Hierarchical spiral-scan trajectory for efficient scanning ion conductance microscopy

doi:10.1016/j.micron.2019.102683

Micron

Volume 123, August 2019, 102683

https://doi.org/10.1016/j.micron.2019.102683 Get rights and content

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Highlights

•
A novel SICM scanning approach is proposed to effectively reduce the retract distance of conventional scanning modes.
•
The spiral trajectory is used in this approach to rapidly detect the highest point of the sample in a layer-by-layer way.
•
Theoretical imaging time and various factors that affect the imaging speed in the new method are analyzed, respectively.
•
PDMS and cell samples were imaged by developed method, hopping mode and raster-based detecting, respectively.

Abstract

Scanning ion conductance microscopy (SICM) is an emerging technique for non-contact, high-resolution topography imaging, especially suitable for live cells investigation in a physiological environment. Despite its rapid development, the extended acquisition time issues of its typical hopping/backstep scanning mode still restrict its application for more fields. Herein, we propose a novel SICM scanning approach to effectively reduce the retract distance of existing hopping/backstep mode. In this approach, the SICM probe first gradually descends in the z-direction. Then by using Archimedes spiral trajectory, which has the advantage of higher angular velocity due to its continuous and smooth trajectory, the probe rapidly detects the highest point of the sample in the xy-plane in a layer-by-layer way. Further, the maximum height that decides the retrace distance of pipet in the detected region can be quickly achieved, avoiding a huge retrace distance usually adopted in the existing methods without any prior knowledge (sample height and steepness in the scanning region). Therefore, this new scanning method can greatly reduce the imaging time by minimizing the retrace height of each measurement point. Theoretical analysis is conducted to compare the imaging time of traditional and new method. And various factors in the new method that affect the imaging speed are analyzed. In addition, PDMS (polydimethylsiloxane) and biological samples (C2C12 cells) were imaged by SICM that was operated in the hopping mode, raster-based detecting and developed method with a single-barrel pipet, respectively. The experimental results suggest that the new method has a faster imaging speed than conventional scanning modes but does not sacrifice the imaging quality.

Keywords

Scanning ion-conductance microscopy (SICM)

Spiral-scan trajectory

Raster trajectory

Detecting the highest point

Imaging rate

1. Introduction

Scanning ion conductance microscopy (SICM), introduced by Hansma et al. (1989) in 1989 and then developed by Korchev et al. (1997a); Korchev et al. (1997b), has become a powerful scanning imaging tool at the micro and nanoscale. SICM employed an electrolyte-filled nanopipette as the scanning probe and its opening radius of the tip can down to nanometer level, which ensures the high-resolution imaging. An ion current can be induced through the opening of the tip by an applied voltage between an electrode in bulk solution and an electrode in pipet. When the pipet approaches the surface and the tip-surface distance reduces to one tip diameter, the decreased ion current can be utilized as the feedback signal to accurately position the pipet in the vertical direction and then reconstruct the surface topography. Based on this non-contact nature, the SICM has been applied in many fields, such as imaging living cells and electrochemical information (electrochemical activity (ion fluxes)) (Page et al., 2017; Momotenko et al., 2016).

Despite the wide application of the SICM, the extended acquisition time issues still restrict its dynamical study of biological samples such as live cells and tissues. There are several alternated imaging modes in SICM, for instance, direct current (DC) scanning mode (Hansma et al., 1989; Korchev et al., 1997a), alternate current modulation (AC) mode with or without physical oscillation of the probe (Proksch et al., 1996; Pastré et al., 2001; Li et al., 2008; McKelvey et al., 2014). To further enhance the imaging capability and stability, research groups have developed hopping/backstep (Novak et al., 2009; Happel and Dietzel, 2009), standing approach modes (Takahashi et al., 2010), etc. The scanning speed of those modes (typically hopping mode) in SICM is impacted by several factors, including approach rate (Novak et al., 2014; Jung et al., 2015; Zhuang et al., 2018a; Watanabe and Ando, 2017), retract distance (determined by the complexity of the surface) (Zhukov et al., 2012; Ida et al., 2017; Zhuang et al., 2017), imaging pixels, etc. The retract distance of probe in the z-direction considerably depends on the sample height and steepness. This is generally unknown in advance, and setting an optimal retract distance that decides the SICM scan time is becoming a crucial issue. Although the pre-scanning approach (Novak et al., 2009) can acquire a low-resolution image and thus provide an optimized retract distance and scan pixels. This two-stage approach is time-consuming and easily loses essential features in its pre-scanning. By considering the predictive capability of tip during its lateral movement across the sample, the SICM can obtain smaller retract distances in their hopping mode (Zhuang et al., 2017). However, this prediction-based method is not suitable for a complex surface. A horizontal fast detecting approach is first adopted to detect the highest point of the sample in each scanning line and thereby a smaller retract distance is achieved (Zhuang et al., 2018b). However, this repetitive move-stop-detect routine is a raster scan-based approach. Therefore, its detecting frequency is limited to 1%–10% of the resonance frequency of the scanner (Yong et al., 2012).

In the conventional scanning modes, the raster scanning method is often employed to collect topography data in a grid in a pixel-by-pixel manner. One lateral axis in the xy-scanner moves back and forth and another axis moves progressively with small step. This raster-based scan method can be easily implemented and has been applied in majority microscopy technique. For the highest point detection based hopping mode (Zhuang et al., 2018b), however, during its detecting procedure with raster trajectory, the abrupt change of detecting direction at the corners can easily result in sample drift, slowing down the detecting speed. To facilitate high-speed detecting the highest point of the sample, various non-raster scan trajectories generated by single-frequency waveforms, including lissajous (Bazaei et al., 2012), spiral (Bazaei et al., 2017; Mahmood et al., 2011; Rana et al., 2014) spirograph (Meyer et al., 2014; Nikooienejad et al., 2018) and cycloid trajectories (Yong et al., 2010) can be used. These trajectories can effectively increase the probe translation rates in the xy-plane. Unlike other non-raster trajectories, the spiral trajectory can progressively cover new sample areas and easily change defined spacing between successive trajectory lines (Bazaei et al., 2017). This trajectory are generated by two sinusoidal waveforms with time-varying amplitudes and identical frequencies, but 90^o phase difference in two axes of the scanner. It is highly suitable for detecting the highest point of the sample in a layer-by-layer way. In this spiral-based detecting trajectory, the distance between two successive spiral lines and descend step of tip in the z-direction should be considered carefully. Those parameters decide the operational efficiency of this trajectory. Recently, several studies (Edwards et al., 2009; Rheinlaender and Schäffer, 2009) have shown that the geometric parameters of the pipet tip have significantly influence on its vertical sensing distance. To maximize this distance, the most straightforward method is to use a pipet with a larger opening radius. However, the larger opening radii tends to reduce its image resolution. Another approach to enhance vertical sensing distance is to use pipet with a larger wall thickness, but it requires to balance the larger wall thickness and its contact-free scanning in the steep sample area (contact between the external surface of the pipet tip and the steep sample area) (Del Linz et al., 2014).

In this study, by employing Archimedes spiral trajectory and single-barrel pipet, we develop a two-stage SICM scanning approach to rapidly detect the highest point of the sample, furthermore effectively reduce the retrace distance of the conventional methods. It can avoid a huge retrace distance that is often artificially set with no any prior knowledge. First, the theoretical analysis of the proposed approach is conducted and then various factors that affect its imaging speed are analyzed. Then, a self-developed SICM system is built that can be operated in an Archimedes spiral trajectory based detecting process. Finally, we compare the imaging quality and rate of SICM that are operated in the conventional scanning modes and the developed approach with various PDMS (Polydimethylsiloxane) and biological samples (C2C12 cells).

2. Theoretical analysis

2.1. Spiral-based detecting trajectory

Two approaches, including constant angular velocity (CAV) and constant linear velocity (CLV) approach, can be utilized to generate a spiral trajectory (Momotenko et al., 2015; Bazaei et al., 2017; Mahmood et al., 2011). For the CLV way, the instant radius and angular velocity are required to vary simultaneously to produce its constant linear velocity. Consequently, the frequency and amplitude of the sinusoidal waveform in the CLV trajectory are varied. Whereas CAV has single frequency waveform with linearly increasing amplitude. And then the angular velocity of the SICM probe can be close to the first resonance frequency of the xy-scanner (Yong et al., 2012). To quickly detect the highest point of the sample, herein we mainly consider the CAV trajectory generated by following signals in the x- and y-axes of the scanner (Fig. 1(a) and (b)):(1)

x = r (t) \cos ω t

(2)

y = r (t) \sin ω t

Where

ω

is the angular velocity.

r (t)

is the instantaneous radius at a time

t

that can be expressed as(3)

r = \frac{P}{2 π} ω t

Where P is the distance between two consecutive intersections of the spiral curve with any line passing through its original (Fig. 1(a)). It can be expressed as(4)

P = \frac{spiral radius \times 2}{number of curves - 1}

Where number of curves is the number of times the spiral curve crossed the line y = 0. The time consumption of the tip moving along this trajectory can be calculated as(5)

t_{t o t a l} = \frac{2 π r_{e n d}}{P ω}

Where r_end is final values of the spiral radius. The CAV spiral trajectory when implemented in the detecting process in SICM, only single-frequency sinusoidal waveforms with slowly varying amplitudes are required to track, which enables the xy-scanner to offer a fast detecting rate for the highest point of the sample.

2.2. Proposed scanning strategy

In the existing scanning modes of SICM, because the highest point of the sample is unknown in advance, a large retrace distance is often adopted to avoid the collisions between tip and surface, slowing down the imaging rate. The pre-scan approach can estimate the maximum height of the sample and then provide a reduced retrace distance, but it is also time-consuming (Novak et al., 2009; Zhukov et al., 2012). Using a larger approach speed of pipet can reduce the acquisition time of each pixel, but the time delay in the vertical tip-position control limits this speed. An alternative way to increase the SICM imaging rate is to drive the pipet tip/sample to move with higher speed in the xy-plane (unobstructed direction). And in which we can use the spiral trajectory that has the advantage of non-repeating, continuous and smooth paths. Herein, we describe our developed detecting strategy based on the spiral trajectory to determine the reduced retrace distance, and thereby to speed up the imaging speed.

Fig. 1 represents the CAV spiral-based detecting and scanning strategy. First, the pipet tip (its coordinates are (x₀, y₀, h₀)) moves from center to boundary along a spiral trajectory with a constant angular velocity ω and defined pitch P (determined by the horizontal sensing capability of tip) (Fig. 1(c)). During this process, if the ion current I_ion does not decrease to a set value I_set, meaning that the tip does not detect the highest point of the sample only by one-time detection (Fig. 1(d)). Then, pipet moves toward the surface vertically, descending a distance Δz, and the pipet will again move along the spiral trajectory but from boundary to center with the identical ω and P values (Fig. 1(c)). This detecting process is performed repeatedly until the current I_ion decreases to I_set, at which time the tip detects the highest point of the sample surface and its coordinates are (x₁, y₁, h₀-kΔz) (see Fig. 1(c), where h₀ - kΔz = h_max, and h_max is the highest height of the sample (Fig. 1(f)). In this detecting procedure, any single-barrel pipet that can provide a larger pitch P and approach step Δz can be employed to detect the highest point of the sample quickly.

After the highest point of the sample has been detected in the circular detected region by a layer-by-layer way, then a minimized retrace distance is set adaptively in this detected circular region. Note that we still use conventional hopping mode to scan this circular region in a pixel-by-pixel manner (Fig. 1(f) and (g), line-by-line).

2.3. Influence factors of imaging speed in the developed detecting approach

Before analyzing the influence factors of this spiral-based fast detecting approach, we compare the scan time of the identical circular regions in the hopping mode and our developed approach. For the hopping mode (Fig. 2(b)), the total scan time with M rows and N(m) pixels in each row can be expressed as follows:(6)

T_{1} = \sum_{m = 1}^{M} \sum_{n = 1}^{N (m)} (\frac{h_{0} - h_{n}^{m}}{v_{z_{1}}} + \frac{h_{0} - h_{n}^{m}}{v_{z_{2}}}) + T_{p 1}

Where

T_{1}

is the total scanning time with a set retracing height h₀ in the z-direction.

h_{n}^{m} (n = 1, 2, 3, ..., N)

is the height of the pipet when its ion current reduces to the set value for the nth pixel.

v_{z_{1}}

and

v_{z_{2}}

are the approach and retract velocity to the sample surface in the z-direction, respectively.

T_{p 1}

is the time required for the sample scanning in the xy-plane. For the new method (Fig. 2(a)), the total scanning time can be expressed as follows:(7)

T_{2} = \frac{h_{0} - h_{m a x}}{Δ z} \cdot \frac{2 π r_{e n d}}{P \cdot ω} + \sum_{m = 1}^{M} \sum_{n = 1}^{N (m)} (\frac{h_{m a x} - h_{n}^{m}}{v_{z_{1}}} + \frac{h_{m a x} - h_{n}^{m}}{v_{z_{2}}}) + T_{p 2}

Where h₀ is the initial height of tip in the z-direction (Fig. 1(f) and (g)). Δz is the approach step of probe towards to sample. r_end is the largest radius of the spiral trajectory (Fig. 1(b)),

ω

is the angular velocity, P is the pitch,

h_{m a x}

is the detected highest point of the sample,

T_{p 2}

is the time required for the sample scanning in the xy-plane, here

T_{p 2} = T_{p 1}

. We subtract Eqs. (7) from (6) to obtain(8)

T_{1} - T_{2} = \sum_{m = 1}^{M} \sum_{n = 1}^{N (m)} (\frac{h_{0} - h_{n}^{m}}{v_{z_{1}}} + \frac{h_{0} - h_{n}^{m}}{v_{z_{2}}}) - \sum_{m = 1}^{M} \sum_{n = 1}^{N (m)} (\frac{h_{m a x} - h_{n}^{m}}{v_{z_{1}}} + \frac{h_{m a x} - h_{n}^{m}}{v_{z_{2}}}) - \frac{h_{0} - h_{m a x}}{Δ z} \cdot \frac{2 π r_{e n d}}{P \cdot ω}

(9)

T_{1} - T_{2} = (\frac{1}{v_{z_{1}}} + \frac{1}{v_{z_{2}}}) (h_{0} - h_{m a x}) [N_{p} - (2 π \cdot \frac{v_{z_{1}} v_{z_{2}}}{v_{z_{1}} + v_{z_{2}}} / P \cdot ω \cdot Δ z) \cdot r_{e n d}]

Where

N_{p}

is the total numbers of imaging pixels in the circular regions, we assume that(10)

β = (2 π \cdot \frac{v_{z_{1}} v_{z_{2}}}{v_{z_{1}} + v_{z_{2}}} / P \cdot ω \cdot Δ z)

For the selected single-barrel pipet (determined P, Δz,

v_{z_{1}}

values) and xy-scanner (maximum

ω

value) in SICM, the value of

β

is determined. In Eq. (10), a smaller

β

can ensure that the imaging rate of the new method is larger than conventional methods. It is affected by the values of P, Δz, ω,

v_{z_{1}}

and

v_{z_{2}}

. The P and Δz values are determined by the sensing capabilities of the selected pipet (determined by its tip geometry). And a pipet with optimal geometry can provide both the larger P and Δz values. The maximum angular velocity ω (

ω = 2 π f

), is determined by xy-scanner and its controller. By utilizing new control algorithm and those xy-scanners with higher resonance frequency (Bazaei et al., 2017; Mahmood et al., 2011), the angular velocity ω can be greatly increased to achieve a faster imaging rate in the new method. The approach velocity

v_{z_{1}}

is limited by the time delay in the vertical tip-position control. The retract velocity

v_{z_{2}}

can be set to a larger value. In summary, at the allowable value of

v_{z_{1}}

and

v_{z_{2}}

, a larger P, Δz and ω reduce the time required in the new method.

To make

T_{1} - T_{2} > 0

, we rewrite the Eq. (9) as follows:(11)

T_{1} - T_{2} = (\frac{1}{v_{z_{1}}} + \frac{1}{v_{z_{2}}}) (h_{0} - h_{m a x}) (N_{p} - β \cdot r_{e n d})

Where

\frac{1}{v_{z_{1}}} + \frac{1}{v_{z_{2}}} > 0

h_{0} - h_{m a x} \geq 0

. We define that(12)

δ = N_{p} - β \cdot r_{e n d}

As described in Eqs. (9), (10), (11), (12), to ensure

δ > 0

(i.e.,

T_{2} < T_{1}

), we should determine the relationship between the values of N_p, β and r_end. For the selected SICM pipet and scanner, here we assume using a pipet with its opening radius r_i of 100 nm, the radio r_o/r_i of 1.5 and half cone angle θ of 7°. Furthermore, we set P = 300 nm, Δz = 100 nm, v_z1 = 200 nm/ms, v_z2 = 1000 nm/ms, ω = 314 rad/s,

h_{0} - h_{m a x} = 3

μm. With these values, we obtain the relationship between T₁-T₂, r_end and

\sqrt{N_{p}}

, which is plotted in Fig. 2(d). It can be observed from Fig. 2(d) that T₁-T₂ value will increase in the constant imaging radius with the increase of imaging pixels (i.e.,

\sqrt{N_{p}}

), illustrating that in this case the imaging time of conventional hopping mode is larger than that of new method. For the constant value of

\sqrt{N_{p}}

, T₁-T₂ value will decrease with the increase of radius in the imaging area (r_end). Finally there are two critical values of

\sqrt{N_{p}}

and r_end, making T₁=T₂. To investigate the effect of approach speed (v_z1) of tip and angular velocity (ω) of the xy-scanner on the value of T₁-T₂, here we set the imaging pixels N_p to 128 × 128, 164 × 164 and 200 × 200 pixels, respectively (r_end = 30 μm). Then we obtained the relationships between T₁-T₂, v_z1 and ω, which are described in Fig. 2(e)–(g), respectively. It can be noticed from Fig. 2(e)–(g) that for the allowable v_z1 value, T₁-T₂ value will increase with the increase of the angular velocity ω of the xy-scanner. This illustrates that the new scanning method is suitable for imaging with higher pixels in constant area.

It is a challenge for the hopping/backstep mode to acquire high-pixel (e.g. pixels≥256) SICM image in several minutes owning to the repeated approach-retract movement of probe for measuring each point. The imaging time increases dramatically if there is no any prior knowledge about steepness or height (decide the retract distance) of the sample in the scanning region. According to Shannon Sampling Theorem, to ensure that the essential feature is not lost during scanning the complex surface, one has to increase the imaging pixels in typical hopping/backstep mode in constant area.

As another hopping mode, STA mode (Takahashi et al., 2010) is also considered here to compare its imaging time with that of new method (Fig. 2(c)). The time consumption of scanning a sample with M rows and N(m) pixels in each row can be expressed as follows:(13)

T_{3} = \sum_{m = 1}^{M} [(\frac{d_{w}}{v_{z_{1}}} + \frac{d_{w}}{v_{z_{2}}}) + \sum_{n = 2}^{N (m)} \frac{d_{w} - (h_{n}^{m} - h_{n - 1}^{m})}{v_{z_{1}}} + \frac{d_{w}}{v_{z_{2}}}] + T_{p 3}

Where T₃ is the total scan time, d_w is its constant withdraw distance in the STA mode.

T_{p 3}

is the time required for the sample scanning in the xy-plane and

T_{p 3} = T_{p 2}

. We subtract Eq. (7) from (13) to obtain(14)

T_{3} - T_{2} = M \cdot d_{w} (\frac{1}{v_{z_{1}}} + \frac{1}{v_{z_{2}}}) + N_{p} d_{w} (\frac{1}{v_{z_{1}}} + \frac{1}{v_{z_{2}}}) - \frac{1}{v_{z_{1}}} \sum_{m = 1}^{M} \sum_{n = 2}^{N (m)} (h_{n}^{m} - h_{n - 1}^{m}) - (\frac{1}{v_{z_{1}}} + \frac{1}{v_{z_{2}}}) \sum_{m = 1}^{M} \sum_{n = 1}^{N (m)} (h_{m a x} - h_{n}^{m}) - \frac{h_{0} - h_{m a x}}{Δ z} \cdot \frac{2 π r_{e n d}}{P \cdot ω}

It can be observed from Eq. (14) that T₃-T₂ value is not only determined by scanning parameters, but also by sample topography feature. Here we assume that(15)

T_{3} - T_{2} = 0

We can obtain a critical withdraw distance d_cw in the STA mode that make both two methods have identical imaging time. d_cw can be expressed as follows:(16)

d_{c w} = \frac{[\frac{1}{v_{z_{1}}} \sum_{m = 1}^{M} \sum_{n = 2}^{N (m)} (h_{n}^{m} - h_{n - 1}^{m}) + (\frac{1}{v_{z_{1}}} + \frac{1}{v_{z_{2}}}) \sum_{m = 1}^{M} \sum_{n = 1}^{N (m)} (h_{m a x} - h_{n}^{m}) + \frac{h_{0} - h_{m a x}}{Δ z} \cdot \frac{2 π r_{e n d}}{P \cdot ω}]}{(M + N_{p}) (\frac{1}{v_{z_{1}}} + \frac{1}{v_{z_{2}}})}

Despite its advantage in imaging time for the flat sample, it is difficult to determine an optimal withdraw distance with predicting the maximum height difference of the adjacent pixels in the steep sample area.

2.4. Tracking performance of the xy-scanner

After the factors that limit the detecting speed are discussed for the constant sample region (i.e., constant r_end), here we test the tracking performance of our xy-scanner in the x-axes at different frequencies so that determine the allowable angular velocityω. We separately input two sinusoidal waveforms with a linearly increasing amplitude with 90^o phase difference in the x-axes and y-axes. In which the value of r_end was set to ˜29 and ˜19 μm, respectively. Note that these parameters are chosen for illustrative purposes only. One also can set different r_end value by referring to the selected pipet (geometric parameters in its tip). As shown in Fig. 3(a)–(d), we can conclude that the speed of x-axes increases with the increase of angular velocity (10–50 Hz). The x-axes of the scanner can easily track the reference cosine wave with the values of angular velocity 10 Hz than that of other angular velocities. With the increase of angular velocity, the tracking performance both in the amplitude and phase degenerates. Note that we here mainly focus on the tracking performance of amplitude that decides whether the pipet tip can move to the reference position. The motion errors of the tip along the spiral trajectory that is smaller than the opening radius of pipet tip (i.e., x and y-axes) are allowed. Furthermore, the time delay (i.e., phase error) in the degenerated tracking performance is also allowed. The degenerated tracking performance for the waveform amplitude in two single axes will result in a smaller circular detected region. Fortunately, by using voltage compensation method, we can achieve an acceptable output displacement of x-axes to the reference position. Fig. 4 shows the tracking performance of the xy-scanner in the x-axes at different frequencies (20, 40, 50 Hz, respectively) with r_end of 19 μm. To track the reference waveform with frequency of 50 Hz in the imaging radius of 19 μm, we used voltage compensation method (r_end = 29 μm) and finally obtained an acceptable tracking performance for the probe tip (Fig. 4(e) and (f)).

3. Experiments

3.1. Instruments and pipettes

We employed a home-built SICM system. It can be operated with the Archimedean spiral in the detecting process and scan samples with hopping mode in the circular detected region. The SICM system mainly consists of coarse and accurate positioning modules. These modules include xy- and z-motor stages (M-111.1DG, Physik Instrument), xy- and z-scanners (P621.2CL and P621.ZCL, Physik Instrument) and corresponding controllers (C-863, E-509, Physik Instrument). A current amplifier and a FPGA (Field Programmable Gate Array) control unit (Fig. 5) are used. In addition, we used a personal computer to implement the set of scanning parameters and display of the scanned topography data.

The SICM pipettes were pulled from borosilicate capillaries (Sutter Instrument Company, USA) by using laser pipette puller (P-2000, Sutter Instrument Company). According to selecting different external, internal diameters of borosilicate capillaries and puller parameters, one can obtain pipettes with different inner, outer opening radii, half cone angle. In our scanning experiment, the geometric parameters of the used pipet, measured by SEM were shown in Fig. 5. Before conducting the experiment, two Ag/AgCl electrodes should be separately inserted to the electrolyte-filled pipet with KCl solution and bulk solution to ensure detecting and scanning function.

3.2. Results and discussion

Before conducting the imaging experiments, we set the ion current decreased by 1% in the experiment, meaning that the highest point of the sample was detected. Several scanning parameters (Δz, P, ω, etc.) are required to set in our proposed approach. Depending upon the tip geometry of the utilized single-barrel pipet (Fig. 5), we separately set the descend step Δz to 120 nm, pitch P to 290 nm, angular velocity f to 20 Hz. Furthermore, we employed the average pixel imaging frequency f_i to compare the imaging rate in the regular hopping mode and new method. Where

f_{i} = K \times N_{p} / \sum_{i = 1}^{K} t_{i}

t_{i}

is the time consumption for scanning the ith image, K is the total number of images scanned by using each scanning method.

A series of contrast experiments were carried out on three PDMS samples that have prismatic, convex and rectangular topographies (i.e., 1^#, 2^# and 3^# PDMS), respectively. We scan the identical sample region with the identical pipet using SICM that can be operated in two scan methods. We set the current threshold of 1.0%, an approach speed of 100 μm/s, retract speed of 800 μm/s, and retrace distance of 6, 8 and 10 μm, respectively.

Fig. 6 shows the imaging results of the 1^#, 2^# and 3^# PDMS samples with the hopping mode (Fig. 6(a), (d) and (g)) and developed method (Fig. 6(b), (e) and (h)); in Fig. 6(a) and (b), both the imaging areas (quantitative evaluation by r_end) are 29 μm (˜100² pixels). It can be observed that the developed method can achieve approximately equal imaging quality like hopping mode for identical areas. With the retrace distance of 10, 8 and 6 μm in the hopping mode, respectively, and identical initial height of tip in the new method, we compared the imaging rate of two scanning methods. The results (Fig. 6(c)) illustrate that the average pixel imaging frequency of developed approach (22.11, 27.35 and 36.49 Hz, respectively) are always considerably larger than that of regular hopping mode (10.29, 14.03 and 19.46 Hz, respectively). The new method can avoid the time consumption caused by the large retract distance due to the unknown prior knowledge.

To investigate the effects of the pixel resolutions on the imaging rate in the developed approach, we conduct the contrast experiment for 2^# PDMS sample by using two scanning methods with the varied pixels of ˜34², ˜70², ˜106², respectively. With the constant retrace distance (8 μm) and imaging area (r_end = 29 μm), the obtained two topographic images (˜106² pixels) are represented in Fig. 6(d) and (e), respectively. And the comparison of imaging rate is plotted in Fig. 6(f). The calculated results show that the average pixel image frequencies of the 2^# PDMS sample are 13.73, 14.54 and 13.62 Hz, respectively, in the regular hopping mode. While in the proposed method these values are 10.38, 22.13 and 28.12 Hz, respectively. It illustrates that both two methods acquire an acceptable topographic images and the imaging rates of the latter is larger than that of the former. In the constant scanning area, the growth rate of imaging time with increased pixel resolutions (˜34², ˜70², ˜106² pixels) in the conventional method is much larger than that of the new method. It indicates that the hopping mode is not applicable to the high-resolution imaging (e.g., 512 × 512 pixels), especially for the sample of unknown height due to its repeated approach and withdrawal movement of the probe in the z-direction. While in the new method, with the appropriate pipet types and its geometries, the SICM probe can detect the highest point of the sample rapidly and then obtain the minimized retrace distance. For the low-resolution SICM imaging, for example, ˜34² pixels in the Fig. 6(f), the new method achieves a lower imaging rate than that of regular hopping mode, mainly because the probe/sample in the new method moves along the relative dense spiral trajectory during the detecting procedure.

Furthermore, we conduct the SICM experiment on 3^# PDMS sample and compare the imaging rates of two methods with the varied imaging area r_end of 23, 34, 45 μm, respectively. Here we set the retrace distance to 8 μm (identical tip height in the new method), pixel resolutions to ˜100² pixels, and angular velocity ω to 30π in the spiral trajectory based detecting process. Fig. 6(g) and (h) show the obtained topographic images of 3^# PDMS sample in two scanning methods, the results suggest that the new method can achieve the same image quality as the conventional hopping mode. Fig. 6(i) shows the comparison of the imaging rate in two scanning methods with the varied imaging area (i.e., r_end are 23, 34, 45 μm, respectively). The calculated results show that the average pixel image frequencies of the 3^# PDMS in the regular hopping mode are 15.14, 14.48 and 15.54 Hz, respectively. While in the new method these values are 29.12, 25.73 and 22.12 Hz, respectively. It can be concluded from Fig. 6(i) that the imaging time of the new method increases with the increase of its imaging area (i.e., r_end). This is mainly because the increased area will result in a more time consumption in the spiral-based detecting process. While in the hopping mode, its imaging rate is only affected by the complexity of topography. But with the further increase of the imaging area (i.e., r_end), the imaging rate of the new method will be slower than that of the conventional method. In that case, we will focus more on the higher pixels resolution rather than a larger imaging area. Consequently, as shown in Fig. 6(i), the new method has more advantageous in the imaging rate for high-resolution imaging than the conventional method.

3.3. Comparison of imaging stability with raster trajectory based detecting method

To further illustrate the superiority of the proposed scanning method, the imaging stability of hopping mode that quickly detect the highest point of each scanning line of the sample with the raster trajectory (Zhuang et al., 2018b) is compared with that of proposed method. In this raster-based method, the highest point of each scanning line of the sample is firstly detected and then each pixel in this line is measured by a point-by-point way. Here both two methods separately detect the highest point of the sample at the same horizontal velocity (e.g. f = 20 Hz). After those highest points are detected, both methods employ conventional hopping mode with the reduced retrace distance to scan each pixel. Note that the raster trajectory based method alternately detects the highest point of each line and scan this line in a point-by-point way. Finally it completes the scanning all points. Obviously, the motion trajectory, changed velocity and direction during detecting the highest point have significant effects on the subsequent point-by-point scan in two different methods.

Fig. 7(a)–(d) shows the obtained topographic images in two methods with the identical horizontal detecting frequency for PDMS and biological samples (C2C12 cells). Where the PDMS sample exhibited five-pointed stars. Here in the new method, the inner square area is scanned in the detected circular area of the sample after completing the detection of the highest point. While the raster based method directly scans all points in the detected square area. As showed in Fig. 7(a)–(d), both two scanning methods can achieve the single acceptable topographic image. However, for the repeated imaging of C2C12 cells, the raster-based detecting method has obviously sample drift in the xy-plane. On the one hand, the abrupt change of detecting direction during its fast detecting procedure result in drift. On the other hand, different friction in the forward and reverse motion directions makes the biological sample easily move toward the direction of low friction. However, avoiding the sample drift in the xy-plane is important during the repeated scanning in the study of cells (Happel and Dietzel, 2009; Novak et al., 2014; Klenerman et al., 2013; Gesper et al., 2015).

For quantitative comparison, we statistically analyze the trajectories of feature points (see green box in Fig. 7(a)–(d)) in obtained twenty images to compare the imaging stability of two methods. Here we define that the coordinates of the jth pixel in the feature area of the qth topographic image is

(x_{j}^{q}, y_{j}^{q})

, and then the center coordinates of the feature area in the qth image is

(\bar{x^{q}}, \bar{y^{q}})

. Where(17)

\bar{x^{q}} = \sum_{j = 1}^{N} \frac{x_{j}^{q}}{N}, \bar{y^{q}} = \sum_{j = 1}^{N} \frac{y_{j}^{q}}{N}

Where N is the number of pixels in each feature area. To quantitatively evaluate the concentration of trajectory points, the variances of the trajectory points in two axes are separately calculated as follows:(18)

D_{x}^{2} = \sum_{q = 1}^{Q} \frac{{(\bar{x^{q}} - \bar{x})}^{2}}{Q}, D_{y}^{2} = \sum_{q = 1}^{Q} \frac{{(\bar{y^{q}} - \bar{y})}^{2}}{Q}

Where Q is the total number of images in each scanning method. Where

\bar{x}

and

\bar{y}

are mean values of

\bar{x^{q}}

and

\bar{y^{q}}

values, respectively. They can be written as follows,

\bar{x} = \sum_{q = 1}^{Q} \frac{\bar{x^{q}}}{Q}

\bar{y} = \sum_{q = 1}^{Q} \frac{\bar{y^{q}}}{Q}

. The calculated trajectory points of two samples in two methods and its variance values in the X- and Y- axes are described in Fig. 8(a’)–(d’) and Table 1), respectively.

Table 1. Variance values of the trajectory points in two axes of two scanning methods.

Samples	PDMS		C2C12 Cells
Methods	Raster-based method	Spiral-based method	Raster-based method	Spiral-based method
Variances (x, y) (μ m²)	(1.36, 1.72)	(0.055, 0.048)	(1.42, 1.93)	(0.049, 0.054)

It can be seen from its enlarged detail that in the raster-based method the motion trajectories of the characteristic points are dispersed and easily move toward a single direction. The calculated variances of the trajectory points using new method in two axes are significantly less than that of the raster-based detecting and scanning method (Table 1). In the new method, the variances of the trajectory points in the x- and y- axes for PDMS sample are decreased by about 24 and 35 times, respectively, compared with that of the raster-based method. For the C2C12 cells sample, these values decreased by 29 and 36 times in the new method, respectively, compared with that of the raster-based method. Obviously, for the cell imaging, this dispersed feature is more obvious (Fig. 8(c’)). Consequently, this disadvantage limits the speed of detecting the highest point of the sample in the raster-based method. Whereas in the new method, the spiral trajectory has more smooth paths. The movement of the sample along this spiral trajectory is a uniform motion, there is no repeated acceleration/deceleration in the detecting process and no abrupt change of detecting direction. The higher derivative of this trajectory still is continuous and smooth. It can progressively cover new areas of the sample and has well-defined spacing between successive scan lines, making this spiral based detecting and scanning method is very suited for implementing high-speed SICM.

4. Conclusion

In this paper, a novel SICM scanning approach was proposed to effectively reduce the retract height of conventional hopping/backstep mode. By using the Archimedes spiral trajectory, the SICM probe/sample can move along this trajectory with a higher angular velocity, and further, the SICM can rapidly detect the highest point of the sample in a layer-by-layer manner. Depending on this highest point, we obtain an optimal retrace height of the entire sample in the detected region for each measurement point. By analyzing the influence factors that decide the operational efficiency of this trajectory, the feasibility of using single-barrel pipet to speed up the detecting speed was verified. Using a self-developed SICM system that can be operated in hopping mode, raster detect based scanning method and this new method, a series of contrast experiments were conducted on three PDMS samples with different scan parameters, including retrace height, imaging area and pixel resolution. By comparing the imaging quality and imaging rate of two scanning methods, the experimental results suggest that the developed approach has a faster imaging speed than regular hopping mode. And it has a higher imaging stability than raster detect based method at the same horizontal detecting speed. The new method is especially suited for high-resolution scanning in a constant area with a sample of unknown height.

Acknowledgments

The authors thanks the National Natural Science Foundation of China (Project No. 51375363), Fundamental Research Funds for the Central Universities and Industrial Research Project of Science and Technology Department of Shannxi Province, China (Project No. 2013GY2-04) for funding this work.

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View Abstract

[1] Bazaei et al., 2012
A. Bazaei, Y.K. Yong, S.R. Moheimani
High-speed Lissajous-scan atomic force microscopy: scan pattern planning and control design issues
Rev. Sci. Instrum., 83 (6) (2012), Article 063701
View in Scopus Google Scholar

[2] Bazaei et al., 2017
A. Bazaei, Y.K. Yong, S.R. Moheimani
Combining spiral scanning and internal model control for sequential AFM imaging at video rate
IEEE/ASME Trans. Mechatron., 22 (1) (2017), pp. 371-380
View in Scopus Google Scholar

[3] Del Linz et al., 2014
S. Del Linz, E. Willman, M. Caldwell, D. Klenerman, A. Fernández, G. Moss
Contact-free scanning and imaging with the scanning ion conductance microscope
Anal. Chem., 86 (5) (2014), pp. 2353-2360
View at publisher
Crossref View in Scopus Google Scholar

[4] Edwards et al., 2009
M.A. Edwards, C.G. Williams, A.L. Whitworth, P.R. Unwin
Scanning ion conductance microscopy: a model for experimentally realistic conditions and image interpretation
Anal. Chem., 81 (11) (2009), pp. 4482-4492
View at publisher
Crossref View in Scopus Google Scholar

[5] Gesper et al., 2015
A. Gesper, D. Thatenhorst, S. Wiese, T. Tsai, I.D. Dietzel, P. Happel
Long-term, long-distance recording of a living migrating neuron by scanning ion conductance microscopy
Scanning, 37 (3) (2015), pp. 226-231
View at publisher
Crossref View in Scopus Google Scholar

[6] Hansma et al., 1989
P.K. Hansma, B. Drake, O. Marti, S.A.C. Gould, C.B. Prater
The scanning ion-conductance microscope
Science, 243 (4891) (1989), pp. 641-643
View at publisher
Crossref View in Scopus Google Scholar

[7] Happel and Dietzel, 2009
P. Happel, I.D. Dietzel
Backstep scanning ion conductance microscopy as a tool for long term investigation of single living cells
Int. J. Nanobiotechnol. Pharm., 7 (2009), p. 7
View at publisher
Crossref View in Scopus Google Scholar

[8] Ida et al., 2017
H. Ida, Y. Takahashi, A. Kumatani, H. Shiku, T. Matsue
High speed scanning ion conductance microscopy for quantitative analysis of nanoscale dynamics of microvilli
Anal. Chem., 89 (11) (2017), pp. 6015-6020
View at publisher
Crossref View in Scopus Google Scholar

[9] Jung et al., 2015
G. Jung, H. Noh, Y.K. Shin, S. Kahng, K.Y. Baik, H. Kim, N. Cho, S. Cho
Closed-loop ARS mode for scanning ion conductance microscopy with improved speed and stability for live cell imaging applications
Nanoscale, 7 (2015), pp. 10989-10997
View in Scopus Google Scholar

[10] Klenerman et al., 2013
D. Klenerman, A. Shevchuk, P. Novak, Y.E. Korchev, S.J. Davis
Imaging the cell surface and its organization down to the level of single molecules
Philos. Trans. Biol. Sci., 368 (1611) (2013), Article 20120027
View at publisher
Crossref View in Scopus Google Scholar

[11] Korchev et al., 1997a
Y.E. Korchev, C.L. Bashford, M. Milovanovic, I. Vodyanoy
Scanning ion conductance microscopy of living cells
Biophys. J., 73 (2) (1997), pp. 653-658
View PDF View article Google Scholar

[12] Korchev et al., 1997b
Y.E. Korchev, M. Milovanovic, C.L. Bashford, D.C. Bennett, E.V. Sviderskaya, I. Vodyanoy, M.J. Lab
Specialized scanning ion-conductance microscope for imaging of living cells
J. Microsc., 188 (1) (1997), pp. 17-23
View at publisher
Crossref View in Scopus Google Scholar

[13] Li et al., 2008
C. Li, N. Johnson, V. Ostanin, A. Shevchuk, L. Ying, Y. Korchev, D. Klenerman
High resolution imaging using scanning ion conductance microscopy with improved distance feedback control
Prog. Nat. Sci., 18 (6) (2008), pp. 671-677
View PDF View article View in Scopus Google Scholar

[14] Mahmood et al., 2011
I.A. Mahmood, S.R. Moheimani, B. Bhikkaji
A new scanning method for fast atomic force microscopy
IEEE Trans. Nanotechnol., 10 (2) (2011), pp. 203-216
View in Scopus Google Scholar

[15] McKelvey et al., 2014
K. McKelvey, D. Perry, J.C. Byers, A.W. Colburn, P.R. Unwin
Bias modulated scanning ion conductance microscopy
Anal. Chem., 86 (7) (2014), pp. 3639-3646
View at publisher
Crossref View in Scopus Google Scholar

[16] Meyer et al., 2014
T.R. Meyer, D. Ziegler, C. Brune, A. Chen, R. Farnham, N. Huynh, J. Chang, A.L. Bertozzi, P.D. Ashby
Height drift correction in non-raster atomic force microscopy
Ultramicroscopy, 137 (2014), pp. 48-54
View PDF View article View in Scopus Google Scholar

[17] Momotenko et al., 2016
D. Momotenko, K. McKelvey, M. Kang, G.N. Meloni, P.R. Unwin
Simultaneous interfacial reactivity and topography mapping with scanning ion conductance microscopy
Anal. Chem., 88 (5) (2016), pp. 2838-2846
View at publisher
Crossref View in Scopus Google Scholar

[18] Momotenko et al., 2015
D. Momotenko, J.C. Byers, K. McKelvey, M. Kang, P.R. Unwin
High-speed electrochemical imaging
ACS Nano, 9 (9) (2015), pp. 8942-8952
View at publisher
Crossref View in Scopus Google Scholar

[19] Nikooienejad et al., 2018
N. Nikooienejad, M. Maroufi, S.R. Moheimani
September. A novel non-raster scan method for AFM imaging
ASME 2018 Dynamic Systems and Control Conference, American Society of Mechanical Engineers (2018)
(pp. V003T40A008-V003T40A008)
Google Scholar

[20] Novak et al., 2009
P. Novak, C. Li, A.I. Shevchuk, R. Stepanyan, M. Caldwell, S. Hughes, T.G. Smart, J. Gorelik, V.P. Ostanin, M.J. Lab, G.W.J. Moss, G.I. Frolenkov, D. Klenerman, Y.E. Korchev
Nanoscale live-cell imaging using hopping probe ion conductance microscopy
Nat. Methods, 6 (2009), pp. 279-281
View at publisher
Crossref View in Scopus Google Scholar

[21] Novak et al., 2014
P. Novak, A. Shevchuk, P. Ruenraroengsak, M. Miragoli, A.J. Thorley, D. Klenerman, M.J. Lab, T.D. Tetley, J. Gorelik, Y.E. Korchev
Imaging single nanoparticle interactions with human lung cells using fast ion conductance microscopy
Nano Lett., 14 (2014), pp. 1202-1207
View at publisher
Crossref View in Scopus Google Scholar

[22] Page et al., 2017
A. Page, D. Perry, P.R. Unwin
Multifunctional scanning ion conductance microscopy
Proc. R. Soc. A, 473 (2200) (2017), Article 20160889
View at publisher
Crossref View in Scopus Google Scholar

[23] Pastré et al., 2001
D. Pastré, H. Iwamoto, J. Liu, G. Szabo, Z. Shao
Characterization of AC mode scanning ion-conductance microscopy
Ultramicroscopy, 90 (1) (2001), pp. 13-19
View PDF View article View in Scopus Google Scholar

[24] Proksch et al., 1996
R. Proksch, R. Lal, P.K. Hansma, D. Morse, G. Stucky
Imaging the internal and external pore structure of membranes in fluid: TappingMode scanning ion conductance microscopy
Biophys. J., 71 (4) (1996), pp. 2155-2157
View PDF View article View in Scopus Google Scholar

[25] Rana et al., 2014
M.S. Rana, H.R. Pota, I.R. Petersen
Spiral scanning with improved control for faster imaging of AFM
IEEE Trans. Nanotechnol., 13 (3) (2014), pp. 541-550
View in Scopus Google Scholar

[26] Rheinlaender and Schäffer, 2009
J. Rheinlaender, T.E. Schäffer
Image formation, resolution, and height measurement in scanning ion conductance microscopy
J. Appl. Phys., 105 (9) (2009), Article 094905
View in Scopus Google Scholar

[27] Takahashi et al., 2010
Y. Takahashi, Y. Murakami, K. Nagamine, H. Shiku, S. Aoyagi, T. Yasukawa, M. Kanzaki, T. Matsue
Topographic imaging of convoluted surface of live cells by scanning ion conductance microscopy in a standing approach mode
J. Chem. Soc. Faraday Trans., 12 (34) (2010), pp. 10012-10017
View at publisherCrossref View in Scopus Google Scholar

[28] Watanabe and Ando, 2017
S. Watanabe, T. Ando
High-speed XYZ-nanopositioner for scanning ion conductance microscopy
Appl. Phys. Lett., 111 (11) (2017), Article 113106
View in Scopus Google Scholar

[29] Yong et al., 2012
Y.K. Yong, S.R. Moheimani, B.J. Kenton, K.K. Leang
Invited review article: high-speed flexure-guided nanopositioning: mechanical design and control issues
Rev. Sci. Instrum., 83 (12) (2012), Article 121101
View in Scopus Google Scholar

[30] Yong et al., 2010
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