Artifact reduction by intrinsic harmonics of tuning fork probe for scanning near-field optical microscopy

Zhaogang Dong; Ying Zhang; Shaw Wei Kok; Boon Ping Ng; Yeng Chai Soh

doi:10.1364/OE.18.022047

1. Introduction

Scanning near-field optical microscopy is an optical imaging technique capable of overcoming the diffraction limit [1]. It scans a sub-wavelength aperture over the proximity of sample surface to detect the evanescent optical waves that carry high spatial frequency components of the topographical or optical properties of the sample. One of commonly-used SNOM scanning modes is the constant gap mode (CGM) where the separation between the aperture and the sample surface remains a constant during the whole scanning process. Although high resolution has been demonstrated by operating a SNOM under CGM, the existence of topographical artifacts has been reported in the SNOM images [2] [3] [4]. The artifacts are due to that the intensity of the light received by the SNOM probe is essentially dependent upon the z-position of the probe. The dependence may result in a non-zero gradient of the light intensity with respect to the z-position of the probe. Thus, the variation of the probe position in z-direction, which results from the probe having to follow the topography of the sample under CGM, contributes a part to the total light intensity received by the probe. This part of signal results in the topographical artifacts such as the globally or locally inverse contrast in SNOM images. The existence of topographical artifacts make it difficult to interpret the optical properties of the sample. Therefore, removal of topographical artifacts has been become one important concern in the applications of SNOM.

In the past years, the formation of topographical artifacts has been studied both in experiment and in theory. For example, the first experimental investigation of topographical artifacts was conducted by Hecht etc. in [2]. The theoretical and numerical models of topographical artifacts were proposed in [5][6]. Other research focused on the investigation of the dependence of the artifacts upon various physical parameters of the sample and/or the SNOM imaging setup [5] [6] [7]. Besides for aperture SNOM systems, the topographical artifacts are also concerned for apertureless SNOM systems [8] [9] [10]. In contrast to the effort devoted to the study of formation of topographical artifacts, methods of removing or reducing topographical artifacts are few. The natural solutions to artifact removal include the ones that operate SNOM in a constant height mode (CHM) or in a constant intensity mode (CIM) [2] [4], because the dependence upon the position of the probe is avoided for these SNOM operation modes and in turn the gradient of light intensity with respect to the z-position of the probe vanishes naturally. Compared to CGM, the CHM and CIM modes require certain homogeneity of the sample surface to achieve high resolution [11]. To compromise, a three-dimensional SNOM imaging approach was proposed [12]. It records all the light readouts including the CGM and CHM readouts that are collected in the process of the probe approaching the sample surface. It removes the topographical artifacts essentially by the same way as in CHM. But the huge data acquisition time and the registration of the approaching at different lateral positions limit the application of the approach. Removal of the topographical artifacts under CGM operation is still preferred due to convenient implementation and high resolution of CGM.

This paper proposes an artifact reduction method by using intrinsic harmonics that result from the oscillation of the tuning fork probe used in a SNOM. The intrinsic harmonics in tuning fork probe oscillation was firstly reported by W. Jhe and coworkers [13]. The harmonics are introduced by small nonlinear oscillation terms in z-direction of the probe oscillation when the tuning fork probe is oscillating laterally like a pendulum subject to a given excitation frequency. Experimental demonstration shows that the optical signal demodulated from the second harmonic can deliver better lateral resolution of SNOM image than the one of the conventional SNOM image [13]. In this paper, the optical signals demodulated from intrinsic harmonics of tuning fork probe are related to the topographical artifacts. It is shown that the optical signal demodulated from the second harmonic is actually the gradient of the received light intensity with respect to the probe position in z-direction. Then, taking the advantage of a SNOM capable of obtaining simultaneously topographical and optical signals, the topographical artifact signals can be obtained by multiplying the topographical signal and the optical signal demodulated from the second harmonic. By subtracting the topographical artifacts, artifacts-reduced SNOM images are recovered for a SNOM operating under CGM. The effectiveness of the proposed approach is demonstrated by imaging a rhombus vanadium grating that is commercially available for SNOM system calibration. The proposed method can be implemented for existing SNOM systems without modification of the system, except for more demodulation processing which can be easily implemented either in software or in hardware in parallel to the existing demodulation in the SNOM systems.

2. Principle of topographical artifact reduction by using intrinsic harmonics in oscillation of SNOM probe

We consider an aperture SNOM system using a tuning fork probe. The tuning fork probe is formed by attaching to one prong of a tuning fork with a fiber probe. The tip part of the probe is coated with gold and has a small aperture at the tip apex. In operation, the tuning fork probe is excited to oscillate laterally with respect to the sample surface [14]. The schematic is shown in Fig. 1.

Fig. 1 Schematic of oscillation of a tuning fork probe.

Download Full Size | PDF

First of all, we describe the harmonics in the oscillation of the tuning fork probe. If the tuning fork is excited to vibrate at a frequency of Ω, the lateral oscillation of the tuning fork probe, denoted by x_osc(t) can be expressed as x_osc(t) = x_AcosΩt where x_A is the amplitude and t is time instance. Here we assume x_A is a constant. Since the tuning fork probe is vibrating like a pendulum, the lateral oscillation induces the oscillation in z-direction which is denoted by z_osc(t). Thus, the lateral oscillation x_osc(t) can also be expressed by x_osc(t) = Rsin(θ (t)) and the vertical oscillation z_osc(t) can be expressed as

z_{o s c} (t) = R - R c o s (θ (t)),

where R is the effective pendulum length and θ (t) is the angle of the pendulum deviating away from the central line, as indicated in Fig. 1.

After simple algebraic manipulation, θ (t) can be expressed by

θ (t) = {s i n}^{- 1} [\frac{x_{A}}{R} c o s (Ω t)] \approx \frac{x_{A}}{R} c o s (Ω t),

where x_A is assumed to be very small comparing to R. This assumption is valid for the tuning fork in SNOM systems since x_A is usually about 40 nm and R is about 4.0 mm [14].

Substituting Eq. (2) into Eq. (1) and expanding z_osc(t) in terms of the bessel functions associated with the corresponding harmonics [10] [15], we have

z_{o s c} (t) = R - R [J_{0} (\frac{x_{A}}{R}) + 2 \sum_{k = 1}^{\infty} {(- 1)}^{k} J_{2 k} (\frac{x_{A}}{R}) c o s (2 k Ω t)] .

This clearly shows that the oscillation of the tuning fork probe has intrinsically harmonic components in z-direction. Since the oscillation amplitude x_osc(t) is very small compared to R, the high order terms in Eq. (3) can be neglected and z_osc(t) can be simplified into

z_{o s c} (t) = \frac{x_{A}^{2}}{4 R} [1 + c o s (2 Ω t)]

.

The above analysis is valid for all positions of the tuning fork probe when the probe is driven to scan over the sample surface. Denote x_c and z_c as the central lateral position and the vertical position of the SNOM probe during the scanning process. When the SNOM is operated under CGM, z_c shall follow the sample surface topography which is characterized by h(x). That is z_c = h(x_c). Here, for clarity of illustration, we consider only one-dimensional extension of the topography, i.e., h(x) is a function of only the lateral dimension x. With these denotations, the lateral position x(t) and the vertical position of the SNOM probe h(x(t)) at any time instance t can be expressed as:

x (t) = x_{c} + x_{A} c o s (Ω t),

h (x (t)) = h (x_{c}) + \frac{x_{A}^{2}}{4 R} [1 + c o s (2 Ω t)] .

Now we characterize the effect of the intrinsic harmonics on the optical signal collected by the SNOM working under CGM. In the literature, there are two conventional schemes to detect the near-field optical signal. In the first scheme, the SNOM signal collected at lateral position x_c is the average intensity of the light that is collected by the probe from the tip aperture [1]. In the second scheme, the SNOM signal is the one obtained from demodulating the intensity of the light collected by the probe with respect to the vibration frequency that is used to excite the tuning fork probe [13].

Denote the intensity of the light collected by the probe as I[x, h(x)]. According to the reference [6], I [x, h(x)] collected under CGM can be expanded into four terms, and it is expressed as follows:

I [x, h (x)] = I_{0} (z_{0}) + \frac{\partial I_{0} (z)}{\partial z} |_{z = z_{0}} [h (x) - z_{0}] + I_{1} (x, z_{0}) + \frac{\partial I_{1} (x, z)}{\partial z} |_{z = z_{0}} [h (x) - z_{0}],

where z₀ is the reference plane to expand the optical field distribution. The four terms in Eq. (6) have different physics signification. The first term I₀(z₀) is the background signal in near-field imaging and it does not include any sub-wavelength information of the sample. Therefore, I₀(z₀) is independent of lateral dimension x. For the illumination mode SNOM as explained in Ref. [6], I₀ represents the direct field transmitted from the aperture-SNOM probe through the flat substrate to the detector and I₀ is a constant signal. The second term is the topographical artifact resulting from the background signal when the SNOM probe is experiencing a z-motion. The third term is the near-field signal, which contains the sub-wavelength information about the sample. The fourth term is the topographical artifact resulting from the near-field signal when the SNOM probe is experiencing a z-motion.

Considering the time-varying probe position, the collected light intensity is also time-varying and it can be expressed explicitly as I[x(t), h(x(t))]. Substituting Eq. (4) and Eq. (5) into Eq. (6), the last three items of Eq. (6) can be expressed respectively by

\frac{\partial I_{0} (z)}{\partial z} |_{z = z_{0}} [h (x (t)) - z_{0}] = \frac{\partial I_{0} (z)}{\partial z} |_{z = z_{0}} [h (x_{c}) + \frac{x_{A}^{2}}{4 R} (1 + c o s (2 Ω t)) - z_{0}],

I_{1} [x (t), z_{0}] = I_{1} (x_{c}, z_{0}) + \frac{\partial I_{1} (x, z)}{\partial x} |_{x = x_{c}, z = z_{0}} x_{A} c o s (Ω t),

\begin{array}{l} \frac{\partial I_{1} [x (t), z]}{\partial z} |_{z = z_{0}} [h (x (t)) - z_{0}] = \frac{\partial I_{1} (x, z)}{\partial z} |_{x = x_{c}, z = z_{0}} [h (x_{c}) + \frac{x_{A}^{2}}{4 R} (1 + c o s (2 Ω t)) - z_{0}] \\ + \frac{\partial^{2} I_{1} (x, z)}{\partial x \partial z} |_{x = x_{c}, z = z_{0}} \times x_{A} c o s (Ω t) [h (x_{c}) + \frac{x_{A}^{2}}{4 R} (1 + c o s (2 Ω t)) - z_{0}] . \end{array}

Thus, it is concluded that the intensity of the light collected by the SNOM probe contains various harmonic components as well due to the intrinsic harmonics of tuning fork vibration. These harmonic components, denoted respectively as I_DC(x_c), I_Ω (x_c), I₂_Ω (x_c) and I₃_Ω (x_c). For easy reference in the following discussion, these harmonics are referred to as the DC SNOM signal, the first harmonic SNOM signal, the second harmonic SNOM signal, and the third harmonic SNOM signal, respectively. They can be obtained by demodulating I[x(t), h(x(t))] through a low-pass filter and a phase lock-in amplifier. More specifically, these signals are expressed respectively by

\begin{array}{l} I_{D C} (x_{c}) & = & I_{0} (z_{0}) + \frac{\partial I_{0} (z)}{\partial z} |_{z = z_{0}} [h (x_{c}) + \frac{x_{A}^{2}}{4 R} - z_{0}] \\ + I_{1} (x_{c}, z_{0}) + \frac{\partial I_{1} (x, z)}{\partial z} |_{x = x_{c}, z = z_{0}} [h (x_{c}) + \frac{x_{A}^{2}}{4 R} - z_{0}], \end{array}

I_{Ω} (x_{c}) = \frac{\partial I_{1} (x, z)}{\partial x} |_{x = x_{c}, z = z_{0}} x_{A} + \frac{\partial^{2} I_{1} (x, z)}{\partial x \partial z} |_{x = x_{c}, z = z_{0}} [h (x_{c}) + \frac{3 x_{A}^{2}}{8 R} - z_{0}] x_{A},

I_{2 Ω} (x_{c}) = \frac{\partial I_{0} (z)}{\partial z} |_{z = z_{0}} \frac{x_{A}^{2}}{4 R} + \frac{\partial I_{1} (x, z)}{\partial z} |_{x = x_{c}, z = z_{0}} \frac{x_{A}^{2}}{4 R},

I_{3 Ω} (x_{c}) = \frac{\partial^{2} I_{1} (x, z)}{\partial x \partial z} |_{x = x_{c}, z = z_{0}} \frac{x_{A}^{3}}{8 R} .

The conventional SNOM signals collected at a lateral position x_c are respectively the DC SNOM signal I_DC(x_c) and the first harmonic SNOM signal I_Ω (x_c). Equation (10) and Eq. (11) show that all the conventional SNOM signals suffer from topographical artifacts which are represented by the terms containing partial differentials with respect to z. It is also noted that the partial differential terms are coincidentally provided by the higher order of harmonic SNOM signals I₂_Ω and I₃_Ω respectively, except for constant coefficients. Also thanks to the capability of a SNOM in obtaining simultaneously the topographical and optical signals, the term of (h(x_c) – z₀) can be obtained from the topographical signal. Hence, the artifacts can be calculated from the product of the partial differentials and the topographical signals as shown in Eq. (10) and Eq. (11).

For example, when removing the topographical artifact from the DC SNOM signal, the second harmonic optical signal can be used. As shown in the above derivation, the second harmonic SNOM signal is proportional to $\frac{\partial I_{0} (z)}{\partial z} + \frac{\partial I_{1} (x, z)}{\partial z}$ . It is the gradient of the genuine SNOM signal (I₀(z₀) + I₁(x_c, z₀)) with respect to the z-motion of the probe. In addition, taking advantage of the SNOM capable of obtaining the topographical signal simultaneously with the optical signals, the topographical artifacts I_artifact,DC (x_c) in the DC SNOM signal is obtained from the product of the second harmonic SNOM signal and the topography $[h (x_{c}) + x_{A}^{2} / 4 R - z_{0}]$ . Similarly, the topographical artifacts I_artifact_,_Ω (x_c) in the first harmonic SNOM signal is obtained by using the third harmonic SNOM signal and the topography. More specifically, the topographical artifacts in I_DC and I_Ω are respectively expressed as:

I_{a r t i f a c t, D C} (x_{c}) = C_{0} I_{2 Ω} (x_{c}) [h (x_{c}) - z_{0}],

I_{a r t i f a c t, Ω} (x_{c}) = C_{1} I_{3 Ω} (x_{c}) [h (x_{c}) - z_{0}] .

where we have neglected the terms

x_{A}^{2} / 4 R

and

3 x_{A}^{2} / 8 R

in Eq. (10) and Eq. (11) by considering the magnitude of x_A is much smaller than the one of R. C₀ and C₁ are two constants including

x_{A}^{2} / 4 R

and

x_{A}^{2} / 8 R

respectively. They will be calibrated in experiment to take into account of topographical reading in voltage. By removing I_artifact,DC (x) from the DC SNOM signal, artifact-reduced DC SNOM image is obtained. The artifact-reduced first harmonic SNOM signal can be obtained similarly. It is worthy to point out that the theoretical derivation given in this section is valid for illumination mode, collection mode and illumination-collection hybrid mode of SNOM under CGM.

3. Experimental results of artifacts reduction by the proposed method

The experimental study is carried out on a home-made SNOM system [16] [17] which schematic is shown in Fig. 2. The heart of the system is the tuning fork probe. The probe is fabricated by a heating-and-pulling method from a single mode fiber (Thorlab with model number 630 HP). Its tip part is coated with gold using a gold sputtering machine. The probe is glued onto one prong of a tuning fork which is chosen with a natural resonance frequency at 32.768 KHz. The other major components of the system include: a He-Ne laser with output wavelength at 632.8 nm, a photomultiplier tube (PMT, Hamamatsu H6780), a current-to-voltage amplifier (Hamamatsu C7319), a lock-in amplifier (Scitec Instruments, 450D dual channel), a x-y-z PZT stage (PI P-733.2 CD) with resolution at 1000 nm/V, a signal generator (IC chip, AD7008), and a personal computer (Dell Optiplex Gx620) with a data acquisition board (National Instruments PCI-6221).

Fig. 2 Experimental setup.

Download Full Size | PDF

The system is operating under an illumination-collection CGM where the probe is used to deliver and collect the light. Driven by the x-y-z PZT stage which the tuning fork is attached to, the tuning fork probe is regulated to the near-field proximity of a sample surface by a standard AFM function of the SNOM system. The light from the He-Ne laser, which is guided through a single fiber and a fiber coupler, is incident on the sample surface through the tuning fork probe. The near-field optical signal is collected through the tuning fork probe and guided back to the PMT through the fiber coupler. The fiber coupler is chosen with splitting ratio of 50:50. The output of the PMT is connected respectively to the low pass filter and the lock-in amplifier, where the DC and harmonic SNOM signals are demodulated in parallel with respect to the fundamental harmonic frequency Ω. The fundamental frequency is provided by the signal generator and used to excite the tuning fork probe for the AFM function of the SNOM system. All the demodulated signals are acquired by the personal computer where the SNOM image is formed by assembling the demodulated signals in the scanning process of the AFM function.

The sample used in the experiment is a rhombus vanadium grating on a glass substrate. It is a commercially-used calibration sample from NT-MDT with model number SNG01. As given in specifications, the width of a grating is about 2.5 um, and the height is about 30–40 nm. Figure 3 shows the optical image of the sample captured by a microscope (Zeiss Axiospect 200 with Axiotron 2 and CSM VIS-UV).

Fig. 3 Image of the rhombus vanadium grating sample using a UV microscopy.

Download Full Size | PDF

In the experiment, the SNOM is operated to scan the rhombus sample. The tuning fork probe is excited by an electric signal with frequency of 31.9612 KHz and amplitude of 250 mV. The current going through the tuning fork is measured in voltage by using a current-voltage amplification circuit [16]. The output voltage from the amplification circuit is 1640.6 mV when the tuning fork probe is working at free-oscillation condition. The set-point voltage to control probe-sample separation is set at 1601.6 mV, and the corresponding probe-sample separation is equivalent to 20 nm. This is calibrated by reading the displacement voltage of the z-PZT driving the tuning fork. In the scanning process, the scanning range is set as 10 μm and the scanning step is controlled at 39 nm for both x- and y- direction by commanding the x-y PZT.

Using the settings, the SNOM system obtains both the topographical and optical images of the scanned area simultaneously. Figure 4(a) and Fig. 5(a) present respectively the topography of the rhombus grating and the DC SNOM signal collected over the same area of the rhombus grating. The unit of the color bar in topography image is in nm. It is the voltage reading indicating the displacement of the z-PZT. The unit of the received optical signal color bar is in volts, which is the output signal from the PMT. For clarity of the following illustration on the artifact reduction, we take the line-scan signals of an identical line of interest in the topographical and optical images. For example, the line-scan profile of Line 170 is displayed in Fig. 4(b) and Fig. 5(b), respectively. Comparing the line scan topographical profile with its optical counterpart, it is noted that the DC SNOM signal does not follow the topographical one when the SNOM probe is scanning over the vanadium grating. Instead, there are the outstanding peaks in the DC SNOM line scan profile at positions respectively given by x=1.50 μm, x=5.98 μm and x=9.80 μm. Such peaks are due to the topographical artifacts. The similar phenomenon of topographical artifacts was also observed but appeared as the dips in the literature [18] which considers imaging the optical field distribution around metallic particles.

Fig. 4 (a) Topography image of rhombus grating, (b) One line-scan profile of topography.

Download Full Size | PDF

Fig. 5 (a) DC SNOM image of rhombus grating, (b) One line-scan profile of DC SNOM signal.

Download Full Size | PDF

As a remark, we further examine whether such a topographical artifact is due to the shear-force error signal during the scanning process. As shown in Fig. 2 of Ref. [9], the artifact can be caused by the shear-force error signal particularly when x_A is drifting with time, but the artifact exhibits an important characteristic. It exhibits different asymmetric contrasts in the forward scanned image and the reverse scanned image. Thus, we also recorded in our experiment the DC SNOM signal that obtained in the reverse scanning direction. The image and the corresponding line profile are presented in Fig. 6. Comparing with the DC SNOM signal obtained in the forward scanning direction as in Fig. 5, the asymmetric contrasts in the two figures are located at the same side of the feature. This observation excludes the possibility of the topographical artifact due to the shear-force error signal. Hence, the artifacts due to the shear-force error are neglected in this paper.

Fig. 6 (a) DC SNOM image of rhombus grating obtained in the reverse scanning direction, (b) One line-scan profile of DC SNOM signal obtained in the reverse scanning direction.

Download Full Size | PDF

As in Eq. (14), the topographical artifact in the DC SNOM signal can be constructed by using I₂_Ω and the topography change [h(x_c) – z₀]. The topography change is available from the displacement reading of the z-PZT stage. Thanks to the capability of SNOM in obtaining different harmonics SNOM signals simultaneously with the topography change. The topographical artifact can be calculated by the multiplying the second harmonic SNOM signal and the topography as given by Eq. (14). Figure 7(a) presents the SNOM image formed by the second harmonic I₂_Ω that is simultaneously obtained with topographic and the DC SNOM image of the same area of the sample. The line scan profile in I₂_Ω corresponding to Line 170 is given in Fig. 7(b).

Fig. 7 (a) Second harmonic SNOM image of rhombus grating, (b) One line-scan profile of the second harmonic SNOM signal.

Download Full Size | PDF

The line scan profile with artifact corrected is shown in Fig. 8(a). Subtracting I_Artifact,DC (x_c) from the DC SNOM signal, the artifact-reduced DC SNOM signal can be obtained. Repeating the correction process line by line, the artifact-reduced DC SNOM image is obtained as shown in Fig. 8(b). By comparing Fig. 8(b) and Fig. 5(a), we can observe that the outstanding peaks in the DC SNOM image are corrected. From this, we can conclude that the topographical artifact I_artifact,DC (x_c) in the DC SNOM image I_DC(x_c) is reduced effectively by employing the second harmonic SNOM signal and topography information.

Fig. 8 Topographical artifacts reduction in the DC SNOM image: (a) Artifact correction for one line scan, (b) Artifact correction for the whole image.

Download Full Size | PDF

For the second conventional SNOM detection scheme, I_Ω represents the obtained SNOM image. It is also available simultaneously with signal I₃_Ω and the topographical signal, but it also contains topographical artifacts as analyzed in the paper. Figure 9 displays the first harmonic SNOM image and the line scan profile captured at Line 170. The first harmonic SNOM signal is demodulated from the x-channel of the lock-in amplifier and the gain of the lock-in amplifier is set at 100. As given by Eq. (11), we know that the optical information embedded in the first harmonic signal consists of $\frac{\partial I_{1} (x, z)}{\partial z}$ and $\frac{\partial^{2} I_{1} (x, z)}{\partial x \partial z}$ terms, where the second term is the associated topographical artifacts and it is just given by I₃_Ω demodulated from the third harmonic as in Eq. (13). Again the third harmonic SNOM signal is obtained simultaneously with the topography, it is shown in Fig. 10. The third harmonic SNOM signal I₃_Ω is demodulated from the x-channel of the lock-in amplifier and the gain of the lock-in amplifier is 1000. By using Eq. (11) and Eq. (13), the artifact denoted by I_artifact,Ω (x_c) can be calculated by Eq. (15) line by line. The results before and after correction for Line 170 are shown in Fig. 11(a). After artifact corrected, the first harmonic SNOM image is shown in Fig. 11(b).

Fig. 9 (a) First harmonic SNOM image of rhombus grating, (b) One line-scan profile of the first harmonic SNOM signal.

Download Full Size | PDF

Fig. 10 (a) Third harmonic SNOM image of rhombus grating, (b) One line-scan profile of the third harmonic SNOM signal.

Download Full Size | PDF

Fig. 11 Topographical artifact reduction in the first harmonic SNOM image: (a) Artifacts and correction in a line scan, (b) Artifact corrected first harmonic SNOM image.

Download Full Size | PDF

As a useful remark, we want to further investigate the effectiveness of the proposed approach by comparing the artifact corrected DC SNOM signal and the artifact corrected first harmonic SNOM signal. As shown in Eq. (10) and Eq. (11), if the topographical artifacts in both DC SNOM signal and the first harmonic SNOM signal are corrected perfectly and there is no noise in both signals, then the numerical derivative of the corrected DC SNOM signal along x direction should be the same as the corrected first harmonic SNOM signal. In order to verify this, we perform the numerical derivative on the line signal in Fig. 8(a) of the corrected DC SNOM signal along x direction, and the result is shown in Fig. 12(a). For convenience of comparison, we display again side-by-side the corrected first harmonic SNOM signal Fig. 12(b). We notice that the peaks of the corrected first harmonic SNOM signal as shown in Fig. 12(b) and the peaks in Fig. 12(a) occur at the exact positions. This shows that the main features of these two signals are the same. Indeed, there are some minor mismatches between the two signals. We attribute these mismatches to the presence of noise in the DC SNOM signal, since numerical derivative of a noisy signal will amplify the noise effect [23].

Fig. 12 Comparison of (a) Numerical derivative of the corrected DC SNOM signal along x direction, (b) Corrected first harmonic SNOM signal.

Download Full Size | PDF

Lastly, to complete the discussion of the paper, we elaborate the procedures of determining the topographical artifact signals in both the DC SNOM signal and the first harmonic SNOM signal from the experimental data.

Firstly, we determine the value of the reference plane z₀ for each line-scan profile. Here we define the maximum value of the topography signal h(x_c) as the reference plane. This means z₀ = max{h(x_c)}. For the sample used in our experiment, the vanadium grating is deposited on the surface of the glass substrate. Therefore, the maximum value of the topography signal z₀ is always at the vanadium region.

Secondly, using the obtained z₀, the topographical artifact signals I₂_Ω (x_c)[h(x_c) – z₀] and I₃_Ω (x_c)[h(x_c) – z₀] can be calculated from the raw data obtained experimentally. Based on these two topographical artifact signals, we can identify the exact locations of the topographical artifact signals in both the DC SNOM signal and the first harmonic SNOM signal. For the sample used here, the topographical artifact signals always occur at the transition regions between the glass substrate and the vanadium region, where the topographical artifact signals are shown in Fig. 8(a) for the DC SNOM signal and in Fig. 11(a) for the first harmonic SNOM signal.

Thirdly, we calibrate the values of C₀ in Eq. (14) and C₁ in Eq. (15). We use some a priori knowledge that the vanadium region is a homogenous material and the reflection from the vanadium region should be the same. To be more specific, we denote the extrapolation value of DC SNOM signal and the first harmonic SNOM signal at the vanadium region as Î_DC and Î_Ω, respectively. For each line-scan profile, let x_i to denote the lateral positions belonging to the vanadium region. Then, we can define the following error functions ξ_DC(C₀) and ξ_Ω (C₁):

ξ_{D C} (C_{0}) = \sum_{i = 1}^{N} {| I_{D C} (x_{i}) - {\hat{I}}_{D C} - C_{0} I_{2 Ω} (x_{i}) [h (x_{i}) - z_{0}] |}^{2},

ξ_{Ω} (C_{1}) = \sum_{i = 1}^{N} {| I_{Ω} (x_{i}) - {\hat{I}}_{Ω} - C_{1} I_{3 Ω} (x_{i}) [h (x_{i}) - z_{0}] |}^{2},

where C₀ and C₁ can be solved by minimizing the error function ξ_DC and ξ_Ω for the vanadium region.

Once these coefficients C₀ and C₁ are determined, the topographical artifact signals I_Artifact,DC (x_c) and I_{Artifact, Ω} (x_c) can be calculated by using Eq. (14) and Eq. (15).

4. Conclusions

This paper presents a new method to reduce the topographical artifacts in SNOM images. The method first leverages the various harmonics intrinsically with the oscillation of tuning fork probe of a SNOM system. The optical information carried by different oscillation harmonics of tuning fork is related to the topographical artifacts. Using the second harmonic, the gradient of the optical SNOM signal with respect to z-direction variation of the probe is obtained. Further leveraging on the SNOM’s capability of simultaneously obtaining topographical and optical signals, the method recovers the topographical artifacts from the product of the second or the third harmonic optical SNOM signal and the topography signal. Deducting the artifacts from the total optical signal received by the SNOM, artifact-reduced SNOM images are obtained. The effectiveness of the proposed method is demonstrated on a rhombus vanadium grating commercially available for SNOM imaging calibration. Since there is no need to modify the SNOM setup except for some add-on demodulation functions, the proposed method provides an convenient and effective way to reduce the topographical artifacts for high quality of SNOM imaging.

References and links

1. D. W. Pohl, W. Denk, and M. Lanz, “Optical stethoscopy: image recording with resolution λ/20,” Appl. Phys. Lett. 44(7), 651–653 (1984). [CrossRef]

2. B. Hecht, H. Bielefeldt, Y. Inouye, D. W. Pohl, and L. Novotny, “Facts and artifacts in near-field optical microscopy,” J. Appl. Phys. 81(6), 2492–2498 (1997). [CrossRef]

3. S. I. Bozhevolnyi, “Topographical artifacts and optical resolution in near-field optical microscopy,” J. Opt. Soc. Am. B 14(9), 2254–2259 (1997). [CrossRef]

4. J.-J Greffet and R. Carminati, “Image formation in near-field optics,” Prog. Surf. Sci. 56(3), 133–237 (1997). [CrossRef]

5. R. Carminati, A. Madrazo, M. Nieto-Vesperinas, and J.-J Greffet, “Optical content and resolution of near-field optical images: Influence of the operating mode,” J. Appl. Phys. 82(2), 501–509 (1997). [CrossRef]

6. P. J. Valle, J.-J. Greffet, and R. Carminati, “Optical contrast, topographic contrast and artifacts in illumination-mode scanning near-field optical microscopy,” J. Appl. Phys. 86(1), 648–656 (1999). [CrossRef]

7. P. G. Gucciardi and M. Colocci, “Different contrast mechanisms induced by topography artifacts in near-field optical microscopy,” Appl. Phys. Lett. 79(10), 1543–1545 (2001). [CrossRef]

8. A. Bek, R. Vogelgesang, and K. Kern, “Optical nonlinearity versus mechanical anharmonicity contrast in dynamic mode apertureless scanning near-field optical microscopy,” Appl. Phys. Lett. 87(16), 163115 (2005). [CrossRef]

9. L. Billot, M. L. de la Chapelle, D. Barchiesi, S.-H. Chang, S. K. Gray, J. A. Rogers, A. Bouhelier, P.-M. Adam, J.-L. Bijeon, G. P. Wiederrecht, R. Bachelot, and P. Royer, “Error signal artifact in apertureless scanning near-field optical microscopy,” Appl. Phys. Lett. 89(2), 023105 (2006). [CrossRef]

10. P. G. Gucciardi, G. Bachelier, M. Allegrini, J. Ahn, M. Hong, S. Chang, W. Jhe, S.-C. Hong, and S. H. Baek, “Artifacts identification in apertureless near-field optical microscopy,” J. Appl. Phys. 101(6), 064303 (2007). [CrossRef]

11. B. Hecht, H. Bielefeldt, D. W. Pohl, L. Novotny, and H. Heinzelmann, “Influence of detection conditions on near-field optical imaging,” J. Appl. Phys. 84(11), 5873–5882 (1998). [CrossRef]

12. C. E. Jordan, S. J. Stranick, L. J. Richter, and R. R. Cavanagh, “Removing optical artifacts in near-field scanning optical microscopy by using a three-dimensional scanning mode,” J. Appl. Phys. 86(5), 2785–2789 (1999). [CrossRef]

13. J-H Park, M. R. Kim, and W. Jhe, “Resolution enhancement in a reflection mode near-field optical microscope by second-harmonic modulation signals,” Opt. Lett. 25(9), 628–630 (2000). [CrossRef]

14. K. Karrai and R. D. Grober, “Piezo-electric tuning fork tip-sample distance control for near field optical microscopes,” Ultramicroscopy 61(1–4), 197–205 (1995). [CrossRef]

15. M. R. Spiegel and J. Liu, Mathematical handbook of formulas and table (2nd Edition, McGraw-Hill, New York, 1999).

16. B. P. Ng, Y. Zhang, S. W. Kok, and Y. C. Soh, “Improve performance of scanning probe microscopy by balancing tuning fork prongs,” Ultramicroscopy 109(4), 291–295 (2009). [CrossRef] [PubMed]

17. Z. Liu, Y. Zhang, S. W. Kok, B. P. Ng, and Y. C. Soh, “Near-field ellipsometry for thin film characterization,” Opt. Express18(4), 3298–3310 (2010), http://www.opticsinfobase.org/abstract.cfm?URI=oe-18-4-3298. [CrossRef] [PubMed]

18. J. Prikulis, H. Xu, L. Gunnarsson, M. Kall, and H. Olin, “Phase-sensitive near-field imaging of metal nanoparticles,” J. Appl. Phys. 92(10), 6211–6214 (2002). [CrossRef]

19. R. Carminati and J.-J. Greffet, “Influence of dielectric contrast and topography on the near field scattered by an inhomogeneous surface,” J. Opt. Soc. Am. A 12(12), 2716–2725 (1995). [CrossRef]

20. P. S. Carney, R. A. Frazin, S. I. Bozhevolnyi, V. S. Volkov, A. Boltasseva, and J. C. Schotland, “Computational lens for the near field,” Phys. Rev. Lett. 92(16), 163903 (2004). [CrossRef] [PubMed]

21. L. Novotny and B. Hecht, Principles of nano-optics (Cambridge University Press, Cambridge, 2006).

22. P. B. Johnson and R. W. Christy, “Optical constants of transition metals: Ti, V, Cr, Mn, Fe, Co, Ni, and Pd,” Phys. Rev. B 9(12), 5056–5070 (1974). [CrossRef]

23. P. Albertos and A. Sala, Multivariable control systems: an engineering approach (Springer Press, London, 2004).

Artifact reduction by intrinsic harmonics of tuning fork probe for scanning near-field optical microscopy

Abstract

1. Introduction

2. Principle of topographical artifact reduction by using intrinsic harmonics in oscillation of SNOM probe

3. Experimental results of artifacts reduction by the proposed method

4. Conclusions

References and links

Cited By

Figures (12)

Equations (17)

Optics Express