signal is delayed at frequencies higher than 400 kHz
because of incomplete compensation. However, the frequency that yields a 45° phase delay is about 700 kHz,
which is approximately five times higher than that of ourpiezoactuator-based z scanner.8

B. Inverse transfer function compensation

Figure 3共a兲 shows the frequency spectra of the cantilever
oscillation induced by the photothermal actuation in water. It
should be noted that the decrease in both the measured gain

C. Feedback bandwidth

The feedback performance of our tapping-mode AFM
with a photothermally driven cantilever was evaluated.

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Rev. Sci. Instrum. 78, 083702 共2007兲

FIG. 4. Block diagrams of delay compensation circuits with a single loop
共a兲 and a double loop 共b兲.

achieve the best feedback condition. Figure 6 shows aclosed-loop transfer function with the cantilever actuation.
The feedback bandwidth, which is defined as the frequency
that yields 45° phase delay, was approximately 100 kHz as
indicated in Fig. 6 共dotted line兲. This value is higher by afactor of 1.4 in comparison to the tip-sample distance control
by our piezoactuator-based z scanner.8 Here, although thegain response shows peaks around 100 and 500 kHz, thegain values at the peaks are less than 3 dB, which is the

FIG. 3. 共Color online兲 共a兲 Frequency spectra of the gain 共upper兲 and phase
共lower兲 for a small cantilever excited by the intensity-modulated IR laser
共solid lines兲 and theoretical frequency spectra for harmonic oscillation 共dotted lines兲. The cantilever amplitude was 10nmp-p. 共b兲 The time-domain
response of the cantilever displacement driven by the laser modulatedwith a rectangular wave. The response shown with dots is fitted by adouble-exponential-function curve 共solid line兲, ␣关1 − exp共−t / ␶1兲兴+ ␤关1 − exp共−t / ␶2兲兴 with time constants of ␶1 ⬃ 8.4 ␮s and ␶2 ⬃ 123 ␮s.

Herein, a small cantilever was oscillated using a piezoactuator at its resonant frequency of 1.2 MHz in water 共Q = 3兲,with a free oscillation amplitude of 5 nm. The tip was intermittently contacted with a mica surface in water, with anaverage amplitude of 3 nm. The cantilever deflection was
modulated by sinusoidal signals, and the output signals fromthe proportional-integral-differential 共PID兲 circuit weremonitored for the closed loop. Here, the modulation frequencies are much lower than the cantilever resonant frequency.
The parameters of the PID controller were adjusted to

FIG. 5. 共Color online兲 Frequency spectra of the gain 共upper兲 and phase
共lower兲 for a small cantilever excited by the intensity-modulated IR laser
with delay compensation and theoretical frequency spectra for harmonic
oscillation 共dotted lines兲.

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Rev. Sci. Instrum. 78, 083702 共2007兲

FIG. 7. 共Color online兲 AFM images of actin filaments gliding on myosin V
under the laser excitation. The images were acquired at 970 ms/frame but
showed every five frames 共as shown by lower number兲. The scan area andpixel size are 800⫻ 800 nm2 and 200 pixel2, respectively. The ends of theactin filament gliding are indicated by open circles.

FIG. 6. 共Color online兲 Frequency spectra of the closed-loop transfer function for the cantilever actuation. While the tip was intermittently contacted
the surface and then the cantilever deflection was modulated by sinusoidal
signals, the output signals from the PID circuit were monitored for theclosed loop. The feedback bandwidth was defined at the frequency with the
45° phase delay.

tolerance for the AFM feedback condition.8 The feedback
bandwidth of 100 kHz is expected to achieve a video-rate
共33 ms/frame兲 imaging because an imaging rate of
48 ms/frame was previously achieved with a feedback bandwidth of 70 kHz.8,10
III. IMAGING OF BIOLOGICAL MOLECULESThe increase in temperature of the cantilever and theirradiation of the intense laser light onto the biologicalsamples may damage the proteins. In fact, we had previously
observed that a violet laser 共405 nm兲 irradiation denatured
proteins such as myosin V and actin filaments. On the other
hand, the IR laser is widely used for optical trapping technique to manipulate biological molecules.19 In the opticaltrapping system, the IR laser with power higher than
100 mW is usually used and still biological molecules are
not significantly denatured.20 Liu et al. have reported that thetemperature rise of a lipid directly irradiated by the IR laser
with 100 mW and a focused spot size of 0.8 ␮m in water
is about 1.5 ° C.21 In our system, the spot size is larger
共⬎1 ␮m兲 for 100 mW and most of the laser illuminates thecantilever, which is separated from the surface about 1 ␮m.
Therefore it is expected that the IR laser does not rise sample
temperature so much. In fact, obvious structural alterationsof proteins were not observed when an IR laser was used.
Fig. 7 shows the gliding movement of actin filaments over a
myosin V-coated surface22 in the presence of adenosine
triphosphate 共ATP兲. The focused IR laser with a power of
100 mW was irradiated onto the small cantilever while imaging. Figs. 7共a兲–7共c兲 are shown every five frames for theimages obtained at 970 ms/frame. One can see actin filaments gliding on the substrate; the ends of the actin filamentgliding are highlighted by open circles. Also, apparent structural damage of myosin V under the IR laser irradiation was
not seen as described later. From this result, we can conclude
that the IR laser beam does not significantly damage theactivities of the proteins under the optical configuration usedin the AFM observation.
Figure 8 compares the imaging performance by the photothermal control of the tip-sample distance with that in ourpiezoactuator-based z scanner8 by using a soft sample 共myosin V molecules兲. The scan speed was set to attain
31 ms/frame for a 240 nm scan range and 100 scan lines.
The sample was prepared in the same manner as described
before.23 Figures 8共a兲 and 8共b兲 show the AFM images obtained using the photothermally driven cantilever. In theseimages, a typical myosin V structure having two heads followed first by long neck regions and then by a coiled-coil tailis evident. Even after approximately 7 s 共i.e., after imaging
233 times兲, no significant structural damages are visible, as
shown in Fig. 8共b兲. On the other hand, by using thepiezoactuator-based z scanner to control the tip-sample distance, the spatial resolution of the image is obviously deteriorated. Moreover, the myosin V molecules are disrupted
due to the very strong tip force caused by the insufficient

FIG. 8. 共Color兲 AFM images of myosin V on mica in a buffer solution
obtained by photothermally driving the cantilever 关共a兲 and 共b兲兴 or by using a
piezoactuator-based z scanner 关共c兲 and 共d兲兴. The scan area is 240⫻ 240 nm2. The frame rate was 31 ms/frame for all the images. Images 共a兲
and 共c兲 are taken at the beginning of imaging and images 共b兲 and 共d兲 aretaken at around 7 and 3 s, respectively.

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083702-5

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feedback bandwidth, as shown in Fig. 8共c兲. Furthermore, after a few seconds, the myosin V molecules are aggregated, as
shown in Fig. 8共d兲.
IV. DISCUSSION

We have presented a novel technique to control the tipsample distance by utilizing the photothermal bending of thecantilever. By characterizing the transfer function of the photothermal response of the cantilever and composing a circuitwith the inverse transfer function of the delay of the photothermal bending, we eliminated the slow photothermal response of the cantilever motion. By using this technique, we
succeeded in the video-rate imaging of myosin V molecules
without damaging them. This technique can easily increase
the feedback bandwidth in AFM without modifying the cantilever and piezoelectric actuator. At the moment such highfeedback bandwidth cannot be achieved by using a piezoelectric actuator although the fast feedback control is essential in tracing precise surface topography and realizing noninvasive imaging on biological samples. A drawback of thismethod may be the limitation of the maximum deflection of
the cantilever 共⬃100 nm兲 due to the small deflection efficiency 共1.1 nm/ mW兲 for the low frequency 共⬍1 kHz兲 powerchange and the maximum power 共100 mW兲 of the IR laser
used. At the moment, the maximum actuation range is about
34 nm for the sample with the spatial frequency less than
100 kHz, which is the limited feedback bandwidth, because
one needs about three times power to compensate the gain
reduction of 10 dB at the frequency of 100 kHz from Fig.
3共a兲. This can be improved by combining a piezoelectric
actuator that operates only for a low-frequency topography
or by using an IR laser with a higher power. Although the
bandwidth for the open loop transfer function is five times
higher than that for our piezoactuator-based z scanner,8 thefeedback bandwidth did not improve as much as expectedfrom the bandwidth of the “cantilever scanner”. This is because the quality factor of the cantilever is approximately 3
in water, while the quality factor of the piezoelectric actuatoris reduced to approximately 0.5 when the active damping
technique is used.8 By reducing the quality factor of the cantilever with an active Q-control method, faster imaging beyond the video rate could be achieved in the near future.

ACKNOWLEDGMENTS

This work was supported by CREST/JST and industrial
technology research grant program in 2004 from New Energy and Industrial Technology Development Organization
共NEDO兲 and the Ministry of Education, Science, Sports andCulture, Grant-in-Aid for Young Scientists 共B兲, 17710095,
2005.
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