1. Introduction

s-SNOM is an emerging technique for optical nano-imaging that exploits the near fields at the sharp metal probe of an atomic force microscope (AFM) to overcome the diffraction limit [1–3]. In s-SNOM, the metal probe is illuminated with a focused laser beam and produces strongly confined and enhanced near fields (nanofocus) at the probe apex. When brought close to a sample, these near fields reflect at the sample surface and are subsequently scattered by the probe to the far field. Recording of the probe-scattered near fields yields information on the dielectric properties of the sample with nanoscale spatial resolution far beyond the diffraction limit. As a result, s-SNOM has found use in a wide range of applications, including the label-free identification of biological nanoobjects [4–9], the compositional mapping of polymer films [10–15], the discovery of exotic optical properties of two-dimensional materials [16–18] and free-carrier mapping in semiconductors [19–21].

Since its development, s-SNOM has experienced several technical innovations that have advanced its analytical potential. First, the introduction of interferometric techniques for the phase-resolved detection of the scattered near fields was a pivotal moment. This is because these techniques – in combination with vertical vibration of the AFM probe and signal demodulation at the higher harmonics of vibration frequency – enabled the full suppression of background scattering that does not contain useful information on the sample, and thus made s-SNOM imaging reliable [22–27]. Among these techniques is pseudoheterodyne (PSH) interferometry [22], which uses a phase-modulation of the reference beam for complete suppression of the background scattering and for providing amplitude and phase measurement of the scattered near fields. PSH interferometry has become one of the most widely implemented techniques for single-wavelength s-SNOM imaging, which can be attributed to its fast acquisition speed, operation in a wide spectral range from visible to THz frequencies and to the fact that it was implemented in a commercial s-SNOM. Second, the commercial availability of new laser technology was an equally important driver for s-SNOM. In its early times, s-SNOM was largely reliant on gas lasers (e.g. CO₂ lasers) for imaging in the infrared spectral range and, as a result, spectral coverage was limited. With the ready availability of modern QCLs [28,29], s-SNOM imaging of molecular and phononic excitations across the infrared spectral region has become standard practice [11,30].

Currently, efforts are underway to realize spectral s-SNOM imaging for the most comprehensive sample characterization. This capability is highly desirable because samples studied by s-SNOM are becoming increasingly complex, yielding spatially varying concentrations of analytes (such as in not biological cells or polymer blends) or dispersive polaritonic excitations, where full characterization requires imaging at several infrared frequencies (e.g. to determine peak ratios and positions). So far, spectroscopic imaging has been mostly implemented by acquiring a sequence of s-SNOM images where the laser wavelength is varied [4,23]. Such approaches require careful image alignment to correct for unavoidable sample drift and cause unnecessary wear of the s-SNOM tip. Most importantly, the imaging speed is limited (by the AFM mechanics) and, hence, the acquisition of a full sequence can be time consuming. Alternatively, spectroscopic imaging can be realized with near-field Fourier transform IR (nano-FTIR) spectroscopy, which is a derivate of s-SNOM imaging and uses broadband infrared light sources to acquire infrared spectra with nanoscale spatial resolution [31–36]. Nano-FTIR has demonstrated high sensitivity in the probing of biomolecules down to the sub-zeptomol level [6,34,37]. For imaging applications, nano-FTIR spectroscopy is generally considered to be a slow method. Recent approaches thus seek to significantly improve the speed of nano-FTIR spectroscopy by (i) rapid acquisition of interferograms on the second-scale [38], (ii) compressed sensing for the full spectral recovery at a reduced number of interferogram points [39–41], and (iii) interferogram subsampling for rapid imaging with narrow to medium bandwidth sources [42,43]. However, power levels of current nano-FTIR sources (of the order of tens to hundreds of μW) are still lower than those of modern QCLs used in s-SNOM imaging (at the single-digit mW level, limited to avoid sample damage). Therefore, QCL-based s-SNOM imaging may provide a better sensitivity in the same acquisition time frame compared to nano-FTIR approaches, and it is appealing to further explore QCL-based solutions for highly sensitive spectroscopic nano-imaging.

Here, we introduce multispectral PSH interferometry for s-SNOM imaging at two or more laser lines simultaneously. We then describe and validate an implementation of multispectral PSH interferometry for s-SNOM imaging at two wavelengths simultaneously. As an application, we demonstrate real-time correction of the negative phase contrast for accurate imaging of very weak absorption in the sample.

2. Theory of multispectral PSH interferometry

For multicolor s-SNOM (Fig. 1(a)), a laser beam consisting of a discrete spectrum of L laser lines of wavelengths, ${\lambda _l}$ ($l = 1..L$), is prepared (e.g., by combining the beams of several monochromatic lasers) and focused onto the metalized tip of an atomic force microscope (AFM) probe. The tip acts as an antenna for light and converts the incident field into a strongly confined and enhanced near field at the tip apex, which serves as a nanoscale light source to illuminate the sample. The near field – reflected at the sample surface – interacts with the tip and scatters to the far field via the tip. This process gives rise to a scattered near field, ${E_{\textrm{NF},l}} = {\sigma _{\textrm{NF},l}}{E_{\textrm{inc},l}}$, where ${\sigma _{\textrm{NF},l}}$ is the near-field scattering coefficient indicative of the reflected near fields and ${E_{\textrm{inc},l}}$ is the incident field at the $l$-the laser line. In addition, there is also a background field, ${E_{\textrm{B},l}}$, that originates from light scattering at the tip shaft and the sample and does not contain any useful information on the sample. To implement PSH interferometry, the field scattered by the tip is interfered with a reference field, ${E_{\textrm{R},l}}$, at the detector. The mirror in the reference arm of the interferometer is vibrated sinusoidally, $d\; = \; \mathrm{\Delta }d\cos ({Mt} )$, where M is the frequency and $\mathrm{\Delta }d$ the vibration amplitude. This vibration introduces a phase modulation of the reference field, which can be written as

Note that the vibration amplitude, $\mathrm{\Delta }d$, is constant and, therefore, the phase modulation depth, ${\gamma _l}$, varies with the wavelength, ${\lambda _l}$, of each laser line. The scattered field, ${E_{\textrm{S},l}}$, and reference field, ${E_{\textrm{R},l}}$, interfere at the detector and produce a signal that is proportional to light intensity (assuming a proportionality constant related to the detector sensitivity, $\kappa = 1$):

To spectrally resolve the light intensity, ${I_{\textrm{D},l}}$, for each laser line, we assume that a suitable mechanism is implemented such as a spectral detector (as illustrated in Fig. 1(a)) or a multiplexing approach (implemented in this work and described in Fig. 4). To suppress the background field, ${E_{\textrm{B},l}}$, and to isolate the scattered near field, ${E_{\textrm{NF},l}}$, the tip is vertically vibrated, $z\; = \; {z_0}\; + \mathrm{\Delta }z\cos \Omega t$, at frequency $\Omega $. The tip vibration produces a strong modulation of the scattered near field, ${E_{\textrm{NF},l}}$, while the background field, ${E_{\textrm{B},l}}$, is only weakly modulated [22]. Thus, demodulation of the detector signal at the $n$-th harmonic, $n\mathrm{\Omega }$, can be applied to suppress the background field. Specifically in PSH, the combined effect of tip oscillation and phase modulation of the reference beam creates yield a rich frequency structure in the detector signal, ${I_{\textrm{D},l}}$, with signal appearing at frequencies ${f_{n,m}} = n\Omega + mM$, which are termed sidebands (illustrated in Fig. 1(b)). Note that frequencies ${f_{n,m}}$ are common for all laser lines. The detector signal, ${I_{\textrm{D},l}}$, is demodulated at frequencies, ${f_{n,1}}$ and ${f_{n,2}}$, which yields the first and second sideband signals, ${Y_{n,l}}$ and ${X_{n,l}}$, respectively [22]:

 

Fig. 1. (a) Illustration of a multispectral s-SNOM setup based on the pseudoheterodyne detection scheme with a spectral detector. AFM: atomic force microscope; BC: beam combiner; BS: beam splitter; d: reference mirror displacement; ${E_{\textrm{inc}}}$: incident electric field;${E_\textrm{B}}$: background electric field; ${E_{\textrm{NF}}}$: near-field signal; ${E_\textrm{R}}$: reference electric field; G: grating; ${\lambda _l}:$ laser wavelength; PD: photodetectors; PM: parabolic mirror; PZT-M: piezoelectric-transducer-driven mirror; z: AFM cantilever displacement. (b) Simulation of the detected signal, I_D,l, for a vibrating reference mirror adjusted to phase modulatin depth, ${\gamma _0}$, as a function of time (left) and its Fourier transform (right).

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We note that multispectral PSH interferometry is based on the separation of amplitude and phase measurement (by using a phase-modulated reference beam and as obtained with Eq. (5)) and spectral resolving capabilities (implemented with the spectral detector). This approach allows for amplitude and phase measurement at all laser lines simultaneously and, in principle, multicolor s-SNOM imaging can be done at the full speed of PSH interferometry. Currently, the only method that would be available for the simultaneous imaging at multiple laser lines is nano-FTIR, which requires the acquisition of interferograms to provide spectral resolution and is thus a rather slow method for spectral imaging.

3. Implementation of multispectral PSH in a commercial s-SNOM

We describe and validate the implementation of multispectral PSH in a commercial s-SNOM, in our case, this is the neaSNOM (attocube systems AG). This microscope performs the signal processing of PSH interferometry at a fixed phase modulation depth, ${\gamma _0} = 2.63$, where the Bessel functions are of equal value, ${J_1}({{\gamma_0}} )= {J_2}({{\gamma_0}} )$. The microscope processes the sidebands, ${Y_{n,l}}$ and ${X_{n,l}}$, to yield the near-field amplitude and phase signals, ${S_{n,l}}$ and ${\mathrm{\Phi }_{n,l}}$, according to (as obtained from Eqs. (5) and (6))

Or, written alternatively as

For correct operation, the user is expected to adjust the vibration amplitude, $\mathrm{\Delta }d$, of the reference mirror to the phase modulation depth, ${\gamma _0}$, according to Eq. (2), which is typically done in a calibration procedure (explained below). However, in multispectral PSH, adjustment of the vibration amplitude, $\mathrm{\Delta }d$, will only be correct for one laser line, while incorrect for the other laser lines. In particular, the user cannot change the phase modulation depth, ${\gamma _0}$, that the signal processing is working at, nor can the sideband signals ${Y_{n,l}}$ and ${X_{n,l}}$ be recorded directly, thus preventing the application of Eq. (5), which is needed for multispectral PSH. In this case, we present a solution that can be used in post process, that is, after the data was recorded. To this end, we first measure ${S_{n,l}}$ and ${\mathrm{\Phi }_{n,l}}$ for all laser lines at the same, fixed vibration amplitude, $\mathrm{\Delta }d$. Then, from ${S_{n,l}}$ and ${\mathrm{\Phi }_{n,l}}$ (which are generally not the correct near-field amplitude and phase measurements) we determine the sideband signals, ${Y_{n,l}}$ and ${X_{n,l}}$, with Eq. (7). Having now the sideband signals, ${Y_{n,l}}$ and ${X_{n,l}}$, we apply the general Eq. (5) to compute the near-field signals, ${s_{n,l}}$ and ${\varphi _{n,l}}$, by taking into account the phase modulation depth, ${\gamma _l}$, for each laser line. This procedure can be summarized as a rescaling of the real and imaginary part of the microscope output signals, ${S_{n,l}}$ and ${\mathrm{\Phi }_{n,l}}$,

In the following, we validate Eq. (9) experimentally. To this end, we performed a single-wavelength experiment on our commercial s-SNOM where we fixed the wavelength of the infrared laser and operated the PSH interferometer at different vibration amplitudes, $\mathrm{\Delta }d$. This configuration mimics the situation where we have illumination at multiple laser lines while the PSH interferometer is operated at a fixed vibration amplitude, $\mathrm{\Delta }d$. In detail, we performed the experiments on a commercial s-SNOM microscope (neaSNOM, attocube systems AG) with standard PtIr-coated AFM tips (Arrow NCPt, Nanoworld AG, apex radius of about 30 nm) as near-field probes. The s-SNOM was operated in tapping mode with tip oscillation amplitude of 100 nm and oscillation frequency around 270 kHz. The sample was a Si substrate, which is non-absorbing in the mid-infrared spectral range considered here (900–1,400 cm^-1). The QCL was tuned to 1,600 cm^-1. The detector signal was demodulated at the 3rd harmonic of the tip oscillating frequency, 3Ω, and we recorded the near-field amplitude and phase signals, ${S_3}$ and ${\mathrm{\Phi }_3}$, as output by the PSH module (Eq. (7)) (we omit index l for this single-wavelength experiment).

In the first experiment, we performed a so-called offset sweep for different vibration amplitudes, $\mathrm{\Delta }d$. Briefly, a small phase variation of the reference beam is introduced by slowly moving the reference mirror up and down in a linear fashion (using the internal function of the s-SNOM which is called offset sweep). The offset sweep allows for adjusting the vibration amplitude, $\mathrm{\Delta }d$, of the PSH interferometer by monitoring and minimizing any variation in near-field amplitude, ${S_3}(t )$. To illustrate the offset sweep procedure, we show in Fig. 2(a) the time trace of the near-field amplitude and phase signals, ${S_3}(t )$ and ${\mathrm{\Phi }_3}(t )$, obtained for an adjusted vibration amplitude, $\mathrm{\Delta }d$. The near-field amplitude, ${S_3}(t )$, is a constant signal (except for noise), while the near-field phase, ${\mathrm{\Phi }_3}(t )$, shows a triangular waveform, as expected for a phase variation of the reference beam. In the complex representation, the near-field signals trace a circle (Fig. 2(b)). In comparison, Fig. 2(d) shows the signals for a de-adjusted case, as obtained by increasing the vibration amplitude, $\mathrm{\Delta }d$, increased by 20% compared to Fig. 2(a). The near-field phase, ${\mathrm{\Phi }_3}(t )$, is now a deformed triangular waveform, and the near-field amplitude, ${S_3}(t )$, shows signification variation compared to Fig. 2(a). In the complex representation, the near-field signals trace an ellipse (Fig. 2(e)). We note that in this de-adjusted case, ${S_3}(t )$ and ${\mathrm{\Phi }_3}(t )$ are not a correct measurement of the scattered near field, ${E_{\textrm{NF}}}$.

 

Fig. 2. (a) Measured time trace of the microscope output amplitude and phase signals, ${S_3}(t )$ (top) and ${\varPhi _3}(t )$ (bottom), while performing an offset sweep with an adjusted reference mirror vibration amplitude, $\mathrm{\Delta d},$ for a wavelength of 1,600 cm^-1. (b) Complex plot of the amplitude and phase signals, ${S_3}$ and ${\varPhi _3}$. (c) Correct near-field signals in amplitude ${s_3}$ and phase ${\varphi _3}$. (d)-(f) Same as (a)-(c) but for a de-adjusted reference mirror vibration amplitude. (g) Bessel functions, ${J_1}$ (black) and ${J_2}$ (gray), as a function of the phase modulation depth $\gamma $. The yellow dot represents $\gamma $= ${\gamma _0}$ while the red dots represent $\gamma $=3.25.

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In order to apply Eq. (9), it is necessary to know the phase modulation depth, $\gamma $, for each particular setting of the vibration amplitude, $\mathrm{\Delta }d$. To this end, we propose to retrieve $\gamma \; $from the offset sweep by using a minimization procedure. In detail, we take the time trace, ${S_3}(t )$ and ${\mathrm{\Phi }_3}(t )$, as obtained from the microscope and then calculate the near-field signal, ${s_3}(t )$, with Eq. (9) using different values for the modulation depth, $\gamma $. The correct value for $\gamma $ is found when ${s_3}(t )$ is constant over time. This condition can be mathematically expressed by minimizing the standard deviation of ${s_3}(t )$ over time, that is, minimizing $f = \textrm{std}({{s_3}(t )} )$. We note that in above minimization, we limit the search to values $\gamma < 5.13$ to avoid higher order solution which are undesirable in experiment owing to the lower signal amplitude (i.e., the Bessel functions ${J_1}(\gamma )$ and ${J_2}(\gamma )$ in Eq. (4) assume small values). We applied this procedure to the data in Fig. 2(d) and obtained $\gamma = 3.25$. Figure 2(f) shows the near-field amplitude and phase signals as obtained with Eq. (9), where the near-field amplitude, ${s_3}(t )$, is now a constant signal (except for noise) and the near-field phase, ${\varphi _3}(t )$, shows a straight triangular waveform (more variations are shown in Supplement 1, Fig. S1). This result confirms that correct near-field measurements are possible with Eq. (9), when the wavelength of the infrared laser is fixed and the vibration amplitude, $\mathrm{\Delta }d$, is varied. Equivalently, the offset sweep with the proposed procedure can be applied to determine the phase modulation depth ${\gamma _l}$ in multispectral PSH, where ${\gamma _l}$ is generally unknown for all laser lines, and Eq. (9) can be applied to obtain the correct near-field signals, ${s_n}$ and ${\varphi _n}$.

In a second experiment, we demonstrate how the correction procedure using Eq. (9) can be applied in an s-SNOM imaging. The sample was a cellulose acetate fiber (110 nm height) placed on a Si substrate (Fig. 3(a)) (fabrication details in Supplement 1, Note 1). The QCL was tuned to a wavelength 1,250 cm^-1, where the fiber exhibits a well-defined (C-O-C asymmetric stretching) absorption. For reference, we first adjusted the vibration amplitude, $\mathrm{\Delta }d$, using the offset sweep and imaged a small area (1 $\mu $m x 0.1 $\mu $m) of the cellulose acetate fiber. The near-field phase image, ${\mathrm{\Phi }_3}$, as obtained from the microscope (Eq. (7)) revealed a positive phase contrast of about $\mathrm{\Delta }{\mathrm{\Phi }_3} = 0.6\; \textrm{rad}$ compared to the substrate as a result of absorption in the cellulose acetate fiber (Fig. 3(b), red box). Next, we de-adjusted the vibration amplitude, $\mathrm{\Delta }d$, recorded an offset sweep to determine the phase modulation depth, $\gamma $, (see Supplement 1, Fig. S1) and repeated the imaging of the fiber. Figure 3(b) shows that the fiber exhibits a larger (smaller) phase contrast, $\mathrm{\Delta }{\mathrm{\Phi }_3}$, when the vibration amplitude, $\mathrm{\Delta }d$, was changed to smaller (larger) values compared to the adjusted vibration amplitude. It is clear that the near-field contrast, $\mathrm{\Delta }{\mathrm{\Phi }_3}$, is incorrect for de-adjusted $\mathrm{\Delta }d$. We then applied Eq. (9) to the near-field signal, ${S_3}$ and ${\mathrm{\Phi }_3}$, at each pixel of the image to obtain the correct near-field amplitude phase images, ${s_3}$ and ${\varphi _3}$. Figure 3(c) shows that the same near-field phase contrast, $\mathrm{\Delta }{\mathrm{\Phi }_3}$, was obtained for all considered values of vibration amplitude, $\mathrm{\Delta }d$, which is further quantified by the line outs in Fig. 3(e), confirming Eq. (9) yields the correct result.

 

Fig. 3. (a) Topography of a cellulose acetate fiber. (b) Repeated imaging of the fiber in panel (a) with PSH detection at 1,250 cm^-1 at different vibration amplitude, $\mathrm{\Delta }d$ (here specified as amplitude (voltage) of the driving signal for vibrating the reference mirror of the PSH module). Each image is showing the microscope phase output contrast, $\mathrm{\Delta }{\Phi _3}$. The red box marks the image recorded at the adjusted vibration amplitude $\mathrm{\Delta }d$. (c) Corrected near-field phase contrast image, $\mathrm{\Delta }{\varphi _3}$, retrieved from (b) by applying the correction (Eq. (9)), with the relative modulation depth (from 1.52 to 3.46 obtained from the offset sweep of Fig. S1). (d),(e) Line profiles of across the fiber as obtained by averaging along the columns in (b),(c).

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We note that Fig. 3(c) reveals a degraded signal-to-noise (SNR) ratio when using either very small or large vibration amplitude, $\mathrm{\Delta }d$, where the phase modulation depth is much smaller ($\gamma \ll {\gamma _0}$) or larger ($\gamma \gg {\gamma _0}$) than the fixed phase modulation depth, ${\gamma _0} = 2.63$ (e.g. $\gamma = 3.46$ in Fig. 3(c)). This behavior can be attributed to the fact that one of the two Bessel functions, ${J_1}(\gamma )$ and ${J_2}(\gamma )$ may become very small (see Fig. 2(g)), which leads to very small signal amplitude in the sidebands, ${Y_n}$ and ${X_n}$ (Eq. (4)). Thus, noise may be amplified when using Eq. (5) or Eq. (9) to obtain the near-field signals, ${s_{n,l}}$ and ${\varphi _{n,l}}$. This behavior sets a limit on the useful range of phase modulation depth, $\gamma $. In case of the data in Fig. 3, we obtained good SNR in a range of $\gamma = 1.74$ to $3.06$ (1.75:1 bandwidth), which is sufficient to cover most of the tuning range of current QCL technology (e.g., 900 to 1,600 cm^-1).

4. Multispectral PSH interferometry by time-division multiplexing

We now describe our implementation of multispectral PSH where a time-division multiplex scheme is applied to separate the individual laser lines (Fig. 4). We used two infrared light sources consisting of a wavelength-tunable QCL (tuned to a wavelength between 1,080 and 1,400 cm^-1, ${\lambda _{\textrm{Sig}}}$) and a CO₂ laser (emitting at a fixed wavelength of 940 cm^-1, ${\lambda _{\textrm{Ref}}}$). Both laser beams were combined at a ZnSe window (BC) and the combined beam was coupled into a near-field microscope. An optical chopper was inserted before the ZnSe window (BC) to modulate the laser beams, where the individual laser beams were passed at opposing ends of the chopper blade (having an odd number of slots) such that one beam passed, and the other beam was blocked for each position of the chopper blade. The combined laser beam, ${E_{\textrm{in}}}$, illuminated the tip of the AFM probe and the tip-scattered light, ${E_\textrm{S}}$, was analyzed with the PSH interferometer and detected with a single infrared detector (PD). The detector signal was demodulated at the 3^rd harmonic, $3\mathrm{\Omega }$. We configured the PSH module in the microscope software (option: analog probes) to output the near-field amplitude and phase signals, ${S_3}$ and ${\mathrm{\Phi }_3}$ (Eq. (7)), as analog signals. We then recorded these signals externally with a DAQ device (National Instrument, model NI USB-6218). This acquisition setup was needed to synchronize the signals, ${S_3}$ and ${\mathrm{\Phi }_3}$, of the PSH module to the optical chopper, and further, allowed for application of Eq. (9) in real time. Note that, in principle, our method can be implemented without an external DAQ, if the pixel rate of the PSH module can be synchronized to the optical chopper rotation, or if the synchronization signal from the optical chopper can be recorded in parallel to ${S_3}$ and ${\mathrm{\Phi }_3}$ in the microscope software. Prior to performing experiments, the reference mirror vibration amplitude, $\mathrm{\Delta d}$, was adjusted to wavenumber 1,250 cm^-1 in a calibration procedure. We then applied a demultiplexing scheme to obtain the near-field amplitude and phase images for each laser line, ${S_{3,\textrm{Sig}}}$, ${\mathrm{\Phi }_{3,\textrm{Sig}}}$ and ${S_{3,\textrm{Ref}}}$, ${\mathrm{\Phi }_{3,\textrm{Ref}}}$, as illustrated in Fig. 4(b,c).

 

Fig. 4. (a) Schematic of our multispectral PSH s-SNOM setup for imaging at two wavelengths simultaneously (symbols are common with Fig. 1). (b) Time trace of the microscope output signals, ${S_3}$ and ${\mathrm{\Phi }_3}$, and the chopper synchronization signal. (c) Demultiplexing of the time trace constructs amplitude and phase images at each individual wavelength.

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In detail, the PSH module of our commercial s-SNOM outputs a new data point for the amplitude and phase signals, ${S_3}$ and ${\mathrm{\Phi }_3}$, at a fixed rate of about 150 Hz when choosing an integration time of 6.5 ms. Internally, this data rate is synchronized to the electric signal P that controls the piezo actuator that moves the reference mirror. We used the electric signal P to synchronize the optical chopper to the data rate of the PSH module. Specifically, we chose $M = 300\; \textrm{Hz}$ and set the modulation frequency of the chopper to ${f_{\textrm{Chop}}} = M/8$, thus yielding four data points from the PSH module for every cycle of the chopper blade. Figure 4(b) shows the time trace of the involved signals, as recorded with the external DAQ. The first data point of the PSH module yields a measurement at wavelength, ${\lambda _{\textrm{Sig}}}$ (blue line in Fig. 4(b)), as, at that time, the chopper blade passed the QCL beam (blue) while the CO₂ laser beam (orange) was blocked, as illustrated in the sketch above the time trace. The second data point yields an invalid measurement (area grayed out in Fig. 4(b)) because both laser beams could pass the chopper blade. The third data point yields the measurement at wavelength, ${\lambda _{\textrm{Ref}}}$ (orange line in Fig. 4(b)), as, at that time, the chopper blade passed the CO₂ laser beam (orange) while the QCL beam (blue) was blocked. The fourth data point yields again an invalid measurement (area grayed out in Fig. 4(b)) because both laser beams could pass the chopper blade. To achieve this sequence in this order, the phase of the optical chopper was adjusted compared to electrical signal P. In addition to the amplitude and phase signals ${S_3}$ and ${\mathrm{\Phi }_3}$ from the PSH module, we also recorded the output signal from the chopper controller (indicates the position of the chopper blade), which showed a falling edge when the QCL beam was passed and a rising edge when the CO₂ beam was passed. To implement demultiplexing, the DAQ was then configured to record one data point at the falling and rising edge of the trigger signal of the chopper to produce two substreams of data, the near-field amplitude and phase signals, ${S_{3,\textrm{Sig}}}$, ${\mathrm{\Phi }_{3,\textrm{Sig}}}$ and ${S_{3,\textrm{Ref}}}$, ${\mathrm{\Phi }_{3,\textrm{Ref}}}$ (as indicated by the vertical lines in Fig. 4(b)). Imaging was performed as follows: First, the microscope was set up to scan a square area of the sample at 400 × 100 pixels, where we applied a 4-fold oversampling in the x-direction (the fast scan direction) to compensate for the 4-fold reduced data rate as a result of demultiplexing. Upon receiving a line synchronization signal from the microscope, the substreams of data, ${S_{3,\textrm{Sig}}}$, ${\mathrm{\Phi }_{3,\textrm{Sig}}}$ and ${S_{3,\textrm{Ref}}}$, ${\mathrm{\Phi }_{3,\textrm{Ref}}}$ were registered to form a two-dimensional image, as illustrated in Fig. 4(c). At the end of the imaging process, we obtained two sets of near-field amplitude and phase images yielding 100 × 100 pixels each. After recording the images, we applied Eq. (9) to obtain the corrected near-field amplitude and phase images at each laser line ${s_{n,\textrm{Sig}}}$, ${\mathrm{\varphi }_{n,\textrm{Sig}}}$ and ${s_{n,\textrm{Ref}}}$, ${\mathrm{\varphi }_{n,\textrm{Ref}}}$. To this end, an offset sweep was performed before each image acquisition to determine the phase modulation depth, ${\gamma _{\textrm{Sig}}}$ and ${\gamma _{\textrm{Ref}}}$. We further removed any interferometer drift that may have occurred during image acquisition by applying a line-by-line referencing of each near-field phase image, ${\mathrm{\varphi }_{n,\textrm{Sig}}}$ and ${\mathrm{\varphi }_{n,\textrm{Ref}}}$, to the near-field phase signal on the substrate adjacent to the fibers.

Note that owing to the multiplexing approach applied here, there is a small delay between the acquisitions of the near-field signals at the two wavelengths (∼13 ms). To correctly characterize material boundaries in the sample, we chose a pixel size (10 nm in Fig. 5) that was smaller than the tip radius (nominal 25 nm), thus effectively implementing 2.5-fold oversampling of the sample as it was also applied in holographic approaches for s-SNOM amplitude and phase imaging [24,43]. Further note that the optical chopper could be replaced by electronic on/off switching of the individual infrared laser, which we expect could be straightforwardly implemented with QCL and offer improved technical simplicity and robustness.

 

Fig. 5. (a) Topography image (left) and profile (right) showing ovalbumin and cellulose acetate fibers. (b),(c) Near-field phase images, ${\varphi _3}$, obtained at ${\lambda _{\textrm{Sig}}}$ 1,200 cm^-1 (b-top), 1,210 cm^-1 (b-center), and 1,250 cm^-1 (b-bottom) and ${\lambda _{\textrm{Ref}}}$ 940 cm^-1 using multispectral PSH. (c). (d) Differential phase images, $\varDelta {\varphi _3} = {\varphi _{3,\textrm{Sig}}} - {\varphi _{3,\textrm{Ref}}}$. (e) Line profiles taken along the dashed line in (b)-(d). (f) Cellulose acetate fiber spectra obtained with multispectral PSH where ${\lambda _{\textrm{Sig}}}$ was varied between 1,100 cm^-1 and 1,400 cm^-1. Black dots show the NPC-corrected data, grey dots are the original data. Lines are guide to the eyes. (g) Same as (f) but relative to ovalbumin fiber. Note: data for (f),(g) was taken with a different AFM tip compared to (b)-(d), thus yielding slightly different values for the near-field contrast.

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5. Real-time correction of the negative phase contrast

An application of s-SNOM imaging at two wavelengths simultaneously is the real-time correction of the negative phase contrast (NPC). Typically, in s-SNOM imaging of samples exhibiting molecular vibrations (weak oscillators), the near-field phase signal, ${\varphi _n}$, can be related to the absorption in the sample, which allows for material identification based on standard infrared databases of molecular vibrations [33,44]. The near-field phase signal, ${\varphi _n}$, of an absorbing sample is increased to that of a non-absorbing reference (e.g., the substrate), yielding a positive phase contrast (e.g., Refs. [4–6,10,11,23,31–34]). Yet, a recent study showed that in certain conditions a NPC may be observed compared to the substrate, which occurs in case of a non-absorbing or very weakly absorbing sample placed on a highly reflective substrate [45]. The NPC is a small effect, but it may lead to misleading results in sample characterization in that a sample may be erroneously classified as non-absorbing when in reality it is weakly absorbing. For the removal of the NPC, a method was demonstrated that consisted in acquiring two s-SNOM images, one at an absorption line of the sample and a reference image taken at a non-absorbing wavelength. By taking the difference of the near-field phase images, it was shown that an NPC-corrected image can be obtained, allowing for a correct measurement of the sample absorption [45]. Yet, such sequential imaging may be negatively affected by drift in the sample position and interferometer, limiting the accuracy of the method. To address this limitation, in the following we show that our setup shown in Fig. 4 can be applied for simultaneous and thus drift-free imaging at two wavelengths for real-time NPC correction. We demonstrate this with a representative sample containing ovalbumin and cellulose acetate fibers on a Si substrate, where a noticeable NPC can be expected because of the relatively low refractive index of the fibers compared to the highly reflective Si substrate (fabrication details in Supplement 1, Note 1).

Topography (Fig. 5(a)) shows ovalbumin and cellulose acetate fibers of about 50 nm and 80 nm thickness, respectively. The QCL (${\lambda _{\textrm{Sig}}}$) was tuned to a few selected wavelengths near the 1,250 cm^-1 absorption (C-O-C asymmetric stretching) of the cellulose acetate fiber, while the CO₂ laser (${\lambda _{\textrm{Ref}}}$) operated at a fixed wavelength of 940 cm^-1 where absorption of both cellulose acetate and ovalbumin was very small and assumed zero (see Supplement 1, Fig. 2 for far field IR spectral data). We first imaged the fibers at 1,200 cm^-1 (${\lambda _{\textrm{Sig}}}$) where cellulose acetate and ovalbumin are weakly absorbing. Indeed, the near-field phase image, ${\varphi _{3,\textrm{Sig}}}$, shows a small NPC on both fibers compared to the Si substrate (blue color, Fig. 5(b), top). Then imaging at 1,210 cm^-1 (${\lambda _{\textrm{Sig}}}$), where cellulose acetate is slightly more absorbing, we observed nearly zero contrast for cellulose acetate and ovalbumin in the near-field phase, ${\varphi _{3,\textrm{Sig}}}$ (white color, Fig. 5(b), middle), indicating that the NPC is compensated by the positive near-field phase contrast caused by the absorption in the fibers. Finally imaging near the C-O-C stretching absorption band of the cellulose acetate fiber at 1250 cm^-1(${\lambda _{\textrm{Sig}}}$), we observed a strong positive contrast (red color) on the cellulose acetate fiber as a result of the NPC now being small compared to the large positive near-field phase contrast caused by the absorption in the fiber (Fig. 5(b), bottom). For reference, Fig. 5(c) shows the near-field phase images, ${\varphi _{3,\textrm{Ref}}}$, taken at a wavelength, ${\lambda _{\textrm{Ref}}}$, of $940\; \textrm{c}{\textrm{m}^{ - 1}}$, where the fibers are non-absorbing, revealing a clear NPC of about 0.06 rad and 0.10 rad for the ovalbumin and cellulose acetate fibers, respectively.

Differently from the method presented in Ref. [45], multispectral PSH allowed for imaging at both wavelengths simultaneously and thus provides for nearly perfect co-registered imaging. This advantage removes the need for careful image alignment (required in Ref. [45]) and avoids misalignments due to sample drift in the AFM (e.g., lateral movement of the sample while taking the images) and interferometer drift (slowly varying optical path length that induces a phase offset on the near-field phase while recording the images). We could thus straightforwardly correct the NPC by calculating the difference of the two near-field phase images, $\mathrm{\Delta }{\varphi _3} = {\varphi _{3,\textrm{Sig}}} - {\varphi _{3,\textrm{Ref}}}$, as obtained with the QCL (${\lambda _{\textrm{Sig}}}$) and CO₂ laser (${\lambda _{\textrm{Ref}}}$), respectively. In the so-obtained difference near-field phase image, $\mathrm{\Delta }{\varphi _3}$, we observed that both fibers always show a positive phase contrast compared to the substrate, consistent with the expectation that sample absorption – weak or strong – causes a positive phase contrast in s-SNOM (Fig. 5(d)). Line outs taken along the dashed line in Figs. 5(b)-(d) quantify the effectiveness of the NPC removal. Remarkably, even in the case of strong absorption (Fig. 5(b), bottom), the single-wavelength near-field phase imaging, ${\varphi _3}({{\lambda_{\textrm{Sig}}}} )$, underestimated absorption in the fibers by a fairly large degree (∼50% in the ovalbumin and ∼20% in the cellulose acetate fiber, NPC is an additive effect). Thus, for accurate and quantitative near-field phase imaging of both weak and strong absorption, correction of the NPC seems to be needed, which multispectral PSH can provide in real time.

The difference (NPC-corrected) near-field phase image, $\mathrm{\Delta }{\varphi _3}$, shows a slightly larger noise compared to that of the individual near-field phase images, ${\varphi _{3,\textrm{Sig}}}$ and ${\varphi _{3,\textrm{Ref}}}$. This is expected because the noise in the individual near-field phase images can be assumed to be uncorrelated (after interferometer drift was corrected for) and thus adds up when taking the difference. By taking the standard deviation on a small area of the substrate, we estimated the noise level in the individual images, ${\varphi _{3,\textrm{Sig}}}$ and ${\varphi _{3,\textrm{Ref}}}$, to be 0.015 mrad compared to 0.019 mrad in case of the NPC-corrected near-field phase image, $\mathrm{\Delta }{\varphi _3}$ (values are given exemplarily for the third data set in Fig. 5(b), 1250 cm^-1 (${\lambda _{\textrm{Sig}}}$)). The noise in all three cases appeared to follow a normal distribution. Therefore, while NPC-correction ($\mathrm{\Delta }{\varphi _3}$) provides unambiguous identification of very weak sample absorption, the sensitivity is reduced, if only very slightly so, compared to the single-wavelength (non-NPC-corrected) image (${\varphi _{3,\textrm{Sig}}}$). To ensure the lowest noise level in the NPC-corrected near-field phase images, stable laser sources are required (a requirement which is well fulfilled by the QCL and the CO₂ laser used here). Laser power should be optimized prior to imaging to obtain the lowest possible noise level in the individual images, ${\varphi _{3,\textrm{Sig}}}$ and ${\varphi _{3,\textrm{ref}}}$.

We next demonstrate that multispectral PSH interferometry can also be applied to obtain near-field phase spectra by means of step-scanning the QCL. To this end, we repeatedly near-field imaged a small portion of the two fibers (1 μm x 0.1 μm around the dashed line), where we stepped the wavelength of the QCL, ${\lambda _{\textrm{Sig}}}$, from 1,100 cm^-1 to 1,400 cm^-1, while keeping the CO₂ laser wavelength, ${\lambda _{\textrm{Ref}}}$, fixed at 940cm^-1. In Fig. 5(f),(g), we extracted and plot the phase contrast on top of the cellulose acetate and ovalbumin fibers, compared to the Si substrate. The original (uncorrected) near-field phase contrast spectrum (gray dots) shows negative values in the range of 1,150 cm^-1 - 1,200 cm^-1 (cellulose acetate) and 1,100 cm^-1 - 1,250 cm^-1 (ovalbumin) (gray dots in Fig. 5(f),(g)), reaching a minimum of about 0.15 rad, which is consistent with what has been observed with similar materials [45]. In comparison, the NPC is strongly reduced in the corrected near-field phase spectra, further supporting our method (black dots in Fig. 5(f),(g)).

6. Discussion

The time-division multiplexing allows for implementations of multispectral PSH without requiring modifications to the s-SNOM system because only a single infrared detector is needed. Modifications are limited to the light source to generate a beam with multiple laser lines and an optical chopper to modulate the individual laser lines. This property makes time-division multiplexing interesting for its use in commercial s-SNOM systems. While data recording was implemented externally in this study (with a DAQ), we expect that multispectral PSH could be fully implemented in the microscope software by (i) providing direct access to the sideband signals, ${Y_n}$ and ${X_n}$, to enable the direct use of Eq. (5) and (ii) providing synchronization signals for the optical chopper.

We anticipate other forms of implementation of multispectral PSH where the single infrared detector is replaced by a spectral detector (as illustrated in Fig. 1(a)), offering several benefits. First, it could provide multicolor s-SNOM imaging at the full speed of PSH interferometry (time-division multiplexing trades speed for requiring only a single infrared detector). Second, this approach could be combined with infrared frequency combs, which emit a broad spectrum of discrete lines [46], where modulation of the individual laser lines is difficult. Third, it could conceivably be used in combination with infrared broadband laser sources with a continuous spectrum, where the spectrometer can be configured to produce beamlets that are sufficiently narrowband so that PSH interferometry can be employed. This approach is particularly interesting as modern infrared broadband laser sources are becoming increasingly more powerful such that single detectors may be driven into saturation (thus requiring attenuation of the laser beam), indicating that a spectral detector could make better use of the available laser power.

7. Conclusion

We demonstrated that PSH interferometry can be applied for s-SNOM imaging at two wavelengths simultaneously. To this end, we have shown and verified that the near-field amplitude and phase signals may be reconstructed over a wide range of laser wavelengths (1.75:1 bandwidth, covering typical tuning range of QCL) even though the PSH interferometry is operated at a fixed reference mirror vibration amplitude. We have applied this method for the real-time correction of the negative phase contrast where the effects of sample and interferometer drift are mitigated. Multispectral PSH could be easily extended for s-SNOM imaging at three or more wavelengths simultaneously. Particularly, current QCL systems are already equipped with four laser tuners. Although current commercial QCL systems are still limited to one active tuner, truly independent operation of all tuners may become available in the near future. Such multicolor s-SNOM imaging could lead to new imaging modalities such as one-pass mapping the distribution of chemical composition at the nanoscale where the individual laser lines are tuned to a few relevant absorption bands in the sample – a strategy that is already exploited to accelerate far-field IR imaging [47–49] and should be explored further for s-SNOM.