Nanoelectromechanical photothermal polarization microscopy with 3 Å localization precision Open Access

Single-molecule microscopy has enabled precise detection of individual characteristics without averaging for biochemical traces. Label-free single-molecule imaging further offers the possibility of detecting the authentic system dynamics without the modifications of the intermolecular interactions resulting from labeling.¹ Label-free techniques also bypass the photobleaching issue of the fluorescent dyes. To achieve a high sensitivity with label-free optical microscopy, detecting absorption of nano-objects has the advantage over detecting scattering, since absorption cross sections scale linearly with its volume while scattering cross sections scale quadratically.² Absorption-based optical microscopy with single-molecule sensitivity has been demonstrated by means of transmission microscopy,^3,4 ground-state depletion microscopy,⁵ and photothermal microscopy.^6–12 Among these techniques, photothermal microscopy measures direct absorption of molecules from their photothermal heating instead of the relative attenuation of incident light in the ppm regime and thus can provide even higher signal-to-noise ratio. With recent discoveries on responsive imaging media, sensitivity of photothermal contrast microscopy has been pushed to the pW/$Hz$ regime with near-critical Xenon.¹² 

As an alternative for conventional photothermal microscopy that relies on the temperature-sensitive refractive index of the medium for imaging, photothermal microscopy using nanomechanical resonators as a temperature-sensitive element has demonstrated unprecedented sensitivity of 16 fW/$Hz$ recently.¹³ The working principle is depicted in Fig. 1. The nanomechanical resonator was spin-coated with samples such as molecules and nanoparticles and scanned with an excitation laser. Upon scanning, optical absorption and photothermal heating of the sample results in a detectable detuning in the mechanical resonance frequency. The image contrast can thus be obtained by tracking the frequency shift of the nanomechanical resonator, and this is generally done with a phase-locked loop (PLL). An averaged localization precision of $32nm$ was extracted from the single-molecule signal previously.¹³ However, in comparison with localization precision better than 10 nm routinely achieved by single-molecule localization microscopy techniques,^14–17 it is clear that there is still space for improvements. We hereby present extensive research on optimizations of nanoelectromechanical (NEMS) photothermal microscopy to achieve better beam profile and localization accuracy. Here, we report on the following optimizations:

• A dedicated optical setup that allows full control of beam diameter, power, polarization, and alignment is established to replace the fixed laser source of the previously used laser-Doppler vibrometer (LDV), as shown in the setup schematic in Fig. 2(a). With this, we achieve a Gaussian beam profile with a beam waist approaching the theoretical limit of the given wavelength and numerical aperture, which is demonstrated in Sec. II. To provide excitation wavelengths for nanoparticles with different geometries and thus different absorption peaks, a diode laser with $633nm$ wavelength (Toptica TopMode) and a titanium-sapphire laser (M Squared SolsTiS) with wavelength locked at $800nm$ are used. Both lasers are linearly polarized. The 633 nm excitation matches the peak absorption wavelength of the 200 nm gold nanoparticles (AuNPs), while the 800 nm excitation matches the peak absorption wavelength of the gold nanorod with a short axis diameter of $≈10$ nm and a long axis diameter of $≈50$ nm used in this study. The output power of the lasers is monitored with the avalanche photodiode, as shown in Fig. 2(a). To identify the scanning regions on the nanomechanical resonator, a halogen lamp is implemented to provide illumination of the sample for imaging on the CCD camera.

• Instead of the optical vibrometric readout with a commercial LDV, an integrated inductive transduction scheme for both readout and actuation is implemented to provide more flexibility and compatibility with the optical setup, as shown in Fig. 2(b). The movement of the gold electrode in the static magnetic field results in an alternating voltage that is first amplified with a low-noise pre-amplifier and fed to the lock-in amplifier, and the frequency is tracked with the phase-locked loop (PLL) (HF2LI, Zurich Instrument). An enhanced Halbach array was used to create a magnetic field of around 1 T over the center distance of 5 mm.

• Scanning is done with a closed-loop piezoelectric nanopositioning stage (PiMars, Physikinstrumente) with 2 nm resolution to provide finer imaging data and thus better localization, as shown in Fig. 2(a). The objective is directly mounted on the scanning stage. The dwell time of each pixel is 200 ms, with a typical imaging time over a 30 $μ$m by 30 $μ$m area of around 10–30 min, depending on the pixel size.

• Instead of nanomechanical drums used in the previous work, NEMS trampoline resonators with a large center area for scanning are used in the present work, as shown in Fig. 2(c). Trampolines maintain sufficient area for imaging while providing higher responsivity with the same initial stress and window size, benefiting from the good thermal isolation of the thin tethers.

Gold nanoparticles (AuNPs) with a diameter of 200 nm are first spin-coated and moved into a straight reference line by means of an atomic-force microscope, in order to get a standard sample for system optimizations and calibrations, as shown in Fig. 3. A rough scan with the 633 nm laser over a bigger area in the center is first performed to locate the AuNP reference line, as shown in Fig. 3(a). The AuNPs reference line remains straight through the image, which is an evidence of good stability and negligible drift of the scanning system. We then performed scans within a smaller region centered at the reference line with different scanning step of 320 nm, 160 nm, and 80 nm. The averaged beam radius (⁠$r$⁠) extracted from the two-dimensional Gaussian fits of the frequency shift images from the gold nanoparticles in Fig. 3(d) is 800 nm, which is quite close to the nominal beam radius around 750 nm of the objective (Mitutoyo 50x, 0.55 N.A.). By comparing the NEMS photothermal microscopy images with the reference scanning electron microscopy (SEM) images, single nanoparticles and aggregates can be identified, as shown in Fig. 3(c). With the scanning beam power (⁠$P$⁠) of 85 $μW$⁠, we can define the responsivity (⁠$δR$⁠) as the relative frequency shift $Δf/f0$ per absorbed power by a single AuNP with an absorption cross section $σabs$ as

where $f0$ is the resonance frequency of the NEMS resonator. The theoretical absorption cross section of a 200 nm AuNPs based on Mie theory becomes $σabs=9×10−14m2$⁠.^2,13,18 A responsivity of $δR=7890W−1$ is extracted, which is around two times higher compared to membranes of the same stress of around 150 MPa and the same window size of 1 mm.^13,19

The frequency shifts from different AuNPs aggregates extracted from Fig. 3(d) are plotted in Fig. 4(a). The arrangement of the aggregates has slight influence on the scanning profile, which can be seen in the bump overlaying on the Gaussian functions. The absorption image results from the convolution between beam profile and the absorbing nanoparticle, and a collection of absorbers in the aggregates can thus produce a profile, which can be decomposed into several Gaussian functions, as shown in Fig. 4(b). In general, the peak frequency shift is approximately proportional to the number of particles per aggregate, as plotted in Fig. 4(c), with the absorption cross section extracted with Eq. (1) from the measured peak frequency shift directly. The effect of the plasmonic coupling is not so dominant for the AuNPs at this wavelength. As a result, NEMS photothermal microscopy can effectively identify the number of particles per aggregates, which can be useful for biochemical quantification purposes.

From Figs. 3(b)–3(d), as the pixel size reduces, the AuNP reference line can be more clearly resolved, and the center positions of the nanoparticles can be more precisely identified. To discuss the effect of pixel size systematically, the localization precision is calculated for different imaging pixel sizes after fitting with a two-dimensional Gaussian point spread function. The localization precision (⁠$Δx$⁠) can be expressed as^20,21

where $s$ is the standard deviation of the Gaussian function, $a$ is the size of the pixels, and $b$ is the background noise from the images. $N$ is the sum of the frequency shift levels resulting from the target absorbers, obtained by normalizing the frequency shift with the frequency noise, corresponding to the conventional definition of total photon counts. To extract $Δx$ from the photothermal images, two-dimensional Gaussian fits were first done on the beam profiles of the single gold nanoparticles, as shown in the images on the right side of Fig. 5. The standard deviation (⁠$s$⁠) of the Gaussian function in both x axis and y axis can be extracted from the fit individually. The sum of the frequency levels (⁠$N$⁠) can also be obtained. For each pixel size, beam profiles of three single nanoparticles were fitted, with six standard deviation (⁠$s$⁠) in both axes extracted, and the values were subsequently plugged in Eq. (2) with corresponding sums of the frequency levels (⁠$N$⁠) and pixel sizes (⁠$a$⁠). The averages and the standard deviations of the calculated localization precision from the three samples were plotted in Fig. 5.

The theoretical model in Fig. 5 is calculated based on perfect focusing with the nominal beam radius of the objective, perfect Gaussian point spread function, and the condition of no background noise of the image (⁠$b=0$⁠). In general, the images of AuNPs demonstrate a beam profile, which is very close to the Gaussian function, as shown in the right columns of Fig. 5. Both the measurements and theoretical limit have shown an improved localization precision with smaller pixel sizes. This improvement mainly comes from the increase in the sum of the frequency shift levels (⁠$N$⁠), making the beam profile better-defined with decreased pixel sizes, while the standard deviations of the Gaussian beam profile from different pixel sizes generally remain constant. However, in reality, to achieve a finer pixel size requires longer overall scanning time for each image, which can be a limiting factor, since the imaging can be subjected to long-term drift, which can distort the beam profile.

With a pixel size of 40 nm, standard deviations (⁠$s$⁠) in the range of 210–240 nm and a sum of frequency level (N) around $6×105$ are obtained from the Gaussian fits of the beam profiles, which results in a localization precision of around 3 Å. The background noise of the image in the measurements is defined by the standard deviation of the pixel frequency to be around 0.3 frequency level. This $Δx$ is almost one order of magnitude better than with a pixel size of 320 nm, which is also the pixel size used in previous work.¹³ This implies the single-molecule localization accuracy of 32 nm, which is lower due to the higher background noise, can be potentially improved by one order of magnitude by using a finer pixel size of 40 nm. The outstanding localization accuracy of the AuNPs in combination with the exceptional chemical stability also make it feasible for diffusion tracking²² as well as a reliable component for drift correction and alignment in super-resolution microscopy.²³ 

To investigate the capability of detecting polarization-dependent absorption, silica-coated gold nanorods with a length of around 50 nm are spin-coated on the NEMS trampoline resonator and scanned with the linearly polarized titanium-sapphire laser locked at 800 nm, as shown in Fig. 6. The absorption peak for the longitudinal polarization of silica-coated gold nanorods is around 808 nm and around 514 nm for transverse polarization. As a result, maximum absorption and thus frequency shift would be achieved when the nanorods arrange in the same orientation with the beam polarization. Two sets of nanorods with different orientations are located on the trampoline resonator, and the NEMS photothermal microscopy images are obtained with different beam polarizations, as shown in Fig. 6(a). The frequency shift of one set of nanorods increases as the polarization angle increases, while the frequency shift of the other set of nanorods decreases. The peak frequency shift of the two nanorods sets is plotted in Fig. 6(c) with respect to cosine of the polarization angle. The absorption cross section of the gold nanorods with such a dimension is around $1×10−15m2$ at 800 nm,²⁴ which is around 90 times less than the absorption cross section of 200 nm gold nanoparticles around $9×10−14m2$⁠. As a result, a maximum frequency shift of less than 10 Hz is expected from single nanorods, which explains the relatively small frequency shift from nanorods observed in Fig. 6, in comparison to 200 nm gold nanoparticles in Fig. 4. The thickness of the silica coating can also shift the absorption spectrum and further reduce the absorption cross section. Since the amount of nanorods is not the same for both sets, the highest frequency shift is not identical. Interestingly, it can still be clearly identified that the average orientations from this two sets of nanorods are almost opposite. This shows another possibility of NEMS photothermal microscopy for identifying polarization-dependent nano-objects. Furthermore, the polarization modulation imaging has been shown to improve the localization precision in fluorescence nanoscopy.²⁵ As a result, this capability can open another door for the optimization of NEMS photothermal microscopy as a localization microscopy.

We demonstrate optimization of NEMS photothermal microscopy with a dedicated optical setup for better beam quality and more control of the beam conditions as a first step toward localization microscopy. The effect of scanning step size on the localization precision is discussed systematically, and an optimal localization precision of 3 Å is achieved for 200 nm AuNPs with a low excitation beam power of $85μW$ and a scanning step of 40 nm. This exceptional localization precision along with the chemical stability of the AuNPs enables this system for diffusion tracking²² and drift-correction components in super-resolution microscopy simply by spin-coating.²³ The detection of the polarization-dependent absorption is also demonstrated with silica-coated gold nanorods, which can potentially boost the localization precision of NEMS photothermal microscopy. NEMS photothermal microscopy provides a non-fluorescent alternative for nano-object imaging and localization and would benefit multiple research domains for microscopic analysis.

We gratefully acknowledge the assistance of Sophia Ewert and Patrick Meyer with sample fabrication and preparation, and the assistance of Florian Patocka with atomic-force microscopy. This work is supported by the European Research Council under the European Unions Horizon 2020 research and innovation program (Grant Agreement No. 716087-PLASMECS).

The data that support the findings of this study are available within the article. For further information, please contact the corresponding author.