1. Introduction

Photothermal (PT) microspectroscopy has emerged as a powerful imaging technique that can offer high sensitivity and chemical bond specificity for the characterization of a wide range of samples. This technique [1] has shown tremendous advancements in the visible to near-infrared wavelength spectrum, where its performance can compare with contrast obtained from state-of-the-art microscopy techniques that require the use of fluorescent tags [2]. Thus, this has opened a path for photothermal methods to enable various applications in single particle spectroscopy [2–5], e.g. of gold nanoparticles as small as 2.5 nm [2] and 2 nm [6], in optical coherence tomography (OCT) [7–9] as well as in imaging of biological tissues [10].

Mid-infrared (mid-IR) photothermal imaging [11–20] has attracted significant interest since it offers a label-free imaging approach: characteristic vibrational resonances in the molecular fingerprint region are targeted, without requiring any fluorescent or exogenous tagging of molecules for contrast. This has fueled a wide range of applications varying from remote sensing to food quality control, from identification of chemical impurities and nanoparticle tracking to biomedical imaging and diagnosis.

Standard methods for mid-infrared spectroscopy and imaging [21,22], including Fourier Transform Infrared Spectroscopy measurements, mostly require cryogenically cooled and complex mid-IR detectors, which can limit overall sensitivity. Further, it has been demonstrated that PT imaging can exceed the sensitivity levels of current conventional Raman scattering based vibrational microscopes by an order of magnitude [17]. PT imaging contrast relies on the inherent absorption properties of the sample, based on the detection of the photothermally induced index gradient, also referred to as thermal lens [23]. Relying on a pump-probe configuration, a shorter wavelength probe beam is used to detect the PT signal with high sensitivity in the near-infrared or visible wavelength regime with state-of-the-art photodetectors. Utilizing such a pump-probe configuration with a high brightness quantum cascade laser (QCL) enables spatial resolution at submicron values [16,24]. Thus, the diffraction limited spot size of mid-IR beams on the order of 10-20 μm in FTIR can be overcome and sub-cellular imaging in biology or imaging of nano-sized features can be enabled. For visible probe beams, spatial resolutions down to 0.6 µm [17] and even 0.3 µm [16] have been demonstrated, determined by the diffraction limited spot size of the probe beam. In this paper, we demonstrate a novel approach to resolve features below the diffraction limited spot size of the probe beam for the first time in vibrational PTM.

In general, contrast and sensitivity in PTM is significantly influenced not only by the object’s chemical and material properties (size, absorption cross-section, thermo-optic coefficient) but also by its surrounding environment: The spatial resolution in PTM is determined by the interaction of the probe beam with the photothermally induced thermal lens whose size is influenced by heat transport phenomena and thermal blurring [25]. Overall tight spatial confinement of the induced temperature profile is required to image at resolutions close to the theoretical diffraction limited value. With a thermotropic liquid crystal as the embedding medium, the imaging contrast has been enhanced by an order of magnitude in the visible, due to its large thermo-optic coefficient [26]. Photothermally induced material phase transitions have resulted close to a 40-fold improvement in the photothermal signals [12,27]. Nonlinear detection of higher harmonic thermal wave generation [28] has resulted in the narrowing of the temperature profile and enabled spatial enhancements up to 15-18% with 1 ps [29,30] and 100 ps pump pulses [31] and 23% enhancements with an ultrafast supercontinuum source [32]. Similar effects have also been demonstrated in PT deflection [33] and photoacoustic microscopy [34]. Utilizing a nonlinear material effect in PTM, super resolution capabilities with values down to tens of nanometers [25] have been shown. The formation of spatially confined distinct phase boundaries (nanobubbles), has resulted in an enhanced PT signal originating from areas smaller than the diffraction limited spot size of the beam [35]. Thus, in this work, we will study the mostly unexplored potential in utilizing similar nonlinear phenomena for mid-infrared PT imaging to enhance sensitivity and spatial resolution.

PTM is often performed by standard lock-in detection, which enables sensitive extraction of signal from small modulations in the probe field intensity. However, phase sensitive lock-in detection has the capability of separating the PT signal that is modulated in-phase and out-of-phase with respect to the excitation signal. The out-of-phase lock-in signal component physically originates from the delayed PT signal generated due to the finite thermal diffusivity of the embedding medium [36]. Thus, the quadrature component has been used to measure the characteristic thermal diffusivity of the medium [37,38] and to differentiate absorbers from nearby non-resonant scatterers [36]. The potential of measurements of the lock-in phase has been acknowledged in a range of different fields, e.g. to determine the thermal diffusivity of materials in photothermal radiometry [39], IR lock-in thermography and thermoreflectance [40–42].

In this paper, we study PT phase-sensitive lock-in detection combined with mid-IR vibrational signatures for the first time and evaluate how this can complement conventional PT amplitude images. While contrast in the amplitude images in PTM is provided by the inherently different thermo-optic dn/dT and absorption coefficients of the target and the embedding medium, by investigating the phase output of a lock-in amplifier, inhomogeneities in the thermal diffusivity and shifts in the rate of heat transport across the sample plane can be mapped with high sensitivity. To perform high quality lock-in phase imaging and to minimize effects of thermal blurring, we perform PT imaging in a spectral regime where both the imaging target and the embedding medium have comparable resonant behavior at the excitation wavelength. We demonstrate that under such conditions lock-in phase imaging as a complementary measurement can provide enhanced spatial resolution power and sensitivity in terms of signal to noise compared to the equivalent amplitude images. By combining this method with nonlinear demodulation at higher harmonics, we demonstrate that the spatial resolution can exceed the mid-IR diffraction limited spot size by a factor larger than three for amplitude images. However, it can be reduced by a factor of 8.6 in the corresponding phase image. Thus, spatial resolutions below a factor of 2.5 of the diffraction limited probe beam spot size are presented, resolving features below the probe diffraction limit for the first time in mid-IR PT imaging.

2. Methods and experimental setup

The photothermal imaging system consists of a pump probe laser configuration (see Fig. 1). The pump source is a tunable quantum cascade laser (Daylight Solutions) with a wavenumber range from 1580 to 1740 cm⁻¹, that is used to target the characteristic vibrational resonances of the sample. The QCL operates with a 100 kHz repetition rate and a pulse duration of 500 ns. The probe source is a low-noise continuous wave near-infrared fiber laser, with a center wavelength at 1550 nm, far away from the absorption peaks of the sample. Both laser beams are combined in a dichroic mirror and collinearly focused on the sample plane by a ZnSe transmission objective. The numerical aperture of the objective has a value of NA = 0.25, resulting in diffraction limited spot sizes for the mid-IR beam and near-IR probe beam around 12.6 μm (for a 6.3 μm wavelength) and 3.1 μm in diameter respectively. The mid-IR absorption induced temperature change in the refractive index profile leads to the build-up of a thermal lens. Incident powers on the sample are measured to be 3.5 mW for a pump wavelength at 1582 cm⁻¹ and 1 mW for the probe beam. The sample at room-temperature is mounted on a piezoelectric stage, which is used for obtaining photothermal images. The modulated forward scatter of the short wavelength probe laser is detected in the far field by an InGaAs photodetector. The PT signal is obtained in a optical heterodyne detection configuration [11], in which the modulated scattered probe field that carries the signal interferes on the photodetector with part of the probe field that remains unperturbed and acts as a local oscillator. The beatnote signal that modulates at the repetition rate of the pump laser is afterwards pre-amplified and extracted by phase sensitive lock-in detection, with an integration time of 71 ms.

 

Fig. 1 Mid-infrared PT imaging set-up with a tunable pulsed QCL pump and near-infrared probe laser, where amplitude (PTS) and phase information of the PT signal and the relative diffused signal ζ is detected at the lock-in.

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In our studies both the amplitude as well as the phase output at the lock-in amplifier are investigated. The phase is defined as $\Theta =\arctan \left(\frac{Y}{X}\right)$, where Y corresponds to the out-of-phase and X to the in-phase signal component. We define the ratio of the out-of-phase component to the total amplitude as $\zeta =\frac{Y}{PTS}=\sin \text{}(\Theta )$, with the PT amplitude signal $PTS=\text{}\text{}\sqrt{X^2+Y^2}$. This quantity ζ, which we will refer to as relative diffused signal in this study, captures the relative contribution of the out-of-phase or thermally diffused signal to the overall PT signal, with values ranging between −1 and 1. Since the ζ value is the out-of-phase lock-in signal normalized with respect to the amplitude, this imaging method features the advantage that the image is fairly independent of the signal strength and the incident pump power.

Melamine beads with a 1 μm diameter embedded in a 2.5 µm thin liquid crystal (LC) layer of 4-octyl-4’-cyanobiphenyl (8CB) serve as the sample under test. The 8CB features a distinct absorption peak for the C = C stretching band centered around 1606 cm⁻¹. The melamine beads show a resonance of the quadrant stretching of the 1,3,5-s-triazine ring around 1559 cm⁻¹ [43].

3. Results and discussion

A 200 μm by 100 μm area of the sample that contains both individual beads and clusters embedded in 8CB is imaged at a QCL pump laser wavenumber of 1582 cm⁻¹ (which falls into an identified spectral region of interest), see Fig. 2. The images are obtained with a 1 μm step size. As seen by the comparison between the amplitude image in Fig. 2(a) and the corresponding ζ-image in Fig. 2(b), the individual beads can hardly be distinguished in the PT amplitude image, as contrast is overshadowed by the presence of strongly absorbing clusters of beads. However, in the ζ-image individual single beads can be clearly differentiated, with high contrast since ζ does not depend on the signal strength. The slight inhomogeneities in the lock-in phase signal that are observed in areas where no beads are present, can be attributed to slight variations in the layer thickness of the embedding medium near the beads and which can influence the material’s thermal diffusive properties. The shadow-like structures around the bead clusters can potentially also be attributed to spatial aberrations since the imaging step size of 1 µm for this image is comparable to the actual bead diameter. To further quantify the image quality, we define the signal-to-noise ratio as the change in signal value between the bead S_m and the adjacent environment S_LC, divided by its standard deviation σ_LC, as $SNR=\text{}\text{}\frac{S_m-S_{LC}}{{\sigma }_{LC}}$. By comparing the PTS and ζ-image, one order of magnitude improvement in the SNR value from 10 for the amplitude image to 96 for the ζ-image can be obtained. In the amplitude images contrast originates from the inherent absorption and thermo-optic properties of the sample, while the ζ images map inhomogeneities in the thermal diffusivity. Even for heterogeneous samples with similar absorption values, the resulting PT phase images can thus provide differentiation with high SNR based on different values of thermal diffusivity.

 

Fig. 2 (a) Amplitude PT image at 1582 cm⁻¹ of a 200 μm x 100 μm sample area containing individual as well as clusters of melamine beads embedded in a 2.5 µm thin layer of 8CB liquid crystal, where contrast originating from single beads is low. (b) Corresponding ζ image of the same area with significantly enhanced contrast for the individual beads.

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As the imaging contrast for the PTS as well as for ζ is influenced by the wavelength dependent absorption, the spectral evolution of the PT signal and the relative diffused signal ζ is evaluated in more detail in Fig. 3 across the wavenumber region from 1577 cm⁻¹ to 1587 cm⁻¹. Here, the spectral response of the 8CB liquid crystal environment is compared to the spectral response taken at the position of a single melamine bead, for both the amplitude signals PTS_LC and PTS_m in Fig. 3(a) and the relative diffused signals ζ_LC and ζ_m in Fig. 3(b). For wavenumbers between 1577 cm⁻¹ to 1580.4 cm⁻¹, the PTS for both the melamine and the liquid crystal are comparable (with a maximum variation not exceeding 0.5 mV), indicating that the bead will be hardly distinguishable in amplitude images. For wavenumbers beyond 1582 cm⁻¹, an offset of 1.4 mV between the PTS_m and PTS_LC is observed indicating that the imaging contrast will gradually increase with higher wavenumbers. This offset eventually reaches a maximum value of 5.5 mV at 1586 cm⁻¹.

 

Fig. 3 (a) Spectral evolution of the PT signal measured for the liquid crystal environment (PTS_LC shown in dotted black) and for a single melamine bead (PTS_m shown in solid blue). (b) The relative diffused signal measured for the liquid crystal environment (ζ_LC shown in dotted black) and for the melamine bead (ζ_m shown in solid blue) obtained after demodulation at 100 kHz. Amplitude images (c) and corresponding ζ images (d) captured for different wavenumbers of i) 1579.3 cm⁻¹, ii) 1579.8 cm⁻¹, iii) 1581 cm⁻¹, iv) 1582 cm⁻¹ and v)  1584 cm⁻¹.

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However, the relative diffused signal in Fig. 3(b) follows a different trend: For wavenumbers below 1577 cm⁻¹ and above 1586 cm⁻¹, the ζ_LC and ζ_m values converge towards values of 1 or −1, respectively. Thus, in those regimes no significant shifts in the rate of heat transport are detected. In the wavenumber region between 1578 cm⁻¹ and 1584 cm⁻¹ (~6 cm⁻¹ span), a significant offset between ζ_m and ζ_LC is observed, as ζ_m gradually decreases with a slope dζ/dν of 0.6 cm, while ζ_LC remains fairly constant up to a wavenumber of 1583.4 cm⁻¹. In addition, around 1579 cm⁻¹ a shift in the sign for ζ_m from a positive to a negative value is observed. This wavenumber associated with the zero-crossing of ζ_m stands out, since the contribution of the relative diffused signal approaches zero at the bead position. Thus, thermal blurring effects are expected to be minimized under these conditions.

By raster-scanning over a single bead, PT amplitude images for selected pump wavenumbers are presented in Fig. 3(c). These images are obtained with a higher resolution 0.1 μm step size, which is an order of magnitude smaller than the actual bead size. For wavenumbers close to 1579 cm⁻¹, the bead is barely resolved, which suggests a small temperature gradient at the position of the bead. For higher wavenumbers, contrast from the bead starts to gradually increase, until the bead is clearly resolved for wavenumbers above 1582 cm⁻¹. Here, SNR values as high as 75 at 1582 cm⁻¹ and 184 at 1584 cm⁻¹ are recorded. In the wavenumber regime between 1585 cm⁻¹ and 1587 cm⁻¹, SNR values of up to 220 can be obtained where the average signal difference between the bead and environment amounts to ~6.8 mV compared to the average noise level of 30 μV. For larger wavenumbers, the difference between the PT signal for the 8CB and bead starts decreasing again. Even though imaging at 1584 cm⁻¹ provides a 2.5-fold improvement in SNR compared to 1582 cm⁻¹, there is an observed increase in the bead FWHM from 3.0 μm to 4.2 μm, corresponding to the wavenumbers 1582 cm⁻¹ and 1584 cm⁻¹, respectively. Thus, a tradeoff between SNR and spatial resolution is observed. This provides a unique approach to directly control the amount of thermal blurring and the resulting imaging parameters to make small features more strongly visible. The recorded FWHM at 1582 cm⁻¹ coincides with the diffraction limited spot size of the probe beam (3.1 μm in diameter for a numerical aperture of NA = 0.25), the theoretical minimum resolution that can be obtained in a linear PT imaging regime. The measured FWHM at 1584 cm⁻¹ of 4.2 μm is 3 times smaller than the diffraction limited spot size of the mid-infrared excitation beam (12.6 μm in diameter at 6.3 μm for 1584 cm⁻¹) and only 1.3 times larger than the diffraction limited spot size of the probe. It should be noted that for wavenumbers higher than 1590 cm⁻¹ contrast is significantly reduced for both amplitude and lock-in phase measurements as the signal from the liquid crystal starts dominating and overshadowing any bead signal contributions.

As demonstrated earlier, complementary imaging of the ζ response can provide improved contrast from single absorbers, based on their inherently different thermal diffusion properties. To study in detail the benefits of phase imaging compared to amplitude imaging, single bead ζ images are shown in Fig. 3(d).

In the ζ images the bead is clearly resolved at the image center with high contrast for all the presented wavenumbers based on different thermal diffusive properties. This demonstrates the capability of phase imaging to provide contrast even when the PT signal from an imaging target and its environment is comparable, as long as their thermal diffusion properties are different. Thus, this detection method provides complementary information related to heat transport effects that is otherwise not directly accessible in the amplitude images. For a wavenumber of 1579.3 cm⁻¹, the FWHM of the bead is minimized with a value of 3.3 μm, which approaches the diffraction limited spot size of the probe beam of 3.1 μm. This coincides with the zero-crossing wavenumber, where the out-of-phase signal component and equivalently the relative diffused signal ζ measured at the bead center approaches zero. This is a spectral region where minimum diffusive heat transport effects are expected near the center of the bead that can lead to higher spatial resolution. With increasing wavenumbers, the diffused signal gradually spreads to a larger spatial extent during the lock-in integration interval of 71 ms, resulting in an overall increase of the FWHM values from 3.1 μm at 1579.3 cm⁻¹ to 5.5 μm at 1582 cm⁻¹ and 8.5 μm at 1584 cm⁻¹. Similarly, as for the amplitude images, the SNR grows for increasing wavenumbers for which the offset between ζ_LC and ζ_m values is larger. Specifically, an increase from SNR = 147 at 1579.3 cm⁻¹ to a value of SNR = 227 at 1582 cm⁻¹ is observed. From this spectral evolution, it can be deduced that the underlying dynamics of heat transport are impacted by different excitation wavenumbers, due to varying amounts of absorption. Augmenting PT amplitude with lock-in phase signal collection can enable high contrast imaging for single absorbers with inherent different thermal parameters compared to their surrounding medium. Thus, phase imaging has the potential for sensitive detection of single absorbers whose spectral resonances overlap with those of the embedding medium.

The presented work focuses on a spectral region (from 1578 to 1587 cm⁻¹) where the absorption originating from single melamine beads and its embedding environment is comparable. Imaging close to the main absorption peak of the 8CB or melamine bead is intuitively an interesting wavenumber regime to study. However, it is found that for wavenumbers at the 8CB absorption peak, the absorption originating from the liquid crystal is significantly higher than that from the single bead and thus overshadows the response of the beads. At the same time, imaging at the bead resonance, is not the most desirable either, since there is hardly any absorption by the liquid crystal environment. In that case thermal diffusion and blurring effects cannot be avoided and the noise levels in lock-in phase imaging will be significantly high. In the case of limited and very small absorption, the phase output randomly fluctuates from –π to π. To detect the weakly absorbing signal from the beads, a regime where the PT signal from the liquid crystal and the bead are similar but have different phase responses is more ideal as shown in Fig. 3. The 8CB liquid crystal is chosen as an embedding medium since for increasing values of incident pump fluence, the PT spectrum undergoes pitchfork type bifurcations accompanied by a nonlinear increase of the signal strength [12]. After multiple bifurcations, residual absorption from the wings of the nonlinear signal can extend over a spectral region beyond its fundamental vibrational band. Thus, by varying the QCL pump power, the absorption response can be tuned to reach the desired regime shown here.

The measured spatial resolution values appear to be limited by the diffraction limited spot size of the probe beam. To study the impact of thermal blurring and the connection to the recorded PT amplitude imaging spot size, the radius of the thermal spot can be estimated as $R_T=R_A+R_B$. Here, R_A refers to the radius of a single absorber and the quantity $R_B=\sqrt{4k{t}_b}$ characterizes the amount of thermal blurring, which is equivalent to the thermal diffusion length R_th under pulsed excitation [6,25]. The latter depends on the medium’s finite thermal diffusivity k and probe pulse duration or signal acquisition time for CW probe sources t_b. Using a diffusivity value for the 8CB liquid crystal [44] of k_LC = $7.17\cdot {10}^{-8}\raisebox{1ex}{$m^2$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$, this leads to an estimated diffusion length of R_{th_LC} = 1.7 µm for a period of 10 µs (corresponding to a lock-in frequency of 100 kHz). This value can serve as a first general approximation, as potential complexities from the diffusivity as a tensor element are not considered. Overall R_T > w₀, where w₀~1.55 µm corresponds to the diffraction limited radius of the detection beam. Thus, for this demodulation rate a resolution below the diffraction limit of 3.1 μm cannot be obtained.

To improve the spatial resolution further, nonlinear concepts have to be considered since the imaging limits have been reached so far. So far, the measurements presented are demodulated at the fundamental repetition rate of the QCL at 100 kHz. However, the modulation frequency plays a significant role in the amount of thermal blurring or equivalently the size of the thermal diffusion length. In addition, the contribution of the diffused signal depends significantly on the relative size of the diffusion length compared to the detection beam waist. It has been shown that an optimal detection of the out-of-phase signal occurs when the thermal diffusion length approaches the dimensions of the probe beam waist [25,36]. Thus, the detection of the out-of-phase signal can be further optimized by decreasing R_th through nonlinear higher harmonic demodulation. In general, with higher demodulation rates and shorter time intervals, smaller diffusion lengths and reduced thermal blurring can be obtained. The generation of second and higher harmonic signals can be attributed to the nonlinearity or temperature dependence of the thermal diffusivity [28,45]: The temperature profile of the generated second harmonic thermal wave is proportional to the square of the temperature profile, resulting in a narrower point spread function [30,32] and a theoretical decrease of the thermal diffusion length by a factor of $\sqrt{2}$ for the second harmonic [34].

To study the impact of higher harmonic demodulation on the sample and on PT phase images for the first time, the lock-in amplifier is set to demodulate at the second harmonic with a frequency of 200 kHz than at the fundamental repetition rate at 100 kHz. In Fig. 4(a), similarly to our previous study, the PT spectrum of the liquid crystal environment PTS_LC-2f is compared to the PT spectral response at the position of the bead PTS_m-2f, detected at the second harmonic. For smaller wavenumbers, comparable absorption values are recorded between the LC and bead, before PTS_m-2f starts increasing more steeply.

 

Fig. 4 (a) Spectral evolution of the PT signal measured at the liquid crystal environment (PTS_LC-2f shown in dotted black), and for a single melamine bead (PTS_m-2f shown in solid blue). (b) The relative diffused signal measured for the liquid crystal environment (ζ_LC-2f shown in dotted black) and for the melamine bead (ζ_m-2f shown in solid blue) obtained after demodulation at 200 kHz. Amplitude images (c) and corresponding ζ images (d) captured for different wavenumbers of i) 1578.7 cm⁻¹, ii) 1579 cm⁻¹, iii) 1580 cm⁻¹, iv) 1582 cm⁻¹ and v)  1584 cm⁻¹.

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In Fig. 4(b), the spectral evolution of ζ_2f at the bead position ζ_m-2f and for the liquid crystal environment ζ_LC-2f is shown. While in this case both ζ contributions start with a negative relative diffusive signal value, both of them change their sign within the wavenumber region studied. The zero-crossing for ζ_m-2f occurs at 1578.7 cm⁻¹, and is slightly shifted by 0.6 cm⁻¹ towards shorter wavenumbers from the corresponding zero-crossing value for the fundamental at 100 kHz in Fig. 3(b). In addition, the width of the region for which there is significant offset between ζ_m-2f and ζ_LC-2f amounts to around 5 cm⁻¹. However, the main difference between the ζ spectrum for the two different demodulation rates, as seen in Fig. 4(b), is that the slope dζ_2f /dν = 4.4 cm at the ζ_2f = 0 point is almost 8 times higher compared to dζ/dν = 0.6 cm for the fundamental. This implies that for a smaller offset in wavenumber, a larger change in the lock-in phase or in the relative diffused signal contribution occurs for the second harmonic compared to the fundamental. As a result, sharper ζ images are expected. We attribute this effect to the nonlinearity of the thermal diffusivity and its temperature dependence which leads to the fact that the rate of heat transport is now more sensitive to temperature variations.

The evolution of the second harmonic PT amplitude images for selected wavenumbers is presented in Fig. 4(c). These images are taken with the same step size and pixel dwell time as for the first harmonic images. It can be observed that, unlike for the amplitude images at 100  kHz in Fig. 3(c), the bead is resolved throughout the whole spectral region featured. The higher resolving power in the second harmonic images can be attributed to the spatially narrower temperature profile which enables the detection of more spatially confined signal. As seen in Fig. 4(c), the amplitude image at 1578.7 cm⁻¹ features negative contrast. Around 1579 cm⁻¹ the contrast starts to gradually shift from negative to positive, as expected from the spectral PT absorption response. This is accompanied by an increase in the FWHM of the resolved bead from 2 µm (at 1579 cm⁻¹) to 4.7 µm (at 1582 cm⁻¹). Additional diffraction rings are also visible in the amplitude images taken at wavenumbers between 1579 cm⁻¹ and 1582 cm⁻¹, which spatially overlap with the contour line of the bead boundaries shown with enhanced contrast and high spatial sharpness in the corresponding ζ images. The wavenumber at which the shift in contrast occurs (close to 1579 cm⁻¹) indicates a similar state of minimum heat transport near the bead center, comparable to the fundamental measurements, and is expected to provide enhanced spatial resolution in the corresponding ζ images as well.

At 1578.7 cm⁻¹, the value of the relative diffused signal at the position of the bead approaches zero, which leads to high spatial resolution in the corresponding ζ image in Fig. 4(d). The FWHM is equal to 1.3 μm, which approaches the real physical size of the melamine bead. For increasing wavenumbers, as also seen in Fig. 4(c), the FWHM gradually increases as the area occupied by diffused signal grows. However, as expected, the higher spectral slope causes enhanced spatial sharpness in the corresponding ζ images.

The main figure of merit performance results between the fundamental and second harmonic detection are compared in Fig. 5. The linescans of the ζ images across the center of the bead are shown in Figs. 5(a) and 5(b) for the first and second harmonic, respectively. From these linescan profiles, the FWHM, contrast and steepness dζ/dy values are being evaluated for different wavenumber shifts Δν from the ζ = 0 crossing. For both the fundamental and second harmonic, the closer the wavenumber to the ζ = 0 wavenumber crossing, the smaller the measured FWHM, as shown in Fig. 5(a). The FWHM recorded for demodulation at 100 kHz varies between a range of 3.3 μm to 8.5 μm, while the FWHM for detection at 200 kHz assumes values between 1.3 μm and 8.1 μm for wavenumber shifts between −2 cm⁻¹ and 6 cm⁻¹. The smallest FWHM recorded at 100 kHz amounts to 3.3 μm, corresponding to the diffraction limited spot size of the probe wavelength. The smallest FWHM of the second harmonic at 200 kHz gets reduced down to 1.3 μm, thus enabling a 2.5 fold improvement in spatial resolution beyond the diffraction limit of the probe laser. These findings are summarized in Fig. 5(c): Imaging close to the ζ = 0 crossing wavenumber can minimize thermal blurring and enhance the spatial resolution beyond the diffraction limited probe spot size for nonlinear demodulation detection. While higher harmonic nonlinear detection has been investigated for PT amplitude images, our findings indicate that for the presented relative diffusive images, the spatial resolution can be enhanced even further due to more optimal detection of the out-of-phase signal component.

 

Fig. 5 Linescan through the center of the bead of the relative diffused signal ζ for increasing wavenumber shifts Δν from the zero-crossing wavenumber for (a) 100 kHz demodulation with a minimum FWHM of 3.3 µm and (b) 200 kHz demodulation with a minimum FWHM of 1.3  µm. (c) Evolution of the FWHM in the fundamental and second harmonic ζ images. (d)   Evolution of contrast in the fundamental and second harmonic ζ images, where values above 90% are reached. (e) The sharpness dζ/dy for demodulation at 200 kHz increases much steeper than for demodulation at 100 kHz.

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In Fig. 5(d) the achievable contrast is plotted, which is defined as $Contrast=\frac{{\zeta }_m-{\zeta }_{LC}}{2}$. Here, the denominator with the value two corresponds to the maximum achievable difference between the measured ζ values. It should be noted that for each wavenumber, the incident on the sample pump fluence is slightly different, following the trend dictated by the QCL gain curve. The incident power increases with longer wavenumbers for this specific spectral regime of interest. However as mentioned earlier, the ζ signal is independent of signal strength. Thus the evolution of the contrast can be mainly attributed to changes in the heat transport dynamics, as determined by the spectral dependent absorption properties. It can be observed that before the ζ = 0 crossing, contrast is slightly higher for the fundamental harmonic. For the wavenumber shift of Δν = 0 corresponding to ζ = 0, comparable contrast is achieved in both cases, whereas for larger wavenumber shifts, contrast is enhanced for the second harmonic. In addition, the contrast value increases almost four times faster for the second harmonic compared to the fundamental, so that a smaller shift in imaging wavenumber is required to achieve maximum contrast. Contrast generally can reach values greater than 90% for a range of wavenumber shifts (at 1582 cm⁻¹ for the fundamental and 1580 cm⁻¹ for the second harmonic). As thermal blurring effects become more impactful with slightly increasing absorption values and wavenumber shifts, the FWHM grows larger. However, there exists an optimum operating regime over a range of ~3 cm⁻¹ where high contrast around 92% can be achieved. For further increasing wavenumbers beyond a 4 cm⁻¹ shift, contrast is reduced again since the difference between the ζ signal measured at the bead and liquid crystal is becoming smaller again, cf. Figure 4(b). The steepness dζ/dy measures the sensitivity in detecting changes in the value of ζ, and is evaluated as the slope of the linear fit from the 10% to the 90% position of the linescan. Before the ζ = 0 wavenumber crossing, the values for both the first and second harmonic are comparable, see Fig. 5(e). At the wavenumber that corresponds to the ζ = 0 crossing the steepness for the second harmonic with a value of 0.7 µm⁻¹ is 2.3 times higher than for the fundamental with a value close to 0.3  µm⁻¹. For larger wavenumber offsets, the steepness in the second harmonic images continues to gradually increase at a much higher rate than for the fundamental, whose maximum recorded steepness amounts to 2.9 µm⁻¹. The slope for the second harmonic reaches a maximum value of 7.7 µm⁻¹ for a wavenumber shift of 3.3 cm⁻¹, which is almost two times larger than the maximum steepness obtained for detection at the fundamental. This steepness value at 200 kHz for a wavenumber of 1582 cm⁻¹ is by a factor of 8.6 larger than the steepness at the same wavenumber for demodulation at 100 kHz with a value of 0.9 µm⁻¹. This regime around 1582 cm⁻¹ coincides with wavenumbers that provide high contrast, but not necessarily the optimized smallest spatial resolution. Thus, the evaluation of performance metrics clearly provides new insights into the wavenumber dependency of optimized imaging conditions: We identified that imaging close to the ζ = 0 wavenumber can provide the highest spatial resolution with reasonable contrast. However, for weakly absorbing features that are desired to be distinguished with high contrast and good sharpness of the features, imaging slightly offset from the ζ = 0 wavenumber for the beads can be advantageous.

4. Conclusion

Overall, we have demonstrated that imaging of the lock-in phase as a complementary measurement to standard amplitude imaging in mid-infrared photothermal microscopy can provide higher contrast and enhanced spatial resolution for the detection of single weakly absorbing features. Contrast of single absorbers can generally be limited in the PT amplitude signal, as it can be overshadowed by clusters and strongly absorbing features. However, phase sensitive lock-in detection relying on thermally diffused signals can provide contrast purely based on the material inherent thermal diffusivity. This technique also enables the detection of features with overlapping spectral profiles and weakly absorbing features. We demonstrate that resolution is higher for the lock-in phase images when the relative contribution of the out-of-phase signal is minimized. By introducing the concept of identifying a ζ = 0 wavenumber crossing, the spatial resolution can be significantly enhanced in the diffusive phase signal. While we can demonstrate spatial resolution limited by the diffraction limited spot size of the probe as shown previously [16,17], in this work, we enhance the spatial resolution even further. By combining out-of-phase imaging with nonlinear demodulation at the second harmonic for the first time in mid-IR PT microscopy, we demonstrate that the probe diffraction limited spot size can be exceeded by a factor of 2.5 due to the nonlinear thermal response. Knowledge of the spectrally varying thermal diffusion properties allows careful material design strategies or post-measurement retrieval calculations of actual object sizes. With a higher numerical aperture objective,a shorter wavelength probe beam and optimization of the detection scheme to enable shorter pixel dwell times, this paves an attractive pathway towards sub-micron mid-IR label-free PTM to identify sub-cellular biological features, nano-particle tracking, identification of chemical impurities and for food control applications.