Optical microscopy is the most important nondestructive real-time imaging technique in life and material sciences; however, the far-field spatial resolution of any standard lens-based optical microscope is limited by the wavelength of imaging light ($\lambda$) and by the numerical aperture (NA) of the lens system due to diffraction of light waves [1]. Surpassing the diffraction limit significantly impacts several disciplines, such as medical and material sciences, microfluidics, and nanophotonics, and therefore has been the subject of considerable recent research effort. A variety of imaging techniques based on near-field scanning probes [2], molecular fluorescence [3], microscale and nanoscale solid immersion lenses [4,5], and metamaterials [6,7] have been devised in recent years to overcome the diffraction limit; however, design complexity, low optical throughput, slow acquisition time, and limited frequency ranges of operation have impeded their use to some extent.

Recent investigations on optical focusing and transport properties of dielectric particles with spherical boundaries, such as microspheres and microcylinders [8–18], have revealed novel optical phenomena, such as super-resolution foci termed “photonic nanojets” [8–12] and “periodically focused modes” [13–18] in individual and arrays of particles, motivating their application in light focusing and imaging devices. Microsphere-assisted imaging is a remarkably simple approach toward achieving sub-diffraction-limited resolution [18–24]. Wang et al. [19] used silica microspheres (refractive index $n\sim 1.46$ and diameters $D\sim 2–9\mathrm{\mu m}$) for far-field imaging of sub-diffraction-limited features by looking “through the sphere” into a virtual image formed underneath the specimen. It was argued that microsphere-assisted imaging is impractical for high-index ($n>1.8$) [19] spheres or spheres entirely immersed [20] in a liquid, which was discouraging for imaging of biological specimens. Darafsheh [18] solved this problem and demonstrated that the combination of high refractive index ($n\sim 1.9–2.1$) microspheres and full immersion in a liquid in fact permits super-resolution imaging.

In this letter, we demonstrate that microsphere-assisted imaging is feasible through employing microspheres embedded in transparent solidified films. In comparison with imaging using full immersion of microspheres in liquids, microspheres are fixed in elastomers in this work. Advantages of immersing spheres in solidified films rather than immersing them in liquids, particularly for biological specimens, are that such films can be pre-fabricated and used as cover slips, imaging can be performed by an inverted microscope, and any potential influence of liquid evaporation on imaging performance is minimized.

Figure 1(a) shows a schematic of the imaging setup in which the microsphere-embedded film is placed over the specimen as a coverslip, and an upright microscope in reflection illumination mode is used for imaging. In this way, the microsphere acts as an auxiliary lens that forms a magnified virtual image underneath the specimen’s surface that is captured by the objective lens [Fig. 1(b)]. As the imaging object, we used a commercial Blu-ray disk (BD). The structure of the BD consists of parallel 200-nm stripes separated by 100-nm grooves.

 

Fig. 1. (a) Schematic of the microsphere-assisted imaging setup in which a microsphere embedded in a PDMS film is shown (not to scale). (b) Ray tracing of virtual image formation by the sphere. The structure of the BD, consisting of 200-nm stripes separated by 100-nm gaps, is resolved by using the microsphere-embedded film through a (c) $D\sim 65\mathrm{\mu m}$ ($n\sim 1.9$) and (d) $D\sim 55\mathrm{\mu m}$ ($n\sim 2.1$) sphere. Conventional microscopy cannot resolve the BD structure.

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In order to fabricate the microsphere-embedded films, monodispersed barium titanate glass (BTG) microspheres (Mo-Sci Corp.) with diameters $D\sim 30–150\mathrm{\mu m}$ and refractive index $n\sim 1.9–2.1$ were distributed over the BD sample and a microscope coverslip as the substrates by self-assembly; then liquid polydimethylsiloxane (PDMS) elastomer (Dow Corning) with index $n_m\sim 1.41$ and proportion $1:10$ of cure compound was extended over the microspheres by using spin-coating. The thickness of the film was controlled by the coating speed and spinning duration. The compound was baked at 65°C for 1 h to dry the mixed compound and form a removable microsphere-embedded film. We fabricated such films with various thicknesses up to 300 μm.

The structure of the BD cannot be resolved by conventional microscopy using a $100\times$ ($\mathrm{N}\mathrm{A}=0.95$) objective lens. However, imaging of the BD structure is possible through high-index BTG microspheres embedded in the PDMS layer, as shown in Figs. 1(c) and 1(d) for microspheres with $D\sim 65\mathrm{\mu m}$ ($n\sim 1.9$) and $D\sim 55\mathrm{\mu m}$ ($n\sim 2.1$) through a $100\times$ ($\mathrm{N}\mathrm{A}=0.9$) objective lens, respectively. We obtained similar results through a $50\times$ ($\mathrm{N}\mathrm{A}=0.45$) objective lens. We found that the films with higher index microspheres ($n\sim 2.1$) give higher magnification factors and larger fields of view. It should be noted that high-index microspheres do not form an image when the ambient medium is air, i.e., prior to immersion in elastomers. However, when they are immersed in liquids or elastomers, due to the modification of the refractive index contrast imposed by the ambient medium, imaging is possible.

In order to evaluate the resolution enhancement factor introduced by the microspheres, the finite size of the structures on the BD must be taken into account in a manner consistent with the classic definition of resolution. There are several classic criteria defining the spatial resolution of an imaging system: among them, the Houston [25] criterion is more practical. According to the Houston criterion, the full-width at half-maximum (FWHM) of the point-spread function (PSF) of the system is used as the measure of the spatial resolution that gives $0.515\lambda /\mathrm{NA}$ for a circular lens. Since the image can be seen as the convolution of the imaging system’s PSF with the object [26], the PSF can be measured through deconvolution of the object and image functions.

We studied the influence of the FWHM of the system’s PSF on the calculated images of the BD through convolution. The theoretical diffraction limit of our microscope setup is $\sim 300\mathrm{nm}$ for the $\mathrm{NA}=0.9$ objective lens (600 nm for $\mathrm{NA}=0.45$). Figure 2(g) shows the calculation result of one-dimensional convolution of a PSF (with Airy pattern) with FWHM value of 300 nm, shown in Fig. 2(d), with 200-nm-width rectangular steps separated by 100-nm gaps corresponding to the structure of the BD [four periods are shown in Fig. 2(a)]. It can be seen in Fig. 2(g) that the structure of the BD cannot be resolved with such a wide PSF. Image profiles calculated for PSFs with FWHM values of 200 and 150 nm are presented in Figs. 2(h) and 2(i), respectively. It can be seen that the 100-nm gap can be visually discerned in Fig. 2(h) corresponding to a PSF with 200 nm FWHM. As the PSF becomes narrower, the ratio of peak-to-saddle intensity becomes greater, indicating a better spatial resolution. These calculations indicate that in order to evaluate the spatial resolution of the imaging system, caution must be exercised when dealing with structures with finite sizes, such as the BD, instead of “point sources”.

 

Fig. 2. (a)–(c) Intensity profiles of the structure of the BD with 200-nm steps separated by a 100-nm gap (four periods are shown). (d)–(f) PSFs with 300, 200, and 150-nm FWHM, respectively. (g)–(i) Calculated image profiles obtained by convolving (a)–(c) with PSFs presented in cases (d)–(f), respectively. Insets show the calculated images.

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Based on the deconvolution calculation shown in Fig. 3(a) on the experimentally obtained images of the BD structure, we found that applying the microsphere-embedded films reduces the FWHM value of the PSF of the imaging system from $\sim 300\mathrm{nm}$ to $\sim 135\mathrm{nm}$ showing an improvement of the imaging resolution by a factor of $\sim 2$. Therefore, the imaging resolution after applying the microspheres is $\sim \lambda /4$, where $\lambda \sim 550\mathrm{nm}$ is the peak spectral response of the imaging system, which is consistent with previous study for large BTG spheres ($D>50\mathrm{\mu m}$) immersed in liquids. The improved resolution of the microsphere-assisted imaging technique, on a fundamental level, is related to the enhancement of the effective numerical aperture of the system due to the reduction of the wavelength of light in the medium and the enhancement of the acceptance cone of the objective lens [18].

 

Fig. 3. (a) Deconvolution fit on the experimental image profile of the BD sample through a $D\sim 50\mathrm{\mu m}$ BTG sphere ($n\sim 2.1$) embedded in PDMS corresponding to a PSF with 135-nm FWHM, (b) Experimental values of lateral magnification and super-resolution FOV as a function of diameter for BTG spheres ($n\sim 1.9$) embedded in PDMS.

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We experimentally studied super-resolution imaging lateral magnification and field-of-view (FOV) as a function of sphere diameter for spheres with $n\sim 1.9$ immersed in PDMS by using the BD as the imaging object. Figure 3(b) shows that for spheres with $D\sim 30–150\mathrm{\mu m}$, as the size of the sphere increases, the magnification value decreases toward a value determined by geometrical optics based on the refractive index contrast between the sphere and the medium ($n^{\prime }=n/n_m$). Geometrical optics calculation gives $|M|=|n^{\prime }/(2-n^{\prime })|\sim 2.1$, where $n^{\prime }\sim 1.35$ is the refractive index contrast. Figure 3(b) shows that the super-resolution FOV, over which the structure of the BD is resolved, increases as spheres’ diameter increases.

We evaluated the feasibility of microsphere-assisted imaging for biological specimens by performing fluorescent (FL) microscopy of U87 human glioblastoma cell lines irradiated by a clinical proton beam at Roberts Proton Therapy Center. We performed immunofluorescent staining of irradiated cells with $\gamma$-H2AX antibodies that reveal nuclear foci formation [Anti-Phospho-Histone H2A.X Ser139 and Alexa Fluor 594 Goat Anti-Mouse IgG ($\mathrm{H}+\mathrm{L}$)]. After washing the samples in phosphate-buffered saline to remove the unbound antibodies, the cells were stained with 4’,6-diamidino-2-phenylindole (DAPI) solution ($n_m\sim 1.45$) to show the location of nuclei.

The cells were imaged using an inverted Zeiss Observer.Z1 microscope equipped with a $20\times$ ($\mathrm{NA}=0.4$) objective lens in FL imaging mode. The partially immersed microspheres in PDMS attached to a microscope coverslip were placed over the specimen. The gap between the partially embedded spheres and the specimen was filled with DAPI solution. Figure 4(a) is a conventional FL micrograph of the cells obtained under excitation at 365 nm with filtering out 440 nm for imaging the cell nuclei. The cells are seen as blue ovals in Fig. 4(a). In Fig. 4(b), the cell is imaged through a 130-μm-diameter BTG sphere. The microscope objective was focused on the virtual image formed underneath the sphere in Fig. 4(b). The image magnification factor introduced by the sphere in Fig. 4(b) is $\sim 3$.

 

Fig. 4. FL image of U87 glioblastoma cells through $20\times$ ($\mathrm{NA}=0.4$) objective lens under excitation at 365 nm with filtering out 440 nm for imaging (a) without using a microsphere and (b) with using a 130-μm-diameter BTG sphere immersed in PDMS and DAPI. FL image under excitations at 365 and 594 nm with filtering out 440 and 620 nm, respectively, for imaging cell nuclei and radiation-induced foci (c) without and (d) with using microsphere. Double-strand DNA breaks, manifested as red foci, are seen through the sphere in (d). Microscope objective was focused on the virtual images formed underneath the sphere in (b) and (d).

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Double-strand DNA breaks, induced by the proton beam, manifested as red foci can be seen through the sphere in Fig. 4(d) under excitation at 594 nm with filtering out 620 nm for imaging. Figure 4(c) is obtained at the best imaging depth without using the sphere. The red foci corresponding to double-strand DNA breaks in the cells cannot be resolved in Fig. 4(c). Comparing Figs. 4(b) and 4(d) with Figs. 4(a) and 4(c) shows the magnification and resolution advantages achieved by using microsphere-assisted imaging technique over conventional fluorescent microscopy.

In summary, we have experimentally demonstrated the feasibility of performing optical microscopy with spatial resolution $\mathit{\lambda }/4$ using high-index microspheres embedded in transparent elastomers. The advantage of this method over liquid-immersion of microspheres are that such films with embedded microspheres can be pre-fabricated and used as cover slips for biological specimens, microscopy can be performed using an inverted microscope, and any potential influence of liquid evaporation on imaging performance is minimized. Our method is very promising for biomedical imaging applications. In cancer research, when cells are irradiated by particles with high linear energy transfer (LET), such as protons, due to much higher damage density in the DNA compared with the case of irradiation by particles with low LET, using microsphere-assisted microscopy to enhance the imaging resolution for DNA damage characterization is favorable. Further work is in progress toward mass fabrication of optimized sphere-embedded-films and DNA double-strand damage characterization of cells irradiated by clinical proton beams through microsphere-assisted imaging.