Introduction

Our understanding of nanoscale chemical systems is hampered by the absence of chemical imaging tools with the requisite resolution. The properties of these chemical systems are generally determined and governed by the degree of coupling between the components that comprise them and the resulting level of complexity, e.g., chemical and physical heterogeneity, phase, and morphology. More often than not, the degree to which we can harness a particular material property into a new technology is based largely on our knowledge and understanding of that system at or below the size scale of the components that comprise it. As important technology sectors such as alternative energy, advanced electronics, and health care exploit the unique properties of nanosystems, chemical imaging with greater and greater resolving power will continue to grow in importance.

The pursuit of higher resolution optical microscopy is much broader and diverse than chemical imaging alone. A number of superresolution (SR) techniques based on florescent microscopy have been developed for applications in life and materials science. Optical superresolution techniques fall into three general categories: optical bandwidth expansion, point spread function (PSF) engineering, and post recovery of optical bandwidth. Optical bandwidth expansion involves the extraction of higher spatial frequency information through the use of high numerical optics, e.g., solid emersion lens, or through spatial modulation techniques like structured illumination microscopy [1–4] to achieve resolution improvements of a factor of two and better. Point spread function engineering has been used to alter the illumination conditions and thus the Rayleigh criterion to theoretically allow for unlimited resolution [5]. An example of a point spread function engineered superresolution technique is stimulated emission depletion microscopy (STED) [6]. STED is a focus-engineered fluorescent microscopy technique that works by actively controlling the centroid of the emission through the depletion of the fluorescence from the outer circumference of a diffraction limited spot. The technique has achieved sub-50 nm scale optical resolution in the as-measured data [7]. Lastly, there are those techniques that require post recovery of superresolution. These techniques can range from deconvolution algorithms [8] to those that augment the microscopes spatial frequency channels (x, y, z) with the temporal channel [9]. These superresolution techniques include photo-activated localization microscopy (PALM) [10] and stochastic optical reconstruction microscopy (STORM) [11] and typically construct a functional superresolution image from thousands or tens of thousands of raw images acquired over the course of several minutes or hours. These post-recovery techniques have achieved position resolution at the tens of nanometer scale.

One of the main drawbacks of the superresolution techniques described above is that they rely on fluorescence detection either from intrinsic or extrinsic fluorophores. While these techniques have advanced life science, a broader impact has not been realized in chemical and materials science. Key barriers that have limited the practical pursuit of superresolution chemical imaging include chemical selectivity, sensitivity, and fabrication of superresolvingoptical elements. Recent developments in four-wave mixing microscopy (namely, coherent Raman microscopy) and in programmable optics (spatial light modulators) provide practical solutions to these limitations. Coherent anti-Stokes Raman (CARS) microscopy is one of the more widely used four-wave mixing (FWM) techniques [12]. CARS is a third order nonlinear optical process that involves multiwave, multicolor excitation comprised of a pump, Stokes, and probe beam. When the energy difference between the pump and Stokes beams matches a vibrational resonance in the sample, the detected signal is strongly enhanced, see Fig. 1(a) . This sensitivity to vibrational resonances makes CARS highly chemically specific, and the amplification caused by the coherent nature of the signal provides for rapid image collection: the CARS process can be many orders-of-magnitude more efficient than conventional Raman. The chemical sensitivity of CARS along with the increased signal has enabled researchers to achieve video-rate, molecular imaging of lipid-rich cells [13] and in vivo imaging of live mouse tissue [14].

 

Fig. 1 (A) Energy diagram for coherent anti-Stoke Raman scattering (CARS). P and S stand for pump and Stokes beams. Ω is the vibrational energy. g is the vibrational ground state; e, excitation state; g’, virtual ground state; e’, virtual excitation state, respectively. (B) P, the focal fields calculated for the flat wave front; S, focal fields for the π-stepped annular (≈0.42 of beam diameter) phase mask; CARS, the product of the squared P and S. Insets in P and S are the illustrations for each wavefront. (C) A cartoon shows how a spatial light modulator (SLM) controls the PSF of microscope. PC; personal computer, OL; objective lens, SiNW; silicon nanowire, BS; beam splitter.

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As in conventional light microscopy, the diffraction limit governs the achievable spatial resolution in FWM microscopy as well. This limits the lateral resolution of linear techniques, e.g. fluorescence, to approximately 300 nm for excitation wavelengths in the near-infrared. The attainable resolution in non-linear microscopies is slightly better than that defined by the diffraction limit: 250 nm for FWM microscopes operating in the near infrared [15]. This is a result of the focal volume in a non-linear microscope being defined by the product of multiple, diffraction limited PSFs: in two-photon microscopy the resulting PSF intensity profile is equivalent to the conventional PSF squared. An illustration of this effect is shown in Fig. 1(b) for the CARS variant of FWM. Here, focal field calculations of a conventional pump (P) and phase filtered Stokes (S) focal fields are multiplied to generate the CARS focal field. Several experimental and theoretical studies, both in the near-field and far-field, have recently been published that seek to enhance the attainable resolution in FWM microscopes. For example, in a near-field scanning optical microscope (NSOM), CARS has been used to visualize DNA networks [16], where the achievable spatial resolution was 15 nm. In a similar study, NSOM coupled with four-wave mixing resolved 60 nm sized isolated gold nanoparticles [17]. In conventional, far-field four-wave mixing microscopies, theoretical studies have been carried out that describe several approaches for achieving resolution enhancement. These approaches range from discontinuous focal phase fields to multiplicative focal volume engineering to coherence emission suppression [18–21]. In the work by Raghunathan and Potma [19], the effects of multiplicative focal field engineering by Toraldo style, pupil phase filters was rigorously calculated. They showed that a resolution enhancement in FWM microscopy of better than a factor of 1.5 could be achieved. Motivated and guided by this work, we have implemented a point spread function engineering approach that uses an annular-shaped pupil phase filter to dramatically limit the excitation volume in the focal plane. The phase filters are digitally synthesized using a spatial light modulator (SLM) scheme similar to the one used previously in our lab for contrast enhancement in CARS, see Fig. 1C [22]. Here, as in our previous work, we use SLM generated pupil phase filters to improve not only the contrast but also to extend the resolution to well below 150 nm. In 1952, Toraldo di Francia had proposed the use of phase filters to engineer a microscope’s PSF to achieve unlimited resolution [5]. The practical limitations of Toraldo’s theoretical treatise involve secondary effects that are introduced as the microscope’s focus becomes highly confined. These secondary effects include satellite peaks or side lobes that become increasingly intense and ultimately complicate the PSF and rendering it unusable for microscopy. In this letter, we demonstrate a superresolution technique that retains the four-wave mixing microscope's ability to acquire materials- and chemical- specific contrast while tightening the spatial resolution to below 150 nm. The functional superresolution effect is achieved by narrowing the microscope’s PSF in the focal plane through the use of a Toraldo-style pupil phase filter coupled with the multiplicative nature of four-wave mixing to mitigate secondary effects. We demonstrate the microscope’s resolution improvement through the imaging of nanostructured materials: gold nanorods, polystyrene beads and silicon nanowires.

Two electronically-synchronized, 2.2 picosecond pulsed lasers were used as pump and Stokes beams for the four-wave mixing generation (see Fig. 2 for the optical setup). The details on optical elements for the control of polarization, intensity and beam manipulation have been outlined previously [23]. The Stokes beam (785 nm) was telescopically expanded to fill the active area (2 cm x 2 cm) of the nematic liquid crystal SLM (X8267, Hamamatsu) [24]. The Stokes beam, once reflected from the SLM, was imprinted with a computer controlled phase profile. This profile was comprised of controllable circular phase steps and a calibrated background field that cancels out systematic phase distortions. The background correction was measured using a Shack-Hartmann wavefront sensor followed by reformatting and phase response calibration to obtain a flat phase field or wavefront. The phase-modulated Stokes beam was then relayed by four convex lenses to the back pupil plane of the microscopic objective (1.3 NA, oil immersion). The output diameter of the Stokes beam from the SLM was matched to the diameter of the pupil plane of the objective. The pump beam was also matched to this diameter using a beam expander. The pump and Stokes beams were collinearly combined by a 50:50 beam splitter. The reflected FWM signal generated by the specimen was separated from excitation beams by use of a non-polarizing beam splitter and bandpass filters.

 

Fig. 2 A schematic diagram of the super-resolution, four-wave mixing microscope. SL; SychroLock, BE; beam expander, CL0 – CL4; convex lenses, TS; a manual xy directional translation stage, BS; beam splitter, SS; piezo-driven xy image scanning stages, NPBS; non-polarizing beam splitter, BF; bandpass filter, CCD; charge coupled device, APD; avalanche photodiode, SLM; spatial light modulator, WS; wavefront sensor.

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In the microscopy measurements, the samples were scanned using a closed-loop, piezoelectric scan stage with 10 nm resolution in x,y and z. The cross-sectional mapping of the focal field distributions were carried out by scanning an isolated nanoparticle through the focus. This was done to verify the intended effects of the SLM generated phase filters. A complete mathematical representation of the converging fields in the focus was adapted from the literature [25]. These calculated focal field distributions for an optical system comprised of an annular phased-step wavefront (phase masked beam) focused by a 1.3 NA oil immersion objective were used for predictive and diagnostic purposes.

The geometry of the annular phase masks used in programming the SLM are shown in Fig. 3(a) . The field variations in the grayscale are the background correction values used to obtain a flat phase field as measured by the wavefront sensor. The annular features (disks) in the grayscale are set to give a π phase step relative to background over the region of interest. The diameter of the annular phase step (d) is denoted relative to the dimension of the backstop of the microscope objective (d₀), i.e., it is normalized to d₀. The range of diameters (d) used in the measurements that follow are shown in Fig. 3(a). Measurements of the resulting xy field distributions were recorded for each value of d by monitoring the two-photon emission, excited at 785 nm, from an isolated gold nanoparticle while scanning the sample, Fig. 3(b), along with the associated calculated xy field distributions, Fig. 3(c) [26]. The prominent features, which include a narrowed center lobe as well as the satellite lobes, in both the experimental and calculated profiles are in good agreement. The xz field distributions were measured and calculated in the same fashion and are shown in Figs. 3(d) and 3(e) respectively. As with the xy field distributions, the calculated and measured values are in excellent agreement. This can be seen both in terms of the feature evolution with increasing values of d as well as the emergence of the side lobe intensity that is coupled with the narrowing of the centroid. Relative to the conventional PSF in the first column in Fig. 3(b), the centroid of the PSF becomes smaller (with a gradual increase in the side lobe intensity) up to a diameter of d = 0.42. As the diameter is increased further, the centroid elongates in xz until splitting in two (at d = 0.56) and then the trend is reversed with a re-emergence of a conventional PSF at d = 0.84. Also of note is the relative drop of intensity in the focal plane, both measured Fig. 3(d) and calculated Fig. 3 (e), from a maximum when d = conventional to a minimum at d = 0.42 and then restored again at d = 0.84: the centroid intensities relative to the conventional PSF (1) were 0.85 at d = 0.14, 0.72 at d = 0.28, 0.51 at d = 0.35, 0.25 at d = 0.42, 0.09 at d = 0.56, 0.31 at d = 0.70, and 0.83 at d = 0.84.

 

Fig. 3 Geometry of the annular phase masks used in programming the SLM. () A background mask which corrects the wavefront distortion in the optical system along with the series of annular masks used to generate the Toraldo phase filters. (B) A series of focal distributions (xy) resulting from application of the associated phase masks in (A) recorded by epi-two photon luminescence imaging of an isolated gold nanoparticle with 785 nm excitation. (C) shows a series of focal field calculations for the each of the annular phase masks in (A). The dimension is indicated by the λ: the wavelength of the incident beam. (D) xz focal field distributions resulting from application of the associated phase masks and recorded in a similar manner as the xy fields. (E) A series of xz focal field calculations.

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We achieve a superresolving PSF free of secondary features/artifacts by multiplicatively combining a conventional pump PSF with a Toraldo filtered Stokes PSF. This schema was critically assessed in terms of our ability to reproduce the calculated FWM field distribution as well as the degree to which the centroid of the PSF could be defined while abating the artifactual, side lobes. Figure 4 shows the results of the calculated (inset) and measured FWM PSF. The calculated values are the products of two conventional, and one phase filtered point spread function from the calculated values shown in Fig. 3(c): PSF_FWM = PSF_conventional * PSF_conventional * PSF_{phase filtered} [27]. The measurements of the FWM PSF were carried out by scanning an isolated region of a normally 100 nm diameter Si nanowire sample. The region is shown in Fig. 4(a) and it is denoted by the dashed line over the bright feature associated with the nanowire. The excitation wavelengths for this FWM measurement were 754 nm for the conventional and 785 nm for the phase filtered beams with each being nominally 1 mW as measured at the objective back stop. The xz FWM field distribution maps are shown in Figs. 4(b) through 4(h). In each image, the resulting PSF is mapped for a range of phase filtered PSFs combined with a conventional PSF. The associated d values for each image are 4(b) = conventional, 4(c) = 0.14, 4(d) = 0.28, 4(e) = 0.42, 4(f) = 0.56, 4(g) = 0.70, 4(h) = 0.83. As can be seen from the results in Fig. 4, the experimental and calculated values are in excellent agreement. The xz maps of the FWM PSFs exhibit the trend seen for the phase filtered PSF in Fig. 3 with a narrowing of the centroid from the conventional PSF in Fig. 4(b) from 300 nm down to nominally 150 nm in Fig. 4(e). More importantly, the side lobe intensity has been reduced dramatically. Additionally, the elongation of the focal volume in the z direction is now less severe than that in Fig. 3. This is also a result of the multiplicative FWM response where the regions of non-overlap of the PSFs do not contribute to the FWM field. Thus the FWM PSF’s side lobes are removed as well as its elongation in z, and the PSF’s centroid is spatially confined to well below the diffraction limit.

 

Fig. 4 (A) FWM microscopy images of Si nanowires on glass taken with 754 nm and 785 nm excitation beams. The arrow indicates the direction of the polarization and the dotted line indicates the region where the xz scans were recorded. (B) Shows the FWM PSF (xz) that results from two conventional beams. FWM PSF images that result from phase filtering with annular masks are shown in (C) for d = 0.14, (D) for d = 0.28, (E) for d = 0.42, (F) for d = 0.56, (G) for d = 0.70 and (H) for d = 0.83.

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To evaluate the resolution enhancement of the SR-FWM PSF, images of an individual, nominally 100 nm Si nanowire were recorded. Figure 5(a) through 5(f) show the results for a range of phase filter geometries: 5(a) = conventional/ d = 0, 5(b) d = 0.14, 5(c) d = 0.28, 5(d) d = 0.35, 5(e) d = 0.46, and 5(f) d = 0.56. As can be seen from this image series, the feature associated with the nanowire is initially broadened by the conventional PSF, 5(a), and then becomes increasingly narrower, 5(b) −5(e), before becoming broadened again, 5(f). As is shown in Fig. 5(g), cross-sectional analysis of the features from the conventional PSF, 5(a), and the SR-PSF, 5(d), shown an improvement of the resolution from nominally 300 nm full-width at half-maximum (FWHM) to nominally 150 nm FWHM. The actual spatial extent of the PSFs will be less than that derived from this analysis due to convolution with the 100 nm diameter nanowires. To further evaluate the true spatial extent of the PSF, simulated cross sections were performed by convolving a feature of width 100 nm with the calculated conventional PSF (inset of Fig. 5(a)) and phase filtered PSFs with associated values for d: inset of Figs. 5(b) for d = 0.14, 5(c) for d = 0.28, 5(d) for d = 0.35, 5(e) for d = 0.46, and 5(f) for d = 0.56 [28]. The resulting cross sections for the conventional and for d = 0.35 PSFs are shown in Fig. 5(h). The broadened feature widths are in excellent agreement with the experimentally obtained values for FWHM. From this analysis we can estimate that the resulting SR-PSF (d = 0.35) has a true spatial extent that approaches 130 nm FWHM (deconvolved) as compared to the measured value of 150 nm FWHM (convolved).

 

Fig. 5 The FWM images of an isolated nanowire using conventional (A) and engineered PSFs corresponding to phase filters with annular diameters of (B) d = 0.14, (C) d = 0.28, (D) d = 0.35, (E) d = 0.42 and (F) d = 0.56. Insets in the lower-left corners correspond to simulated images using the calculated PSF for each phase filter. (G) The line profiles for the white dotted lines noted as (1, 2) in (A) and (D) are the average of three adjacent line scans: there was a mean variation of ~5% from line to line. (H) Simulated cross sections from the calculated images (inset) of a 100 nm feature using a conventional FWM PSF (black) and a SR-PSF (red). Note: The color scales are normalized, and the total signal strength relative to the conventional PSF case (maximum) is down a factor of 3.2 (minimum) for the d = 0.35 case.

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As stated above, a key variant of FWM microscopy is coherent Raman microscopy, namely CARS microscopy. This is due in large part to the outstanding sensitivity and chemical selectivity of the CARS process. To illustrate the use of a SR-PSF in a CARS microscope, we carried out measurements of dispersed polystyrene beads on glass. Chemically sensitive CARS contrast is achieved by probing the 1000 cm⁻¹ C-C ring vibrational mode of polystyrene. To do this, a 727.8 nm pump (≈2 mW at the objective) and 785 nm (≈4 mW at the objective) Stokes beams were used with the resulting CARS signal collected in an epi geometry. Figure 6(a) shows a Raman spectrum from a cluster of polystyrene beads. The positions for the vibration modes used in Fig. 6(b) (1000 cm⁻¹ = on resonance) and 6(c) (900 cm⁻¹ = off resonance) are indicated in the Raman spectrum, and the resulting contrast is shown in Figs. 6(b) and 6(c). Additionally, a contrast gap is indicated by two parallel lines in Fig. 6(b). This contrast gap was created by momentarily removing the temporal overlap between pump and Stokes pulses by ≈800 ps and further illustrates that the image contrast is from FWM. The polystyrene beads imaged in this study were nominally 0.50 µm for Figs. 6(b) and 6(c) and 0.30 µm in diameter for Figs. 6(d) through 6(g). Figure 6(d) shows a 20 µm x 20 µm CARS image recorded on the 1000 cm⁻¹ resonance and with a conventional PSF. A signal-to-noise level > 100 was obtained with morphological features such as rafts of beads and isolated beads similar to those observed in other microscopy studies of these particles [29]. In Fig. 6(d), the individual, 0.30 µm particles that comprise the raft features are not clearly resolved. In Fig. 6(e), the same area was imaged with a SR-PSF (d = 0.35). The individual 0.30 µm beads are now more clearly defined in this SR-CARS image. Three dimensional (3D) renderings of subportions, denoted by dashed rectangles, of these images provide for a closer comparison and show the degree to which the particles are resolved from each other in the SR-CARS image (Fig. 6(f)) relative to the conventional CARS image (Fig. 6(g)). Features of note in these 3D images include that of the two particles on the left and the degree to which they are resolved in the two cases (conventional vs. superresolution) as well as the appearance of the three particles in the feature on the right in the SR-CARS image, Fig. 6(g), that appears as only a single peaked feature in the conventional image, Fig. 6(f).

 

Fig. 6 (A) A Raman spectrum of polystyrene beads. CARS images tuned to (B) 1000 cm⁻¹ and (C) 900 cm⁻¹. The contrast gap in (B) corresponds to a region when the phases of the laser pulses are temporally mismatched. (D) Identical 20 µm x 20 µm regions of dispersed 0.30 µm diameter polystyrene beads imaged with CARS and (E) SR-CARS. CARS Images were taken using 728 nm pump (≈2 mW) and 785 nm Stokes (≈4 mW) beams; 0.35 d₀ sized annular mask was used to record the image in (E). The dotted rectangle denotes the subportion of the images (D) and (E) shown in 3D rendering in (F) and (G) respectively.

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In summary, we demonstrate that the resolving power of FWM microscopy can be improved below the diffraction limit while retaining the microscope's ability to acquire materials- and chemical- specific contrast. The functional superresolution effect was achieved by narrowing the microscope’s excitation volume in the focal plane through the combined use of a Toraldo-style pupil phase filter with the multiplicative nature of four-wave mixing. The SR-FWM microscopy images of isolated nanoparticles demonstrated that resolution approaching 130 nm was obtainable with adequate signal-to-noise. Work is on-going to address the questions of the practical limits of this approach in terms of ultimate resolving power, detection limits, and the utility of this scheme for imaging microscopically complex/extended sample systems where the effects of coherency will become prominent.